Applications enabled by plasmonic nano-finger and analog computing based on memristive devices

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Content APPLICATIONS ENABLED BY PLASMONIC NANO-FINGER AND
ANALOG COMPUTING BASED ON MEMRISTIVE DEVICES
By
Pan Hu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2023
Copyright 2023 Pan Hu
ii

Dedication

To my family for your support and love.

iii

Acknowledgements
The accomplishment of my Ph.D. program could not be possible without the mentoring, guidance,
and support from my advisor Prof. Wei Wu. Your attitude to research, pursuing of science and
curiosity in unknown phenomena significantly affects me and encourages me to overcome the
difficulties in my study. I learned how to become a better person from you as well. Your patience,
kindness and modesty to people set a positive example for all your friends and students. It is my
pleasure to have such a wise and kind advisor for my Ph.D. study.
I would like to thank the rest of my qualifying exam committee and dissertation committee, Prof.
Stephen B. Cronin, Prof. Aiichiro Nakano, Prof. Chongwu Zhou, Prof. Joshua Yang, for your
brilliant comments and suggestions.
I thankfully acknowledge the support from my collaborators. I would like to thank Prof. Stephen
B. Cronin and Zhi Cai for the dielectric deposition, Dr. Bofan Zhao for Raman spectroscopy, Prof.
Fanxin Liu, Prof. Stephan Haas and Hefei Liu for the help on nanofinger-related projects. The
inspirations, suggestions and enthusiasm of these excellent scientists have enabled me to finish my
Ph.D. study.
I would like to thank all our research group members. The friendly, enthusiastic and encouraging
group provides me with a perfect environment for my Ph.D. study. Here I want to specially thank
Dr. Yuanrui Li for mentoring me and carrying me through the initial stage of my Ph.D. study. I
would also like to thank Dr. He Liu, Dr. Yuhan Yao, Dr. Yifei Wang and Dr. Boxiang for sharing
your research experience and knowledge, Dr. Hao Yang, Dr. Buyun Chen, Dr. Deming Meng,
Yunxiang Wang, Tse-Hsien Ou, Zerui Liu, Sushmit Hossain and Jiacheng Ye for your kindly
iv

support in both my research and daily life. I am so fortunate to join this group and all my
achievements contain the contributions from you.
I am grateful to have some friends outside group, including but limiting to Lurui Zhao, Yongkui
Tang, Jun Tao, Junfeng Gao, Wei Chen, Jin Liu, Chao Che, Rui Wang and Dong Duan. Thank you
for accompanying me so many years and our friendship will last forever.
Last but not least, I would like to thank my parents. Although words are not enough to express my
gratitude, none of this would be possible without you. I also want to thank my wife, Bilin Zheng.
She and her family continuously support me to pass through the difficult times. I could not
complete all the achievements without the help of you.

v

Table of Contents
Dedication ....................................................................................................................................... ii
Acknowledgements ........................................................................................................................ iii
List of Tables ............................................................................................................................... viii
List of Figures ................................................................................................................................ ix
Abstract ........................................................................................................................................ xiv
Topic 1. Plasmonic Dye-Sensitized Solar Cells through Collapsible Gold Nanofingers ............... 1
Chapter 1 Introduction of Plasmonic Dye-sensitized Solar Cells (DSSCs) ................................ 2
Chapter 2 Device Characterization ............................................................................................. 5
2.1 Numerical Simulations on TiO2-Au/Al2O3/Au Nanofingers ............................................. 5
2.2 SEM and Optical Properties of Plasmonic DSSCs ............................................................ 6
2.3 Fluorescence Enhancement of N719 Dye on Photoanode ................................................ 9
2.4 Electrical Characterizations of Plasmonic DSSCs .......................................................... 10
2.5. Comparison between Normal DSSCs and Plasmonic DSSCs ....................................... 13
Summary ................................................................................................................................... 16
Topic 2. Collapsed Nanofingers by DNA-Functionalization as SERS Platform for Mercury
Ions Sensing .................................................................................................................................. 17
Chapter 3 Introduction of DNA-modified Plasmonic Nanofinger Platform for Chemical
Sensing ...................................................................................................................................... 18
Chapter 4 Device Fabrication .................................................................................................... 20
Chapter 5 Device Characterization ........................................................................................... 22
5.1 Optical Performance of DNA-modified Nanofingers ..................................................... 22
5.2 SERS Detection of Hg
2+
based on DNA-modified Nanofingers ..................................... 24
5.3 Numerical Simulations on Au/DNA/Au Coupled Nanofingers ...................................... 25
Summary ................................................................................................................................... 27
Topic 3. Tuning Photoluminescence of CsPbBr3 Quantum Dots through Plasmonic
Nanofingers ................................................................................................................................... 28
Chapter 6 Introduction of Plasmonic-assisted Perovskite Quantum Dots (QDs) Emission ..... 29
Chapter 7 Device Characterization ........................................................................................... 32
7.1 Schematic of CsPbBr3 QDs Emission on Ag Nanofingers ............................................. 32
vi

7.2 Photoluminescence of CsPbBr3 QDs on Ag Nanofingers ............................................... 34
7.3 Effect of Plasmonic Near Field on Light Emission of CsPbBr3 QDs ............................. 36
Chapter 8 Theoretical Study of Strong Coupling between CsPbBr3 QDs and Surrounding
Ag Nanofingers ......................................................................................................................... 39
Summary ................................................................................................................................... 42
Topic 4. Hybrid Tuning of Sub-filaments to Improve Analog Switching Performance in
Memristive Devices ...................................................................................................................... 44
Chapter 9 Introduction of Memristive Devices ......................................................................... 45
Chapter 10 Theoretical Demonstration of Dynamic Range Improvement by Sub-filaments ... 47
10.1 Effect of Pt Islands on Memristor Dynamic Range ....................................................... 47
10.2 Size Effect of Pt Islands on Device Performances ........................................................ 50
Chapter 11 Device Fabrication .................................................................................................. 52
Chapter 12 Device Characterization ......................................................................................... 54
12.1. Hybrid Tuning of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor ........................ 54
12.2. Analog Performances of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor ............. 57
12.3. Electrical Characteristics of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor
under Negative Voltage Sweep and 100 ns Voltage Pulse .................................................... 60
12.4. Engineering of Sub-filaments ....................................................................................... 61
12.5. Sub-memristors for Coarse and Fine Resistance Tuning ............................................. 64
12.6. Validation of Sub-filaments Coexistence ..................................................................... 66
Summary ................................................................................................................................... 70
Topic 5. Complex Eigenfunction Solver based on Memristor Array ........................................... 71
Chapter 13 Introduction of Memristor-based Complex Eigenfunction Solver ......................... 72
Chapter 14 Memristor-based Real Eigenfunction Solver.......................................................... 74
14.1. Design of Memristor-based Real Eigenfunction Solver ............................................... 74
14.2. Sample Problems Solved by Memristor-based Real Eigenfunction Solver ................. 76
Chapter 15 Memristor-based Complex Eigenfunction Solver .................................................. 79
15.1 Design of Memristor-based Complex Eigenfunction Solver ........................................ 79
15.2 Sample Problems Solved by Memristor-based Complex Eigenfunction Solver ........... 83
Summary ................................................................................................................................... 85
Conclusion and Future Work ........................................................................................................ 86
References ..................................................................................................................................... 88
Publications ................................................................................................................................... 99
vii

Experimental Sections ................................................................................................................ 100
1. Plasmonic Dye-Sensitized Solar Cells through Collapsible Gold Nanofingers .................. 100
2. Collapsed Nanofingers by DNA-Functionalization as SERS Platform for Mercury Ions
Sensing .................................................................................................................................... 101
3. Tuning Photoluminescence of CsPbBr3 Quantum Dots through Plasmonic Nanofingers .. 103
4. Hybrid Tuning of Sub-filaments to Improve Analog Switching Performance in
Memristive Devices ................................................................................................................. 104
5. Complex Eigenfunction Solver based on Memristor Array ................................................ 106

viii

List of Tables
Table 2.4. Characterizations of plasmonic DSSCs. Group A presents DSSCs based on the
photoanode of TiO2/Al2O3/Au films as the comparison, and Group B presents plasmonic
DSSCs based on the collapsed Au nanofingers. ........................................................................... 11
Table 12.4. Electroforming and RESET Characteristics of Control Memristors ......................... 63

ix

List of Figures
Figure 1.1. Schematic configuration of Plasmonic DSSCs under illumination of sunlight. (a)
DSSCs consist of a photoanode that is fabricated by 2 nm TiO2 film deposited on the collapsed
Au/Al2O3/Au nanofingers with 5 nm gap, and a counter electrode with ITO glass. (b)
Schematic electrons traveling into the TiO2 photoanode network and a redox process typically
by I
-
/I
3-
electrolyte. .......................................................................................................................... 4
Figure 2.1. Top view EM field distributions of the Au/Al2O3/Au nanofingers. (a) and TiO2-
Au/Al2O3/Au nanofingers (b) at 540 nm. Cross-sectional distribution of the EM field on the
Au/Al2O3/Au nanofingers (c) at 540 nm. ........................................................................................ 5
Figure 2.2. SEM and Optical properties for the photoanode of TiO2-Au/Al2O3/Au nanofingers.
(a) SEM image of Au-nanofingers matrix. (b) SEM side view image of TiO2-Au/Al2O3/Au
nanofingers. (c) Reflectance spectra measurements. Red line presents the TiO2-Au/Al2O3/Au
collapsed nanofingers; Black line presents the Au/Al2O3/Au collapsed nanofingers; Blue line
presents the Au/Al2O3/TiO2 composite films. (d) Cross-sectional distribution of the EM field
on the TiO2-Au/Al2O3/Au nanofingers at 660 nm. ......................................................................... 8
Figure 2.3. Fluorescence enhancement of N719 dye on the photoanode. (a) Fluorescence
intensity of N719 dyes on TiO2-Au/Al2O3/Au nanofingers (red line), and Au/Al2O3/TiO2
composite films (blue line). (b) Magnified view of fluorescence intensity of N719 dyes on
Au/Al2O3/TiO2 composite films. .................................................................................................. 10
Figure 2.4. Dark Current-voltage plot of DSSCs with photoanodes of TiO2-Au/Al2O3/Au
nanofingers (blue line), and TiO2/Al2O3/Au composite films (red line). ..................................... 12
Figure 2.5. Characterizations of plasmonic DSSCs. (a) Photo of fabricated DSSCs. Red one
represents DSSCs based on the collapsed Au nanofingers (defined as plasmonic DSSCs) and
the blue one is DSSCs based on the photoanode of Au/Al2O3/TiO2 films (defined as normal
DSSCs). (b) Photocurrent density -voltage plot of DSSCs with photoanodes of TiO2-
Au/Al2O3/Au nanofingers (red dot line), and Au/Al2O3/TiO2 composite films (blue line). (c)
Magnification of Photocurrent density -voltage plot of DSSCs for green rectangular dot line
in (b). (d) Fill factor and the maximum power output of solar cells. In the measurement, we
perform 5 groups for both plasmonic DSSCs and normal DSSCs. In the plot, red solid
rectangular and red hollow rectangular present fill factor and the maximum power output of
plasmonic DSSCs, respectively. Blue solid circular and blue hollow circular present fill factor
and the maximum power output of normal DSSCs, respectively. ................................................ 15
Figure 4.1. Schematic SERS detection of Hg
2+
by collapsed Au nanofingers with DNA
functionalization. (a) Configuration of DNA aptamer consisting of two segments of both
thymine (T, red color) as the Hg
2+
recognition and the capture segment (blue color) containing
guanine (G) and adenine (A). (b) When DNA aptamers are immobilized to Au surface via
thiol binding (HS), sing-strand DNA arrays horizontally lay on the Au surface due to good
affinity of adenine to Au. (c) After Hg
2+
are bonded with thymine, DNA arrays are vertically
distributed on Au surface. (d) Based on above principle, DNA were firstly connected on
x

flexible Au nanofingers via thiol binding (e). After DNA solution air dried, DNA
Functionalized Au nanofingers were physically touched each other via a capillary force-
induced collapsing process so that Au/DNA/Au coupled nanofingers were achieved in which
DNA aptamer was as the space layer (f). Finally, when Hg
2+
were dropped on the Au/DNA/Au
coupled nanofingers, DNA aptamers arrays became vertical on Au surface from the horizontal
direction (g) so that adenine is a little away from Au surface and its enhanced Raman signals
decreases. By the ratio of guanine to adenine Raman signals, Hg
2+
is successfully detected. ..... 21
Figure 5.1. Characterizations for DNA modified Au nanofingers. (a) SEM image of
nanofingers before collapse. (b) SEM image of DNA modified Au-nanofingers after collapse.
(c) TEM cross-sectional view of collapsed Au nanofingers. (d) Transmittance spectra of prior
to collapse for Au nanofingers and after DNA modification and collapse for Au/DNA/Au
nanofingers. ................................................................................................................................... 23
Figure 5.2. SERS detection of Hg
2+
based on DNA aptamer. (a) The SERS signals of the
oligomer T(10)G(8)A(8) used in this detection system in response to Hg
2+
ions of various
concentrations. (b) The relative SERS ratio of I(736 cm
−1
) /I(650 cm
−1
) versus Hg
2+

concentrations. .............................................................................................................................. 25
Figure 5.3. Numerical Simulations of Au nanofingers. (a) Transmission spectrum of Au
nanofingers before and after the collapse process with 2 nm gap and the inserts present the
charge distribution. (b) Cross-sectional distribution of the electric field on the collapsed
nanofingers and zoomed-in view of electric field distribution. .................................................... 27
Figure 7.1. Ag nanofingers/CsPbBr3 QDs hybrid system. (a) Schematic of light emission in
Ag nanofingers/CsPbBr3 QDs hybrid system. (b) Oblique-view SEM image of 1 nm ta-C
coated Ag nanofingers after collapse with a 500 nm scale bar. Insert figure: magnified TEM
cross-sectional view of collapsed nanofinger paired with 50 nm scale bar. (c) TEM images of
the CsPbBr3 QDs with 10 nm scale bar. Insert figure: 0.58 nm lattice fringe characterized by
high-resolution TEM image. ......................................................................................................... 33
Figure 7.2. Photoluminescence of CsPbBr3 QDs on Ag nanofingers. (a) Absorption spectra
and PL spectra of CsPbBr3 QDs. The insert figure shows a photograph of CsPbBr3 QDs
solution. (b) PL spectra of the CsPbBr3 QDs on the nanofingers and SiO2 substrate. (c) PL
lifetime of the CsPbBr3 QDs on different substrates. (d) PL spectra of the CsPbBr3 QDs on
the nanofingers and SiO2 substrate with different polarization incident light. All PL spectra
were acquired by the CW excitation at 405 nm wavelength. ....................................................... 35
Figure 7.3. Effect of plasmonic near field on light emission of CsPbBr3 QDs. (a) The
experimentally measured dark field scattering spectra for the nanofinger structures before and
after collapse process. (b) Numerical simulation of the scattering spectra for the nanofinger
structures before and after collapse process. (c) Electric field distribution for the nanofinger
pair at scattering peak of 539 nm. Insert figure: corresponding charge distribution. (d)
Schematic of proposed elementary steps for plasmonic induced photoexcitation enhancement
in hybrid system, red arrow: plasmonic induced resonant energy effect, dark blue arrow: hot
electron transfer effect, light blue arrow: plasmonic induced charge transfer effect.................... 37
xi

Figure 8.1. Power dependent PL spectra of CsPbBr3 QDs. (a, b) Power dependent PL spectra
of CsPbBr3 QDs on SiO2 and Ag nanofinger substrate under CW laser excitation at 405 nm.
(c, d) Peak intensity and FWHM of PL spectra of QDs on SiO2 and Ag nanofinger substrate
under different incident power. (e) Peak intensity of PL spectra for Ag nanofingers/ CsPbBr 3
QDs hybrid systems as a function of squared incident power. ..................................................... 40
Figure 10.1. Schematic of hybrid tuning of sub-filaments. (a) Schematic of sub-filaments in
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor. Two sub-filaments are divided by Pt
islands and the whole memristor can be considered as a series connection of two sub-
memristors. (b) Simulation of Electric field distribution in Al2O3 switching layer when there
is a spherical Pt island (2 nm diameter) inside. Electric field is stronger near the Pt island and
the dopants inside the switching layer tend to move towards the island. ..................................... 49
Figure 10.2. Size effect of Pt island on device performance. (a) Simulation of electric field
distribution in Al2O3 switching layer when the width of Pt island is 8 nm and the vertical
dimension is 3 nm. Compared to the spherical island with 2 nm diameter, island with larger
lateral dimension induces weaker electrical field nearby. (b) I-V characteristics of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor with 2 nm deposited Pt as the island layer.
The memristor requires high voltage and current for switching, the electrical breakdown
occurs easily during the switching processes. ............................................................................... 51
Figure 11.1. Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt cross-point memristor. (a)-(d) Device
fabrication process. Photolithography, electron-beam metal evaporator and liftoff were
performed to pattern the top and bottom electrodes, the Al2O3 switching layer was deposited
by ALD process. The intermediate Pt and Ti layers inside the switching layer were also
deposited by electron-beam metal evaporator. (e) Optical microscope image of a fabricated
cross-point memristor. (f) SEM image of 3 nm Pt on Si substrate. .............................................. 53
Figure 12.1. Hybrid tuning of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor. (a) I-V
characteristics of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor within LRDR. The
corresponding dynamic range is 600 Ω - 19 kΩ. (b) I-V characteristics of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor within HRDR. The corresponding
dynamic range is 19 kΩ - 50 kΩ. (c) Switching from LRDR to HRDR by applying a higher
negative voltage (blue curve). (d) Switching from LRDR to HRDR by applying higher
positive current and voltage (orange curve). (e) Multilevel states within LRDR (orange lines)
and HRDR (blue lines). (f) Relation between resistance and programming current of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor within LRDR (orange curve) and HRDR
(blue curve). .................................................................................................................................. 56
Figure 12.2. Analog Performances of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor. (a)
Multilevel conductance states of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor. (b)
Comparison of multilevel conductance states between memristors with and without Pt islands.
The number of conductance states of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor is
enhanced from 157 states to 1112 states. (c) The retention test of Pt/Ta/Al2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristor within 1200 s. (d) Switching endurance test of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor during 300 cycles. (e) Analog
xii

programming of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor under voltage pulses. The
pulse amplitude is 0.7 V and width is 500 ns. .............................................................................. 59
Figure 12.3. Electrical Characteristics of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor.
(a) I-V curves of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor under negative voltage
sweeps (0 to -0.1 V). (b) Resistance shift of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor
after a single voltage pulse (1 V, 100 ns)...................................................................................... 60
Figure 12.4. Electrical characteristics of control memristors. (a) I-V characteristics of
Pt/Ta/Al2O3/Pt/Al2O3/Pt memristor. The insertion of 1 nm Pt into the switching layer
significantly increases the required voltage and current for switching. (b) I-V characteristics
of Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt memristors with different Ti thicknesses. The memristors
require relatively low voltage and current for switching. (c) Resistance tuning characteristics
of Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt memristors with different Ti thicknesses. A thicker Ti layer
leads to a lower device resistance. ................................................................................................ 62
Figure 12.5. Electrical characteristics of sub-memristors and Resistance evolution of sub-
filaments formation. (a) Structure of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor. It can
be considered as a combination of two sub-memristors separated by Pt islands. (b) I-V
characteristics of Pt/Ta/Al2O3/Pt sub-memristors with different Al2O3 thicknesses. The
memristor requires relatively low voltage and current for switching. The insert figure is the
resistance tuning characteristics of Pt/Ta/Al2O3/Pt memristors with different Al2O3
thicknesses. (c) I-V characteristics of Pt/TiOx/Al2O3-x/Pt sub-memristor. The memristor
requires high voltage and current for switching, no consecutively tunable resistance states can
be observed on it. (d) The evolution of filament formation. The formation details can be
studied by recording the resistance of SET process. (e) 1st SET processes of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor after electroforming. Two abrupt
resistance drops can be observed. (f) Following SET processes of Pt/Ta/Al2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristor. With more SET-RESET cycles, the first abrupt resistance
transition becomes smoother......................................................................................................... 66
Figure 12.6. Resistance evolution of filament formation. (a) Electroforming and first 4 SET
processes of Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt memristor with 2 nm Ti. With more SET-RESET
cycles, the abrupt resistance transition becomes smoother. (b) 1st SET processes of
Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt memristor with different Ti thicknesses. Only one resistance
drop can be observed during the 1st SET process. (c) 1st SET processes of Pt/Ta/Al 2O3/Pt
memristor with different Al2O3 thicknesses. Only one resistance drop can be observed during
the 1st SET process. ...................................................................................................................... 67
Figure 14.1. Memristor-based real eigenfunction solver. ............................................................. 76
Figure 14.3. Comparison between numerical calculation and real eigenfunction solver of two-
dimensional infinite potential well. (a) three eigenstates calculated by MATLAB. (b) three
eigenstates calculated by LTspice. ................................................................................................ 78
Figure 15.1. Memristor-based complex eigenfunction solver. ..................................................... 82
xiii

