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Design and characterization of metal and semiconducting nanostructures and nanodevices

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Design and characterization of metal and semiconducting nanostructures and nanodevices

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Content DESIGN AND CHARACTERIZATION OF METAL AND SEMICONDUCTING NANOSTRUCTURES AND NANODEVICES by Jesse Robert Theiss A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) December 2013 Copyright 2013 Jesse Robert Theiss ii EPIGRAPH “You will prevail outward in concentric circles!! Concentric circles!!” - Richard Simmons iii DEDICATION To my parents, Bob and Charlene, and my late Aunt Karen (Buppy) iv ACKNOWLEDGMENTS I would like to start with a huge thank you to all of my family, my parents and especially my siblings, Jon, Erin, Jakob, and Jarrod, and my aunt Karen. This has been a long arduous journey made all the more difficult by only being able to visit you home two or three weeks of the year since my move to California. Thank you all for your love and support (and sibling rivalry). I dearly wish my aunt Karen could have seen the day I finally left school after some twenty six years. Thank you to all of my high school and college friends for keeping in touch with me despite the hundreds or thousands of miles of separation and life. Thanks to Eric Jabart for being my brother in arms in the never-ending quest for the Ph.D. I’d like to thank all of the members in the Cronin research group throughout the years who helped with my research or simply made my time here both memorable and enjoyable. Perhaps a little bittersweet to me, this list covers the entire lifetime of our group. I know some of us will remain lifelong friends. Thanks to Rajay Kumar, Adam Bushmaker, Mehmet “Memo” Aykol, David Valley, Wei-Hsuan “Wayne” Hung, I-Kai Hsu, Fernando Souto, Chia-Chi Chang, Chun-Chung Chen, Wenbo Hou, Zuwei Liu, Rohan Dhall, Shun-Wen Chang, Moh Amer, Zhen Li, Jing Qiu, Shermin Arab, and Guangtong Zeng. I offer a special thanks to Memo, who was a true lab technician, with whom I spent countless hours learning, building, aligning, and tweaking experimental optical setups. It was a blast. And thank you to Prat for getting me started in FDTD and being a part of “House Plasmonics” in Alhambra for 1.5 years. v I’d like to thank my adviser Steve Cronin for taking me into this laboratory back in 2007. It has been a tough climb to build up the experimental plasmonic research capability here from scratch, and I’d like to thank him for all the guidance and funding he was able to put into it. Thank you to all of the members of my qualifying exam and defense committees, Prof. Ari Requicha, Prof. Michelle Povinelli, Prof. Wei Wu, Prof. Ed Goo, and Prof. Alex Benderskii. I want to offer additional gratitude to Dr. Requicha for originally encouraging me to come to USC to work in the Laboratory for Molecular Robotics. Despite the setbacks, it was a valuable learning experience and one I enjoyed. Though it was pretty sad having more AFMs than group members that last year! Thanks to Prof. Dan Dapkus and the USC cleanroom for funding me through the RA position that is the Raith superuser. I’m glad you had the confidence in me to take over the job and hope I’ve exceeded your expectations. To the Raith e_LiNE tool itself, did you really have to break the week of my defense!? I really shouldn’t be surprised. I also have to thank “Sandwich Lady” at Sandwich Island in University Village. She has fueled my research for nearly a decade and is truly a testament to the capacity of human memory. I’m sure she’ll remember my favorite sandwiches for twenty more years . Most importantly, I have to thank my little Richard Simmons. Susan, I don’t know where I’d be without you. You have been there to see me through all my stress and freak outs and are truly the best thing I’ve gotten out of my ten years in California. You are the whimsy and cheerleader my life needs. Thank you for your love and support. vi TABLE OF CONTENTS Epigraph .................................................................................................................. ii Dedication .............................................................................................................. iii Acknowledgments.................................................................................................. iv List of Figures ...................................................................................................... viii Abstract ................................................................................................................ xvi Chapter 1: Introduction ........................................................................................... 1 1.1 Plasmonics ............................................................................................... 1 1.2 Raman spectroscopy and SERS ............................................................ 20 1.3 Carbon nanotubes .................................................................................. 23 1.4 Raman spectroscopy and carbon nanotubes .......................................... 28 Chapter 2: Plasmonic Nanoparticle Arrays with Nanometer Separation for High-Performance SERS Substrates ..................................................................... 31 2.1 Abstract ................................................................................................. 31 2.2 Introduction ........................................................................................... 32 2.3 Experimental and simulation details ..................................................... 34 2.4 Results and discussion ........................................................................... 39 2.5 Conclusion ............................................................................................. 47 Chapter 3: Fano Interference and Effects of Asymmetry on Near-field and Far-field Scattering of Plasmonic Heterodimers................................................... 49 3.1 Abstract ................................................................................................. 49 3.2 Introduction ........................................................................................... 50 3.3 Experimental and simulation details ..................................................... 52 3.4 Results and discussion ........................................................................... 56 3.4.1 TEM-based measurement and simulation ................................ 56 3.4.2 Test bed simulations ................................................................. 82 3.4.3 Comparison to previously observed Fano interferences ........... 92 3.5 Conclusion ............................................................................................. 93 Chapter 4: Applications of the AFM Cutting Technique in Carbon Nanotube Studies .................................................................................................. 95 4.1 Abstract ................................................................................................. 95 4.2 Introduction ........................................................................................... 95 4.3 Length dependence effects in Raman scattering ................................... 97 4.3.1 Experimental details ................................................................. 97 4.3.2 Results and discussion ............................................................ 104 vii 4.4 Length-dependence of thermal contact resistance .............................. 111 4.4.1 Experimental details ............................................................... 111 4.4.2 Results and discussion ............................................................ 112 4.5 Conclusion ........................................................................................... 120 Chapter 5: Future Directions ............................................................................... 122 5.1 Hall measurement of GaAs nanowires ................................................ 122 5.1.1 Introduction ............................................................................. 122 5.1.2 Synthesis and material issues .................................................. 125 5.1.3 Fabrication details ................................................................... 127 5.1.4 Preliminary results .................................................................. 130 5.1.5 Future work ............................................................................. 133 Chapter 6: Conclusion......................................................................................... 135 Appendix A: Permittivity Functions Used in Computational Simulations ......... 152 Appendix B: Removal of Amorphous Carbon Deposited by TEM Imaging ...... 154 Appendix C: Lumerical FDTD Solutions Scripts and MATLAB CODES ........ 155 Appendix D: AFM Cutting Code ........................................................................ 159 Appendix E: EBL Fabrication Process for Hall Effect Devices ......................... 161 viii LIST OF FIGURES Figure 1.1: Real and imaginary parts of the dielectric function of the free electron gas (solid line) fitted to the experimental dielectric data (dots) from Johnson and Christy [63] for gold (top) and silver (bottom). Images from ref [86]. ..................................................................................................... 5 Figure 1.2: Diagram of homogeneous isotropic sphere placed in a static electric field. .................................................................................................................. 8 Figure 1.3: Extinction cross section calculated for a silver sphere in air (black) and silica (gray) with dielectric function data from Johnson and Christy [63]. Taken from ref [86] ................................................................... 12 Figure 1.4: Scattering and extinction spectra for different shapes and sizes of nanoparticles. (a) Size dependent extinction spectra for solutions of colloidal gold nanoparticles with diameters of 10 – 100 nm. Courtesy of nanoComposix. (b) Shape dependent scattering spectra for differently shaped colloidal nanoparticles. Taken from ref [92]. ................... 13 Figure 1.5: Sketch of charge distribution of lowest energy plasmon modes on NP sphere. The dipole (n=1), quadrupole (n=2), and octupole (n=3) modes are shown. ....................................................................................................... 14 Figure 1.6: Extinction and absorption spectra for two gold nanospheres (dimer) with different separations. (a) Measured extinction spectra for two NPs with polarization aligned along the common dimer axis. (b) Calculated extinction spectra for NPs with polarization perpendicular to common dimer axis. From ref [119]. (c) Calculated absorption spectra for different NP separations showing excitation of higher-order resonances. From ref [122]. ............................................................................ 16 Figure 1.7: Fano resonances in different ensembles of metal nanoparticles. (left) Dolmen-type and (right) nanocross configurations show dark-modes interacting with broad dipolar resonances of the ensemble that produce narrow dips and peaks in far-field scattering. Figures taken from [145] and [146]. ........................................................................................................ 18 Figure 1.8: Diagram of Raman scattering process. (a) Generation of Stokes and anti-Stokes radiation by scattering events with molecular phonons. (b) Depiction of nonresonant and resonant Raman scattering processes and an example of a Raman scattering spectrum. Taken from ref [69]. ................ 20 ix Figure 1.9: Structure of a carbon nanotube based on graphene. (left) A 2-D graphene sheet with chiral vector h C defined on hexagonal lattice by chiral angle θ with respect to 1 a .(right) Examples of capped (a) armchair, (b) zigzag, and (c) chiral nanotubes, with chiralities of (5,5), (9,0), and (10,5), respectively. Taken from ref [39]. ...................................... 24 Figure 1.10: Electronic dispersion relation in graphene and extended to carbon nanotubes. (a) Electron energy dispersion for graphene. (b) Circumferential and axial wavevectors for carbon nanotube. (c) 2-D graphene dispersion relation plotted with zigzag nanotube cutting lines satisfying the cylindrical quantization of the wavevector. (d) Electron conduction (white) and valence (yellow) bands near the Fermi level. From ref [91]. .................................................................................................. 25 Figure 1.11: Electronic density of states for a (10,0) and (9,0) carbon nanotube. The dashed lines represent the dispersion relation for graphene. Taken from ref [123]. ................................................................................................. 27 Figure 1.12: Measuring and visualizing atomic vibrations in carbon nanotubes. (a) Raman spectrum of two CNTs on a silicon/silicon dioxide substrate, showing the prominent bands used to characterize the CNT structure and properties. (b) Schematic diagram of the RBM and the two G mode vibrations for a CNT. Adapted from ref [66]. ....................................... 29 Figure 2.1: Schematic diagram of the angle evaporation technique for fabricating nm-size gaps in a controlled manner. ............................................................. 35 Figure 2.2: (a) Low magnification TEM image of Ag nanoparticle arrays deposited using the angle evaporation technique on a SiN membrane. (b) and (c) high magnification TEM images of Ag nanoparticle pairs with nm-sized gaps. ........................................................................................ 36 Figure 2.3: Gap sizes for successful nanogaps between nanoparticles, as measured by transmission electron microscopy. ............................................................. 37 Figure 2.4: Raman spectra of p-ATP molecules bonded to Ag nanoparticle arrays deposited by angle-evaporation taken at several points corresponding to the TEM shown in the right. The spectrum in red was taken at the location indicated by the red “X” with incident light polarized along the axis of the nanoparticle pairs. The blue spectrum corresponds to the same location taken with light polarized perpendicular to the nanoparticle dimer axis. The black spectrum and the green spectrum correspond to spectra taken at the black and green X’s, respectively. ........... 40 x Figure 2.5: (a) TEM image of a 5x5 matrix of cells containing different nanoparticle geometries. Spatial mapping with a 632.8 nm laser exciting the 1576 cm -1 p-ATP Raman peak across this matrix of various Ag nanoparticle geometries with polarization (b) perpendicular and (c) parallel to the axis of the nanoparticle pairs. ...................................... 41 Figure 2.6: (a) TEM image and FDTD simulations of the electric field intensity around a silver nanoparticle dimer with 2 nm separation with incident light polarized (b) perpendicular and (c) parallel to the axis of the nanoparticle pair. The electric field intensity is plotted on a logarithmic scale. ............................................................................................ 43 Figure 3.1: Schematic diagram of the angle evaporation technique used to create nanogap heterodimers. For overlapping depositions, the gap size is a function of first evaporation thickness (t 1 ) and the relative angle between the two evaporations (θ). For non overlapping depositions, the gap size is a function of the height of the top masking layer and the relative angle. .................................................................................................. 53 Figure 3.2: Schematic diagram of dark-field spectroscopy setup. The microscope objective is used as both the focusing condenser and collection optic. Incoming polarized white light is spatially filtered through a pinhole aperture and reflected off a beam splitter into the objective off the center axis. A beam blocker is used to eliminate reflected light, while the remaining scattered light is sent to the spectrometer. ............................... 54 Figure 3.3: (a) TEM image of an asymmetric nanoparticle dimer, heterodimer A. (b) Measured scattering spectra of dimer with polarization aligned parallel (black) and perpendicular (red) to the common NP axis. (c) Simulated scattering spectra based on dimer geometry in (a). ....................... 56 Figure 3.4: (a) TEM image of an asymmetric nanoparticle dimer, heterodimer B. (b) Measured scattering spectra of dimer with polarization aligned parallel (black) and perpendicular (red) to the common NP axis. (c) Normalized simulated scattering spectra based on dimer geometry in (a). ................................................................................................................... 60 Figure 3.5: (a) TEM image of an asymmetric nanoparticle dimer, heterodimer C. (b) Measured scattering spectra of dimer with polarization aligned parallel (black) and perpendicular (red) to the common NP axis. (c) Normalized simulated scattering spectra based on dimer geometry in (a). ................................................................................................................... 61 Figure 3.6: Electric field intensity |E| 2 cross sections for heterodimer A with parallel polarization at λ = 618 nm for z = 1 nm (a) and z = 15 nm (b) xi and at λ = 667 nm for z = 1 nm (c) and z = 15 nm (d). (e) and (f) are for perpendicular polarization at λ = 630 nm and z = 1 nm and 15 nm, respectively. Scale bar is logarithmic. ............................................................ 63 Figure 3.7: Electric field intensity |E| 2 xy cross sections for heterodimer C with parallel polarization at λ = 608 nm for z = 1 nm (a) and z = 15 nm (b) and at λ = 672 nm for z = 1 nm (c) and z = 15 nm (d). (e) and (f) are for perpendicular polarization at λ = 617 nm and z = 1 nm and 15 nm, respectively. (g) and (h) show intensity in xz cross-section at y = 5.6 nm, at 608 and 672 nm wavelength, respectively. Scale bar is logarithmic. ..................................................................................................... 64 Figure 3.8: Simulated scattering of heterodimers with (red) and without (black) residual nanoparticles. (a) Heterodimer A with residual NPs in the gap region causes significant reduction of second scattering peak. (b) Heterodimer C with no residual NPs in the gap shows little change in scattering response. ......................................................................................... 66 Figure 3.9: Scattering spectrum for parallel (red) and perpendicular (black) polarized light incident on heterodimer C, and three-dimensional charge distributions corresponding to λ = 622 nm, 650 nm, and 715 nm. The upper charge distribution mapping shows the surface charge of the full heterodimer. The lower charge distributions show the same distribution but on the individual nanoparticles, rotated for clarity. A mixed dipole-quadrupole coupled mode is visible on both particles at 650 nm (left). A bonding dipole-dipole mode is visible at 715 nm (right), representing the broad superradiant scattering envelope. For perpendicular polarization, a hybridized mode featuring two in-phase dipole modes is visible at 622 nm (top), with evidence for other mode coupling visible in the charge distribution in the nanogap region. ................. 68 Figure 3.10: Simulated scattering spectrum for heterodimer C with parallel (black) and perpendicular (red) polarization. Charge distributions depicted for the calculated scattering peaks instead of bright envelope and dark dip shown in Figure 3.9. Insets show three-dimensional charge distributions for parallel polarization at λ = 608 nm (lower left) and 672 nm (lower right) and perpendicular polarization at λ = 622 nm (upper right). Blue represents positive charge and red represents negative charge. Lower charge distributions show the same charge distribution but on the individual nanoparticles, rotated for clarity. Complex charge distributions occur in the nanogap between the nanoparticles for both polarizations. ............................................................... 69 Figure 3.11: (a) Simulated scattering spectra as gap size is incrementally increased from measured value of 1.2 nm for heterodimer C. The xii dashed line indicates the scattering dip in the spectra. (b) Normalized scattering spectra of the heterodimer modeled from the TEM image (red) and for two elliptical cylinders with comparable spatial and nanogap dimensions (black). .......................................................................... 72 Figure 3.12: Simulated scattering of heterodimer C with (black) and without (red) 10 nm thick silicon nitride substrate. Insets show charge distributions at designated scattering peaks and dips with parallel polarization. ................ 73 Figure 3.13: (b) Simulated absorption spectra for heterodimer C on silicon nitride (black), the heterodimer in vacuum (magenta), the larger nanoparticle only (red dashed), and the smaller nanoparticle only (blue dashed). Limited or no Fano interference effects are visible in the isolated NP absorption spectra or the heterodimer in vacuum in the absence of substrate-mediated mode coupling. ................................................................ 75 Figure 3.14: (a) Charge distributions for individual dipolar modes and quadrupolar modes on silicon nitride substrate. Dielectric-metal interface concentrates more charge near the substrate. (b) Strong mixing of dipole-dipole coupled mode and quadrupole-quadrupole coupled mode enabled by concentration of charge in nanogap region. .......... 76 Figure 3.15: Simulated scattering spectra for heterodimer C on different dielectric substrates: 10 nm silicon oxide (black), 1 nm silicon oxide + 9 nm silicon nitride (red), 10 nm silicon nitride (blue), and 40 nm silicon nitride (magenta). ............................................................................................ 78 Figure 3.16: Simulated scattering spectrum for heterodimer A with parallel (black) and perpendicular (red) polarization. Insets show three- dimensional charge distributions for parallel polarization at λ = 641 nm (upper) and 790 nm (lower). Rotated for clarity. ...................................... 79 Figure 3.17: Simulated scattering spectra for heterodimer B without the cap layer on top of the larger nanoparticle (black) and with the cap layer (red). ........... 82 Figure 3.18: Scattering spectra for nanoblock heterodimer for symmetric (red) xy dimensions (x = y = 50 nm for both particles) and asymmetric (black) dimensions (x = y= 30 nm for second particle). First and second particle have heights of 30 nm and 15 nm, respectively. Insets show charge distributions on nanoparticles at indicated scattering peaks/dips........ 83 Figure 3.19: (a) Scattering spectra for nanoblock dimer as gap size is incrementally increased. Inset shows that the interference dip rapidly decreases as gap size is increased. (b) Scattering spectra as the second nanoblock is laterally offset from the nanoparticle axis. Inset shows xiii the behavior of the scattering dip with increasing offset. All incident excitation is with parallel polarization. ........................................................... 86 Figure 3.20: Scattering spectra as the height of the second nanoparticle is varied on substrate (a) and in vacuum (b). ................................................................. 88 Figure 3.21: (a) Simulated scattering spectra of two cylindrical nanoparticles with diameters of 50 nm and heights of 30 nm on substrate thicknesses of 10 nm (black), 71 nm (red) and 200 nm (blue). (b) Simulated scattering spectra of cylindrical nanoparticles with symmetric heights of 30 nm (black) and asymmetric heights of 30 / 15 nm (red). ...................... 89 Figure 3.22: Simulated scattering spectra of two rounded cylindrical nanoparticles with diameters of 50 nm with one particle having a height of 30 nm and the second particle having a height of 30 nm (left) and 15 nm (right) with gap sizes of 2 nm (black), 4 nm (red), and 6 nm (blue). .............. 91 Figure 3.23: Simulated scattering spectra of two 50 nm diameter spheres on 10 nm silicon nitride membrane (solid line) and in vacuum (dashed line) with gap sizes of 2 nm (black) and 8 nm (red). Inset shows charge distribution on spherical NPs. ......................................................................... 91 Figure 4.1: (a) Schematic diagram of tapping mode operation of atomic force microscope. Image taken from brukerafmprobes.com. (b) Illustration of the AFM probe technique used to cut carbon nanotubes through high field emission at the probe tip. Not to scale. ......................................... 100 Figure 4.2: AFM images of successful nanotube cutting. (a) Image of the height profile of cut carbon nanotube and substrate. Dashed line indicates cutting line. (b) Image of the amplitude data as a function of x and y, showing two successful cuts separated by 40 nm. ........................................ 101 Figure 4.3: AFM images of CNT #1. (a) Zoomed out 4 μm x 4 μm AFM image showing nanotubes with nearby numbered grid marker for locating CNT under AFM and optical microscope. (b) Zoomed in image of the boxed region in (a) taken after successive cuts. The lines and numbers indicate the position, orientation, and sequence of the cut. .......................... 104 Figure 4.4: Raman scattering spectra before and after sequential cutting of CNT #1. Inset shows an optical microscope image of the numbered reference grid and focused laser spot. ........................................................... 106 Figure 4.5: AFM images of CNT #2. (a) Zoomed out AFM image showing nanotubes with nearby grid markers for locating CNT under AFM and optical microscope. (b) Zoomed in 1 μm x 1 μm image of the boxed xiv region in (a) taken after successive CNT cuts. Dashed lines indicate the position and orientation of cuts. .............................................................. 107 Figure 4.6: Raman scattering spectra before and after cutting CNT #2 into 250 nm long segments. (a) Two spectra were taken before cutting and four spectra taken after cutting at slightly offset xy stage positions. Inset shows magnified region of three spectra taken after nanotube cutting. (b) Extended scan including the G’ Raman band. ........................................ 109 Figure 4.7: (a) G band Raman spectra measured at different temperatures. (b) G band frequency as a function of temperature. ............................................... 112 Figure 4.8: (a) SEM image of a carbon nanotube suspended across a 3 μm wide trench with a significant contact length on the right substrate. A dotted line was drawn over the CNT for clarity. (b) AFM image corresponding to the boxed region in (a) imaged after cutting. The white dotted lines mark the positions of the sequential AFM cuts. .............. 113 Figure 4.9: (a) Temperature derived from the G band Raman downshift measured in the center of the suspended CNT in Figure 4.8a plotted as a function of the laser power before cutting and after each cut. Solid lines are linear fits to measured fits. (b) Rate of temperature increase per unit laser power as a function of the contact length. ............................................ 114 Figure 4.10: (a) Measured temperature increase at the center of a suspended CNT plotted as a function of laser power taken at different contact lengths. (b) AFM image of the CNT on substrate to the right side of the trench. Dotted lines indicate positions of cuts. ......................................................... 116 Figure 4.11: Schematic diagram of the experimental setup and an equivalent thermal circuit for the locally heated suspended CNT with substrate contacts. ........................................................................................................ 117 Figure 4.12: Thermal contact resistance of CNT on a substrate, calculated based on Equation 4.4, for (a) different ratios of thermal resistance and thermal coupling to substrate per unit length and (b) different thermal conductivities for the CNT............................................................................ 119 Figure 5.1: (left) Calculated free carrier density versus dopant impurity concentration for GaAs NWs with different diameters. (right) Illustration of depleted NW cross section. .................................................... 124 Figure 5.2: Schematic representation of experimental measurement of the Hall voltage (V H ) in a (a) thin film sample and (b) a nanowire sample. Taken from ref [77]. ...................................................................................... 124 xv Figure 5.3: Images of successfully fabricated NW Hall devices. (a) and (b) SEM image of electrodes for Hall measurement patterned on 205 nm and 120 nm diameter NWs. Scale bars are 500 nm. (c) Higher magnification SEM image of one of the Hall electrode pairs with a 50 nm separation across the wire. (d) Schematic diagram of of the AuGe/Ni/Au metal electrodes evaporated on top of the nanowire. .............. 129 Figure 5.4: High resistance I-V curves between source and drain contacts of NW devices. (a) I-V curve of n-type NW after two RTA processes. (b) I-V curve of two different p-type NW devices after one RTA process. .............. 131 Figure 5.5: (left) Hall Voltage plotted as a function of bias current measured for a GaAs nanosheet at different magnetic field strengths. (right) SEM image shows the nanosheet Hall device. Scale bar is 2μm. .......................... 133 Figure A.1: Lumerical polynomial fits of the dielectric function for gold used for simulation work presented in Chapter 3. ...................................................... 152 Figure A.2: Lumerical polynomial fits of the dielectric function of silver used for simulation work presented in Chapter 2. ...................................................... 153 Figure B.1: Measured dark-field scattering spectra taken before (left) and after (right) a single O2 plasma treatment of heterodimer A. ............................... 154 Figure E.1: Screenshots from AutoCAD showing (a) the pattern design of the four alignment marks separated by 9 μm to fit inside the 10,000× write field and (b) the overlay of an SEM image after metallization and lift- off of the four alignment marks. All subsequent electrode alignment is done with these small alignment marks. ....................................................... 163 Figure E.2: Manual and automatic alignment process with Raith patterns. (a) Illustration of the two layers with (brown) manual mark scan and (green) automatic mark scan layers. (b) SEM image taken with manual mark scan. Small crosshair at center represents actual center of the SEM image while large crosshair represents user selected desired center. (c) Screenshot of one “exposure” of an automatic mark scan. Thresholding algorithm with settings at right determines the x or y center from one arm of the cross................................................................... 165 Figure E.3: (a) AutoCAD screenshot showing the patterning of thin Hall probe electrodes and larger wires connecting the electrodes to the contact pads. (b) SEM image showing the device after fabrication. ......................... 166 xvi ABSTRACT This dissertation presents several studies that look at the unique properties and applications of metals and semiconductors when the dimensions of these materials are confined to the nanoscale. Chapter 1 provides background material that will aid in understanding the research presented in this dissertation. It begins with an introduction to plasmonics and an analytical derivation of the electromagnetic resonance conditions that have made this field so popular in the last 10-15 years. Particular interest is given to localized surface plasmon resonances that occur when light is incident on metallic nanoparticles, and how these plasmon resonances interact with one another. The second half of the introductory chapter turns to a slightly older but still exciting material, the carbon nanotube, whose electronic and optical properties vary significantly due to a slight change in crystal orientation. We discuss both of these topics in the context of Raman spectroscopy, where plasmons can be used to enhance the scattering process and Raman can be used to give detailed information about the structure of nanotubes. Chapter 2 presents the first plasmonics research project, where we demonstrate an angle evaporation method for fabricating arrays of metal nanoparticle pairs with separations on the order of a single nanometer. We image the small separations between particles, which we often refer to as “nanogaps,” using high resolution transmission electron microscopy (TEM). Then, we use Raman spectroscopy to characterize the high electric field enhancements produced when the particles are illuminated with a visible xvii wavelength laser. We find a very strong polarization dependence of the Raman intensity. We use numerical simulations to confirm both the high electric field enhancements and the observed polarization dependence for a particular nanoparticle geometry imaged by TEM, suggesting these particles might provide exceptionally high field enhancements and Raman scattering intensities. Chapter 3 investigates these nm-separated nanoparticle pairs further. The previous Raman study uses a very narrow wavelength probe to characterize metallic nanostructures with a much broader spectral response. This study builds on the previous work by characterizing the spectral scattering from these “nanogap” structures in the visible and near-IR part of the spectrum, where we built a specialized near-normal incidence dark-field microscopy system to measure particle scattering on TEM- compatible membranes. We find that nanoparticles with these nm-separations tend to exhibit significant dips in their far-field scattering spectra. We further investigate this phenomenon by numerical simulation and find that these dips are a Fano interference that results from strong coupling to higher-order plasmon resonances. This Fano interference is unique compared to other reports in the last four years, where opposing charge distributions at the top and bottom of the nanogap destructively interfere in far-field scattering. We show that the enhanced interparticle coupling is not only due to the small separation between the particles but also due to an enhanced interaction with image charges induced in the underlying substrate. In Chapter 4, we study the length dependence of vibronic and thermal transport properties in carbon nanotubes. The atomic force microscope, a common characterization xviii tool in nanotechnology, is adapted to locally cut through a nanotube’s carbon-carbon bonds. The first study looks for changes in phonon energy and Raman scattering intensity as an individual nanotube is divided into smaller pieces. The second study uses Raman scattering from a suspended carbon nanotube to measure the temperature as a laser probe provides localized heating. The temperature in the suspended section of the carbon nanotube drastically increases as we create a bottleneck for heat flow at the nanotube- substrate contact. Chapter 5 details the fabrication process and experimental setup needed for a Hall effect measurement that will be used to characterize the charge carrier density in doped gallium arsenide nanowires. With the described fabrication techniques, metal electrodes can be positioned with an accuracy of ten nanometers across the 100 nm diameter of an individual nanowire. The initial measurements on nanowire samples were plagued by material doping and Ohmic contact issues, but we show a successful Hall measurement with a 2-D nanostructure of similar gallium arsenide material. This technique may be easily extended to other semiconductor materials and nanostructure geometries. 