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Optoelectronic properties and device physics of individual suspended carbon nanotubes

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Optoelectronic properties and device physics of individual suspended carbon nanotubes

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Content OPTOELECTRONIC PROPERTIES AND DEVICE PHYSICS OF INDIVIDUAL SUSPENDED CARBON NANOTUBES by Shun-Wen Chang 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 (PHYSICS) May 2015 Copyright 2015 Shun-Wen Chang 1 Dedication This thesis is dedicated to my parents for their constant support. 2 Acknowledgements I would like to thank my research advisor, Dr. Stephen B. Cronin. Thank him for the constant support and understanding of my personality. Thanks to all my lab mates, Chia-Chi Chang, Mehmet Aykol, Jesse Theiss, Rohan Dhall, Prathamesh Pavaskar, Zhen Li, Wenbo Hou, I-Kai Hsu, Chun-Chung Chen, Adam Bushmaker, Jing Qiu, Guan-Tong Zheng, Bingya Hou, Jihan Chen, Shermin Arab, Moh Amer, and Nirakar Poudel for the valuable discussion and ideas. Thanks to Haitian Chen, Bilu Liu, and Jia Liu from Dr. Zhou’s group for their kind help on CNT device fabrication. I would like to thank the professors and staffs in physics and EE-electrophysics departments, Betty, Lisa, Shanna, and Kim. Thanks to our academic advisors, Dr. Stephan Haas and Dr. Robin Shakshaft. Thanks to Dr. Tony Levi. I learnt a lot of experimental techniques in optics in his lab. Thanks to Blake Mason, Kevin Bergemann, Dr. Stephen Forrest, Dr. Sato Kentaro, and Dr. Saito Riichiro for extending yourselves in collaboration with us. 3 Table of Contents Dedication .............................................................................................................................. 1 Acknowledgements ................................................................................................................ 2 List of Tables ......................................................................................................................... 5 List of Figures ........................................................................................................................ 6 Abstract ................................................................................................................................ 11 Chapter 1: Background ........................................................................................................ 12 1.1 Carbon Nanotube Physics ......................................................................................... 12 1.2 Raman Scattering in Carbon Nanotubes ................................................................... 18 1.3 Excitonic Effects in Carbon Nanotubes .................................................................... 21 1.4 Carbon Nanotube p-n Junctions ................................................................................ 23 1.5 Photoluminescence and Electroluminescence in Carbon Nanotubes ........................ 26 Chapter 2: Pronounced Electron-phonon Interactions in Suspended Metallic Carbon Nanotubes ................................................................................................................. 28 2.1 Introduction ............................................................................................................... 28 2.2 Experimental Details ................................................................................................. 29 2.3 Results and Discussion .............................................................................................. 31 2.4 Conclusion ................................................................................................................. 41 Chapter 3: Evidence for Structural Phase Transitions and Large Effective Band Gaps in Suspended Metallic Carbon Nanotubes ............................................................... 42 3.1 Introduction ............................................................................................................... 43 3.2 Experimental Details ................................................................................................. 44 3.3 Results and Discussion .............................................................................................. 45 3.4 Conclusion ................................................................................................................. 55 Chapter 4: Non-Ideal Diode Behavior and Band Gap Renormalization in Carbon Nanotube p-n Junctions ............................................................................................ 56 4.1 Introduction ............................................................................................................... 56 4.2 Experimental Details ................................................................................................. 58 4.3 Results and Discussion .............................................................................................. 60 4.4 Conclusion ................................................................................................................. 72 Chapter 5: Photocurrent Spectroscopy of Exciton and Free Particle Optical Transitions in Suspended Carbon Nanotube pn- Junctions ..................................... 73 5.1 Introduction ............................................................................................................... 74 4 5.2 Experimental Details ................................................................................................. 76 5.3 Results and Discussion .............................................................................................. 79 5.4 Conclusion ................................................................................................................. 84 Chapter 6: Thermoacoustic Transduction in Individual Suspended Carbon Nanotubes ................................................................................................................. 86 6.1 Introduction ............................................................................................................... 86 6.2 Experimental Details ................................................................................................. 88 6.3 Results and Discussion .............................................................................................. 92 6.4 Conclusion ................................................................................................................. 98 Bibliography ....................................................................................................................... 100 Appendices ......................................................................................................................... 109 5 List of Tables Table 4.1 - Open circuit voltage (VOC), short circuit current (ISC) observed under illumination with a 532 nm wavelength laser, and fitting parameters for the dark I-V characteristics taken at various split-gate voltages. Vg1/Vg2 are the gate voltages; 1 refers to the Schottky diode and 2 refers to the P-N diode; I01 and I02 are the reverse saturation currents from diode 1 and diode 2, respectively; RP1 and RP2 are the parallel shunt resistances from diode 1 and diode 2, respectively. ............................................................................................... 66 6 List of Figures Figure 1.1 – (a) Real space and (b) reciprocal lattices of graphene[2]. ................................ 14 Figure 1.2 – (a) Wrapping vectors and allowed k-states for three different chiralities CNTs[1]. The degeneracy at the K point is allowed only for (3,0) and (3,3) CNTs, which are quasi-metallic. The (4,2) CNT contains no degeneracy, therefore having a band gap. (b) Kataura plot. ......................................................... 17 Figure 1.3 – Typical Raman spectrum of CNTs (a) and corresponding vibrational modes(b)[4]. ............................................................................................................. 19 Figure 1.4 – Two photon absorption-emission energy diagram and spectral data plot from Wang et al. ...................................................................................................... 22 Figure 1.5 – (a) CNT p-n junction diodes device structure in this thesis. (b) Typical CNT p-n junction current vs. voltage characteristics fitted to the idea diode equation (red line). The subscript DS means “source to drain.” .............................. 23 Figure 1.6 – The energy band diagram of a p-n junction at zero bias voltage. The absorbed photons excite electron-hole pairs and the built-in potential separates the electrons and holes and creates current flowing through the device. ...................................................................................................................... 25 Figure 1.7 – Photoluminescence image (a) and spectrum (b) of a suspended 100μm- long CNT from Lefebvre et al[3]. ............................................................................ 26 Figure 1.8 – EL spectra from CNT p-n photodiodes with +8V/-8V gate voltages. The FWHM is 50 meV[5]. .............................................................................................. 27 Figure 2.1 – (a) Schematic diagram of a CNT field-effect transistor (FET) device with source/drain electrodes made from Pt/W. (b) Scanning electron microscopy (SEM) image of a CNT FET device, the red line indicating where CNTs usually grow. ................................................................................................. 30 Figure 2.2 – (a) Current-voltage characteristics of a typical CNT device. The negative differential conductance (NDC) indicates that the CNT is suspended. (b) Conductance-gate voltage characteristics of a metallic CNT device. ...................... 31 Figure 2.3 – (a) Raman G band at Vg=0V and Vg=-8V from device A, showing both intensity and frequency changes with gate voltage. (b) G band Raman shift as a function of applied gate voltage from the same device, showing the signature W shape profile. ....................................................................................... 32 7 Figure 2.4 – Room temperature gate voltage dependence of the G- band Raman shift and intensity for (a) device B, showing the signature W shape profile indicating breakdown of the Born-Oppenheimer approximation(Regime 1) and (b) device C, showing no evidence of non-adiabatic behavior (Regime 2). ............................................................................................................................. 34 Figure 2.5 – Gate voltage dependence of the G band Raman shift and G band Raman intensity for device D at (a) T= 300K, consistent with Regime 2, and (b) at T=4.2K, consistent with Regime 1. .......................................................................... 35 Figure 2.6 – Correlation between the ratio of gated and ungated G band Raman intensities for various devices plotted as a function of the maximum gate- induced downshift of the G band Raman frequency due to the non-adiabatic Kohn anomaly. Each point on this plot corresponds to a different nanotube sample. ..................................................................................................................... 37 Figure 2.7 - Relative Raman shift of the G- band with respect to Vg=0 for (a) device E and (b) device A taken at various temperatures.................................................... 38 Figure 2.8 - The real part of Π(𝜔 , 𝐸𝐹 ) from Equation 1 at T=300K and T=150K, with (a) no band gap in the electron band structure and (b) a band gap of 160meV. .................................................................................................................................. 40 Figure 3.1 – Typical Raman 2D band of a metallic CNT with 633nm excitation. .............. 45 Figure 3.2 – (a) Gate voltage dependence of the 2D band Raman shift and (b) conductance-gate voltage curve for a suspended metallic CNT taken at room temperature. .............................................................................................................. 46 Figure 3.3 – (a) Gate voltage dependence of the 2D band Raman shift and (b) conductance-gate voltage curve for a suspended metallic CNT taken at room temperature. .............................................................................................................. 48 Figure 3.4 – Experimentally measured (a) G and (c) 2D Raman modes taken from the same nanotube at room temperature. Non-adiabatic calculations of the gate dependence of the (b) G and (d) 2D bands. ...................................................... 51 Figure 3.5 – (a,b) 2D band Raman integrated area intensities and (c,d) Raman shifts for two different quasi-metallic devices (Device A and B). .................................... 53 Figure 4.1 – (a) Schematic diagram of a split-gate CNT FET device. Dual gates are separated by 2μm and CNTs are 4μm long. (b) Colorized SEM image of a split-gate CNT device. Red line indicates where CNT grows across the catalyst islands. ........................................................................................................ 59 8 Figure 4.2 – (a) Typical current-voltage (I-V) characteristics of the CNT device, with Vg1 = -9 V and Vg2 = +9 V, exhibiting rectifying behavior. (b) The log plot of the same data. (c) Device conductance plotted as a function of gate voltage with Vg1= Vg2 and Vbias=0.2V in air at T=300K, showing ambipolar behavior. (d) Spatial scan of the short circuit current taken under focused illumination along the length of the CNT device, fitted to a Gaussian curve. ............................. 60 Figure 4.3 - (a) Short circuit photocurrent and (b) open circuit photovoltage plotted as functions of the gate voltages Vg1 and Vg2, taken under ambient conditions at T=300K for device D1. Values in the color bars are given in units of (a) amps, and (b) volts. .................................................................................................. 61 Figure 4.4 - (a) Typical I-V characteristic of an electrostatically doped P-N junction CNT showing non-ideal behavior at high currents corresponding to VDS > 0.2V. (b) Equilibrium diode band diagram where the gate voltages are Vg1 > 0V and Vg2 < 0V, and device equivalent circuit represented by two diodes in opposite directions. Here, EF is the Fermi energy and RP1 and RP2 are the shunt resistances of the Schottky and P-N junctions, respectively. ......................... 63 Figure 4.5 - I-V characteristics and fitting results of device D1 at various gate voltages Vg1, Vg2. The first row (a-b) shows I-V characteristics under uniformly N-doped and P-doped conditions, the second row (c-e) shows I-V characteristics in the P-N configuration, and the last row (f-h) shows I-V taken in the N-P configuration. The black dots are data points and red lines are fits. ...................................................................................................................... 65 Figure 4.6 - Dependence of (a) the reverse saturation currents (Vg1= -Vg2) and (b) the parallel resistance on doping for device D2. Error bars were extracted from the data of device D1................................................................................................ 67 Figure 4.7 - Relationship between Ea and doping, fit (line) to a square-root dependence on the doping. This gives a band gap of 600 ± 40 meV, with error given by the shaded region. ............................................................................. 69 Figure 4.8 - Dependence of the reverse saturation current on gate voltage (Vg1= -Vg2) at various temperatures. Both diodes show similar temperature dependence, suggesting two P-N diodes existing in the device. ................................................... 71 Figure 4.9 - Dependence of the reverse saturation current on doping for a different device showing a more pronounced asymmetry between the two diodes. .............. 71 9 Figure 5.1 - (a) Schematic diagram illustrating the device structure of our CNT pn- junction devices. (b) SEM image of our device showing a single suspended CNT across the trench. (c) Spatial map of the photocurrent plotted along the length of nanotube from the source to the drain electrode showing the peak photocurrent is in the center of the suspended region away from the contacts. .................................................................................................................................. 77 Figure 5.2 – Photocurrent spectra taken from individual suspended carbon nanotubes under various electrostatic gating conditions for (a) a single-gate device with the laser focused on the metal contact and (b) a dual gate device that did not exhibit reversible rectifying behavior. Neither device shows a gate dependence of the photocurrent peaks indicating that there is no control over the charge separating fields in devices dominated by a Schottky contacts. ............. 78 Figure 5.3 - Current-voltage characteristics of our CNT pn-junction devices with (a) pn and (b) np doping configurations. These devices exhibit rectifying behaviors, which flips polarity as the gate doping is changed from pn to np configurations. .......................................................................................................... 79 Figure 5.4 - Photocurrent spectra taken from individual carbon nanotubes under various pn-gating conditions (i.e., Vg1=-Vg2) for (a) Device 1 and (b) Device 2. (c) Photocurrent peak intensities of the E11 exciton and E11 free carrier band plotted as a function of gate voltages. Hollow shapes are from Device 1 and filled shapes are from Device 2. ............................................................................... 82 Figure 5.5 – Schematic diagram illustrating the photocurrent generation mechanisms for exciton and free particle transitions. ................................................................... 83 Figure 5.6 – Photocurrent spectra taken from individual carbon nanotubes under various pn-gating conditions (i.e., Vg1=-Vg2) in the E22 and E33 energy range. ........ 84 Figure 6.1 - (a) Schematic diagram of our device geometry, which contains a source, a drain, and a gate electrode. (b) SEM image showing one of our individual suspended carbon nanotube devices......................................................................... 90 Figure 6.2 - (a) Picture of the experimental setup inside the hemi-anechoic chamber. (b) Current-bias voltage characteristics, and the inset shows current-gate voltage characteristics, of one of our individual suspended CNT FET devices. .................................................................................................................................. 