Figure 15.2. Simulated voltages at the inverting input of inverting amplifier. The analytical
correct values of the imaginary parts of eigenvalues are 3.3333 and 1.6667. (a) Scanning over
real part when imaginary part is 3.3333. (b) Scanning over real part when imaginary part is
1.6667. (c) Scanning over real part when imaginary part is 3. (d) Scanning over real part when
imaginary part is 1.8. .................................................................................................................... 84

xiv

Abstract
This dissertation summarizes the five topics in my Ph.D. study. My research mainly focuses on
applications enabled by plasmonic nano-finger and analog computing based on memristive devices.
The first part (chapter 1-2) is about plasmonic dye-sensitized solar cells through collapsible gold
nanofingers. Here, we demonstrate plasmonic dye-sensitized solar cells (DSSCs) using collapsible
Au nanofingers to build photoanode to enhance light absorption. In this plasmonic DSSCs, by
balancing local field enhancement due to gap-plasmon resonance and dye fluorescence quenching,
the optimal gap size in collapsed Au/Al2O3/Au nanofingers is designed by twice the Al2O3
thickness and then deposited a TiO2 layer as photoanode. The results show that the PCE of DSSCs
is mostly improved as compared to DSSCs with photoanode of Au/Al2O3/TiO2 films, which can
be ascribed to the coupled local field enhancement within the sub-nanometer gaps. In addition,
fluorescence of dyes on plasmonic nanofingers is nearly 10 times higher than plain Au/Al2O3/TiO2
films, which further proves the dye absorption enhancement. These plasmonic nanofingers enable
the precise engineering of gap-plasmon modes and can be scaled up to wafer scale with low cost
by the nanoimprint lithography technique, which suggests the feasibility of applying our result in
constructing the photoanode for other types of solar cells.
The second part (chapter 3-5) is about collapsed nanofingers by DNA-functionalization as SERS
platform for mercury ions sensing. In this work, we report a coupled Au/DNAs/Au gap plasmon
platform that provides remarkable SERS enhancement and sensitivity for mercury ion sensing.
Through nanoimprint lithography, large area of Au nanofingers can be fabricated with excellent
uniformity and flexibility. These Au nanofingers can be further modified by DNA aptamers to
construct Au/DNAs/Au gap plasmon nanostructures with well-defined gap sizes. Due to the
subnanometer gap size, strong interaction between collapsed Au nanofingers can be induced to
xv

create extremely enhanced near-field with nanoscale mode volume. When Hg
2+
ions exist around
the platform, they can specially bind to thymine (T) bases of DNA and form T-Hg
2+
-T pairs
between adjacent single strand DNAs. As a result, DNAs that initially lie on the Au surface are
forced to stand in rigid duplex-structures. This morphology change can be directly indicated by
the ratio between adenine (A) and guanine (G) SERS signals to reveal the Hg
2+
concentration.
Given the strong field enhancement as well as the close distance between DNA and hotspot,
ultralow Hg
2+
concentration down to 10
−9
M is successfully detected. This work demonstrates a
SERS platform with high selectivity and sensitivity, which exhibits significant potential for
molecule sensing applications.
The third part (chapter 6-8) is about tuning photoluminescence of CsPbBr3 quantum dots through
plasmonic nanofingers. We demonstrate the optical coupling between the CsPbBr3 quantum dots
(QDs) and gap plasmon through placing QDs in a 2 nm tetrahedral amorphous carbon gap region
of collapsible Ag nanofingers. Compared to the CsPbBr3 QDs on SiO2, the photoluminescence
(PL) of CsPbBr3 QDs on collapsed nanofinger is enhanced by 4 times and the lifetime decreases
from 11.04 ns to 3.8 ns. A Purcell-enhanced emission can be achieved by combining QDs and
plasmonic nanofingers. In addition, the intensity of PL can be manipulated by the polarization of
incident light because of the different polarization responses of dimer nanofingers. More
importantly, PL intensity shows a quadric dependence on the incident power and lasing-like PL
spectra can be observed at room temperature by continuous-wave laser excitation. Such
observations can be ascribed to the strong coupling between CsPbBr3 QDs and surrounding Ag
nanofingers. This finding indicates that it is possible to achieve lasing-like PL through coupling
CsPbBr3 QDs to the near-field of plasmonic nanostructures, which can enrich the applications of
CsPbBr3 QDs in nanolasing devices.
xvi

The fourth part (chapter 9-12) is about hybrid tuning of sub-filaments to improve analog switching
performance in memristive devices. We invent a method to improve the analog switching
performance of memristors through a hybrid tuning (coarse and fine tuning) of two sub-filaments.
The creation of sub-filaments inside the dielectric switching layer is realized by deploying Pt metal
islands in the switching layer. Given the different material stack configurations of the two sub-
filaments, they exhibit different switching properties to play the roles of coarse and fine tuning
respectively in the memristor. Based on the above mechanism, a Pt/Ta/Al2O3/Pt island/Al2O3-
x/TiOy/Al2O3-x/Pt memristor was proposed and fabricated. Through the hybrid tuning of two sub-
filaments, a combined dynamic range of 600 Ω - 50 kΩ is achieved. Compared to the reference
Pt/Ta/Al2O3/Pt memristors (dynamic range: 600 Ω - 8 kΩ), both dynamic range and multilevel
resistance states are increased significantly. Meanwhile, the energy efficiency is improved because
the resistance of tunable states can be set to larger values. Furthermore, this mechanism can be
incorporated into various existing memristors to improve their dynamic range and multilevel states,
which extensively enriches the applications of memristors.
The last part (chapter 13-15) is about the complex eigenfunction solver based on memristor array.
We design a memristor platform to solve complex eigenfunctions for various problems such as
photonic simulation and quantum mechanism problems. This eigenfunction solver is capable of
solving complex eigenfunctions through mapping given matrix A into the memristor array and
scanning over possible eigenvalues. Correct complex eigenvalues can be achieved accurately and
efficiently because they are located at the local minimum voltages at the inverting input of the
inverting amplifier. The trend of the voltage can provide enough information for the fast capture
of the local minimum points. LTspice simulations are conducted and the results confirm the
excellent calculation performances of the complex eigenfunction solver.
1

Topic 1. Plasmonic Dye-Sensitized Solar Cells through Collapsible
Gold Nanofingers

2

Chapter 1 Introduction of Plasmonic Dye-sensitized Solar Cells
(DSSCs)
The demands for clean, renewable energy sources have become one of the mostly urgent issues
for our society. Utilization of solar energy through photovoltaic technology is a solution. A variety
of photovoltaic devices are developed in past years, such as, silicon solar cells, dye-sensitized solar
cells (DSSCs), perovskite solar cells etc[1-6].

In order to improve the performance of solar cells,
the new techniques which mainly include structural design, new materials, efficiently and highly
stable dyes, have been developed to improve the light trapping and power conversion efficiency
(PCE) further[7-11]. Among them, plasmonic solar cells are an attractive technology because
plasmonic nanostructures at resonant excitations can efficiently trap the incident light within
nanoscale space and form an extremely strong local electromagnetic (EM) field near the surface
of nanostructures, and thus efficiently enhance the sunlight absorption[12-14]. DSSCs contains
photoanode, counter electrode, electrolyte and dyes in which dye sensitized photoanode absorbs
sunlight to generate electrons. At present, plasmonic nanoparticles are broadly investigated to
design photoanode of DSSCs so that the extinction of dye can be mostly increased, leading to a
high PCE[15-18]. However, the distribution of metal nanoparticles in TiO2 network is not uniform
due to the reproducibility in fabrication over a large area. Therefore, a design of ordered plasmonic
nanostructure is necessary.
Metallic gap-structures with gap-plasmon resonance can produce an extremely strong EM field
within a sub-nanometer gap that is decided by both the classical EM theory and quantum
mechanics[19-26]. For example, the aggregates of metal nanoparticles could create nanometer
junctions with maximum enhancement of (E/Ein)
2
up to 10
6
fold[27, 28]. However, to achieve the
3

optimized enhancement decided by quantum plasmons, the fabrication of ordered nanostructures
with atomic precision of tunable gap is still a challenge. Most conventional methods including
electron-beam lithography and physical etching for creating sub-nanometer gap are constrained by
the lithography resolution limit[29-35]. Thus, precise tailoring of the gap size at sub-nanometer
scale over a large area is critical to form strong and reproducible enhanced EM field. On the other
hand, emission quenching of dyes is associated with the direct contact between the dye and the
metal, which is decided by the separation distance between the metal and the dye[17, 18]. It has
been demonstrated that the optimal separation distance is at sub-5 nm scale[36, 37]. Therefore, the
construction of ordered plasmonic nanostructures with high EM field enhancements and the
control of dye-metal distance are very important to enhance the efficiency of plasmonic DSSCs.
Previously we demonstrated the collapsible nanofingers that show strong EM field enhancement
by precisely controlling the gap size at the subnanometer scale. This collapsible nanofingers could
be fabricated over large area by nanoimprint lithography (NIL), reactive-ion etching (RIE) and
atomic-layer deposition (ALD)[24]. The flexible Au-nanofinger matrix have a high aspect ratio,
and each nanofinger is composed of a polymer nanopillar capped with an Au nanodisk. The
subsequent dielectric layer coating on the nanofingers and collapse process can realize the
precisely tuning of gap size by twice the thickness of dielectric layer.
In present work, the collapsible nanofingers are studied to design a photoanode in DSSCs, which
can precisely control the gap size and the dye-metal distance, achieving high reliability and high
throughput at low cost[24, 38-41]. First, a thin conformal Al2O3 layer of 2.5 nm is deposited
uniformly by ALD onto flexible Au nanofingers. Through exposing them to ethanol, a 5 nm
nanogap is formed under capillary force[24].

Second, the collapsed Au/Al2O3/Au nanofingers are
further deposited with a 2 nm TiO2 film as the photoanode. The configuration of plasmonic DSSCs
4

containing both dye and electrodes is shown in Figure 1.1(a), in which the electrolyte is typically
I
-
/I
-3
. Upon the absorption of sunlight, the dye injects an electron into the TiO2 network. The
electron travels through this network until it is collected. The resulting dye radical is reduced to its
ground state by a redox process of I
-
/I
3-
, as shown in Figure 1.1(b)[17].

In this plasmonic DSSCs,
the resulting extremely strong local EM field through collapsed Au/Al2O3/Au nanofingers can
improve the absorption of incident sunlight and the extinction of dyes simultaneously, which leads
to a high enhancement of PCE. The results show that the PCE is mostly improved as compared to
the normal photoanode of Au/Al2O3/TiO2. This new structure with low cost is also applicable to
other types of solar cells.

Figure 1.1. Schematic configuration of Plasmonic DSSCs under illumination of sunlight. (a) DSSCs consist
of a photoanode that is fabricated by 2 nm TiO 2 film deposited on the collapsed Au/Al 2O 3/Au nanofingers
with 5 nm gap, and a counter electrode with ITO glass. (b) Schematic electrons traveling into the TiO2
photoanode network and a redox process typically by I
-
/I
3-
electrolyte.

5

Chapter 2 Device Characterization
2.1 Numerical Simulations on TiO2-Au/Al2O3/Au Nanofingers
To quantitatively demonstrate the EM field enhancements, we run simulations for near-filed
distribution and localized EM field enhancement using a commercial finite-element method-based
software package (COMSOL Multiphysics). In the simulations, the quantum effects are excluded
due to the relatively large gap size (5 nm). The permittivity of Au is interpolated from the
experimental data[42], and the refractive index of the polymer support is set as 1.48[39], based on
our measurements. Here, the 540 nm plane wave that is at the non-resonance condition is also
calculated due to the absorption of N719 dye, as shown in Figure 2.1(a)-(c). At the non-resonance
of 540 nm, the local EM field enhancement((E/Einc)
2
) at the dielectric area reaches up to ~ 100-
fold due to the coupling of surface charge, which is beneficial to DSSCs. The simulation confirms
that the coupled nanostructures can efficiently improve the absorption of the DSSCs.

Figure 2.1. Top view EM field distributions of the Au/Al 2O 3/Au nanofingers. (a) and TiO 2- Au/Al 2O 3/Au
nanofingers (b) at 540 nm. Cross-sectional distribution of the EM field on the Au/Al 2O 3/Au nanofingers (c)
at 540 nm.

6

2.2 SEM and Optical Properties of Plasmonic DSSCs
Plasmonic DSSCs based on the collapsed Au nanofingers are mainly described in the experimental
sections. In the collapsed Au/Al2O3/Au nanofingers, the gap size is precisely defined by twice the
Al2O3 thickness, which is 5 nm. Since the tunneling barrier height is 2.52 eV that is defined by the
difference between the Fermi level of Au (5.1 eV) and the electron affinity (EA) of Al2O3 layer
(2.58 eV), the strongest field enhancement occurs at a 2 nm Al2O3 dielectric gap determined by
classical EM theory and quantum mechanics[24].

However, by considering fluorescence
quenching, we have demonstrated that 5 nm Al2O3 dielectric gap is the optimal distance[43]. Thus,
a 2.5 nm Al2O3 dielectric film is deposited here to realize 5 nm nanogap. It is noted that a 2 nm
amorphous TiO2 layer is successfully proved to afford efficient electron transport in DSSCs and
thus 2 nm TiO2 layer is selected[17]. Furthermore, since the Al2O3 layer has the lower permittivity
than TiO2 film, thicker high permittivity TiO2 film will lead the EM field to be much more confined
inside of the dielectric gap, which is not useful to the extinction of dyes. In addition, Al2O3 layer
can provide a higher tunneling barrier and a stronger screening for the radiation field than TiO2,
which leads to strong fluorescence enhancement for a dye[43, 44]. Therefore, we combine a 2.5
nm Al2O3 layer with a 2 nm TiO2 layer to construct the photoanode in which the 2 nm amorphous
TiO2 layer only affords efficient electron transport network in DSSCs.
Figure 2.2(a) shows a scanning electron microscopy (SEM) image of 2.5 nm Al2O3 coated Au
nanofingers prior to the collapsing process. The diameter and height of each nanofinger are 70 nm
and 300 nm, and the lattice spacing is 130 nm. The lattice spacing and Au cap size can be adjusted
by the designed mold with atomic precision, which is fabricated by double interference
lithography. Through the collapsing process, the nanofingers with the height of nearly 300 nm tend
to form tetramer Au/Al2O3/Au nanostructures. The coverage of Al2O3 film on the Au tip of
7

nanofinger was demonstrated by cross-sectional TEM in our previous result[24]. Based on this
tetramer Au/Al2O3/Au nanofingers, a 2 nm TiO2 layer is coated on their surface, as shown in Figure
2.2(b). In addition, some nanofingers at a small area with the defects of remaining a single
nanofinger have not collapsed due to the uniformity of RIE etching process, as shown in Figure
2.2(b). However, for such large area, the effect of these defects on the performance of DSSCs are
very small. To study the optical properties of collapsed nanofingers, the reflectance spectra are
measured, as shown in Figure 2.2(c). The results show that the collapsed Au/Al2O3/Au nanofingers
have a resonance band centered at approximately 660 nm, which can be ascribed to the bonding
mode of the localized surface plasmon resonance (LSPR) of Au caps coupling each other to form
bonding-LSPR[40],

as shown by the black line in Figure 2.2(c). After the deposition of TiO2 film,
the TiO2-Au/Al2O3/Au nanostructures show a little redshift and is centered approximately at 670
nm, as shown by the red lines in Figure 2.2(c). This little difference in the central wavelength for
the coupled bonding-LSPR is ascribed to high index of TiO2 films. The resonance can cover a
broadband range from ~ 550 nm to ~ 800 nm which is consistent with energy spectra of sunlight.
For comparison, the photoanode of Au/Al2O3/TiO2 films on the plain glass has small response to
the spectra range for the sunlight, as shown by the blue line in Figure 2.2(c). Therefore, the
plasmonic nanostructure can induce scattering and absorption which can enhance the sunlight
absorption. To quantitatively demonstrate EM field enhancements in collapsed nanofingers, we
run simulations for near-filed distribution and localized EM field enhancement using a commercial
finite-element method-based software package (COMSOL Multiphysics). The permittivity of Au
is interpolated from the experimental data[45], and the refractive index of the polymer support is
set as 1.48[39]. The 660 nm plane waves that is at the resonance condition is polarized parallel to
the gap direction, which corresponds to bonging-LSPR[46].

The cross-sectional distribution of
8

coupled EM field for the tetramer Au/Al2O3/Au nanofingers is depicted in Figure 2.2(d). It shows
that the strong EM field between the two approaching Au/Al2O3 nanofingers is ascribed to
hybridization of the dipole resonances into the bonding-dipole plasmon modes. In this case, the
local electric field enhancement ((E/Einc)
2
), reaches up to ~10
4
. In addition, at the non-resonance
of 540 nm due to the absorption of N719 dye, the local EM field enhancement ((E/Einc)
2
) at the
dielectric area is ~100-fold due to the coupling of surface charge as shown in Figure 2.1. Therefore,
by plasmonic nanofingers, the incident photons efficiency can be improved, and the charge carrier
density for the sensitizing dyes can be further boosted. It is noted that in our design, since the
tunneling barrier heights for Au/Al2O3 and Au/TiO2 are 2.58 eV and 0.9 eV, respectively, and thus
the near-field EM enhancement to dyes emissions process dominates the electrons injection to
TiO2 network, and hot electrons injection from Au to TiO2 network is not major contribution[44].

Figure 2.2. SEM and Optical properties for the photoanode of TiO 2-Au/Al 2O 3/Au nanofingers. (a) SEM
image of Au-nanofingers matrix. (b) SEM side view image of TiO 2-Au/Al 2O 3/Au nanofingers. (c)
9

Reflectance spectra measurements. Red line presents the TiO 2-Au/Al 2O 3/Au collapsed nanofingers; Black
line presents the Au/Al 2O 3/Au collapsed nanofingers; Blue line presents the Au/Al 2O 3/TiO 2 composite
films. (d) Cross-sectional distribution of the EM field on the TiO 2-Au/Al 2O 3/Au nanofingers at 660 nm.

2.3 Fluorescence Enhancement of N719 Dye on Photoanode
In order to further verify plasmon induced DSSCs performance enhancement, we investigate the
fluorescence enhancement of N719 dye on the nanofingers because the fluorescence enhancement
is a direct evidence for the absorption enhancement in plasmonic DSSCs[37, 47].