1 CHAPTER 1: INTRODUCTION 1.1 Plasmonics Plasmons are plasma oscillations, which in the case of metals, can be described as collective oscillations of the free electron gas (FEG) against the fixed lattice of ion cores [86]. An applied electric field can act to separate these electrons from the ions, resulting in an electric field that effectively cancels the applied field within the metal. A natural resonance occurs due to the restoring force of Coulombic attraction between the electrons and positive ions. The optical properties of metals can be analyzed by an analytical plasma model, in which a gas of free electrons moves against a fixed background of positive atomic ion cores. While for alkali metals this applies over a wide frequency range down to ultraviolet wavelengths, noble metals such as gold and silver feature interband transitions between sp- and d-bands that limit treatment by this plasma model. The electrons oscillate in response to an applied electromagnetic field. Their motion is damped by collisions which occur with frequency   1  , where  is the relaxation time of the FEG (typically on the order of 10 -14 s or a frequency of 100 THz at room temperature). The equation of motion for the electron gas subjected to the external field E is: E x x e m m        (1.1) where m is the effective optical mass of an electron with charge e . If we assume a harmonic time dependence of t i t    e ) ( 0 E E for the applied electric field with  being 2 the frequency of the driving field, a particular solution to this equation is t i t    e ) ( 0 x x . The solution yields ) ( ) ( ) ( 2 t i m e t E x     (1.2) which incorporates the phase shift between the driving field and electron response. The polarization is related to the displacement of electrons x P ne   , where n is the electron density. We can write an explicit equation for the polarization as E P ) ( 2 2   i m ne   . (1.3) Using the constituent relation E D   , we can write E D                i p 2 2 0 1 (1.4) where 0  is the permittivity of free space and the plasma frequency of the free electron gas is defined by 0 2 2   m ne p  . (1.5) This allows us to write the dielectric function of the free electron gas, known as the Drude model for the dielectric function of metals, which is      i p    2 2 1 ) ( . (1.6) This is generally split into the real and imaginary components of the complex dielectric function ) ( ) ( ) (            i which are given by 3 2 2 2 2 1 1 ) (           p (1.7) ) 1 ( ) ( 2 2 2            p . (1.8) It is useful to study equation 1.6 for different frequency regimes with respect to the collision frequency or relaxation time. We restrict this analysis to frequencies which retain the metallic character below the plasma frequency, that is, p    . For large frequencies close to p  , negligible damping occurs as 1   , and  becomes primarily real. We can write the undamped free electron dielectric function as 2 2 1 ) (     p   . (1.9) As noted earlier, this equation is not true in noble metals at frequencies involving interband transitions which increase the optical absorption and the imaginary part of the dielectric function    . At very low frequencies, where 1     , we find       and the real and imaginary parts of the complex refractive index,   n , become equal. From Maxwell’s equations, we can derive that for a electromagnetic wave traveling through a medium 2 2 2 2 1 2           n (1.10) and we can then approximate in low frequency that    2 2 p n     . (1.11) In this region, metals are absorbing with an absorption coefficient given by 4 2 / 1 2 2 2          c p    (1.12) where c is the speed of light in vacuum. Using the expression for DC-conductivity, 0 2 2 0    p w m ne   , we can rewrite the previous equation as 0 0 2     . (1.13) Applying Beer’s law of absorption shows that , for low frequencies, the fields fall off inside the metal exponentially as  / e z  , where the skin depth is 0 0 2 2       . (1.14) For typical metals at room temperature,   100 nm (compared to the mean free path of electrons of about 10 nm). The plasma model of the metal has so far assumed an ideal free-electron metal, but it must be modified for real metals. In the free electron model, 1   if p    which is not correct. The model is extended for the case when p    where a separate term is defined to represent the residual polarization of positive ion core background, and the polarization P used earlier now represents the polarization due to free electrons. In this case, we define a dielectric constant   (typically having a value between 1 and 10) and reformulate equation 1.6 as       i p     2 2 ) ( . (1.15) 5 While this approach now handles the case of high frequencies, it still fails to incorporate interband transitions in metals important for plasmonics such as gold, silver, and copper. Figure 1.1 shows the real and imaginary components of the FEG dielectric function fitted to experimentally determined dielectric function data for gold and silver tabulated in Johnson and Christy [63]. We can see the failure of the FEG model due to the interband transitions in the visible part of the spectrum. The interband transitions main effects are increased damping and increased competition for plasmonic excitations. The Drude model was very important when incorporated in time-domain based numerical computations such as finite-difference time-domain (FDTD) methods, because it allows for a direct computation of induced currents. The model can be modified by Figure 1.1: Real and imaginary parts of the dielectric function of the free electron gas (solid line) fitted to the experimental dielectric data (dots) from Johnson and Christy [63] for gold (top) and silver (bottom). Images from ref [86]. 6 adding an additional damping term to the simple FEG equation of motion (equation 1.1) assuming a bound electron with a fixed resonance frequency. This, however, may require several such equations to be solved for individual contributions to the total polarization response and the free electron dielectric function [147]. In modern FDTD solvers such as Lumerical FDTD Solutions, numerical fits can be made to the experimentally tabulated optical data for the permittivity or index of refraction of metals. The fit tolerance, number of coefficients used in fitting, frequency range of interest, and other parameters can all be tuned to yield the best balance of numerical data fit to computational time needed for the simulation. The appendix shows numerical fits used in FDTD simulations for silver and gold particles presented later in this dissertation. There are several different types of plasmons: bulk plasmons, surface plasmons, and localized surface plasmons. Bulk (or volume) plasmons are longitudinal oscillations of charge within the bulk material. These plasmons are responsible for the visible shininess of metals, where incident light with frequency below the plasma frequency p  is reflected from the interface, while light above the plasma frequency is transmitted further into the interface. Above the plasma frequency, typically in the ultraviolet for most metals, electrons are unable to move quickly enough to cancel the applied field, allowing for a nonzero net electric field within the metal. Volume plasmons are very difficult to excite with visible light because they are inherently longitudinal oscillations that cannot couple to the transverse electromagnetic excitation and require particle impact for excitation. Conversely, since the modes are longitudinal, volume plasmons also only decay by Landau damping with energy transfer to single electrons. Experimentally, the 7 plasma frequency of metals can be measured by electron energy loss experiments, with most metals having a measured plasma frequency between 5 – 15 eV. Surface plasmons are collective charge oscillations that are localized to and propagate along metal-dielectric interfaces. Visible excitation of surface plasmons is achieved by using prism or grating geometries that match the momentum or wave vector of the incident photons to that of the supported surface plasmon waves in the metal. While surface plasmons are widely used in plasmonic applications, they are less relevant to this body of work. A more detailed discussion of their electromagnetic character is left out of this introduction but can be found in introductory texts [86]. Localized surface plasmons (LSPs) are similar non-propagating charge oscillations that arise when the dimensions of the supporting material are confined to the nanometer scale. An incident electromagnetic wave will induce an oscillating charge on the nanoparticle (NP) that can resonate at certain discrete frequencies or modes. Such an oscillation is referred to as a localized surface plasmon resonance (LSPR), and excitation at these resonances results in dramatically increased electric field intensity in the near- field of the particle. Unlike bulk plasmons and surface plasmons, the spatial, sub- wavelength confinement or curved shape of the metal surface allows excitation by direct light. To treat the localized plasmon resonance analytically, we will assume the simple case of a homogeneous, isotropic sphere in a uniform electric field that varies harmonically with time. In the case where the dimensions of the particle are much smaller than the wavelength of the incident light in the surrounding medium (   a ), 8 we can assume the quasi-static approximation which says that phase of the oscillating electromagnetic field is constant at all points in the sphere. We can solve the simpler problem of a spherical particle in an electrostatic field and add the time dependence to the spatial solution. This case can be treated analytically as done in electromagnetic textbooks [61]. We assume a form of the static electric field z E ˆ 0 E  . The spherical particle has radius a , complex dielectric function ) (   , and is centered at the origin. The surrounding medium is assumed isotropic and non-absorbing with a real dielectric constant m  . We solve the Laplace equation for the potential, 0 2    , from which we can solve for the electric field    E . We can find the general solution to the potential in spherical coordinates           0 ) 1 ( ) (cos ) , ( l l l l l l P r B r A r   , (1.16) a 0 E P r  z m   Figure 1.2: Diagram of homogeneous isotropic sphere placed in a static electric field. x y 9 where ) (cos  l P are the Legendre polynomials of order l and  is the angle between the position vector r and the z-axis. Since the potentials must be finite at the origin, we can separate the potential into potentials inside and outside the sphere      0 ) (cos ) , ( l l l l in P r A r   (1.17)           0 ) 1 ( ) (cos ) , ( l l l l l l out P r C r B r   . (1.18) The coefficients l A , l B , and l C are determined from the boundary conditions at the sphere surface a r  and   r . Skipping these steps, we can finally write      cos 2 3 ) , ( 0 r E r m m in     (1.19) 2 3 0 0 cos 2 cos ) , ( r a E r E r m m out              . (1.20) We note that potential outside the sphere is a superposition of the applied field and a dipole located at the origin inside the sphere. We can rewrite this potential by defining a dipole moment p : 3 0 0 4 cos ) , ( r r E r m out     r p      (1.21) 0 3 0 2 4 E p m m m a          . (1.22) From the relation 0 0 E p    m  , we find the polarizability m m a       2 4 3    . (1.23) 10 This is the complex polarizability of a small sphere of sub-wavelength diameter in the electrostatic approximation. From the above equation, we can see a resonant condition occurs when polarizability reaches a maximum or when m   2  is minimized. For a small or slowly-varying imaginary part of the dielectric function ) (     near the resonance, this simplifies to m    2 ) (    . This is called the Fröhlich condition, and it specifies the frequency of the dipole surface plasmon of the metal nanoparticle. For a spherical particle with a dielectric function specified by the Drude model, the condition is met at the frequency 3 / 0 p    . The Fröhlich condition equation also shows how the resonance is sensitive to its environment, where the resonance frequency redshifts as m  increases, making it useful for optical sensing of changes in local media. We can solve for the electric field inside and outside the sphere to find 0 2 3 E E m m in      (1.24) 3 0 0 1 2 4 3 r m out        p p) n(n E E . (1.25) The resonance in polarizability also causes a resonant enhancement in both the internal and external dipolar electric field surrounding the particles. This field-enhancement makes metal nanoparticles very useful in applications such as Raman spectroscopy, carrier generation, and nonlinear optical effects. As noted earlier, the electrostatic solution is used to find the time-varying fields in the quasi-static limit. For a plane wave with t i t    e ) , ( 0 E r E , an oscillating dipole is excited with dipole moment 11 t i m t       e ) ( 0 0 E p . The radiation of this dipole is the scattering of the plane wave by the sphere. It is also useful to consider how efficiently the metal nanoparticle scatters and absorbs light. The scattering and absorption cross sections can be calculated by the Poynting vector for the total fields of a dipole to be [15] 2 6 4 2 4 sca 2 3 8 6 m m a k k C            (1.26)             m m ka k C       2 4 Im 3 abs , (1.27) where the wave number   / 2  k . For small particles such that   a , absorption efficiency is higher than the scattering efficiency, which scale as 3 a and 6 a , respectively. The extinction cross section is the sum of the scattering and absorption cross sections and represents all of the light that is either scattered or absorbed by the nanoparticle, which can be measured in optical transmittance experiments. An analytical result for the extinction cross section for a sub-wavelength silver sphere in two different dielectric environments is shown in Figure 1.3. However, these expressions apply not only to metallic spheres but also dielectric spheres. Because of the extreme dependence of the scattering cross section on particle size, the scattering of small objects is very difficult to measure in a background of slightly larger scatterers. Imaging and spectroscopy of nanoparticles with very small dimensions thus requires special techniques. 12 Figure 1.3: Extinction cross section calculated for a silver sphere in air (black) and silica (gray) with dielectric function data from Johnson and Christy [63]. Taken from ref [86] An analytical treatment of scattering by larger particles that break the assumption of the quasi-static approximation requires a much more rigorous treatment. Curiously, the analysis was worked out more than 100 years ago by a German physicist named Gustav Mie. The complete mathematics of the Mie theory are not needed to understand the work presented in this dissertation, but its derivation can be found in other texts [15]. The results can be treated as a first-order correction to the earlier calculated polarizability found for the sphere in the quasi-static approximation. It is sufficient to understand the physical effects observed in increasing the particle size. When the phase of the driving field is no longer constant throughout the nanoparticle, the charges on one side of the nanoparticle now become dephased with respect to those on the other side of the nanoparticle, which results in a broadening of the plasmon resonance. In addition, as the size is increased and the distance between the charges at opposite ends of the nanoparticle, the Coulombic restoring force is reduced which also lowers the resonance 13 Figure 1.4: Scattering and extinction spectra for different shapes and sizes of nanoparticles. (a) Size dependent extinction spectra for solutions of colloidal gold nanoparticles with diameters of 10 – 100 nm. Courtesy of nanoComposix. (b) Shape dependent scattering spectra for differently shaped colloidal nanoparticles. Taken from ref [92]. frequency. These effects can be seen in the extinction spectra for different sized gold colloid solutions of Figure 1.4a. Another consequence of Mie theory is that the correction of higher order terms in the polarizability of the spherical particle also allows for higher-order resonances. The scattering and extinction cross sections can be written for the n-th mode:   2 2 2 ) ( ca ) 1 2 ( 2 n n n s b a n x C    (1.28) ) Re( ) 1 2 ( 2 2 ) ( ext n n n b a n x C    , (1.29) where 0 2  a x  is the size parameter with sphere radius a , and the Mie coefficients n a and n b are given by: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( mx x x mx m mx x x mx m a n n n n n n n n n                (1.30) 14 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( mx x m x mx mx x m x mx b n n n n n n n n n                , (1.31) where m m    and n  and n  are the Riccati-Bessel functions [15]. These equations can be solved numerically for different mode order n and incident wavelength 0  . The sketch in Figure 1.5 shows the charge distribution of the lowest energy resonances on a spherical nanoparticle. While numerous higher-order modes exist, the distribution of charge on the sphere does not allow such modes to radiate efficiently to the far-field due to misaligned electric dipole moments between positive and negative charges on the particles. Likewise, these modes can be more difficult to excite with plane-wave excitation, and generally require the introduction of asymmetry or near-field excitation to be induced efficiently. In most cases, the dipole resonances dominate optical scattering. The LSPR is influenced by both the NP properties and those of the environment, depending on the nanoparticle’s size, shape & material, the surrounding dielectric medium, and proximity to other NPs [5, 51, 87, 88, 100, 117, 132]. While the bulk plasmon resonances of gold and silver lie in the UV, their LSPRs lie in the visible region and can be tuned by varying NP size and shape. Varying the shape can result in very Figure 1.5: Sketch of charge distribution of lowest energy plasmon modes on NP sphere. The dipole (n=1), quadrupole (n=2), and octupole (n=3) modes are shown. Energy n = 1 n = 2 n = 3 Ε 15 different charge distributions and scattering spectra, as shown in Figure 1.4b. We have already seen that the dielectric medium surrounding a particle can lower the plasmon energy and redshift the observed resonance, but small numbers of molecules can also attach to the metal surfaces and form metal-adsorbate complexes that can also significantly change the plasmon energy [95]. The LSPR in metallic NPs is strongly influenced by near-field coupling to other NPs. When two metallic spherical NPs are brought close to one another, the charge oscillations of one particle can affect the charges of the other particle. The configuration of two nanoparticles is often referred to as a dimer. This interaction between the two particles can result in coupling between the two plasmon modes, producing an interparticle coupled mode that can be lower or higher in energy than the single particle modes depending on the nature of the interaction. If we consider the case of two dipole plasmons on the two NPs being driven by an electric field that is aligned to the common NP axis (as shown in the inset of Figure 1.6a), we can understand this change in energy in terms of the Coulombic forces. When the two dipoles are oscillating in-phase with each other such that the positive charge of one particle faces the negative charge on the opposite particle, this produces an attractive force in the opposite direction as the restoring force of the individual nanoparticle’s charges. This results in a lower resonance frequency or energy, as can be seen in the measured extinction spectra 17 nm thick gold nanodiscs with diameters of 150 nm, shown in Figure 1.6a. The measured resonance redshifts as the particle spacing is decreased. For the case of perpendicular polarization in Figure 1.6b, we see the opposite trend as the resonance frequency blueshifts as the 16 spacing is decreased. In this case, with the positive and negative charges of each NP still oscillating in-phase and aligned to the applied field, the attractive force from the other particle now acts in the same direction as the plasmon restoring force, which effectively increases the frequency and energy. Out-of-phase dipole oscillations can also occur for both polarizations. However, these out of phase modes are generally impractical to measure since the out-of-phase oscillations create out-of-phase electric dipoles that effectively cancel each other out as seen in the far-field region. Breaking the size and shape symmetry of the two nanoparticles can enable these modes to radiate more efficiently though. Figure 1.6: Extinction and absorption spectra for two gold nanospheres (dimer) with different separations. (a) Measured extinction spectra for two NPs with polarization aligned along the common dimer axis. (b) Calculated extinction spectra for NPs with polarization perpendicular to common dimer axis. From ref [119]. (c) Calculated absorption spectra for different NP separations showing excitation of higher-order resonances. From ref [122]. a) b) c) 17 Figure 1.6c shows the absorption spectra calculated for different separations between two gold nanospheres of radius 60 nm. The same redshifting behavior of the lowest energy mode is observed for polarization aligned parallel to the common dimer axis. As the separation becomes very small, new peaks are introduced as the small separation also allows for coupling between higher-order modes as well. It should be noted that these coupled modes do not have to be between plasmons of the same order (dipole-dipole or quadrupole-quadrupole) but can also be between modes of different order (dipole-quadrupole). As mentioned previously, higher-order modes do not couple efficiently with plane-wave excitation. However, the small separations in dimers can concentrate charge in the gap region between the two particles so that the net electric dipole moment becomes nonzero. Mixed order coupling can also allow previously “dark” modes to become “bright” and radiate t o the far-field more efficiently. One popular conceptualization of the interaction between metallic NPs is that of plasmon hybridization theory, in which a fundamental plasmon mode of a coupled multi- particle system can be expressed as a linear combination of all the individual NP plasmon modes [103, 117, 118]. Analogous to molecular orbital theory, the lowest energy dipolar plasmon modes of the individual particles begin to interact with one another, as well as higher order plasmon modes, resulting in a significant splitting of these lowest energy states into bonding and antibonding hybridized modes. The red and blue-shifting behavior of these plasmon modes in extinction, absorption, and scattering spectra is easily understood in such a picture. While this theory is educational and generally matches experimental results, it is technically inaccurate as both gold and silver have 18 interband electronic transitions energetically competing with the plasmon modes that result in dampening and deviation from theory and simulation. While complicating the hybridization theory, modifying the imaginary part of the dielectric function to account for interband absorption in simulations yields better agreement with experiment. As a result of the interparticle coupling, modes that radiate strongly to the far- field can interact with modes that radiate weakly or cannot be excited by illumination from the far-field. When such modes couple strongly, the dark modes can produce narrow dips in the broad radiant scattering envelope, which is the summation of the individual dipole modes of each NP. Such interactions are shown in Figure 1.7, where the charge distributions at the dips produce misaligned electric dipole moments. Such scattering profiles are useful for applications in chemical and biosensing. Figure 1.7: Fano resonances in different ensembles of metal nanoparticles. (left) Dolmen- type and (right) nanocross configurations show dark-modes interacting with broad dipolar resonances of the ensemble that produce narrow dips and peaks in far-field scattering. Figures taken from [145] and [146]. 19 The interparticle coupling not only affects the energy of the plasmon resonance but also effects the concentration of the electric fields in the near-field of the nanoparticle. As the particle spacing is reduced between two particles, the distance between the positive and negative charges on the two particles becomes smaller. In the case of two nearly touching particles at the nanometer scale, this can create an incredibly high electric field in the gap separating the two dense collections of opposing charge. The calculations of Schatz et al., using an interacting dipole model, showed an enhancement factor to the electric field intensity, , of over 10 6 at the plasmonic resonance between two nearly touching nanoparticles [155]. The electric field enhancement increases sharply for nanoparticle separations approaching a nanometer. Jiang et al. calculated that two 60 nm diameter spherical Ag nanoparticles separated by 9 nm, 3 nm, and 1 nm produced Raman enhancement factors of 1.5 x 10 4 , 1.7 x 10 6 , and 5.5 x 10 9 , respectively [62]. The Raman scattering process is extremely dependent on the electric field intensity and will be discussed later in this introduction. Numerical finite difference time domain (FDTD) simulations have also shown that coupled nanoparticles produce large electric field enhancements between 100-150 times larger than that of the incident field [107]. Enhancements of this order are at least 10 to 100 times more than that which can be achieved by a single NP, making the use of multi-particle aggregates and configurations very appealing for plasmonic applications that seek to increase the local electric field intensity. 20 1.2 Raman spectroscopy and SERS The Raman effect is the inelastic scattering of a photon where an incident photon excites or absorbs vibrations or phonons in a molecule. The case of the creation (absorption) of a phonon is known as a Stokes (anti-Stokes) scattering event, and is depicted in Figure 1.8a. Raman scattering can involve vibrational and rotational modes and is governed by selection rules, requiring a net change in polarizability with respect to the vibrational direction. Symmetric stretching and bending modes thus tend to be Raman-active. A spectrum of these active modes, the Raman scattering intensity plotted as a function of the Raman shift, which is the energy difference from the excitation photon, can provide important crystallographic information and a unique fingerprint for non-crystalline molecules. As a non-absorption event, tuning the incident photon frequency to match molecular energy levels is not necessary, but resonance with an electronic energy level can increase the Raman intensity significantly so those specific vibronically coupled modes dominate the Raman spectrum. Of particular interest is the Figure 1.8: Diagram of Raman scattering process. (a) Generation of Stokes and anti- Stokes radiation by scattering events with molecular phonons. (b) Depiction of nonresonant and resonant Raman scattering processes and an example of a Raman scattering spectrum. Taken from ref [69]. a) b) 21 fact that vibrational scattering intensity from an isolated molecule is linearly proportional to the incident electric field intensity 2 E . We can write the total power of a Stokes scattered beam as ) ( ) ( L RS S S v I N v P   . (1.32) where N is the number of Stokes-active Raman scattering molecules in the excitation spot, S v and L v are the frequencies of the Raman scattered photons and the laser photons, respectively, I is the intensity of the excitation beam, and RS  is the Raman scattering cross section of the Raman-active molecule. For comparison, typical values of RS  range from 10 -31 to 10 -29 cm 2 /molecule, which is at least ten orders of magnitude smaller than typical fluorescence scattering cross sections. The Raman scattering intensity’s electric field dependence shows that methods to increase the local electric fields perturbing molecules will greatly increase the scattered intensity or scattering cross-section. As described earlier, the LSPRs of metallic nanoparticle(s) provide huge E-field enhancement in the near-field of the NP surfaces. Therefore, a large increase in scattered light intensity from a molecule positioned in these regions of enhancement occurs. The enhancement as described so far is potentially understated—the action of the LSPR is not only to increase the local incident field seen by the molecule but also to increase the Raman-scattered field from the molecule. The average enhancement of the incident field g may be written as 0 E E g NF  where NF E is the electric field near the surface of the particle (near-field) and 0 E is the electric field of the incident wave. The enhancement of the Raman-scattered field may be written 22 similarly as NF R E E g   , where R E is the enhanced field of the scattered light by the NP. Thus, the electric field of the outgoing scattered light may be given by 0 E g g E R   , and the intensity is proportional to the square of the electric field, yielding 0 2 2 I g g I R   , where R I and 0 I are the intensities of the scattered and incident fields. It is important to note that g and g  are not the same since the scattered light is shifted by the vibrational phonon energy. In the regime of small phonon energy (Raman shift) and given the broad resonance of a typical LSPR, one may approximate g g   such that . As characterizes the enhancement of the electric field induced by the presence of the NP(s), one can see that the Raman scattered light intensity from a molecule in close proximity to such NPs depends on the electric field strength to the fourth power, . While a value of 20  g may not be impressive in terms of electric field strength, the compound enhancement can provide a signal ~1.6 x 10 5 times larger than that of scattering from a molecule in the absence of NPs. It must be noted that the Raman-shifted peak intensities may also change due to a change in polarizability of the molecule, especially when adsorbed to the surface, so care must be taken in attribution of enhancement due to the electric field alone. A concurrent and independent chemical mechanism may also provide enhancement due to chemisorption of the molecule to the metal surface. This interaction may produce an intermediate charge-transfer complex with increased Raman scattering cross-section or quantum-mechanically alter the electronic states of the analyte molecule [22, 70, 106]. However, it is generally accepted that this contribution is limited to a few 23 orders of magnitude and that electric field enhancement dominates the Raman scattered signals in the small gaps between metal NPs [37, 64]. The use of surface plasmons to enhance Raman scattering has been termed Surface Enhanced Raman Spectroscopy (SERS) and was pioneered in 1977 [42]. In the last decade and a half, the field has exploded with hundreds of publications, if not more, with enhancements reported as high as 10 14 , enabling the detection of the Raman scattering from a single molecule near the surface of metallic NPs [70, 102]. This has made SERS a powerful tool in chemical identification and differentiation. Most SERS studies have been done on electrochemically roughened metal surfaces and assembled colloidal NP aggregates. A less random and more highly engineered surface is desired to measure and characterize the Raman spectra. 1.3 Carbon nanotubes Carbon nanotubes (CNTs) are hollow cylinders composed of only carbon atoms in a hexagonal lattice structure. This unique structure gives rise to exceptional electronic and mechanical properties, which have made them an exciting material to study and utilize since their discovery in 1991 [59]. This unique “one -dimensional” system results in a quantized electronic structure and has physical properties that have merited well over 50,000 publications studying the electrical, thermal, and mechanical properties of CNTS. CNTs have been shown, both experimentally and theoretically, to have exceptionally high electron mobilities of 100,000 cm 2 /V·s, thermal conductivities as high as 6,600 W/m·K, and Young’s modulus values reaching up to 1.8 TPa [11, 41, 142]. These properties make CNTs a promising material for nanoelectronic, thermal management, and nanomechanical applications. 24 A single-walled carbon nanotube is conceptualized as a seamless rolled up sheet of two-dimensional graphene, featuring varying electrical, optical, and mechanical properties dependent on the orientation at which the hexagonal sp 2 carbon lattice is wrapped onto the tubule. This structure is characterized by the diameter d t and chiral angle θ, as shown in Figure 1.9. The hexagonal grid has basis vectors 1 a and 2 a , and the unit cell of the nanotube is indicated by the box OAB’B, where the circumferential chiral vector, h C , forms an angle θ with 1 a . Non-negative integer coefficients (n,m) define each carbon nanotube such that 2 1 a a C m n h   is satisfied. The length of this chiral vector is the circumference of the carbon nanotube and can be written as t d  . The cases of 0  m and n m  specify two special classes of CNTs called armchair and zigzag nanotubes. All other nanotubes are chiral nanotubes. Figure 1.9: Structure of a carbon nanotube based on graphene. (left) A 2-D graphene sheet with chiral vector h C defined on hexagonal lattice by chiral angle θ with respect to 1 a .(right) Examples of capped (a) armchair, (b) zigzag, and (c) chiral nanotubes, with chiralities of (5,5), (9,0), and (10,5), respectively. Taken from ref [39]. 