91 Figure 6.3 - (a) Voltage detected by the microphone when an input AC voltage is applied to the CNT device. The black line represents the baseline signal when there is no input voltage applied. (b) The measured acoustic pressure plotted as a function of the electrical input power for several different devices, which all show a linear relation between input power and output pressure. ...................... 93 10 Figure 6.4 - Dependence of the thermoacoustic efficiency (prms/Pin) on the heat capacity per unit area (Cs) calculated according to Arnold and Crandall’s model (blue line) and Xiao’s model (yellow shaded region). The black dot indicates the value from CNT films, and the green squares correspond to the experimental values observed from our individual suspended CNT devices. ......... 96 Figure 6.5 - Sound pressure plotted as a function of device volume for various acoustic transducers. ................................................................................................ 98 11 Abstract Carbon nanotubes (CNTs) have been studied extensively over the last two decades due to their remarkable mechanical, electronic, and thermal properties. Despite these numerous studies, there are still several important aspects of CNTs that are not well understood. The advance in fabricating ultra-clean, nearly defect-free, suspended single- walled carbon nanotubes has been developed. This allows us to study many interesting physical phenomena due to CNTs’ one-dimensional nature. Raman spectra are collected from CNTs at different gate voltages. When metallic CNTs are doped with an applied gate voltage, non-adiabatic Kohn anomaly is shut off, and large modulations in Raman intensity are observed. A relationship between the strength of the non-adiabatic Kohn anomaly and the intensity modulation of the Raman G- band is established. Possible structural phase transition is also proposed as an underlying mechanism for a Raman shift anomaly in 2D band. CNTs can be made into a p-n junction photodiode using dual gate FET structure. Photocurrent spectra are collected and a few exciton transitions can be distinguished. A gate voltage dependence on photocurrent intensity is observed and explained. In addition to CVD grown suspended CNTs, surfactant-wrapped CNT solutions are also studied for photoluminescence (PL) and electroluminescence. We developed a PL imaging system to efficiently find CNTs that have emission energy in the Si detector range. 12 Chapter 1: Background This thesis includes four main topics in carbon nanotube physics: electron phonon interactions, structural phase transition, band gap renormalization, and exciton dissociation in single suspended carbon nanotubes. Chapter 1 briefly reviews the background knowledge and concepts for these studies. In Section 1.1, we review the physical structures and properties of single-walled carbon nanotubes. In Section 1.2, we review the Raman process and electron-phonon interactions in carbon nanotubes. In Section 1.3, we review the excitonic effects and related optical properties of carbon nanotubes. In Section 1.4, we review the transport properties of a p-n junction formed by electrically doping the nanotube field-effect transistor (FET) devices. In Section 1.5, we review the photoluminescence and electroluminescence in a CNT system. 1.1 Carbon Nanotube Physics Carbon nanotubes (CNT) were first discovered by Sumio Ijima in 1991[6]. A carbon nanotube can be described as a grapheme sheet rolled into a cylindrical shape. There are two types of CNTs depending on the number of carbon layers: single-walled carbon nanotube (SWNT) and multi-walled carbon nanotube (MWNT). The diameter of a SWNT is typically between 1-2 nm, while that of a MWNT ranges between 5-50 nm. In this thesis, unless otherwise mentioned, all CNTs refer to single-walled carbon nanotubes. The structural, electronic, and thermal properties of carbon nanotubes have been extensively studied over the past two decades. Advances in fabrication techniques have led to the discovery of new 13 and exotic properties of carbon nanotubes. Their one dimension nature leads to many special properties, such as high electron mobility (~100,000 cm 2 /V∙s)[7], high thermal conductivity (~6600 W/m∙K)[8], and large Young’s modulus (~1 TPa)[9]. In order to understand CNT physics, we first need to study the electronic dispersion relationships in graphene. In graphene, carbon atoms are arranged in a hexagonal lattice in the same plane with separation of acc = 0.142 nm. There are two carbon atoms per unit cell, with unit vectors 𝒂 𝟏 = ( √ 3 2 𝑎 , 𝑎 2 ), 𝒂 𝟐 = ( √ 3 2 𝑎 , − 𝑎 2 ), where 𝑎 = |𝒂 𝟏 | = |𝒂 𝟐 | = √ 3𝑎 𝑐𝑐 = 0.246 nm is the lattice constant. Correspondingly the unit vector b 1 and b 2 of the reciprocal lattice are given by 𝒃 𝟏 = ( 2𝜋 √ 3𝑎 , 2𝜋 𝑎 ), 𝒃 𝟐 = ( 2𝜋 √ 3𝑎 , − 2𝜋 𝑎 ), where 𝑏 = |𝒃 𝟏 | = |𝒃 𝟐 | = 4𝜋 √ 3𝑎 is the lattice constant in the reciprocal space, as shown in Fig.1.1. The dispersion relation of graphene is calculated from the tight-binding model[10, 11] to be: 𝐸 ± ( 𝑘 𝑥 , 𝑘 𝑦 ) = ±𝑡 √3 + 2 cos ( 𝒌 ∙ 𝒂 𝟏 )+ 2 cos ( 𝒌 ∙ 𝒂 𝟐 )+ 2cos ( 𝒌 ∙ ( 𝒂 𝟐 − 𝒂 𝟏 ) ) = ±𝑡 √ 1 + 4 cos( √ 3𝑎 𝑘 𝑦 2 ) cos( 𝑎 𝑘 𝑥 2 ) + 4 cos 2 ( 𝑎 𝑘 𝑥 2 ) (1.1) (1.2) (1.3) (1.4) 14 Where t is the hopping integral describing the interactions of the two π electrons between nearest neighbors. There many ways to “roll up” the graphene sheet to form a CNT, resulting in many chiralities of CNTs. The vector going around the circumference of the CNT is called the chiral vector, C = na 1 + ma 2 . (n,m) is commonly known as the chirality of the nanotube. From here, we can calculate many quantities of the nanotube: The circumference of the nanotube is 𝐿 = |𝑪 | = 𝑎 √ 𝑛 2 + 𝑚 2 + 𝑛𝑚 . The diameter is given by 𝑑 𝑡 = 𝐿 𝜋 . The chiral angle θ is the angle between C and a 1 , given as (1.5) (1.6) (a) (b) Figure 1.1 – (a) Real space and (b) reciprocal lattices of graphene[2]. 15 θ = tan −1 √ 3𝑚 2𝑛 +𝑚 . The value can be between 0 and π/6. When θ = 0 it is called a zigzag CNT, and when θ = π/6 it is called an armchair CNT. The translation vector of a unit cell is 𝑻 = 𝑡 1 𝒂 𝟏 + 𝑡 2 𝒂 𝟐 , where t1 and t2 are 𝑡 1 = 2𝑚 + 𝑛 𝑑 𝑅 , 𝑡 2 = − 𝑚 + 2𝑛 𝑑 𝑅 , and dR is the greatest common divisor of (2m+n, m+2n). The length of T is: |𝑻 | = √ 3𝐿 /𝑑 𝑅 . The number of hexagons in the nanotube unit cell is N = 2( 𝑛 2 + 𝑚 2 + 𝑛𝑚 ) 𝑑 𝑅 . The electronic structure of CNTs can be derived from graphene using the zone- folding technique. In the reciprocal lattice of the nanotube, the lattice vectors K 1 (around the circumference) and K 2 (along the nanotube axis) should satisfy the following relations, 𝐂 ∙ 𝑲 𝟏 = 2𝜋 , 𝑻 ∙ 𝑲 𝟏 = 0 𝐂 ∙ 𝑲 𝟐 = 0, 𝑻 ∙ 𝑲 𝟐 = 2𝜋 (1.7) (1.8) (1.9) (1.11) (1.10) (1.12) 16 From these relations we get expressions for K 1 and K 2 : 𝑲 𝟏 = ( −𝑡 2 𝒃 𝟏 + 𝑡 1 𝒃 𝟐 ) 𝑁 , 𝑲 𝟐 = ( 𝑚 𝒃 𝟏 − 𝑛 𝒃 𝟐 ) 𝑁 In CNTs, K 1 is quantized because of the periodic boundary conditions. The cutting lines represents the allowed k values for the electronic wavevector in the 2D graphene dispersion relationship. Figure 1.2a shows that the cutting lines of K through the reciprocal lattice can either come across any of the lattice points or none, depending on the chirality of the CNTs. Mod3(n-m) = 1 or 2 CNTs are semiconductors, with band gap energies between 0.2 eV – 2.5 eV. Mod3(n-m) = 0 CNTs are metallic, with small band gap energies due to curvature effects (except in armchair CNTs). Therefore, they are also called quasi-metallic CNTs. The Kataura plot (Fig. 1.2b) shows the electronic transition energies Eii vs. CNT diameter dt calculated by the first-neighbor tight binding method, neglecting CNT curvature effects. (1.13) 17 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 2.5 3.0 d t (nm) E ii (eV) E11(sc) E22(sc) E11(m) E33(sc) Figure 1.2 – (a) Wrapping vectors and allowed k-states for three different chiralities CNTs[1]. The degeneracy at the K point is allowed only for (3,0) and (3,3) CNTs, which are quasi-metallic. The (4,2) CNT contains no degeneracy, therefore having a band gap. (b) Kataura plot. (a) (b) 18 1.2 Raman Scattering in Carbon Nanotubes Raman scattering was first discovered by C. V. Raman and K. S. Krishnan in 1928[12]. When photons are scattered from an atom or molecule, most photons are elastically scattered (Rayleigh scattering), when photons scattered are of the same energy as the incident photons. However, a small amount of photons are scattered by an excitation, and a phonon is either emitted (Stokes shift) or absorbed (anti-Stokes shift) as the incoming photon scatters into the outgoing photon. The Raman spectra of CNTs exhibit radial breathing modes (RBMs), D band, G band, and 2D (G’) band. The RBM is due to the vibrational motion of carbon atoms in the radial direction of the CNT, therefore depends on the nanotube diameter by this empirical relation[13]: 𝜔 𝑅𝐵𝑀 ~ 248 𝑑 𝑐𝑚 −1 , where d is the diameter of the CNT. The Raman shifts for RBM in this study are usually between 150 to 250 cm -1 range, meaning that our CVD grown CNTs have diameters between 0.9 to 1.6 nm. The D band is due to defects in the CNTs, and the Raman shift for D band is around 1350 cm -1 . The G band has two components: G+ and G- bands. They are from the vibrations of carbon atoms parallel and perpendicular to the tube axis, respectively. In semiconductor CNTs, the G+ and G- bands are both sharp and G+ band is significantly larger than G- band. However, for metallic CNTs, the G- bands are broadened and downshifted due to coupling to a continuum of electronic states[14-16]. Figure 1.3a shows a typical Raman (1.14) 19 spectrum of CNTs and the effect of this coupling on the optical phonon dispersion relationship[17]. The 2D band is the double phonon mode of the D band. In second-order Raman scattering, q and - q scattering wave vectors are involved, so that an electron can return to its original k position after scattering. Second-order Raman scattering consists of (1) two- Figure 1.3 – Typical Raman spectrum of CNTs (a) and corresponding vibrational modes(b)[4]. G+ G- 2D G + RBMs D G+ G- (a) (b) 20 phonon scattering events, or (2) one-phonon and one-elastic scattering event. In second- order Raman processes the electron (1) absorbs a photon at a k state, (2) scatters to k + q states, (3) scatters back to a k state, and (4) emits a photon by recombining with a hole at a k state. Because the two-phonon double-resonance Raman shift can involve two inelastic scatterings by emitting two phonons, the existence of 2D band does not necessarily mean there is defect in the CNT. 21 1.3 Excitonic Effects in Carbon Nanotubes Coulomb interactions are significantly enhanced in one-dimensional (1D) systems. CNTs provide an ideal model system for studying these effects. Theoretical studies predict that optically produced electron-hole pairs should form strongly correlated entities, due to their mutual Coulomb interactions. Now these entities are known as excitons. Previous work show that the optically excited states of CNTs are excitonic in nature. Unlike bulk semiconductors, excitonic interactions are not small perturbations but play an important role in the optical properties of small-diameter semiconductor CNTs, even metallic CNTs. The exciton binding energy is observed to be as large as 400 meV, almost half the band gap energy of CNTs. The excitonic transitions dominate the optical spectra, and continuum transitions are negligible. Therefore, in order to understand the optical transitions of CNTs we need to first understand the exciton effects in CNTs. In 2005, the excitonic nature was experimentally confirmed using two-photon photoluminescence spectroscopy by Wang et al[18]. It is shown that the excitonic transitions dominate the optical spectra, and the continuum states are rather negligible. Figure 1.4 shows the exciton states below the single-particle continuum states, and the corresponding two- photon absorption and emission data in this paper. The optical transition energy have three components: 𝐸 𝑜𝑝𝑡𝑖𝑐𝑎𝑙 = 𝐸 𝑖𝑖 + Σ 𝑠𝑒𝑙𝑓 − Δ 𝑒𝑥 (1.15) 22 The predicted single particle and excitonic transition energies are almost the same, because the quasi-particle self-energy, Σ 𝑠𝑒𝑙𝑓 , nearly cancels out the exciton binding energy Δ 𝑒𝑥 . However, the nature of the excitation is completely different for these two scenarios. Each excitonic state is 16 times degenerate, with 12 triplet states and 4 singlet states[19]. The electron-hole interaction lifts the fourfold degeneracy of the singlet states. Two of them are formed by an electron and a hole from the same valley. The other two are formed by an electron and a hole taken from different valleys. The latter bands therefore cannot be directly coupled to light. They are the dark exciton states. Figure 1.4 – Two photon absorption-emission energy diagram and spectral data plot from Wang et al. 23 1.4 Carbon Nanotube p-n Junctions The p-n junction diodes form the basis for nearly all modern semiconductor devices. Two charge carriers, electrons and holes, are created when photons of sufficient energy are absorbed. CNTs have an advantage for this kind of photovoltaic effect, because they can provide a wide range of band gaps to match the solar spectrum. When a CNT is doped half n-type and half p-type, a p-n junction can be formed in the middle of the CNT. The diode characteristics is slightly different from bulk silicone materials. For example, they have a much smaller turn-on voltage, about 0.2V, compared to 0.7V in silicone diodes. Figure 1.5a shows a possible CNT p-n diodes device structure, with a band diagram indicating where the band bending happens. Figure 1.5b shows a typical CNT p-n junction current vs. voltage characteristics fitted to the ideal diode equation with n~1.2. p n E g SiO 2 Pt Si SiN x -0.2 -0.1 0.0 0.1 0.2 0.0 20.0n 40.0n 60.0n I DS (A) V DS (V) Data Fit (a) (b) Figure 1.5 – (a) CNT p-n junction diodes device structure in this thesis. (b) Typical CNT p-n junction current vs. voltage characteristics fitted to the idea diode equation (red line). The subscript DS means “source to drain.” 24 A Schottky junction might also be formed between metal electrodes and semiconductor CNTs in the device structure in Fig. 1.5a. The difference in the work function between these two materials results in the built-in electric field. However, this kind of junctions make inefficient photovoltaic devices because of high leakage currents. In this thesis, we focus our study on p-n junction diodes by making the device contact resistance low (~100kOhm). In order to understand the p-n junction device physics, we introduce the ideal diode equation, which applies to all diode current-voltage characteristics: 𝐼 𝐷𝑆 = 𝐼 0 ( 𝑒 𝑞 𝑉 𝐷𝑆 𝑛 𝑘 𝐵 𝑇 − 1) , where 𝐼 0 is the reverse saturation current, q is the electronic charge, 𝑉 𝐷𝑆 is the voltage across the junction, n is the ideality factor, kB is the Boltzmann constant, and T is the environment temperature. The value of the ideality factor n can be from 1 to 2, depending on the performance of the diode. n=1 for an ideal diode and n=2 for materials with defects. (1.16) 25 Figure 1.6 – The energy band diagram of a p-n junction at zero bias voltage. The absorbed photons excite electron-hole pairs and the built-in potential separates the electrons and holes and creates current flowing through the device. 26 1.5 Photoluminescence and Electroluminescence in Carbon Nanotubes When a photon with energy equal to the E22 transition energy in the CNT comes in, it can excite an electron-hole pair into the E22 state. Both electron and hole rapidly relax to E11 states and then recombine into a photon with energy equal to E11 transition. This is the basic principle for photoluminescence process in CNTs. The relaxation time is very quick, about 20-200 picoseconds[20]. The nanotube photoluminescence is intrinsically inefficient due to low-lying dark exciton states, and is dependent on chiralities. However, it can be improved by several approaches. So far an efficiency of 16% has been achieved using the incorporation of the sp3 states[21]. Photoluminescence may be quenched by applying electric field along[22] and perpendicular on CNTs[23] and is very sensitive to the environmental effect. Therefore, in order to see photoluminescence in CNTs, CNTs have to either be suspended from substrate or wrapped in surfactant, such as sodium dodecyl sulfate (SDS) or toluene. Figure 1.7 – Photoluminescence image (a) and spectrum (b) of a suspended 100μm-long CNT from Lefebvre et al[3]. (a) (b) 27 The emission of photons in CNTs can be driven optically (PL) or electrically (EL). In our study, we fabricate CNT p-n diodes to study electroluminescence (EL). P-n junction diodes are the basic building blocks of almost all today’s optoelectronic devices, such as photo detectors and LEDs. Therefore, light emission from CNT p-n diodes is a fundamental step towards potential use of CNTs as nano-scale light sources. In general, electrically excited light emission from semiconductor CNTs can be produced under 1.) ambipolar[24, 25] or 2.) unipolar[26, 27] operation. In the first case, both electrons and holes are injected simultaneously into the CNT and their radiative recombination generates light. In the second case, a single type of carriers (either electrons or holes) is accelerated under high electric field and accumulates enough energy to create excitons via impact ionization[26]. It is found that the light emission intensity increases exponentially with the driving current. The EL efficiency is estimated to be ~0.5-1 x 10 -4 photons per injected electron-hole pair, and the non-radiative lifetime is in the order of a few picoseconds[5], smaller than what observed in PL. Figure 1.8 shows EL spectra from Mueller et al. in Nature Nanotechnology 2010. Figure 1.8 – EL spectra from CNT p-n photodiodes with +8V/-8V gate voltages. The FWHM is 50 meV[5]. 28 Chapter 2: Pronounced Electron-phonon Interactions in Suspended Metallic Carbon Nanotubes In this work, we investigate the intensity modulation of the G- band Raman mode by changing the electrostatic gating. We observe a much greater strength of Kohn anomaly (KA) in our clean, almost defect-free metallic CNTs than theoretically predicted. By establishing a quantitative correlation between the strength of the nonadiabatic KA and the modulation of Raman G- band intensity, we determine that the underlying physics that leads to both effects is the same. Then, we change the environment temperature and find that metallic CNTs can switch between a regime where the nonadiabatic KA is clearly observed and a regime where it is absent. In the regime where nonadiabatic KA is absent we see a suppression of the Raman intensity under electrostatic gating. 