In the
experiment, the photoluminescence (PL) of the N719 dye on the 2 nm TiO2 film coated
Au/Al2O3/Au nanofingers which is the same as the photoanode of plasmonic DSSCs, and the
Au/Al2O3/TiO2 films on the plain glass are measured, as shown in Figure 2.3. The emission peak
position of N719 dye almost does not shift and only the fluorescence intensity increases. The
results show that the PL enhancement of N719 dye on the plasmonic nanofingers is nearly 10 times
higher than the normal photoanode, which is the main reason for the strong plasmonic EM field
enhancement. In addition, the LSPR position is only partially overlapped with the emission peak
position of N719 dye. By the optimization between the plasmonic resonance and the emission band
of dyes, the efficiency of DSSCs can be further improved.

10

Figure 2.3. Fluorescence enhancement of N719 dye on the photoanode. (a) Fluorescence intensity of N719
dyes on TiO 2-Au/Al 2O 3/Au nanofingers (red line), and Au/Al 2O 3/TiO 2 composite films (blue line). (b)
Magnified view of fluorescence intensity of N719 dyes on Au/Al 2O 3/TiO 2 composite films.

2.4 Electrical Characterizations of Plasmonic DSSCs
To investigate the performance of plasmonic DSSCs, we carried out the measurements. A full list
of the solar cells data is shown in Table 2.4. The Table 2.4 contains various characterizations for
describing Solar Cells’ performances which include open circuit voltage (Voc), short circuit current
(Isc), short circuit current density (Jsc), measured maximal voltage (Vmax), measured maximal
current (Imax), measured maximal power (Pmax), fill factor (FF) and power convert efficiency
(PCE), the following R at Voc and R at Isc represent the measured resistance respectively at open
circuit voltage and short circuit current, and the Exposure represents the exposure time in the
simulative sun light which characterizes a measured parameter for Solar Cells. Open circuit
voltage indicates the voltage describes as electrical potential between two terminals of the solar
cell while short circuit current indicates a maximal current when the solar cell circuit has no load,
11

the PCE described as power convert efficiency indicates the ability of sun energy converts to
electrical energy which is the most important characterization for Solar Cells. The measurement
shows that the plasmonic DSSCs have better performances than normal DSSCs. The normal
DSSCs have an average Voc of 0.50 V and an average Jsc of 0.058 mA/cm
2
while the plasmonic
DSSCs show a higher Voc of 0.73 V and a higher Jsc of 0.136 mA/cm
2
. However, the Fill Factor
plasmonic DSSCs decreases from 40 to 26 for comparison with normal DSSCs, which can be
ascribed to the lower conductivity of substrate for nanofingers. All in all, the plasmonic DSSCs
have a PCE of 0.03% which three times higher than the normal DSSCs’ PCE of 0. 01%.
Table 2.4. Characterizations of plasmonic DSSCs. Group A presents DSSCs based on the photoanode of
TiO 2/Al 2O 3/Au films as the comparison, and Group B presents plasmonic DSSCs based on the collapsed
Au nanofingers.
Voc Isc Jsc Imax Vmax Pmax Fill
Factor
PCE R at Voc R at Isc Exposure
Unit V A mA/cm
2
A V mW Ω Ω s
A1 0.5119529 0.00001493 0.059736 0.00000979 0.31027996 0.00303804 39.7362 0.0001 13542.75798 18068.868 25.031
A2 0.50738243 0.00001475 0.058994 0.00000975 0.30878491 0.00300984 40.2215 0.0001 13861.21389 17604.748 24.609
A3 0.49767457 0.00001468 0.058707 0.00000972 0.29927374 0.002909 39.8263 0.0001 14206.70709 17880.558 24.844
A4 0.46882946 0.00001373 0.054923 0.00000955 0.27873964 0.00266326 41.3718 0.0001 13297.02664 17412.502 24.828
A5 0.46264817 0.00001352 0.054062 0.00000958 0.27844114 0.0026663 42.6412 0.0001 13040.81306 17306.741 24.141
B1 0.71718935 0.00003255 0.130191 0.00001729 0.36501215 0.00631235 27.0419 0.0003 20834.90908 27056.656 22.969
B2 0.73347285 0.00003363 0.134503 0.00001768 0.36687555 0.00648712 26.3024 0.0003 21890.75192 25531.296 22.969
B3 0.7469219 0.00003407 0.136286 0.00001776 0.36877877 0.00655064 25.7405 0.0003 22919.18506 24801.626 22.969
B4 0.76049373 0.00003412 0.136487 0.00001769 0.37121927 0.00656852 25.3128 0.0003 24246.98111 24733.894 22.969
B5 0.77324649 0.0000338 0.135199 0.00001742 0.37376996 0.00651122 24.9133 0.0003 25863.14354 24811.19 22.953

12

Furthermore, we have carried out the dark current measurement as shown in Figure 2.4. The result
shows that our plasmonic DSSCs have high resistance, which is the main reason for the low FF.
The FF is mostly dependent on the separation of electron and hole from a dye under the excitation.
The photo-excited electrons rapidly transferring into the TiO2 network will cause a high FF. In
our plasmonic photoanode of TiO2-Au/Al2O3/Au nanofingers, since the small dye molecules are
mostly trapped on the top surface of nanofingers, the electron does not easily transfer into the
feedthrough in photoanode. In addition, the polymer base has lower conductivity while the
conductive wire connects to the photoanode to export the current from the Al2O3 coated polymer,
which is confirmed by the high resistance at Isc in measurement as shown in Table 2.4.

Figure 2.4. Dark Current-voltage plot of DSSCs with photoanodes of TiO 2-Au/Al 2O 3/Au nanofingers (blue
line), and TiO 2/Al 2O 3/Au composite films (red line).
13

2.5. Comparison between Normal DSSCs and Plasmonic DSSCs
Figure 2.5(a) shows the picture of assembled DSSCs, in which the red one represents plasmonic
DSSCs based on the collapsed Au nanofingers and the blue one is DSSCs based on the photoanode
of Au/Al2O3/TiO2 films (noted as normal DSSCs) for comparison. The current of the device can
be measured when it is electrical biased and sunlight illuminated[42]. During the current density–
voltage (J–V) measurements, the active area of DSSCs is set to 0.25 cm
2
. The J–V characteristics
of DSSCs are measured under sunlight conditions (AM1.5G, 100 mW cm
-2
, with a xenon lamp
light source). Figure 2.5(b) shows the J–V curves of DSSCs. To clearly observe, the curve in the
green dotted square region in Figure 2.5(b) is zoomed in and shown in Figure 2.5(c). The
fluctuation of J–V curve for normal DSSCs may due to the quality of the deposited film. It is
clearly seen that the open circuit voltage (Voc) of plasmonic DSSCs increases from 0.50 V to 0.73
V, and the Jsc increases from 0.058 mA/cm
2
to 0.136 mA/cm
2
, as compared to normal DSSCs.
Further, for our plasmonic DSSCs, the PCE improves from 0.01% to 0.03% (as shown in Table
2.4), and the maximum power output (Pmax) enhances from 2.7 μw to 6.5 μw as shown in Figure
2.5(d). The enhancements of PCE and the Pmax are consistent with the trend of the Jsc improvement
for plasmonic DSSCs. In our design, since TiO2 layer is directly deposited on the collapsed
nanofingers, the sensitized surface area is not increased by compared to normal DSSCs and the
enhancement of Jsc in plasmonic DSSCs is mainly due to the improvement of sunlight absorption.
Therefore, the improvements of the PCE and Pmax are mainly induced by plasmonic nanofingers.
However, as shown in Figure 2.5(d), the Fill Factor (FF) for plasmonic DSSCs decreases from 40
to 26 for comparison to normal DSSCs. The FF is mostly dependent on the separation of electron
and hole from a dye under the excitation. The photo-excited electrons rapidly transferring into the
TiO2 network will cause a high FF. In our plasmonic photoanode of TiO2-Au/Al2O3/Au
14

nanofingers, since the small dye molecules are mostly trapped on the top surface of nanofingers,
the electron does not easily transfer into the feedthrough in photoanode. In addition, the polymer
base has lower conductivity while the conductive wire connects to the photoanode to export the
current from the Al2O3 coated polymer, which is confirmed by the measurement of high resistance
at Isc (short circuit current), as shown in Table 2.4. Furthermore, the dark current measurement also
proves this high resistance, as shown in Figure 2.4. These factors decrease the separation of
electron and hole from the dyes and cause a relative low FF. Here, we note that though the
performance of our plasmonic DSSCs has an obvious improvement, the PCE of solar cell is still
small as compared to the published data[17], which can be ascribed to the simple assembly of the
solar cells. In our assembly, the conductive wire directly connects to the TiO2 layer of photoanode,
and thus causing low conductivity. By optimizing the fabrication flow, for example, using ITO as
base and precoating an Au layer on the polymer base, the performance can be further improved.
Except for low conductivity of photoanode, as compared to DSSCs with thicker, porous TiO2
films, our deposited TiO2 film is only 2 nm by the consideration of the incident light to excite the
LSPR mode of Au nanofinger. The load of dye on this ultrathin TiO2 film is very low, which make
the PCE lower. It is also consistent with the previous report for DSSCs with thinner amorphous
TiO2 films[17].

Here, we only consider a proof of concept for our coupled nanofingers in the
application of plasmonic solar cells.
15

Figure 2.5. Characterizations of plasmonic DSSCs. (a) Photo of fabricated DSSCs. Red one represents
DSSCs based on the collapsed Au nanofingers (defined as plasmonic DSSCs) and the blue one is DSSCs
based on the photoanode of Au/Al 2O 3/TiO 2 films (defined as normal DSSCs). (b) Photocurrent density -
voltage plot of DSSCs with photoanodes of TiO2-Au/Al 2O 3/Au nanofingers (red dot line), and
Au/Al 2O 3/TiO 2 composite films (blue line). (c) Magnification of Photocurrent density -voltage plot of
DSSCs for green rectangular dot line in (b). (d) Fill factor and the maximum power output of solar cells. In
the measurement, we perform 5 groups for both plasmonic DSSCs and normal DSSCs. In the plot, red
solid rectangular and red hollow rectangular present fill factor and the maximum power output of plasmonic
DSSCs, respectively. Blue solid circular and blue hollow circular present fill factor and the maximum
power output of normal DSSCs, respectively.
16

Summary
In summary, we have demonstrated the plasmon enhanced DSSCs through coupled nanofingers.
In plasmonic DSSCs, considering the local field enhancement and dye quenching which is both
dependent on the separation distance, the collapsed Au/Al2O3/Au nanofingers with 5 nm Al2O3
gap are deposited with 2 nm TiO2 as photoanode to enhance the absorption of sunlight. The results
show that, for our designed plasmonic DSSCs, the PCE can be mostly improved, and the maximum
power output enhances from 2.7 μw to 6.5 μw as compared to that based on the photoanode of
Au/Al2O3/TiO2 films. The improvement of plasmonic DSSCs performance can be ascribed to the
coupled EM field enhancement within the sub-nanometer gap. In addition, fluorescence
enhancement of N719 dyes on the plasmonic nanofingers is measured with nearly 10 times higher
than that on the plain Au films, which further proves the strong plasmonic effect on DSSCs
performance. This plasmonic nanostructure enables the precise engineering of the gap-plasmon
modes and can be successfully fabricated by nanoimprint lithography into large areas with low
cost, which has huge potentials to be used as photoanode for other types of solar cells, such as
organic solar cells, perovskite solar cells.

17

Topic 2. Collapsed Nanofingers by DNA-Functionalization as SERS
Platform for Mercury Ions Sensing

18

Chapter 3 Introduction of DNA-modified Plasmonic Nanofinger
Platform for Chemical Sensing
Surface-enhanced Raman scattering (SERS) based on plasmon resonance of metallic
nanostructures is an emerging approach for label-free molecule fingerprint sensing with high
sensitivity, and thus has broad applications including environmental pollutant detection, disease
clinical assay, and chemistry[48-52]. In SERS, in order to avoid the disturbance of other
substances, simultaneously capturing and localizing molecules into plasmonic hotspots become
extremely challenging due to the requirements of high selectivity and sensitivity in
applications[53-55]. In addition, in comparison to individual metallic nanoparticles, the gap
plasmon nanostructures with sub-nanometer scale gap can generate a strongly coupled electric
field, and thus are preferred in SERS[22, 26, 27, 29, 56]. To achieve high-sensitivity detection,
SERS platform with precisely constructed gap plasmons nanostructures and capable of capturing
the target molecules to hot spot is crucial. By use of DNA or antibody molecules combining with
metallic nanostructures, the achieved metal/DNA/metal gap plasmon composite nanostructures are
an effective strategy especially for disease markers detection[57-59]. For example, the DNA
origami technique was employed to accurately position the individual gold nanoparticles which
created the dimer plasmonic nanostructures with reliable sub-5nm gap sizes[60]. DNA-tailorable
technology was also designed to realize well-defined gold nano-bridged nanogap particles with
uniform and hollow gap (~ 1 nm) between the gold core and gold shell[61]. However, based on
the periodic nanostructures SERS substrates that are fabricated by physical mold etching
techniques, using DNA modification technology to construct gap plasmons at sub-nanometer scale
and producing an in-plane coupled electric field are still very challenging[35, 62].

19

In this topic, we report that using DNA modification and collapsed metallic flexible nanofingers,
a novel gap plasmon periodic nanostructure was achieved. The strongly enhanced in-plane electric
field is concentrated within an ultrathin DNA gap with a well-defined gap size down to sub-
nanometer scale. The existence of DNA gap layer simultaneously captured and localized
molecules into plasmonic hotspots so that the molecules could be detected selectively and
sensitively. Mercury (II) (Hg
2+
) detection with ultra-low concentration by our suggested
Au/DNA/Au coupled nanofingers was illustrated[63-67]. Our method to achieve DNA modified
gap plasmonic nanostructures is applicable to a broad range of other antibodies to construct
Au/antibody/Au coupled systems and has wide application in different disease clinics.

20

Chapter 4 Device Fabrication
A schematic for the formation of Au/DNA/Au and Hg
2+
detection is shown in Figure 4.1. The
interaction principle between the DNA and Hg
2+
is shown in Figure 4.1(a)(b)(c)[67]. High-density
array of Au nanofingers with flexible polymer support on the glass substrates were fabricated by
our well-defined nanoimprint lithography (NIL) and reactive-ion etching (RIE) (Figure 4.1(d))[24,
38, 40]. These flexible nanofingers were incubated in a DNA solution, taken out and air-dried. The
singlestranded DNA were connected to Au surface via thiol binding[67], as shown in Figure 4.1(e).
In the air-dried process, Au tips of flexible nanofingers finely touched each other driven by
capillary force, and Au/DNA/Au coupled nanofingers were achieved in which DNA aptamer was
as the space layer, as shown in Figure 4.1(f). When Hg
2+
were dropped on Au/DNA/Au coupled
nanofingers, DNA aptamers array became vertical on Au surface from the horizontal direction as
shown in Figure 4.1(g), which makes adenine slightly away from Au surface and its Raman signal
decreases as a consequence[63]. Hg
2+
is detected as indicated by the ratio of guanine to adenine
Raman signals.
21

Figure 4.1. Schematic SERS detection of Hg
2+
by collapsed Au nanofingers with DNA functionalization.
(a) Configuration of DNA aptamer consisting of two segments of both thymine (T, red color) as the Hg
2+

recognition and the capture segment (blue color) containing guanine (G) and adenine (A). (b) When DNA
aptamers are immobilized to Au surface via thiol binding (HS), sing-strand DNA arrays horizontally lay
on the Au surface due to good affinity of adenine to Au. (c) After Hg
2+
are bonded with thymine, DNA
arrays are vertically distributed on Au surface. (d) Based on above principle, DNA were firstly connected
on flexible Au nanofingers via thiol binding (e). After DNA solution air dried, DNA Functionalized Au
nanofingers were physically touched each other via a capillary force-induced collapsing process so that
Au/DNA/Au coupled nanofingers were achieved in which DNA aptamer was as the space layer (f). Finally,
when Hg
2+
were dropped on the Au/DNA/Au coupled nanofingers, DNA aptamers arrays became vertical
on Au surface from the horizontal direction (g) so that adenine is a little away from Au surface and its
enhanced Raman signals decreases. By the ratio of guanine to adenine Raman signals, Hg
2+
is successfully
detected.
22

Chapter 5 Device Characterization
5.1 Optical Performance of DNA-modified Nanofingers
Our well-defined high-density arrays of Au nanofingers with a flexible polymer support on the
glass substrates were fabricated using NIL and RIE and the details were shown in method (Figure
5.1(a))[24]. The typical diameter of each nanofinger and lattice spacing is 70 nm and 130 nm
respectively, and the height is controlled to 300 nm including UV nanoimprint resist fingers and
50 nm Au layer on top for forming tetramer structures in the collapsible process. In addition, the
geometric parameters of nanofingers can be finely tuned to achieve the different plasmonic
resonances according to the mother molds in NIL[40]. These flexible Au nanofingers then were
incubated in a 10
-3
M DNA solution for 12 hours in 4
◦
C refrigerator before they were taken out
and air-dried. Due to the pre-treated process for DNA aptamer, the single stranded DNAs were
connected to Au surface via thiol bindings and tended to horizontally lay on the surface of Au
nanofingers due to good affinity of adenine to Au at the tail of DNA aptamer, and flexible Au
nanofingers simultaneously touched each other via a capillary-force-induced collapsing process so
that Au/DNA/Au coupled nanofingers were formed with DNA aptamer as the spacer layer, as
shown in Figure 5.1(b). Finally, these DNA aptamers modified Au nanofingers were washed
carefully in DI water several times and dried in fume hood without interruption. Once Au
nanofingers touch each other, they will not separate any more due to the good affinity of adenine
to Au.
To characterize the collapsed nanofingers, the high-resolution transmission electron microscope
(HR-TEM) cross-sectional analysis was acquired, as shown in Figure 5.1(c). It clearly indicates
that Au nanofingers completely touch each other through DNA modification process. It is noted
that the DNA spacer layer is invisible because the molecules cannot be observed in normal TEM
23

analysis. The optical measurement is an indicator to reflect the coupling strength of the
neighboring collapsed nanofingers. The transmittance spectra were measured, as shown in Figure
5.1(d). Prior to collapse, Au nanofingers have a localized surface plasmon resonance (LSPR) band
centered at approximately 580 nm, which is due to the plasmon-induced dipole resonance of the
Au nanofingers. After collapse, the LSPR of DNA aptamer modified Au nanofingers has a
significant redshift that is centered at approximately 650 nm (Figure 5.1(d)), which indicates
enhanced electric field coupling than non-collapsed nanofingers. It shows our collapsed nanofinger
configuration is crucial to SERS enhancements.

Figure 5.1. Characterizations for DNA modified Au nanofingers. (a) SEM image of nanofingers before
collapse. (b) SEM image of DNA modified Au-nanofingers after collapse. (c) TEM cross-sectional view
of collapsed Au nanofingers. (d) Transmittance spectra of prior to collapse for Au nanofingers and after
DNA modification and collapse for Au/DNA/Au nanofingers.