25 The periodic boundary condition applied along one dimension in the 2-D graphene lattice results in different band structures for CNTs of varying chirality. Thus, carbon nanotubes can be either metallic or semiconducting depending on the geometry defined by their growth and nucleation. The electronic dispersion relation for graphene can be calculated using a simple tight binding model which considers the interaction of a carbon atom with its near neighbors. A plot of this energy relationship with the in-plane electron wavevectors k x and k y is shown in Figure 1.10a. The resulting dispersion relation Figure 1.10: Electronic dispersion relation in graphene and extended to carbon nanotubes. (a) Electron energy dispersion for graphene. (b) Circumferential and axial wavevectors for carbon nanotube. (c) 2-D graphene dispersion relation plotted with zigzag nanotube cutting lines satisfying the cylindrical quantization of the wavevector. (d) Electron conduction (white) and valence (yellow) bands near the Fermi level. From ref [91]. a) b) c) d) 26 produces a maximum in energy at the Γ point and minima at the K and K’ points in the corners of the hexagonal Brillouin zone. Graphene is described as a semi-metal because the conduction and valence bands meet in these corners, forming a Dirac cone. In carbon nanotubes, the electron wavevector around the circumference,  k , is quantized by the periodic boundary conditions, as shown in Figure 1.10b. The cutting lines shown in Figures 1.10c and 1.10d represent the allowed values for  k plotted on the graphene dispersion relation, which form sub-bands in the valence and conduction bands. Near the Fermi level, these cutting lines will cross the Dirac cone to form either hyperbolic bands with a band gap or linear metallic bands, dependent on the chirality of the nanotube. This shows how the chirality determines the metallic or semiconducting properties of a CNT. The hyperbolic band structure creates sharp van-Hove singularities in the electronic density of states. Examples for a metallic (9,0) CNT and a semiconducting (10,0) CNT are shown in Figure 1.11. The electronic energy differences for transitions between singularities (symmetric about zero energy) are often labeled E ii , where 1  i represents the lowest energy transition between the van-Hove singularities closest to zero energy. For the metallic tube, we note a finite density of states between the singularities near zero energy. The other nanotube shows no electron density between the singularities at zero energy, where E 11 denotes the bandgap of the semiconducting CNT. The unique pseudo one-dimensional geometry of a carbon nanotube not only results in a unique electronic band structure but also a unique phonon band structure. The combination of these geometrically-defined electron and phonon band structures results in unique vibronic properties that can be probed by optical spectroscopy. Raman spectroscopy 27 Figure 1.11: Electronic density of states for a (10,0) and (9,0) carbon nanotube. The dashed lines represent the dispersion relation for graphene. Taken from ref [123]. provides a unique scattering spectrum where a limited number of vibrational modes can provide information about the nanotube radius, chirality, and electronic properties. The electronic density of states greatly enhances the scattering cross-section of optical transitions when the photon energy is resonant with transitions between van Hove singularities defined by the “1 -D” nanostructure. This makes Raman spectroscopy a powerful tool to characterize CNTs and examine the effects of electrical, optical, chemical, and mechanical probes and perturbations. 28 1.4 Raman spectroscopy and carbon nanotubes Raman spectroscopy is an extremely useful tool for studying 0-, 1-, 2-, and 3-D carbon-based materials given their crystallinity and unique electronic band structures. As shown earlier, the chirality of a CNT determines the band structure of a carbon nanotube and whether it has metallic or semiconducting behavior. Wrapping of 2-D graphene into a “1-D” tubule produces unique van Hove singularities in the electronic density of states. Photons that match the energy difference between these singularities can resonantly excite electrons from the valence and conduction bands in the CNT. If this electron then undergoes an inelastic scattering event with a phonon and decays back to the valence band, the CNT produces a Raman-scattered photon, where the intensity or number of scattered photons is greatly enhanced by the electronic resonance. Similarly, the intensity of scattering events where the emitted photon is resonant with the electronic transitions is also greatly enhanced. Even though a CNT has an extremely tiny geometric cross section, its effective Raman scattering cross section is remarkably high (estimated to be on the order of 10 -22 cm 2 /sr compared to 10 -31 cm 2 /sr for non-resonant molecules) [14]. The Raman scattering spectrum features several prominent modes or bands that reveal a wealth of information about the CNT. The most significant Raman modes are the radial breathing modes (RBMs) and the higher energy D (disorder), G (graphite), and G’ or 2D (second-order D-band) modes, observed in the spectral scattering of Figure 1.12. The RBM mode is a unique feature of CNTs which does not occur in 2D and 3D carbon allotropes. This mode is associated with the tube’s isotropic radial expansion or the symmetric vibration of the carbon atoms in the radial direction. Analytical expressions 29 can be used to derive the diameter of a SWCNT from its Raman shift or vibrational energy (between 75 – 300 cm -1 ), by which the two are inversely proportional to one another. Figure 1.12: Measuring and visualizing atomic vibrations in carbon nanotubes. (a) Raman spectrum of two CNTs on a silicon/silicon dioxide substrate, showing the prominent bands used to characterize the CNT structure and properties. (b) Schematic diagram of the RBM and the two G mode vibrations for a CNT. Adapted from ref [66]. 30 The D band is a longitudinal optical phonon referred to as the disorder or defect mode, because it requires a defect (e.g. substitutional atom, vacancy, grain boundary) or other disorder (finite-size effect, edges) that break the symmetry of the semi-infinite sp 2 carbon lattice. Thus, its relative intensity compared to other bands can give information about the quality of the nanotube lattice. The G’ band is a second order mode of the D band that does not require defects or disorder to be observed. Finally, the G band is an optical phonon characterized by the tangential shear stretches in the 2-D plane of graphene. However, the mode splits into a lower energy G - mode and higher energy G + mode due to the confinement along the circumference of a CNT. The G + and G - modes correspond to the axial and circumferential motion of atoms on the nanotube surface. The G + band has no significant dependence on tube diameter, while the G - band weakens or downshifts as the diameter decreases. In general, the G - band can be used to distinguish between a metallic and semiconducting CNT, where a metallic tube typically exhibits a broad peak and a semiconducting tube exhibits a sharp peak [4]. This is believed to be due to phonons coupling strongly to free electrons in metallic CNTs [11]. 31 CHAPTER 2: PLASMONIC NANOPARTICLE ARRAYS WITH NANOMETER SEPARATION FOR HIGH-PERFORMANCE SERS SUBSTRATES This chapter is similar to Theiss et al. [140], published in Nano Letters. 2.1 Abstract We demonstrate a method for fabricating arrays of plasmonic nanoparticles with separations on the order of 1 nm using an angle evaporation technique. Samples fabricated on thin SiN membranes are imaged with high resolution transmission electron microscopy (HRTEM) to resolve the small separations achieved between nanoparticles. When irradiated with laser light, these nearly touching metal nanoparticles produce extremely high electric field intensities, which result in surface enhanced Raman spectroscopy (SERS) signals. We quantify these enhancements by depositing a para- aminothiophenol (p-ATP) dye molecule on the nanoparticle arrays and spatially mapping their Raman intensities using confocal micro-Raman spectroscopy. Our results show significant enhancement when the incident laser is polarized parallel to the axis of the nanoparticle pairs, whereas no enhancement is observed for the perpendicular polarization. These results demonstrate proof-of-principle of this fabrication technique. Finite difference time domain (FDTD) simulations based on HRTEM images predict an electric field intensity enhancement of 82,400 at the center of the nanoparticle pair, and an electromagnetic SERS enhancement factor of 10 9 -10 10 . 32 2.2 Introduction Raman spectroscopy is an invaluable tool for many applications. By measuring the precise vibrational energies of molecules, Raman spectroscopy provides a unique signature for chemical identification and differentiation. Its utility is limited, however, by the small Raman scattering cross-sections characteristic of most molecules, typically 10 6 times smaller than Rayleigh scattering. The low Raman intensities can be greatly improved through surface-enhanced Raman spectroscopy (SERS). Since its discovery in 1977, hundreds of papers on the subject of SERS have been published [42]. SERS enhancement factors up to fourteen orders of magnitude have been reported in the literature [70, 102]. Since a vast majority of the previous work in this field has involved roughened metal surfaces and nanoparticles in solution, imaging the exact geometry of the nanoparticle complex was not possible [21]. Furthermore, the number of molecules contributing to a SERS enhanced signal is generally unknown and is usually ascertained through statistical analysis [70, 102] and/or a discriminating selection of analyte molecules [35, 36]. Consequently, several unexplored experimental factors remain, including the separation between the nanoparticles, the number of nanoparticles within the focal volume, the number of molecules on each nanoparticle, and the extent to which nanoparticles couple plasmonically to each other. Methods for providing reliable SERS substrates, whose parameters can be controlled precisely on the 1nm-scale are much needed, and will help bring forth a more complete understanding of SERS and enable new applications of Raman spectroscopy achievable with handheld spectrometers. The calculations of Schatz et al., using an interacting dipole model, showed an electric field intensity enhancement factor over 10 6 for the plasmonic resonance between 33 two nearly touching nanoparticles [155]. The electric field enhancement increases sharply for nanoparticle separations below 2 nm. Jiang et al. calculated that two 60 nm diameter spherical Ag nanoparticles separated by 9 nm, 3 nm, and 1 nm produced Raman enhancement factors of 1.5 x 10 4 , 1.7 x 10 6 , and 5.5 x 10 9 , respectively [62]. Numerical finite difference time domain (FDTD) simulations have also shown that coupled nanoparticles produce large electric field enhancements, with SERS enhancement factors up to 10 10 for a nanoparticle separation of 1 nm [107]. A concurrent and independent chemical mechanism may also contribute to the SERS enhancement due to chemisorption of the analyte molecule to the metal surface. This interaction may produce an intermediate charge-transfer complex with increased Raman scattering cross-section or quantum-mechanically alter the electronic states of the analyte molecule [22, 70, 106]. However, it is generally accepted that this contribution is limited to a few orders of magnitude [37, 64]. Based on this work, it is now well established that the SERS enhancement, enabling single molecule detection, is dominated by the high electric fields that occur in the small gaps between metal nanoparticles [55, 62, 78, 113, 155]. Several research groups have performed experimental studies of metal nanoparticle dimers fabricated by standard electron beam lithography. However, the nanoparticle separations in these works were limited by the lithographic techniques to 10-20 nm [5, 136], which is one order of magnitude larger than that predicted theoretically to produce significant electric field enhancement. Shadow evaporation is a well-known method for making sub- 10-nm gaps between metal structures that has been extensively used for making electrodes, although the feature sizes are generally larger than those of plasmonic 34 nanodevices [8, 114, 137]. Angle evaporation was used in conjunction with nanosphere lithography to produce triangular nanoparticles with angle-controlled gaps measured in the range of 4-25 nm [53]. This method limits the shape and size of the particles, which are determined by the hexagonally-packed nanosphere mask. The use of a self-assembled monolayer and electron beam lithography can also produce a high yield of 2 nm gaps for nanodevices but contaminates the metal surfaces with a thiolated molecular layer [99]. Other successful methods that can produce molecular-sized gaps include break junctions [120], electroplating [94], and electromigration [110, 111]. The yield of electromigrated nanogaps has improved significantly, making it a good candidate for the study of SERS phenomena [148], however, the density is ultimately limited by the electrode geometry. Hence, new methods are desired for controllably creating nanogaps in the range 0.5 to 2 nm for providing reliable SERS substrates. 2.3 Experimental and simulation details We fabricate arrays of metal nanoparticles with separations on the order of 1 nm using electron beam lithography combined with an angle evaporation technique. This work builds on previous research using controlled angled deposition to fabricate nano- scale tunnel junctions used to form single electron transistors [125] and spintronic devices [143]. Figure 2.1 shows a schematic diagram of the angle evaporation technique. In this scheme, a layer of ZEP-520 electron beam resist is spun on top of a layer of methyl methacrylate (MMA) resist. Since the MMA is more chemically sensitive to electron radiation, electron exposure results in a large undercut by over-exposing the more sensitive MMA layer, leaving a free-standing ZEP mask, as shown in Figure 2.1. 35 Figure 2.1: Schematic diagram of the angle evaporation technique for fabricating nm-size gaps in a controlled manner. In patterning the nanogaps, a thin layer of metal is first deposited at normal incidence. The sample is then tilted by a small angle (5-10°), and a second layer of metal is deposited. The size of the nanogap is determined by the angle of the second evaporation, θ, and the thickness of the first evaporation, , and is given by θ. Therefore, an angle of θ = 10° and a thickness of t 1 = 10 nm will yield a gap of 1.8 nm. By decreasing the angle of evaporation to θ = 5°, the gap size is reduced to 0.87 nm. We pattern these nanogap structures on thin silicon nitride membranes, which are then imaged using a JEOL JEM-2100F high resolution transmission electron microscopy (HRTEM). HRTEM enables the nanoparticle geometry and gap size to be determined with less than 0.2 nm resolution. In this work, a JEOL 9300FSZ electron beam lithography system is used to write 25 sets of nanoparticle arrays, as shown in Figure 2.2a. Each of these sets covers an approximately 6 µm x 6 µm area and contains a slightly different nanoparticle geometry (i.e., size, shape, separation). A TEM image of one such array is shown in Figure 2.2b. 36 Figure 2.2: (a) Low magnification TEM image of Ag nanoparticle arrays deposited using the angle evaporation technique on a SiN membrane. (b) and (c) high magnification TEM images of Ag nanoparticle pairs with nm-sized gaps. (a) 25 µm (b) 250 nm (c) 10 nm 37 Figure 2.2c shows a high magnification TEM image of one nanoparticle pair with a gap size of 2 nm. This nanoparticle pair (or dimer) was fabricated with = 30 nm and θ = 5°, which is consistent with the trigonometric formula given above ( θ). The second evaporation results in a second nanoparticle that is smaller than that of the first evaporation. This occurs for two reasons. First, the deposition of material tends to close the holes in the lithographic mask. And second, the holes’ effective cross -sections are decreased at oblique incidence. We estimate a 43.4% success rate overall for gap formation of the various nanoparticle geometries on our samples. The success rate for these nanogaps depends strongly on the shape and size of the metal particles, as a bridging of two particles in the gap is statistically more probable with a larger overlap region between the two evaporations. Of these successful nanogaps, we measure a gap 0 1 2 3 4 0 2 4 6 8 10 Number of Gaps Gap Size (nm) Figure 2.3: Gap sizes for successful nanogaps between nanoparticles, as measured by transmission electron microscopy. 38 size of 2.0 ± 0.9 nm. Figure 2.3 shows a histogram for the gap sizes measured by transmission electron microscopy for successfully fabricated nanogap separations. After fabrication, these silver nanoparticle samples were coated with a non- Raman-resonant dye molecule, para-aminothiophenol (p-ATP). The thiol group of the p- ATP molecule has a high affinity for gold and silver surfaces and forms monolayers in dilute solutions followed by rinsing to remove the unbonded molecules. Samples were incubated at room temperature in a 1 mM solution of p-ATP in ethanol for 24 hours, rinsed repeatedly with ethanol and DI water, and then dried with a gentle stream of nitrogen gas. Raman spectra were measured in a Renishaw inVia micro-Raman spectrometer. A 632.8 nm HeNe laser spot is accurately positioned using a high precision Prior ProScan II microscope stage, which enables spatial mapping of the Raman spectra. The laser was focused to a small Gaussian spot (~0.5 µm diameter) through a 100X objective lens with a numerical aperture of 0.9. A cylindrical lens was inserted in the beam path before the objective lens to spread the laser into an elliptical spot, enabling faster mapping of the Raman intensity across the sample. The cleanliness of the fabricated silver nanostructures is an important concern due to the confounding spectral peaks that may originate from organic contamination [38, 74, 105, 121]. Common treatments such as oxygen plasma or UV ozone to remove lithographic residues are limited because of the highly reactive silver surfaces. In this work, we functionalize the nanoparticles with a p-ATP monolayer immediately after the lift-off process and store them in a vacuum dessicator to protect the nanoparticles from further contamination and degradation. Raman spectra collected on samples without the 39 p-ATP molecules generally show no observable peaks at our experimental laser intensities, however, broad peaks of amorphous carbon were occasionally seen, most notably at higher incident powers. The thermal stability of these delicate, resonant nanostructures is another important concern, given the poor heat sink of the underlying 100 nm silicon nitride membrane [127]. However, no degradation was observed in TEM images taken before and after laser exposure with the powers used in this work (0.88 mW/μm 2 ). A couple of sites exhibiting moderate to high Raman intensity showed altered spectral profiles, which we attribute to the decomposition of the nearby p-ATP molecules. 2.4 Results and discussion We measure the SERS response of these p-ATP/Ag nanoparticle arrays by spatially mapping their Raman intensities. The Raman intensity is proportional to the fourth power of the electric field |E| 4 for small phonon energies, and therefore serves as a good measure of the electric field enhancement and relative plasmonic strength. For higher phonon energies, |E| 4 still serves as an upper limit to experimental calculations of the SERS electric field enhancement. Figure 2.4 shows the Raman spectra taken at several different locations on the 5x5 nanoparticle grid array, shown in the TEM image on the right. An increase in Raman intensity is clearly visible for the spectrum taken with light polarized along the axis of the nanoparticle pairs, whereas the intensity is much lower in cells with polarization aligned perpendicular to the nanoparticle pairs. The red and blue spectra in particular show the polarization dependence at the same point in the nanoparticle cell. However, due to the nanoparticle density and focal spot size, this spectrum cannot be attributed to a single nanoparticle pair. 40 Figure 2.4: Raman spectra of p-ATP molecules bonded to Ag nanoparticle arrays deposited by angle-evaporation taken at several points corresponding to the TEM shown in the right. The spectrum in red was taken at the location indicated by the red “X” with incident light polarized along the axis of the nanoparticle pairs. The blue spectrum corresponds to the same location taken with light polarized perpendicular to the nanoparticle dimer axis. The black spectrum and the green spectrum correspond to spectra taken at the black and green X’s, respectively. Figures 2.5b and 2.5c show the Raman intensity spatial maps of the 5x5 matrix shown in Figure 2.5a coated with p-ATP, taken with the incident laser polarization oriented perpendicular (Figure 2.5b) and parallel (Figure 2.5c) to the axis of the nanoparticle pairs. A significant increase in the Raman intensity is observed in several nanoparticle cells when the polarization is matched to the angle-evaporated nanometer size gaps, demonstrating the electric field enhancement of the plasmonically coupled nanoparticles. The lack of uniformity in the SERS intensity over these cells is likely due to the inherent sensitivity of the electromagnetic response to the geometry of these nearly touching nanostructures. A small variation in the particle or gap size can result in a large shift in the resonant frequency [156], pushing the particle off-resonance for a fixed X X X X 5 µm ║ ║ ┴ ┴ 41 Figure 2.5: (a) TEM image of a 5x5 matrix of cells containing different nanoparticle geometries. Spatial mapping with a 632.8 nm laser exciting the 1576 cm -1 p- ATP Raman peak across this matrix of various Ag nanoparticle geometries with polarization (b) perpendicular and (c) parallel to the axis of the nanoparticle pairs. (c) Parallel Polarization (a) (b) Perpendicular Polarization 42 excitation frequency. We believe we may only measure a few fortuitous hotspots that fell within the range of the 632.8 nm laser source. By comparing the SERS-enhanced cells of Figure 2.5c with the TEM image of Figure 2.5a, it is clear that the SERS enhancement does not simply correspond to the metal filling factor of these cells. This further demonstrates the plasmonic nature of this SERS enhancement mechanism, which relies intimately on the plasmonic interaction between adjacent nanoparticles. Based on the TEM image shown in Figure 2.6a, we can simulate the electromagnetic response of this Ag nanoparticle pair by defining the spatial extent of the metal nanoparticles from this high resolution TEM image. The x and y dimensions of the particles were determined from the TEM image, while evaporation thicknesses of 15 nm and 30 nm were used to specify the height of the left and right particle, respectively. FDTD simulations [138] were performed in USC’s multi -teraflop supercomputing facility, which consists of 5,472 CPUs connected by a high-performance, low-latency Myrinet network. Here, full three-dimensional simulations are performed using a grid of 14 million points to discretize the spatial extent of the electric and magnetic fields with up to 2.5 Å resolution in the gap region, and carrying out 200,000 time steps. The dielectric function we use is based on a fit of the experimental data obtained by Johnson and Christy to a Lorentz-Drude formula [63]. Figures 2.6b and 2.6c show the electric field intensity distributions of this silver nanoparticle dimer integrated over the z- dimension, irradiated at normal incidence at the plasmon resonance frequency. For incident light polarized along the axis of the nanoparticle dimer (Figure 2.6c), the maximum electric field intensity lies in the gap between the nanoparticles, with a value 43 82,400 times that of the incident field intensity at the calculated plasmon resonance occurring at 552 nm. For Figure 2.6: (a) TEM image and FDTD simulations of the electric field intensity around a silver nanoparticle dimer with 2 nm separation with incident light polarized (b) perpendicular and (c) parallel to the axis of the nanoparticle pair. The electric field intensity is plotted on a logarithmic scale. ( b) 1 0nm ( a) 1 0nm Parallel Polarization Perpendicular Polarization (a) (b) (c) 10 nm 10 nm 10 nm 44 this nanoparticle pair, the SERS enhancement factor at the most intense point is given by the square of this electric field intensity enhancement factor, giving a value of 6.9 x 10 9 . With polarization perpendicular to the nanoparticle axis, the SERS enhancement factor at the most intense point is calculated to be 6.4 x 10 4 at this same frequency. Integrating over the area shown in Figure 2.6c, we find a total SERS EF of 1.4 x 10 11 for parallel polarization. We can also estimate the areal SERS enhancement factor over the area inside the focal volume. Based on the electric field distribution shown in Figure 2.6b, we calculate the expected areal SERS enhancement by integrating E 4 over the simulation area and then dividing by the incident electric field to the fourth power E 0 4 integrated over the area. Areal SERS Enhancement Factor =   dxdy E dxdy E 4 0 4 (2.1) Following this procedure, we estimate an areal electromagnetic SERS enhancement factor from our FDTD simulation of 5.8 x 10 3 integrated over a 0.4 µm x 0.4 µm area using equation 2.1. The areal EM enhancement factors of our samples are expectedly low due to sub-optimal densities of nanoparticle coverage, as seen in Figure 2.2. From our Raman measurements, it is difficult to quantify the SERS enhancement factor because the number of molecules in the focal volume of the laser spot and in the 2 nm x 2 nm x 15 nm SERS enhancement volume is unknown. An estimate is made using this SERS enhancement volume from the simulation results and the fact that these signals are collected from multiple nanoparticle pairs within the focal volume. 45 Evidence suggests that the SERS enhancement of the 1436 cm -1 vibrational mode of metal-bonded p-ATP molecule is significantly enhanced due to a charge transfer mechanism in addition to the electromagnetic enhancement for incident radiation at 532 nm and 632.8 nm [9, 62, 104]. This intense peak is only observed in surface-bonded molecules, which further complicates the comparison of SERS spectra with those of bulk reference samples of p-ATP. The 1077 and 1590 cm -1 Raman peaks are believed to be primarily EM-enhanced [9] and are measurable in unbonded p-ATP, making them well- suited for accurately determining the EF. The EF is defined as: bulk bulk ads SERS N I N I EF / /  (2.2) where I SERS is the intensity of the Raman mode taken on the SERS-active substrates and I bulk is the spectral intensity of the same Raman mode for the “crystalline” p -ATP solid. I SERS and I bulk are easily obtained from experiment and normalized for acquisition time and laser power, with an additional factor to account for the decrease in laser power density (~1/10) when using an elliptical beam spot. N bulk is the number of molecules within the laser-illuminated volume of p-ATP solid. Here, this active volume is a cone defined by a focused circular laser spot 0.5 µm in diameter at the surface, with an estimated penetration depth of 8µm. Using the density of solid p-ATP (1.18 g/cm 3 ), N bulk is calculated to be about 2.97 x 10 9 molecules. We estimate the number of dye molecules bonded to the silver surface in the hot spot area by assuming a coverage of 2 nm around the hot spot on each nanoparticle. Multiplying by the respective evaporation thicknesses (15 nm and 30 nm) yields an overall sidewall coverage area in the nanogap region of 46 about 90 nm 2 . The dye is estimated to cover the gold surfaces with a density of approximately 0.25 nm 2 /molecule [47, 93, 135, 151], which yields approximately 360 molecules per nanoparticle pair. The diffraction limited 632.8 nm laser spot was passed through a cylindrical lens producing a slightly larger effective sampling area such that approximately 10 nanoparticle pairs contribute to each measured spectrum. We thus take N SERS to be about 3600 molecules. Taking I SERS and I bulk measured to be 1890 and 55,800 respectively and adding compensation factors for the reduced laser power density due to the cylindrical lens (1/10) and CCD collection method (1/4), we estimate a SERS enhancement factor of 1.1 x 10 6 . This experimental EF is over three orders of magnitude smaller than the 6.9 x 10 9 value from our simulations, which may result from exciting the nanoparticle pair slightly off-resonance and overestimating the number of molecules contributing to the measured Raman intensity. Dieringer et al. have developed a method for verifying that there is only one dye molecule in the SERS enhanced Raman spectra using isotopologues of Rhodamine 6G [35]. This enables an accurate measurement of the SERS enhancement factor. This method requires extensive synthesis capabilities, and is beyond the scope of the present work. SERS enhancement is known to arise from two factors, a dominating electromagnetic enhancement and a less significant chemical enhancement, that may work in unison and further complicate our ability to accurately determine the true field enhancement in the nanogaps. The p-ATP molecule has been one of the most commonly studied systems for observing chemical enhancement. One explanation of the chemical 47 enhancement mechanism is a Raman-like process involving charge transfer between metallic energy levels and molecular levels situated around the Fermi level of the metal. These transitions can resonate at specific incident laser energies and also couple vibronically to each other [83]. Experimental and theoretical work into the polarization dependence of the Raman intensity under the chemical mechanism shows differences by a factor of only 5-6X under different polarization and molecular transition moment alignments [64, 83]. Based on these observations and our simulations, we find our results stem from strong plasmonic coupling between nanoparticle pairs. Our experimental electric field enhancements may be expectedly less due to off-resonance excitation of the nanostructures and an inability to tune the wavelength of the excitation source to the absorption peaks. While most of the gaps produced in this work are larger than 1 nm, quantum mechanical tunneling of electrons between nanoparticles separated by gaps smaller than 1 nm may significantly lower the measured electromagnetic field enhancement and blue-shift the optical absorption [156]. However, our data demonstrates proof-of-principle of SERS enhancement by the plasmonic coupling of nearly touching Ag nanoparticles. 2.5 Conclusion We have demonstrated a method for fabricating nanoparticle pairs with nanometer separations. A significant increase in the Raman intensity is observed when the polarization is matched to the angle-evaporated nanometer size gaps, demonstrating the electric field enhancement of the plasmonically coupled nanoparticles. Numerical simulation of the electromagnetic response of these nanoparticles show significant enhancements in the calculated electric field and SERS signal, which also depend 48 strongly on the polarization of the incident light. Based on the 10 9 -10 10 SERS enhancement factor, these substrates could be used in devices approaching chemical detection at the single molecule level. This research was supported in part by ONR award No. N00014-08-1-0132, AFOSR award No. FA9550-08-1-0019, ARO award No. W911NF-09-1-0240, NSF award No. CBET-0854118, and NASA SURP No. 1346414. Electron beam lithography was performed by Richard E. Muller. This research was partially carried out at the Jet Propulsion Laboratory, California Institute of Technology. 49 CHAPTER 3: FANO INTERFERENCE AND EFFECTS OF ASYMMETRY ON NEAR-FIELD AND FAR-FIELD SCATTERING OF PLASMONIC HETERODIMERS 3.1 Abstract We fabricate arrays of metallic nanoparticle dimers with nanometer separation using electron beam lithography and angle evaporation. These “nanogap” dimers are fabricated on thin silicon nitride membranes to enable high resolution transmission electron microscope imaging of the specific nanoparticle geometries. Plasmonic resonances of the pairs are characterized by dark-field scattering micro-spectroscopy, which enables the optical scattering from individual nanostructures to be measured by using a spatially-filtered light source to illuminate a small area. Scattering spectra from individual dimers are correlated with transmission electron microscope images and finite- difference time-domain simulations of their electromagnetic response, with excellent agreement between simulation and experiment. We observe a strong polarization dependence with two dominant scattering peaks in spectra taken with the polarization aligned along the dimer axis. This response arises from a unique Fano interference, in which the bright hybridized modes of an asymmetric dimer are able to couple to the dark higher-order hybridized modes through substrate-mediated coupling. The presence of this interference is strongly dependent on the nanoparticle geometry that defines the plasmon energy profile but also on the intense localization of charge at the dielectric surface in the nanogap region. 