2.1 Introduction In metallic CNTs, the strong electron-phonon coupling has a significant effect on the G band Raman mode, which leads to a Kohn anomaly (KA)[16, 28] and is predicted to cause a Peierls distortion (PD) at T = 0K[29, 30]. Time-dependent density functional theory (DFT) calculations predict a breakdown of the Born-Oppenheimer approximation in CNTs due to their fast vibrational motion of the carbon atoms (0.02 ps) and long electron lifetimes (0.2- 3.0 ps[31]). The breakdown of Born-Oppenheimer approximation, also known as the 29 nonadiabatic KA[15], has been studied previously in both CNTs[32, 33] and graphene[34]. In the nonadiabatic KA regime, the gate voltage dependence of the G- phonon mode follows a W-shape profile[15, 32]. In previous studies, CNTs were lying on a substrate and had undergone lithographic processing, which may induce defects and surface contaminants. Hens, a vast majority of the literature on Raman spectroscopy of gated metallic CNTs show no evidence of a nonadiabatic KA[16, 30]. It is important to have an ultra-clean, nearly defect-free system in order to observe this effect. Our CNTs are “as grown” and suspended from the substrate, having minimum surface perturbation. In fact, we have observed a much stronger effect than both previous experimental work and predictions made theoretically[15, 35]. We also found that CNTs can transition between a regime where the nonadiabatic KA is clearly evident to a second regime, where there is no sign of the nonadiabatic KA, by varying the temperature. 2.2 Experimental Details We adopted our sample fabrication technique from previously reported[36, 37]. The fabrication starts with a 4" p–type Si wafer with 1μm SiO2 and 100 nm Si3N4 on both sides of the wafer. The fabrication of the wafer is completed at Nanofabrication Facility of University of California, Santa Barbara. Source and drain electrodes consisting of 5 nm of W and 35-100 nm of Pt are patterned on the wafer, along with a gate electrode in an 500- 800nm deep, 2μm wide trench. W is used as an adhesion layer and Pt is the final electrode metal. Pt is used for the electrode metal since it can withstand 800-900°C where the carbon 30 nanotube growth takes place. The thickness of the Pt should be adjusted depending on the final growth temperature. We have observed 100 nm of Pt would withstand 900°C growth temperatures. An aqueous solution of alumina supported Fe(NO3)3 and Mo nanoparticles is deposited in the lithographically defined catalyst windows patterned on the source and drain electrodes. CNTs are then grown by chemical vapor deposition (CVD) in a 1" quartz furnace at 825°C using a mixture of argon gas bubbled through ethanol and hydrogen. The CNT growth is the final step in our sample fabrication, which ensures that the CNTs are not contaminated by any chemical residues and therefore are ultra-clean. Current-bias voltage (I-V) and conductance-gate voltage (I-Vg) are examined in order to select single suspended metallic CNTs for later measurement. High-bias transport properties showing NDC (Fig. 2.2a) indicates the CNT is suspended, and the maximum current value gives the information of how many CNTs are grown across the trench, based Si/SiO2 Si3N4 Source electrode Drain electrode CNT Gate electrode Figure 2.1 – (a) Schematic diagram of a CNT field-effect transistor (FET) device with source/drain electrodes made from Pt/W. (b) Scanning electron microscopy (SEM) image of a CNT FET device, the red line indicating where CNTs usually grow. (a) (b) 31 on the 10/L rule developed by Pop et al[38]. Raman spectra are collected with either 532nm or 633nm laser and we make sure that each device does not exhibit a defect-induced D-band Raman mode near 1350 cm -1 [4]. Measurements are performed in an optical cryostat (Cryo Industries, Inc.) under vacuum at various temperatures between 4K and 400K. The laser is focused through a 40X objective lens onto a 1-μm spot. Raman G- band spectra are taken at different gate voltages and fit to Lorentzian curves. 2.3 Results and Discussion Figure 2.3a shows the raw G band Raman spectrum at Vg=0V and Vg=-8V. Figure 2.3b shows the G- band Raman shift plotted as a function of the gate voltages. It clearly shows the W-shape profile predicted theoretically for the nonadiabatic KA. Time-dependent DFT predicts the maximum downshift in phonon frequency with gate voltage at room temperature to be approximately 3 cm -1 [33, 39]. Our result shows a maximum downshift of Figure 2.2 – (a) Current-voltage characteristics of a typical CNT device. The negative differential conductance (NDC) indicates that the CNT is suspended. (b) Conductance-gate voltage characteristics of a metallic CNT device. -1 0 1 -8.0µ -4.0µ 0.0 4.0µ 8.0µ V g = -5V Current(A) Bias Voltage(V) -6 -4 -2 0 2 4 6 0.0 5.0µ 10.0µ 15.0µ 20.0µ 25.0µ 30.0µ Conductance(S) Gate Voltage(V) (a) (b) 32 15 cm -1 at room temperature, a much stronger dependence of phonon energy on gate voltage than predicted. The significantly more pronounced W-shape profiles observed in our CNT devices indicate the existence of strong electron-phonon interaction in quasi-metallic CNTs and also the ultra-cleanliness of our suspended CNT samples fabricated in this fashion. Most of our devices have a more significant G- peak than the G+ peak, as seen in Fig. 2.3a. From devices that also show a G+ band, we find that the G+ band Raman shift and intensity do not change with gate voltages. We have also taken the same measurement on several different semiconducting CNT devices but found no dependence at all on the gate voltage. This further proofs that the semiconducting CNTs have very weak electron-phonon interaction. 1400 1500 1600 1700 1800 0 200 400 600 Intensity (a.u.) Raman shift (cm -1 ) Vg=0V Vg=-8V Figure 2.3 – (a) Raman G band at V g =0V and V g =-8V from device A, showing both intensity and frequency changes with gate voltage. (b) G band Raman shift as a function of applied gate voltage from the same device, showing the signature W shape profile. -10 -5 0 5 10 1550 1560 1570 1580 G - Band Raman Shift (cm -1 ) Gate Voltage(V) T=300K 15 cm -1 T=300K (a) (b) 33 Graphene and CNT samples prepared on Si/SiO2 substrates, are prone to spatial fluctuations of Fermi level, making it harder to observe these effects. Comparing our results with the calculations of Tsang et al.[33], we conclude that the electron-phonon interaction matrix element squared is approximately 500 eV 2 Å -2 for these suspended pristine quasi- metallic CNTs. This number is about five times greater than values reported previously, both by experimental methods[33] and theoretical calculations[39]. We collect data from 25 different CNTs and found they all exhibit either one of those behavior which we will refer to as Regime 1 and Regime 2. In Regime 1, shown in Fig. 2.4a, the Raman intensity is suppressed at Vg=0V and increase with the gate voltage. Also, the G- band Raman shift exhibits a strong nonadiabatic KA or W-shape profile. In Regime 2, shown in Fig. 2.4b, the Raman intensity is significantly enhanced near the charge neutrality point. No gate voltage dependence is observed in the G- band Raman shift in this regime. Regime 1 behavior was observed in 11 out of 25 devices measured in this study. On the other hand, over half of the devices do not exhibit a W-shape profile, meaning that the electron-phonon coupling is weak. 34 More interestingly, many of our devices measured in this study were found to transition from Regime 2 to Regime 1 as the temperature was lowered. Figure 2.5 shows the gate dependence of the G- band for the same device measured at 300K and 4K. At 300K, no sign of KA is observed and the Raman intensity is enhanced at Vg=0V, agreeing with the behavior in Regime 2. At 4K, however, we see the W-shape profile (Fig. 2.5b) and the Raman intensity is suppressed at Vg=0V, agreeing with the behavior in Regime 1. Noted that in this particular device, the full W-shape profile is not seen because we do not want to gate the device too strong. If the device were to be gated strong enough we should be able to see the full W-shape. This transition from 300K to 4K in gate dependence was reversible and repeatable as we cooled down and warmed up the sample. Therefore, any contamination or -6 -4 -2 0 2 4 6 1572 1576 1580 1584 1588 Raman Intensity Raman Shift Raman Intensity Raman Shift (cm -1 ) Gate Voltage (V) -6 -4 -2 0 2 4 6 1572 1576 1580 1584 Raman Intensity Raman Shift Raman Intensity Raman Shift (cm -1 ) Gate Voltage (V) Figure 2.4 – Room temperature gate voltage dependence of the G - band Raman shift and intensity for (a) device B, showing the signature W shape profile indicating breakdown of the Born-Oppenheimer approximation(Regime 1) and (b) device C, showing no evidence of non-adiabatic behavior (Regime 2). (a) (b) 35 damage to the CNT can be ruled out as an underlying cause of this temperature-induced transition. These results indicate that there is a correlation between the Raman intensity modulation and the nonadiabatic KA strength. We then quantify the intensity modulation using the ratio of the Raman G- band intensities of the gated and ungated CNTs. Similarly, we quantify the strength of the nonadiabatic KA from the maximum downshift observed in the G- band Raman frequency from Vg=0V, in other words, the depth of the minima in the W-shape profile. Figure 2.6 shows the intensity modulation ratio v.s. the maximum Raman downshift. We see a linear relation between these two quantities. Noted that all devices in Regime 2 lie near the origin, since the Raman intensity of the doped CNT is much smaller -6 -3 0 3 6 -10 -8 -6 -4 -2 0 Raman Shift Raman Intensity Raman Intensity Relative Raman Shift (cm -1 ) Gate Voltage(V) -6 -3 0 3 6 -10 -8 -6 -4 -2 0 2 Raman Shift Raman Intensity Raman Intensity Relative Raman Shift (cm -1 ) Gate Voltage(V) Figure 2.5 – Gate voltage dependence of the G band Raman shift and G band Raman intensity for device D at (a) T= 300K, consistent with Regime 2, and (b) at T=4.2K, consistent with Regime 1. (a) (b) 36 than the undoped one. While both a band gap the the electronic lifetime affect nonadiabaticity, based on our limited dataset, we are unable to confidently distinguish between changes due to a band gap and due to a change in electronic lifetimes. The G- band linewidths in our study spanned a wide range from 33 cm -1 to 83 cm -1 . No correlation could be established between the linewidth and either the maximum Raman downshift or the intensity modulation ratio. The linear correlation obtained between the depth of the minima in the W-shape profile and the Raman intensity, as shown in Fig. 2.6, suggests that intensity modulation is also a manifestation of the same mechanism as KA, i.e. electron-phonon interaction. In fact, the depth of the minima is directly proportional to the electron-phonon coupling matrix element, and because of the wide range of chiralities in our study, this amount also spans a range from 0 to 18 cm -1 . The abrupt change in the Raman intensity shown in Fig. 2.4a can arise from a structural phase transition, for example a Mott insulator transition or a Peierls transition. We have further evidence of this hypothesis in Chapter 3. 37 Although the depth of the minima in the W-shape profile have been predicted to increase significantly as the temperature is lowered for metallic CNTs and graphene, we have not observe this trend in some of our devices. Even with the CNTs that show this effect, it is not as pronounced as predicted. This is because the previous calculations are based on the assumption of zero-band gap, which does not apply to quasi-metallic CNTs. For quasi- metallic CNTs the band gaps are not really zero. They are in the order of 10-100 meV. In Fig.2.7 we show the gate dependence of the G- band Raman shift relative to the Raman shift at Vg=0V, at different temperatures for two different CNT devices (E and A). Both devices show a W-shape profile. However, at 4K the device in Fig. 2.7a clearly shows a deepening 0 5 10 15 20 0.0 6.5 13.0 Intensity Modulation Ratio Maximum Raman Downshift (cm -1 ) Figure 2.6 – Correlation between the ratio of gated and ungated G band Raman intensities for various devices plotted as a function of the maximum gate-induced downshift of the G band Raman frequency due to the non-adiabatic Kohn anomaly. Each point on this plot corresponds to a different nanotube sample. . 38 of the minima in Raman shift, while the device in Fig. 2.7b shows no change in the depth at all. We generally observe these two kinds of trend with half and half frequency. From second-order time-dependent perturbation theory, the phonon self-energy is given as Π( 𝜔 , 𝐸 𝐹 ) = 2 ∑ ( |𝑉 𝑘 | 2 ℏ𝜔 − 𝐸 𝒌 𝑒 ℎ + 𝑖 Γ/2 − |𝑉 𝑘 | 2 ℏ𝜔 + 𝐸 𝒌 𝑒 ℎ + 𝑖 Γ/2 ) 𝒌 ( 𝑓 ℎ − 𝑓 𝑒 ) , where the prefactor 2 comes from spin degeneracy. Here, 𝑓 ℎ,𝑒 are the Fermi distribution functions for hole and electron, and 𝐸 𝒌 𝑒 ℎ = 𝐸 𝒌 𝑒 − 𝐸 𝒌 ℎ . 𝑉 𝑘 is the electron-phonon matrix element that converts a phonon into an electron-hole pair. KA occurs in quasi-metallic CNTs when a phonon excites an electron-hole pair across the small band gap of the CNT. The -10 -5 0 5 10 -20 -15 -10 -5 0 5 10 15 20 300K 150K 4.5K Relative Raman shift (cm -1 ) Gate Voltage (V) -5 0 5 -9 -6 -3 0 300K 4.5K Relative Raman Shift (cm -1 ) Gate Voltage (V) Figure 2.7 - Relative Raman shift of the G - band with respect to V g =0 for (a) device E and (b) device A taken at various temperatures. (a) (b) (2.1) 39 created electron-hole pair then renormalizes the phonon self-energy. A renormalized phonon self-energy is written as the sum of the unrenormalized energy and the real part of the phonon self-energy. By doping the CNT, we increase its Fermi energy and when 𝐸 𝐹 = ℏ𝜔 2 , all the electronic states that can be excited by a phonon are occupied, which switches off the KA. Therefore, the phonon renormalization is extremely sensitive to the band gap of the CNT. Using a finite-mass Dirac dispersion relation ( 𝐸 = √𝑚 2 + ( ℏ𝜐 𝐹 𝑘 ) 2 ) in the non-adiabatic case at T=0, we obtain Re[Π( 𝜔 , 𝐸 𝐹 ) ] = −𝛼 2 [𝐸 𝐶 − 𝐸 𝐹 − { ( ℏ𝜔 ) 2 −( 2𝑚 ) 2 4ℏ𝜔 } ln| |𝐸 𝐹 |− ℏ𝜔 2 |𝐸 𝐹 |+ ℏ𝜔 2 |], where 𝛼 and 𝐸 𝐶 are constants and 2𝑚 is the band gap[35]. The deepening of the minima is the W-shape profile is due to logarithm singularity in this equation. We can see that if the band gap energy is close to the phonon energy, this singularity can be eliminated, which explains why some CNTs do not show a strengthening of the KA at lower temperatures. Unfortunately in our study we do not have the information of the CNT chirality in order to estimate 𝑉 𝑘 and the curvature induced minigap. Figures 2.8a and 2.8b show the calculated Re[Π( 𝜔 , 𝐸 𝐹 ) ] based on eq. 2.1 plotted as a function of the applied gate voltage, for two different temperatures. Figure 2.8a assumes no band gap in the electron band structure in the metallic CNT. Here we see a clear deepening of the minima in the W-shape profile, as reported previously[33, 39, 40]. However, if we include a small band gap (~120 meV ≫ 𝑘 𝐵 𝑇 ), at T=150K the renormalization of phonon energy can be reduced in the band structure, as shown in Fig. 2.8b. The electron-phonon (2.2) 40 coupling matrix element, |𝑉 𝑘 |, is assumed to be the same for all cases in Fig. 2.8. Both cases have been observed in our study (Fig. 2.8a and 2.8b), indicating a possible band gap opening in the metallic CNT as the temperature is lowered. Small band gaps of ~100meV have been observed experimentally in metallic CNTs[41, 42], and have been attributed to the effect of curvature and electron-electron interactions[42]. In fact, in the next chapter we will see that as large as 240meV of band gap energy has been observed in our metallic CNT samples. However, these calculations involve several simplifications, making it difficult to provide any exact estimate for the electron-phonon interaction from our experimental data. A more detailed analysis would require the information about the chirality of the CNT to precisely calculate |𝑉 𝑘 |. Unfortunately, we have no information of radio breathing mode from all of our CNT samples due to technical issues we had at the time. -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 Real( ) Gate Voltage (V) 300K, E g =0eV 150K, E g =120meV -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 Real( ) Gate Voltage (V) 300K, E g =0eV 150K, E g =0eV Figure 2.8 - The real part of Π(𝜔 , 𝐸 𝐹 ) from Equation 1 at T=300K and T=150K, with (a) no band gap in the electron band structure and (b) a band gap of 160meV. (a) (b) 41 2.4 Conclusion In conclusion, the immense strength of the electron-phonon interactions in quasi- metallic CNTs causes their phonon energies to depend strongly on the free carrier density. We find that these pristine nanotubes exist in one of two regimes – (1) having no sign of the breakdown of the Born Oppenheimer approximation and showing a suppression of the G- band Raman intensity with electrostatic gating and (2) showing a breakdown of the adiabatic approximation and accompanied by a dramatic gate-induced enhancement of G- band Raman intensity. We establish that the coupling between electrons and phonons in metallic CNTs is approximately five times stronger than previous theoretical and experimental reports, and that the strength of this coupling is correlated with the gate-induced Raman intensity modulation. The abrupt changes in the Raman intensity can arise from a structural phase transition, (e.g., charge density wave), which lowers the symmetry of the crystal, and can change these vibrational modes from Raman active to Raman inactive. We feel that, in the light of this evidence, the electron-phonon interactions in metallic CNTs should be theoretically re-examined. 42 Chapter 3: Evidence for Structural Phase Transitions and Large Effective Band Gaps in Suspended Metallic Carbon Nanotubes We report evidence for a structural phase transition in individual suspended metallic CNTs by examining their Raman spectra and electron transport under electrostatic gate potentials. The current-gate voltage characteristics reveal anomalously large quasi-metallic band gaps as high as 240meV; the largest reported to date. For nanotubes with band gaps larger than 200meV, we observe a pronounced M-shape profile in the gate dependence of the 2D band (or G’ band) Raman frequency. The pronounced dip (or softening) of the phonon mode near zero gate voltage can be attributed to a structural phase transition (SPT) that occurs at the charge neutrality point (CNP). The 2D band Raman intensity also changes abruptly near the CNP, providing further evidence for a change in the lattice symmetry and a possible SPT. Pronounced non-adiabatic effects are observed in the gate dependence of the G band Raman mode, however, this behavior deviates from non-adiabatic theory near the CNP. For CNTs with band gaps larger than 200meV, non-adiabatic effects should be largely suppressed, which is not observed experimentally. This data suggests that these large effective band gaps are primarily caused by a SPT to an insulating state, which causes the large modulation observed in the conductance around the CNP. Possible mechanisms for this SPT are discussed, including electron-electron (e.g., Mott) and electron-phonon (e.g., Peierls) driven transitions. 