24

5.2 SERS Detection of Hg
2+
based on DNA-modified Nanofingers
The DNA aptamers not only exist in the gap of adjacent nanofingers but also on top and sidewall
of nanofingers, which leads to Raman signal enhancement in SERS due to the strongly coupled
electric field. The DNA aptamer used in the experiment is HS-(CH2)6-T(10)G(8)A(8) that consists
of two segments of both thymine (T) as the Hg
2+
recognition and the capture segment containing
guanine (G) and adenine (A)[66, 67]. In Au/DNA/Au coupled nanofingers, the single stranded
DNA tended to lay down horizontally on the surface of Au nanofingers due to good affinity of
adenine to Au at the tail of DNA aptamer before the Hg
2+
is dropped on them[67], which makes
the guanine (G) and adenine (A) segments with relatively strong SERS signals. After Hg
2+
solution
was dropped onto the surface of DNA functionalized Au nanofingers, Hg
2+
ions tend to specially
bind to thymine bases and form T-Hg
2+
-T pairs through N-Hg
2+
-N J-coupling bonding between
adjacent single strand DNA[65, 66]. The T-Hg
2+
-T pairs can convert DNA aptamer from laying
on the surface to relatively rigid duplex-structure that is vertical to the Au surface[67]. For this
duplex-structures of DNA aptamer on Au surface, the adenine will leave from the contacted Au
surface, so that distance between the adenine and the maximum enhanced electric field at the
interface increases, which induces the SERS signal of adenine decrease due to the exponentially
decay of localized electric field from the surface. Based on this principle, the Hg
2+
ions can be
quantitatively detected using the ratio of adenine SERS intensity to guanine SERS intensity (here,
it is noted by IA/IG), which can avoid the uncertainty brought by the operation and nonuniformity
of SERS substrates. SERS spectra with 785 nm excitation are used to characterize Hg
2+
ion
concentration from 1×10
−3
M to 10
−9
M as shown in Figure 5.2(a)[68]. The results show that, at
the absence of Hg
2+
, the adenine and the guanine have relative strong SERS signals, centered at
736 cm
-1
and 650 cm
-1
, respectively. After the presence of Hg
2+
, the SERS signal of 736 cm
-1
for
25

adenine weakens. Therefore, the IA/IG will become smaller with the increase of Hg
2+
. The
recorded IA/IG with the Hg
2+
ions concentrations from 1×10
−3
M to 10
−9
M for the quantitative
measurement for Hg
2+
is shown in Figure 5.2(b). The results show that IA/IG is nearly linear with
the Hg
2+
, and the detection limit of 10
-9
M has been achieved.

Figure 5.2. SERS detection of Hg
2+
based on DNA aptamer. (a) The SERS signals of the oligomer
T(10)G(8)A(8) used in this detection system in response to Hg
2+
ions of various concentrations. (b) The
relative SERS ratio of I(736 cm
−1
) /I(650 cm
−1
) versus Hg
2+
concentrations.

5.3 Numerical Simulations on Au/DNA/Au Coupled Nanofingers
To theoretically study the electric field enhancements for Au/DNA/Au coupled nanofingers with
DNA functionalization, numerical simulations using a commercial finite-element method-based
software package (COMSOL Multiphysics) were implemented. The quantum tunneling effect is
neglected for simplicity[22, 24]. The parameters of the nanofingers in simulations are consistent
to the experiment and the permittivity of Au is interpolated from the experimental data[45], and
26

the refractive index of the polymer support is set as 1.48 the same as measured value. Figure 5.3(a)
shows the numerical simulations of the transmission spectrum for Au nanofingers. Prior to the
collapse, there is a valley in the transmission curve at ~ 530 nm with an incident electric field
parallel to the gap direction, which corresponds to dipole resonance as shown in insert of Figure
5.3(a). This LSPR of the single Au-nanofinger is slightly different with the experimental
observation. After the collapse, under the incident electric field polarized along the dimer axis, the
stronger near-field interactions of the two approaching Au nanodisks hybridize the dipole
resonances into the bonding-dipole plasmon modes identified by the typical surface charge
distribution shown in Figure 5.3(a), which presents a clear redshift to the 650 nm that is almost
consistent with the experimental observations[46]. By careful analysis for experimental and
simulation results, the red shifts by dipole hybridization are 70 nm (from 580 to 650 nm) and 120
nm (from 530 to 650 nm) which is probably induced by the electrons tunneling due to spatial
configuration of DNA aptamer[24, 29]. In addition, the calculated cross-sectional distributions of
the coupled EM field enhancement of the collapsed nanofingers depicted in Figure 5.3(b) shows
the coupled EM field. In this case, the SERS enhancement factor, which is generally proportional
to the fourth power of the local electric field enhancement ((E/Einc)
4
), reaches up to ~1×10
8
and
enables the single molecule detection sensitivity in SERS. Thus, our proposed Au/DNA/Au
coupled nanofingers can provide an extremely low-concentration molecules detections.

27

Figure 5.3. Numerical Simulations of Au nanofingers. (a) Transmission spectrum of Au nanofingers before
and after the collapse process with 2 nm gap and the inserts present the charge distribution. (b) Cross-
sectional distribution of the electric field on the collapsed nanofingers and zoomed-in view of electric field
distribution.

Summary
In summary, by combining DNA modification and Au nanofingers collapsed, we demonstrate a
SERS platform which enables the ultra-high sensitivity Hg
2+
detection. DNA aptamers are firstly
modified on the surface of Au nanofingers through thiol binding. Then, collapsing process driven
by capillary force during the evaporation process of DNA solution forms gap plasmons between
pairs of nanofingers in which DNA acts as the spacer layer. Through the formation of thymine-
Hg
2+
-thymine in DNA aptamers to change the spatial configuration of DNA, we demonstrate the
Hg
2+
detection up to 10
-9
M. Our strategy can be extended by the antibody modification to form
Au/antibody/Au coupled nanostructures which can produce a strong plasmonic electric field. This
Au/antibody/Au coupled nanofingers can simultaneously capture the antigen disease markers and
precisely localize them into plasmonic hotspots between pairs of nanofingers, which can enable
the broad applications of disease SERS detection with high selectivity and sensitivity.
28

Topic 3. Tuning Photoluminescence of CsPbBr3 Quantum Dots
through Plasmonic Nanofingers

29

Chapter 6 Introduction of Plasmonic-assisted Perovskite Quantum
Dots (QDs) Emission
All-inorganic lead halide perovskites (CsPbBr3) materials have drawn great attention due to their
unique optoelectronic properties, such as tunable bandgap, high efficiency quantum yield, narrow
emission spectrum and long carrier lifetime[69-73]. Hence, they become the promising candidates
for many applications including light emitting diodes[74, 75], solar cells[76], and
photodetectors[77]. In particular, CsPbBr3 materials in the forms of thin films and nanocrystals
have shown great potential in laser emissions at room temperature[78, 79]. The laser emissions of
perovskites can be excited by pulsed lasers and continuous wave (CW) pumped lasers. While CW
excitation is more efficient and industry-compatible than the pulsed laser excitation, hence lasing
pumped by CW excitation is a key stepping stone on the path to an electrically pumped laser
diode[80]. Recently, hybrid organic–inorganic lead halide perovskite films such as MAPbX3 have
be used as the gain media to realize CW-pumped lasing at room temperature[80-82]. However, the
relatively large device sizes of perovskite films limit their integration to on-chip systems. In this
case, fabricating nanolasing devices based on the perovskite nanocrystals such as quantum dots
(QDs) becomes an effective way to miniaturize the size of perovskite-based lasers. The light
emission efficiency of QDs is usually low within the weak coupling regime. To enhance the light
emission efficiency, strong coupling regime needs to be created. Especially, localized surface
plasmon resonance (LSPR) induced by metallic nanostructures is known to concentrate light into
subwavelength volumes with dramatic localized near field enhancement[83],

which can improve
the light emission performance of perovskite QDs. Therefore, the plasmonic nanostructure can
serve as a practical platform to manipulate the light emission of these perovskite QDs. At present,
the studies on incorporating perovskite QDs and metallic nanostructures have been widely
30

conducted[84-87], and these hybrid systems show excellent performances. For example, in the
chemically synthesized hybrid CsPbBr3@metal nanocrystals, plasmonic-assisted low-threshold
laser emission was successfully observed at room temperature under the excitation of pulsed
laser[88, 89].
Among these plasmonic metallic nanostructures, the gap plasmon systems are attractive and
preferred because of the strong coupled near field at the gap region. The strength of the coupled
near field increases exponentially as the gap size gradually decreases to the sub-nanometer scale
and this near field is defined as a hot spot due to its remarkable field enhancement[27, 34].

However, the quantum effects such as nonlocality and electron tunneling may reduce the
achievable near field enhancement when the gap size is too small[21, 90].

Although the strongest
near field usually locates at the metal surface, the PL of QDs is quenched rather than enhanced
when the perovskite QDs are located closely to metal surface due to the transfer of non-radiative
energy to metal[36, 37]. Chemically synthesized hybrid CsPbBr3@metal nanocrystals often have
functional surfactant ligands as the gap layer between the metal and QDs and the emissions
enhancement can be observed[91]. While for the metal nanostructures fabricated by physical
deposition, a suitable dielectric layer is necessary to avoid quenching. Therefore, finding the
optimal dielectric thickness as well as the appropriate distance between QDs and metal surface is
critical to improve the optical properties of perovskite QDs when the metal is grown by physical
deposition. Plasmonic nanogap structures with controllable dielectric gap spacer are proposed as
an effective way to reach this target[92].

Nevertheless, the fabrications of gap plasmon
nanostructures with precisely controllable gap sizes down to the sub-nanometer are still
challenging. Through the traditional fabrication methods such as photolithography and e-beam
31

lithography, it is difficult to fabricate uniform, reproducible and low-cost gap plasmon
nanostructures with the sub-nanometer gap sizes[35, 62].

At present, nanoparticle-over-mirror (NPOM) system is a popular gap-mode plasmonic nanocavity
in which a metal nanoparticle is dispersed on the surface of dielectric coated gold films. When a
single CsPbBr3 QD is located between a metal nanoparticle and a gold substrate, CW-pumped
nanolasing can be observed at low temperature of 120K[93]. However, this NPOM system is not
suitable to construct an on-chip device since its operation requires a low temperature environment.
In this topic, through incorporating CsPbBr3 perovskite QDs into the physically contacted Ag
nanofinger pairs with a 2 nm tetrahedral amorphous carbon (ta-C) gap, we demonstrated a strong
optical coupling between the gap plasmon and CsPbBr3 QDs. Due to the high permittivity and low
electron affinity of ta-C film, the proposed gap plasmon structures enable the localized electric
field redistribution and produce a significant field enhancement within the ta-C gap region to
improve the optical emission of QDs. It is noteworthy that the PL of the hybrid devices exhibit
remarkable boosting and polarization tunability. More importantly, it is found that the plasmonic-
assisted CsPbBr3 QDs show lasing-like PL curves at room temperature under the excitation of a
CW laser.

32

Chapter 7 Device Characterization
7.1 Schematic of CsPbBr3 QDs Emission on Ag Nanofingers
A schematic of the PL of CsPbBr3 QDs in collapsed Ag nanofingers is shown in Figure 7.1(a).
Here, the gap plasmonic mode is a key factor for the optical manipulation. The high-density
nanofinger dimer arrays were firstly fabricated by our well-developed nanoimprint lithography
and reactive-ion etching. The typical diameter and height of each polymer (PDMS) nanofinger are
70 nm and 650 nm, respectively. The lattice parameter and the distance between adjacent
nanofingers are 500 nm and 130 nm, respectively. Then, Ag layer with 50 nm thickness was
deposited on top of nanofingers by e-beam evaporation. Subsequently, 1 nm ta-C film was
deposited on the Ag nanofingers by filtered cathodic vacuum arc technology, and the samples were
tilted at 45-degree angle and rotated for a better coverage. It is noted that the ultrathin ta-C film
has high permittivity, low electron affinity and good biocompatibility. More importantly, the ta-C
film with sp
3
-bonding content over 90% has a dense structure even at a thickness of several
nanometers. Such dense structure can protect Ag from oxidation in air and improve the chemical
stability so that the plasmonic responses of Ag nanofingers can be maintained[40]. Finally, after
soaking the samples into ethanol and air-dried, the adjacent flexible nanofingers were collapsed to
form the physically touched dimer arrays by the capillary force. In this case, the gap size of each
Ag dimer is defined as twice of the ta-C film thickness. Figure 7.1(b) shows the scanning electron
microscopy (SEM) and transmission electron microscopy (TEM) images of the nanofinger arrays
after the collapse process, which are well consistent with the design. More details of the fabrication
can be found in our previously reports[24, 40]. Compared to NPOM system[93], strong electric
field confinement is achieved between the two contacted nanofingers as a gap-mode plasmonic
nanocavity. Its significantly enhanced electric field can provide a strong coupling regime for QDs,
33

the optical emission is excited more efficiently with the normal incident light. As shown in Figure
7.1(c), the synthesized CsPbBr3 QDs are characterized as the uniformly distributed monodisperse
particles with an average diameter of 8 nm. And the high-resolution TEM image shows nearly 0.58
nm lattice fringe that is corresponding to the (200) crystal planes of the CsPbBr3 perovskite
structure.

Figure 7.1. Ag nanofingers/CsPbBr 3 QDs hybrid system. (a) Schematic of light emission in Ag
nanofingers/CsPbBr 3 QDs hybrid system. (b) Oblique-view SEM image of 1 nm ta-C coated Ag
nanofingers after collapse with a 500 nm scale bar. Insert figure: magnified TEM cross-sectional view of
collapsed nanofinger paired with 50 nm scale bar. (c) TEM images of the CsPbBr 3 QDs with 10 nm scale
bar. Insert figure: 0.58 nm lattice fringe characterized by high-resolution TEM image.

34

7.2 Photoluminescence of CsPbBr3 QDs on Ag Nanofingers
To compare the optical properties of CsPbBr3 QDs on collapsed nanofingers and silica (SiO2)
substrates, their absorption and PL spectra were measured. It is noted that all PL spectra in the
experiments were acquired under the CW laser excitation at 405 nm wavelength. The measured
absorption spectra and PL spectra of CsPbBr3 QDs on SiO2 substrates are shown in Figure 7.2(a).
The typical absorption edge is near 510 nm, which is corresponding to the 2.4 eV direct band gap
of CsPbBr3 QDs. And the PL peak is located at 518nm with 18 nm full width at half maximum
(FWHM). As mentioned above, the plasmonic nanofingers can provide strong near field
enhancement to improve the PL emission of QDs. Herein, the diluted CsPbBr 3 QDs were
uniformly placed on the collapsed nanofingers arrays to achieve significant field enhancement. As
shown in Figure 7.2(b), the PL spectra of CsPbBr3 QDs coupled to the gap plasmonic mode show
an obvious enhancement which can reach up to 4 times as large as the PL of QDs on SiO2.
Furthermore, time-resolved PL measurements of CsPbBr3 QDs on nanofingers and SiO2 substrate
were performed as shown in Figure 7.2(c). The PL spectra of CsPbBr3 QDs coupled to the gap
plasmonic mode show a faster spontaneous emission compared to QDs on SiO2, the decay time of
CsPbBr3 QDs decreases from 11.04 ns to 3.80 ns when they are on collapsed nanofingers. The
underlying physics is that the plasmonic structures can provide an additional high-rate
recombination channel. According to the PL lifetimes, a Purcell enhancement factor of 2.9 can be
calculated consequently. In addition, the light emission of QDs can be manipulated by the
polarization of incident light as shown in Figure 7.2(d). The results show that the PL intensities of
CsPbBr3 QDs on SiO2 substrate with x or y polarized incident light are nearly equal, while the PL
intensity of CsPbBr3 QDs on nanofinger with x-polarization incident light is three times as strong
35

as it with y-polarization incident light. Such polarization dependence results from the dimer gap
plasmonic modes provided by the nanofinger structure.

Figure 7.2. Photoluminescence of CsPbBr 3 QDs on Ag nanofingers. (a) Absorption spectra and PL spectra
of CsPbBr 3 QDs. The insert figure shows a photograph of CsPbBr 3 QDs solution. (b) PL spectra of the
CsPbBr 3 QDs on the nanofingers and SiO 2 substrate. (c) PL lifetime of the CsPbBr 3 QDs on different
substrates. (d) PL spectra of the CsPbBr 3 QDs on the nanofingers and SiO 2 substrate with different
polarization incident light. All PL spectra were acquired by the CW excitation at 405 nm wavelength.

36

7.3 Effect of Plasmonic Near Field on Light Emission of CsPbBr3 QDs
To better demonstrate the effect of plasmonic near field on the light emission of CsPbBr3 QDs, the
dark field scattering measurement was performed, as shown in Figure 7.3(a). The result shows that
an obvious scattering peak at 475 nm (black line) is observed and then red shift to 550 nm (red
line) after the collapse process, this red shift results from the induced bonding-dipole mode after
collapsing. In numerical simulation based on COMSOL Multiphysics, the geometrical parameters
were set to be consistent with the experimental design. The permittivity of Ag was chosen from
the COMSOL built-in material library. The refractive index of ta-C and PDMS were set as 2.44
and 1.41, respectively. The traveling direction of the plane wave was set along the negative z-axis
direction with x-direction polarization, and boundary condition of the simulation domain was set
to perfect matched layer (PML) condition. As shown in Figure 7.3(b), the result shows a dominant
scattering peak at 445 nm for 130 nm gap size (black line) and a 539 nm peak for 0 nm gap size
(red line). The simulation result well fits the experimental measurement except a slight shift in
resonance wavelength. This shift might be attributed to the geometric deviation of nanofingers
between the experiments and simulations. As shown in Figure 7.3(c), the typical surface charge
distribution and electric field distribution at 539 nm excitation confirm the bonding-dipole
plasmonic mode with large near field enhancement at the gap region, and the enhancement factor
can reach up to hundreds of times. Considering that the PL of CsPbBr3 QDs can be enhanced
significantly only near the gap regions of nanofingers and the collected PL also contains the signal
from the QDs located away from the gap region. This is the reason why the actual measured PL
enhancement is lower than the theoretical calculation. It is worth noting that the strongest electric
field at resonance would be spatially redistributed to ta-C/air interface rather than Ag/ta-C interface
due to the high refractive index of ta-C film. The key factor here is the competition between the
37

decay of electric field from the Ag/ta-C interface and the continuity condition of electric
displacement at ta-C/air interface[24, 40]. In addition, the electron affinity of ta-C is 1.50 eV, and
the work function of Ag is 4.26 eV, a resultant large tunneling barrier height (2.76 eV) suppresses
the electron tunneling across the gap even with the ultra-small gap size. Therefore, a strong local
electric field can be created within the gap for the enhancement of QDs emission.

Figure 7.3. Effect of plasmonic near field on light emission of CsPbBr 3 QDs. (a) The experimentally
measured dark field scattering spectra for the nanofinger structures before and after collapse process. (b)
Numerical simulation of the scattering spectra for the nanofinger structures before and after collapse
process. (c) Electric field distribution for the nanofinger pair at scattering peak of 539 nm. Insert figure:
corresponding charge distribution. (d) Schematic of proposed elementary steps for plasmonic induced
38

photoexcitation enhancement in hybrid system, red arrow: plasmonic induced resonant energy effect, dark
blue arrow: hot electron transfer effect, light blue arrow: plasmonic induced charge transfer effect.

A schematic of proposed elementary steps for plasmonic induced photoexcitation enhancement in
the hybrid system is shown in Figure 7.3(d). Firstly, the plasmonic induced resonant energy
transfer (red arrow) will dramatically enhance the density of photon states, which is beneficial to
the electron transition from the valence band to the conduction band in CsPbBr 3 QDs. Secondly,
the hot electrons transfer effect (dark blue arrow) and the plasmonic induced charge transfer effect
(light blue arrow) will further improve the photoexcitation[94]. At resonant wavelength, the LSPR
induced hot electrons stride over the Schottky barrier and inject from the Fermi level of Ag
nanofingers to the conduction band of CsPbBr3 QDs. As for the photoemission process, the
plasmonic induced resonant energy transfer will improve the spontaneous emission rate of
CsPbBr3 QDs. Furthermore, the high tunneling barrier height generated by ta-C film can suppress
the nonradiative loss caused by PL quenching effects. Therefore, a remarkable enhancement of PL
can be achieved in the CsPbBr3 QDs/Ag nanofingers hybrid system.