50 3.2 Introduction Plasmonic excitations take advantage of the strong interaction between light and metal surfaces to provide nanoscale confinement and localization in subwavelength dimensions while providing high field enhancement. This area of research has exploded in the last decade due to our ability to fabricate, simulate, and microscopically image such nanostructures. Plasmonics has found numerous applications in areas such as biological and chemical sensing [3, 97, 128, 149], surface-enhanced Raman spectroscopy (SERS) [70, 102], cancer therapy [56], solar energy conversion [34, 44, 96, 115, 124], photodetectors [60, 139], lasers [32, 108], waveguiding [88], and magnetic recording [133]. Advances in fabrication tools (e.g., electron beam and ion beam lithography) and characterization techniques (e.g., scanning and transmission electron microscopy, near- field scanning microscopy, atomic force microscopy, electron energy loss spectroscopy/cathodoluminescence) are also providing new insight into the character of plasmons at the nanoscale [40, 73, 126]. It is very important to both fabricate and calculate the electromagnetic response of these nanostructures as their size and separation reach the scale of a single nanometer in order to further improve their performance in these applications. When two metallic nanoparticles (NPs) are brought into close proximity, the local electric field intensity scales dramatically with decreasing separation. The high fields created by plasmonic nanostructures may be used to greatly enhance physical processes like vibrational Raman scattering [70, 102], carrier generation [68, 71, 75], and nonlinear optical effects [17, 33, 67, 80, 109]. Presently, there is no reliable method for producing consistent sub 2-nm gap sizes between nanoparticles with a larger macroscopic order 51 suitable for device applications. Top-down lithographic methods are still limited to reliable resolutions on the order of ten nanometers despite the recent advances in fabrication. While higher resolution is achievable down to a size of 2 nm, the tools and materials used can often limit the utility of the fabrication for practical devices, due to substrate limitations and thin resist layers [40, 89]. Other methods such as electromigration can be used in nanometer-separated electrode configurations but each junction must be created independently with a lack of control in the exact position of the formed nanogap [54, 98, 148]. A self-aligned technique offers parallelism without restriction to electrode configurations through two-step lithography and a sacrificial cap to create spacings of 2 – 10 nm, but non-uniform growth of the cap layer results in geometric inconsistency in the physical gap size [45, 54]. Bottom-up fabrication techniques such as chemical and DNA functionalization offer a more reliable method of controlling the spacing between two or more nanoparticles but lose large scale order offered by top-down methods, requiring multiple level self-assembly techniques to avoid random placement and orientation once dispersed on a substrate [1, 2, 20, 26, 129]. These functionialized techniques may also limit the accessible hot spot area resulting in a lower utilization of the field enhancement properties. Our previous work demonstrated an angle evaporation technique with top-down lithography able to produce two metal nanoparticles with separations on the order of a single nanometer [140]. These nanostructures (nanoparticle dimers) were characterized by Raman spectroscopy and high resolution transmission electron microscopy (HRTEM). Finite-difference time-domain (FDTD) simulations showed that the technique could 52 produce nanoparticles with SERS enhancement factors as high as 10 10 . In the work presented here, similar nanostructures are isolated and measured using dark-field micro- spectroscopy with correlated HRTEM imaging of each individual dimer. We use this combination of techniques to systematically study the effects of the precise geometry on the optical scattering of such asymmetric dimers. We model the structures using FDTD simulations, which provide more detailed information about the charge and electric field distributions associated with specific features in their far-field scattering spectra. 3.3 Experimental and simulation details Gold nanoparticles are fabricated using a two-step angle evaporation technique, as shown in Figure 3.1 [140]. Electron beam lithography is used to pattern 40-120 nm diameter holes in a thin bi-layer of MMA-MAA and PMMA 950K resist. MMA-MAA is used to produce a large undercut necessary for the angled second deposition, while the top layer of PMMA serves as the masking layer. A thin layer of metal (e.g. Au or Ag) is first deposited at normal incidence. The sample is then tilted by a small angle (10-20°) and a second layer of metal is deposited. For overlapping depositions, the size of the nanogap is estimated by the relative angle between the two evaporations, θ, and the thickness of the first evaporation, , and is given by tan θ. For non-overlapping depositions with larger particle size or tilt angles, the gap size is a function of the mask layer height, t, the relative angle θ, and the hole diameter, , and is given by tan θ . The second nanoparticle is inevitably smaller than the first due to undesired deposition on the sidewalls of the hole in the lithographic mask and a smaller effective cross section to evaporate through when the mask is tilted. The nanoparticles are fabricated on 53 Figure 3.1: Schematic diagram of the angle evaporation technique used to create nanogap heterodimers. For overlapping depositions, the gap size is a function of first evaporation thickness (t 1 ) and the relative angle between the two evaporations (θ). For non overlapping depositions, the gap size is a function of the height of the top masking layer and the relative angle. commercially available non-porous silicon nitride membrane windows (SiMPore, Inc.) toenable high-resolution transmission electron microscope imaging using a JEOL JEM- 2100F advanced field emission TEM. In order to obtain scattering spectra from individual nanoparticle dimers, a confocal dark-field micro-spectroscopy setup was built similar to that of Fan et al. [43], as illustrated schematically in Figure 3.2. This setup uses a Fianium SC450 supercontinuum light source to provide collimated light from 450 nm to 2000 nm. The output is polarized and sent into a small pinhole aperture to spatially filter the light so that only a small point source enters through the back aperture of the objective lens (Mitutoyo NIR 50X, NA=0.42). The objective serves as both the condenser and collection objective Lithographic mask Substrate 54 lenses, as shown in Figure 3.2. The position of the pinhole can be adjusted so that the light is aligned parallel to the objective but off center. A beam blocker is used just before the objective to remove the reflected light from the sample surface entering on the opposite side of the objective lens. The incident angle is governed by the numerical aperture of the objective lens and the off-axis distance of the spatially filtered light (~12- 15° in practical use). The scattered light is analyzed using a grating spectrometer with a thermoelectrically cooled CCD camera. The collected scattered light is reimaged on another pinhole aperture (150 μm) before it is sent into the spectrometer to limit Figure 3.2: Schematic diagram of dark-field spectroscopy setup. The microscope objective is used as both the focusing condenser and collection optic. Incoming polarized white light is spatially filtered through a pinhole aperture and reflected off a beam splitter into the objective off the center axis. A beam blocker is used to eliminate reflected light, while the remaining scattered light is sent to the spectrometer. 55 collection to a very small spatial area (~3 μm), enabling the measurement of isolated scattering from single nanoparticle pairs. The experimental instrumentation is critical to this work as it overcomes several problems encountered when trying to measure optical scattering from membrane substrates with typical dark-field spectroscopy setups. Standard commercial dark field condenser objective lenses are designed to illuminate a large sample area (~20-100 m), which induces a large amount of background scattering from the membrane edges where the nitride meets the supporting silicon substrate. While our implementation uses a pinhole filter to limit the collection area of the spectrometer, it also uses a spatially filtered source to illuminate a much smaller area (~5 m) of the membrane (100 m x 100 m) to prevent undesired scattering. The low angle of illumination in this configuration also provides near-normal excitation, which minimizes retardation effects and improves the signal-to-background ratio [43]. Finally, this technique also employs a dry objective, which alleviates difficulties associated with using small, fragile TEM membranes with oil immersion objectives. Electromagnetic simulations are performed with the Lumerical FDTD Solutions package running on USC’s 0.53 petaflop HPCC supercomputer cluster, where we typically make use of 256 or 512 processors running in parallel over a high peformance, low latency Myrinet network. A grid spacing of 2 Å is used in the immediate vicinity of the small 1-2 nm separations between particles, while a larger grid spacing of 4 Å covers the remaining space of the metallic nanoparticles. A temporal grid spacing of 0.001 fs is used with a total of 100,000 time steps, where an initial plane wave source irradiates the 56 metal nanoparticles with a Gaussian pulse in the frequency domain of wavelengths ranging from 350 nm to 1000 nm. The frequency response of the system is recovered by taking a Fourier transform of the time response. Perfectly matched layer boundary conditions are used with 12 layers to decrease the size of the simulation space. The dielectric function of gold is based on optical data obtained by Johnson and Christy that is fit to a Lorentz-Drude formula [63]. 3.4 Results and discussion 3.4.1 TEM-based measurement and simulation Figure 3.3a shows a high resolution transmission electron microscopy image of a gold nanoparticle heterodimer fabricated using the angle evaporation technique. The Figure 3.3: (a) TEM image of an asymmetric nanoparticle dimer, heterodimer A. (b) Measured scattering spectra of dimer with polarization aligned parallel (black) and perpendicular (red) to the common NP axis. (c) Simulated scattering spectra based on dimer geometry in (a). b) c) a) 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) parallel perpendicular 400 500 600 700 800 900 Measured Scattering Intensity Wavelength (nm) parallel perpendicular 57 heterodimer is a nanoparticle pair with asymmetry in the size, shape, and/or material of the constituent NPs. Our angle evaporation fabrication process produces a large asymmetry between the two particles in all spatial dimensions while yielding a gap that varies between 1.7 – 5 nm. This process also produces a large number of smaller residual gold nanoparticles surrounding the two intended nanoparticles, as shown in Figure 3.3a. This is likely due to scattering of metal atoms from the sides of the PMMA mask opening as well as a slightly omni-directional flux of metal source vapor coupled with the island- like growth formation of thin metallic films on oxide and nitride surfaces. While the far- field scattering from individual particles of such size is negligible, they can play a strong role in the near-field and far-field electromagnetic behavior depending on the particular geometry. For this particular dimer, the residual nanoparticles in the nanogap effectively reduce the gap spacing to 0.5 nm at two different points, the effect of which will be discussed later. The normalized scattering spectrum for this dimer, heterodimer A, is shown in Figure 3.3b. Two resonant peaks are visible at 622 nm and 655 nm with polarization aligned parallel to the common dimer axis, and perpendicular scattering shows a single peak around 618 nm. For the case of perpendicular polarization, there is weak interaction between the modes of the two particles, and scattering is dominated by the perpendicular mode of the largest nanoparticle. In symmetric nanoparticle dimers, the red-shifting of resonances relative to the single particle resonance is explained by the hybridization of the lowest energy dipolar plasmon modes of each particle, where decreasing separation enables significant coupling between modes close in energy [5, 103]. However, such dimers are characterized by a single in-phase (bonding) dipole- 58 dipole coupled mode in a polarization-dependent far-field scattering spectrum. The out- of-phase (anti-bonding) dipole-dipole mode conversely blueshifts with decreasing separation, but the out-of-phase dipole moments of the induced charge oscillation effectively cancel far-field scattering. Likewise, the symmetry of higher order modes prevents radiation to the far-field. It should be noted that the formalism of plasmon hybridization is strictly only valid in the quasistatic limit where there is no radiative damping or phase retardation, but we will use the term “hybridized mode” to describe a coupled mode in a heterodimer where the larger particle may slightly exceed this limit [19]. Symmetry breaking can allow formerly dark modes to couple with bright modes and add peaks to radiative scattering [6, 19, 50, 52, 129, 131]. Asymmetry in the nanoparticle size and shape can result in significantly different plasmon mode energy profiles for the two particles, which can separate the low energy modes from each other but also overlap higher order modes of one particle with lower order modes of the other particle [19]. The scattering spectra of the heterodimers, as measured by this dark-field technique, were simulated using the FDTD method based on lateral dimensions defined by the TEM image and the evaporation thicknesses. The spatial x and y dimensions of each metallic nanoparticle are defined by transmission electron microscope images at magnifications between 60-100kX. We use threshold algorithm to convert the high contrast grayscale TEM images into a binary black and white image. This image is imported into the Lumerical FDTD Solutions package to define the x and y coordinates of a metallic structure. The z dimensions of the two heterodimer nanoparticles are defined to be the evaporation thicknesses of 30 nm and 15 nm. The smaller residual particles are 59 also defined by the binary image, where the height of these particles is estimated from their individual size. For circular cross sections in the xy image, the radius of this circular area is used for the height of the residual particle. For elliptical particles, the height is set to be the minor radius of the particle. For more complicated cross-sectional shapes, the particles are subdivided into major sections where approximations of the previous two techniques are combined. Figure 3.3c shows the simulated scattering spectra for the modeled nanoparticle dimer for the two incident polarizations, showing two peaks at 620 nm and 667 nm for parallel polarization and one peak at 630 nm for perpendicular polarization, respectively. The results exhibit narrower resonances than those measured experimentally, which may stem from the vertical sidewalls and sharp corners defined in the simulated model. The fabricated nanostructures are polycrystalline in nature as evident from TEM imaging. Roughness from such grains increases the surface plasmon losses and broadens the LSPR resonance [13, 81]. We find that annealing these structures helps to decrease the polycrystallinity and may reduce such losses but can also fuse the heterodimer into a single asymmetric particle. Despite our idealization, excellent agreement between simulation and experiment is observed. Dimers with longer gap regions like that shown in Figure 3.4 can also be fabricated with a gap size of less than 2 nm running along an 80 nm length between the nanoparticles. Since the spatial offset in the center of the two particles is fixed by the masking layer resist height and the relative tilt angle between evaporations, a larger mask 60 Figure 3.4: (a) TEM image of an asymmetric nanoparticle dimer, heterodimer B. (b) Measured scattering spectra of dimer with polarization aligned parallel (black) and perpendicular (red) to the common NP axis. (c) Normalized simulated scattering spectra based on dimer geometry in (a). hole results in larger particles but with the same fixed offset as the smaller particles. This increases the amount of overlap between the two particles and thus the gap length along the edge. The parallel polarization again shows two peaks in the scattering spectrum, occurring at 660 nm and 755 nm. Perpendicular polarization shows a slightly asymmetric profile with a dominant peak centered at about 655 nm. The spectra are generally red- shifted with respect to those of the smaller dimer in Figure 3.3 due to size-dependent retardation effects. A much larger separation in the two parallel peak positions than that of the peaks in heterodimer A is also notable. The long crescent-shaped particle and its conformation to the edge of the larger particle also offer a path for excitation of the gap modes through perpendicular polarization, which can explain the asymmetry on the low 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) parallel perpendicular a) b) c) 400 500 600 700 800 900 Measured scattering intensity Wavelength (nm) parallel perpendicular 61 Figure 3.5: (a) TEM image of an asymmetric nanoparticle dimer, heterodimer C. (b) Measured scattering spectra of dimer with polarization aligned parallel (black) and perpendicular (red) to the common NP axis. (c) Normalized simulated scattering spectra based on dimer geometry in (a). energy side of the perpendicular polarization resonance. Deviations from the ideal cylindrical shape of the first NP and the position & orientation of the second NP can also allow weak excitation of the modes dominant in the opposite polarization. Figure 3.5 shows heterodimer C, similar in size to the first dimer presented but with a smaller number of surrounding residual nanoparticles. This heterodimer also shows two nanogap “nodes” at the top and bottom of the gap region, with particle spacing of 1.2 and 2.0 nm, respectively. The experimental and simulated scattering spectra again show good agreement with two peaks in the parallel polarization with the same relative intensity. The experimental spectrum shows a less exaggerated dip in the center of the two measured peaks and a general blue shift with respect to the simulation by about 40 400 500 600 700 800 900 Normalized Scattering Intensity Wavelength (nm) parallel perpendicular 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) parallel perpendicular a) b) c) 62 nm. The sharply defined cylindrical geometry assumed of our particles in the simulation and a local change in index of refraction due to multiple surface treatments with oxygen plasma to remove amorphous carbon, respectively, are two possible reasons for this discrepancy. The oxygen plasma treatment also acts to thermally anneal the gold particles, reducing the polycrystallinity of the lithographically patterned structures. Fewer grains are observed in these metallic structures after annealing (Figure 3.5a) than in structures before annealing (Figure 3.3a and Figure 3.4a). Thermal annealing also reduces the number of residual nanoparticles surrounding the dimers, where the residuals either coalesce with one another or fuse into the two larger heterodimer particles. We can further understand the plasmonic character of the heterodimers by looking at the near-field behavior of the electric field and charge density profiles in the FDTD simulations. Figure 3.6 shows the electric field intensity spatial profiles calculated for the heterodimer A at 620 and 667 nm wavelengths for heights of z = 1 and 15 nm, showing fields just above the surface of the substrate and at the top of the smaller heterodimer particle at two different polarizations. Figures 3.6a - 3.6d show that the fields are largely concentrated in the nanogap between the two particles, with |E/E 0 | 2 ranging from 1500 to 8000 in the smallest separation between the particles several nanometers above the membrane. The fields near the surface of the membrane are higher with electric field intensity enhancements of 10,000 – 25,000 calculated in the nanogaps. Figure 3.7 shows the calculated electric field intensity maps for heterodimer C at the two simulated resonance wavelengths of 608 and 672 nm. The fields exhibit a dipolar response, like heterodimer A and dimer systems in general, with the highest intensity 63 fields concentrated in the nanogaps between the two particles and the highest of these enhancements concentrated near the substrate. Figure 3.7g and 3.7h show xz cross- sections at the top nanogap node of the heterodimer at the resonances. We observe that Figure 3.6: Electric field intensity |E| 2 cross sections for heterodimer A with parallel polarization at λ = 618 nm for z = 1 nm (a) and z = 15 nm (b) and at λ = 667 nm for z = 1 nm (c) and z = 15 nm (d). (e) and (f) are for perpendicular polarization at λ = 630 nm and z = 1 nm and 15 nm, respectively. Scale bar is logarithmic. λ = 618 nm λ = 667 nm λ = 630 nm a) b) c) d) e) f) y (μm) y (μm) y (μm) y (μm) y (μm) y (μm) x (μm) x (μm) x (μm) x (μm) x (μm) x (μm) z = 15 nm z = 1 nm 64 Figure 3.7: Electric field intensity |E| 2 xy cross sections for heterodimer C with parallel polarization at λ = 608 nm for z = 1 nm (a) and z = 15 nm (b) and at λ = 672 nm for z = 1 nm (c) and z = 15 nm (d). (e) and (f) are for perpendicular polarization at λ = 617 nm and z = 1 nm and 15 nm, respectively. (g) and (h) show intensity in xz cross-section at y = 5.6 nm, at 608 and 672 nm wavelength, respectively. Scale bar is logarithmic. a ) b ) c ) d ) e ) f ) g ) h ) a) b) c) d) e) f) g) h) λ = 608 nm z = 15 nm λ = 672 nm λ = 617 nm z = 1 nm y (μm) y (μm) y (μm) y (μm) y (μm) y (μm) x (μm) x (μm) x (μm) x (μm) x (μm) λ=608 nm λ=672 nm x (μm) 65 the electric field distribution is different in the z-dimension depending on the resonance mode. The fields of the lower energy resonance are predominantly concentrated at the interface between the silicon nitride membrane and the metal particles, while the higher energy mode localizes more of its field at the top (z = 15 nm) of the smaller particle. At λ = 672 nm, field intensities as high as 12,000 occur near the top of the smallest nanogap compared to those near the substrate of 2000-3000, but for 608 nm wavelength, field intensities of over 35,000 are calculated at z = 1 nm above the substrate versus values of 5000 at z = 15 nm. The simulations show that the field distribution at the substrate is diffusely spread onto the nearby residual nanoparticles close to the membrane surface. While these nanoparticles are too small to scatter strongly into the far-field and to couple efficiently to the plasmon modes of the larger particles, they do act to increase the local distribution of electromagnetic energy within the near-field. As can be seen in Figures 3.6a and 3.6c, the residual particles that lie within the near-field scattering regions of the larger particle will further scatter that field locally to produce high enhancements near the substrate along the common nanoparticle axis. This behavior also exists for excitation with perpendicular polarization as residuals at the top and bottom of the largest particle locally scatter the near-field light. From Figures 3.6e and 3.6f, we can observe that enhancement also occurs in the nanogaps between the two primary particles for this polarization, where the non-ideal particle shape and orientation break symmetry about the x- and y-axes and remove any orthogonal response to the two polarizations. 66 We also investigated the effect of residual nanoparticles on the scattering spectra. While the predominant effect of the residuals is only to scatter the light in the near-field of the larger heterodimer, a residual nanoparticle within the heterodimer’s nanogap may significantly change the coupling between the heterodimer particles and thus alter the far- field scattering. Figure 3.8a shows the scattering spectrum calculated both with and without residuals for heterodimer A. As seen in Figure 3.3a, this heterodimer has two small residual particles in the intended gap region that when removed significantly change the scattering profile. We expect weaker coupling between the two primary particles when this residual is removed due to the increase in gap size, which may cause both a resonance shift and a change in scattering intensity. Removing the residuals from this dimer strongly increases the second scattering peak around 680 nm with a slight blue shift to 670 nm. The residual nanoparticles were included to more accurately simulate the measurable scattering, but we find that the model without residuals provides a better fit to the experimental data in this case. This suggests that the effects of these smaller NPs are 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) w/o residuals with residuals 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) w/o residuals with residuals Figure 3.8: Simulated scattering of heterodimers with (red) and without (black) residual nanoparticles. (a) Heterodimer A with residual NPs in the gap region causes significant reduction of second scattering peak. (b) Heterodimer C with no residual NPs in the gap shows little change in scattering response. b) a) 67 even more subtle in reality, where the geometric definition overemphasizes the field intensity at the sharply defined edge facets. It should also be noted that the presence of these residuals in the gap decreases the gap size to almost 0.5 nm, which according to recent reports is just large enough to avoid quantum charge transport effects in the plasmon coupling, but such effects could contribute to the discrepancy between simulation and experimental data [29, 40, 126, 156]. However, for a heterodimer without residuals in the gap region, such as heterodimer C, only a slight decrease in the far-field scattering intensity occurs due to transfer of energy into the near-field vicinity of the neighboring residuals, and both models consistently fit the measured spectra. The underlying nature of the modes responsible for the simulated scattering can be understood by looking at the frequency dependent charge distribution, as shown in Figure 3.9. The two peak scattering observed in these heterodimers is the result of interference between a broad dipolar hybridized plasmon mode and a dark quadrupolar hybridized mode, often referred to as a Fano interference [84]. These modes are shown in the charge profiles of heterodimer C in Figure 3.9 at two different wavelengths, λ = 650 nm and 715 nm. The charge map at 715 nm provides a clear visualization of the bonding dipole-dipole coupled resonance of the heterodimer. This mode forms a broad superradiant envelope for scattering as the summation of the individual electric dipole moments of the two nanoparticles. The significant overlap of a subradiant “dark” mode alters the charge distribution where the superradiant mode peaks, so a wavelength is chosen in the tail of the superradiant mode to demonstrate the dipolar nature of this resonance without interference. The surface charge map at 650 nm shows distinctly 68 Figure 3.9: Scattering spectrum for parallel (red) and perpendicular (black) polarized light incident on heterodimer C, and three-dimensional charge distributions corresponding to λ = 622 nm, 650 nm, and 715 nm. The upper charge distr ibution mapping shows the surface charge of the full heterodimer. The lower charge distributions show the same distribution but on the individual nanoparticles, rotated for clarity. A mixed dipole-quadrupole coupled mode is visible on both particles at 650 nm (left). A bonding dipole-dipole mode is visible at 715 nm (right), representing the broad superradiant scattering envelope. For perpendicular polarization, a hybridized mode featuring two in-phase dipole modes is visible at 622 nm (top), with evidence for other mode coupling visible in the charge distribution in the nanogap region. 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) parallel perpendicular 622 nm 650 nm 715 nm 69 Figure 3.10: Simulated scattering spectrum for heterodimer C with parallel (black) and perpendicular (red) polarization. Charge distributions depicted for the calculated scattering peaks instead of bright envelope and dark dip shown in Figure 3.9. Insets show three-dimensional charge distributions for parallel polarization at λ = 608 nm (lower left) and 672 nm (lower right) and perpendicular polarization at λ = 622 nm (upper right). Blue represents positive charge and red represents negative charge. Lower charge distributions show the same charge distribution but on the individual nanoparticles, rotated for clarity. Complex charge distributions occur in the nanogap between the nanoparticles for both polarizations. 608 nm 672 nm 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) parallel perpendicular 622 nm 70 different coupling between the particles, where the lower 5 nm portion of the two facing metal surfaces of the heterodimer have an opposite charge polarity than the upper portion of the faces. Since the charge density is concentrated in the nanogap region of the heterodimer, these charges create two strong but opposing electric dipole moments spanning the top and bottom of the nanogap. The magnitudes of the dipole moments are not the same due to differences in charge concentration near the substrate and the top of the particles. The net result is a reduced dipole moment that produces a strong decrease in far-field radiation. The charge map at the scattering dip shows a mixture of dipolar and quadrupolar character, disproportioned by the localization of the charges at the nanogap. From the charge distributions, we can see that the quadrupolar-like modes involved in the subradiant mode are not quadrupolar in the xy-plane, but predominantly “xz -modes” where the sign of the charge near the substrate is flipped with respect to the charge at the top of the particles. The asymmetry of the two particles and the nanogap separation causes a nonuniform distribution of charge in the dipole-dipole interactions of the particles, which is made more complex by the interaction with the dark quadrupolar mode. Figure 3.10 shows the three-dimensional surface charge density for the scattering peaks at 608 nm and 672 nm with parallel polarization and 622 nm with perpendicular polarization. The nanometer scale separation between the two particles induces a very intense localization of the charges in the nanogap region. A complex distribution of charge exists at different points along the gap with a variable profile in the z-direction. At the lower energy peak, the face of the smaller nanoparticle in the nanogap has a predominantly negative charge 71 with a very small but dense concentration of positive charge localized near the substrate at the smallest nanogap separation. The charges on this face induce an opposite surface charge density on the opposing face of the larger nanoparticle. At the higher energy peak, the same face shows a larger amount of positive charge, where positive charge extends from the bottom to the top of the nanoparticle at the node with the smallest gap. However, at the other node with a slightly larger separation, the charge changes from positive to negative about 6 nm above the substrate. For perpendicular polarization, we see predominantly dipolar character in both nanoparticles at the scattering peak of 622 nm. However, the dimer’s asymmetry also allows weak excitation of the mod es predominantly excited by parallel polarization, such as the dark quadrupolar modes across the nanogap. We see evidence for this in the charge distribution at 622 nm in Figure 3.10, where the charges in the nanogap region switch polarity near the substrate and differ from the general perpendicular dipolar charge distribution of each particle. Due to the significant asymmetry in the three-dimensional size of the two NPs, the energetic overlap of these modes on the two particles is generally unfavorable yet enabled by strong coupling induced when the particles are spaced by just a couple of nanometers on a dielectric substrate. Figure 3.11a shows the simulated scattering from heterodimer C as the spacing between the first and second nanoparticle is increased incrementally. As the separation between the particles is increased from 1.2 nm to around 5-6 nm, the strong dip of the sub-radiant mode moderately blue-shifts and quickly loses intensity. The interference is lost for separations larger than 6 nm, and we observe a single scattering peak of bonding dipole-dipole modal character that slowly blue-shifts as 72 500 600 700 800 +20 nm +15 nm +8 nm +6 nm +4 nm +2 nm Simulated Scattering Intensity Wavelength (nm) +1 nm 500 600 700 800 Simulated Scattering Intensity Wavelength (nm) Figure 3.11: (a) Simulated scattering spectra as gap size is incrementally increased from measured value of 1.2 nm for heterodimer C. The dashed line indicates the scattering dip in the spectra. (b) Normalized scattering spectra of the heterodimer modeled from the TEM image (red) and for two elliptical cylinders with comparable spatial and nanogap dimensions (black). the gap size is increased. We note that the superradiant mode exhibits a very gradual redshift with decreasing gap size, which we attribute to weak coupling from the large energy difference in the lowest energy dipole plasmons of the two nanoparticles (due to the large size asymmetry). The gap-dependent frequency shift observed in bonding dipole-dipole plasmons of homodimers is much more rapid due to the stronger coupling of two equally energetic modes. Figure 3.11b shows the scattering spectra of two different heterodimers, one based on the TEM image and another based on simple elliptical cylinders, with the same 1.2 nm separation between the particles. The major/minor radius of the smaller and larger nanoparticle is chosen to approximate the NP dimensions measured by TEM (17/11 nm and 42/35 nm, respectively). The TEM- based simulation features a nanogap that varies in size with two nodes of smallest separation of 1.2 and 2.0 nm spacing, while the two elliptical cylinders are separated by a single node of 1.2 nm spacing. The simulations show that a small variation of the a) b) 73 nanogap geometry has a minor impact on the scattering spectrum and the Fano interference, and that the prominence of the interference is more influenced by the particle dimensions that specify the plasmon energies and the smallest nanogap spacing that determines the strength of coupling between modes. Figure 3.12: Simulated scattering of heterodimer C with (black) and without (red) 10 nm thick silicon nitride substrate. Insets show charge distributions at designated scattering peaks and dips with parallel polarization. 