43 3.1 Introduction The ability to grow ultra-clean, nearly defect free, suspended carbon nanotube field- effect transistors was first developed by Cao et al. in 2005[43]. Since then, several interesting phenomena have been observed in these pristine, unperturbed nanotubes, including non- equilibrium phonon populations[44], pronounced Kohn anomalies due to strong electron- phonon interactions[45], non-adiabatic effects and breakdown of the Born-Oppenheimer approximation[46], Wigner crystallization[47], and possible Mott insulator behavior due to strong electron-electron interactions[42]. These phenomena are only seen in pristine unperturbed nanotubes, indicating how sensitive this one-dimensional material is to slight defects, surface contaminants, and substrate interactions[48]. For example, the observation of non-adiabatic effects (i.e., breakdown of the Born Oppenheimer approximation) in carbon nanotubes was not a surprising finding, based on their long electron lifetimes and the short vibrational cycle of the tightly bound carbon atoms. However, this was not observed prior to 2009 in substrate-supported nanotubes[16, 33, 49, 50]. Desphande et al. first pointed out that the quasi-metallic band gaps observed in these ultra-clean, nearly defect free, suspended nanotubes were anomalously large, exceeding the band gaps predicted from curvature induced effects[42, 51]. In particular, they showed that metallic armchair nanotubes, which should have no curvature-induced band gap[51], had finite band gaps on the order of 10- 100meV. A Mott insulator transition was proposed as a possible explanation, in which the strong Coulomb repulsion at half filling of the energy bands localize electrons, one electron per atom site, to form a Mott insulator[52]. This typically results in slight changes in the lattice structure of the material. Raman intensity modulation has been reported previously 44 for Mott insulator transitions in other materials systems, including LaSrTiO3 and YCaTiO3, due to a lowering of the crystal symmetry and an increase in the effective mass m* associated with the Mott state[53]. Previous experiments of bulk Mott insulators use chemical impurity doping, which introduces additional disorder in the system. Carbon nanotubes, however, offer the opportunity to study electronic phenomena without interference from disorder by electrostatic doping. A Peierls distortion would also produce a band gap in this system, but has only been predicted theoretically in nanotubes with very small diameters (~0.5nm) and at very low temperatures, and is not expected to occur in the relatively large diameter nanotubes grown in this study. Previous Raman studies of ultra-clean, nearly defect free, suspended carbon nanotubes focused primarily on the G band Raman mode[44, 46, 54]. In this paper, we present the electrostatic doping dependence of the 2D band (also known as G’ band) Raman mode, which is not significantly affected by the Kohn anomaly or non-adiabatic effects in the nanotube and, thus, provides a more direct means for observing changes in the lattice structure and bond strengths of the nanotube. The effects observed in the Raman spectra are correlated with I-Vgate transport data, which exhibit large effective band gaps ~200meV. 3.2 Experimental Details Suspended CNTs are grown by the same technique as in Chapter 2, along with the same characterization. Typical CNTs have a length of 2 um. Figure 3.1 shows a Raman 2D band spectrum from device A. We collect Raman spectra with either 633nm or 532nm wavelength radiation. The laser beam is focused to an approximately 1 m spot size and 45 attenuated by neutral density filters to ensure that heating is minimal, with a power of 20μW. None of the devices reported here exhibited any detectible defect-induced D band Raman mode around 1350cm -1 . 3.3 Results and Discussion Figure 3.2a shows the gate voltage dependence of the 2D Raman mode for a single suspended metallic carbon nanotube measured at room temperature, exhibiting a clear “M” shape profile. This “M” shape profile has a linear background with a slope of approximately -0.33cm -1 /V, which can be attributed to doping-induced weakening of the carbon-carbon bonds, and hence softening of the phonon modes. The dip occurring around zero gate voltage can be understood as the result of a structural phase transition (SPT) occurring at the charge Figure 3.1 – Typical Raman 2D band of a metallic CNT with 633nm excitation. 2400 2500 2600 2700 2800 0.0 500.0 1.0k 1.5k 2.0k Intensity (a.u.) Raman shift (cm -1 ) V g =0V 46 neutrality point, causing a slight change in the lattice symmetry/bond strength, as discussed below. Figure 3.2b shows the conductance-gate voltage characteristics for the same CNT shown in Figure 3.2a. This data was fit using a Landauer transport model to estimate/determine the band gap of the nanotube to be 220meV. Here, we fit the I-Vgate data using a Landauer model, as discussed previously[48, 55]. Briefly, the low bias conductance of the device can be expressed as: 𝐺 = ( 4𝑒 2 ℎ ) ∫ ( 𝜆 𝑒𝑓𝑓 𝜆 𝑒𝑓𝑓 + 𝐿 ) ( −𝜕𝑓 𝜕𝐸 )𝑑𝐸 ∞ −∞ -6 -4 -2 0 2 4 6 2621 2622 2623 2624 2625 2626 2D Raman Shift (cm -1 ) Gate Voltage (V) -6 -4 -2 0 2 4 6 0 5 10 15 20 Measurement Fit Conductance ( S) Gate Voltage (V) (a) (b) Figure 3.2 – (a) Gate voltage dependence of the 2D band Raman shift and (b) conductance-gate voltage curve for a suspended metallic CNT taken at room temperature. (3.1) 47 where λeff is the effective mean free path (given by Matthiessen’s rule), L is the device length, and 𝜕𝑓 𝜕𝐸 is the derivative of the Fermi-Dirac distribution[56]. Using a hyperbolic energy dispersion relation, we integrate over the density of states which is given by 𝐷 ( 𝐸 ) = ∑ | 𝑑 𝐸 𝑗 ( 𝑘 ) 𝑑𝑘 | −1 𝑁 𝐽 =1 Here, the density of states is zero inside the band gap, Eg. The Fermi energy in the nanotube is related to the applied gate voltage according to the following relation[55, 57, 58]: 𝐸 𝐹 + 𝑄 𝐶 = 𝑒 𝑉 𝑔𝑎𝑡𝑒 where EF is the Fermi energy, Q is the electric charge on the nanotube, and C is the geometric capacitance. The charge is calculated by 𝑄 = ∫ 𝐷 ( 𝐸 ) 𝑓 ( 𝐸 ) 𝑏𝑎𝑛𝑑𝑠 𝑑𝐸 , where 𝐷 ( 𝐸 ) is the density of states, and 𝑓 ( 𝐸 ) is the Fermi function. Figure 3.3a shows the gate voltage dependence of the 2D band for another suspended quasi-metallic CNT device. Here, a slight monotonic decrease in the 2D band frequency is observed under applied gate voltages with a slope of approximately -0.25cm -1 /V, consistent with doping-induced expansion of the carbon-carbon bond. A band gap of 56meV was determined from a Landauer fit of the Conductance-Vgate data shown in Figure 3.3b. This behavior was observed consistently in 4 other nanotubes measured whose effective transport band gaps were below 100meV. (3.2) (3.3) (3.4) 48 As reported in Chapter 2, the gate dependence of the G band Raman mode exhibits a pronounced W-shape profile, as shown in Figure 3.4a, which arises from non-adiabatic behavior observed through the strong Kohn anomaly in the nanotube. This W-shape profile was first predicted theoretically[15, 33, 51, 59] and later observed experimentally[45, 46]. Figure 3.4b shows the non-adiabatic doping dependence of the G band calculated at room temperature using second order perturbation theory for a quasi-metallic nanotube with various band gaps. Following the treatment of Sasaki et al.[51], we calculate the phonon self-energy, Π(ω,EF), using the expression in eq 3.5. Π( 𝜔 , 𝐸 𝐹 ) = 2 ∑( |𝑉 𝑘 | 2 ℏ𝜔 −𝐸 𝒌 𝑒 ℎ + 𝑖 Γ 2 − |𝑉 𝑘 | 2 ℏ𝜔 +𝐸 𝒌 𝑒 ℎ + 𝑖 Γ 2 ) 𝒌 ( 𝑓 ℎ − 𝑓 𝑒 ) , where V k is the electron-phonon coupling matrix element, ℏ𝜔 is the phonon energy (0.196eV), E eh =E e -E h , where E e(h) is the electron(hole) state energy, given by the hyperbolic -6 -4 -2 0 2 4 6 2661 2662 2663 2664 2665 Raman Shift (cm -1 ) Gate Voltage (V) -4 -3 -2 -1 0 1 2 3 4 0 10 20 30 Measurement Fit Conductance ( S) Gate Voltage (V) Figure 3.3 – (a) Gate voltage dependence of the 2D band Raman shift and (b) conductance-gate voltage curve for a suspended metallic CNT taken at room temperature. (3.5) 49 dispersion, fe(h) is the Fermi occupation function for electrons(holes), and Γ is determined self consistently from the imaginary part of the phonon self-energy. The real part of the phonon self-energy gives the renormalization of the phonon energy due to electron-phonon interaction. Figure 3.4b shows the calculated relative Raman shift of the G band due to non- adiabatic phonon renormalization. Here, the W-shape profile becomes significantly weaker for a band gap of 100meV, and is completely absent for a nanotubes with a band gap of 200meV. That is, when the band gap of the nanotube is larger than the optical phonon energy (196meV), the dominant contribution for perturbation (E eh =ħ ) is suppressed. Also, notice that the slope of the G band Raman shift with respect to gate voltage is non-zero in the experimental data near the charge neutrality point (CNP), whereas theory predicts a zero slope. This deviation from theory is observed consistently in all metallic nanotubes measured with large band gaps. The pronounced non-adiabatic W-shape profile observed experimentally indicates that the actual separation between the conduction and valence bands must be smaller than 200meV. This suggests that the large effective band gaps observed in the I-Vg characteristics are primarily caused by a SPT to an insulating state, which causes a large modulation in the conductance around the CNP. Figure 3.4c shows the gate dependence of the 2D band, which also shows the same M-shape profile seen in Fig. 3.2a. Near the CNP, the 2D band exhibits a monotonically decreasing gate dependence with a slope of approximately -0.5cm -1 /V. The 2D band Raman mode is affected much less by the Kohn anomaly than the G band and, thus, provides a more reliable means for observing changes in the lattice structure and bond strengths of the 50 nanotube. Figure 3.4d shows the non-adiabatic doping dependence of the 2D Raman mode calculated using eq 3.5. Since the 2D band does not exhibit significant non-adiabatic effects, the M-shape profile shown in Fig. 3.4c indicates the existence of a different mechanism for phonon softening at the CNP. Araujo et al. observed an upside down V-shape gate dependence in the 2D band of single layer graphene[60]. This behavior was attributed to non-adiabatic effects; however, no rigorous calculations were given. In the 2D data shown in Figs 3.2a and 3.4c, the downturns at the two ends of the M-shape profile could be due to non-adiabatic effects, while the dip at the CNP is due to the SPT. 51 We also observe dramatic changes in the 2D band Raman intensity, as shown in Figs. 3.5a and 3.5b. Our previous measurements of the G band Raman intensity have shown similar changes with doping[45, 54]. Typically, changes in the Raman intensity of CNTs are attributed to a change in the resonance condition ( Eii). Such a large change in the Raman -0.4 -0.2 0.0 0.2 0.4 2660 2661 2662 2663 2D Raman shift (cm -1 ) Fermi Energy (eV) Figure 3.4 – Experimentally measured (a) G and (c) 2D Raman modes taken from the same nanotube at room temperature. Non-adiabatic calculations of the gate dependence of the (b) G and (d) 2D bands. -8 -4 0 4 8 1545 1550 1555 1560 1565 1570 1575 1580 G Raman Shift (cm -1 ) Gate Voltage(V) -6 -4 -2 0 2 4 6 2620 2622 2624 2626 2628 2D Raman Shift (cm -1 ) Gate Voltage (V) -0.2 -0.1 0.0 0.1 0.2 G Band Raman Shift (a.u.) Fermi Energy (eV) E g =0meV E g =100meV E g =200meV (a) (b) (c) (d) 52 intensity (5X) would require a change in the resonant optical transition energy of Eii ≥50meV. It is tempting to attribute the changes observed in Raman frequency and Raman intensity to strain induced by the electrostatic gate force. However, this can be ruled out for several reasons. First, the nanotube will be pulled towards the bottom of the trench with a force given by 𝐹 = 1/2𝐶 ′ 𝑉 𝑔 2 , where C' = dC/dz is the derivative of the capacitance with respect to the distance between the nanotube and the gate electrode. Assuming a Young’s modulus of 1TPa[61] and a strain-induced downshift rate of d G’/d=-5.2cm - 1 /GPa[62], a tension of 0.38GPa would be required to produce the 2cm -1 change in the Raman shift that is observed experimentally. This corresponds to an applied gate voltage of more than 40V[63, 64], which is one order of magnitude higher than the actual gate voltage applied in this study, and thus negligible. Furthermore, any change in Raman shift due to gate voltage induced strain would produce a monotonically decreasing change, not an abrupt M shaped change, where there is first a phonon hardening and then a softening. Second, we have not observed any changes in the radial breathing mode (RBM) anti-stokes/stokes intensity ratio, which is extremely sensitive even to small changes in the optical transition energies (i.e., Eii) due to strain[54]. Lastly, no gate-induced changes in the Raman intensity or Raman frequency have ever been observed for suspended semiconducting nanotubes, further indicating that the phenomena observed here are not due to electromechanical forces. Here, we believe that a SPT occurring near the CNP results in significant changes in the matrix elements associated with the Raman process. The exact nature of this SPT, however, is still unknown and will require further studies. As a comparison, the CNT device in Fig. 3.3 (Eg=56meV) showed no gate dependence of the Raman intensity. 53 Several possible mechanisms have been proposed to explain the band gaps observed in metallic CNTs. Early scanning tunneling microscopy (STM) studies of metallic nanotubes attributed these small energy gaps to the curvature of the nanotube[65]. The curvature- induced band gaps are given by 2 ) 3 cos( t gap d C E   , where C is 60meV· nm 2 , dt is the -6 -4 -2 0 2 4 6 0 10k 20k 30k 40k 50k 300K 2D Band Area Gate Voltage (V) -6 -4 -2 0 2 4 6 2621 2622 2623 2624 2625 2626 300K 2D Raman Shift (cm -1 ) Gate Voltage (V) -6 -4 -2 0 2 4 6 2620 2622 2624 2626 2628 2630 300K 4.5K 2D Raman Shift (cm -1 ) Gate Voltage (V) -6 -4 -2 0 2 4 6 0 5k 10k 15k 20k 300K 4.5K 2D Band Area Gate Voltage (V) Figure 3.5 – (a,b) 2D band Raman integrated area intensities and (c,d) Raman shifts for two different quasi-metallic devices (Device A and B). Device A Device A Device B Device B (a) (b) (c) (d) 54 nanotube diameter, and  is the chiral angle[51, 66]. For the range of diameters in this work, we expect band gaps of Egap≈0-50meV, which is more than 4 times smaller than the band gaps we observe. Armchair nanotubes, which theoretically should have Egap=0, have also been shown to exhibit substantial band gaps experimentally[42]. Like curvature, uniaxial strain can also result in a band gap[67, 68]; however, these types of symmetry-breaking band gaps can be closed with the application of an axial magnetic field, which was not observed experimentally in suspended CNTs[42], indicating that another underlying mechanism must be responsible for the observed band gaps. As mentioned above, the relatively large band gaps observed in ultra-clean, suspended quasi-metallic CNTs have been attributed to a Mott insulator transition arising from strong electron-electron interactions[42]. However, this mechanism has not been verified, and the exact nature of the Mott state is not known, whether it exhibits a charge density wave, spin density wave, or otherwise[69, 70]. Many authors have calculated a Peierls instability in nanotubes, as early as 1992, predicting that this transition is unlikely because of the energy sub-band structure[59, 71-74]. Both a Peierls distortion and a Mott transition would result in a large modulation of the Raman intensity through a lowering of the crystal symmetry and an increase in the effective mass m * . However, Peierls distortions have been predicted theoretically only in nanotubes with very small diameters (~0.5nm) and is not expected to occur in the relatively large diameter nanotubes grown in this study. Both transitions are extremely sensitive to slight changes in the free charge density in the system[75, 76]. A change in the lattice constants and optical transition energies with Fermi energy have been predicted by first principles calculations in metallic nanotubes near the first pair of van Hove singularities[77]. Structural stabilization 55 by a naturally occurring torsion of the nanotube has also been predicted to produce a band gap in metallic nanotubes[78]. Future studies are needed in order to establish the precise mechanism underlying the structural phase transition reported in this letter. It is likely that this modulation has not been observed until now because most previous studies of electrostatically gated carbon nanotubes were performed on nanotube-on-substrate devices rather than pristine, suspended devices. The Mott insulating state (and Peierls distortion) requires the presence of a well-defined charge neutrality point[20], which may not occur in samples with defects, substrate contact, or post-processing residue. 3.4 Conclusion In conclusion, the electrostatic doping dependence of the Raman spectra and electron transport in ultra-clean suspended carbon nanotubes show evidence for a structural phase transition. Near the charge neutrality point (CNP), effective band gaps as large as 240meV are observed in the current-gate voltage characteristics of quasi-metallic nanotubes. A pronounced dip in the 2D band is also observed at the CNP indicating a change in the lattice or electronic structure. The measured gate dependence of the G and 2D band Raman shifts and intensities deviate from non-adiabatic calculations near the CNP, indicating the existence of another mechanism affecting the phonon modes. For nanotubes with smaller quasi-metallic band gaps (~50meV), these Raman features are not observed near the charge neutrality point, indicating that the Raman and transport phenomena are related. 