39

Chapter 8 Theoretical Study of Strong Coupling between CsPbBr3
QDs and Surrounding Ag Nanofingers
At room temperature, obvious lasing-like PL curves under the CW laser excitation at 405 nm start
emerging with the increasing incident power on the CsPbBr3 QDs/Ag nanofingers hybrid device.
As shown in Figure 8.1(a)(c), the PL peak intensity of CsPbBr3 QDs on SiO2 grows linearly with
the increase of pumping light power. The FWHM of the PL spectra is 17.5 nm, which is almost
unchanged even though the pumping power is increased from 1 mw to 5 mw. In contrast, the PL
spectra for CsPbBr3 QDs on collapsed nanofingers exhibit a different power dependence as shown
in Figure 8.1(b)(d). The CsPbBr3 QDs/Ag nanofingers hybrid structure under low excitation power
presents a broad emission spectrum with the peak centered at 508 nm and the FWHM of 20 nm.
With the increasing pumping power, the PL peak intensity increases quadratically at room
temperature. While the FWHM of the PL spectra shows an opposite trend, it reduces quickly with
the increasing incident power.
40

Figure 8.1. Power dependent PL spectra of CsPbBr 3 QDs. (a, b) Power dependent PL spectra of CsPbBr 3
QDs on SiO 2 and Ag nanofinger substrate under CW laser excitation at 405 nm. (c, d) Peak intensity and
FWHM of PL spectra of QDs on SiO 2 and Ag nanofinger substrate under different incident power. (e) Peak
intensity of PL spectra for Ag nanofingers/ CsPbBr 3 QDs hybrid systems as a function of squared incident
power.

41

The realization of lasing-like PL spectra at room temperature under the CW excitation can be
attributed to the strong coupling between the CsPbBr3 QDs and their surrounding Ag nanofingers.
Interestingly, PL intensity of CsPbBr3 QDs on Ag nanofinger substrate exhibits a quadratic
dependence on the incident power as shown in in Figure 8.1(e). Such quadratic relation can be
explained by a coupled-oscillator model between QDs and nanofingers[95]. The oscillator motion
of QDs and surface plasmon can be described using the following equations:

𝑟 ̈𝑆𝑃
(𝑡 )+ 𝛶 𝑆𝑃
𝑟 ̇𝑆𝑃
(t) + 𝜔 𝑆𝑃
2
𝑟 𝑆𝑃
(t) +g𝑟 ̇𝑄𝐷
(t)=𝐹 𝑆𝑃
(t) (1)
𝑟 ̈𝑄𝐷
(𝑡 )+ 𝛶 𝑄𝐷
𝑟 ̇𝑄𝐷
(t) + 𝜔 𝑄𝐷
2
𝑟 𝑄𝐷
(t) +g𝑟 ̇𝑠𝑝
(t)=𝐹 𝑄𝐷
(t) (2)

Here 𝑟 𝑆𝑃
and 𝑟 𝑄𝐷
represent the coordinates of surface plasmon and QDs oscillator motion, 𝐹 𝑆𝑃
and
𝐹 𝑄𝐷
indicate the external driving force for the oscillation. 𝛶 𝑆𝑃
, 𝛶 𝑄𝐷
, 𝜔 𝑆𝑃
and 𝜔 𝑄𝐷
are the transition
linewidth and oscillation frequency of surface plasmon and QDs respectively, g is the coupling
strength. Since the extinction of QDs is negligible compared to the surrounding nanofingers, it is
reasonable to assume 𝐹 𝑄𝐷
<< 𝐹 𝑆𝑃
. In this case, we can get the formula of 𝑟 𝑆𝑃
and 𝑟 𝑄𝐷
when the
light with frequency ω is incident on the coupled oscillators.

𝑟 𝑆𝑃
(𝑡 )=Re(
(𝜔 𝑄𝐷
2
– 𝜔 2
– 𝑖 𝛶 𝑄𝐷
𝜔 )𝐹 𝑆𝑃
(t)
(𝜔 2
– 𝜔 𝑆𝑃
2
+ 𝑖 𝛶 𝑆𝑃
𝜔 )(𝜔 2
– 𝜔 𝑄𝐷
2
+ 𝑖 𝛶 𝑄𝐷
𝜔 ) – 𝜔 2
𝑔 2
) (3)
𝑟 𝑄𝐷
(𝑡 )=Re(
−𝑖 g𝜔 𝐹 𝑆𝑃
(t)
(𝜔 2
– 𝜔 𝑆𝑃
2
+ 𝑖 𝛶 𝑆𝑃
𝜔 )(𝜔 2
– 𝜔 𝑄𝐷
2
+ 𝑖 𝛶 𝑄𝐷
𝜔 ) – 𝜔 2
𝑔 2
) (4)
The oscillator strength 𝑓 of a transition from a state |1⟩ to another state |2⟩ can be defined by:

𝑓 =
2𝑚 ∗
ħ
2
(𝐸 2
− 𝐸 1
)|⟨1|𝑟 |2⟩|
2
(5)
42

Based on above equation, the oscillator strength of QDs is proportional to the square of the
coordinate of oscillation, which then has a quadratic dependence on the driving force. Such
theoretical derivation fits our experimental results that PL intensity scales as square of the incident
power. As a result, the significant PL enhancement is confirmed to be correlated to the strong
coupling between the CsPbBr3 QDs and their surrounding Ag nanofingers. Meanwhile, the FWHM
of PL peaks exhibit an obvious decrease with the increasing excitation power. Such observation
can be explained by the Coulomb screening of quantum-confined Stark effect (QCSE)[96]. Given
an increasing excitation power, the internal electric field induced by the photogenerated carriers
weakens the QCSE. When the screening effect starts dominating the emission process, it results in
a reduction of FWHM[97]. As shown in Figure 8.1(d), the large FWHM of this lasing-like PL
spectra can be ascribed to the thermal effect under the CW excitation. While this lasing-like
emission behavior can still provide an effective method for realizing the nanolasing devices based
on the perovskite nanocrystals under the CW excitation. Furthermore, the dimer nanofingers can
be precisely defined by the initial electron-beam lithography (EBL) and then reproduced faithfully
by NIL, the geometric parameters of the nanofingers can be easily adjusted to match the bandgap
of diverse perovskite QDs for the potential applications in plasmonic-assisted perovskite QDs
nanolasers.

Summary
In summary, we have produced a CsPbBr3 QDs/Ag nanofingers hybrid structure with unique
optical performances. Here, the nanostructure is consisted of physically contacted Ag nanofinger
pairs with 2 nm ta-C layer as an ultra-small dielectric gap. Due to the localized electric field
43

redistribution and the strong field enhancement at the ta-C gap region, the PL performances of
CsPbBr3 perovskite QDs can be improved remarkably. Furthermore, the PL behavior of QDs
shows polarization dependence on the incident light after incorporating QDs into the plasmonic
dimer nanogap. Such polarization dependence can potentially serve as a special tuning method to
adjust the PL properties of QDs. More importantly, lasing-like PL curves can be observed at room
temperature by the CW excitation, which indicates the unique optical properties of the hybrid
structure. The results demonstrate that the integration of CsPbBr3 QDs and well-designed
nanofingers is an effective strategy to improve the photoemission performances of QDs, and it can
also be extensively applied in other optoelectronic nano-devices.

44

Topic 4. Hybrid Tuning of Sub-filaments to Improve Analog
Switching Performance in Memristive Devices

45

Chapter 9 Introduction of Memristive Devices
Memristive devices with continuously tunable resistance states possess tremendous potential for
analog computing applications such as neuromorphic computing because the internal resistance
states of memristors can be adaptively changed to emulate the biological synapses[98-105]. It is
generally accepted that the progressive resistance tuning of memristors is associated with the
charged dopants in the switching layer, oxygen deficiency (n-type), oxygen excess (p-type) and
metal cations can serve as dopants in the memristors[106-111]. Under the external stimulus such
as voltage and current, the directional motion of dopants causes internal resistive switching due to
the chemical and phase changes within the switching layer[112-115]. Once a large enough bias is
applied, a conductive dopant channel can be formed inside the switching layer and this channel is
usually called filament which has tens or hundreds of nanometers in diameter[116-118].
With the development of memristor-based analog computing, there is an increasing demand for
memristors with wide dynamic ranges and large amounts of multilevel states because they offer
more programable states[119-123]. The memristors can be tuned to multiple resistance states by
manipulating the maximum applied voltage and current, the total number of tunable states heavily
depends on the dynamic range[124]. Given a limited dynamic range, the number of multilevel
resistance states is difficult to be enhanced[125]. Meanwhile, even a large dynamic range does not
always lead to more multilevel states since a huge resistance jump may happen between two
neighboring states[126]. The incomplete understanding of the complex switching mechanisms also
obstructs the relevant studies. Many methods have been implemented such as doping or adding
different metal oxide films into the memristors, while the improvement is still restricted[105, 127,
128].
46

In this work, we report a new method to improve the analog switching performance of memristors
through a hybrid tuning of two sub-filaments. One sub-filament takes charge of a coarse resistance
adjustment, and the other is responsible for a fine adjustment. The two sub-filaments are created
by deploying Pt metal islands inside the oxide switching layer. Because of a stronger electric field
strength near Pt islands under applied bias, the dopant ions tend to move toward the metal islands.
A complete filament is then cut into two sub-filamentary sections by the islands. By selecting
appropriate material stacks and thicknesses, two sub-filaments exhibit different switching behavior
to play diverse roles (coarse and fine tuning). To experimentally demonstrate the above mechanism,
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors with Pt islands and ultra-thin Ti layer were
fabricated and characterized. This thin Ti layer is used to provide extra dopants to lower the
required voltage and current for the switching process. The hybrid tuning of two sub-filaments
results in a dynamic range from 600 Ω to 50 kΩ, such range is significantly broader than the
dynamic range (600 Ω - 8 kΩ) of a reference Pt/Ta/Al2O3/Pt memristor without sub-filaments. It
is noteworthy that large numbers of multilevel conduction states are uniformly distributed within
this broad dynamic range. More importantly, the mechanism of creating sub-filaments is
compatible with existing memristors, it can provide guidance for the future research on large
dynamic range and energy-efficient memristors.

47

Chapter 10 Theoretical Demonstration of Dynamic Range
Improvement by Sub-filaments
10.1 Effect of Pt Islands on Memristor Dynamic Range
For a conceptual explanation of how the insertion of metal islands improves the dynamic range of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors, a schematic of sub-filaments structure is
shown in Figure 10.1(a). Based on a Pt/Ta/Al2O3/Pt memristor, ultra-thin Pt and Ti layers are
deposited inside the Al2O3 switching layer to form a Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
structure. Pt acts as metal islands to divide each filament into two sub-filaments[129], and Ti
provides extra dopants for the switching process (more details of Pt and Ti roles are discussed in
Results and Discussion). Pt island stays in the middle of the switching layer and blocks the
diffusion of dopants across it. Then two sub-filamentary sections are formed and separated by the
Pt island, the island can be regarded as the bottom electrode of the upper sub-filament as well as
the top electrode of the lower sub-filament. Therefore, the entire memristor can be assumed as a
series connection of two individual sub-memristors. The upper sub-memristor has an identical
material stack to Pt/Ta/Al2O3/Pt memristors, the electrical characterization of Pt/Ta/Al2O3/Pt
memristors indicates that continuously tunable states can be achieved in the device.
Simultaneously, due to a different material stack of the lower Pt/Al2O3-x/TiOy/Al2O3-x/Pt sub-
memristor, it behaves diversely from the upper sub-memristor. Only two states, high and low
resistance states, were experimentally observed without any intermediate tunable states in the
control Pt/TiOx/Al2O3-x/Pt memristors. In this case, the upper sub-filament works as a fine
adjustment for the resistance of the entire memristor and the lower sub-filament is responsible for
a coarse adjustment (More details of electrical characteristics of upper and lower sub-memristors
are given in the Results and Discussion session). Compared to the initial Pt/Ta/Al2O3/Pt memristor
48

without metal islands, the entire dynamic range of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristors is enlarged because of the hybrid tuning of two sub-filaments.
However, there is considerable uncertainty in the forming locations of filament, not to mention
that the metal islands are also deposited at random positions. While in our design, metal island
must be exactly located in the path of a filament to divide it into two sections. A Comsol
Multiphysics simulation was performed to validate that the filament tends to explicitly situate at
the locations of metal islands. As shown in Figure 10.1(b), when there is a Pt island existing in the
Al2O3 switching layer under applied bias (1 V), the electric field strength becomes stronger near
the top and bottom of the island. The resistive switching process of Pt/Ta/Al 2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristors is mainly driven by electric field, which is verified by its bipolar
switching behavior in the electrical characterization[130]. Meanwhile, the drift process of dopants
has been proved to be primarily affected by the electric field before the completion of filament
formation[131]. Hence, the dopants have the tendency to aggregate near the metal island and
compose a filamentary channel there under applied bias.

49

Figure 10.1. Schematic of hybrid tuning of sub-filaments. (a) Schematic of sub-filaments in
Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al2O 3-x/Pt memristor. Two sub-filaments are divided by Pt islands and the
whole memristor can be considered as a series connection of two sub-memristors. (b) Simulation of Electric
field distribution in Al 2O 3 switching layer when there is a spherical Pt island (2 nm diameter) inside. Electric
field is stronger near the Pt island and the dopants inside the switching layer tend to move towards the island.
50

10.2 Size Effect of Pt Islands on Device Performances
To study the size effect of Pt island on the device performance, a Comsol simulation of electrical
field distribution inside the switching layer with larger lateral dimension Pt island was performed
as shown in Figure 10.2(a). When the lateral dimension of the island is 8 nm and its vertical
dimension is kept at 3 nm, the electric field strength near the island is 0.89 × 10
8
V/m. For a
spherical Pt island with 2 nm diameter as shown in Figure 10.1(b), the strongest field amplitude is
1.25 × 10
8
V/m. Therefore, the electric force applied on the charged dopants becomes weaker if
the Pt layer tends to form a film. Figure 10.2(b) shows the I-V curves of Pt/Ta/Al2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristor with 2 nm deposited Pt as the islands. This device requires high
voltage and current for the switching process and such observation is corresponding to the fact that
induced electric field is weaker in the switching layer and higher voltage is required for the
switching process. However, high switching voltage and current lead to the endurance issue, the
electrical breakdown occurs easily during the switching processes.

51

Figure 10.2. Size effect of Pt island on device performance. (a) Simulation of electric field distribution in
Al 2O 3 switching layer when the width of Pt island is 8 nm and the vertical dimension is 3 nm. Compared
to the spherical island with 2 nm diameter, island with larger lateral dimension induces weaker electrical
field nearby. (b) I-V characteristics of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al2O 3-x/Pt memristor with 2 nm
deposited Pt as the island layer. The memristor requires high voltage and current for switching, the electrical
breakdown occurs easily during the switching processes.

52

Chapter 11 Device Fabrication
Our fabrication approach of the cross-point memristors is shown in Figure 11.1(a)-(d). Si wafers
with 300 nm insulated SiO2 were used as substrates. The bottom electrodes were patterned using
Photolithography, followed by the deposition of 2nm Ti and 20nm Pt via electron-beam metal
evaporator and liftoff. Afterwards, Al2O3 in the switching layer was grown at 80 °C using Atomic-
Layer Deposition (ALD) which is able to control film thickness at atomic precision. 1 nm Pt and
2nm Ti layers inside the switching layer were deposited by electron-beam metal evaporator. In the
end, photolithography, metal evaporation and liftoff were performed again to define the top
electrodes (8nm Ta, 20nm Pt). An Optical microscope image of the cross-point memristor is shown
in Figure 11.1(e). Figure 11.1(f) shows the SEM image of 3 nm Pt on Si substrate, discontinuous
film topography can be observed. Discontinuous film topography is captured on 3 nm Pt layer,
hence 1 nm Pt is in island form and such observation also matches other published work[129, 132].
53

Figure 11.1. Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt cross-point memristor. (a)-(d) Device fabrication
process. Photolithography, electron-beam metal evaporator and liftoff were performed to pattern the top
and bottom electrodes, the Al 2O 3 switching layer was deposited by ALD process. The intermediate Pt and
Ti layers inside the switching layer were also deposited by electron-beam metal evaporator. (e) Optical
microscope image of a fabricated cross-point memristor. (f) SEM image of 3 nm Pt on Si substrate.

54

Chapter 12 Device Characterization
12.1. Hybrid Tuning of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor
The typical I-V curves of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor are shown in Figure
12.1(a)-(b). Different from normal memristive devices which only exhibit a single relation
between voltage and current, two separate resistance tuning ranges can be observed on each
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor. One I-V curve is corresponding to the tuning
range under relatively low device resistance (Figure 12.1(a)), while the other happens when the
device is maintained at higher resistance (Figure 12.1(b)). Here low resistance dynamic range
(LRDR) and high resistance dynamic range (HRDR) are used to distinguish these two distinct
switching performances. The orange curve in Figure 12.1(a) shows the I-V curve under LRDR
(600 Ω - 19 kΩ), in which the applied RESET bias should be controlled less than -2 V. In particular,
the lower sub-filament is kept at low resistance state because its RESET threshold voltage is not
reached. After applying a higher RESET bias (blue curve), the device can be switched to a higher
resistance (50 kΩ) state when the lower sub-filament is reset as shown in Figure 12.1(c). As this
time, if the compliance current (highest current limit) of SET process is controlled correctly (≤ 2
mA), the resistance of the device is merely switched to 19 kΩ instead of 600 Ω by the reason that
the lower sub-filament requires larger voltage and compliance current to be set to low resistance
state. Consequently, the device can stay within HRDR (19 kΩ - 50 kΩ) as shown in Figure 12.1(b).
Once larger voltage and compliance current are applied (orange curve), the memristor can jump
from HRDR back to LRDR because the lower sub-filament is turned into low resistance state as
shown in Figure 12.1(d). Depending on the required resistance range, each memristor can be
switched repeatedly between HRDR and LRDR. To investigate the multilevel states within HRDR
and LRDR, current pulses (130 ms) were used to tune the memristor to various resistance states.
55

The memristor was switched to either HRDR or LRDR first and then the multilevel states were
measured within the corresponding dynamic range. As shown in Figure 12.1(e), a large amount of
multilevel resistance states can be obtained in both HRDR (blue curves) and LRDR (orange
curves). The corresponding resistance tuning characteristics are provided in Figure 12.1(f), two
separate tuning curves coexist in a single memristor because of the unique HRDR and LRDR, the
overall resistance tuning range is from 600 Ω to 50 kΩ.

56

Figure 12.1. Hybrid tuning of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor. (a) I-V characteristics of
Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor within LRDR. The corresponding dynamic range is 600
Ω - 19 kΩ. (b) I-V characteristics of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor within HRDR. The
corresponding dynamic range is 19 kΩ - 50 kΩ. (c) Switching from LRDR to HRDR by applying a higher
57

negative voltage (blue curve). (d) Switching from LRDR to HRDR by applying higher positive current and
voltage (orange curve). (e) Multilevel states within LRDR (orange lines) and HRDR (blue lines). (f)
Relation between resistance and programming current of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt
memristor within LRDR (orange curve) and HRDR (blue curve).

12.2. Analog Performances of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor
As discussed above, the conductance tuning range of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristor ranges from 20 to 2000 μS. To study the number of programmable states,
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor was set to different conductance states (Figure
12.2(a)) and the standard deviation of tuning the memristor to an exact conductance state is 0.89
μS. As a result, the number of programmable states in Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristor is 1112 states. As shown in Figure 12.2(b), compared to Pt/Ta/Al2O3/Pt memristor
without Pt islands in the switching layer, the number of conductance states of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor is enhanced from 157 states to 1112 states
because of its extra conductance tunable range. Although continuously tunable states are
confirmed on Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor, these conductance states are
required to be stable enough for practical analog computing applications[133]. The retention test
of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor is shown in Figure 12.2(c). The device is
programmed to various conductance states and then reading pulses are applied on the device every
10 seconds to record the conductance value of the device. The device keeps good stability within
at least 1200 s and the conductance variation is always less than 5 μS. Different from the switching
endurance tests of normal memristors which only demonstrate the switching between low
conductance state (LCS) and high conductance state (HCS), the switching endurance of a middle
58

conductance state (MCS) is uniquely provided for Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristor because the sub-filament switching of the device results in an extra conductance state
between the switching of HRDR and LRDR. In the endurance test, Pt/Ta/Al2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristor can be switched reliably at least 300 cycles among the three different
conductance states as shown in Figure 12.2(d). Figure 12.2(e) shows the analog programming
process of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor under voltage pulses with 0.7 V
amplitude and 500 ns width. The memristor is initially set to 2.82 kΩ within LRDR and a single
500 ns pulse is enough to program the device to another state (2.17 kΩ), the device will keep stable
in a final state (1.95 kΩ) after 2 voltage pulses and the following pulses won’t affect the state
anymore.