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) 10 nm SiN vacuum 650 nm 590 nm 608 nm 74 The dielectric substrate is critical to the prevalence of the dark mode interference, as shown in Figure 3.12. We observe a notable change in the scattering spectra of the heterodimer with removal of the dielectric membrane. There is a general blueshift in the scattering spectrum due to the removal of dielectric screening charges that effectively lowers the plasmon energies, but most importantly, the dark plasmon now has an almost negligible impact on the bright mode. The charge profiles at the scattering peak have the same general distribution in vacuum and on substrate, governed by the asymmetric NP geometry, but the latter is more localized near the dielectric interface. While the image charges induced in a dielectric substrate act back on each particle plasmon to simply lower that same plasmon’s energ y, the induced charges can further mediate coupling between that plasmon mode and other plasmon modes that induce the same image charge. These effects are strongest for planar structures where the plasmon surface charges are in very close proximity to dielectric screening charges in the substrate. The dielectric substrate is very influential in the observation of Fano interference even in a single plasmonic nanoparticle [72]. Experimental and theoretical work has previously shown that a dielectric can induce interference in an isolated metallic nanocube through substrate-mediated interaction between its own bright and dark modes [130, 154]. The primitive dipole plasmon mode and quadrupole mode have similar charge distributions on the face in contact with the substrate, which induces similar image charges in the dielectric that enables the dipole and quadrupole plasmons to couple and form mixed modes. Such an interaction gives rise to two hybridized modes localized at different heights above the substrate, one at the top of the silver nanocube and the other at 75 400 500 600 700 800 900 Simulated Absorption Intensity Wavelength (nm) Heterodimer Heterodimer vacuum Large NP only Small NP only Figure 3.13: (b) Simulated absorption spectra for heterodimer C on silicon nitride (black), the heterodimer in vacuum (magenta), the larger nanoparticle only (red dashed), and the smaller nanoparticle only (blue dashed). Limited or no Fano interference effects are visible in the isolated NP absorption spectra or the heterodimer in vacuum in the absence of substrate-mediated mode coupling. the nanocube-substrate interface. However, depending on the nanoparticle geometry and dielectric constant of the substrate, this interaction may not necessarily yield a Fano interference, where the bright and dark modes are pushed far enough apart that there is limited spectral overlap. Figure 3.13 shows the local absorption spectra for heterodimer C (both with and without the nitride membrane) and the individual nanoparticles that compose it. The larger nanoparticle shows no signs of interaction with its dark modes, while the smaller nanoparticle shows a small dip on the high energy side of its absorption peak, induced by interaction with a dark quadrupolar plasmon like that in Figure 3.14a. We find that substrate-mediated coupling is just as influential in multi-particle systems such as our heterodimers, where rather than coupling between primitive plasmon 76 Figure 3.14: (a) Charge distributions for individual dipolar modes and quadrupolar modes on silicon nitride substrate. Dielectric-metal interface concentrates more charge near the substrate. (b) Strong mixing of dipole-dipole coupled mode and quadrupole-quadrupole coupled mode enabled by concentration of charge in nanogap region. modes of a single nanoparticle, the two-particle coupled or hybridized modes (e.g. dipole-dipole) are able to interact with more complex hybridized modes (dipole- quadrupole, quadrupole-quadrupole, etc.) through interaction with the substrate. Figure 3.14 illustrates the potential mode mixing enabled by the silicon nitride membrane, beginning with the “primitive” dipolar and quadrupolar modes that exist on the isolated particles. In vacuum, the quadrupolar mode has an even distribution of charges at the top and bottom of the particle. However with the dielectric in contact with the bottom of the particles, the charges become largely localized at the metal-dielectric interface. As the spacing between the particles is reduced, the charge at the edges or faces of one particle becomes drawn toward the opposing charge on the other particle, such that the charge is more densely confined to region with the smallest separations. The dielectric opposingly mirrors these plasmon charges right at its surface under these particles. When the a) b) 77 separation is small enough to form the “nanogap,” a very hi gh density of charge exists around the nanogap such that the image charges are also highly localized around the nanogap at the metal-dielectric interface. Other dissimilarities between the charge distributions become relatively less significant as charge concentrates in the gap region. The coupling between the dipole-dipole and quadrupole-quadrupole plasmon modes thus becomes stronger and stronger with decreasing gap size due to substrate-mediated coupling through the screening charges at the nanogap. This results in a plasmon mode that is an admixture of both bonding dipole-dipole and quadrupole-quadrupole hybridization, as shown in Figure 3.14b. The material or dielectric function and thickness of the substrate play roles in the scattering spectrum, as they determine the amount and degree of the polarizability of the screening charges. As shown in the introduction, the general effect of an increased permittivity of the surrounding medium is to redshift the plasmon resonances to lower energy. However, since the planar heterodimers are not embedded in a dielectric medium of silicon nitride but rather sit on top of it, the amount of redshift is much less due to screening charges only on the bottom of the NPs. Furthermore, each mode exhibits a different dependence on the dielectric due to its spatial charge distribution and how strongly it can interact with the substrate image charges. Figure 3.15 shows the scattering spectra for heterodimer C as simulated on several different dielectric membranes. For the weaker dielectric of silicon oxide ( 9 . 3  r  in the visible spectrum), the dimer’s scattering spectrum is blueshifted with respect to that on silicon nitride ( 5 . 7  r  ). A simulation was also run with a 1 nm thick silicon oxide layer on top of a 9 nm thick 78 500 600 700 800 40 nm Si 3 N 4 10 nm Si 3 N 4 1 nm SiO 2 + 9 nm Si 3 N 4 Simulated Scattering Intensity Wavelength (nm) 10 nm SiO 2 Figure 3.15: Simulated scattering spectra for heterodimer C on different dielectric substrates: 10 nm silicon oxide (black), 1 nm silicon oxide + 9 nm silicon nitride (red), 10 nm silicon nitride (blue), and 40 nm silicon nitride (magenta). silicon nitride layer to study the effect of a thin oxidized layer of silicon nitride due to oxygen plasma treatments. The most important observation in these scattering spectra is that the superradiant and subradiant modes do not share the same linear dependence with the dielectric function of the underlying substrate, which can be seen in the relative shifts of the superradiant envelope and the subradiant dip. The three simulations on 10 nm thick membranes show that the subradiant mode’s interaction with the substrate is localized closer to the metal-dielectric interface than that of the superradiant modes. With the thin layer of silicon oxide removed from the nitride, the scattering dip undergoes a larger redshift relative to the envelope, moving the dip from the high to the low energy side of the envelope. Comparing the spectra as the silicon nitride thickness is increased from 10 to 40 nm, we can see that the subradiant dip undergoes a smaller shift than the 79 superradiant envelope, which again suggests that the subradiant mode interacts with the dielectric substrate more locally than the superradiant mode and shows less dependence on substrate thickness. Heterodimer A also shows a scattering dip due to Fano interference involving a complex dark mode, as shown in Figure 3.16. At the calculated scattering dip of 646 nm wavelength, we see evidence for higher order modes with opposite charge localized at the bottom of the dimer nanogap. Heterodimer A is similar to heterodimer C in that both dimer gaps are characterized by two nanogap nodes, one point with smallest separation between particles and a separate point with the second smallest separation. For heterodimer A, though, the difference between the gap sizes at these two nodes (1.7 and 4.0 nm) is more substantial to those of heterodimer C (1.2 and 2.0 nm). Examination of Figure 3.16: Simulated scattering spectrum for heterodimer A with parallel (black) and perpendicular (red) polarization. Insets show three-dimensional charge distributions for parallel polarization at λ = 641 nm (upper) and 790 nm (lower). Rotated for clarity. 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) parallel perpendicular 790 nm 646 nm 80 the λ = 646 nm surface charge in the nanogap of Figure 3.16 shows that while the smallest nanogap node has a flipped charge polarity at the top of the gap to that near the substrate, the second node features a uniform charge polarity from top to bottom. As a consequence, only about half of this dimer’s nanogap features opposing electric dipole moments, and there is less destructive interference than in heterodimer C. At the scale of these gaps, nanometer increases in the gap size significantly decrease the strength of coupling between the nanoparticles. We note that the dipole-quadrupole mode is coupled dominantly through the smaller nanogap node for this dimer, due to a weaker coupling at the second node with twice the gap size as the first node. This differs from dimer C where the more similar gap sizes at the two nodes allows for similar strength coupling through both nodes. Figure 3.16 shows a plasmon mode at λ = 790 nm that appears as a very small peak in far-field scattering but appears more prominently in local absorption. This mode is distinctive in that it occurs at an energy level below the superradiant dipolar-dipolar envelope (around 600-700 nm) yet still has strong dipolar quality. The mode resembles a bonding dipole-dipole resonance with strong coupling through the smallest nanogap but has misaligned NP dipole moments. The electric dipole moment of the small particle is almost 90 degrees misaligned to the dimer axis, while that of the larger particle is oriented about 60 degrees off-axis. Alternatively, since most of the charge density is confined to the gap region, we can see that nanogap dipole moments connecting charge on the larger particle to the opposite charge on the smaller particle are misaligned in one half of the nanogap region versus those in the other half, resulting in weak radiation to 81 the far-field. However, we also note that perpendicular polarization can also excite this mode given the orientation of the NP dipole moments. Despite the inefficient far-field scattering, this mode produces very high electric fields in the vicinity of the nanogap. A yet unaddressed issue is the deposition of metal on top of the larger nanoparticle from the second evaporation. With small diameter particles or large relative evaporation angles, the overlap of the two evaporations is minimal and TEM images of the actual nanostructures show little topographical evidence for a second deposition or “cap” layer on top of the first layer. However, for large particles or small relative angles, there is a large amount of overlap between the two evaporations which leads to a more pronounced cap layer. The TEM image of heterodimer B in Figure 3.4a shows the cap layer as the dark region on the larger nanoparticle near the nanogap. Comparison with the other two heterodimer TEM images shows these dimers have no cap layer deposition. The effect of the capping layer is shown in Figure 3.17, in which the scattering spectra for simulations that include and exclude the capping layer are very similar, with the capped dimer having a slight increase in the overall scattering intensity. As we have seen in the previous simulations, the two features that dominate the scattering of the dimers are the superradiant and subradiant modes. The subradiant mode results from substrate interaction and is highly localized at the bottom of the nanogap near the substrate. Thus, the inclusion of the cap layer has little influence on the properties of this coupling. On the other hand, the superradiant mode is the summation of the dipolar resonances of the individual particles. Since these dipole modes are planar xy-modes, the addition of the smaller cap layer on top of the larger NP in the z-dimension does not significantly alter 82 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) Figure 3.17: Simulated scattering spectra for heterodimer B without the cap layer on top of the larger nanoparticle (black) and with the cap layer (red). the dipole properties of the larger particle. Since our measurement technique is a near- normal incidence technique, we expect limited effects from such cap layers. However, for more typical high-angle dark-field microscopy setups, this increase in the nanoparticle thickness will produce spectral changes due to retardation effects where these vertical modes can be excited. 3.4.2 Test bed simulations We also performed FDTD simulations with a simpler heterodimer to further illustrate this behavior. Rectangular solids (nanoblocks) having dimensions of 50 x 50 x 30 nm and 30 x 30 x 15 nm are placed 2 nm apart on a 10 nm silicon nitride substrate. The smallest nanoblock is offset 4 nm from the nanoparticle axis running through the center of the two nanoparticles to represent a spatial shift due to misalignment of the second metal NP in the angle evaporation process. The edges and corners of the 83 nanoblocks were rounded with a radius of curvature of 2 nm to avoid concentration of fields and charges at unphysical sharp corners and edges. This configuration also offers a uniform gap size between the two nanoparticles that is absent in our TEM-based simulations. Figure 3.18 shows the scattering spectra and surface charge profile for the nanoblock heterodimer described above. The observed interference dip occurs in the high Figure 3.18: Scattering spectra for nanoblock heterodimer for symmetric (red) xy dimensions (x = y = 50 nm for both particles) and asymmetric (black) dimensions (x = y= 30 nm for second particle). First and second particle have heights of 30 nm and 15 nm, respectively. Insets show charge distributions on nanoparticles at indicated scattering peaks/dips. Dipole-dipole 400 500 600 700 800 900 Normalized Scattering Intensity Wavelength (nm) symmetric asymmetric Dipole-quadrupole Dipole-dipole Dipole-quadrupole 84 energy side of the superradiant mode, leaving the dominant scattering peak at 665 nm with bonding dipole-dipole character. The charge distribution giving rise to the scattering dip again shows coupling of the bonding dipolar mode with higher order modes. In this case, we note that the smaller particle distribution resembles a normal dipolar plasmon but with all of its positive charge concentrated at the bottom edge of the nanogap region, while the negative charge concentrates at the top edge of the nanogap and spreads over the rest of the nanoparticle. This is a similar distribution to the charge distribution calculated for heterodimer C (see Figure 3.9). We observe a different distribution on the larger nanoblock particle. While negative charge concentrates at the bottom edge in the nanogap and positive charge spreads over the face in the nanogap region and most of the nanoparticle faces, the back face of the larger nanoblock has a negative charge. This distribution resembles a quadrupole but with most of its negative charge concentrated at the edge touching the substrate. The opposing charges in the nanogap region again explain the decreased scattering. The charge density at the higher energy scattering peak shares similar multi-mode character, but the charges are aligned such that the dipole moment across the nanogap remains uniform causing the observed peak. Figure 3.18 also shows the scattering spectrum for a more symmetric nanoblock heterodimer where the smaller particle’s length and width (x and y dimensions) are equal to those of the larg er particle (50 x 50 nm). We observe a significant 60 nm redshift of the dominant scattering peak and almost negligible effects from coupling to higher-order modes. The increased size of the smaller particle now brings its lowest energy dipole plasmon closer to that of the larger particle’s dipole, which allows for stronger in -phase coupling between these 85 modes and a resulting lower energy hybrid mode. The quadrupolar mode of this particle also decreases in energy, but the hybridized modes it forms with the larger particle are far enough in energy to not alter the superradiant envelope significantly. It should be noted that a dipole-quadrupole interference is still observed around 600 nm in the tail of the scattering peak. This demonstrates that although bringing two planar nanoparticles into near contact allows for significantly stronger coupling into high order modes through substrate interactions, its effect on optical scattering is still governed by the plasmon mode energy alignments determined by the geometry of the nanoparticles. Figure 3.19a shows the effect on the scattering spectrum with increasing gap size of the initial nanoblock heterodimer. We find that an observable interference is lost even when the gap size is increased just to 3 nm in size. On the other hand, we observe a large redshift in the superradiant scattering peak with decreasing gap size, stronger than that observed in the superradiant mode of heterodimer C. The combination of the small interference in the tail of the scattering peak and its significant energy shift with gap size suggests that the dipole plasmon of the smaller particle is closer in energy to the dipole rather than the quadrupole mode of the larger particle. Likewise, the strong presence of the Fano interference and weak shift in the superradiant mode in heterodimer C suggests a better alignment of the dipole plasmon energy with the quadrupole plasmon energy. Figure 3.19b shows another influence of geometry on the scattering interference, where the second nanoparticle is offset laterally from first nanoparticle. These small offsets arise from slight misalignments introduced in sample loading for the angle evaporation process or from non-uniform filling of the mask hole. The simulations suggest that 86 600 700 800 +10 nm +8 nm +6 nm +4 nm +3 nm +2 nm 2 nm Simulated Scattering Intensity Wavelength (nm) +1 nm gap size 600 700 800 Simulated Scattering Intensity Wavelength (nm) 0 nm 4 nm 8 nm 10 nm 12 nm 15 nm 580 600 620 640 Wavelength (nm) Figure 3.19: (a) Scattering spectra for nanoblock dimer as gap size is incrementally increased. Inset shows that the interference dip rapidly decreases as gap size is increased. (b) Scattering spectra as the second nanoblock is laterally offset from the nanoparticle axis. Inset shows the behavior of the scattering dip with increasing offset. All incident excitation is with parallel polarization. 570 600 630 b) a) 87 increasing the offset between the particles redshifts the subradiant mode as the superradiant mode remains fixed at relatively constant wavelength. However, as the second nanoparticle begins to extend beyond the edge of the larger particle (offset > 10 nm), the dipole modes become more oriented toward the corners of the nanoblocks, increasing the separation between the dipole plasmon charges on each particle and creating a redshifted and broader superradiant mode. The results suggest that an intentional lateral offset can be used to fine tune the position of the Fano interference. Figure 3.20a shows that the height mismatch between the two particles plays a significant role in the bright and dark mode overlap. As seen in previous simulations, there is only a small amount of overlap between the dark mode in the tail of the bright mode for a nanoblock heterodimer with a 2 nm gap and a second particle with dimensions of 30 nm x 30 nm x 15 nm. The simulation results show that a height in the range of 20 to 25 nm produces a stronger interference in which the subradiant mode significantly overlaps the superradiant mode. We also observe that the superradiant mode redshifts as the height of the second nanoparticle decreases. This is due to the dielectric screening effects which become stronger as the charge and electric fields become more concentrated near the substrate with decreasing particle height. Figure 3.20b shows that the different height of the nanoparticles has an effect on the plasmon coupling and scattering spectrum in the absence of the substrate as well, but the Fano interference induced by substrate-mediated coupling does not appear in the spectra with a 20 or 25 nm high second particle. 88 600 700 800 25 nm 30 nm 20 nm 15 nm Simulated Scattering Intensity Wavelength (nm) 10 nm 500 600 700 800 Simulated Scattering Intensity Wavelength (nm) 30 nm 25 nm 20 nm 15 nm 10 nm Figure 3.20: Scattering spectra as the height of the second nanoparticle is varied on substrate (a) and in vacuum (b). Cylindrical particles on nitride membranes were also simulated to study the geometrical dependence of the interference. In the first set of simulations, two cylindrical particles (nanodics) with diameters of 50 nm and heights of 30 nm were placed on dielectric nitride membranes of different thicknesses. Similar to the TEM-based b) a) 89 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) 10 nm Si 3 N 4 71 nm Si 3 N 4 200 nm Si 3 N 4 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) symmetric asymmetric height Figure 3.21: (a) Simulated scattering spectra of two cylindrical nanoparticles with diameters of 50 nm and heights of 30 nm on substrate thicknesses of 10 nm (black), 71 nm (red) and 200 nm (blue). (b) Simulated scattering spectra of cylindrical nanoparticles with symmetric heights of 30 nm (black) and asymmetric heights of 30 / 15 nm (red). heterodimer, we find that the substrate thickness has a minimal impact on the wavelength at which the scattering interference occurs (~695 nm), as shown in Figure 3.21a, suggesting this interaction is highly localized to less than 10 nm below the metal- dielectric interface. The superradiant envelope of the nanodisc homodimer is observed to redshift with increased dielectric thickness. These simulations suggest that a homodimer with nm-separation can also strongly couple to higher order modes through interaction with the substrate. As shown in Figure 3.21b, when an asymmetry is added by reducing the height of one NP to 15 nm, both the superradiant and subradiant modes shift to different energies, with the dark mode now overlapping the higher energy side of the bright mode. The intensity of the scattering dip is much higher than those calculated for the TEM-based dimers and the rounded nanoblock heterodimers. This is attributable to the sharp corners of the cylinders where they meet the dielectric interface and the symmetry of the nanoparticle shape about the nanogap point. Figure 3.22 shows the gap a) b) 90 size dependence of similar cylindrical dimers where the corners are rounded with a radius of curvature of 2 nm. For h = 30 nm, we see the Fano interference for gap sizes of 2 and 4 nm, but the position and magnitude of the scattering dip are changed with respect to the previous dimer with sharp corners. The scattering dip is much less pronounced with rounded corners despite having the same separation between the two nanodiscs, because the concentration of the plasmon charges at the nanogap is slightly raised 1 – 2 nm above the substrate, and the effective gap size is slightly increased by the rounded corners. This changes both the intensity of the electric dipole near the substrate that cancels far-field radiation and the plasmon energies which shifts the subradiant frequency. For the asymmetric case with h = 15 nm, the Fano interference is almost entirely removed from the scattering spectra except for tiny separations, where the size asymmetry limits the mode mixing between the plasmon modes of different energy and the reduced influence of the substrate-mediated coupling. These simulations show that the substrate-mediated Fano interference is not limited to heterodimers like those fabricated and analyzed experimentally. However, as shown in Figure 3.23, the nm-separation is unable to couple the higher order modes of 50 nm gold spheres, due to the lack of substrate-mediated coupling. With the nm-separation occurring 25 nm above the substrate, the image charges mainly mirror the weak charge density at the bottom of the nanospheres and cannot mix the dipole-dipole mode with quadrupolar hybridized modes. While the angle evaporation technique used here necessarily produces asymmetry, this effect should also be observed in experimental work studying homodimers with nm-separations localized at the substrate surface. For 91 500 600 700 800 h = 15 nm 2 nm 4 nm 6 nm Simulated Scattering Intensity Wavelength (nm) 2 nm 4 nm 6 nm h = 30 nm 500 600 700 800 Wavelength (nm) Figure 3.22: Simulated scattering spectra of two rounded cylindrical nanoparticles with diameters of 50 nm with one particle having a height of 30 nm and the second particle having a height of 30 nm (left) and 15 nm (right) with gap sizes of 2 nm (black), 4 nm (red), and 6 nm (blue). 400 500 600 700 800 900 Simulated Scattering Intensity Wavelength (nm) 2 nm gap on nitride 8 nm gap on nitride 2 nm gap in vacuum 8 nm gap in vacuum Figure 3.23: Simulated scattering spectra of two 50 nm diameter spheres on 10 nm silicon nitride membrane (solid line) and in vacuum (dashed line) with gap sizes of 2 nm (black) and 8 nm (red). Inset shows charge distribution on spherical NPs. 92 instance, this effect could be present in bowtie nanoantennas that have been probed most recently by electron energy loss spectroscopy (EELS). [40] However, the energy resolution of 0.1 eV is about the same as the widths of the measured and simulated scattering dips produced here (0.12 – 0.2 eV), which could make previous electron-based observation of these interferences hard to detect. Optically, near-normal dark-field has only recently been employed in plasmonics. This near-normal incidence dark-field technique could easily be applied to structures such as these bowtie antennas on membranes which are already TEM-compatible, so that optical spectroscopy and EELS can be quantitatively compared and correlated with spatial geometry. 3.4.3 Comparison to previously observed Fano interferences Two of the common planar platforms exhibiting Fano interference are the dolmen (dimer/monomer) slab arrangement and the non-concentric ring/disc arrangement of nanoparticles [52, 145]. In the dolmen case, a homodimer (nanoparticle pair with identical geometry and material) is used to act as an effectively larger nanoparticle whose quadrupolar mode has an energetic overlap with that of the dipole mode of the third isolated nanoparticle. These planar structures bear a strong resemblance to our asymmetric heterodimers fabricated by the top-down angle evaporation technique. Fano resonances have also been observed and studied in heterodimers previously with bottom- up assembly techniques that link combinations of nanospheres and nanoshells of different size and shape and also round nanorods of different lengths [19, 150]. These structures also compare to our heterodimer as they consist of two physically distinct particles with large size asymmetry but differ in their spherical and rod shape. The dimers also have 93 their smallest nanogap as a single point node located many nanometers above the substrate, which decreases the influence of substrate-mediated coupling. In both the assembled and fabricated dimers, the Fano interference comes from the interaction of modes that yield dipole moments across the particles that cancel one another in the xy- plane of excitation (that of the transverse E and H fields in a z-propagating wave). Our simulations show that our heterodimers are unique in that dominant source of destructive interference comes from local dipole moments that cancel one another in the xz-plane. 3.5 Conclusion Our study is one of the first to analyze top-down lithographically-patterned heterodimers with nm-separations and includes fabrication, microscopy, and simulation to provide a complete understanding of observed effects and phenomena. For field enhancement applications, nm-separation between nanoparticles is extremely important for intensifying the local electric field. Such small separations induce very strong interparticle plasmon coupling that can lead to very pronounced and sensitive effects in the electromagnetic near- and far-field regions. We have found that these planar heterodimers interact strongly with both each other and the dielectric substrate, and that this interaction can mediate a Fano interference in the radiative scattering of such a dimer. The simulations show that the prominence of this interference is governed by the physical dimensions of the two nanoparticles, which determines the energy of the plasmon modes on the individual particles, and the amount of separation between the particles, which determines not only how strongly these modes couple to each other but also how strongly the substrate couples the interparticle or hybridized modes. 94 This research was supported by ONR Award No. N00014-12-1-0570 and NSF Award No. CBET-0854118. 95 CHAPTER 4: APPLICATIONS OF THE AFM CUTTING TECHNIQUE IN CARBON NANOTUBE STUDIES The second half of this chapter was done in collaboration with Dr. I-Kai Hsu. 4.1 Abstract In this chapter, we study the length dependence of vibronic and thermal transport properties in carbon nanotubes. The first study looks at the raw Raman scattering spectrum of an individual nanotube as it is subdivided into smaller segments looking for changes in phonon energy and scattering intensity. The second study uses the Raman scattering spectrum of a suspended carbon nanotube to determine the carbon nanotube temperature as the laser probe is also used for non-contact optical heating. The calibrated downshift of the G-band of the carbon nanotube spectrum is used to infer the temperature increase at different laser powers. We show that the temperature in the suspended portion of the carbon nanotube significantly increases as the portion of the nanotube in contact with the substrate is successively shortened. 4.2 Introduction Carbon nanotubes (CNTs) have been an exciting material since their discovery in 1991 [59]. These structures are generally considered as a rolled up sheet of two- dimensional graphene and feature varying electro-optical properties dependent on the orientation, or chirality, at which the carbon lattice is wrapped onto the tubule. The zone folding that occurs with the periodic boundary condition along one dimension of the two- dimensional graphene lattice results in different band structures for tubes of varying 96 chirality. Thus, carbon nanotubes can be either metallic or semiconducting depending on the geometry defined by their growth and nucleation. This unique “one-dimensional” system results in a quantized electronic structure and has physical properties that have merited well over 50,000 publications studying the electrical, thermal, and mechanical properties of CNTS. In particular, CNTs have been shown to have exceptionally high electron mobilities of 100,000 cm 2 /V·s, thermal conductivities as high as 6,600 W/m·K, and Young’s modulus values reaching up to 1.8 TPa both experimentally and theoretically [11, 41, 142]. These properties have made CNTs a promising material for nano-electronic, thermal management, and nano-mechanical applications. For thermal management applications, the theoretical limit of the thermal conductivity exceeds the bulk values of traditional metals, e.g. copper and aluminum, used in commercially produced heat sinks and spreaders. However, large variations in measured thermal conductivities exist in different CNT-based thermal management implementations, due to carbon nanotube quality, environmental factors, and the thermal contact resistance of carbon nanotubes. The unique pseudo one-dimensional geometry of a carbon nanotube not only results in a unique electronic band structure but also a unique phonon band structure. The combination of these geometrically-defined electron and phonon band structures results in unique vibronic properties that can be probed by optical spectroscopy. In particular, Raman spectroscopy provides unique scattering spectra where a limited number of vibrational modes can provide information about the nanotube radius and chirality and the electronic density of states greatly enhances the scattering cross-section of optical 97 transitions when photon energy is resonant with transitions between van Hove singularities defined by the “1 -D” structure. This makes Raman spectroscopy a powerful tool to characterize CNTs and examine the effects of electrical, optical, chemical, and mechanical probes and perturbations. In this chapter, we study the length dependent Raman scattering of individual and bundled single-walled CNTs (SWCNTs). The first study takes a fundamental look at the Raman scattering spectrum as a carbon nanotube is systematically divided into smaller segments. The second study focuses on the thermal heat dissipation of a suspended carbon nanotube bundle, using a non-contact laser heating technique and Raman spectroscopy to determine the temperature gradient as the CNT-substrate contact length is shortened. 