56 Chapter 4: Non-Ideal Diode Behavior and Band Gap Renormalization in Carbon Nanotube p-n Junctions P-N junction diodes are formed by electrostatic doping using two gate electrodes positioned beneath individual, suspended CNTs. These devices exhibit nearly ideal diode behavior within a small bias voltage range near 0 V. At higher bias (> |0.2V|), non-ideal diode behavior is observed arising from Schottky contacts formed between the nanotube and its metal contact electrodes and the presence of electron tunneling between the N- and P- doped regions. We introduce a back-to-back diode model to explain the observed current versus voltage (I-V) characteristics. The reverse saturation current, parallel resistance, and open circuit voltage dependence on gate voltage provide quantitative evidence for the theoretically predicted doping-induced band gap shrinkage in carbon nanotubes. The minority carrier lifetimes are also estimated from this model. 4.1 Introduction The ability to fabricate ultra-clean, nearly defect-free, suspended carbon nanotubes (CNTs) has enabled several interesting phenomena to be observed, including non-adiabatic behavior (i.e., breakdown of the Born-Oppenheimer approximation)[46], mode selective electron-phonon coupling (leading to negative differential resistance and non-equilibrium phonon populations)[79]gate-controllable modulation of Raman intensity[45, 80], and a 57 possible structural phase transition[42, 80]. These effects are not seen in substrate-supported nanotubes, and the elimination of substrate interactions, defects, and surface contaminants is essential to their observation[81]. While diode-like rectification has been achieved in CNT P-N junctions formed by chemical doping[82, 83], polymer coating[84], impurities[85], asymmetric contacts[86, 87], and intramolecular junctions[88], P-N junctions can also be formed by electrostatic gating[89-93] that enables doping of nanotubes without introducing defects, impurities, or surface contaminants. These imperfections can scatter electrons, increase electron-hole recombination, create sub-band gap states, and ultimately lead to non- ideal diode behavior. Several studies have focused on CNTs lying on a substrate and/or on densely-packed CNT films[84, 94, 95]. Residue from lithographic processing and imperfections induced at the nanotube-substrate interface perturb the one-dimensional conducting carbon nanotube as the electrons experience random fluctuations in potential along the tube length[81]. Electrostatically doped P-N junctions in suspended CNTs have shown ideality factors, n≈1, suggesting the near absence of charge recombination during transport [90, 93]. Current annealing has been shown to remove adsorbates, further improving the ideality factor[96]. However, most of these studies have been limited to fixed gate voltages and relatively small bias voltages across the nanotube (< |0.2V|). Many-body theory has predicted that the band gaps and exciton binding energies in semiconducting CNTs will significantly decrease with doping due to dynamic screening by acoustic plasmons[97]. This band gap reduction is approximately ten times larger than in bulk semiconductors at the same doping level (~800 58 meV for densities of ρ = 0.6 holes or electrons per nm), however, this phenomenon has up to this point gone largely unstudied. 4.2 Experimental Details In this work, we study CNT P-N junction diodes under relatively large applied bias voltages over a broad range of electrostatic doping conditions imposed by two isolated gate electrodes, as illustrated in Fig. 4.1a. A two-diode model is developed to explain the non- idealities in current vs. voltage (I-V) behavior observed at high bias. This model includes band gap renormalization which is particularly important under high electrostatic doping. I- V characteristics are also taken under illumination to further elucidate the charge-carrier dynamics at the P-N junction. Samples are fabricated by etching a 4μm-wide, 500nm-deep trench in a Si/SiO2/Si3N4 substrate, as described previously[32]. Two 1μm-wide and 35nm-thick Pt/W gate electrodes (30nm Pt/5nm W adhesion layer) separated by 2μm are deposited on the bottom of the trench, as shown schematically in Fig. 4.1a. Source and drain electrodes with the same Pt/W thicknesses are patterned lithographically on each side of the trench. The CNTs are then grown by chemical vapor deposition (CVD) at 850 °C with Fe and Mo catalysts using argon bubbled through ethanol for 10 minutes. Figure 4.1b is an SEM image of our device with a dashed line indicating where the CNT typically grows. 59 The diameters of the CNTs are typically 1.2 ± 0.1 nm. Current-annealing is performed in argon at Vbias = ±1.5V. Typical I-V transport properties are shown in Figs. 4.2a and 4.2b. We only select single suspended CNTs based on the empirical Imax rule[38] for our measurement. The I-V characteristics are taken both in the dark and under illumination using a variable output power, λ = 532 nm wavelength diode-pumped solid-state laser. The laser is focused to an approximately 0.5 μm-diameter spot, and the power of the laser spot incident on the nanotube ranged from 20 µW to 200 µW. Si/SiO2 Si3N4 Source electrode Drain electrode CNT Dual gate electrode Figure 4.1 – (a) Schematic diagram of a split-gate CNT FET device. Dual gates are separated by 2μm and CNTs are 4μm long. (b) Colorized SEM image of a split-gate CNT device. Red line indicates where CNT grows across the catalyst islands. (a) (b) Gate1 Gate2 Catalyst island 60 4.3 Results and Discussion Figures 4.3a and 4.3b show the short circuit photocurrent and open circuit photovoltage plotted as functions of the gate voltages, Vg1 and Vg2. These data were taken under  = 532 nm wavelength illumination in ambient at T = 300 K, and represent 1089 (33×33) different gate bias conditions. The four quadrants in these photo-response maps -8 -4 0 4 8 100n 1µ 10µ 100µ Conductance(S) Gate Voltage (V) 0 2 4 6 0 1 2 I SC (nA) Position( m) Data Fit Figure 4.2 – (a) Typical current-voltage (I-V) characteristics of the CNT device, with V g1 = -9 V and V g2 = +9 V, exhibiting rectifying behavior. (b) The log plot of the same data. (c) Device conductance plotted as a function of gate voltage with V g1 = V g2 and V bias =0.2V in air at T=300K, showing ambipolar behavior. (d) Spatial scan of the short circuit current taken under focused illumination along the length of the CNT device, fitted to a Gaussian curve. (a) (c) (d) (b) -0.2 -0.1 0.0 0.1 0.2 0.0 20.0n 40.0n 60.0n Current(A) Bias Voltage (V) Data Fit -0.2 -0.1 0.0 0.1 0.2 1E-11 1E-10 1E-9 1E-8 1E-7 Current(A) Bias Voltage (V) Fit Data 61 correspond to P-N, N-P, P-P, and N-N regions, as indicated in Fig. 4.3a. In the P-N and N- P regions, the photocurrents and photovoltages are typical of conventional P-N junction behavior in semiconductor devices. In the P-doped quadrant, however, large photocurrents are observed when one of the gates is at zero bias. Interestingly, we see no corresponding photovoltage in this region. As discussed below, photocurrent generated in this region is observed in all three devices studied, and is due to the Schottky contact formed between the CNT and the Pt electrode[98]. Figure 4.4a shows the dark I-V characteristics of the device taken at Vg1 = -4 V and Vg2 = 4 V. Non-ideal diode behavior can be seen at >0.2V. To understand the device behavior, the band diagram in Fig. 4.4b is modeled by assuming the existence of two back- -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8 V g1 (V) V g2 (V) -2.10E-9 -1.12E-9 -1.40E-10 8.40E-10 1.82E-9 2.80E-9 Current unit: A -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8 V g1 (V) V g2 (V) -6.50E-2 -4.43E-2 -2.37E-2 -3.00E-3 1.77E-2 3.83E-2 5.90E-2 7.97E-2 9.00E-2 Voltage unit : V Figure 4.3 - (a) Short circuit photocurrent and (b) open circuit photovoltage plotted as functions of the gate voltages V g1 and V g2 , taken under ambient conditions at T=300K for device D1. Values in the color bars are given in units of (a) amps, and (b) volts. (a) (b) N-doped P-doped N-P P-N 62 to-back diodes shown by the accompanying equivalent circuit. Here, diode 1 corresponds to the Pt-contact Schottky barrier diode, whereas diode 2 represents the electrostatically doped P-N junction. These two diodes have different turn-on voltages under forward bias, thereby limiting the current at high voltage. Under uniformly P-doped gating conditions (Vg1 = Vg2 = -4 V) shown in Fig. 4.5b, the device exhibits ohmic behavior. However, under uniformly N-doped conditions (Vg1 = Vg2 = 4 V) in Fig. 4.5a, the I-V characteristics suggest a back-to-back diode behavior. Since the nanotube is uniformly electrostatically doped when the gate voltages are equal, there is no formation of an internal junction, and hence both of the series-connected diodes result from contact rectification. Hence, the P-doped metal-CNT junction produces an ohmic contact whereas the N-doped junction results in a high energy barrier Schottky contact, as depicted in Figure 4.4b. 63 To understand the device behavior, we assume a model comprising two back-to-back diodes, as illustrated in the band diagram of Fig. 4.4b. Our approach is similar to previous study of semiconductor, which includes two Schottky barriers connected back to back and a series resistor in between these barriers[99]. Here, the diode labeled “con” corresponds to the Pt-contact Schottky barrier diode, and “cnt” represents the electrostatically doped P-N junction. These two diodes have different turn-on voltages under forward bias, thereby limiting the current at high voltage. We represent the tunneling current in the device with a pair of shunt resistances, R P con and R P cnt . Thus, the current through the device can be written as: -0.4 -0.2 0.0 0.2 0.4 0 1 2 3 4 Data Fit Current (nA) Bias Voltage (V) V g1 =-4V, V g2 =4V High current roll-off Figure 4.4 - (a) Typical I-V characteristic of an electrostatically doped P-N junction CNT showing non-ideal behavior at high currents corresponding to V DS > 0.2V. (b) Equilibrium diode band diagram where the gate voltages are V g1 > 0V and V g2 < 0V, and device equivalent circuit represented by two diodes in opposite directions. Here, E F is the Fermi energy and R P1 and R P2 are the shunt resistances of the Schottky and P-N junctions, respectively. (b) (a) 64 I = I 0 con (exp( -qV con kT ) -1)+ ( V con R P con ) = I 0 cnt (exp( qV cnt kT ) -1)- ( V cnt R P cnt ), where V con and V cnt are the voltages dropped across the reverse- and forward-biased diodes, respectively, and 𝐼 0 𝑐𝑜𝑛 and 𝐼 0 𝑐𝑛𝑡 are their respective reverse saturation currents. Hence, the total voltage is 𝑉 = 𝑉 𝑐𝑜𝑛 + 𝑉 𝑐𝑛𝑡 . We solve eq. 4.1 for V, to obtain: V=I( R P con +R P cnt ) +I 0 con R P con -V th ∙W ( I 0 con R P con V th exp ( (I+ I 0 con ) R P con V th ))- I 0 con R P cnt +V th ∙W ( I 0 cnt R P cnt V th exp ( (I+ I 0 cnt ) R P cnt V th )) The thermal voltage is 𝑉 𝑡 ℎ = kT/q, where k is Boltzmann’s constant, T is the temperature, q is the electron charge, and W is the Lambert W-function[100, 101] defined as the solution to y = x𝑒 𝑥 . The W-function is introduced to allow for exact analytical solutions of eq. 4.2. Typical values for 𝐼 0 and 𝑅 𝑃 are 0.5 nA and 0.7 GΩ, respectively. Table 4.1 has a complete list of values. The ideality factors (n1 and n2) do not have a significant effect on the fits, and therefore n1,2= 1 in all cases. Figure 4.5 shows the I-V characteristics of the device in Fig. 4.3 taken under several different gating conditions resulting in N-P, P-N, N-N, and P-P configurations. These data exhibit a wide range of behaviors, all of which can be fit using eq. 4.2, as shown by the red solid lines in the figure. (4.1) (4.2) 65 -0.2 -0.1 0.0 0.1 0.2 -3 -2 -1 0 1 V g1 = 8V, V g2 = -8V Current(nA) V DS (V) -0.2 -0.1 0.0 0.1 0.2 -1.0 -0.5 0.0 V g1 = 5V, V g2 = -5V Current(nA) V DS (V) -0.2 -0.1 0.0 0.1 0.2 -0.3 -0.2 -0.1 0.0 0.1 0.2 V g1 = 2V, V g2 = -2V Current(nA) V DS (V) -0.2 -0.1 0.0 0.1 0.2 -0.2 0.0 0.2 0.4 V g1 = -2V, V g2 = 2V Current(nA) V DS (V) -0.2 -0.1 0.0 0.1 0.2 -0.5 0.0 0.5 1.0 1.5 2.0 Current(nA) V DS (V) V g1 = -5V, V g2 = 5V -0.2 -0.1 0.0 0.1 0.2 0 2 4 6 8 Current(nA) V DS (V) V g1 = -8V, V g2 = 8V -0.4 -0.2 0.0 0.2 0.4 -1 0 1 V g1 = 4V, V g2 = 4V Current(nA) V DS (V) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 -1000 0 1000 V g1 = -4V, V g2 = -4V Current(nA) V DS (V) Figure 4.5 - I-V characteristics and fitting results of device D1 at various gate voltages V g1 , V g2 . The first row (a-b) shows I-V characteristics under uniformly N-doped and P-doped conditions, the second row (c- e) shows I-V characteristics in the P-N configuration, and the last row (f-h) shows I-V taken in the N-P configuration. The black dots are data points and red lines are fits. a b c d e f g h 66 Vg1/Vg2(V) I01(A) I02(A) RP1 (Ω) RP2 (Ω) VOC(V) ISC(A) (-8,8) 2.34E-10 1.70E-09 1.52E+09 1.85E+07 4.70E-02 -1.25E-09 (-7,7) 2.09E-10 1.48E-09 1.62E+09 4.02E+07 5.30E-02 -1.46E-09 (-6,6) 1.71E-10 1.49E-09 1.62E+09 7.46E+07 6.10E-02 -1.80E-09 (-5,5) 1.41E-10 1.31E-09 1.55E+09 2.04E+08 0.068 -2E-09 (-4,4) 1.25E-10 9.97E-10 1.65E+09 3.21E+08 0.075 -2.2E-09 (-3,3) 1.06E-10 6.37E-10 1.83E+09 4.83E+08 0.081 -2.2E-09 (-2,2) 8.58E-11 2.73E-10 1.87E+09 1.08E+09 0.083 -1.7E-09 (-1,1) 9.22E-11 1.2E-10 2.29E+09 1.77E+09 0.068 -1.1E-09 (1,-1) 1.03E-10 7.96E-11 1.55E+09 1.82E+09 -0.071 8.88E-10 (2,-2) 1.72E-10 9.02E-11 1.29E+09 1.73E+09 -0.078 1.29E-09 (3,-3) 3.46E-10 1.12E-10 1.01E+09 1.52E+09 -0.073 1.46E-09 (4,-4) 5.77E-10 1.29E-10 8.98E+08 1.42E+09 -0.068 1.56E-09 (5,-5) 7.8E-10 1.47E-10 8.51E+08 1.35E+09 -0.064 1.55E-09 (6,-6) 9.58E-10 1.7E-10 8.49E+08 1.26E+09 -0.059 1.51E-09 (7,-7) 1.15E-09 1.75E-10 5.21E+08 7.48E+08 -0.056 1.48E-09 (8,-8) 1.35E-09 2.16E-10 88959419 4.41E+08 -0.049 1.15E-09 Figure 4.6 shows the reverse saturation currents (𝐼 0 𝑐𝑜𝑛 and 𝐼 0 𝑐𝑛𝑡 ) and equivalent tunneling resistances ( R P ) plotted vs. gate voltage for the Schottky and P-N diodes, Table 4.1 - Open circuit voltage (V OC ), short circuit current (I SC ) observed under illumination with a 532 nm wavelength laser, and fitting parameters for the dark I-V characteristics taken at various split-gate voltages. V g1 /V g2 are the gate voltages; 1 refers to the Schottky diode and 2 refers to the P-N diode; I 01 and I 02 are the reverse saturation currents from diode 1 and diode 2, respectively; R P1 and R P2 are the parallel shunt resistances from diode 1 and diode 2, respectively. 67 respectively. Here, RP, decreases exponentially with the square root of the gate voltage, and hence band gap, as shown in Fig. 4.6b. Interestingly, the reverse saturation current increases with doping, which is the opposite of expectations for conventional diffusion-limited diodes[102]. This is due to band gap renormalization (BGR), which results in a decrease in band gap with increased doping due to dynamical screening mediated by acoustic plasmons[97]. This effect is considerably stronger in CNTs than in conventional semiconductors due to the 1D confinement of carriers. To relate the reverse saturation current to doping, we start with the CNT conduction band density of states[93, 103]: -0.4 -0.2 0.0 0.2 0.4 p-n diode Contact diode Doping Concentration (Dopants/nm) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 -0.4 -0.2 0.0 0.2 0.4 p-n diode Contact diode Doping Concentration (Dopants/nm) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 I 0 (nA) Figure 4.6 - Dependence of (a) the reverse saturation currents (V g1 = -V g2 ) and (b) the parallel resistance on doping for device D2. Error bars were extracted from the data of device D1. (a) (b) 68 D(E, E c ) = D 0 E E 2 - E c 2 , E > E c where Ec is the energy of the conduction band minimum and D0 is the effective density of states at the conduction band minimum. From the density of states, we calculate the minority carrier density in the doped regions[104]: 𝑛 𝑝 = 𝐷 0 𝑒 − 𝐸 𝑎 𝑘𝑇 ∫ 𝐸 +𝐸 𝑐 √𝐸 2 +2𝐸 𝑐 𝐸 ∞ 0 𝑒 − 𝐸 𝑘𝑇 𝑑𝐸 , where Ea is equal to the energy difference between the conduction band minimum and the Fermi energy in the P-doped region (Ec - EF,p). The integral is solved for a conduction band minimum energy of 300meV. The reverse saturation current is expressed as[105]: 𝐼 0 = 𝑞 𝐷 𝑖𝑓𝑓 ( 𝑛 𝑝 + 𝑝 𝑛 ) / √ 𝐷 𝑖𝑓𝑓 𝜏 , where Diff is the diffusion coefficient and τ is the minority carrier lifetime. Substituting eq. 4.4 into eq. 4.5 gives: 𝐼 0 = ( 0.12 𝑒𝑉 ) 𝐷 0 𝑞 √ 𝐷 𝑖𝑓𝑓 𝜏 𝑒 − 𝐸 𝑎 𝑘𝑇 . where the factor of 0.12 eV is obtained from the numerical solution of eq. 4.4. By measuring the temperature dependence of I0, it is possible to extract both Ea and τ. The diffusion coefficient Diff is calculated from the Einstein relation using a mobility of 2 × 10 4 cm 2 /V·s.[106] We find that τ = 0.10 ± 0.02 ns, assuming that Diff, D0, and τ are doping- independent. This value is similar to recent observations of time-resolved (4.3) (4.4) (4.5) (4.6) 69 photoluminescence.[107] Here, Ea is doping-dependent and spans a range from 0.25 – 0.18eV, as shown in Fig. 4.7. Spataru and Leonard used many-body simulations to understand the shift in band gap due to BGR, determining that the change of the band gap, ΔEgap, ∝ √𝜌 [108]. Assuming that the change in Ea is proportional to the BGR, we can write gap a a E A E E    0 , where 0 a E is the activation energy in the undoped nanotube and A is a fitting parameter. For a Fermi level in the middle of the band gap in the undoped nanotube, 0 a E = ½ Egap, yielding:  B E E gap a   2 , (4.7) 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 0.05 0.10 0.15 0.20 0.25 Activation Energy (eV) Doping Concentration (Dopants/nm) Figure 4.7 - Relationship between E a and doping, fit (line) to a square-root dependence on the doping. This gives a band gap of 600 ± 40 meV, with error given by the shaded region. 70 where B is a fitting parameter and ρ is calculated from the capacitance between the nanotube and the gate electrodes. Approximating the CNT as an infinite conducting cylinder over a conducting plane, we obtain  = 0.05 dopants/nm∙V, which is comparable to previous reports[109]. Using our values for Ea, we find the nanotubes have a zero-bias band gap of approximately 600meV. The temperature-dependent data (Fig. 4.8) exhibit characteristics similar to that of two back-to-back P-N diodes, rather than one P-N diode and one Schottky diode. This is likely due to local doping of the CNT by the metallic contact causing the formation of a second, internal P-N junction instead of a standard Schottky contact, labeled as contact diode in Fig. 4.4b. This phenomenon has been previously observed in spatially resolved photocurrent measurements[110]. Other devices measured in this study showed a more pronounced asymmetry between the two diodes, with one exhibiting typical P-N rectifying characteristics, and the other showing a minimal change with temperature, characteristic of a tunneling Schottky contact, as shown in Fig. 4.9. 