59

Figure 12.2. Analog Performances of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt Memristor. (a) Multilevel
conductance states of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt Memristor. (b) Comparison of multilevel
conductance states between memristors with and without Pt islands. The number of conductance states of
Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor is enhanced from 157 states to 1112 states. (c) The
retention test of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor within 1200 s. (d) Switching endurance
test of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor during 300 cycles. (e) Analog programming of
Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor under voltage pulses. The pulse amplitude is 0.7 V and
width is 500 ns.

60

12.3. Electrical Characteristics of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt Memristor under
Negative Voltage Sweep and 100 ns Voltage Pulse
Under negative voltage sweeps (0 to -0.1 V), Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor
shows linear I-V curves at different conductance states as well (Figure 12.3(a)). To demonstrate
that the memristor can have even faster programming speed, 1 V voltage pulse with 100 ns width
is applied on Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor (Figure 12.3(b)). The
memristor is initially set to 5.38 kΩ, after a single pulse, the memristor is switched to 0.88 kΩ.
Due to the slow sampling rate of the measurement setup, the resultant pulse shape slightly
deformed. While the memristor exhibits obvious resistance switching (5.38 – 0.88 kΩ) after
applying one single pulse, such observation confirms the fast-programming speed of
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor under voltage pulses. Meanwhile, the switching
energy consumption is merely 257 pJ. The switching energy consumption can be even smaller if
a narrower width pulse is adopted for the programming.
Figure 12.3. Electrical Characteristics of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt Memristor. (a) I-V curves
of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor under negative voltage sweeps (0 to -0.1 V). (b)
61

Resistance shift of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor after a single voltage pulse (1 V, 100
ns).

12.4. Engineering of Sub-filaments
A thin TiOy layer is used to lower the required switching voltage and current for SET and RESET
processes through offering more dopants for the switching process. Pt/Ta/Al 2O3/Pt/Al2O3/Pt
memristors with 1 nm Pt layer were the initial design to achieve sub-filamentary sections in the
switching layer. Pt was selected due to its inert properties that avoid the unexpected reactions in
the switching layer[134]. However, the required switching voltage and current of
Pt/Ta/Al2O3/Pt/Al2O3/Pt memristors are high enough to induce the electrical breakdown. The
required voltages for electroforming and following RESET process can be found in Table 12.4,
each value is calculated based on an average value of 10 devices. 12.78 V had to be enforced to
completely electroform the devices, which made the devices easy to break down during the
switching cycles. Considering the fact that the dopants prefer moving towards metal islands due
to a stronger electric field there, and the existence of Pt islands obstructs the diffusion of dopants
to affect the switching of the Pt island/Al2O3/Pt bottom electrode part. As a result, large voltage
and current are necessary for the switching process of the memristors but such large voltage and
current result in the compromise of device reliability. Typical electroforming and RESET I-V
curves of Pt/Ta/Al2O3/Pt/Al2O3/Pt memristors are shown in Figure 12.4(a) in the Supporting
Information.

62

Figure 12.4. Electrical characteristics of control memristors. (a) I-V characteristics of
Pt/Ta/Al 2O 3/Pt/Al 2O 3/Pt memristor. The insertion of 1 nm Pt into the switching layer significantly increases
the required voltage and current for switching. (b) I-V characteristics of Pt/Ta/Al 2O 3-x/TiOy/Al 2O 3-x/Pt
memristors with different Ti thicknesses. The memristors require relatively low voltage and current for
switching. (c) Resistance tuning characteristics of Pt/Ta/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristors with different
Ti thicknesses. A thicker Ti layer leads to a lower device resistance.
Ti is known as an oxygen-reactive metal and it can enrich the dopant density for switching
process[135, 136], and hence lower the switching and electroforming voltages of the memristors.
To demonstrate this, Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt memristors with different thickness Ti layers
were then fabricated and tested. The resistances of all control memristors after the electroforming-
RESET cycle are summarized in Table 12.4 to act as dopant density indicators. It can be clearly
seen that the memristors without Ti layer have resistances larger than 10^3 kΩ after
electroforming-RESET cycle, low dopant densities can be expected in these memristors. However,
the presence of Ti in the switching layer significantly reduces the resistance of Pt/Ta/Al2O3-
x/TiOy/Al2O3-x/Pt memristors after the electroforming-RESET cycle (more information can be
found in the Supporting Information Figure 12.4(b)-(c). Given the potential transition of Ti to its
sub-oxidation states TiOx during the device fabrication process and electroforming process, the
emergence of more dopants in the memristors can be reasonably explained. Near the Ti-rich region,
63

the Ti sub-oxides are more stable than Al2O3, it is possible for Ti to grab oxygen ions from Al2O3
near the Ti-rich region [137, 138]. Furthermore, the formation Gibbs free energy of possible Ti
sub-oxides such as Ti2O3 is very close to or even lower than Al2O3 of −1582.3 kJ/mol, the oxidation
of Ti is thermodynamically favorable in the switching layer[139]. When oxygen vacancies
(dopants) are formed, conduction electrons are simultaneously released in order to maintain the
total charge balance[116]. Also, high resistance was observed on 2nm Ti film after deposition
which confirmed its oxidation to Ti sub-oxides TiOy. Different from Ti, Pt is known as an inert
metal. The introduction of Pt should impose negligible influence on the dopant density. This is
confirmed by the similar resistance between Pt/Ta/Al2O3/Pt/Al2O3/Pt memristors and
Pt/Ta/Al2O3/Pt memristors (Table 12.4) after the electroforming-RESET cycle. In conclusion,
oxygen-reactive Ti and inert Pt behave differently inside Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristors. Ti assists in the production of additional dopants to lower the switching voltage and
current, while Pt is aimed to create sub-filaments.
Table 12.4. Electroforming and RESET Characteristics of Control Memristors
Memristor Structure Switching Layer Electroforming
Voltage (V)
RESET
Voltage (V)
Resistance after
Electroforming-RESET
Pt/Ta/Al2O3/Pt/Al2O3/Pt Al2O3/Pt/Al2O3 (8 nm/ 1 nm/ 8 nm) 12.78 -2.77 >10^3 kΩ
Pt/Ta/Al2O3-
x/TiOy/Al2O3-x/Pt
Al2O3-x/TiOy/Al2O3-x (8 nm/ 1 nm/
8 nm)
7.54 -2.03 483 kΩ
Al2O3-x/TiOy/Al2O3-x (8 nm/ 2 nm/
8 nm)
5.71 -2.21 31 kΩ
Al2O3-x/TiOy/Al2O3-x (8 nm/ 4 nm/
8 nm)
4.97 -2.18 6 kΩ
Pt/Ta/Al2O3/Pt Al2O3 (8 nm) 3.6 -1.83 >10^3 kΩ
Al2O3 (16 nm) 5.93 -1.93 >10^3 kΩ

64

12.5. Sub-memristors for Coarse and Fine Resistance Tuning
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor can be roughly considered as a combination of
two sub-memristors separated by Pt islands as shown in Figure 12.5(a). Although the switching
characteristics of this combination may not be completely identical to the actual device, the study
on sub-memristors can still provide valuable information to identify their different roles in the
switching process. Therefore, we fabricated Pt/Ta/Al2O3/Pt and Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristors to study the characteristics of each sub-filament. The upper sub-filament possesses a
Pt/Ta/Al2O3/Pt stack, which is also the initial memristor architecture without metal islands.
Nevertheless, such sub-memristor has a shorter filament length defined by the thickness of Al2O3
switching layer. To study the effect of Al2O3 thickness on the final device performance, two
different Al2O3 thicknesses 8 nm and 16 nm were selected, because Al2O3 thickness less than 8
nm makes the switching process of memristors unstable (memristors are initially ON without
electroforming). A higher voltage is demanded for the electroforming of 16 nm Al2O3 memristors
compared to 8 nm Al2O3 devices, and similar RESET voltages are observed on both memristors as
shown in Table 12.4. Their I-V curves after multiple switching processes are shown in Figure
12.5(b) respectively, the results indicate that two memristors have similar electrical characteristics
after several SET-RESET cycles. It is noticeable that the variation of Al2O3 thicknesses in
Pt/Ta/Al2O3/Pt memristors results in a negligible change on the final resistance tuning behavior,
both devices have comparable dynamic ranges between 600 Ω and 8 kΩ as shown in Figure 12.5(b)
insert figure. Therefore, Pt/Ta/Al2O3/Pt memristors with different Al2O3 thicknesses are confirmed
to have continuously tunable resistance states, the resistance of upper sub-filament can be adjusted
finely.
65

As mentioned earlier, the lower part of a Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor can be
approximately regarded as a Pt/Al2O3-x/TiOy/Al2O3-x/Pt sub-memristor with 2 nm Ti in the
switching layer. In our experiments, Pt/TiOx/Al2O3-x/Pt memristors were fabricated to estimate the
performance of lower sub-filaments instead of Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors because Pt
electrode has poor adhesion to Al2O3 layer. Figure 12.5(c) shows the corresponding I-V curves of
electroforming and following RESET processes, the device can be hardly electroformed (average
7.81 V calculated from 10 memristors). Moreover, the memristor is difficult to be switched OFF
(average -8.93 V calculated from 10 memristors). No consecutively tunable resistance states could
be achieved, only high resistance and low resistance states were observed on this memristor. In
this case, the lower sub-filament should be responsible for a coarse resistance adjustment of the
entire device.

66

Figure 12.5. Electrical characteristics of sub-memristors and Resistance evolution of sub-filaments
formation. (a) Structure of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor. It can be considered as a
combination of two sub-memristors separated by Pt islands. (b) I-V characteristics of Pt/Ta/Al 2O 3/Pt sub-
memristors with different Al 2O 3 thicknesses. The memristor requires relatively low voltage and current for
switching. The insert figure is the resistance tuning characteristics of Pt/Ta/Al 2O 3/Pt memristors with
different Al 2O 3 thicknesses. (c) I-V characteristics of Pt/TiO x/Al 2O 3-x/Pt sub-memristor. The memristor
requires high voltage and current for switching, no consecutively tunable resistance states can be observed
on it. (d) The evolution of filament formation. The formation details can be studied by recording the
resistance of SET process. (e) 1st SET processes of Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor after
electroforming. Two abrupt resistance drops can be observed. (f) Following SET processes of
Pt/Ta/Al 2O 3/Pt/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor. With more SET-RESET cycles, the first abrupt
resistance transition becomes smoother.

12.6. Validation of Sub-filaments Coexistence
Although unique resistance tuning behavior of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors
can be reasonably explained by the coarse and fine adjustments of sub-filaments, more evidences
are required to prove the existence of sub-filaments. Through the study on the evolution of filament
formation during the switching process, valuable information can be acquired to validate the
coexistence of two sub-filaments divided by Pt islands. During the electroforming and following
SET processes, gradually increasing current pulses (130 ms) were applied on the memristor to
induce the switching of internal states. Every time after enforcing an increased current pulse, the
corresponding device resistance was measured to record the current situation of filament because
resistance values of memristors are strongly related to the inner filament morphology[140]. The
evolution of electroforming and the first 4 SET processes of Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt
67

memristor are shown in Figure 12.6(a). After electroforming, the device is reset to a high resistance
(33 kΩ) state which is the initial resistance state of the next SET process (1
st
SET). In the following
1
st
SET process, the memristor maintains its 33 kΩ resistance until the applied current is larger
than 75 mA. Then the device is suddenly turned into a low resistance (600Ω) state, there is an
abrupt resistance drop that represents the formation of a filament in the switching layer. During
the next two SET processes (2
nd
and 3
rd
SET), the memristor requires a lower current to be switched
to the 600Ω state but equivalent abrupt resistance changes are also observed. A smoother resistance
transition is obtained in the 4
th
SET process, which indicates the existence of intermediate tunable
resistance states between 600 Ω and 33 kΩ states. The 1
st
SET processes of Pt/Ta/Al2O3-
x/TiOy/Al2O3-x/Pt memristor with different Ti thicknesses are shown in Figure 12.6(b), all the
memristors exhibit a sudden resistance shift from the high resistance to the low resistance states.
The 1
st
SET procedures of Pt/Ta/Al2O3/Pt memristor (8nm & 16 nm Al2O3) are provided in Figure
12.6(c), both devices experience similar resistance drops after certain current thresholds. To sum
up, only one abrupt resistance transition is encountered in Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt and
Pt/Ta/Al2O3/Pt memristors, which implies the formation of a single filament in the switching layer.

Figure 12.6. Resistance evolution of filament formation. (a) Electroforming and first 4 SET processes of
Pt/Ta/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor with 2 nm Ti. With more SET-RESET cycles, the abrupt
68

resistance transition becomes smoother. (b) 1st SET processes of Pt/Ta/Al 2O 3-x/TiO y/Al 2O 3-x/Pt memristor
with different Ti thicknesses. Only one resistance drop can be observed during the 1st SET process. (c) 1st
SET processes of Pt/Ta/Al 2O 3/Pt memristor with different Al 2O 3 thicknesses. Only one resistance drop can
be observed during the 1st SET process.
Unlike above two types of memristors, the resistance evolution of Pt/Ta/Al2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristors reveals interesting phenomena as shown in Figure 12.5(d). After
electroforming, the device is reset to a resistance around 45 kΩ. In the following 1
st
SET process,
the device resistance is kept around 45 kΩ for a moment and then reduced to 20 kΩ in a sudden
transition under 1 mA current (Figure 12.5(e)). A second abrupt drop in resistance happens when
the current is larger than 1.9 mA. There are totally two fast resistance drops occurring in the 1
st

SET process. Given the fact that only one sudden resistance shift is detected in Pt/Ta/Al 2O3-
x/TiOy/Al2O3-x/Pt and Pt/Ta/Al2O3/Pt memristors, the presence of extra resistance drop implies the
existence of extra sub-filamentary section in Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors.
Remember that the only structural difference between Pt/Ta/Al2O3-x/TiOy/Al2O3-x/Pt and
Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors is the extra 1 nm Pt layer, the incorporation of
this Pt layer introduces one more resistance drop for the Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristors. Thus, it is reasonable to conclude that the two sub-filaments are separated by Pt islands
rather than Ti layer.
Moreover, the afterwards SET-RESET cycles gradually smoothen the sudden resistance drops
from 45 kΩ to 20 kΩ in Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors (Figure 12.5(f)). The
continuity in resistance transition simply suggests the tunable resistance states within this range.
While the second drop from 20 kΩ to 600 Ω is still abrupt even after 10 SET-RESET cycles, such
difference further confirms the diverse electrical responses of different sub-filaments. The
69

resistance transition from 45 kΩ to 20 kΩ indicates a construction of the first sub-filament (f1) that
contains consecutively tunable states within the 25 kΩ tuning range. The other transition ranging
from 20 kΩ to 600 Ω reflects the formation of the second sub-filament (f2) with merely low
resistance (600 Ω) and high resistance (20 kΩ) states. Hence, it is reasonable to assume that f1 is
the filament section ranging from top Pt electrode to the middle Pt islands in the switching layer
for the fine adjustment (Pt/Ta/Al2O3/Pt sub-memristor). Meanwhile, there are only high and low
resistance states in f2, this sub-filament section plays a coarse adjustment role which is consistent
with filament section from middle Pt islands to the bottom Pt electrode (Pt/TiO x/Al2O3-x/Pt sub-
memristor). It has been discussed earlier that Pt/TiOx/Al2O3-x/Pt sub-memristors require larger
voltage and current to be switched ON compared to Pt/Ta/Al2O3/Pt sub-memristors. Such
observation also coincides with the fact that the voltage and current thresholds of f2 are higher than
f1. The resistance tuning of f1 should not affect the internal resistance state of f2 if the applied
current and voltage are less than the thresholds of f2. It is worth noting that above sub-filaments
arrangement is corresponding to the actual dynamic range of Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-
x/Pt memristor. The overall tuning performance of the memristor can be roughly calculated as a
resistance summation of f1 (0 kΩ - 25 kΩ) and f2 (600 Ω or 20 kΩ). When sub-filament f2 is kept
at low resistance (600 Ω) state, the dynamic range of the entire memristor can be estimated
between 600 Ω and 25 kΩ. This range almost matches the LRDR (600 Ω - 19 kΩ). Once f2 is
maintain at high resistance (20 kΩ) state, the resultant tuning range (20 kΩ - 45 kΩ) is also close
to HRDR (19 kΩ - 50 kΩ). Here, the slight mismatch between calculated tuning ranges and real
tuning range (LRDR and HRDR) can be attributed to the RESET process variation because the
device may be reset to a slightly different resistance after each SET-RESET cycle.

70

Summary
In summary, we have proposed and experimentally demonstrated Pt/Ta/Al2O3/Pt/Al2O3-
x/TiOy/Al2O3-x/Pt memristors with a hybrid tuning mechanism of sub-filaments for the
improvement of analog switching performance. By deploying Pt islands into Al2O3 switching layer,
an entire filamentary channel can be divided into two sub-filaments. Owing to the different
material stacks between two sub-filaments, their correlated properties are completely inconsistent.
The sub-filament ranging from top Pt electrode to Pt island exhibits continuously tunable
resistance range and is considered as a fine resistance adjustment for the overall tuning range. The
other sub-filament that connects the Pt island and Pt bottom electrode is responsible for a coarse
adjustment because it only possesses high and low resistance states. Compared to Pt/Ta/Al 2O3/Pt
memristor whose dynamic range is from 600 Ω to 8 kΩ, the overall dynamic range is significantly
extended (600 Ω - 50 kΩ) in Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristors. The coexistence
of sub-filaments is confirmed by investigating the resistance evolutions of switching processes.
Not only a broader dynamic range is achieved in Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt
memristor, but the total amount of stable multilevel states is also increased. In particular, the
improvement of dynamic range and multilevel states would be beneficial to the energy efficiency
of memristors as well. Our study demonstrates a new method to improve the analog switching
performance of memristors, and we anticipate this method can be used to enrich the applications
of memristive devices for analog computing.

71

Topic 5. Complex Eigenfunction Solver based on Memristor Array

72

Chapter 13 Introduction of Memristor-based Complex Eigenfunction
Solver
Numerical computations are ubiquitous in both scientific research and daily life because many
tasks require efficient methods to simulate, predict and optimize the outcomes such as weather
forecasting and economic[141, 142]. Compared to the digital von Neumann computing
architecture based on complementary metal–oxide–semiconductor (CMOS) scaling, memristor-
based analog computing exhibits performance improvement in both energy consumption and
calculation efficiency[143]. Recently, cross-point memristor array architecture has been proposed
and demonstrated to solve linear algebra problems such as linear equations and vector–matrix
multiplication (VMM)[144]. Through mapping a vector into applied voltages and matrix’s
elements into memristor array, the linear algebra problems can be solved accurately and efficiently
based on Ohm’s law and Kirchhoff’s law[145].
Solving eigenfunction is a fundamental problem in many computing scenarios including quantum
mechanics, photonic simulation and vibration analysis[146, 147]. The original equations of these
problems are usually second-order partial differential equations, and discretization of spatial or
time coordinates is required to transfer the differential equations into eigenfunctions[148, 149].
Consequently, the eigenfunction can be encoded into VMM operation and solved by cross-point
memristor array architecture. Most published memristor platforms are designed to solve real
functions, while memristor platforms with capability to solve complex eigenfunctions are
demanded especially when dealing with wavefunctions due to their complex nature.
In this work, we design a memristor array platform to solve complex eigenfunctions accurately
and efficiently. The design of a real eigenfunction solver is presented first for the demonstration
73

of the working mechanism and then the design of a complex eigenfunction is discussed. The basic
idea is to use the circuit feedback loop to find out the correct complex eigenvalues and eigenvectors
of the eigenfunctions. The real parts of eigenvalues are represented by the conductance value of
the feedback memristors in the transimpedance amplifiers, and the imaginary parts are mapped by
memristor sub-arrays. Unlike real eigenfunction solvers which just need to sweep over one-
dimension, the complex eigenfunction solver requires the ability to search for the correct solutions
on a two-dimensional complex plane. However, this searching process might take infinite time
that is unacceptable for efficient computing. The voltage at the inverting input of inverting
amplifier is noticed to be a perfect indicator for the fast capture of correct complex eigenvalues.
By sweeping over the possible eigenvalues, the correct results stay at the local minimum voltages
at the inverting input of inverting amplifiers. Correct eigenvectors can be achieved by the
corresponding eigenvalues as well. Based on this design, LTspice simulations are performed for
the verification of numerical calculations. The circuit simulations confirm that the memristor-
based complex eigenfunction solver is able to solve the complex eigenfunctions with high accuracy
and fast speed.

74

Chapter 14 Memristor-based Real Eigenfunction Solver
14.1. Design of Memristor-based Real Eigenfunction Solver
After appropriate discretization of spatial or time coordinates, the second-order partial differential
equation can be represented by an eigenfunction:
𝐴𝜑 =𝜆𝜑 ,
where 𝐴 is a known Matrix given by different problems and boundary conditions, 𝜆 and 𝜑 are the
eigenvalue and the eigenvector to be solved respectively. In matrix A, the elements may be positive,
negative and zero. The mapping of 𝐴𝜑 =𝜆𝜑 to memristor platform is described as shown in
Figure 14.1 using a sample matrix A:
𝐴 =[−
𝐴 11
−𝐴 12
0
𝐴 21
𝐴 22
−𝐴 23
0 −𝐴 32
𝐴 33
],
where the elements A11, A12, A21, A22, A23, A32, A33 are all positive. To realize the sign difference
between positive and negative elements, the memristor array is separated into two sub-arrays. The
bottom 𝐴 11
, 𝐴 22
and 𝐴 33
are in the positive sub-array and the top 𝐴 12
, 𝐴 21
, 𝐴 23
and 𝐴 32
are in the
negative sub-array, the sign difference is created by the three inverting amplifiers between the
positive and negative sub-arrays. The feedback resistance and input resistance of the inverting
amplifiers are kept the same so only the voltage signs are reversed without affecting their absolute
values. There are two ways to represent zero elements in the circuit, one is to keep the cross-
points/terminals open at the zero element locations and the other is to attach memristors with
extremely large resistance (OFF state). More memristors can be added to the sub-arrays based on
different discretization methods and the contents of matrix A.
75

The eigenvector (
𝜑 1
𝜑 2
𝜑 3
) are reflected by the output voltages, the induced current after the memristor
sub-arrays can be transferred into a voltage times a coefficient 𝜆 (conductance of the feedback
memristor at TIAs) by the transimpedance amplifiers (TIAs). The coefficient 𝜆 is the eigenvalue
to be found out, 𝐴𝜑 =𝜆𝜑 can be satisfied in the feedback loop based on the Ohm’s law and
Kirchhoff’s law when the eigenvalue 𝜆 is correct. The three inverting amplifiers on the right
side of TIAs are used to compensate for the negative sign induced by TIAs without changing
the absolute voltage values. The correct eigenvectors can be achieved by scanning over the
possible eigenvalues 𝜆 . Ideally the circuit will only output 0 if eigenvalue 𝜆 is wrong and
output correct eigenvector if eigenvalue 𝜆 is correct. However, since there are no extra
voltage or current sources in the circuit, the simulated output voltages are too small to be
measured practically even when the eigenvalue 𝜆 is correct. Therefore, a voltage source is
added to the first output column to force 𝜑 1
to be a measurable value. In this case, the rest of
the output columns can be automatically adjusted according to the constraint 𝐴𝜑 =𝜆𝜑 of
the feedback loop. As a result, the generated voltages are within the measurable range
through choosing the appropriate voltage value of the source. The correctness of eigenvalue
𝜆 can be figured out by measuring the voltage values at the inverting input of the inverting
amplifier marked using the red circle in Figure 14.1. Given the infinite resistance between
inverting input and non-inverting input of the amplifier, the voltage at the inverting input
should be zero in the ideal case. Nevertheless, the wrong eigenvalue 𝜆 can lead to an
increased voltage at the inverting input because the constraint 𝐴𝜑 =𝜆𝜑 can not be satisfied.
By scanning over possible eigenvalues and recording corresponding voltages at the inverting
76

input, the correctness of eigenvalues can be distinguished since they will be located at the
local minimum voltages.

Figure 14.1. Memristor-based real eigenfunction solver.

14.2. Sample Problems Solved by Memristor-based Real Eigenfunction Solver
Some problems are formulated to study the capability of the memristor-based real eigenfunction
solver. As mentioned above, quantum mechanics problems involve the calculation of
eigenfunctions and infinite potential well problem is one of the most famous problems in quantum
mechanics. For an initial demonstration, finding the eigenstates and wavefunctions of a particle in
a one-dimensional infinite potential well with length L is adopted. To compare the results gotten
77

by the eigenfunction solver and the theoretical calculation, MATLAB is used to get the numerical
solutions of the problems. In both cases, the length L of the potential well is discretized into 10
points. The result comparison is shown in Figure 14.2, all three eigenstates are solved and each
one has a corresponding eigenvalue. The results indicate that the memristor-based real
eigenfunction solve can solve the eigenfunction accurately compared to the existing approaches.

Figure 14.2. Comparison between numerical calculation and real eigenfunction solver of one-
dimensional infinite potential well. (a) first eigenstate. (b) second eigenstate. (c) third eigenstate.

In addition to one-dimensional case, the eigenstates and wavefunctions of a particle in a two-
dimensional potential well with equal x and y lengths are solved as well. The lengths L over x axis
and y axis are discretized into 5 points respectively, and the comparison between MATLAB results
and LTspice results is shown in Figure 14.3. There is no doubt that the simulated results of real
eigenfunction solver correspond to the numerical calculation. Such observation confirms the great
calculation capability of real eigenfunction for different problems.

78

Figure 14.3. Comparison between numerical calculation and real eigenfunction solver of two-dimensional
infinite potential well. (a) three eigenstates calculated by MATLAB. (b) three eigenstates calculated by
LTspice.

79

Chapter 15 Memristor-based Complex Eigenfunction Solver
15.1 Design of Memristor-based Complex Eigenfunction Solver
Compared to a real eigenfunction solver, a complex eigenfunction solver requires more
complicated circuit design. The intuitive method to solve complex eigenfunctions using circuit is
calculating real and imaginary parts of the complex eigenfunctions separately. While all the
elements in the eigenfunction 𝐴𝜑 =𝜆𝜑 can be complex, one challenge is to propose a suitable
circuit layout because the calculations involve the multiplication of complex elements.
Furthermore, searching for complex eigenvalues requires an efficient method since the searching
process is on a two-dimensional solution plane.
Although the basic working principle of the complex eigenfunction is similar to the real
eigenfunction solver, extra components are necessary in the complex solver for the calculation of
same size matrix solved by the real eigenfunction solver. A complex 3×3 matrix can be expressed
by:
𝐴 =[
𝐴 11
+𝑖 𝐴 11
∗
𝐴 12
+𝑖 𝐴 12
∗
𝐴 13
+𝑖𝐴 13
∗
𝐴 21
+𝑖 𝐴 21
∗
𝐴 22
+𝑖 𝐴 22
∗
𝐴 23
+𝑖𝐴 23
∗
𝐴 31
+𝑖 𝐴 31
∗
𝐴 32
+𝑖 𝐴 32
∗
𝐴 33
+𝑖𝐴 33
∗
],
where all the elements in A can possibly be complex numbers. Meanwhile, the eigenvector
(
𝜑 1
+𝑖𝜑
1
∗
𝜑 2
+𝑖𝜑
2
∗
𝜑 3
+𝑖𝜑
3
∗
) and eigenvalue 𝜆 =𝜆 𝑟 +𝑖 𝜆 𝑖 ∗
are both complex. As a result, 𝐴𝜑 =𝜆𝜑 can be
expressed by:
[
𝐴 11
+𝑖 𝐴 11
∗
𝐴 12
+𝑖 𝐴 12
∗
𝐴 13
+𝑖 𝐴 13
∗
𝐴 21
+𝑖 𝐴 21
∗
𝐴 22
+𝑖 𝐴 22
∗
𝐴 23
+𝑖 𝐴 23
∗
𝐴 31
+𝑖 𝐴 31
∗
𝐴 32
+𝑖 𝐴 32
∗
𝐴 33
+𝑖 𝐴 33
∗
]×(
𝜑 1
+𝑖𝜑
1
∗
𝜑 2
+𝑖𝜑
2
∗
𝜑 3
+𝑖𝜑
3
∗
)=(𝜆 𝑟 +𝑖 𝜆 𝑖 ∗
)×(
𝜑 1
+𝑖𝜑
1
∗
𝜑 2
+𝑖𝜑
2
∗
𝜑 3
+𝑖𝜑
3
∗
).
80

Then we can get:
{

(𝐴 11
+𝑖 𝐴 11
∗
)×(𝜑 1
+𝑖𝜑
1
∗
)+(𝐴 12
+𝑖 𝐴 12
∗
)×(𝜑 2
+𝑖𝜑
2
∗
)+(𝐴 13
+𝑖 𝐴 13
∗
)×(𝜑 3
+𝑖𝜑
3
∗
)
=(𝜆 𝑟 +𝑖 𝜆 𝑖 ∗
)×(𝜑 1
+𝑖𝜑
1
∗
)
(𝐴 21
+𝑖𝐴 21
∗
)×(𝜑 1
+𝑖𝜑
1
∗
)+(𝐴 22
+𝑖 𝐴 22
∗
)×(𝜑 2
+𝑖𝜑
2
∗
)+(𝐴 23
+𝑖𝐴 23
∗
)×(𝜑 3
+𝑖𝜑
3
∗
)
=(𝜆 𝑟 +𝑖 𝜆 𝑖 ∗
)×(𝜑 2
+𝑖𝜑
2
∗
)
(𝐴 31
+𝑖𝐴 31
∗
)×(𝜑 1
+𝑖𝜑
1
∗
)+(𝐴 32
+𝑖 𝐴 32
∗
)×(𝜑 2
+𝑖𝜑
2
∗
)+(𝐴 33
+𝑖𝐴 33
∗
)×(𝜑 3
+𝑖𝜑
3
∗
)
=(𝜆 𝑟 +𝑖 𝜆 𝑖 ∗
)×(𝜑 3
+𝑖𝜑
3
∗
)
.
After separating the real and imaginary parts of the equations, six equations can be achieved based
on the previous three equations:
{

𝐴 11
𝜑 1
−𝐴 11
∗
𝜑 1
∗
+𝐴 12
𝜑 2
−𝐴 12
∗
𝜑 2
∗
+𝐴 13
𝜑 3
−𝐴 13
∗
𝜑 3
∗
=𝜆 𝑟 𝜑 1
−𝜆 𝑖 ∗
𝜑 1
∗
𝐴 11
𝜑 1
∗
+𝐴 11
∗
𝜑 1
+𝐴 12
𝜑 2
∗
+𝐴 12
∗
𝜑 2
+𝐴 13
𝜑 3
∗
+𝐴 13
∗
𝜑 3
=𝜆 𝑟 𝜑 1
∗
+𝜆 𝑖 ∗
𝜑 1
𝐴 21
𝜑 1
−𝐴 21
∗
𝜑 1
∗
+𝐴 22
𝜑 2
−𝐴 22
∗
𝜑 2
∗
+𝐴 23
𝜑 3
−𝐴 23
∗
𝜑 3
∗
=𝜆 𝑟 𝜑 2
−𝜆 𝑖 ∗
𝜑 2
∗
𝐴 21
𝜑 1
∗
+𝐴 21
∗
𝜑 1
+𝐴 22
𝜑 2
∗
+𝐴 22
∗
𝜑 2
+𝐴 23
𝜑 3
∗
+𝐴 23
∗
𝜑 3
=𝜆 𝑟 𝜑 2
∗
+𝜆 𝑖 ∗
𝜑 2
𝐴 31
𝜑 1
−𝐴 31
∗
𝜑 1
∗
+𝐴 32
𝜑 2
−𝐴 32
∗
𝜑 2
∗
+𝐴 33
𝜑 3
−𝐴 33
∗
𝜑 3
∗
=𝜆 𝑟 𝜑 3
−𝜆 𝑖 ∗
𝜑 3
∗
𝐴 31
𝜑 1
∗
+𝐴 31
∗
𝜑 1
+𝐴 32
𝜑 2
∗
+𝐴 32
∗
𝜑 2
+𝐴 33
𝜑 3
∗
+𝐴 33
∗
𝜑 3
=𝜆 𝑟 𝜑 3
∗
+𝜆 𝑖 ∗
𝜑 3
.
To map the above six equations into a circuit layout, the right side of each equations should only
contain one element instead of the summation or subtraction of two elements. Therefore, the final
expressions of the six equations should be:
{

𝐴 11
𝜑 1
−𝐴 11
∗
𝜑 1
∗
+𝐴 12
𝜑 2
−𝐴 12
∗
𝜑 2
∗
+𝐴 13
𝜑 3
−𝐴 13
∗
𝜑 3
∗
+𝜆 𝑖 ∗
𝜑 1
∗
=𝜆 𝑟 𝜑 1
𝐴 11
𝜑 1
∗
+𝐴 11
∗
𝜑 1
+𝐴 12
𝜑 2
∗
+𝐴 12
∗
𝜑 2
+𝐴 13
𝜑 3
∗
+𝐴 13
∗
𝜑 3
−𝜆 𝑖 ∗
𝜑 1
=𝜆 𝑟 𝜑 1
∗
𝐴 21
𝜑 1
−𝐴 21
∗
𝜑 1
∗
+𝐴 22
𝜑 2
−𝐴 22
∗
𝜑 2
∗
+𝐴 23
𝜑 3
−𝐴 23
∗
𝜑 3
∗
+𝜆 𝑖 ∗
𝜑 2
∗
=𝜆 𝑟 𝜑 2
𝐴 21
𝜑 1
∗
+𝐴 21
∗
𝜑 1
+𝐴 22
𝜑 2
∗
+𝐴 22
∗
𝜑 2
+𝐴 23
𝜑 3
∗
+𝐴 23
∗
𝜑 3
−𝜆 𝑖 ∗
𝜑 2
=𝜆 𝑟 𝜑 2
∗
𝐴 31
𝜑 1
−𝐴 31
∗
𝜑 1
∗
+𝐴 32
𝜑 2
−𝐴 32
∗
𝜑 2
∗
+𝐴 33
𝜑 3
−𝐴 33
∗
𝜑 3
∗
+𝜆 𝑖 ∗
𝜑 3
∗
=𝜆 𝑟 𝜑 3
𝐴 31
𝜑 1
∗
+𝐴 31
∗
𝜑 1
+𝐴 32
𝜑 2
∗
+𝐴 32
∗
𝜑 2
+𝐴 33
𝜑 3
∗
+𝐴 33
∗
𝜑 3
−𝜆 𝑖 ∗
𝜑 2
=𝜆 𝑟 𝜑 3
∗

A typical complex 3×3 matrix after applying outgoing boundary condition can be expressed by:
𝐴 =[
𝐴 11
+𝑖 𝐴 11
∗
−𝐴 12
0
−𝐴 21
𝐴 22
−𝐴 23
0 −𝐴 32
𝐴 33
+𝑖 𝐴 33
∗
].
81

The mapping of matrix A is shown in Figure 15.1. Different from the real eigenfunction solver
which only possesses two memristor sub-arrays for the separation of positive and negative values,
the complex eigenfunction solver contains eight memristor sub-arrays to completely reflect the
complex VMM operations. Six output voltages are captured to fully solve the complex eigenvector
(
𝜑 1
+𝑖𝜑
1
∗
𝜑 2
+𝑖𝜑
2
∗
𝜑 3
+𝑖𝜑
3
∗
) and the conductance of feedback memristors at TIAs just implies the real parts of
the complex eigenvalues. As for the imaginary parts of the complex eigenvalues, they are
represented by the conductance values of memristors in the sub-arrays as shown in Figure 15.1.
There are twelve inverting amplifiers in the circuit, six inverting amplifiers on the right side of
TIAs are used to compensate the voltage sign difference caused by TIAs and the rest serve as the
sign inverters to distinguish the positive and negative elements. Similar to the previous real
eigenfunction solver, a voltage source is applied at the first output column for the measurable
output voltages. Since the eigenvalue 𝜆 =𝜆 𝑟 +𝑖 𝜆 𝑖 ∗
is a complex number, fast scanning for correct
solutions is necessary to realize a practical eigenfunction solver. Initially 𝜆 𝑖 ∗
is set to a small value,
then scanning over 𝜆 𝑟 can possibly find out some right values. Then 𝜆 𝑖 ∗
is increased to a higher
value, scanning over 𝜆 𝑟 again may get other correct values. By implementing above steps
iteratively, all 𝜆 𝑟 values can be figured out. All 𝜆 𝑖 ∗
values can be revealed through the scanning
over 𝜆 𝑖 ∗
at fixed 𝜆 𝑟 . As a result, all complex eigenvalues can be discovered through the above
method. However, if a small increment step is required for the accurate capture of eigenvalues, the
entire scanning process might take infinite time since it can be considered as a scanning process
over a two-dimensional complex plane. The voltage value at the inverting input of the inverting
amplifier is proved to be a perfect indicator to solve this issue. Through measuring the
voltage values at the inverting input of the inverting amplifier marked using the red circle,
82

the correct real or imaginary parts of eigenvalues should stay at the local minimum voltage
points. In this case, the correct values can be predicted based on the trend of the measured
voltage of the inverting input and a rough scanning with large steps is enough for the efficient
searching of eigenvalues.

Figure 15.1. Memristor-based complex eigenfunction solver.

83

15.2 Sample Problems Solved by Memristor-based Complex Eigenfunction Solver
The ability of calculating correct eigenvectors has been discussed in section 14.2. In this section,
we will focus on demonstrating how the memristor-based complex eigenfunction solver finds out
the complex eigenvalues correctly and quickly. A sample problem with a given matrix is
formulated for the complex eigenfunction solver, the matrix is expressed by:
𝐴 =[
2−0.6𝑖 −1 0
−1 2 −1
0 −1 2−0.6𝑖 ].
The most unique feature of the memristor-based complex eigenfunction solver is the fast searching
for correct complex eigenvalues. The correct complex eigenvalues numerically solved by
MATLAB is given as:
𝜆 ={
0.295+3.3333𝑖 0.5+1.6667𝑖 1.618+3.3333𝑖 .
As discussed in section 15.1, the overall scanning method involves scanning over the real part
under the fixed imaginary part and scanning over the imaginary part under the fixed real part,
respectively. The corresponding simulated voltage values at the inverting input of inverting
amplifier when scanning over real part of eigenvalue under different imaginary part values are
given in Figure 15.2. When the imaginary parts of the eigenvalues are correct at 3.3333 and 1.6667,
the scanning results indicate that the local minimum voltages are situated at the correct real parts
of the eigenvalue at 0.295, 0.5 and 1.618 as shown in Figure 15.2 (a) and (b). In Figure 15.2 (c)
and (d), the scanning process can still find out the correct real parts of the eigenvalue at 0.295, 0.5
and 1.618 at the local minimum voltage positions even when the imaginary parts of the eigenvalue
are incorrectly set to 1.8 and 3. Thus, the scanning process doesn’t require very high scanning
precision, the trend of the scanning curve can provide enough information to obtain the correct
84

complex eigenvalues. By using this eigenfunction solver, the right complex eigenvectors and
eigenstates can be calculated accurately and efficiently.

Figure 15.2. Simulated voltages at the inverting input of inverting amplifier. The analytical correct values
of the imaginary parts of eigenvalues are 3.3333 and 1.6667. (a) Scanning over real part when imaginary
part is 3.3333. (b) Scanning over real part when imaginary part is 1.6667. (c) Scanning over real part when
imaginary part is 3. (d) Scanning over real part when imaginary part is 1.8.

85

Summary
As a summary, we have designed the memristor-based eigenfunction solver for both real
eigenfunction and complex eigenfunctions. The eigenfunction solver consists of the memristor
array and feedback loops. By mapping given matrix A and scanning over possible eigenvalues, the
right eigenvectors and eigenvalues can be detected based on the feedback loops and the local
minimum voltages at the inverting input of the inverting amplifier. LTspice simulations have been
performed for the verification of this designed platform. According to the simulation results, the
memristor-based complex eigenfunction solver is capable of scanning over the two-dimensional
complex plane and finding out the solutions with high accuracy and fast speed.

86

Conclusion and Future Work
In this dissertation, all my Ph.D. studies are summarized and concluded with experimental details.
Photonic and electronic devices for different applications are designed, fabricated and
characterized. The characterization results indicate that the performances of these devices meet or
exceed the requirements.
In the first three topics, we report the three applications enabled by plasmonic nanofinger structure
including improving the power conversion efficiency of dye-sensitized solar cells, enhancing
SERS detection accuracy of mercury ions and tuning the photoluminescence of CsPbBr3 quantum
dots. By adopting appropriate methods to modify the nanofinger structure, the induced strong local
field enhancement can result in remarkable performance improvements for various applications.
The corresponding design, fabrication and optical characterization processes of these photonic
devices are demonstrated in detail.
Topics 4 and 5 involve the studies about analog performance improvement of memristive devices
and complex eigenfunction solver based on memristor array. We report a mechanism to improve
the dynamic range and programmable conductance states of memristors through inserting Pt
islands into the switching layer. The electrical characterization of this device verifies the
significant enhancement in its analog performance for analog computing. Such improvement is
also beneficial to the design of a memristor-based complex eigenfunction solver for different
problems including photonic simulation and quantum mechanics problems (Topic 5). The circuit
simulations have been performed, and the simulated results confirm the calculation accuracy and
efficiency of the solver for different sample problems.
87

In the last topic of my dissertation, the design and simulation results of the complex eigenfunction
solver are provided. However, practical circuit construction is still required for the experimental
demonstration. My colleague Sushmit Hossain is currently working on it. We anticipate that the
memristor-based complex eigenfunction solver can be experimentally implemented and used for
practical problems in the future.

88

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99

Publications
1. Su, G.*, Hu, P.*, Xiao, Y., Hu, J., Pan, D., Zhan, P., ... & Liu, F. Tuning Photoluminescence
of CsPbBr3 Quantum Dots through Plasmonic Nanofingers. Advanced Optical Materials,
2202750. (*equal contribution)
2. Su, G.*, Hu, P.*, Hu, J., Wang, X., Wu, G., Shang, Y., ... & Wu, W. (2023). Collapsed
nanofingers by DNA functionalization as SERS platform for mercury ions sensing. Journal of
Raman Spectroscopy, 54(1), 6-12. (*equal contribution)
3. Fang, W.*, Hu, P.*, Wu, Z., Xiao, Y., Sui, Y., Pan, D., ... & Wu, W. (2021). Plasmonic Dye-
Sensitized Solar Cells through Collapsible Gold Nanofingers. Nanotechnology, 32(35),
355301. (*equal contribution)
4. Liu, Z., Meng, D., Su, G., Hu, P., Song, B., Wang, Y., ... & Wu, W. (2022). Ultrafast Early
Warning of Heart Attacks through Plasmon ‐Enhanced Raman Spectroscopy using Collapsible
Nanofingers and Machine Learning. Small, 2204719.
5. Sui, Y., Hu, P., Pan, D., Jiang, Z., Song, Q., Su, G., ... & Liu, F. (2022). Long-range
interference of localized electromagnetic field enhancement in plasmonic nanofinger lattices.
Frontiers in Physics, 816.
6. Chen, B., Yang, H., Song, B., Meng, D., Yan, X., Li, Y., Wang, Y., Hu, P., ... & Wu, W.
(2020). A memristor-based hybrid analog-digital computing platform for mobile robotics.
Science Robotics, 5(47), eabb6938.
7. Yang, H., Liu, H., Song, B., Li, Y., Meng, D., Chen, B., Hu, P., ... & Wu, W. (2020). Effects
of roughness and resonant-mode engineering in all-dielectric metasurfaces. Nanophotonics,
9(6), 1401-1410.
8. Yang, H., Chen, B., Song, B., Meng, D., Tiwari, S., Krishnamoorthy, A., Yan X., Liu, Z.,
Wang, Y., Hu, P., ... & Wu, W. (2020). Memristive device characteristics engineering by
controlling the crystallinity of switching layer materials. ACS Applied Electronic Materials,
2(6), 1529-1537.
9. Song, B., Jiang, Z., Liu, Z., Wang, Y., Liu, F., Cronin, S. B., Yang, H., Meng, D., Chen, B.,
Hu, P., ... & Wu, W. (2020). Probing the mechanisms of strong fluorescence enhancement in
plasmonic nanogaps with sub-nanometer precision. ACS nano, 14(11), 14769-14778.
10. Li, Y., Mao, H., Hu, P., Hermes, M., Lim, H., Yoon, J., ... & Wu, W. (2019). Bioinspired
functional surfaces enabled by multiscale stereolithography. Advanced Materials
Technologies, 4(5), 1800638.
11. Mao, H., Leung, Y. S., Li, Y., Hu, P., Wu, W., & Chen, Y. (2017). Multiscale
stereolithography using shaped beams. Journal of Micro and Nano-Manufacturing, 5(4).

100

Experimental Sections
1. Plasmonic Dye-Sensitized Solar Cells through Collapsible Gold
Nanofingers
Fabrication of Nanofingers array and DSSCs assembly: The fabrication of high-density arrays
of Au nanofingers with flexible polymer support on the glass substrates was referred in our
previous report[24, 150].

First, high-density arrays of Au nanofinger with a flexible polymer
support on the plain glass were fabricated by our well-developed NIL method. To get the tetramer
nanostructures in the subsequent collapse process, the Au films were deposited at a normal
incidence to form Au nanodisks and the height of nanofingers were controlled with 300 nm. As
compared to dimeric structures, the tetrameric structures can realize the independence of
polarization and much more hotspots so that the sunlight absorption can be efficiently enhanced.
Subsequently, an ultrathin 2.5 nm Al2O3 film was deposited on them via ALD (Ultratech Simply
ALD). Thirdly, the Au nanofingers were soaked into ethanol and then air-dried at room
temperature, which form tetramer nanostructures by a group of four nanofingers through the
microcapillary force, and Van der Waals forces kept these tetramer nanofingers from separating
once they collapse[24]. Finally, a 2 nm amorphous TiO2 was deposited on the collapsed
nanofingers by ALD to form the photoanode. For comparison, we fabricated another photoanode
by depositing the Au film, Al2O3 film and TiO2 film on the plain glass with the same parameters.
The DSSCs assembly is shown in the following procedure. Dissolving 5.3 mg of N719 dye in 15
mL ethanol to prepare a 0.3 mM dye solution and then the dye solution was injected into test cubes
with equal 5 mL by syringe[151-155]. The conductive wire connected to the feedthrough from the
surface of TiO2 film in the photoanode. After immersed into the 0.3 mM N719 dye solution for 10
101

hours for sensitization, the samples were cleaned with ethanol and dried with N2 gas. The counter
electrode was the ITO glass substrates with 2 nm Pt layer deposited by ALD which kept the high
transparency to incident sunlight. Then dropping the iodide/triiodide (I
-
/I
3-
) electrolyte to the
photoanode sensitized by N719 dyes, putting counter electrode on the whole assembly and
clamping the two parts with two bookends. Finally, the DSSCs was finished as a solar cell under
the illumination in sunlight.
SEM and fluorescence measurements: SEM images were taken by an SEM (Hitachi, S4800)
operating at an accelerating voltage of 2 kV and an average working distance of 8.2 mm.
Fluorescence spectra of N719 dyes were performed by a Renishaw inVia Raman microscope. The
laser excitation wavelength was 514 nm, and a 50X standard objective was used and the spot focus
mode was selected. The incident light polarization was along the dimer direction.
DSSCs solar cell data measurements: The I–V characteristics of the DSSCs were measured
under sunlight conditions (AM1.5G, 100 mW cm
-2
), with a xenon lamp light source equipped with
the Oriel Sol3A Class AAA solar simulator (Newport, USA). During the I–V measurements, we
adjusted the active area of DSSCs to 0.25 cm
2
.

2. Collapsed Nanofingers by DNA-Functionalization as SERS
Platform for Mercury Ions Sensing
Nanofingers Fabrication: The high-density arrays of Au nanofingers with a flexible polymer
support on the glass substrates were fabricated by our well-developed nanoimprint lithography
(NIL) and reactive-ion etching (RIE). This polymer material is a UV-curable NIL resist (I-UVP,
EZ-Imprinting Inc.), which is different from the conventional photoresist (much more cross-
102

linked). The resultant polymer nanofinger has excellent robustness and can be used under high
intensity laser light without degradation. The two-dimensional grid mother molds for NIL were
fabricated using custom-built interference lithography system. The typical diameter of each
nanofinger is 70 nm, and the height is finely controlled to 300 nm including UV nanoimprint resist
fingers and 50 nm Au layer on top for forming tetramer structures in the collapsible process, which
is preferred to polarization independence. In addition, the geometric parameters of nanofingers can
be finely tuned to achieve the different plasmonic resonances by the mother molds.
Samples Preparation: The purchased DNA aptamer used in the experiment was HS-(CH2)6-
TTTTTTTTTTGGGGGGGGAAAAAAAA that consisted of two segments of both thymine (T)
as the Hg
2+
recognition and the capture segment containing guanine (G) and adenine (A). After
the suggested pre-treatment for DNA aptamer, the flexible Au nanofingers were firstly incubated
in a 10
-3
M DNA solution for 12 hours in 4
◦
C refrigerator, taken out and air-dried. Based on the
above process, the single stranded DNAs were connected to Au surface and tended to lay on the
surface of Au nanofingers due to good affinity of adenine to Au, and flexible Au nanofingers were
simultaneously touched each other via a capillary force induced collapsing process so that
Au/DNA/Au coupled nanofingers were formed in which DNA aptamer was as the space layer.
Finally, these aptamer-modified Au nanofingers were washed carefully in ultrapure water several
times and dried in fume hood without interruption.
Raman Measurement: To perform SERS detection for Hg
2+
, Hg(NO3)2 was firstly dissolved in
ultra-pure water with different concentrations from 1×10
−3
M to 10
−9
M. Hg
2+
solution was then
dropped onto the surface of DNA Functionalized collapsed Au nanofingers. Before drying, SERS
spectra of DNA were recorded using a Renishaw inVia Raman microscope at excitation
wavelength of 785 nm. A 50X objective lens was used and the spot focus mode was selected.
103

Electron Microscopy Characterization: SEM images were taken by a scanning electron
microscope (Hitachi, S4800) operating at an accelerating voltage 2 kV and an average working
distance of 8.2 mm. The interface analysis of sample was performed by a transmission electron
microscope (TEM) (JEOL, JEM2100F). The specimen was thinned by dual beam FIB (Seiko
4050MS). It is noted that the C and Cr coating layers are firstly pre-coated to protect the interface
of the samples and provide better cross-sectional analysis during FIB process.

3. Tuning Photoluminescence of CsPbBr3 Quantum Dots through
Plasmonic Nanofingers
Nanofinger Fabrication and dielectric layer deposition: The high-density Ag nanofinger dimer
arrays with flexible polymer support on the glass substrates were firstly fabricated by our well-
developed nanoimprint lithography and reactive ion etching. Subsequently, the Ag film was
deposited on top of nanofingers by e-beam evaporation. The ultrathin ta-C film was deposited
using a multifilm deposition system (Shimadzu, MR3) combined with an FCVA gun. The
deposition rate monitored by an ellipsometer was ~0.5 Å s
−1
. Prior to deposition, all the substrates
were cleaned by RF-plasma sputtering using Ar ion plasma to remove the contaminations.

Numerical Simulation: The numerical simulations of the scattering spectra and near field
distributions for Ag nanofinger dimer coated with ta-C layer were based on COMSOL
Multiphysics. The geometrical parameters were consistent with the experimental design. The
permittivity of Ag was chosen from the COMSOL built-in material library. The refractive index
of ta-C and PDMS were set as 2.44 and 1.41, respectively. The traveling direction of the plane
104

wave was set along the negative z-axis direction with x-direction polarization, and boundary
condition of the simulation domain was set to perfectly matched layer condition.

Spectral measurement: The self-built dark field scattering measurement system and PL spectra
measurement system were used in the experiment. A 50× standard objective lens was used in all
spectral measurement system. A halogen light source (wavelength range from 400 to 1000 nm)
was used in dark field scattering measurement. And the CW laser excitation wavelength was 405
nm in PL spectra measurement.

4. Hybrid Tuning of Sub-filaments to Improve Analog Switching
Performance in Memristive Devices
Device Fabrication: The Pt/Ta/Al2O3/Pt/Al2O3-x/TiOy/Al2O3-x/Pt memristor was fabricated on a
Si wafer with 300 nm SiO2 film. To fabricate the bottom electrode, a layer of photoresist (AZ 5214,
3000 rpm spin coating for 1 min and baking at 118 °C for 2 min) was coated on the substrate and
cured by UV light exposure (54.3 mJ/cm
2
) under a photomask. Then the sample was immersed in
the developer solution (AZ 400K Developer) for 1 min. 2 nm Ti (adhesion layer) and 20 nm Pt
(bottom electrode) were deposited on the photoresist by e-beam evaporator (Kurt J. Lesker E-
Beam Evaporator) at a growth rate of 0.5 Å/s. Afterwards, a lift-off process was performed on the
sample to remove residual photoresist using ultrasonic vibration. The bottom electrode was then
covered by 8 nm Al2O3 grown by ALD process (Veeco Thermal ALD) under 80 °C. Above 8 nm
Al2O3 layer, 2 nm Ti, 4nm Al2O3, 1 nm Pt and 4nm Al2O3 were deposited alternatively by e-beam
evaporator and ALD. In the end, 8 nm Ta and 20 nm Pt top electrode was patterned by a second
105

photolithography, e-beam evaporator and lift-off process through the same recipe we used to
fabricate the top electrode.

Characterization: The optical microscope image was taken using a Nikon Eclipse LV150N
microscope. DC electrical characterizations, multilevel resistance state measurements, resistance
evolution measurements, retention test and switching endurance test were all carried out with the
Keithley 4200A-SCS parameter analyzer system. In the multilevel states measurements and
resistance evolution measurements, the devices were programmed to different resistance states by
current pulses (130 ms), and the resistance was read at 100 mV. For the calculation of
programmable states, the memristor was tuned to a conductance state and then measured its
conductance states for 500 times. The standard deviation σ of these 500 conductance values was
calculated to indicate the standard deviation of setting the memristor to an exact conductance state.
The number of states could be calculated using the conductance tuning range divided by twice of
standard deviation (𝑁 =
𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑡𝑢𝑛𝑖𝑛𝑔 𝑟𝑎𝑛𝑔𝑒 2σ
). For the retention test, the devices were
programmed to different resistance states, then reading pulses with 100 mV were sent to the
devices every 10 seconds to measure the conductance and the total test time is 1200 s. In the
switching endurance test, the devices were switched between LCS, MCS and HCS continuously
for 300 cycles. The voltage pulse measurement was carried out with Keysight B1500A, the devices
were programmed to different conductance states by 500 ns or 100 ns voltage pulses and their
conductance was measured after each pulse under 100 mV.

106

Computational Details: The electric field distribution within Al2O3 switching layer with a Pt
island was investigated by Comsol Multiphysics, the Electrostatics Model was adopted for the
computation. The thickness of switching layer was defined as 16 nm and the radius of Pt island
was assigned to be 1 nm. The material of the switching layer was set to Al 2O3, and the metal
material of island was set to Pt (Al2O3 and Pt materials chosen from Comsol Multiphysics
Materials Library). A 1 V bias was applied to the top electrode and the bottom electrode was set
to ground, the calculated electric field within the switching layer is shown in Figure 1(b).

5. Complex Eigenfunction Solver based on Memristor Array
Circuit Simulation: The circuit simulations were performed using LTspice and Cadence.
Resistors were used in the simulation to represent the corresponding memristors since there was
no memristor component in the software library. The conductance value of resistors indicated the
element value in the eigenfunction problem. The type of operational amplifier (op amp) in the
simulation was set to AD823 and ± 1.5 V were applied at the power supplies of the op amps. The
simulation time was set to 30 s to observe the stability of the whole circuit.

Asset Metadata

Creator Hu, Pan (author)

Core Title Applications enabled by plasmonic nano-finger and analog computing based on memristive devices

Contributor Electronically uploaded by the author (provenance)

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2023-05

Publication Date 05/09/2024

Defense Date 05/04/2023

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

Tag analog computing,memristor,OAI-PMH Harvest,plasmonic nanostructure,ReRAM

Format theses (aat)

Language English

Advisor Wu, Wei (committee chair)

Creator Email panhu@usc.edu,panhu11111111@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113120634

Unique identifier UC113120634

Identifier etd-HuPan-11815.pdf (filename)

Legacy Identifier etd-HuPan-11815

Document Type Dissertation

Format theses (aat)

Rights Hu, Pan

Internet Media Type application/pdf

Type texts

Source 20230511-usctheses-batch-1041 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name University of Southern California Digital Library

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Abstract (if available)

Abstract This dissertation summarizes the five topics in my Ph.D. study. My research mainly focuses on applications enabled by plasmonic nano-finger and analog computing based on memristive devices. The first part (chapter 1-2) is about plasmonic dye-sensitized solar cells through collapsible gold nanofingers. Here, we demonstrate plasmonic dye-sensitized solar cells (DSSCs) using collapsible Au nanofingers to build photoanode to enhance light absorption. The second part (chapter 3-5) is about collapsed nanofingers by DNA-functionalization as SERS platform for mercury ions sensing. In this work, we report a coupled Au/DNAs/Au gap plasmon platform that provides remarkable SERS enhancement and sensitivity for mercury ion sensing. The third part (chapter 6-8) is about tuning photoluminescence of CsPbBr3 quantum dots through plasmonic nanofingers. We demonstrate the optical coupling between the CsPbBr3 quantum dots (QDs) and gap plasmon through placing QDs in a 2 nm tetrahedral amorphous carbon gap region of collapsible Ag nanofingers. Compared to the CsPbBr3 QDs on SiO2, the photoluminescence (PL) of CsPbBr3 QDs on collapsed nanofinger is enhanced by 4 times and the lifetime decreases from 11.04 ns to 3.8 ns. The fourth part (chapter 9-12) is about hybrid tuning of sub-filaments to improve analog switching performance in memristive devices. We invent a method to improve the analog switching performance of memristors through a hybrid tuning (coarse and fine tuning) of two sub-filaments. The last part (chapter 13-15) is about the complex eigenfunction solver based on memristor array. We design a memristor platform to solve complex eigenfunctions for various problems such as photonic simulation and quantum mechanism problems.