4.3 Length dependence effects in Raman scattering 4.3.1 Experimental details For this work, it is important to hold constant as many nanotube and environmental parameters as possible while varying the length. Even two nanotubes of comparable length and identical chirality lying on the same sample may exhibit slightly different spectra due to substrate interactions or interactions with other nanotubes or molecules. Chirality is often determined by fitting measured band peaks of a single nanotube to known mean values and nanotube diameter from the radial breathing mode frequency for a particular spectroscopy system. This makes it difficult to ascribe specific differences to specific length variations with two different carbon nanotubes. Cutting a single nanotube into variably-sized segments allows the most independence from other 98 variables. A small cut is desired to keep about the same amount of Raman active nanotube length in the laser spot. Several options exist for segmenting the carbon nanotubes. One method involves the use of a focused low-energy electron beam of a scanning electron microscope (SEM) to selectively destroy small regions along the nanotube axis [153]. A second method is to use an atomic force microscope (AFM) or scanning tunneling microscope (STM) tip to mechanically break a nanotube with a force applied perpendicular to the axis. However, this method requires a rigid connection between the nanotube and substrate, which limits the reliability of smaller cuts and actual segment length due to physical displacement of the ends near a break. The chosen third method is essentially a combination of the two methods, where a voltage is applied to a conductive AFM tip to produce localized high field emission [58]. This flow of current between the sharp tip and sample provides the necessary energy to break the carbon-carbon bonds. One can cut by bringing a conductive voltage-carrying tip into contact with the substrate and translating the X and Y motor stages to drag the tip across the nanotube. This method is chosen as it gives clean, localized cuts with minimal contamination (e.g. amorphous carbon contamination from SEM). The AFM technique also allows for a quick turnaround between imaging, cutting, and collecting spectra. The technique used here developed from an original scanning probe microscopy field emission technique that used a scanning tunneling microscope (STM) in ultra high vacuum at room temperature [144]. However, STMs are limited by the need for conductive substrates and a vacuum environment, so AFM implementations followed, 99 where one could work outside of vacuum and on non-conductive substrates. The earliest AFM method developed from a single in-place indentation that could cut and nick carbon CNTs [112]. This progressed into a contact-mode AFM that mimicked the STM implementation using translation of the substrate and line cutting [65]. The last and more complicated AFM version uses noncontact/tapping-mode for imaging [58]. To enable field emission based cutting on atomic force microscope, some modifications of the standard image scanning process must be made. Atomic force microscopes in tapping mode operate by a proportional integral feedback control system, in which a cantilever beam with a sharp probe tip is oscillated near its resonant frequency, as shown in Figure 4.1a. This produces a freely oscillating amplitude that is typically probed through the displacement of a laser beam reflected off the back of the cantilever that is detected by a photodiode array. When this oscillating tip is brought into contact with a surface, a reduced displacement of the oscillation occurs as the tip bends against the surface, and the photodiode will measure reduced root-mean-square voltage amplitude. The force of tip on the surface, or equivalently, the displacement of the cantilever tip or photovoltage amplitude, can be held constant through the use of a feedback control system that uses a piezoelectric motor to vary the height or distance from the substrate to maintain a desired “set point ” of force or oscillation (or photovoltage). Typical set point values vary between 50% and 80% of the free amplitude of the tip vibration. By using piezeoelectric motors to control the X and Y position of the sample under the tip, an image can be made by raster scanning the substrate in the X and Y dimensions while operating in feedback mode at a given set point and reading out the Z 100 Figure 4.1: (a) Schematic diagram of tapping mode operation of atomic force microscope. Image taken from brukerafmprobes.com. (b) Illustration of the AFM probe technique used to cut carbon nanotubes through high field emission at the probe tip. Not to scale. (a) (b) CNT 101 Figure 4.2: AFM images of successful nanotube cutting. (a) Image of the height profile of cut carbon nanotube and substrate. Dashed line indicates cutting line. (b) Image of the amplitude data as a function of x and y, showing two successful cuts separated by 40 nm. height of the tip or sample as a function of time (or X and Y position). Other variables can also be monitored for image data, such as the tip amplitude or phase with respect to the driving force. The amplitude is in some sense the derivative of the height channel, detecting abrupt changes in the height profile of the sample, making it excellent for imaging low profile objects such as carbon nanotubes with single nanometer thicknesses. This standard operating process is modified for electrical cutting of carbon nanotubes. Feedback parameters are set so that the tip is brought into or nearly into contact with the substrate. A voltage between -10 and -12 V is applied to the tip as it is translated in a line across the substrate. The feedback parameters are reset once the tip finishes the movement and the raster scanning of imaging mode is restored. Successful cuts are shown in Figure 4.2. These methods were shown to cut beyond negative bias thresholds of (-6 to -8 V) that are dependent on tip velocity. Both single-walled and multi-walled CNTs can be cut using these methods, though reliability decreases with distance from deposited electrodes unless a more negative bias is applied. It is important (a) (b) 102 to use heavily doped or metal-coated silicon AFM probes for cutting to ensure a strong, localized field emission. A Digital Instruments MultiMode SPM operating in AFM Tapping Mode is used for both imaging and electrical cutting of the nanotubes. The SPM machine jumper settings and Extender module were set such that the electrical signal from Analog 2 was connected to the metal base clip supporting the AFM tip, which provides the cutting bias voltage. Several different types of AFM tips were used in these experiments: standard noncontact silicon cantilever tips (unknown manufacturer), standard tips with a conductive coating deposited by Cr/Au evaporation, magnetic force microscopy tips (unknown manufacturer), and Digital Instruments MESP (MFM) tips. All of the cutting operations were implemented using the Nanoscript feature of the MultiMode control software. The Nanoscript programming interface allows the use of a set of lithographic functions for translating the X and Y stages and driving various signals and parameters with user programmable values. The code in Appendix A shows the standard protocol used for cutting. The procedure above can be summarized as: disengage normal scanning, move the AFM tip to the center of the current scan window, initialize Analog 2 output pin to 0 volts, save the old set point, engage the lower set point to bring the tip into/near contact, ramp the Analog 2 signal from ground to the negative cutting voltage over 10 seconds (to avoid sudden increases in electrical field), translate across the sample with these settings, ramp down the voltage to ground over 10 seconds, and finally restore the imaging set point and scan mode. 103 Single walled CNTs synthesized by the arc discharge method are deposited from a sonicated dichloroethane solution onto a silicon substrate coated with a 1 μm layer of silicon dioxide [31]. A numbered grid made of Cr/Au is patterned on the substrate using electron beam lithography, allowing correlation of Raman spectroscopy with AFM. Several different substrates were used in the course of this work, and it was found that metal contacts and a properly grounded substrate were imperative for reliable cutting. The thick silicon oxide layer limits the grounding to the nanotube, so that CNTs without source or drain electrode contact could rarely be cut. A commercial Renishaw inVia micro-spectrometer was used to measure the scattering spectra of the carbon nanotubes. A 532 nm Spectra-Physics solid state laser is attenuated to a power of about 10 mW and focused through a 100X Leica objective lens with a numerical aperture of 0.9 to generate a ~0.5 μm diameter laser spot . A standard collection time of 60 s for extended and fixed grating scans is used. The Raman spectroscopy system is used to identify resonant nanotubes and record their position relative to the numbered fiducial grid , which is controlled by a PRIOR ProScan II high precision microscope stage with submicron resolution in the x, y and z directions. Once a resonant nanotube is detected, the sample is imaged by AFM to ensure that the CNT is sufficiently isolated from other nanotubes and random debris. The basic procedure after taking an initial Raman spectrum measurement is to make a bisecting cut along a nanotube, perpendicular to the nanotube axis, and then take another spectral measurement in the working area. We continue this bisection of each resulting CNT segment while monitoring for spectral changes. The cutting area was 104 extended in later measurements so that errors in laser positioning along the nanotube would not result in contributions from uncut CNT segments. Two types of measurements are taken after the cutting cycle: a broad spectral sweep from -600 to 3200 cm -1 to keep an eye on significant changes, and a narrower sweep from 1200 to 1700 cm -1 to monitor changes in the prominent D and G bands. 4.3.2 Results and discussion Figure 4.3 shows AFM images of the first nanotube, CNT #1, used for the length dependent CNT experiments. This nanotube is estimated to have a diameter of 1.1 nm from AFM height sections, suggesting it is indeed a single SWCNT. As mentioned above, this nanotube is selected by a Raman map scan using the 532 nm laser for excitation due to its resonance and high signal-to-noise in its scattering spectrum. This selection process does not inherently screen out off-resonance CNTs that may be only nanometers away or even bundled with the resonant CNTs, which fall within the Figure 4.3: AFM images of CNT #1. (a) Zoomed out 4 μm x 4 μm AFM image showing nanotubes with nearby numbered grid marker for locating CNT under AFM and optical microscope. (b) Zoomed in image of the boxed region in (a) taken after successive cuts. The lines and numbers indicate the position, orientation, and sequence of the cut. (a) (b) 1 2 2 3 3 105 illumination and collection area of the objective and might contribute small confounding signals. Due to the high density of deposited nanotubes we try to probe regions clear of multiple CNTs, but this was difficult given the limited availability of resonant CNTs. Figure 4.3b shows the approximate position and orientation of the sequence of linear cuts made along CNT #1 with the AFM probe. A first cut is initially made at the center of the CNT, labeled 1. Then two more cuts are made after Raman measurement at both 250 nm above and below the first cut, labeled 2. The remaining 250 nm segments of the CNT were bisected with two more cuts after Raman measurement, producing four ~125 nm long CNT segments of the same chirality with 5 cuts. Figure 4.4 shows the Raman spectra recorded before and after each cutting operation, showing both the D - band at around 1350 cm -1 and the G - and G + bands near 1584 and 1594 cm -1 . The D band shows no relative change in intensity which might be surprising since this peak is often used to characterize the crystalline quality or disorder of the nanotube. In graphene and CNTs, the D band involves scattering from a defect which breaks the symmetry of the two-dimensional sp 2 carbon lattice. However, the “damage” introduced by t his cutting technique is a highly localized breaking of the C-C bonds only at the ends of each nanotube segment, while the remaining length between these ends maintains its inherited disorder or lack thereof. We therefore might not expect much increase in the D band since the bulk of the nanotube maintains the same disorder. The G bands of CNT #1 show a downshift as the segment length is shortened, with the G - and G + peaks shifting to 1578.5 and 1586 cm -1 , respectively. 106 1300 1350 1550 1600 1650 1700 0 cuts 1 cut 3 cuts 3 cuts * 5 cuts Normalized Raman Intensity Raman Shift (cm -1 ) Figure 4.4: Raman scattering spectra before and after sequential cutting of CNT #1. Inset shows an optical microscope image of the numbered reference grid and focused laser spot. We must be careful to ascribe this behavior to the segmentation of CNT #1 and not to other problems inherent in the experimental analysis. The motorized scanning stage of the Raman spectrometer microscope has an accuracy of 0.250 μm (about half the size of the 0.5 μm beam diameter). Consistent positioning of this tightly focused Gaussian beam can cause significant changes in the measured scattering intensity. This is not a major issue for a sufficiently isolated CNT, where only a change in intensity occurs with the scattering peak shifts or energies unchanged, but positioning errors can also cause neighboring CNTs to receive a larger number of photons and increase their relative 107 contribution to the measured spectrum. However, since only a limited number of CNTs on the substrate are resonant with this laser wavelength, the probability is small that other CNTs in this focal spot are resonant. As demonstrated by the two spectra taken after 3 cuts, it is more likely that errors in position resulted in collection from the uncut portion of CNT #1. The first curve labeled “3 cuts” shows a similar spectrum to uncut original CNT. After repositioning the xy-stage, the spectrum labeled “3 cuts *” is recorded and follows the trend followed with 1 and 5 cuts. This also suggests that the spectra taken with 3+ cuts are the superposition of segmented and uncut CNT Raman scattering. Future length dependent Raman studies should accommodate for this issue. One solution is to increase the length of the nanotube that is subdivided. However, the AFM cutting technique was unreliable when segments were further cut. This is due to the loss of electrical ground through the contact electrodes. Future cutting studies could work on a more conductive substrate where electrical ground is not conditional to electrode contact. Figure 4.5: AFM images of CNT #2. (a) Zoomed out AFM image showing nanotubes with nearby grid markers for locating CNT under AFM and optical microscope. (b) Zoomed in 1 μm x 1 μm image of the boxed region in (a) taken after successive CNT cuts. Dashed lines indicate the position and orientation of cuts. (a) (b) 108 Figure 4.5 shows AFM images for CNT #2 on the same chip. The diameter of this nanotube was determined from the AFM height profile to be about 1.6 nm, indicating it is likely a single SWCNT and not a bundle of two nanotubes. This nanotube was initially cut into 250 nm long segments to accommodate potential misalignments of the motorized stage during spectroscopy. Cuts were extended above and below the AFM image of Figure 4.5b. However, CNT #2 had a surprising number of short and hidden nanotubes in the working area, as seen in the magnified AFM image. Slight repositioning of the laser spot showed dramatically different Raman scattering even before cutting, as shown in Figure 4.6a, with the second spectrum showing two G band peaks at 1584 and 1595 cm -1 . After cutting, multiple spectral measurements were taken again by slightly misaligning the focused laser spot to observe the variation in the scattering spectrum. The spectra all show the same Raman shift energies as the pre-cutting spectrum discussed above. However, the ratio of the intensities of the two G band peak intensities changes significantly. This suggests that there are two resonant carbon nanotubes in the working area, which is supported by the observation of several nanotubes in the AFM images above. Curiously, the other spectrum measured before cutting was not reproduced in any of the subsequent measurements after cutting. As shown in the extended Raman scan of Figure 4.6b, the before and after spectra also show moderately different G’ bands (the second harmonic of the D band which does not require defects or disorder to be observed), which likely indicate more than one resonant tube in the collection volume. No D band scattering was observed in any of the measurements taken for CNT #2, before and after cutting. 109 1600 1650 Raman Intensity (a.u.) Raman Shift (cm -1 ) no cuts no cuts 2 250 nm cuts 250 nm cuts 2 250 nm cuts 3 250 nm cuts 4 1550 1600 1650 2600 2700 2800 Raman Intensity (a.u.) Raman Shift (cm -1 ) no cuts 250 nm cuts Figure 4.6: Raman scattering spectra before and after cutting CNT #2 into 250 nm long segments. (a) Two spectra were taken before cutting and four spectra taken after cutting at slightly offset xy stage positions. Inset shows magnified region of three spectra taken after nanotube cutting. (b) Extended scan including the G’ Raman band. a) b) 110 The results for CNT #1 and CNT #2 were inconclusive due to several problems already elucidated. For both of these samples, subsequent attempts to further subdivide the CNT segments either failed or seriously damaged the carbon nanotube. Due to the high localized fields and charged tip, debris can be pulled into the working area and deposited on the cutting line. Large pieces of debris destroyed CNT #1 and prevented further study, although as discussed earlier, subdivision into smaller segments may have failed due to a suitable ground for electron flow and breaking bonds. It is worth discussing some potential size-dependent effects, such as the G band downshift with decreasing CNT length observed in CNT #1. As the Raman scattering process effectively probes the electron-phonon coupling in CNTs, the reduced CNT length may be altering the interaction of phonons and electrons. In high quality nanotubes, electron transport is ballistic with very low scattering, resulting in electron mean free paths due to acoustic phonon scattering of 1 μm or greater. CNT segments with sizes or 250 nm or smaller will likely not show significant changes due to the electron- phonon interaction but to the phonon properties themselves. The Raman shift measures the vibrational energy of these phonon bands, where the G + and G - peaks correspond to the axial and circumferential motion of the carbon atoms. A downshift indicates a weakening in the chemical bonds between the atoms in these directions. Residual or induced strain is known to shift the G band of CNTs, but this downshift occurs with increased strain. The cutting technique should release any such strain and produce an upshift after the first cut [25, 31]. We can expect size effects to increase the intensity of the D band scattering, since the cut ends of the nanotube will break symmetry as they 111 become a more substantial portion of the nanotube segment at very small lengths. Furthermore, confinement introduced by cutting will result in additional quantization of the wavevectors along the axis of the tube, in addition to the circumferential periodic boundary condition, making the nanotube more “0 -D.” This will effectively shift the subband energy levels of the valence and conduction bands and change the E ii optical transition energies, analogous to a quantum well structure. This could push the CNT off resonance with the 532 nm (2.33 eV) laser, or conversely, push the CNT more into resonance, which would decrease or increase the Raman scattering intensity, respectively. However, the positional errors and small focal volume make it difficult to analyze changes in intensity. At the smallest segment lengths investigated in this work (125 nm), such effects are assumed negligible. 4.4 Length-dependence of thermal contact resistance 4.4.1 Experimental details Single-walled carbon nanotubes are grown using chemical vapor deposition across 3 μm wide trenches etched in to a Si/SiO 2 substrate [18]. Suspended SWCNTs with substrate contact lengths of several microns are selected for this study through SEM imaging. A 532 nm Spectra-Physics solid state laser is focused through a 100X Leica objective lens with a numerical aperture of 0.9 to generate a ~0.5μm diameter laser spot, which serves as a localized heat source and the Raman probe. The position of laser spot is controlled by a PRIOR ProScan II high precision microscope stage with sub-micron resolution in the x, y and z directions. A Digital Instruments MultiMode SPM operating in AFM tapping mode is used for imaging, cutting, and measuring CNT diameters. AFM 112 cutting is performed by turning off the feedback loop of the AFM, applying a voltage of - 12V to the tip, and running a line scan across the nanotube perpendicular to its axis, as discussed in more detail earlier in this chapter. This allows us to iteratively trim the portion of the CNT that is in contact with the substrate. The temperature of the suspended carbon nanotube can be determined from the G band Raman mode. A linear relationship between the Raman peak scattering energy (Raman shift) and temperature is found as described in the next section, where the temperature coefficient of the G band downshift for the CNTs is measured in a Linkam THMSE 600 temperature-controlled stage. We measure G band Raman spectra with a 532 nm laser incident in the center of the suspended carbon nanotube before and after each cut so that the dependence of CNTs temperature on thermal contact lengths can be extracted from the G band downshifts. 4.4.2 Results and discussion The temperature-induced downshift of the G band vibrational frequency is mainly influenced by the lattice contraction and phonon-phonon scattering processes [4, 16, 27]. 1540 1560 1580 1600 1620 110 o C 155 o C 270 o C 250 o C 190 o C Raman Intensity (a.u.) Raman Shifts (cm -1 ) 50 o C 0 50 100 150 200 250 300 1581 1582 1583 1584 1585 1586 1587 1588 Temperature [ o C] G band Frequency (cm -1 ) Figure 4.7: (a) G band Raman spectra measured at different temperatures. (b) G band frequency as a function of temperature. a) b) 113 Although the thermally induced C-C bond contraction contributes an upward shift to the G band vibrational frequency, the overall G band frequency decreases due to a dominant anharmonic 4-phonon scattering process. Figure 4.7 shows calibration spectra of the G band taken in a temperature controlled sample chamber. The fits of these spectra display a linear temperature dependence with a slope of -0.0226 cm -1 /K, which is consistent with previous measurements in the literature [4, 27]. We now use this temperature coefficient to infer the local temperature of a carbon nanotube due to the laser induced heating from the vibrational energy of the G band scattering. Figure 4.8a shows an SEM image of a SWCNT suspended across a 3 μm wide trench, with a significantly long contact length on the right side of the trench and a negligible contact length on the left side of the trench. The diameter of this CNT was measured to be 1.9 nm from the AFM height profile. The right contact length is gradually reduced from 4.74 μm to 2.29 μm after a sequence of four AFM cuts. Figure 3.1b shows Figure 4.8: (a) SEM image of a carbon nanotube suspended across a 3 μm wide trench with a significant contact length on the right substrate. A dotted line was drawn over the CNT for clarity. (b) AFM image corresponding to the boxed region in (a) imaged after cutting. The white dotted lines mark the positions of the sequential AFM cuts. 1μm a) 500nm CNT b) 1st 2nd 3rd 4th 114 0 500 1000 1500 2000 2500 0 100 200 300 400 500 Raman G band Temperature after no cuts 1st cut 2nd cut 3rd cut 4th cut Temperature Increase (K) Laser Power ( W) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.2 0.4 0.6 0.8 1.0 x10 6 Temperature Increase / Laser Power (K/W) Contact Length ( m) Figure 4.9: (a) Temperature derived from the G band Raman downshift measured in the center of the suspended CNT in Figure 4.8a plotted as a function of the laser power before cutting and after each cut. Solid lines are linear fits to measured fits. (b) Rate of temperature increase per unit laser power as a function of the contact length. 115 the location of the AFM cuts along the length of the nanotube, as indicated by the white dotted lines. When moving the AFM tip across the CNT, other unintended manipulations like bending or nicking of carbon nanotubes can also occur. In such cases, we move slightly up the nanotube toward the trench and create a new cut so that the measurement is not influenced by these errors. Figure 4.9 shows a significant temperature change by decreasing the contact length on the right side. Raman spectra are measured with laser powers from 0.2 to 2.5 mW at to examine the downshifting behavior of the G band as the effective heating power is increased. This is done before cutting and after each cutting step. Figure 4.9a shows the temperature at the center of the suspended CNT as a function of the laser power, where the temperature increase is determined from the measured G band downshift relative to its low power peak position and the temperature coefficient calibrated in the temperature-controlled chamber. Each data set shows that the temperature depends linearly on the laser power, with a stronger dependence observed for shorter contact lengths. We can plot the rate of temperature increase with laser power (the slope of the data in Figure 4.9a) for the CNT before and after each cut as a function of the contact length, as shown in Figure 4.9b. The rate of temperature increase with laser power is about 6.5 times larger with a contact length of 2.29 μm than the original contact length of 4.74 μm. The trend of this contact length dependence shows that the temperature increase will get very high for even shorter contact lengths where the CNT-substrate interface acts as a bottleneck for heat flow out of the suspended CNT. We believe that the strong dependence on contact length in this nanotube is due to the extremely short contact length 116 Figure 4.10: (a) Measured temperature increase at the center of a suspended CNT plotted as a function of laser power taken at different contact lengths. (b) AFM image of the CNT on substrate to the right side of the trench. Dotted lines indicate positions of cuts. on the left side of the trench as seen Figure 4.8a. This short contact is a very poor heat sink, which makes the right contact the main channel for heat dissipation. Decreasing the length of this heat sink thus causes the CNT temperature to increase drastically with higher laser power. Figure 4.10 shows data for a second suspended nanotube after it was cut by AFM to reduce the contact length on the right side of the nanotube. Unlike the previous CNT, this nanotube shows no consistent change in the temperature at high heating powers even as the contact length is reduced to just 240 nm. We believe this is due to the left contact having a much smaller thermal resistance than the right side initially (before cutting) such that heat dissipation was dominated by the left contact. The thermal transport observed in this measurement can be described by the Fourier heat equation, R c cnt cnt L c cnt right left laser R x L r T R x r T Q Q Q , , ) (             , (4.1) 0 400 800 1200 1600 0 100 200 300 400 500 600 L contact = 3.02 m L contact = 2.37 m L contact =1.87 m L contact = 1.43 m L contact = 0.66 m L contact = 0.24 m Temperature [K] Laser Power [ W] (a) 117 where laser Q  is the heating power generated by the incident laser spot, left Q  and right Q  are the respective thermal power flows out of the left and right sides of the CNT, cnt r is the nanotube’s thermal resistance per unit length, R c,L and R c,R are the respective left and right thermal contact resistances at the sides of the trench, cnt L is the suspended length of the CNT, and x is the distance of the laser spot from the left edge of the trench. The two terms in the denominator represent the thermal resistances of the left and right segments of the nanotube including the left and right thermal contact resistances, respectively. The temperature increase in the CNT, T  , at a given heating power will be proportional to the sum of the thermal resistances of the suspended length of the CNT and the thermal contact resistances. We can fit the contact length dependent temperature versus laser power data with Equation 4.1 to determine both the thermal resistance of the CNT per unit length and the thermal contact resistance per unit length. Figure 4.11 shows a schematic diagram of the experiment and the equivalent thermal circuit described by the Fourier heat equation above. Once the heat propagates Figure 4.11: Schematic diagram of the experimental setup and an equivalent thermal circuit for the locally heated suspended CNT with substrate contacts. Cutting Direction Q  532nm laser ) ( x L r cnt cnt  R c R , L c R , x r cnt Right Q  Left Q  Carbon Nanotube AFM tip Cutting Direction Q  532nm laser ) ( x L r cnt cnt  R c R , L c R , x r cnt ) ( x L r cnt cnt  R c R , L c R , x r cnt Right Q  Left Q  Carbon Nanotube AFM tip 118 away from the localized heating source through the suspended CNT, heat is dissipated at the interface with the substrate on the left and right sides of the trench. The temperature of the substrate remains relatively the same due to its large size. The total heat transport along the CNT in the substrate region is equal to the total heat transfer across its thermal contact resistance into the substrate, given by c cnt contact r T x T dx x T d r l Q 0 2 2 ) ( ) (    , (4.2) where cnt r , c r , contact l , and 0 T are the thermal contact resistance of the CNT, the total thermal constriction resistance of unit axial length of the contact, the contact length, and the temperature at the end of the CNT, respectively. The total power flow into the CNT on the substrate can be solved by applying an adiabatic boundary condition at the end of the CNT in Equation 4.2:            contact c cnt c cnt contact l r r T r r l Q tanh max , (4.3) where max T  is the temperature difference between the edge of the CNT and the substrate [12]. The thermal contact resistance can then be solved by the relation             contact c cnt c cnt c l r r r r Q T R coth max [12, 152]. (4.4) cnt r depends on the thermal conductivity ( cnt k ) and the diameter (d cnt ) of the nanotube. The value c r is determined by constriction thermal resistance between the CNT and the substrate [7, 116, 152]. Figure 4.12 shows the thermal contact resistance c R calculated 119 0.01 0.1 1 10 0.01 0.1 1 10 100 1000  cnt = 2000 W/mK X10 9 l contact ( m) R c (K/W) r cnt /r c = 10 12 m -2 r cnt /r c = 10 13 m -2 r cnt /r c = 10 14 m -2 r cnt /r c = 10 15 m -2 X10 9 0.01 0.1 1 10 0.1 1 10 r cnt /r c =10 13 m -2 l contact ( m) R c (K/W)  cnt = 1000 W/mK  cnt = 2000 W/mK  cnt = 3000 W/mK  cnt = 4000 W/mK Figure 4.12: Thermal contact resistance of CNT on a substrate, calculated based on Equation 4.4, for (a) different ratios of thermal resistance and thermal coupling to substrate per unit length and (b) different thermal conductivities for the CNT. by Equation 4.4 with varying ratios of c cnt r r and different values of cnt  , based on a nanotube length of 3 μm and diameter of 1.8 nm. For all values of cnt  and c cnt r r , the thermal contact resistance decreases with contact length until a critical length beyond which contact resistance saturates at a minimum value. From Figures 4.12a and 4.12b, we observe that this minimum thermal contact increases with c cnt r r and decreases with cnt  , respectively. Using this Equation 4.4 for thermal resistance and Equation 4.1, we can express the change of temperature as a function of laser power with a laser positioned in the center of the nanotube as   1 , coth 1 1 ) (                 contact c cnt c cnt L c cnt laser contact l r r r r R x r Q l T  . (4.5) 120 The heat generated in the CNT by the incident laser power, laser Q  , is equal to the product of the applied laser power, laser P , and the photon absorption probability (  ). The rate of temperature increase with laser power ( laser dP dT / ) can then be written as a function of contact length. With the assumption of a much larger thermal contact resistance on the left side of the trench, and a relatively small thermal resistance for the suspended CNT compared to the contact resistances, laser contact Q l T  / ) (  is equal to the thermal contact resistance on the right side of the trench. This equation is fit to the experimental data shown in Figure 4.9b to determine the unknown quantities of cnt r , c r , and  , which were found to be 5.94 × 10 13 K/m·W, 49.9 m·K/W, and 2.21 × 10 13 , respectively. The quantity c r between a carbon nanowire and silicon nitride has been measured and estimated in previous works to be in the range of 1.15 – 5.15 m·K/W [116, 152]. The order of magnitude difference may be due to a larger constriction thermal resistance between the CNT and silicon oxide compared to that with silicon nitride and may also be due to the much smaller diameter of our CNT (1.8 nm) compared to the larger diameter carbon nanofibers (156 nm) studied in those works. 4.5 Conclusion We have shown that the combination of atomic force microscopy and Raman spectroscopy enables unique studies at the nanoscale. In addition to standard imaging and profilometry, AFM cutting lets us segment the length of a carbon nanotube into smaller pieces, which can alter the fundamental atomic vibrations, optical properties, and electron-phonon coupling. This technique has the advantage of only creating a highly 121 localized amount of damage and sequential studies of the same CNT, which minimizes dependencies on other environmental variables. The first study lays the foundation for further work where individual isolated CNTs can be segmented and studied through changes in relative intensity and frequency shifts observed in Raman scattering as segment length is reduced. The observation of a potential downshift in the G band of one CNT sample merits further investigation. In the second study, the thermal contact resistance of a suspended carbon nanotube is measured as a function of its contact length. We used the AFM cutting technique to shorten the CNT length in contact with the substrate to observe laser-induced temperature changes in the suspended portion of the nanotube. The thermal resistance of the CNT and thermal coupling to the substrate per unit length are estimated from the relative changes in temperature, determined by changes in the CNT’s Raman scattering. We calculate values for cnt r and c r of 5.94 × 10 13 K/m·W and 49.9 m·K/W, respectively. 122 CHAPTER 5: FUTURE DIRECTIONS 5.1 Hall measurement of GaAs nanowires 5.1.1 Introduction Semiconducting nanowires (NWs) have drawn a lot of attention due to their potential applications in solar cells [10, 30, 46, 49, 90] and light emitting diodes [48, 76]. Nanowires offer a unique capability to combine a wide range of semiconducting materials thanks to their ability to relax strain. The growth of a semiconducting NW on top of a bulk semiconducting substrate of another material accommodates lattice mismatch between the two crystalline materials, where the nanowire geometry allows for strain relaxation radially outward in the NWs after tens of nanometers [57]. Nanowires also allow for more efficient carrier collection, with core-shell and axial p-n junction geometries, and can enhance optical absorption through guided modes inherent in their individual nanostructure geometry or collective properties in photonic crystal-like arrays. The ability to control the fabrication and properties of NWs for such applications is crucial and requires the characterization of individual NWs. Either core-shell or axial p-n junction nanowires can be synthesized by controlling dopant flow rates and growth temperature. Selective area growth metal organic chemical vapor deposition (SAG MOCVD) has recently been used to eliminate the need for metal catalyzed growth [24, 85]. These methods allow for the growth of gallium arsenide (GaAs) NWs on top of silicon substrates, which could enable a tandem solar cell device. To this end, it is 123 important to characterize the dopant or free carrier concentration in these nanowires after growth which will determine their effectiveness in photovoltaics. GaAs suffers from pronounced effects associated with its surface states, which have prevented GaAs metal-oxide-semiconductor field-effect transistors (MOSFET) from becoming a viable technology. This problem is also reflected in GaAs's extremely high surface recombination velocity (10 6 cm/s), which is three orders of magnitude higher than most other III-V semiconductors [82, 101]. The surface depletion effect in GaAs is nanowires because of their high surface-to-volume ratios. In moderately doped nanowires, the depletion region forms a cylindrical shell over a cylindrical conducting channel in the middle of the nanowire. However, if the doping level is too low, the depletion region may fully extend into the conducting core, removing free carriers needed for transport in electrical applications. Figure 5.1 shows the free carrier density plotted as a function of the dopant concentration for several nanowire diameters, calculated by solving the Poisson equation with Fermi-Dirac statistics, where mid-gap pinning of surface Fermi level is assumed. For a 100 nm diameter nanowire, doping concentrations below 10 17 cm -3 yield completely depleted nanowires. Because of these surface states, dopant impurity concentrations above approximately 7 10 17 cm -3 are needed in order to generate a significant amount of free carriers in the nanostructure. As long as the nanowires are sufficiently doped, the depletion effect may be negligible. The Hall measurement described in this chapter is one method often used to probe the free carrier concentration, carrier mobility and majority carrier type of a material. 