71 -8 -4 0 4 8 1E-10 1E-9 300K 320K 340K 360K I 0 (A) V g1 ,-V g2 (V) -8 -4 0 4 8 1E-10 1E-9 300K 320K 340K 360K I 0 (A) V g1 ,-V g2 (V) -8 -4 0 4 8 1E-10 1E-9 CNT p-n diode Contact diode I 0 (A) V g1 ,-V g2 (V) Figure 4.8 - Dependence of the reverse saturation current on gate voltage (V g1 = -V g2 ) at various temperatures. Both diodes show similar temperature dependence, suggesting two P-N diodes existing in the device. Figure 4.9 - Dependence of the reverse saturation current on doping for a different device showing a more pronounced asymmetry between the two diodes. (a) (b) 72 4.4 Conclusion In conclusion, we have found that suspended carbon nanotube P-N junction diodes exhibit nearly ideal behavior for small bias voltages. At higher bias, the metal-semiconductor contacts limit current injection, resulting in a back-to-back diode characteristic with the P- doped side having an ohmic contact and the N-doped side having a Schottky contact with the underlying Pt electrodes. The parallel tunneling resistance also significantly influences current at high bias. Our model of the doping dependence of the reverse saturation current, parallel resistance, and open circuit voltage provide evidence for the theoretically predicted band gap renormalization by dynamic screening by acoustic plasmons in carbon nanotubes. 73 Chapter 5: Photocurrent Spectroscopy of Exciton and Free Particle Optical Transitions in Suspended Carbon Nanotube pn- Junctions We study photocurrent generation in individual, suspended carbon nanotube pn- junction diodes formed by electrostatic doping using two gate electrodes. Photocurrent spectra collected under various electrostatic doping concentrations reveal distinctive behaviors for free particle optical transitions and excitonic transitions. In particular, the photocurrent generated by excitonic transitions exhibits a strong gate doping dependence, while that of the free particle transitions are gate independent. Here, the built-in potential of the pn-junction is required to separate the strongly bound electron-hole pairs of the excitons, while free particle excitations do not require this field-assisted charge separation. We observe a sharp, well defined E11 free particle interband transition in contrast with previous photocurrent studies. Several steps are taken to ensure that the active charge separating region of these pn-junctions is suspended off the substrate in a suspended region that is substantially longer than the exciton diffusion length and, therefore, the photocurrent does not originate from a Schottky junction. The photocurrent spectra of these individual nanotube pn-junctions exhibit many peaks that are not seen in photoluminescence spectra or Rayleigh spectra, which we believe correspond to dark exciton and/or localized exciton states. While dark exciton transitions are typically forbidden in most optical processes because of symmetry considerations, they can be observed readily in these pn-junction devices where the symmetry is broken by the built-in field of the junction. 74 5.1 Introduction The presence of strong Coulomb interactions have made exciton formation the dominant mechanism of optical absorption in carbon nanotubes (CNTs), rather than the formation of free electron-hole pairs. Theory has predicted exciton binding energies of 300- 400meV for CNTs with diameters on the order of 1nm.[111] These uniquely large exciton binding energies are due to the strong spatial confinement of the 1D structure of CNTs, which result in interesting photophysics that is quite different from most known bulk materials.[112-116] Weisman and coworkers reported the first experimental study of excitons in CNTs in 2002 with the observation of photoluminescence (PL) from micelle encapsulate nanotubes using chemical surfactants.[112, 117-119] It is interesting to note that photoluminescence was not observed in CNTs until 11 years after their discovery[6] because of their high surface-to-volume ratio, which makes them extremely sensitive to their environment. From these first photoluminescence spectra, it became clear that the single particle picture was not accurate in nanotubes and that excitonic effects were substantial even at room temperature. More recent studies have established the exciton diffusion length of air suspended carbon nanotubes to lie between 300-600nm with a diffusion coefficient of D=44cm 2 /s and lifetime of 85psec.[3, 120] In 2007, Lee and coworkers measured the photocurrent spectra of a suspended CNT pn-junction device consisting of carbon nanotubes grown over two gate electrodes buried under a dielectric oxide separated by a small trench 0.5µm wide[121, 122]. Later in 2011, Lee’s group measured a series of bright exciton peaks through photocurrent spectroscopy[109] and calculated the quantum efficiency and capture cross section of the excitonic transitions of these pn-junction devices[123]. Minot’s group 75 were able to identify chiralities through photocurrent spectra using suspended CNT devices with single gate. Zwiller’s group in 2012 demonstrated the polarization dependence of the dual-gate suspended CNT p-n devices[124]. Later in 2014 they separated two different mechanisms for the photocurrent generation process. The photothermal effect dominates in metallic CNTs while the photovoltaic effect dominates in semiconductor CNTs[125]. On the contrary to Zwiller’s theory, Steele’s group argued that photothermal effect also plays a role in semiconductor CNTs and is doping dependent[126]. Despite these previous studies, there have been no reports to date on the gate dependence of exciton and free carrier peaks in the photocurrent spectra of an individual suspended CNT pn-junction devices. Furthermore, we have taken the photocurrent spectra in a more extended continuous range than before. In the work presented here, we measure the photocurrent spectra of individual suspended CNTs as a function of the magnitude of the pn-junction gate voltage applied (i.e., Vg1=-Vg2). From over 100 devices fabricated and 20 devices measured, only individual, suspended CNTs that exhibit rectifying behavior that is not dominated by Schottky contacts are selected for further study. This is particularly difficult to achieve because of the high Schottky barriers for electrons at the Pt contacts, which tend to dope the entire nanotube p- type under all gating conditions. Several steps are taken to ensure that the active charge separation region of these pn-junctions is suspended off the substrate in a region away from the contacts, including reversible rectifying I-V curves (i.e., pn and np configurations) and spatial mapping of the photocurrent, as described below. By studying the gate voltage dependence of photocurrent spectra of an individual nanotubes, we are able to distinguish exciton from free particle excitations. 76 5.2 Experimental Details CNT samples are fabricated by etching a 4μm wide, 500nm deep trench in a Si/SiO2/Si3N4 substrate, as described previously[127][32]. Two 1μm-wide Pt gate electrodes separated by 2μm are deposited on the bottom of the trench, as shown in Figures 5.1a and 5.1b. The CNTs are grown using chemical vapor deposition (CVD) at 850 °C with Fe and Mo catalysts and ethanol as the carbon feedstock. High bias transport measurements are taken with Vg1=Vg2 in an argon environment to determine whether the device is suspended, which is indicated by a region of negative differential conductance (NDC).[38] The value of the maximum current enables us to determine if the device is a single isolated CNT or a bundle, as established by Pop et al.[38] Individual suspended CNTs that pass these selection criteria are selected and wire-bonded for further characterization. Current annealing is performed in argon at a bias voltage of ±1.4V in order to remove any surface contaminants, which cause electron–hole recombination, before photocurrent spectra are taken. It should be noted that current annealing greatly improved the photocurrent spectra of these devices. Scanning electron microscope (SEM) images are taken after all photocurrent measurements were completed to avoid amorphous carbon deposition by the electron beam. Photocurrent spectra are collected by illuminating our devices with a Fianium supercontinuum white light laser used in conjunction with a double monochromater to produce monochromatic light over the 450-1600nm wavelength range (0.78-2.76eV). In order to improve the signal-to- noise ratio, data were taken using a chopper and a lock-in amplifier. All measurements were taken at room temperature. As a comparison, photocurrent spectra taken from devices dominated by the Schottky contact exhibited no gate dependence, as shown in Figure 5.2. 77 p n E g SiO 2 Pt Si SiN x Figure 5.1 - (a) Schematic diagram illustrating the device structure of our CNT pn-junction devices. (b) SEM image of our device showing a single suspended CNT across the trench. (c) Spatial map of the photocurrent plotted along the length of nanotube from the source to the drain electrode showing the peak photocurrent is in the center of the suspended region away from the contacts. (a) CNT Laser Spot (b) (c) 0 2 4 6 0.0 0.5 1.0 1.5 Photocurrent (nA) Position ( m) Data Fit Trench 1µm 78 Under pn-gating conditions (i.e., Vg1=-Vg2=+9V), we observe rectifying behavior in the forward bias direction, as shown in Figure 5.3a. When the gate voltages are reversed (i.e., Vg1=-Vg2=-9V), we observe rectifying behavior in the reverse bias direction, as shown in Figure 5.3b. The ideality factor of our device is around 1.3, contact resistance is around 300kOhm, and built-in potential is about 0.7V. The reversibility of the rectifying behavior (i.e., achieving pn and np) is important in establishing that the rectifying behavior does not originate from a Schottky contact between the nanotube and the underlying metal contacts, as was the case in a vast majority of our devices, particularly for shorter devices. In order to further establish that the pn-junction is located away from the contacts in the suspended Figure 5.2 – Photocurrent spectra taken from individual suspended carbon nanotubes under various electrostatic gating conditions for (a) a single-gate device with the laser focused on the metal contact and (b) a dual gate device that did not exhibit reversible rectifying behavior. Neither device shows a gate dependence of the photocurrent peaks indicating that there is no control over the charge separating fields in devices dominated by a Schottky contacts. 1.6 1.8 2.0 2.2 2.4 2.6 0 10 20 30 40 50 Photocurrent (nA) Photon Energy (eV) V g =3V V g =6V V g =9V V g =12V (a) 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 0 50 100 150 200 250 300 Photocurrent (pA) Photon Energy(eV) 9V/-9V 7V/-7V 5V/-5V (b) 79 region of the nanotube, we spatially mapped the photocurrent along the length of the nanotube, as shown in Figure 5.1c. Here, the maximum photocurrent clearly originates from the center of the CNT, rather than at the two Schottky contacts at the ends of the nanotube, as in previous studies.[128-132] 5.3 Results and Discussion Figures 5.4a and 5.4b show the photocurrent spectra taken from two different CNT devices (Device 1 and 2) under various pn-gating conditions with Vg1=-Vg2. By increasing the gate voltage, we increase the doping concentrations in the p- and n-regions of the CNT, and hence we increase the built-in field at the pn-interface. Both Devices 1 and 2 show peaks corresponding to a bright E11 exciton peak and an E11 free carrier band, approximately 0.4eV Figure 5.3 - Current-voltage characteristics of our CNT pn-junction devices with (a) pn and (b) np doping configurations. These devices exhibit rectifying behaviors, which flips polarity as the gate doping is changed from pn to np configurations. (b) (a) -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0 10 20 30 Current (nA) Bias Voltage (V) 9V/-9V -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 -100 -50 0 50 Current (nA) Bias Voltage (V) -9V/9V 80 higher in energy. From these spectra, we estimate the exciton binding energy to be 400meV for Device 1 and 360meV for Device 2, which agrees with previous reports in the literature.[111] The E11 exciton peak intensities exhibit a strong gate dependence, while the E11 free carrier peaks do not. Figure 5.4c shows the gate voltage dependence of these peak intensities for the two devices, which exhibit a clear gate dependence for the exciton peaks and gate independence for the free carrier peaks. Figure 5.5 illustrates the basic mechanism of photocurrent generation in these CNT pn-junctions. When photons are absorbed, they excite electron-hole pairs and excitons. In order to produce a photocurrent, the strongly bound excitons have to be separated by the built-in potential of the junction (Vbi). This built-in potential is given by the band offsets between the p- and n-regions, which is determined by the applied gate voltages. Excitons can also recombine before the electrons and holes are separated, which do not produce a photocurrent. This exciton dissociation process depends strongly on the built-in potential for all excitonic states. The energy of the bound electrons (holes) lie below (above) the conduction (valence) band edge, therefore requiring additional energy to push them up (down) into the free particle bands, enabling them to contribute to the measured photocurrent. This is accomplished by the built-in field of the pn-junction.[132] It is for this reason that we observe an increase in the exciton photocurrent as we increase the pn-doping concentration. For free particle excitation, on the other hand, photo-induced carriers can produce a photocurrent without a large built-in field. Therefore, we see no gate dependence associated with the free-carrier photocurrent peak. This gate-dependence effect might look similar to what has been observed before[132]. However, the mechanism behind those are 81 different. Ref. 132 attributed the gate-dependence effect to Fowler-Nordheim tunneling of electrons, while in our system the gate-dependence is due to the charge separation by the built-in field in the p-n junction. 82 Figure 5.4 - Photocurrent spectra taken from individual carbon nanotubes under various pn-gating conditions (i.e., V g1 =-V g2 ) for (a) Device 1 and (b) Device 2. (c) Photocurrent peak intensities of the E 11 exciton and E 11 free carrier band plotted as a function of gate voltages. Hollow shapes are from Device 1 and filled shapes are from Device 2. 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Photocurrent Energy (eV) 8V/-8V 6V/-6V 4V/-4V 2V/-2V Free carrier peak Exciton peak (a) 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Photocurrent Energy (eV) 9V/-9V 7V/-7V 5V/-5V Exciton peak Free carrier peak (b) 2 4 6 8 E 11 exciton (Device 1) E 11 free carrier (Device 1) Photocurrent Peak Intensity Gate Voltage (V g1 = -V g2 ) (V) E 11 exciton (Device 2) E 11 free carrier (Device 2) (c) Phonon side band E22 Phonon side band 83 One of the distinctive features in our spectra (e.g., Figure 5.4a) that should be pointed out is the sharp van Hove singularity observed at the free particle band edge. While this is consistent with theoretical predictions, previous experimental studies showed only a very small free particle photocurrent that increased monotonically with photon energy. In these previous reports, all peaks in the photocurrent spectra were assigned to excitonic transitions and their phonon sidebands. The gate-dependent results shown here, however, indicate that these previous peak assignments may, in fact, be incorrect. Figure 5.6 shows photocurrent peaks around the second and third optical transition (E22 and E33) in the CNT pn-devices under various electrostatic gate doping conditions. Essentially all of these higher energy peaks exhibit strong pn-gate dependences, reflecting their bound exciton nature. Here, we observe multiple photocurrent peaks, which we attribute to bright excitons, possibly dark excitons, and localized excitons, which were not observed in previous studies. Even the small side peak at 1.35eV in Figure 5.4a shows a Figure 5.5 – Schematic diagram illustrating the photocurrent generation mechanisms for exciton and free particle transitions. p n E F E C E V V bi E ex E fp - + + - photon 84 strong gate dependence and likely corresponds to a dark exciton state. Bright excitons have s-symmetry and can absorb and emit light readily, whereas dark excitons have p-symmetry and can only be produced by two-photon processes under normal conditions. In the pn- junction, however, the symmetry is broken allowing dark excitons be observed in these devices. We believe that the main reason these features were not resolved in previous studies is that the shorter suspended lengths and, more importantly, that the active charge separating region was not entirely suspended off the substrate. The non-suspended regions provide recombination centers which quench these excitons, before the charge can be separated. 5.4 Conclusion In conclusion, the photocurrent spectra of individual, suspended carbon nanotube pn- junctions show distinctive behavior for free particle optical transitions and excitonic Figure 5.6 – Photocurrent spectra taken from individual carbon nanotubes under various pn-gating conditions (i.e., V g1 =-V g2 ) in the E 22 and E 33 energy range. 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Photocurrent Energy (eV) -2V/2V -6V/6V -8V/8V 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Photocurrent Energy (eV) -8V/8V -6V/6V -4V/4V -2V/2V E33 85 transitions. The photocurrent generated by excitonic transitions is strongly dependent on the magnitude of the pn-doping, while the free particle photocurrent is gate independent. Here, the built-in potential of the pn-junction is required to separate the strongly bound electron- hole pairs of the excitons, while free particle excitations do not require field assisted charge separation. We find that this field-assisted exciton dissociation mechanism is observed for all other higher energy transitions beyond the E11 ground state exciton and free particle band. The photocurrent spectra of these individual nanotubes exhibit many peaks that are not seen in previous spectra and correspond to dark exciton states that are observable due to the long and suspended nature of our devices, which ensures that the charge separation occurs in the suspended region of the devices rather than at a Schottky contact. 86 Chapter 6: Thermoacoustic Transduction in Individual Suspended Carbon Nanotubes We report an experimental measurement of the acoustic signal emitted from an individual suspended carbon nanotube (CNT) approximate 2µm in length, 1nm in diameter, and 10 -21 kg in mass. This system represents the smallest thermoacoustic system studied to date. By applying an AC voltage of 1.4V at 8 kHz to the suspended CNT, we are able to detect the acoustic signal using a commercial microphone. The acoustic power detected is found to span a range from 0.1 to 2.4 attoWatts or 0.2 to 1 µPa of sound pressure. This corresponds to thermoacoustic efficiencies ranging from 0.007 to 0.6 Pa/W for the seven devices were measured in this study. Here, the small lateral dimensions of these devices cause large heat losses due to thermal conduction, which result in the relatively small observed thermoacoustic efficiencies. 6.1 Introduction Most loudspeakers used today consist of an electromagnetic coil whose basic principle of operation dates back to 1924 invented by Rice and Kellogg[133]. These coils are bulky and cannot be integrated with standard silicon CMOS fabrication techniques. The first CMOS-MEMS microspeaker was developed in 2002 by Gabriel and coworkers[134]. CMOS-MEMS micromachining techniques have enabled the integration of hundreds to 87 thousands of microspeakers on a single chip together with sound optimization electronics. These CMOS-MEMS microspeakers typically have problems caused by nonlinearities, which can be controlled through membrane geometry design and tailoring of the material properties. More recently, an electrostatic graphene speaker consisting of multilayer graphene 7 mm in diameter was demonstrated by Zhou et al. and others[135, 136]. The first fundamental work characterizing thermoacoustic transduction was performed by Arnold and Crandall at the Western Electric Company labs in 1917[137]. Their work focused on sound production via thermoacoustic transduction from a 700 nm thick Pt film, which they called the “Thermophone”. They found that when an AC current is passed through a thin conductor, periodic heating at the surface causes periodic thermal expansion in the surrounding medium, which creates acoustic waves that propagate away from the surface. Acoustic emission was also reported in single 5 cm 2 filaments made of carbon/polycarbonate[138]. More recently, Xiao et al.[139] and others[140-143] have demonstrated intense thermoacoustic energy conversion using carbon nanotube (CNT) films. Thermoacoustic transduction has also been demonstrated in other thin-film structures, such as mesh-films of silver nanowires[144] and graphene[145-147], and there are several recent patents in this area[148-150] indicating commercial interest in the application of this technology. While several micro- and nano-scale systems have been studied, as described above, the minimum length scale of an object that can emit sound audible with standard macroscopic sensors, has not been established. Individual carbon nanotubes (CNTs) represent one of the smallest possible conductors with electrical, mechanical, and thermal properties that exceed most known bulk materials. Two particularly unique physical 88 properties of CNTs are their extremely low heat capacity compared to that of other conductors and their high surface to volume ratio[151]. The combination of these two properties makes single-walled CNTs especially effective for thermoacoustic transduction. Here, we report the first observation of thermoacoustic transduction from an individual molecule (1nm in diameter), which is four orders of magnitude smaller than any previous thermoacoustic system studied, reducing the CNT-based thermoacoustic loudspeaker to its smallest fundamental element, a single CNT. This work tests assumptions made in previous models used to describe 2D thermoacoustic films. We correlate the thermoacoustic efficiencies of these nanotube devices with their electrical impedance in order to understand loss mechanisms. 6.2 Experimental Details Suspended CNTs are grown by chemical vapor deposition (CVD) on pre-patterned wafers using ferric nitrate catalyst at 825°C as reported previously[32, 152, 153]. Before growth, platinum source and drain electrodes are patterned on a Si/SiO2/Si3N4 wafer, together with a gate electrode in a 800 nm deep, 2-5 μm wide trench etched into the wafer[54]. The resulting field effect transistor (FET) device geometry is illustrated in Figure 6.1a. The nanotube growth is the final step in this sample fabrication process, which ensures that these nanotubes are not contaminated by any chemical residues from the lithographic fabrication processes. Figure 6.1b shows a scanning electron microscope (SEM) image of one of our CNT devices. The devices are then probed and wire-bonded to a 14-pin chip mount. Mounted chips are placed inside a home built hemi-anechoic chamber, as shown in 89 Figure 6.2a. A nitrogen gas environment is used to purge the anechoic chamber (1 atm) to avoid oxidization of the CNT in air. An ultra-low noise RØ DE NT1-A cardioid microphone was placed 12 mm directly above the chip. The output of the microphone was directly connected to a Stanford Research SR830 DSP lock-in amplifier via BNC cable. First, the lock-in time constant was set to 300 ms to allow for quick decay of the residual noise in the microphone. Next, the time constant was increased to 10 s and an AC bias voltage between 1.2 Vrms-2.4 Vrms was applied across the source and drain electrodes of the CNT device at a driving frequency of 8 kHz. Based on our previous work using Raman spectroscopy, we expect these suspended CNTs to reach temperatures of >1000K under these large applied bias voltages[32, 154, 155]. The second harmonic of the driving frequency was set as the reference frequency for the input signal to the lock-in amplifier (i.e, 16 kHz), since the frequency doubles due to the fact that the CNT heats up twice per cycle during thermoacoustic transduction (P=I 2 R). Negative DC gate voltages (Vg=-4V) were applied in order to minimize the contact and CNT resistance. Figure 6.2b shows the typical electron transport characteristics of our CNT devices. The saturation of the current at high bias indicates heating in the device, as studied previously[38, 44, 156, 157]. The inset shows the current-gate voltage characteristics with a charge neutrality point at 0.5 V. A total of seven devices, including both semiconducting and quasi-metallic nanotubes were found to have measurable thermoacoustic signals. 90 (b) Figure 6.1 - (a) Schematic diagram of our device geometry, which contains a source, a drain, and a gate electrode. (b) SEM image showing one of our individual suspended carbon nanotube devices. (a) 91 Rode NT1-A 28 pin mount Grounded SMB – BNC cables to control Figure 6.2 - (a) Picture of the experimental setup inside the hemi-anechoic chamber. (b) Current-bias voltage characteristics, and the inset shows current-gate voltage characteristics, of one of our individual suspended CNT FET devices. 0.0 0.5 1.0 1.5 2.0 0.0 500.0n 1.0µ 1.5µ 2.0µ Current (A) Bias Voltage (V) -4 -2 0 2 4 0 200n 400n 600n 800n Current (A) V gate (V) (a) (b) 92 6.3 Results and Discussion Figure 6.3a shows the AC voltage detected in the microphone (at 16 kHz) plotted as a function of time. A clear increase from a baseline of 2 nV to 25 nV is seen after the AC input signal (1.4 Vrms) is applied to the CNT. The sensitivity of our microphone is 32mV/Pa. From this value, we can convert the detected voltage of 2 3nV to a sound pressure level of - 28 dB. The acoustic power P is represented as: 𝑃 = 𝐴 𝑝 2 𝑍 , where A is the total area the sound waves spread out to at the distance measured, p is the sound pressure detected, and Z is the acoustic impedance of nitrogen gas (Z=406N· s/m 3 at 300K). From here, we can calculate the acoustic power corresponding to the 23 nV detected in the microphone to a sound power of 1.3 aW (1.3 x 10 -18 W). The same measurement was repeated on seven different devices. Figure 6.3b shows the output acoustic pressure plotted as a function of the input power for four different devices. They all exhibit linear relationships between the input and output power, as expected. (6.1) 93 0 10 20 30 40 50 60 0.0 0.5 1.0 1.5 2.0 2.5 C1011 C1043 C1042 C1039 P out (aW) P in ( W) 100 150 200 250 300 0 5n 10n 15n 20n 25n 30n Voltage (V) Time (sec) Power Off Power On Signal On Figure 6.3 - (a) Voltage detected by the microphone when an input AC voltage is applied to the CNT device. The black line represents the baseline signal when there is no input voltage applied. (b) The measured acoustic pressure plotted as a function of the electrical input power for several different devices, which all show a linear relation between input power and output pressure. (b) (a) 0 10 20 30 40 50 60 0.2 0.4 0.6 0.8 1.0 C1011 C1043 C1042 C1039 p out ( Pa) P in ( W) 94 In order to fit the experimental data obtained from their Pt thin films, Arnold and Crandall derived the first model for thermoacoustic transduction relating the RMS sound pressure generated (𝑝 𝑟𝑚𝑠 ) to the input electrical power (𝑃 𝑖𝑛𝑝𝑢𝑡 )[139]: 𝑝 𝑟𝑚𝑠 = √ 𝛼 𝜌 0 2√ 𝜋 𝑇 0 ∙ 1 𝑟 ∙ 𝑃 𝑖𝑛𝑝𝑢𝑡 ∙ √𝑓 𝐶 𝑠 , where 𝐶 𝑆 is the heat capacity per unit area of the CNT, r is the distance between the conductor and the microphone, and f is the frequency of the AC driving voltage. T0, α, and ρ are the ambient temperature, thermal diffusivity, and density of the surrounding gas, respectively. This equation defines an inverse relationship between the heat capacity per unit area 𝐶 𝑆 of a material and its potential as a thermoacoustic transducer. Single-walled carbon nanotubes with an ultra-low 𝐶 𝑠 (typically 10 -4 J/K· m 2 ) are therefore an ideal material for this transduction as opposed to platinum foil, which has a substantially higher 𝐶 𝑠 (typically 2 J/K· m 2 ). The input electrical power 𝑃 𝑖𝑛𝑝𝑢𝑡 is calculated as Isd Vsd. At high source-drain bias voltages, the majority of the power dissipation occurs in the CNT due to optical phonon scattering, allowing us to neglect power dissipated in the contacts. More recently, Xiao et al. modified the Arnold and Crandall model to fit their thermoacoustic data taken from carbon nanotube thin films. This revised model takes into account the rate of heat loss per unit area of the conductor per unit rise of temperature relative to the surrounding environment, βo, and the instantaneous heat exchange per unit area due to thermal conduction between the heated material and its surrounding environment. 𝑝 𝑟𝑚𝑠 = √ 𝛼 𝜌 0 2√ 𝜋 𝑇 0 ∙ 1 𝑟 ∙ 𝑃 𝑖𝑛𝑝𝑢𝑡 ∙ √𝑓 𝐶 𝑆 ∙ 𝑓 𝑓 2 √( 1+√ 𝑓 𝑓 1 ) 2 +( 𝑓 𝑓 2 +√ 𝑓 𝑓 1 ) 2 , (6.2) (6.3) 95 𝑓 1 = 𝛼 𝛽 0 2 𝜋 𝜅 2 , 𝑓 2 = 𝛽 0 𝜋 𝐶 𝑠 , where κ is the thermal conductivity of the surrounding gas environment. 𝑓 1 represents the heat loss of the thin film due to conduction, convection, and radiation; 𝑓 2 is related to the instantaneous heat exchange between the thin film and its surrounding air due to thermal conduction[139]. We define the thermoacoustic efficiency as the ratio of the sound pressure generated to the input electrical power (prms/Pin). In Figure 6.4, we show the theoretical prediction of both the Arnold-Crandall model and the Xiao model. The black dot indicates the experimental value for a CNT film from Xiao’s paper. The green squares indicate the experimental values obtained from our single CNT thermoacoustic devices, which span a wide range from 0.007 to 0.56 Pa/W. This is 3-4 orders of magnitude below the Arnold and Crandall model. One of the main reasons for this discrepancy is the high temperatures (>1000K) reached in these individual CNT devices, which causes a large portion of the heat generated in the CNT to be conducted to the supporting substrate, thus decreasing the thermoacoustic efficiency of the system. This is not as significant a problem in large, disordered network films of CNTs, since the thermal conductivity to the substrate is considerably lower than in the case of our individual CNT devices. Another related problem arises when Cs is small. Here, there is inherently more heat loss to conduction to the underlying substrate due to the short aspect ratio of our devices. By adjusting the heat exchange due to thermal conduction  o (and hence f1 and f2) to span a range from 5000 to (6.4) (6.5) 96 800000 W/m 2 · K, the Xiao model can be used to fit an upper and lower bound of our experimental data, as plotted in the yellow shaded region in Figure 6.4. These values are 2- 4 orders of magnitude larger than those of Xiao et al. ( o = 29 W/m 2 · K for 1-layer CNT film), who used the bulk value of the thermal conductivity of the CNT film ~200 W/m· K[158]. However, the heat dissipation/conduction in our devices is dominated by the extremely high thermal conductivity of these individual suspended CNT, which is around 3600 W/m· K[159]. Figure 6.4 - Dependence of the thermoacoustic efficiency (p rms /P in ) on the heat capacity per unit area (C s ) calculated according to Arnold and Crandall’s model (blue line) and Xiao’s model (yellow shaded region). The black dot indicates the value from CNT films, and the green squares correspond to the experimental values observed from our individual suspended CNT devices. C s (J/K· m 2 ) 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4 Thermoacoustic Efficiency (Pa/W) Individual CNTs CNT film 97 Figure 6.5 shows a graph of the sound pressure generated from several different types of acoustic transducers plotted as a function of device volume. The conventional electromagnetic coil has the largest volume on the order of 500 cm 3 and a typical sensitivity rating of about 90 dB, corresponding to an RMS sound pressure of 0.6 Pa. For a CMOS- MEMS speaker, the membrane volume is around 0.06mm 3 , which produces a sound pressure of 0.1 Pa with a 75 V electrical pulse[134]. This corresponds to an electrical input power of about 8mW and a conversion efficiency of 12.5 Pa/W. For monolayer graphene thermoacoustic device[147], the graphene volume is 1.75×10 -13 m 3 and the sound pressure produced is 50 mPa with 0.02 W input power. This corresponds to a conversion efficiency of 0.35 Pa/W. Our individual CNT devices have a volume of 6×10 -24 m 3 and represent the smallest thermoacoustic devices studied to date. Under 63 µW of electrical excitation, they produce a sound pressure of 0.8 µPa, which corresponds to a thermoacoustic efficiency of 0.01 Pa/W. 98 6.4 Conclusion In conclusion, we have reported the smallest acoustic system to date, consisting of a 2 µm long individual single walled carbon nanotube. Seven devices were measured, which exhibited electrical-to-acoustic conversion efficiencies ranging from 0.007-0.56 Pa/W. 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R2514. 109 Appendices I-V, I-Vg, and G- band Raman Data for All 2μm Suspended Quasi-Metallic CNT Samples in this Thesis Here list all the sample details for the study in Chapter 2.  527-1 -10 -5 0 5 10 0 200 400 600 800 300K 150K 4.5K Height Vg (V) -10 -5 0 5 10 -20 0 20 300K 150K 4.5K Frequency shift(cm-1) Vg (V) -10 -5 0 5 10 0 30 60 90 300K 150K 4.5K FWHM (cm-1) Vg (V) -10 -8 -6 -4 -2 0 2 4 6 8 10 10k 20k 30k 40k 4.5K 150K 300K Area Vg (V) -8 -6 -4 -2 0 2 4 6 8 0.0 5.0µ 10.0µ conductance(s) vg(v) -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -2.0µ -1.0µ 0.0 1.0µ 2.0µ I(A) Vb(V) 110  491-15 -5 0 5 100 200 300K peak height Vg (V) -5 0 5 -5 0 4.5K 300K Freq(cm-1) Vg -10 -5 0 5 10 0 30 60 90 300K 4.5K FWHM Vg (V) -6 -4 -2 0 2 4 6 3000 3500 4000 4500 5000 5500 300K Area Vg (V) -4 -2 0 2 4 0.0 5.0µ 10.0µ 15.0µ 20.0µ 25.0µ 30.0µ 35.0µ 40.0µ (S) Vg(V) -1.0 -0.5 0.0 0.5 1.0 -6.0µ -4.0µ -2.0µ 0.0 2.0µ 4.0µ 6.0µ I(A) Vb(V) 111  525-3 -5 0 5 100 200 300 300K Peak height Vg -5 0 5 1584 1588 300K Freq Vg -6 -4 -2 0 2 4 6 10 20 30 40 300k FWHM Vg -5 0 5 5000 6000 7000 8000 300K Area Vg -5 0 5 5.0µ 10.0µ 15.0µ 20.0µ 25.0µ 30.0µ Conductance (S) Vb (V) -1 0 1 -8.0µ -4.0µ 0.0 4.0µ 8.0µ I(A) Vb(V) 112  524-26 -5 0 5 100 200 300 400 300K Peak height Vg -5 0 5 1580 1582 300K Freqency(cm-1) Vg -6 -4 -2 0 2 4 6 20 30 300K FWHM Vg -6 -4 -2 0 2 4 6 7000 8000 9000 300K Area Vg -4 -2 0 2 4 10.0µ 20.0µ 30.0µ 40.0µ 50.0µ (S) Vg(V) 113  487-15 -5 0 5 50 100 150 200 250 300K Peak Height Vg -5 0 5 1560 1570 1580 300K Freqency(cm-1) Vg -5 0 5 40 80 300K FWHM Vg -6 -4 -2 0 2 4 6 0.0 5.0k 10.0k 15.0k 20.0k 25.0k 300K Area Vg -6 -4 -2 0 2 4 6 0.0 5.0µ 10.0µ 15.0µ 20.0µ 25.0µ 30.0µ conductance Vg(V) -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -4.0µ -2.0µ 0.0 2.0µ 4.0µ 6.0µ Vg=-3V I Vb 114  504-22 -4 0 4 40 80 120 300K Peak height Vg (V) -4 0 4 1584 1586 300K Freqency(cm-1) Vg (V) -5 0 5 20 30 300K FWHM Vg (V) -4 0 4 2.0k 4.0k 6.0k 300K Area Vg (V) -3 -2 -1 0 1 2 3 10.0µ 15.0µ 20.0µ 25.0µ conductance Conductance(s) vg 115  427-20 -5 0 5 0 200 400 600 300K 370K Peak Height Vg (V) -5 0 5 -10 -5 0 370K 300K Freqency(cm-1) Vg (V) -5 0 5 20 40 60 300K 370K FWHM Vg (V) -5 0 5 5.0k 10.0k 15.0k 20.0k 300K 370K Area Vg (V) -3 -2 -1 0 1 2 3 0.0 5.0µ 10.0µ 15.0µ Conductance(s) vg conductance -0.2 -0.1 0.0 0.1 0.2 -1.0x10 -6 -5.0x10 -7 0.0 5.0x10 -7 1.0x10 -6 1.5x10 -6 current Current(A) Vb(V) 116  525-21 -4 -2 0 2 4 100 200 300 400 Peak height Peak height Vg -4 -2 0 2 4 1530 1540 1550 1560 1570 1580 Freq Freq Vg -4 -3 -2 -1 0 1 2 3 4 100 150 200 250 FWHM FWHM Vg -4 -2 0 2 4 10k 20k 30k 40k 50k 60k Area Area Vg -5 0 5 -2.0µ 0.0 2.0µ 4.0µ 6.0µ 8.0µ 10.0µ 12.0µ 14.0µ 16.0µ 18.0µ 20.0µ Conductance (S) Vb (V) 117  490-26 -5 0 5 100 200 300 400 300K Height Vg (V) -5 0 5 1566 1568 1570 1572 300K Frequency (cm-1) Vg (V) -5 0 5 20 40 60 300K FWHM (cm-1) Vg (V) -5 0 5 10.0k 15.0k 300K Area Vg (V) -6 -4 -2 0 2 4 6 1.5µ 2.0µ 2.5µ 3.0µ 3.5µ 4.0µ (S) Vg(V) 118 2D band Raman Data for All 2μm Suspended Quasi-Metallic CNT Samples in this Thesis Here lists all the sample details for the study in Chapter 3. I-V characteristics data can be found according the device number in the previous section.  487-15 -6 -4 -2 0 2 4 6 100 200 300 400 500 300K Height Vg -6 -4 -2 0 2 4 6 2664 2665 2666 2667 2668 2669 2670 2671 2672 300K Freq Vg -6 -4 -2 0 2 4 6 10k 300K Area Vg -6 -4 -2 0 2 4 6 20 30 300K FWHM Vg 119  491-15  525-21 -5 0 5 2661 2662 2663 2664 2665 300K Freq (cm-1) Vg (V) -5 0 5 60 70 80 90 100 300K Height Vg (V) -5 0 5 2k 3k 4k 5k 300K Area Vg (V) -5 0 5 25 30 35 300K FWHM Vg (V) -5 0 5 500.0 1.0k 1.5k 300K Peak Height Vg (V) -5 0 5 2621 2622 2623 2624 2625 2626 300K Freq (cm-1) Vg (V) 120  525-3 -5 0 5 0.0 20.0k 40.0k 300K Area Vg (V) -5 0 5 20 21 22 23 24 300K FWHM Vg (V) -5 0 5 90 100 110 120 130 300K Peak Vg (V) -5 0 5 2662 2664 2666 300K Freq (cm-1) Vg (V) -5 0 5 4k 5k 6k 300K Area Vg (V) -5 0 5 30 35 300K FWHM Vg (V) 121  527-1  490-26 -5 0 5 200 400 600 300K 4.5K Peak Height Vg (V) -5 0 5 2620 2624 2628 300K 4.5K Freq (cm-1) Vg (V) -5 0 5 5.0k 10.0k 15.0k 20.0k 300K 4.5K Area Vg (V) -5 0 5 22 24 26 28 30 32 300K 4.5K FWHM Vg (V) -5 0 5 110 120 130 140 150 160 Peak height Peak height Vg (V) -5 0 5 2662 2663 2664 2665 2666 2667 small vg gap large vg gap Freq Vg (V) 122 -5 0 5 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 Area Area Vg (V) -6 -4 -2 0 2 4 6 17 18 19 20 21 22 FWHM FWHM Vg (V)

Abstract (if available)

Abstract Carbon nanotubes (CNTs) have been studied extensively over the last two decades due to their remarkable mechanical, electronic, and thermal properties. Despite these numerous studies, there are still several important aspects of CNTs that are not well understood. The advance in fabricating ultra‐clean, nearly defect‐free, suspended single‐walled carbon nanotubes has been developed. This allows us to study many interesting physical phenomena due to CNTs’ one‐dimensional nature. ❧ Raman spectra are collected from CNTs at different gate voltages. When metallic CNTs are doped with an applied gate voltage, non‐adiabatic Kohn anomaly is shut off, and large modulations in Raman intensity are observed. A relationship between the strength of the non‐adiabatic Kohn anomaly and the intensity modulation of the Raman G- band is established. Possible structural phase transition is also proposed as an underlying mechanism for a Raman shift anomaly in 2D band. ❧ CNTs can be made into a p-n junction photodiode using dual gate FET structure. Photocurrent spectra are collected and a few exciton transitions can be distinguished. A gate voltage dependence on photocurrent intensity is observed and explained. ❧ In addition to CVD grown suspended CNTs, surfactant‐wrapped CNT solutions are also studied for photoluminescence (PL) and electroluminescence. We developed a PL imaging system to efficiently find CNTs that have emission energy in the Si detector range.

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Creator Chang, Shun-Wen (author)

Core Title Optoelectronic properties and device physics of individual suspended carbon nanotubes

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Physics

Publication Date 04/15/2015

Defense Date 12/01/2014

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

Tag carbon nanotube,device physics,material characterization,nanoscience,OAI-PMH Harvest,optoelectronics,photodiode

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Daeppen, Werner (committee chair), Däppen, Werner (committee chair), Bickers, Nelson Eugene (committee member), Cronin, Stephen B. (committee member), Wu, Wei (committee member), Zhou, Chongwu (committee member)

Creator Email esther3587@gmail.com,shunwenc@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-548236

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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...

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