124 Figure 5.1: (left) Calculated free carrier density versus dopant impurity concentration for GaAs NWs with different diameters. (right) Illustration of depleted NW cross section. As shown in Figure 5.2a, the Hall effect arises when an electric field is applied to a material to pass a current through it, as a mutually orthogonal magnetic field is applied that acts to separate the positive and negative charges to opposite sides of the material, inducing a potential difference across its width, called the Hall voltage (V H ). While a simple technique for thin film samples, applying this method to NWs is quite a challenge Figure 5.2: Schematic representation of experimental measurement of the Hall voltage (V H ) in a (a) thin film sample and (b) a nanowire sample. Taken from ref [77]. 10 15 10 16 10 17 10 18 10 19 10 5 10 7 10 9 10 11 10 13 10 15 10 17 10 19 N D d=100nm d=200nm d=300nm d=400nm d=500nm Free Carrier Density (cm -3 ) Impurity Concentration (cm -3 ) Conducting channel Depletion region 125 due to the 1-D geometry and nanoscale size. The Hall probes have to be symmetrically fabricated on opposite sides of the nanowire without shorting, as shown in Figure 5.2b. Typical nanowires have diameters ranging from 500 nm down to even less than 100 nm. Specialized engineering techniques must be employed to place these electrodes with such accuracy. Furthermore, sufficient metal thicknesses or alterative lifting layers must be used to ensure the metal electrodes on top of the nanowire connect to the metal electrodes on substrate. An electron beam lithography (EBL) process was recently used by Storm et al. to successfully measure the Hall effect in a 300-400nm wide InP nanowire, with multiple Hall electrodes used to show a change in carrier concentration along the length of the NW [134]. This chapter explains a similar technique that will be used to characterize the free carriers in doped GaAs NWs with widths two or three times smaller than the previous report. 5.1.2 Synthesis and material issues Hexagonal GaAs nanowires are synthesized by metal organic chemical vapor deposition (MOCVD) with selective area growth (SAG) [28, 141]. Trimethylgallium (TMGa), trimethylaluminum (TMAl), and arsine are used as precursors for Ga, Al, and As deposition, respectively. High density arrays of GaAs nanowires are grown along the (111) direction on silicon substrates. A thermally grown silicon oxide layer is used as a mask for the SAG growth. A Raith e_LiNE electron beam lithography system is used to pattern a 1 mm 1 mm array of holes with 600 nm pitch. A short (20-30 second) buffered HF etch is performed to expose the crystalline silicon surface before loading the sample into the MOCVD reactor. The sample is first annealed in hydrogen at 920 C for 5 minutes 126 to remove the native oxide. Then arsine is flowed while the temperature is cooled from 850 C to 440 C. Nucleations of GaAs are grown at 440 C for 8 minutes with partial pressures of 3.74 10 -7 atm and 4.78x10 -5 atm for TMGa and arsine, respectively. After nucleation, the temperature is increased to 790 C for nanowire growth with the same partial pressures of TMGa and arsine. The growth rate is approximately 8.33 Å/s. Under these conditions, nanowires are grown with a very uniform cross-section along the NW length reaching up to 10 m long. For individual nanowire measurements, a patterned substrate of nanowires is immersed in isopropyl alcohol and sonicated for several minutes to release NWs into solution. Nanowires can then be drop-coated onto suitable substrates. Standard Ohmic contact to bulk n-type GaAs is obtained by evaporating multilayer gold-germanium/nickel/gold (AuGe/Ni/Au) metal contacts, followed by a rapid thermal annealing (RTA) process. However, we have observed that GaAs nanowires can be partially or completely dissolved into the electrodes at relatively high annealing temperatures (350 - 450 C) used in standard recipes. The eutectic point of germanium-gallium arsenide alloy occurs just in this range (356 C) and is similar to the gold-gallium arsenide eutectic temperature (350 – 400 C). The layer of nickel should prevent migration of the gallium arsenide into the large 2-D contacts, but our experience suggests that great care must be taken during the anneal to make good contact to these much smaller 1-D nanowires with electrodes of 100 – 500 nm width. The use of lower annealing temperatures results in non-linear, high resistance Schottky contacts. Higher quality contacts have been formed with p-type GaAs nanowires using depositions of Ti/Pt/Au or simpler Ti/Au [79]. 127 5.1.3 Fabrication details GaAs nanowires are first transferred onto a SiO 2 /Si substrate with lithographically-defined grid markers, which enable us to record the location of individual nanowires for further fabrication steps. We note that these nanowires have a hexagonal cross section, where the diameter of a polygon is defined as the largest distance between two vertices. For a hexagon, the diameter is simply twice the facet width. In order to measure the Hall effect in a single GaAs NW, four metal electrodes are lithographically patterned using EBL. Two electrodes act as the source and drain contacts to drive current along the NW. Another pair of electrodes is patterned on opposite sides of the nanowire, running perpendicular to the nanowire axis. Typical NW diameters used in this work range from 100 – 200 nm, which is a very limited space to pattern two electrodes across on opposite sides of the NW without shorting. This necessitates the use of automatic alignment procedures available in the Raith e_LiNE EBL tool and some patterning tricks due to thermal drift and charging effects inside the scanning electron microscope. High precision placement of the Hall electrodes requires two steps of electron beam lithography. The initial substrate is pre-patterned by photolithography with a numbered reference grid and large electrical contact pads made of titanium/gold (Ti/Au) with thicknesses of 20/100 nm. Optical or scanning electron microscopy is used to locate isolated NWs with respect to the reference grid. The sample is then spun with a bilayer of MMA-MAA and PMMA 950K electron beam resists producing an undercut profile for the lift-off process. The first step of EBL patterns fine alignment marks in a 10 μm square 128 centered on the NW. We operate at a high magnification compared to conventional EBL that gives better spatial resolution for beam scanning, where the electron beam can only scan a 10 μm area at 10,000× magnification. After metallization of the alignment marks, the nanowires are imaged by SEM to image each nanowire with respect to the four fine alignment marks around it. The positions of the final Hall electrodes can now be placed very precisely with respect to the fine alignment marks. The sample is then spun with a trilayer stack of resists, featuring two layers of MMA-MAA and one layer of PMMA 950K, each with a thickness of about 100 nm. This is done to elevate the masking layer well above the top of the nanowire (~100 – 200 nm high) to avoid fabrication issues when a trilayer stack of 50/15/50 nm thick AuGe/Ni/Au metal is evaporated for electrical contact. EBL tools unfortunately suffer from spatial drift due to thermal fluctuations and vibrations. In order to accurately position the metallic wires, an automated alignment process in the Raith tool is used to adjust the electron beam scanning for magnification, rotation, and translational shift based on line scan images taken of the four alignment marks patterned earlier. The four electrodes are then immediately and quickly written within the 10 μm write field surrounding the nanowire to minimize any errors due to drift. Following this quick write, a longer write can be made which writes the longer, thicker connections to the pre-patterned contact pads. More details regarding the EBL patterning process are provided in Appendix B. Before evaporation of the metal contacts, a short oxygen plasma (10 s at 60W) is performed to remove the resist residues. This also forms an oxide on NW surface that is removed using a solution of HCl:H 2 O (1:1). 129 Figure 5.3a and 5.3b show SEM images for two successfully aligned NW Hall devices. These nanowires have diameters of 205 and 120 nm, respectively, as determined from high mangificaiton SEM images. A high magnification SEM in Figure 5.3c shows the diameter and facet width of the NW in Figure 5.3a with a pair of Hall electrodes lying Figure 5.3: Images of successfully fabricated NW Hall devices. (a) and (b) SEM image of electrodes for Hall measurement patterned on 205 nm and 120 nm diameter NWs. Scale bars are 500 nm. (c) Higher magnification SEM image of one of the Hall electrode pairs with a 50 nm separation across the wire. (d) Schematic diagram of of the AuGe/Ni/Au metal electrodes evaporated on top of the nanowire. a) b) c) d) 205 nm 50 nm 115 nm 130 perpendicularly across it. These 100 nm wide electrodes have a separation of 50 nm across the diameter of the NW. Jagged edges formed at the source and drain electrodes are the result of a mismatch between a large step size (the spacing between exposure points by the EBL system) and the higher magnification used to write the electrodes, and simply accounted for by user error. The schematic diagram of Figure 5.3d shows an idealized model of the geometry of the trilayer (AuGe/Ni/Au) metal electrodes fabricated across the n-type NW for the Hall measurement. It is worth mentioning that very small spacing between these electrodes may become problematic for GaAs NWs, where RTA processing diffuses dopant atoms into the NW which may have diffusion lengths long enough to effectively short the two electrodes together. From several successfully alignments and fabrications, we estimate that the Raith EBL automatic alignment technique can reliably pattern electrodes to an accuracy of 10 - 20 nm using the high magnification and fine alignment mark geometry discussed in this section. 5.1.4 Preliminary results Successfully fabricated samples are wire-bonded into commercially available 28- pin PLCC chip carriers that can be mounted into chip sockets for electrical characterization. The initial I-V characterization of the nanowire devices was performed with a Keitheley Model 2400 Series SourceMeter controlled by an in-house LabView code. For the Hall measurement, electrical characterization is performed with an HP Agilent 4156c Precision Semiconductor Parameter Analyzer, where two ports serve as the current source I DS to the NW device, and the two other ports are programmed as a voltage monitor to measure V H across the Hall probes. The 4156c analyzer is used due to its ability to measure voltage with a resolution of 100 μV. The sample is mounted in a 131 chip carrier that is inserted into a large electromagnet unit capable of magnetic field strengths up to 1 Tesla. -20 -15 -10 -5 0 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 Resistance 90.3 GigaOhm 77.6 GigaOhm I DS (nA) V DS (V) After 1st RTA After 2nd RTA -10 -5 0 5 10 -0.2 -0.1 0.0 0.1 0.2 Resistance 72.0 GigaOhm 246 GigaOhm I DS (nA) V DS (V) grid2_3 grid2_4 Figure 5.4: High resistance I-V curves between source and drain contacts of NW devices. (a) I-V curve of n-type NW after two RTA processes. (b) I-V curve of two different p- type NW devices after one RTA process. a) b) 132 Plots of I DS vs V DS are shown in Figure 5.4a and 5.4b for n-type and p-type NWs, respectively, fabricated into Hall devices as described above. After fabrication, thermal annealing is generally performed to form an Ohmic contact between the metal electrodes and the GaAs material. For n-type devices, an RTA temperature of 360 C was held for 40 seconds for each cycle. However, we found very poor IV characteristics for our first and second batches of both n-type and p-type devices. As mentioned earlier, lack of care in RTA can actually destroy the NWs by pulling the GaAs material into the electrodes. However, NW integrity was verified by SEM imaging after processing. I-V characteristics on the order of 100 MΩ were found for all devices, and subsequent annealing steps were found to make limited improvement of the measured resistance. Such high resistances limit our ability to pump sufficient current through the NW for an appreciable Hall voltage. It is not clear if the Ohmic process recipe is working or if the doping level is too low for sufficient free carriers in the NWs. If the Ohmic contact is not achieved, this may also be limiting our ability to measure the Hall voltage with these contacts. While the GaAs NW Hall devices have yet to produce a measurable Hall voltage above the noise level, previous yet recent work at USC successfully produced an observable Hall voltage in a 2-D, n-type GaAs “nanosheet” that permitted the measurement of its charge carrier density [23]. Figure 5.5 shows an SEM of the two- dimensional sheet and relatively simpler device structure, along with a plot of the Hall voltage as a function of the source-drain current. We observe a measurable increase of V H at a fixed bias current as the magnetic field strength is increased from .08 to .90 T. We 133 0 5 10 15 20 0.0 0.4 0.8 1.2 V H (mV) I DS ( A) 0.90T 0.79T 0.68T 0.41T 0.18T 0.08T Figure 5.5: (left) Hall Voltage plotted as a function of bias current measured for a GaAs nanosheet at different magnetic field strengths. (right) SEM image shows the nanosheet Hall device. Scale bar is 2μm. can use the standard expression for the Hall voltage given by ned B I V DS H  . (5.1) where B is the magnetic field strength, n is the free charge density, e is the unit of electron charge, and d is the spacing between the electrodes measuring the voltage. Based on the geometry measured for the Hall device in SEM and the measured voltages as a function of current, we can solve Equation 5.1 for the free charge density and find an estimate of n = 9.26 × 10 17 cm -3 . This result was corroborated by photoluminescence spectra which estimated n at 1.2× 10 18 cm -3 . 5.1.5 Future work This chapter has built the foundation for a Hall measurement from GaAs NWs with diameters as small as 100 nm and potentially smaller NWs. The alignment and fabrication process described here was successful, but problems with either the GaAs 134 NW doping or Ohmic contact to these NWs prevented a measurable Hall voltage. We have seen that Hall measurements are possible on a larger GaAs nanosheet structure, which measured a charge carrier density of electrons on the order of 10 18 cm -3 . Once the doping or contact issues are solved, this fabrication process and measurement technique can easily be applied, with corrections to the Ohmic contact recipe if necessary, to characterize the carrier concentration in GaAs NWs for solar cell applications. It should be noted that this fabrication process and device measurement can easily be applied to other material systems where doping and contact problems are solved issues. 135 CHAPTER 6: CONCLUSION This dissertation has presented a collection of fabrication, experiment, and simulation in the research of plasmonic nanostructures, manipulated carbon nanotubes, and semiconducting nanowires. We demonstrated an angle evaporation technique that when combined with electron beam lithography can produce arrays of nanoparticles with nanogaps,or separations of about 1 nm. These nearly touching metal nanoparticles produce extremely high electric field intensities when illuminated with laser light, which we probed with Surface-Enhanced Raman Spectroscopy (SERS). We saw significant enhancement of the Raman scattering intensity when the incident laser was polarized along the two nanoparticles. Finite-difference time-domain simulations based on transmission electron microscopy images of our metal nanostructures predicts an electric field intensity enhancement of 82,400 in this nanogap, which could produce an electromagnetic SERS enhancement factor between 10 9 and 10 10 . In the second study, we showed evidence for a unique Fano interference resulting from the strong plasmonic coupling between two nanoparticles with a nanogap. Our study is one of the first to analyze lithographically-patterned asymmetric particle pairs with nm-separations and includes fabrication, microscopy, and simulation to provide a firm understanding for our experimental observations. We have found that these planar heterodimers interact strongly not only with each other but also the dielectric substrate, and that this interaction can mediate a Fano interference in the radiative scattering with 136 particles of the right geometry. We found that these particles are not only useful for high field enhancement applications like SERS but are even more interesting from a physics point of view and may be useful in other biosensing applications that utilize the sensitivity of a Fano resonance. We have also demonstrated that atomic force microscopy and Raman spectroscopy can enable unique studies at the nanoscale. We used a conventional multimode scanning probe microscope for the unconventional application of cutting carbon nanotubes through high electric field pulses. We used this technique to initially explore the fundamental physics of smaller nanotubes by looking for changes in their Raman scattering spectra. We saw evidence for a decrease in vibrational energy with decreasing nanotube length, which further work can seek to confirm. We also used the AFM cutting technique to shorten a carbon nanotube’s substrate contact length and observed laser-induced temperature changes in the suspended portion of the nanotube. We were able to estimate the thermal resistance and thermal coupling to the substrate per unit length of the nanotube from the relative changes in temperature, determined by changes in the nanotube’s vibronic scattering . This work determined values for cnt r and c r of 5.94 × 10 13 K/m·W and 49.9 m·K/W, respectively. The final project detailed in this dissertation demonstrated the ability to fabricate a Hall effect device with nanowires having diameters of only 100 nm. One can lithographically align and pattern electrodes with an accuracy of 10 – 20 nm with this electron beam lithography fabrication technique. 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Nordlander, "Quantum Description of the Plasmon Resonances of a Nanoparticle Dimer," Nano Letters, 9 (2), 887-891 (2009). 152 APPENDIX A: PERMITTIVITY FUNCTIONS USED IN COMPUTATIONAL SIMULATIONS Figure A.1: Lumerical polynomial fits of the dielectric function for gold used for simulation work presented in Chapter 3. 153 Figure A.2: Lumerical polynomial fits of the dielectric function of silver used for simulation work presented in Chapter 2. 154 APPENDIX B: REMOVAL OF AMORPHOUS CARBON DEPOSITED BY TEM IMAGING Transmission electron microscopy deposits a thin film of amorphous carbon whose thickness depends on the exposure time to the electron beam. This layer of carbon was found to quench or obscure the Fano interference in these nanoparticle dimers. An oxygen plasma treatment was used to remove this amorphous carbon, which then permitted the observation of the double-peaked interference scattering spectrum. Typical O 2 plasma exposures were performed at a power of 60 W in a pressure of 100 mTorr for a time of 6-12 s. Figure B.1 shows the scattering spectra from heterodimer A, presented in Figure 3.3, measured before and after plasma treatment. Care must be taken during the O 2 plasma treatment due to the effects of thermal annealing due to the poor thermal conductivity of silicon nitride, which can change the dimer geometry and gap size. 400 500 600 700 800 900 Scattering Intensity Wavelength (nm) parallel perpendicular 400 500 600 700 800 900 Scattering Intensity Wavelength (nm) parallel perpendicular Figure B.1: Measured dark-field scattering spectra taken before (left) and after (right) a single O2 plasma treatment of heterodimer A. 155 APPENDIX C: LUMERICAL FDTD SOLUTIONS SCRIPTS AND MATLAB CODES Current versions of Lumerical FDTD Solutions contain a script to calculate the 3- dimensional charge density by saving the E x , E y , and E z coordinates over a meshed volume and then calculating the 3D divergence of the electric field at each point. This code can be found in the software or at Lumerical’s website. The calculated divergence is then saved to a MATLAB m-file as a 3D or 4D array depending on whether a simulation was run at a single frequency or several different frequencies. The following Lumerical script saves the components of the electric field as well as the arrays of x, y, and z coordinates and the simulated frequency. charge=divE.divE; f=divE.f; lam=divE.wavelength; x=divE.x; y=divE.y; z=divE.z; matlabsave(“dimer1_charge”,dive,x,y,z,f,lam); The following MATLAB code plots a 3D representation of the surface charge density using a 3D volume rendering algorithm and adjustments to the alpha channel to reduce transparency of the lower charge density areas. % 3D array 'charge' of (x,y,z) format is loaded into MATLAB from % Lumerical load(dimer1_charge.m); % indexing from end:-1 flips the y dimension of the array for % desired visualization, indexing from 11:end is used to remove % substrate charge from visualization var=real(charge(:,end:-1:1,11:end)); 156 %% for 4D array of (x,y,z,freq) format, select single frequency %% to display only used in simulations with smaller grid sizes %% where multiple freq data can be collected in a one simulation % freqpt=15; % var(:,:,:)=real(charge(:,:,:,freqpt)); % var=var(:,:,11:end); % use vol3d to plot charge by texture mapping % view(3) to set 3d view and set background to white for colormap h=vol3d('CData',var); view(3); axis equal off; set(gcf,'color','w'); % set a jet colormap with 256 cm_n=256; colormap(jet(cm_n)); % alternative colormaps (red to white to blue) can be made by % editing existing colormap and saving to .m file and recalling % by the load command % read default min and max limits of the mapping to colormap climits=get(gca,'CLim'); % finds the closest value of the linearly spaced colormap to 0 % builds a correlated colormap which makes the charge density % close to 0 transparent and the charge density values near the % min and max more opaque % note: values can be adjusted by user for desired effect [m1,i1]=min(abs(linspace(climits(1),climits(2),cm_n))); alphamap([linspace(1,.05,i1-1) 0 linspace(.05,1,cm_n-i1)]); % adjust the caxis for better contrast caxis([-1e9 1e9]); % set the azimuth and elevation angles of the viewpoint view(130,36); % erase var for future plot routines with different sized arrays clear var; vol3d.m is an updated version of a code by Joe Conti written by Oliver Woodford and is freely available on the MATLAB Central File Exchange and other Internet sources. The absorption and scattering spectra for the dimers on substrate were simulated in Lumerical with the definition of a total field scattered field source (TFSF). The TFSF 157 source is defined by a rectangular solid of 6 faces, defining an incident plane wave source, but at the boundaries of this box, the incident field is subtracted at the boundaries so that the only fields outside the box are those scattered by the objects inside the TFSF region. The use of analysis groups monitoring the power flow through a rectangular solid box encapsulating each dimer is used to measure the absorption and scattered fields with respect to frequency. A power monitor group inside the TFSF source boundaries effectively gives the near field region surrounding the dimer and the absorption spectrum of the contents inside the source. A power monitor group outside the box gives the scattering spectrum in the far-field region of the dimer. The power monitor analysis group has been added in recent implementations of the Lumerical software package. For older implementations, the following code is used to calculate the electromagnetic absorption spectrum, normalized by the frequency dependent power spectrum of the TSFS source. %normalize simulation data by injected source power cwnorm; frq = getdata("top","f"); pa = -transmission("top"); ps = transmission("bottom"); pr = -transmission("right"); pl = transmission("left"); pf = transmission("front"); pb = -transmission("back"); %sum the power flowing out of the faces of the box and %multiply by source power. Dividing this by source %intensity gives the absorption cross section pabs = (pa + ps + pr + pl + pf + pb) * sourcepower(frq); sigma = pabs / sourceintensity(frq); plot(2.9979e8 / frq,sigma); lam = 2.9979e8 / frq; %save data for import to MATLAB matlabsave("dimer1_abs",sigma,lam); 158 The far-field scattering spectrum is calculated with a similar script. cwnorm; frq = getdata("sfront","f"); pa = transmission("stop"); ps = -transmission("sbottom"); pr = transmission("sright"); pl = -transmission("sleft"); pf = -transmission("sfront"); pb = transmission("sback"); pscatt = (pa + ps + pr + pl + pf + pb) * sourcepower(frq); sigma = pscatt / sourceintensity(frq); plot(2.9979e8 / frq,sigma); lam=2.9979e8 / frq; matlabsave("dimer1_scatt",sigma,lam);. 159 APPENDIX D: AFM CUTTING CODE The code below is an example of that used as the standard operating procedure for cutting carbon nanotubes using the Digital Instruments MultiMode scanning probe microscope operating in AFM Tapping Mode using the Nanoscript programming interface provided with the default software. The Extender module must be used with the system in order to apply voltages between tip and substrate through the Analog 2 port. #include <litho.h> void main() { LITHO_BEGIN LithoDisplayStatusBox(); // display litho status box LithoScan(FALSE); // turn off scanning LithoCenterXY(); // move tip to center of field LithoPause(1.0); double setpoint; double xdisp = -0.200; // length of cut in x direction double ydisp = 0.0; // length of cut in y direction double rate = .1; // rate of speed double depth = -0.3; // push the tip in 20 nm to draw lines double z_rate = 0.060; // move the tip down at 40 nm/s double cutVolt = -12.0; // cutting voltage on tip double lowSetPoint = .001; // low setpoint for cutting LithoPause(1.0); LithoSet(lsAna2, 0.0); // set Ana2 to 0V setpoint=LithoGet(lsSetpoint); // store old setpoint LithoSet(lsSetpoint,lowSetPoint); // setpoint to low value LithoPause(1.0); // pause for 1 second LithoRamp (lsAna2, 0.0, cutVolt, 10.0); // slowly ramp Ana2 // to –V 160 LithoPause(1.0); // pause for 1 second LithoTranslate(xdisp, ydisp, rate); // translate for cut LithoRamp(lsAna2, cutVolt, 0.0, 10.0); // ramp down to 0V LithoSet(lsSetpoint,setpoint); // restore old setpoint LITHO_END // return control to scanner } 161 APPENDIX E: EBL FABRICATION PROCESS FOR HALL EFFECT DEVICES The first step of EBL is used to pattern a set of finer alignment marks surrounding each selected nanowire (a cross of two intersecting lines of 1 μm length and 100 nm width). Standard EBL patterning uses relatively low magnification for typical writing (1000× provides a write field size of 100 μm that can be accurately scanned by the magnetic lenses of the SEM), but higher magnification offers slightly better resolution and more accurate spatial scanning at the cost of writing time. We make use of this spatial accuracy by working at a higher magnification of 10000× with a write field size of 10 μm. We position four of these fine alignment marks just inside the four corners of the 10 μm square defined by this field size . These four alignment marks are added to an AutoCAD file containing the layout of the photolithographic mask used to pattern the contact pads and optical reference marks. To position these alignment marks on the nanowire, an optical microscope image taken at 20, 50, or 100× magnification is overlayed into the AutoCAD file with the attach command and aligned to the large optical reference marks. SEM images can also be used, but since the fine alignment marks take over electrode alignment after this step, a few microns of error can be tolerated by simply using optical images. The new CAD pattern is converted to a GDSII file and imported into the Raith e_LiNE pattern writer software. (A special note to users using this same technique is that all references to optical/SEM images imported into AutoCAD must be deleted and their references removed in the file before conversion and 162 import into the e_LiNE software. This can be done by typing xref and then unloading and detaching all of the external image references.) Operating at high magnification, one must be careful in the step size by which the exposure is subdivided. Standard writing step sizes range from 50 to 200 nm at 1000×, but a step size of 5 - 10 nm is used at 10,000×. Following the first metallization, the nanowire sample must be SEM’ed with a new image containing the additional four alignment marks. This image can then be overlayed into AutoCAD like the previous step, but now the SEM overlay is made with respect to the four fine alignment marks around each nanowire and not the large numbered grid. The electrode pattern is broken into two layers: one for the smallest electrodes that actually make contact to the nanowire, and another set of larger electrodes that will make the connection between these small electrodes and the larger contact pads. All of the small electrodes should fall within a square of the 10 x 10 μm write field surrounding the nanowire, demarcated by the four fine alignment marks at the corners. An explanation for this separation is given later. Once the second pattern with electrodes is imported into the e_LiNE software, the user must add additional layers: manual mark scans and auto mark scans. If a small number of samples are to be written or less accuracy is needed, manual mark scans should be sufficient. A manual mark scan is essentially a way in CAD to tell the machine to take an SEM raster scan of the rectangular area it outlines in layer 63 of the software. The user may then expose layer 63 to take an SEM image and denote the desired center point of the fine alignment mark after correction. This is akin to using the mouse in manual write field alignment with contamination dots or small particles, to tell the system 163 Figure E.1: Screenshots from AutoCAD showing (a) the pattern design of the four alignment marks separated by 9 μm to fit inside the 10,000× write field and (b) the overlay of an SEM image after metallization and lift-off of the four alignment marks. All subsequent electrode alignment is done with these small alignment marks. where the desired center of the image should be, but the correction is applied with respect to an existing pattern instead of movements introduced by the laser-controlled stage. In this way, it can correct for small errors in scaling, rotation, and shift introduced by the a) b) 164 user/system in the first lithography or in misalignment of the 3-point alignment in the current lithography. We create four squares (1.5 x 1.5 μm) of layer 63 that are centered on each of the cross marks. (Note to users: this is added through the menu bar, Add -> Manual Mark Scan, in the software and not actually drawing rectangles in layer 63). This layer can then be exposed in sequence with other layers, where preference is given to alignment layers in each stitch field of the pattern. It must be noted that at least 3 marks must exist in a stitch field for the corrections made by this technique to be applied. Furthermore, if a working area of the pattern is used where the first stitch field does not contain any alignment layers, they will not be executed until the pattern writer moves to the stitch field containing them. So corrections will not be made on the first portion of the pattern until these alignments are executed, and then applied to all subsequent stitch fields. As mentioned above, another alignment can be done by automatic mark scans. The basic purpose and result of this function is the same, but determination of the image center is made by line scans with the electron beam, and the center is found by a threshold algorithm in the software with the 1-D lines of SEM contrast data. In this manner, two automatic mark scans of layer 61 must be placed on the arms the cross- shaped alignment marks, one to correct for the x-direction and one to correct for the y- direction. Figure E.2 clarifies this implementation. The properties of manual and automatic mark scans can be adjusted to increase averaging or size of scan area if image quality is poor or alignments are quite off. These can be exposed just like the manual mark scans without user intervention. However, the user should ensure the first automatic 165 line scan produces a successful execution (i.e., a single peaked line scan is produced like that shown in Figure E.2c. Figure E.2: Manual and automatic alignment process with Raith patterns. (a) Illustration of the two layers with (brown) manual mark scan and (green) automatic mark scan layers. (b) SEM image taken with manual mark scan. Small crosshair at center represents actual center of the SEM image while large crosshair represents user selected desired center. (c) Screenshot of one “exposure” of an automatic mark scan. Thresholding algorithm with settings at right determines the x or y center from one arm of the cross. a) b) c) 166 Figure E.3: (a) AutoCAD screenshot showing the patterning of thin Hall probe electrodes and larger wires connecting the electrodes to the contact pads. (b) SEM image showing the device after fabrication. a) b) 167 Figure E.3b shows an SEM of a completed device, the same shown in Figure 5.3b. As mentioned, it is important to separate the electrodes into two separate layers. This is because thermal drifts and substrate charging can cause shifts in the sample or electron beam scanning. So it is important to write the small electrodes immediately after running the manual or automatic mark scans to avoid any accumulation of drift since the scan completed. Then, in a separate exposure, the larger electrodes can be written, where an overlap is made between the two layers to accommodate small shifts since the first exposure. Due to a large step size in the second exposure for the large wires, a staircase effect can be seen in the bottom electrode.

Abstract (if available)

Abstract This dissertation presents several studies that look at the unique properties and applications of metals and semiconductors when the dimensions of these materials are confined to the nanoscale. ❧ Chapter 1 provides background material that will aid in understanding the research presented in this dissertation. It begins with an introduction to plasmonics and an analytical derivation of the electromagnetic resonance conditions that have made this field so popular in the last 10-15 years. Particular interest is given to localized surface plasmon resonances that occur when light is incident on metallic nanoparticles, and how these plasmon resonances interact with one another. The second half of the introductory chapter turns to a slightly older but still exciting material, the carbon nanotube, whose electronic and optical properties vary significantly due to a slight change in crystal orientation. We discuss both of these topics in the context of Raman spectroscopy, where plasmons can be used to enhance the scattering process and Raman can be used to give detailed information about the structure of nanotubes. ❧ Chapter 2 presents the first plasmonics research project, where we demonstrate an angle evaporation method for fabricating arrays of metal nanoparticle pairs with separations on the order of a single nanometer. We image the small separations between particles, which we often refer to as ""nanogaps,"" using high resolution transmission electron microscopy (TEM). Then, we use Raman spectroscopy to characterize the high electric field enhancements produced when the particles are illuminated with a visible wavelength laser. We find a very strong polarization dependence of the Raman intensity. We use numerical simulations to confirm both the high electric field enhancements and the observed polarization dependence for a particular nanoparticle geometry imaged by TEM, suggesting these particles might provide exceptionally high field enhancements and Raman scattering intensities. ❧ Chapter 3 investigates these nm-separated nanoparticle pairs further. The previous Raman study uses a very narrow wavelength probe to characterize metallic nanostructures with a much broader spectral response. This study builds on the previous work by characterizing the spectral scattering from these ""nanogap"" structures in the visible and near-IR part of the spectrum, where we built a specialized near-normal incidence dark-field microscopy system to measure particle scattering on TEM-compatible membranes. We find that nanoparticles with these nm-separations tend to exhibit significant dips in their far-field scattering spectra. We further investigate this phenomenon by numerical simulation and find that these dips are a Fano interference that results from strong coupling to higher-order plasmon resonances. This Fano interference is unique compared to other reports in the last four years, where opposing charge distributions at the top and bottom of the nanogap destructively interfere in far-field scattering. We show that the enhanced interparticle coupling is not only due to the small separation between the particles but also due to an enhanced interaction with image charges induced in the underlying substrate. ❧ In Chapter 4, we study the length dependence of vibronic and thermal transport properties in carbon nanotubes. The atomic force microscope, a common characterization tool in nanotechnology, is adapted to locally cut through a nanotube's carbon-carbon bonds. The first study looks for changes in phonon energy and Raman scattering intensity as an individual nanotube is divided into smaller pieces. The second study uses Raman scattering from a suspended carbon nanotube to measure the temperature as a laser probe provides localized heating. The temperature in the suspended section of the carbon nanotube drastically increases as we create a bottleneck for heat flow at the nanotube-substrate contact. ❧ Chapter 5 details the fabrication process and experimental setup needed for a Hall effect measurement that will be used to characterize the charge carrier density in doped gallium arsenide nanowires. With the described fabrication techniques, metal electrodes can be positioned with an accuracy of ten nanometers across the 100 nm diameter of an individual nanowire. The initial measurements on nanowire samples were plagued by material doping and Ohmic contact issues, but we show a successful Hall measurement with a 2-D nanostructure of similar gallium arsenide material. This technique may be easily extended to other semiconductor materials and nanostructure geometries.

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Asset Metadata

Creator Theiss, Jesse Robert (author)

Core Title Design and characterization of metal and semiconducting nanostructures and nanodevices

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 09/13/2013

Defense Date 08/02/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag atomic force microscope,carbon nanotube,electromagnetics,Fano interference,Hall effect,nanoparticle,nanotechnology,nanowire,OAI-PMH Harvest,plasmonics,SERS

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Cronin, Stephen B. (committee chair), Benderskii, Alexander V. (committee member), Povinelli, Michelle L. (committee member)

Creator Email jesse.theiss@gmail.com,jtheiss@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-328695

Unique identifier UC11293581

Identifier etd-TheissJess-2037.pdf (filename),usctheses-c3-328695 (legacy record id)

Legacy Identifier etd-TheissJess-2037.pdf

Dmrecord 328695

Document Type Dissertation

Format application/pdf (imt)

Rights Theiss, Jesse Robert

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA