The Pennsylvania State University

The Graduate School

College of Engineering

VANADIUM DIOXIDE TUNNEL JUNCTIONS AND STRUCTURAL

EVOLUTION OF ELECTRICALLY DRIVEN INSULATOR TO METAL

TRANSITION

A Thesis in

Electrical Engineering

by

Eugene Freeman

c© 2013 Eugene Freeman

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

December 2013

The thesis of Eugene Freeman was reviewed and approved∗ by the following:

Suman DattaProfessor of Electrical EngineeringThesis Advisor

Srinivas TadigadapaProfessor of Electrical Engineering

Kultegin AydinProfessor of Electrical EngineeringHead of the Department of Electrical Engineering

∗Signatures are on file in the Graduate School.

Abstract

Silicon CMOS becomes increasingly difficult to scale with every generational node andthere is great interest in developing novel low power and high performance switchingmechanisms. Among the various candidates are high speed and abrupt metal insulatortransition based switches.

The metal insulator transition in vanadium dioxide is sub 100 fs and abrupt. Vana-dium dioxide has a low mobility and thus is a poor choice as a channel replacementmaterial. However, modulation of its 0.6 eV bandgap offers a promising method toenable realization of a high speed, metal insulator tunnel field effect transistor.

In this thesis the mechanism for a metal insulator based tunnel junction is proposed.An experimental demonstration of a two order of magnitude change in tunneling con-ductance in nanoscale vanadium dioxide tunnel junctions is shown as a proof of conceptof the proposed device. The large conductance change is modeled using direct tunnelingand Poole-Frenkel conduction.

There exists significant debate on the exact switching mechanism in vanadium diox-ide. The structural evolution of tensile strained vanadium dioxide undergoing an elec-trically induced insulator to metal transition is investigated using hard X-ray diffraction.A metallic rutile filament is found to be the dominant source of conduction after anelectronically driven transition, while the majority of the channel area remains in themonoclinic M1 phase. Further analysis revealed that the width of the R filament can betuned externally using resistive loads in series, enabling tunability of the M1/R phaseratio. Additionally, time resolved X-ray diffraction performed on vanadium dioxide os-cillators shows that the oscillations are a result of repeatedly reforming and breaking ofan R filament and structural phase transition from M1 to R and back to M1 plays anintegral role in the oscillations.

iii

Table of Contents

List of Figures viii

List of Tables xiv

Acknowledgments xv

Chapter 1

Introduction 1

1.1 Introduction to Metal Insulator Transition Based Tunnel Junctions . . . 1

1.2 Metal Insulator Transition in VO2 . . . . . . . . . . . . . . . . . . . . 6

1.2.1 VO2 Transition by External Stimuli . . . . . . . . . . . . . . . 7

1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Chapter 2

Metal Insulator Transition Theory 10

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 The Peierls Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Standing waves in a periodic potential . . . . . . . . . . . . . . 11

2.2.2 Metal Insulator Transition by Ion Dimerization . . . . . . . . . 12

iv

2.2.3 Evidence of Peierls Transition in VO2 . . . . . . . . . . . . . . 14

2.3 The Mott-Hubbard Transition . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 Correlated Electrons and Localization . . . . . . . . . . . . . . 15

2.3.2 Evidence of Mott-Hubbard Transition in VO2 . . . . . . . . . . 18

2.4 The Hall Effect in VO2 . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 The Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Hall Measurements in VO2 . . . . . . . . . . . . . . . . . . . . 20

Chapter 3

Nanoscale Structural Evolution of the Electrically Driven Transition in

Vanadium Dioxide 24

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Bragg’s Law of Diffraction . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Structure Factor . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Two Terminal VO2 Fabrication . . . . . . . . . . . . . . . . . . 26

3.3.2 Nanoscale hard X-ray Setup . . . . . . . . . . . . . . . . . . . 28

3.4 Nanoscale X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . 30

3.4.1 Spatially Resolved Nanoscale X-ray diffraction . . . . . . . . . 30

3.4.2 Filament Size Extraction . . . . . . . . . . . . . . . . . . . . . 35

3.4.3 Dynamics of the Rutile Filament . . . . . . . . . . . . . . . . . 38

3.4.4 Time resolved X-ray Diffraction of VO2 Oscillators . . . . . . . 40

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

v

Chapter 4

Vanadium Dioxide Tunnel Junctions 43

4.1 Introduction to tunneling in VO2 . . . . . . . . . . . . . . . . . . . . . 43

4.2 Device Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3 Tunneling Modulation in VO2 . . . . . . . . . . . . . . . . . . . . . . 45

4.3.1 Direct Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.3.2 Poole-Frenkel Conduction . . . . . . . . . . . . . . . . . . . . 48

4.4 Conductive Atomic Force Microscopy of VO2 Tunnel Junctions . . . . 50

4.4.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4.2 Tunneling Current Modulation Across the MIT . . . . . . . . . 51

4.4.3 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Chapter 5

Conclusion 57

5.1 Conclusions on VO2 Nanoscale Tunnel Junctions . . . . . . . . . . . . 57

5.2 Conclusions on Nanoscale Hard X-ray of the Electrically Driven Tran-

sition in VO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Appendix A

2-Terminal Process Flow 60

Appendix B

Nanoscale Tunnel Junction Process Flow 63

vi

Bibliography 71

vii

List of Figures

1.1 Thermal power dissipation of modern CPUs has stopped increasing and

is about 100 W per chip. Adapted from [1] . . . . . . . . . . . . . . . . 2

1.2 Illustration of an Id-Vg curve highlighting the importance of the switch-

ing slope to device performance for a fixed Ion/Ioff . The red curve

shows a Boltzmann transport limited device, which requires the most

gate voltage to saturate the device, the sub 60 mV/dec device achieves

the same current for a lower gate voltage, translating into lower power

usage. The ideal curve, shown in blue represents a device that turns on

at the smallest possible finite gate bias. . . . . . . . . . . . . . . . . . . 3

1.3 Illustration of a band diagrams showing the tunnel junction with a thin

tunneling dielectric as the barrier material. (a) In the insulating state a

bandgap forms in the MIT material making it impossible for electrons

to directly tunnel, resulting in a high resistance state. (b) In the metallic

state the bandgap collapses in the MIT material and electrons can tunnel

into the empty states of the MIT material. . . . . . . . . . . . . . . . . 4

viii

1.4 Metal insulator transition of various materials. The near room temper-

ature transition and large change in resistivity makes VO2 an attrac-

tive material to prototype novel devices utilizing the MIT. VO2 bulk,[2]

V2O3 & V8015,[3] VO,[4] V9O17,[5] Ti2O3,[6] NiSe,[7] EuO,[8] LSFO,[9]

Ti3O5,[10] NdNiO3.[11] . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 One dimensional periodic lattice of atoms. . . . . . . . . . . . . . . . . 11

2.2 One dimensional periodic lattice of atoms with pairing of atoms, also

known as dimerization, leading to a doubling of the lattice parameter to

2a. This shifts the Brilluion zone to π2a

. . . . . . . . . . . . . . . . . . 12

2.3 (a) E-K diagram for a half filled 1-D crystal of monovalent atoms, with

a Brilluion zone at πa

. (b) Dimerized crystal of 1-D monovalent atoms

result in a new Brilluion zone at π2a

. The avoided crossing phenomenon

at the Brilluion zone lowers the total electronic energy of the system. . . 13

2.4 Crystal structure of VO2, showing only the vanadium ions, in (a) low

temperature monoclinic phase, with dimerization and doubling of the

unit cell, characteristic of Peierls transition and (b) high symmetry rutile

phase with high conductivity. Modified from [12] . . . . . . . . . . . . 15

2.5 Experimental correlation between the effective Bohr radius and the crit-

ical carrier density of the Mott transition. The solid line represents

n1/3αo > 0.26. ’e-h’ refers to electron hole photo excitation. Adopted

from [13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.6 Illustration of the Mott-Hubbard model showing the U and t term acting

on an electron trying to move from site i-1 to i to enter the 2nd state in

the d orbital at i. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

ix

2.7 Schematic of the hall bar fabricated on VO2. The hall effect measure-

ments are performed while cooling from 330 K to 270 K across the MIT. 19

2.8 Resistivity vs. temperature of the 13 monolayer (3.9 nm) VO2 sample

used in the hall measurements. . . . . . . . . . . . . . . . . . . . . . . 22

2.9 Hall measurements on VO2 (a) The Ns vs. T shows VO2 has an Ns of

1.01x1023#/cm3 in the semiconducting state and 2.99x1018#/cm3 in

the metallic state, where the difference between the two states is about

3.4x104x. (b)The µ vs. T shows a VO2 has a mobility of 9.36 cm2/v − s

in the semiconducting state and 0.46 cm2/v − s in the metallic state,

where the different between the two states is about 20x. . . . . . . . . . 23

3.1 Illustration explaining the derivation of the Bragg equation where the

extra path length seen by the wave reflected from the 2nd layer is deter-

mined to be 2dsinθ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 (a) Illustrated cross section of the fabricated 2-terminal VO2 device. (b)

SEM of the fabricated device, measured to be 6.0 µm long and 9.4 µm

wide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Circuit diagram of the electrical biasing and measurement. A voltage is

measured off a 38 kΩ load resistor Rload and voltage division is used to

determine the voltage drop on the VO2 device under test. . . . . . . . . 29

3.4 θ/2θ scan at 260 K (red line) and 310 K (blue line) of the R 002 and

M1 402 Bragg peaks, respectively. The expected position of the M2

040 Bragg peak is calculated to be 51.08 . A 2θ angle of 51.714

was chosen for the subsequent mapping to provide maximum contrast

between the different VO2 phases. . . . . . . . . . . . . . . . . . . . . 30

x

3.5 2D nanoscale X-ray maps of a VO2 device with applied voltages of

(a) 0 V, (b) 8 V, (c) 10 V, and (d) 12 V and a series resistor of 38 kΩ

which shows the dynamical growth of an R phase filament in the chan-

nel. Note in (a) that a remnant of the filament persisted when no voltage

was applied across the channel. The white dashed lines represent the

approximate edge of the gold electrodes. . . . . . . . . . . . . . . . . . 33

3.6 (a) Voltage pulse applied to the VO2 and 38 kΩ resistor in series. (b)

The corresponding time dependent X-ray intensity from the filament

region and (c) resistance of the entire channel. The changes in the X-ray

intensity accompanied by changes in channel resistance are attributed to

a structural phase transition in the VO2 from the between the insulating

M1 and metallic R phase. . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.7 (a) Illustration of the equivalent circuit used to extract the filament width.

(b) ρ vs. temperature for a thermally driven transition, showing a 571x

change in resistivity. (c) The extracted resistivity when considering the

whole 9.4 µm channel width results in a 17x change, if after 9.6 V only

the 290 nm width that goes through a structural phase is considered full

magnitude of the resistivity change is restored. . . . . . . . . . . . . . . 37

xi

3.8 (a) Circuit schematic overlaid on an illustration of the VO2 channel in

LRS state with a resistor Rseries in series. (b) The filament width depen-

dence on the series resistor. At higher currents (lower series resistance)

the whole channel width can be utilized as seen by the data points falling

on the dashed line, representing a 1:1 relationship between the extracted

and patterned filament width. (c) The calculated filament width depen-

dence on the current displays a linear relationship until joule heating

increases resistivity, which is not accounted for in this model and incor-

rectly shows a reduction in filament width. . . . . . . . . . . . . . . . 39

3.9 Time dependent X-ray diffraction of a VO2 oscillator. The increased

XRD photons in the first 20 µs indicated a transition to the R phase has

occurred. Within the first 40 µs the film transitions back into M1 for the

remainder of the period of oscillation. . . . . . . . . . . . . . . . . . . 41

4.1 Illustrated cross-section of the fabricated nano-pillars. . . . . . . . . . . 44

4.2 (a) The OFF state occurs when VO2 is below the transition temperature,

where a bandgap of 0.6 eV opens around the Fermi level creating a defi-

ciency of states to tunnel into. Transport is by Poole-Frenkel conduction

through trap states. (b) The ON state, when VO2 is below Tc, results

in an MIM structure and direct tunneling contributions to the transport.

This process enables conductance modulation. . . . . . . . . . . . . . . 46

4.3 (a) Band diagram of a symmetrical MIM structure in equilibrium. (b)

Symmetrical MIM under bias, where V > φ0 . . . . . . . . . . . . . . . 47

4.4 Schematic band diagram of Poole-Frenkel emission under bias. . . . . . 49

xii

4.5 (a) Scanning electron micrograph (SEM) of the fabricated nano-pillar

arrays. (b) Zoomed in SEM of an individual nano-pillar. (c) Topogra-

phy scan of the area under investigation. The single pillars are clearly

discernible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.6 I-V traces for temperatures between 260 to 340 K in 5 K intervals as

indicated by the legend for 3 individual pillars. . . . . . . . . . . . . . . 52

4.7 Conductance vs. temperature for 3 nano-pillars showing a tunneling

conductance response to the abrupt MIT in VO2. . . . . . . . . . . . . . 53

4.8 (a) Typical J-V off-state curve (pillar B 270 K) in the MIS case and the

corresponding fit using Poole-Frenkel conduction. The inset shows a

linear relationship of ln(I/V) vs.√V , which is characteristic of Poole-

Frenkel conduction. (b) Typical J-V trace (pillar B from 330 K) of an

on-state with the device in an MIM case, along with fitting showing the

Poole-Frenkel (red curve) and direct tunneling (green curve) contribu-

tion; the total is shown in blue. The parameters used are detailed in

table 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xiii

List of Tables

3.1 Extracted R filament dimensions . . . . . . . . . . . . . . . . . . . . . 37

3.2 X-ray counts for 20 µs time bins starting at 0, 40, 80, and 120 µs after

the rising edge, labeled as B1-B4 respectively. No background subtrac-

tion is applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 Constants and fitting parameters used for direct tunneling and Poole-

Frenkel conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

xiv

Acknowledgments

I would like to dedicate this thesis to my parents, who always believed in me and sup-

ported my academic career and without their love this work would not be possible.

Foremost, I would like to thank my adviser, Professor Suman Datta for giving me

the opportunity to work on novel electronic materials. His enthusiasm, motivation and

guidance throughout my research was invaluable. I would also like to thank Professor

Srinivas Tadigadapa for serving on my Master’s committee and the use of his equipment.

I am indebted to the great work by Hanjong Paik, Joshua Tashman and Professor Darrell

Schlom of Cornell University for growing all the VO2 films used in this work. Thank

you to Professor Roman Engel-Herbert for always guiding me in the right direction

when I was lost. Special thanks to Nikhil Shukla and Ayan Kar for their many hours of

fruitful discussions, support, friendship and good humor.

Thank you to Greg Stone, Professor Venkatraman Gopalan, Martin Holt, Haiden

Wen and Zhonghou Cai for their help with the x-ray analysis and measurements. Thank

you to Magdalena Huefner and Professor Jennifer Hoffman of Harvard University, for

their AFM measurements. This work would not have been possible without the assis-

tance of Rajiv Misra, Jarrett Moyer and Professor Peter E. Schiffer from the Department

of Physics at Penn State. I express my indebtedness to Rajiv for the Hall measure-

ments and valuable discussions. A big thank you to all the members of the Nanoelec-

xv

tronic Devices and Circuits Laboratory (NDCL) - Euichul Hwang, Mike Barth, Arun

Thathachary, Matt Hollander, Ashish Agrawal, Nidhi Agrawal, Lu Liu, Bijesh Rajamo-

hanan, Euichul Hwang, Ashkar Ali, Feng Li, Himanshu Madan, Dheeraj Mohata.

xvi

Chapter 1

Introduction

1.1 Introduction to Metal Insulator Transition Based Tun-

nel Junctions

Since the discovery of the solid state transistor in 1947 by Schockley, Bardeen and

Brattain, the semiconductor industry has steadily scaled transistor size and as of 2013,

logic chips with as many as 6.8 billion transistors, enough for nearly every human being

on Earth, can be produced on a single chip.[14] As the transistor count has increased,

the performance bottleneck has become power consumption [1] as shown in Fig. 1.1.

Dynamic power consumption is proportional to CV2, and until recently scaling has fol-

lowed Dennard’s law,[15] which has reduced voltage by approximately 0.7x each gener-

ation. The vast majority of modern transistors are field effect transistors (FETs), which

accomplish switching by adjusting a potential barrier trough the use of an electric field.

However, the response of the carriers to the lowering of the barrier is limited by Boltz-

mann statistics where the increase in current by one decade is achieved by approximately

60 mV of barrier lowering at room temperature, effectively setting a minimum voltage

2

1990 1995 2000 2005 2010 201510

100

1000

CP

U P

ow

er

(W)

Year

Figure 1.1. Thermal power dissipation of modern CPUs has stopped increasing and is about 100W per chip. Adapted from [1]

for a desired Ion/Ioff ratio, disrupting Dennard’s predictions for voltage scaling.

Novel device design and materials which exhibit non-Boltzmann limited transport

are needed to realize super-steep slope (<60 mV/dec) transistors. The benefit of steep

switching is made clear in Fig. 1.2 which shows how the same Ion/Ioff can be achieved at

lower voltages, translating into power savings. Some of the alternatives being explored

are spinFETs, MEMFETs, negative capacitance FETs, and tunnel FETs (TFETS), all

of which show promise for high speed low power applications. The TFET relies on

quantum tunneling phenomenon of electrons to travel through a barrier instead of having

to surmount it, thereby overcoming the Boltzmann tyranny. The TFET has traditionally

been realized through bandgap engineering of III-V materials, which offer a rich variety

3

Boltzmann Limit 60mV/dec

Steep Slope Transistor < 60mV/dec

VG

Log

(I D

) Ideal Switch ~0mV/dec

Figure 1.2. Illustration of an Id-Vg curve highlighting the importance of the switching slopeto device performance for a fixed Ion/Ioff . The red curve shows a Boltzmann transport limiteddevice, which requires the most gate voltage to saturate the device, the sub 60 mV/dec deviceachieves the same current for a lower gate voltage, translating into lower power usage. The idealcurve, shown in blue represents a device that turns on at the smallest possible finite gate bias.

of bandgaps.[16] Recently sub 60 mV/dec switching has been achieved with TFETs.[17]

However, III-V TFETs are hampered by low on-state current due to their low density of

states.

Recently, metal insulator transition (MIT) materials have been proposed as a selector

for tunneling junctions.[18, 19] In the metallic state a large density of states would

facility direct tunneling of carriers from a source electrode into the MIT material and exit

through the drain electrode, passing through a conventional band insulator, resulting in a

high conductivity on-state as illustrated in Fig. 1.3(a). In the insulating state a bandgap

4

Figure 1.3. Illustration of a band diagrams showing the tunnel junction with a thin tunnelingdielectric as the barrier material. (a) In the insulating state a bandgap forms in the MIT materialmaking it impossible for electrons to directly tunnel, resulting in a high resistance state. (b) Inthe metallic state the bandgap collapses in the MIT material and electrons can tunnel into theempty states of the MIT material.

forming in the MIT material would make direct tunneling into the drain impossible,

creating a low conductivity off state, as illustrated in the band diagram in Fig. 1.3(b).

Conduction in the on-state is determined by the band insulator thickness, barrier height

and density of states of the metal. Ideally, the off-state is determined by thermionic

emission over the tunneling barrier. A third terminal, the gate, would externally control

the state of the MIT material.

Vanadium dioxide (VO2) is a material that exhibits a metal insulator transition with

up to five orders of magnitude change in resistivity at 340 K in unstrained films.[2]

The MIT can be externally triggered using thermal,[4] electronic,[20] optical[12] or

strain stimuli.[21] While the exact origin of the transition is still under debate,[22] it has

5

been demonstrated to be as fast as 75 fs[12] by time resolved optical pumping. In the

insulating state, VO2 has an optically measurable bandgap of 0.6 eV,[23] which abruptly

collapses as it undergoes an insulator-to-metal transition. The collapse of the bandgap

and ultra-fast switching holds promise for high speed correlated tunnel FETs.[19]

When an MIT material is in the metallic state, the metal-insulator-MIT material

structure forms a metal-insulator-metal (MIM) tunnel junction. In the insulating state

the opening of a bandgap cuts off states for direct tunneling (JDT ) into the MIT mate-

rial. Direct tunneling is expected to dominate MIM tunnel junctions but the absence

of states near the Fermi level in the insulating state will drastically lower the tunneling

current. In the insulating state, traps in the tunneling oxide would dominate transport

through Poole-Frenkel (JPF ) conduction and other defect mediated transport. The mod-

ulation of density of states near the Fermi level leads to a high conductance state in the

MIM case and low conductance when the bandgap forms, as illustrated in the band dia-

grams in Fig. 1.3 (a) and (b), respectively. This is fundamentally different from conven-

tional semiconductor based tunnel junctions where the tunnel conductance is modulated

by band-bending and Fermi level movement.[24] Metal-insulator-VO2 tunnel junctions

were first demonstrated by Martens, et al., [18] on large area devices (200 µm & 300 µm

diameter) and using hot (200 oC and higher) atomic layer deposition (ALD), resulting

in approximately one order of magnitude conductance change when thermally driving

across the transition. High temperature processing has been shown to create permanent

metallic regions in VO2, creating MIM shunting paths.[25] Large area device can be

susceptible to shunting paths making it difficult to quantify the true potential of the tran-

sition. This thesis explores nanoscale tunnel junctions of 200 nm diameter with a low

temperature ALD dielectric deposition process for the tunneling insulator.

6

0 200 400 600 80010

-6

10-4

10-2

100

102

104

106

108

1010

1012

VO2 Bulk

VO2 (001 TiO

2)

V2O

3

VO

V8O

15

V9O

17

Ti2O

3

NiSe

EuO

LSFO

Ti3O

5

NdNiO3

ρ(Ω

-cm

)

Temperature (K)

This

Work

Figure 1.4. Metal insulator transition of various materials. The near room temperature transitionand large change in resistivity makes VO2 an attractive material to prototype novel devices uti-lizing the MIT. VO2 bulk,[2] V2O3 & V8015,[3] VO,[4] V9O17,[5] Ti2O3,[6] NiSe,[7] EuO,[8]LSFO,[9] Ti3O5,[10] NdNiO3.[11]

1.2 Metal Insulator Transition in VO2

MIT is not unique to VO2; many other materials, especially vanadate based oxides offer

a rich variety of transition temperatures, magnitudes and mechanisms. Fig. 1.4 is a plot

of the resistivity change in a select set of transition metal oxides with MIT, highlighting

their magnitudes and transition temperatures. The near room temperature accessibility

and large change in magnitude for VO2 is one reason why it is used as a prototype MIT

material.

VO2 shows a complex interaction between the crystal structure and electronic prop-

7

erties. Depending on the temperature and strain, VO2 supports three stable states,

two insulating monoclinic (M1 and M2) and a metallic rutile (R) phase, along with

a metastable triclinic (T) phase and a complex triple point.[26] Several models have

been proposed to explain the MIT in VO2,[27, 22, 28, 29, 30, 31] attributing it to vary-

ing levels of contribution from a Mott-Hubbard type phase transition and a Peierls-like

structural instability. Significant research efforts are geared towards a better understand-

ing of the phase transition mechanisms in VO2 to elucidate which description is most

accurate. Recent work has provided evidence that an electrically driven MIT in VO2 can

be achieved in the monoclinic phase without a change in the crystal symmetry, hinting at

the possibility of an experimental observation of a Mott transition without a Peierls-like

structural phase transition,[32] enabled by the Mott M2 phase.[33]

Unlike a thermally driven MIT, the formation and growth of a filament plays an

important role in an electrically driven MIT.[20, 34, 35, 36] However, no conclusive

evidence exists regarding the underlying crystal structure of this filament. In this work,

the structural properties of the filament created during an electrically driven MIT in VO2

thin films are investigated by nanoscale hard X-ray diffraction (XRD) spatial mapping.

The structural evolution of the film and the geometric dimensions of the filament were

measured as a function of the applied electric field.

1.2.1 VO2 Transition by External Stimuli

The metal insulator transition in VO2 has been demonstrated using various external

stimuli. As stated earlier, heating bulk unstrained VO2 film to 340 K results in an MIT.

However, the speed of thermal stimulation is limited by thermal diffusivity and is not

ideal for high speed operation. Electronic switching by applying a bias across VO2 is

shown in this work and has been demonstrated by several other groups[37, 38], but Zim-

8

mers, et al.,[20] has shown that the cause of the effect is through Joule heating. High

speed transitions with VO2 have been achieved by optical excitation showing ultra-fast

sub 75 fs transition speeds[12], which causes the destabilization of the V dimers.[39, 40]

Recently, Jeong et al. have shown MIT control in VO2 using ionic liquids, however they

concluded that the effect was not due to electrostatically induced carriers, but rather to

field induced oxygen vacancy migration.[41] Strain induced transitions have also been

demonstrated,[21] but a transduction FET using VO2 has yet to be achieved experimen-

tally.

1.3 Thesis Outline

This thesis aims to investigate a novel using MIT based tunneling phenomenon in VO2

and the structural evolution of the electrically driven MIT in VO2. This work develops

a thorough understanding of the transport mechanisms in VO2 based tunnel junctions

across the abrupt metal insulator transition. Nanoscale VO2 tunnel junctions with 100x

modulation of tunneling current across the metal insulator transition are presented, and

the transport is modeled. Additionally, structural evolution of the MIT in VO2 during

an electrically driven transition is determined by nanoscale hard X-ray. The formation

of nanoscale R filaments in VO2 during an electrically driven transition are explored the

dynamic nature of these filaments as a function of device load are quantified. further-

more, the time dependent structural evolution of a VO2 oscillator is investigated using

time resolved X-ray diffraction.

This thesis will be organized in the following way. Chapter 2 will develop the current

understanding of MIT in VO2. The theoretical picture of the Peierls and Mott-Hubbard

based metal insulator transitions are discussed. Recent experimental evidence of both

types of transitions in VO2 is presented and discussed.

9

In chapter 3, the mechanism for a MIT based tunneling junction is proposed. The

results of VO2 based nanoscale tunnel junctions using a low temperature ALD process

are presented and modeled using direct tunneling and Poole-Frenkel conduction.

In chapter 4, a novel experimental procedure detailing how to probe the local struc-

tural transition is discussed and a method to differentiate M1, M2 and R crystal struc-

tures in VO2 is presented. Next, the nanoscale rutile filaments observed using X-ray

diffraction are quantified and their dynamic nature is explored. Additionally, the time

dependent structural evolution of a VO2 oscillator is presented and discussed.

Finally, in chapter 5, The key conclusions from the tunneling transport and nanoscale

X-ray work are summarized and suggestions for future studies are discussed.

Chapter 2

Metal Insulator Transition Theory

2.1 Introduction

In this chapter, the theoretical explanation for the metal insulator transition is introduced

using the Peierls and Mott-Hubbard model. Hall effect measurements are performed on

VO2 to quantify the free carrier concentration and mobility across the MIT. The current

state of research offering evidence for a Peierls or Mott-Hubbard transition is reviewed.

2.2 The Peierls Transition

The origin of the Peierls transition can be understood by first considering the origin of

the bandgap in a periodic lattice and then showing how dimerizing pairs of ions can lead

to lower energies and the complete filling of a band, leading to an insulator. Finally,

experimental evidence of the Peierls model in VO2 are discussed.

11

a

(a)

atom

Figure 2.1. One dimensional periodic lattice of atoms.

2.2.1 Standing waves in a periodic potential

The free electron wave function

(r) = exp(ik · r) (2.1)

and the energy dispersion

Ek =~2k2

2m(2.2)

describe plane waves in space. Where k is the wave vector, ~ is Plancks constant, and

m is the effective mass.

Now consider a one dimensional periodic potential applied to these plane waves,

such as those formed by atoms in a crystal lattice as shown in Fig. 2.1. From the Bragg

diffraction condition (k+G)=k2, where G is the reciprocal lattice vector of the lattice,

k is wavevector of the incident beam and k is the magnitude. For one dimension this

becomes

k = ±1

2G = ±nπ/a (2.3)

leading one to conclude that reflections and the potential for an energy gap occur at

the following wavevectors

k = ±nπ/a (2.4)

12

2a

Figure 2.2. One dimensional periodic lattice of atoms with pairing of atoms, also known asdimerization, leading to a doubling of the lattice parameter to 2a. This shifts the Brilluion zoneto π

2a

where n is an integer, where n=1 is the first Brilluion zone.

At πa

periods of k the wave functions are made up of waves that are Bragg reflected

at each Brilluion zone and cannot travel left or right, therefor becoming standing waves.

From this understanding the Bloch function and the Kronig-Penney model can be used to

determine the wave equation in a periodic lattice. However for the purpose of explaining

Peierls transitions we only need to understand that the bandgap forms at k = ±πa

.

2.2.2 Metal Insulator Transition by Ion Dimerization

If a crystal lattice forms pairs of ions, which effectively doubles the lattice spacing as

shown in Fig. 2.2 it can be shown that the energy of the system is minimized because

electrons move to a lower energy state.

An electron has two spin states, this implies that an ideal one dimensional crystal

with divalent atoms will just fill the lowest band with electrons. The states are com-

pletely filled and an electric field will not move the electrons, creating an insulator. If

a monovalent atom is used the band only half fills, allowing for electrons to move to

empty states with the application of an electric field, creating a metal. For the half filled

metal case the dispersion curve is filled up to π2a

, half of the available momentum space

as shown by the illustration in Fig. 2.3(a) for a crystal of period a. If the ions were to pair

up and double the lattice spacing as described previously in Fig. 2.2 the bandgap would

move to π2a

creating a fully filled lower band as shown in Fig. 2.3(b). This phenomenon

13

Energy

π/a-π/a

EF

π/a-π/a π/2aπ/2a

EF

Energy

Wavevector Wavevector

(b)(a)

Figure 2.3. (a) E-K diagram for a half filled 1-D crystal of monovalent atoms, with a Brilluionzone at πa . (b) Dimerized crystal of 1-D monovalent atoms result in a new Brilluion zone at π

2a .The avoided crossing phenomenon at the Brilluion zone lowers the total electronic energy of thesystem.

where the Brilluion zone and the Fermi surface lineup is known as Fermi surface nest-

ing. The lowering in energy comes from the fact that at dispersion at the Brilluion zone

exhibits the avoided crossing phenomenon, where the upper and lower energy bands will

not cross at the Brilluion zone. The energy near the zone boundary may be estimated by

the equation below

E ' ~2

2m

(G

2

)2

± U +~2K2

2m

(1± 2

λg/2U

)(2.5)

where G is the reciprocal lattice vector, U is the potential energy of the periodic

potential, λ = ~2K2

2mand K = k − 1

2G.

The temperature plays a role in the transition because below the Peierls transition

temperature the Fermi tail is reduced to a point where the reduction in electronic energy

14

from the transition exceeds the increase in crystal energy to dimerize the ions and move

the Brilluion zone to π2a

where the avoided crossing phenomenon results in the Fermi

level of the filled band at π2a

, from the new a2

lattice spacing, to be lower than the original

undistorted lattice spacing of a.

2.2.3 Evidence of Peierls Transition in VO2

The most striking evidence of a Peierls transition in VO2 is the crystal structure. The low

temperature, insulating monoclinic (M1) phase illustrated in 2.4(a) has a dimerization

of the quasi 1-D lattice of vanadium atoms and a doubling of the unit cell from the high

temperature, metallic rutile phase illustrated in 2.4(b). Density function calculations

using the local density approximation method reveal a Peierls-like instability of the d||

band is the cause of the insulating M1 phase,[27] but the opening of the bandgap was not

as large as experimentally observed. Ultra-fast pump-probe spectroscopy has suggested

that a structural bottleneck of 75 fs exists in VO2 when going from insulator to metal

suggesting the structure plays a critical role in forming the metallic state. [12]

15

Dimerization(b)(a)

Low T - Monoclinic High T - Rutile

Figure 2.4. Crystal structure of VO2, showing only the vanadium ions, in (a) low tempera-ture monoclinic phase, with dimerization and doubling of the unit cell, characteristic of Peierlstransition and (b) high symmetry rutile phase with high conductivity. Modified from [12]

2.3 The Mott-Hubbard Transition

2.3.1 Correlated Electrons and Localization

In 1938 Wigner suggested that an electron gas of low concentration might crystalize

or become localized.[42] An electron and a positive ion will attract each other with a

columbic force described by the equation below.[43]

e1e2kr2

(2.6)

Where r is the distance between the charges, e1 and e2 are the charge of the respective

16

ions, and k = 4πεo, where εo is the dielectric constant of free space. At absolute

zero such a system cannot carry a current due to localization of the electron to the ion.

However, if there is a significant concentration of free carriers injected into the system

the columbic force is described by

−e2

krexp(−qr) (2.7)

Where q is a screening constant described by the Thomas-Fermi approximation

shown below.

q2 =4me2n1/3

k~2(2.8)

e is the elementary charge of an electron, m is the mass of an electron, n is the carrier

concentration, and ~ is Plancks constant. Mott predicted that in such a system if enough

free carriers are injected there will be a discontinuous transition from insulating to a

metallic state.[44] The effect is discontinuous because as some electrons escape from

their pairs, they further increase the screening and free other carriers in an avalanche

process.

Mott also proposed an estimate of the critical carrier concentration for which this

transition occurs. Friedel describes a condition for which pairing will not occur as (2.9).

q >

(k~2

me2

)−1(2.9)

Substituting the Thomas-Fermi screening constant (2.8) into (2.9), results in the Mott

criterion

n1/3αo > 0.25 (2.10)

Where αo = k~2/me2, also known as the Bohr radius.

17

Figure 2.5. Experimental correlation between the effective Bohr radius and the critical carrierdensity of the Mott transition. The solid line represents n1/3αo > 0.26. ’e-h’ refers to electronhole photo excitation. Adopted from [13]

This critical density of carriers has been used very successfully to describe the Mott

transition in a wide variety of materials such as Ge, Si, CdS, NH3 and Ar [13] as seen in

Fig. 2.5.

The Mott model can be extended to a case of repelling electrons causing localization.

The Mott-Hubbard model describes such a situation, where strong columbic interactions

between neighboring atoms create a repealing force that prevents conduction and local-

18

d1d1d1 d1-1 d1+1

U

t

Site

i-2 i-1 i i+1 i+2

Electron

Figure 2.6. Illustration of the Mott-Hubbard model showing the U and t term acting on anelectron trying to move from site i-1 to i to enter the 2nd state in the d orbital at i.

izes electrons. Now, consider an ion with one filled state, there exists an energy costs to

fill the 2nd state due to columbic repulsion from the filled state as illustrated in Fig. 2.6.

The relationship is described by the Mott-Hubbard Hamiltonian

H = −t∑〈ij〉σ

C†jσCiσ + U∑i

ni↑ni↓ (2.11)

Where the t term is the hopping amplitude, which describes band overlap between states

(the energy available to hop from site to site), the U term is the columbic interaction

term (onsite repulsive energy). C†jσ and Ciσ are annihilation and creation operators

respectively, and ni↓ and ni↑ are density of state operators for the sites.If the hopping

term is >> than the interaction term, electrons will be free to move from site to site

and metallic behavior is observed; If the hopping term is << than the interaction term,

insulating behavior is observed.

2.3.2 Evidence of Mott-Hubbard Transition in VO2

Spectroscopic ellipsometry on VO2 reveals a strong electron-electron correlation in the

metallic phase.[45] Also, a divergent effective mass at the transition point is associated

with strong electron-electron correlation.[46] Some have speculated that VO2 exhibits

19

(1) L = 400μm

W =

50

μm

Contacts

(1) (2)

(3) (4)

(5) (6)

Figure 2.7. Schematic of the hall bar fabricated on VO2. The hall effect measurements areperformed while cooling from 330 K to 270 K across the MIT.

a Peierls assisted Mott transition where a Peierls instability enhances columbic interac-

tions leading to a reduced energy state, instead of the traditional Fermi-surface nesting

process described in. 2.2.2

2.4 The Hall Effect in VO2

The hall effect is a common technique used for determining free carrier concentration

(Ns), carrier type (n or p) mobility (µ) and sheet resistance (Rs). A typical hall bar

structure is illustrated Fig. 2.7 with the electrodes labeled 1-6. Other hall structures

which use from 4 to 8 electrodes are also commonly used.[47]

20

2.4.1 The Hall Effect

The parameters are determined from two sets of measurements. The Rs is determined by

using the electrodes in a 4pt probe configuration and evaluating the following equation

Rsh =V34W

LI12(2.12)

Where V34 is the differential voltage from electrode 3 and 4, W is the width of the

hall bar, L is the distance between electrode 3 and 4. The Ns, carrier type and µ are

determined by measuring the transverse voltage between electrodes 3 and 5 or 4 and 6

(it is common for an average between the two to be taken, also known as the hall voltage

Vhall for an applied current I12 and a perpendicular magnetic field B. The carrier type is

extracted from the sign of the hall voltage. Ns is determined from the equation below

Ns = − IB

Vhallq(2.13)

Once Ns is known µ is calculated from

µ =1

qNsRsh

(2.14)

Where, q is the elementary charge of an electron.

2.4.2 Hall Measurements in VO2

To fabricate the hall devices, Pd/Au electrodes are deposited and patterned by lift-off. A

bar of VO2 is isolated using a CF4 etch as illustrated in 2.7. The hall voltage is collected

from magnetic fields ranging from ± 40 kG while cooling from 330 to 270 K in 10 K

steps.

21

First, resistivity vs. temperature is measured in using 4pt. probe in a Van der Pauw

configuration and the resistivity is determined for each temperature. The change is re-

sistivity is determined to be 1480X as shown in Fig. 2.8 and the transition temperature

is approximately 298 K when heating and 286 K when cooling. The hall voltage is

found to be negative and therefor the dominant carrier is n-type. Cooling from metallic

to insulating state reduces the carrier concentration by about 3.3x104x, as seen in Fig.

2.9(a), from 1.01x1023 ± 1.74x1022 #/cm3 to 2.99x1018 ± 4.32x1017 #/cm3. During

this cooling the mobility increased by approximately 20x from 0.46± 0.097 cm2/v − s

to 9.36± 0.035 cm2/v − s, as seen in Fig. 2.9(b). The combination of these two results

in a resistivity change of 1666x, close to the 1480x measured by Van Der Pauw method.

The abrupt change in resistivity observed in VO2 is dominated by the abrupt change in

carrier concentration and to the 2nd order, a change in mobility.

22

180 210 240 270 300 330 360

10-4

10-3

10-2

10-1

100

Cooling

Heating

ρ (

Ω−cm

)

Temperature (K)

Figure 2.8. Resistivity vs. temperature of the 13 monolayer (3.9 nm) VO2 sample used in thehall measurements.

23

260 280 300 320 3400

2

4

6

8

10

Mo

bili

ty (

cm

2/V

-s)

Temperature(K)

(a)

(b)

260 280 300 320 3401E18

1E19

1E20

1E21

1E22

1E23C

arr

ier

De

nsity (

#/c

m3)

Temperature(K)

Figure 2.9. Hall measurements on VO2 (a) The Ns vs. T shows VO2 has an Ns of1.01x1023#/cm3 in the semiconducting state and 2.99x1018#/cm3 in the metallic state, wherethe difference between the two states is about 3.4x104x. (b)The µ vs. T shows a VO2 has a mo-bility of 9.36 cm2/v − s in the semiconducting state and 0.46 cm2/v − s in the metallic state,where the different between the two states is about 20x.

Chapter 3

Nanoscale Structural Evolution of the

Electrically Driven Transition in

Vanadium Dioxide

3.1 Introduction

In this chapter the mechanism behind the electrically driven insulator to metal transition

in two terminal VO2 is investigated by analyzing local phase formation by nanoscale

hard X-ray diffraction. First, Bragg diffraction theory and the diffraction condition are

introduced. Next the experimental design which allows for probing of VO2 phases M1,

M2 and R is discussed. Conducting R filaments are observed by X-ray probing and their

contribution to the channel conductance is quantified. The differences between an elec-

trical and thermally induced, magnitude of transition are explained using a network of

resistors to model filamentary conduction in VO2. Further analysis reveals how the VO2

can be biased to tune M1/R phase co-existence which can have important implications

on circuit designs. Finally, the structural evolution of a VO2 oscillator is revealed by

25

d

atom

Figure 3.1. Illustration explaining the derivation of the Bragg equation where the extra pathlength seen by the wave reflected from the 2nd layer is determined to be 2dsinθ

time resolved X-ray diffraction.

3.2 Bragg’s Law of Diffraction

Waves reflecting off periodic planes will have different path lengths. Only certain path

lengths that are integer multiples of the incident wavelength will have constructive in-

terference. For a fixed wavelength, the constructive interference is achieved by meeting

the condition

2d sin θ = nλ (3.1)

where θ is the incident angle, d is the distance between periodic planes, λ is the wave-

length, and n is an integer. The derivation of 3.1 can be understood from Fig. 3.1, where

the 2d sin θ is the extra distance the wave travels as it reflects off the 2nd periodic layer.

26

3.2.1 Structure Factor

In a 3-D crystal not all planes will give constructive interference. To determine which

planes meet the diffraction condition the structure factor of the basis (SG) is calculated

for the space group of the crystal by the equation below

SG =∑j

fj exp [−i2π(ν1xj + +ν2yj + ν3zj)] (3.2)

where x,y,z are the normalized locations of the atom in the unit cell and ν1,ν2,ν3

define the crystal plane. A null SG indicates destructive interference. The diffraction

amplitude is directly proportional to SG and as expected the case for destructive inter-

ference produces no diffraction peak.

3.3 Experimental Setup

3.3.1 Two Terminal VO2 Fabrication

The VO2 films under investigation were 10-nm-thick grown epitaxially on semi-insulating

TiO2 (001) substrates employing reactive oxide molecular beam epitaxy using a Veeco

GEN10 system. The lattice mismatch of 0.86% effectively shortens the c-axis of VO2

oriented normal to the film surface.[48] Two-terminal test structures were fabricated

using standard lithographic techniques. Electrical contacts were patterned on the VO2

surface using electron beam lithography and a 20-nm-thick Pd/80-nm-thick Au metal

stack was deposited in the defined patterns by electron beam evaporation, followed by

lift-off. The active channel and device isolation was then patterned by electron beam

lithography followed by a CF4 dry etch and residual e-beam resist was stripped with

a 70 C bath of Remover 1165. A cross of the final device structure is illustrated in

27

500 µm TiO2 (001)

10 nm VO2

20nm Pd 20nm Pd

80nm Au 80nm Au(a)

(b)

Figure 3.2. (a) Illustrated cross section of the fabricated 2-terminal VO2 device. (b) SEM of thefabricated device, measured to be 6.0 µm long and 9.4 µm wide.

Fig. 3.2(a). Step by step details of the process is described in Appendix A. Finally,

the sample is mounted on a ceramic package and the electrodes from the sample are

wire-bonded to external leads. A scanning electron micrograph of the device probed by

XRD, which is 6 µm long, 9.4 µm wide, is shown in Fig. 3.2(b).

28

3.3.2 Nanoscale hard X-ray Setup

The structure of the VO2 film as it transformed from the HRS to LRS was investigated

using the nanoscale scanning X-ray probe at the 2-ID-D beamline at the Advanced Pho-

ton Source at Argonne National Laboratory. A 10.1 keV hard X-ray probe with a spot

size as small as 250 nm full-width-half-maximum was achieved by an Au Fresnel zone

plate (1.6 µm thick, 160 µm diameter, 100 nm outer most zone width, 40 µm center disk,

40 µm central beam stop) in conjunction with a 20 µm order sorting aperture. Two-

dimensional (2D) structural maps of a VO2 channel were obtained by raster scanning

the device under the X-ray probe at a fixed θ/2θ angle while simultaneously monitoring

the intensity of the diffracted beam using a single avalanche photodiode detector as a

function of applied voltages across the device. A liquid nitrogen cryostream (Oxford

UMC0060) was used to maintain the sample at the desired temperature. For beam in-

tensities above 1 MW/m2 it was found that the X-ray caused a permanent transition into

the M1 phase. The MIT control in VO2 with high energy radiation has been observed

by other groups.[49] The exact X-ray beam intensity threshold and mechanism of this

phenomenon is still being investigated. In our case, a lower intensity of 750 W/m2 was

achieved by inserting attenuation filters into the X-ray beam prior to the zone plate and

defocusing the beam to a 1 µm diameter spot size on the sample. The device channel

was scanned using 500 nm steps along the length of the channel (in the direction of the

applied electric field) and in 300 nm steps along the width (transverse to the applied

electric field), providing information in the nanoscale regime.

The electrical measurements and biasing were made by connecting the leads of the

package to an Agilent 81150A arbitrary waveform generator and an Textronix DPO3034

oscilloscope in 1 MΩ impedance mode is used to measure the applied voltage. A 38 kΩ

resistor is placed in series with the device to prevent permanent damage to the film

29

Rload =38 kΩ

RS

cope1 M

Ω

VO2DUT

RScope1 MΩ

Figure 3.3. Circuit diagram of the electrical biasing and measurement. A voltage is measuredoff a 38 kΩ load resistor Rload and voltage division is used to determine the voltage drop on theVO2 device under test.

during the electrically induced transition and the voltage is read off the series resistor as

illustrated by the circuit diagram in Fig. 3.3. At 260 K the device with the series resistor

is found to transition from a high resistance state (HRS) to a low resistance state (LRS)

at 9.6 V.

Figure 3.4 shows the R 002 and M1 402 Bragg peaks measured at 310 K and 260 K,

respectively, on the VO2 thin film, along with the expected location of the M2 040 peak.

Due to the metastable nature of the triclinic phase, it is not considered in this analysis.

A 2θ angle of 51.714 was selected to provide the maximum intensity contrast between

the M1 and R phases. At this angle an increase in intensity indicates the presence of the

R phase while a decrease would signify the presence of the M2 phase, which may appear

30

50.5 51.0 51.5 52.0 52.50

1

2

3

4

5

6

M1 = 1.0

R = 4.4

Nor

mal

ized

Inte

nsity

2θ (°)

260 K (Insulating/M1) 310 K (Metallic/R)

Detector Position2θ = 51.714 °

ExpectedM2 Peak = 51.08 °

Figure 3.4. θ/2θ scan at 260 K (red line) and 310 K (blue line) of the R 002 and M1 402 Braggpeaks, respectively. The expected position of the M2 040 Bragg peak is calculated to be 51.08. A 2θ angle of 51.714 was chosen for the subsequent mapping to provide maximum contrastbetween the different VO2 phases.

in an electrically driven MIT. Although, thermally driving the film across the transition

while scanning θ/2θ did not reveal any evidence of an M2 phase, in agreement with the

recently published VO2 temperature-stress phase diagram.[26]

3.4 Nanoscale X-ray Diffraction

3.4.1 Spatially Resolved Nanoscale X-ray diffraction

Nanoscale XRD maps were collected for a range of applied voltages both above and

below the electronically driven MIT. Figure 3.5 shows the intensity maps for the device

at 260 K, for 0, 8, 10, and 12 V bias applied to the VO2 device and 38 kΩ series resistor.

To highlight the structural changes from the M1 phase for different applied voltages,

31

the intensity of the XRD maps was normalized with respect to the M1 intensity. In

Fig. 3.5, the green regions are diffraction signals from the M1 phase of VO2, blue is

where the VO2 etched out, and red areas represent R domains. Figure 3.5(a) shows that

the VO2 channel was mainly in the M1 phase (HRS) under zero bias condition except

for a small R filament at the center of the channel. This filament is likely a remnant

from previous electrically driven transitions (i.e. memory effect); however, repeatedly

cycling the device across the MIT and rescanning the channel did not always result in an

observable remnant filament. At 0 V, the total channel resistance was 95.6 kΩ and the

device was in HRS. The small R filament did not significantly contribute to the in-plane

conduction, but can act as a shunting path for out of plane transport for vertical devices.

For 8 V bias, a larger filament, approximately 3.2 µm long, was observed at the center,

but did not bridge the entire channel, shown in Fig. 3.5(b). This filament at 8 V reduced

the channel resistance by about half to 49.0 kΩ and forms before the device transitions

to a LRS. Increasing the bias to 10 V, the VO2 channel underwent an electrically driven

transition into the LRS and channel resistance dropped sharply to 5.9 kΩ. Figure 3.5(c)

shows that in this state, the filament bridged the entire length of the 6 µm channel;

however its width is only a fraction of the lithographically defined 9.4 µm channel width.

Finally, at 12 V applied voltage, the channel resistance was 5.5 kΩ, a 17x decrease from

the equilibrium state at 0 V. The filament seen in Fig. 3.5(d) had a slightly increased

width compared to the 10 V bias. At 12 V bias the peak XRD intensity from the filament

region was found to be only 2.1x (2.0x at 10 V bias) that of M1, which is significantly

lower than the 4.4x expected increase observed in the bulk film for a thermally driven

MIT. Assuming uniform X-ray illumination, this suggests that the filament occupied

approximately 1/3 of the full 1 µm diameter beam size, indicating a filament width of

approximately 300 nm. Additionally, no drop in intensity was observed in the channel

that could be attributed to an M2 phase; as mentioned before this was expected from a

32

tensile strained VO2 film such as the one used in this experiment.

33

Leng

th (µ

m)

0

2

4

6

Width (µm)

Nor

mal

ized

Inte

nsity

0.0

0.5

1.0

1.5

2.0

0 2 4 6 8 10 12 140

2

4

6

0

2

4

6

0

2

4

6

0 V

8 V

10 V

12 V

R=95.6 kΩ

R=49.0 kΩ

R=5.9 kΩ

R=5.5 kΩ

(a)

(b)

(c)

(d)

Figure 3.5. 2D nanoscale X-ray maps of a VO2 device with applied voltages of (a) 0 V, (b) 8V, (c) 10 V, and (d) 12 V and a series resistor of 38 kΩ which shows the dynamical growth ofan R phase filament in the channel. Note in (a) that a remnant of the filament persisted when novoltage was applied across the channel. The white dashed lines represent the approximate edgeof the gold electrodes.

34

To confirm that the increased XRD intensity response was due to the MIT and to

demonstrate repeatability, the diffraction intensity and the VO2 resistance were simulta-

neously measured over several cycles of electrically induced transitions. A pulse train,

shown in Fig. 3.6(a), was cycled from 1.3 V to 10 V, as 9.6 V was found to be sufficient

to induce the electronic transition, while 1.3 V was low enough to return to an insulat-

ing state yet provide a finite current to confirm the resistance of the VO2. The X-ray

beam was focused on the conducting filament and the diffracted intensity was collected

while simultaneously monitoring the channel resistance. Figure 3.6(b-c) shows that the

LRS coincided with an increased intensity attributed to the R phase, whereas the HRS

coincided with the M1 phase.

35

0

4

8

120 10 20 30 40 50 60 70

0.81.01.21.41.6

0 10 20 30 40 50 60 70103

104

105

Vso

urce

(V)

Nor

mal

ized

Inte

nsity

RV

O2(

Ω)

Time (s)

(a)

(b)

(c)

R

M1

Figure 3.6. (a) Voltage pulse applied to the VO2 and 38 kΩ resistor in series. (b) The corre-sponding time dependent X-ray intensity from the filament region and (c) resistance of the entirechannel. The changes in the X-ray intensity accompanied by changes in channel resistance areattributed to a structural phase transition in the VO2 from the between the insulating M1 andmetallic R phase.

3.4.2 Filament Size Extraction

To explain the difference in the channel resistivity change between the thermal (571x)

and electrically (17x) driven transitions, the total resistance was calculated by incor-

porating the coexistence of low and high resistive phases. The channel was treated as

a set of series and parallel resistors with the equivalent circuit diagram given in Fig.

3.7(a), overlaid on an illustration of an M1 channel with a rutile filament in the center.

36

The total resistance of the equivalent circuit is given in Eq. (3.3) where Rpara−R is the

parallel resistor describing the rutile filament, Rseries−M and Rpara−M are resistors with

the resistivity characteristic of the monoclinic phase. Rseries−M components were com-

bined into a single series resistor and similarly the Rpara−M components were lumped

into a single parallel resistor. ρM and ρR are the resistivities of the monoclinic and ru-

tile phases, respectively; while L, W and t are the length, width and thickness of the

respective region. The regions were assumed to be uniform throughout the entire film

thickness. The length of the filament was estimated from the 2D-XRD maps and the

width of the filament was calculated by solving for Wpara−R in Eq. (3.3) for a ρM and

ρR of 0.16 Ω-cm and 2.8x10−4 Ω-cm, respectively, as determined from the ρ vs. T curve

in Fig 3.7(b).

RV O2 = Rseries−M + (Rpara−R||Rpara−M)

RV O2 = ρMLseries−MWseries−M t

+

[ (ρRLpara−RWpara−Rt

)(ρMLpara−MWpara−Mt

)(ρRLpara−RWpara−Rt

)+

(ρMLpara−MWpara−Mt

)]

(3.3)

When the transition to LRS occurs, the R filament length was set to the channel

length and the Rseries−M term goes to zero. At 10 and 12 V a filament width of 270

and 290 nm was determined, respectively; in excellent agreement with the experimen-

tal estimation of approximately 300 nm from the XRD intensity maps. A summary of

the filament dimensions extracted from the X-ray imaging and Eq. (3.3) is shown in

Table 3.1. Figure 3.7(c) plots the extracted resistivity of the entire channel during an

electrically driven transition. However, if considering only the 290 nm wide R-phase,

the entire 571x resistivity change can be observed. These results emphasize the impor-

tance of understanding and quantifying the presence and dimensions of R filaments in

the channel.

37

(a)

(b)

571x

17x

(c)

571x

240 260 280 300 320 340

1E-4

1E-3

0.01

0.1

1

ρ (Ω

-cm

)

Temperature (K)

Cooling Heating

0 2 4 6 8 10 12

Voltage (V)

Width = 9.4 μm Width = 290 nm

Rseries-M

Rseries-M=

R para

-M

R para

-M= R pa

ra-R

=

Drain

Source

Rutile Filament

Figure 3.7. (a) Illustration of the equivalent circuit used to extract the filament width. (b) ρvs. temperature for a thermally driven transition, showing a 571x change in resistivity. (c) Theextracted resistivity when considering the whole 9.4 µm channel width results in a 17x change,if after 9.6 V only the 290 nm width that goes through a structural phase is considered fullmagnitude of the resistivity change is restored.

Table 3.1. Extracted R filament dimensionsV R Length (µm) R Width (nm) I (µA) RV O2 (kΩ)0 0.5 50 - 95.68 3.2 200 92.0 49.0

10 6.0 270 227.8 5.912 6.0 290 275.9 5.5

38

3.4.3 Dynamics of the Rutile Filament

VO2 has recently been demonstrated as an effective switching element in high density

memory cells.[50] The memory cell exists as high or low load resistance, depending

on its digital state, and understanding the role of R filament formation is critical for

realizing ideal volume, write speeds, and performance for such a device. To quantify

the effect of load resistance on VO2 channel utilization, resistors from 3 k to 38 kΩ

were placed in series with a 6 µm long channel of varying widths from 4 to 20 µm as

illustrated in Fig. 3.8(a). The devices were biased in the LRS at a fixed voltage (18 V)

to ensure that the rutile filament length is fixed at the channel length (6 µm), so that the

width can be extracted. The filament width was a function of series resistance, see Fig.

3.8(b). The device can be biased in such a way that either phase coexistence in the VO2

channel or a complete transformation of the entire channel to the R phase is achieved.

For the 3 kΩ load, a channel width up to approximately 17 µm can be fully utilized. By

increasing the series resistance the decreasing current flow results in a smaller filament.

This shows that for some given load resistance a further increase in VO2 channel width

does not significantly decrease LRS resistance of the VO2. As shown in Fig. 3.8(c) the

filament of a 4 µm wide device in the LRS state is linearly proportional to the current

until it becomes comparable to the patterned width of the device (shown as a dashed

line). After which, Joule heating increases the resistivity of the metallic R channel and

the extraction method (which assumes a fixed rutile resistivity) incorrectly shows the

filament width as decreasing.

39

0.0 0.5 1.0 1.5 2.0 2.5

0

1

2

3

4

Fila

me

nt

Wid

th (

µm

)

Current (mA)

ρr increase from

Joule heating

0 5 10 15 20 250

5

10

15

20

25

Fila

me

nt W

idth

, W

pa

ra-R

(µ

m)

Patterned Channel Width (µm)

Rseries

1:1 10 kΩ

3 kΩ 17 kΩ

5 kΩ 27 kΩ

8 kΩ 38 kΩ

(a)

(b)

(c)

Figure 3.8. (a) Circuit schematic overlaid on an illustration of the VO2 channel in LRS statewith a resistor Rseries in series. (b) The filament width dependence on the series resistor. Athigher currents (lower series resistance) the whole channel width can be utilized as seen by thedata points falling on the dashed line, representing a 1:1 relationship between the extracted andpatterned filament width. (c) The calculated filament width dependence on the current displaysa linear relationship until joule heating increases resistivity, which is not accounted for in thismodel and incorrectly shows a reduction in filament width.

40

3.4.4 Time resolved X-ray Diffraction of VO2 Oscillators

A VO2 channel may be biased by a DC voltage to produce oscillatory behavior.[35, 51]

To investigate the structural dynamics of VO2 oscillators the channel used in the local

structural mapping experiment described earlier is cooled to 255 K and 67.6 kΩ resistor

is placed in series. The oscilloscope is set to produce an external trigger to a delay

generator (SRS DG535) on each rising edge. Variations in the VO2 oscillation frequency

requires that the delay generator is synchronized to each rising edge to ensure the same

time period is measured after each oscillation. The delay generator is programmed to

produce four 20 µs square pulses with 40 µs periods. This creates 20 µs time bins

starting at 0, 40, 80, and 120 µs after the rising edge, labeled as B1-B4 respectively. The

X-ray beam is positioned on the filament and the channel is biased to produce sustained

oscillations. The diffracted photon counts are integrated for 300 seconds. The waveform

of a typical oscillation is shown in Fig. 3.9, where the left axis is the voltage on the load

resistor.

41

0.0 100.0µ 200.0µ 300.0µ0

5

10

15

20

Time (s)

Vlo

ad(V

)

0

200

400

600

800

1000

Counts

(Arb

. Units

)

B1 R

B2 B3 B4

M1

Figure 3.9. Time dependent X-ray diffraction of a VO2 oscillator. The increased XRD photonsin the first 20 µs indicated a transition to the R phase has occurred. Within the first 40 µs thefilm transitions back into M1 for the remainder of the period of oscillation.

Superimposed on the waveform are the total XRD photon counts, shown on the right

axis, for each of the 4 bins plotted relative to the rising edge. The total counts for each

bin, seen in table 3.2, show a 50% higher photon count in B1 than B2-4, providing

evidence of an R phase formation after the rising edge. The three subsequent bins B2-

B4 are approximately equal and significantly lower than B1, indicating M1 phase for the

Bin Counts (Arb. Units)B1 917B2 605B3 595B4 552

Table 3.2. X-ray counts for 20 µs time bins starting at 0, 40, 80, and 120 µs after the rising edge,labeled as B1-B4 respectively. No background subtraction is applied

42

majority of the oscillation. If the X-ray beam is positioned away from the filament, but

still on the channel and the experiment is repeated B1-B4 are all approximately equal.

This suggests that the filament observed in the electrically induced switching described

earlier in section 3.4.1 is repeatedly reformed and broken during each VO2 oscillation,

and structural phase transition from M1 to R and back to M1 plays an integral role in

the oscillations.

3.5 Conclusion

In-situ nanoscale X-ray mapping with resistivity measurements on VO2 have revealed

the formation of an R metallic filament in an insulating M1 film during an electrically

driven MIT. Additionally, time resolved XRD revealed that the filament observed in the

electrically induced switching is repeatedly reformed and broken in VO2 oscillators, and

structural phase transition from M1 to R and back to M1 plays an integral role in the

oscillations. This work also demonstrates that nanoscale R filaments comprising only a

small portion of the total device area can exist in the VO2 channel below biases required

to switch to LRS, highlighting the importance of enhancing spatial resolution for the

study of electrically driven phase transitions. The extracted filament size revealed that,

depending on the load, the ratio of R/M1 phase can be externally controlled, which can

have important implications on circuit designs using VO2 to drive resistive loads.

Chapter 4

Vanadium Dioxide Tunnel Junctions

4.1 Introduction to tunneling in VO2

In this chapter we investigate the tunneling transport of VO2 nanoscale junctions across

a thermally induced phase transition. First, the mechanism for tunneling current modu-

lation as the VO2 undergoes a MIT transition is explained. Next, the fabrication process

using a low temperature ALD is described. Experimental results showing two orders

of magnitude change in tunnel conductance in metal-insulator-VO2 tunnel junctions are

discussed and the large conductance change is presented and modeled using direct tun-

neling and Poole-Frenkel conduction.

4.2 Device Fabrication

The sample under investigation is a nano-pillar array of VO2 tunnel junctions. 10 ±0.5

nm thick VO2 is epitaxially grown on conducting Nb-doped TiO2 (001) via reactive

oxide molecular beam epitaxy using a Veeco GEN10 system. 1 nm thick Al2O3 followed

by 1 nm thick HfO2 is then deposited by atomic layer deposition (ALD) at 100 oC

44

Al2O3

Nb‐TiO2 (001)

VO2

Pd

Au

500 μm

10 nm

1 nmHfO2 1 nm

20 nm

80 nmNano‐pillar

200 nm

Figure 4.1. Illustrated cross-section of the fabricated nano-pillars.

and 110 oC, respectively. Trimethylaluminium and tetrakis (dimethylamino) hafnium

metal organic precursors are used for the Al2O3 and HfO2 respectively, with H2O as the

oxygen source. Previous studies have shown that annealing VO2 at temperatures as low

as 150 oC can cause irreversible metallic regions to form on the surface,[25] therefor

a low temperature ALD process is selected to preserve the VO2 tunneling interface

quality. The top electrodes are electron beam evaporated 20 nm thick Pd and 80 nm thick

Au nano-pillars patterned by a lift off process using positive electron beam lithography.

The final structure cross section of the fabricated device is illustrated in Fig. 4.1. Step-

by-step details of the process can be found in Appendix B.

45

4.3 Tunneling Modulation in VO2

When VO2 is in the metallic state, a metal-insulator-VO2 structure acts as a metal-

insulator-metal (MIM) tunnel junction. In the insulating state the opening of a 0.6 eV

bandgap around the Fermi level, cuts off states required for direct tunneling (JDT ) from

the metal, through the insulator into the VO2. Direct tunneling is expected to be the

dominant mechanism in MIM tunnel junctions. However, the absence of states near the

Fermi level in the insulating state of VO2 will drastically lower the tunneling current.

In the insulating state, traps in the tunneling oxide are expected to dominate transport

through Poole-Frenkel (JPF ) conduction.[25] The change in density of states near the

Fermi level leads to a high conductance state in the MIM case and low conductance

when the bandgap forms. The change in density of states near the Fermi level leads to a

high conductance state in the MIM case and low conductance when the bandgap forms,

as illustrated in the band diagrams in Fig. 4.2 (a) and (b), respectively.

46

ON

4.2eV

2.8eV

VO2

(Metallic)

Pd

E

EF

OFF

VO2

(Insulating)

3d||

3d||/3dπ

3d||/3dπ

Hybrid Upper

Hubbard Band

Lower Hubbard

Band

2pπ

2.8eV

Pd

HfO

2

Al 2O3

EJPF

HfO

2

Al 2O3

JPF

JDT

(b)(a)

Figure 4.2. (a) The OFF state occurs when VO2 is below the transition temperature, where abandgap of 0.6 eV opens around the Fermi level creating a deficiency of states to tunnel into.Transport is by Poole-Frenkel conduction through trap states. (b) The ON state, when VO2 isbelow Tc, results in an MIM structure and direct tunneling contributions to the transport. Thisprocess enables conductance modulation.

4.3.1 Direct Tunneling

A symmetrical MIM junction with a thin tunneling dielectric is illustrated in Fig. 4.3(a),

where EF is the Fermi level, φ0 is the barrier height and d is the dielectric thickness.

When bias is applied, all of the voltage is assumed to drop on the dielectric, resulting

in the non-equilibrium band diagram seen in Fig. 4.3(b). The current through this MIM

junction can be expressed as

47

(b)(a)

EFEF

d

M1 M2I

d*

EFEF

qV

0qφ0qφ

Figure 4.3. (a) Band diagram of a symmetrical MIM structure in equilibrium. (b) SymmetricalMIM under bias, where V > φ0

J =

Em∫0

D(Ex)ξdEx (4.1)

where D(Ex) is the tunneling probability derived from the WKB approximation. ξ

is the density of states available for tunneling from electrode 1 to electrode 2, defined as

ξ = ξ1 − ξ2

ξ1 =4πm2q

h3

∞∫0

f(E)dEr

ξ2 =4πm2q

h3

∞∫0

f(E + eV )dEr

(4.2)

where, the integral is calculated over all energies, m is the effective mass, h is Planck’s

48

constant, q is the elementary charge of an electron, V is the applied bias, and f is the

Fermi-Dirac distribution. For moderate applied bias (0 ≤ V ≤ φ0), d*=d, and φ0 = φ0,

the current density is given by [52]

JDT =

[Jo

(Φo −

V

2

)exp

(−C

√(Φo −

V

2

))−(

Φo +V

2

)exp

(−C

√(Φo +

V

2

))](4.3)

Where,

Jo =q2

2πhd2(4.4)

C =4πd√

2mq

h(4.5)

4.3.2 Poole-Frenkel Conduction

Poole-Frenkel conduction is trap assisted thermionic emission process observed in dielectrics.[53]

A trap in the dielectric creates a potential well and an external field applied reduces the

potential barrier seen by a carrier in the well by

∆U =

√qE

πε(4.6)

Where, q is the elementary charge, E is the electric field, and ε is dielectric constant.

Thermionic emission of electrons into a conduction band is proportional to

∝ exp

[−ΦB

kBT

](4.7)

Where U0 is the ionization energy, k is Boltzmanns constant and T is temperature.

49

Oxide

EF

EF

BΦ

Electric Field

Figure 4.4. Schematic band diagram of Poole-Frenkel emission under bias.

In the presence of a field the barrier is lowered by (4.6) and the emission becomes

proportional to

∝ exp

[−(U0 −∆U)

kBT

](4.8)

Resulting in the Poole-Frenkel conduction equation

JPF = KE · exp

[− q

kBT

(ΦB −

√qE

πε

)](4.9)

where K is a constant.

50

4.4 Conductive Atomic Force Microscopy of VO2 Tun-

nel Junctions

4.4.1 Experimental setup

Scanning electron micrographs of the pillar array is shown in 4.5 (a), and an individual

200 nm diameter pillar is shown in 4.5 (b). Electrical and topographic measurements

are recorded using a custom built low temperature scanning probe microscope. The

cantilever used is a Cr-Au µmasch NSC-16 with a nominal tip radius smaller than 35

nm. Electrical connections are made to the substrate which acts as a common bottom

electrode and the top contact to each individual device is established by making me-

chanical contact between the cantilever and the nano-pillar under investigation. The

current is corrected for a presumably instrument originated constant 20 pA current. For

topographic measurements, the deflection of the cantilever is measured by laser based

interferometry. Topographical measurements of the devices are shown in Fig. 4.5 (c),

where individual nano-pillars are clearly observable. The measurements are performed

without breaking vacuum and at a controlled temperature.

51

198 nm

30

0 n

m

(a) (b)

(c)

Figure 4.5. (a) Scanning electron micrograph (SEM) of the fabricated nano-pillar arrays. (b)Zoomed in SEM of an individual nano-pillar. (c) Topography scan of the area under investiga-tion. The single pillars are clearly discernible.

4.4.2 Tunneling Current Modulation Across the MIT

Using the setup described above, the voltage is swept and the current across the nano-

pillar tunnel junctions are measured. For each temperature and every nano-pillar, 20 I-V

traces are recorded and averaged under identical conditions. The averaged I-V traces

between 260 to 360 K are collected in 5 K steps are shown in Fig. 4.6 (a-c) for three

individual nano-pillars. Pillars A and B show an abrupt increase in the tunneling current

at 285 K and pillar C shows a similar increase at 290 K. The difference in transition

temperature (Tc) could be due to variation in local strain and stoichiometry.[25] As the

devices are heated across Tc, the tunneling current abruptly increases as a result of the

52

-0.4 -0.2 0.0 0.2 0.4

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

Cu

rre

nt

(A)

Voltage (V)

-0.4 -0.2 0.0 0.2 0.4

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

Cu

rre

nt

(A)

Voltage (V)

-0.4 -0.2 0.0 0.2 0.4

1E-13

1E-12

1E-11

1E-10

1E-9

1E-8

Cu

rre

nt

(A)

Voltage (V)

Temperature (K)

Pillar A Pillar B

Pillar C(c)

(b)(a)

260 305

265 310

270 315

275 320

280 325

285 330

290 335

295 340

300

Figure 4.6. I-V traces for temperatures between 260 to 340 K in 5 K intervals as indicated bythe legend for 3 individual pillars.

collapsing bandgap.

For each nano-pillar, the conductance as a function of temperature (T) at different

voltages is shown in Fig. 4.7 (a-c). At Tc, the conductance of the pillars changes by

approximately two orders of magnitude at ±0.3 V, where the precise magnitude of cur-

rent increase depends on the voltage at which the comparison is carried out. While the

tunneling conductance abruptly changes across Tc when VO2 changes phase, it is nearly

constant at all temperatures below Tc (2x10−11 S at ±0.3 V for pillar A) when VO2 is

insulating and for temperatures above Tc (2x10−9 S at±0.3 V for pillar A) when VO2 is

metallic indicating the tunneling is heavily dependent on the insulating or metallic state

of VO2.

53

Pillar A Pillar B

Pillar C

(c)

(b)(a)

260 280 300 320 340

1E-12

1E-11

1E-10

1E-9

1E-8

Cond

ucta

nce (

S)

Temperature (K)

260 280 300 320 340

1E-12

1E-11

1E-10

1E-9

1E-8

Co

ndu

cta

nce (

S)

Temperature (K)

260 280 300 320 340

1E-12

1E-11

1E-10

1E-9

1E-8C

on

ducta

nce

(S

)

Temperature (K)

Voltage -0.5 0.5

-0.4 0.4

-0.3 0.3

-0.2 0.2

-0.1 0.1

Figure 4.7. Conductance vs. temperature for 3 nano-pillars showing a tunneling conductanceresponse to the abrupt MIT in VO2.

4.4.3 Modeling

The transport before and after the MIT transition is modeled using Poole-Frenkel con-

duction and direct tunneling. Shown in Fig. 4.8(a) is a typical J-V trace for Pillar B in

the low conductance state (270 K), with Poole-Frenkel, JPF conduction (4.9) superim-

posed and shows a good agreement to the measured current. The inset in Fig. 4.8 (a)

shows a linear relationship between ln(I/V) vs.√V , which is characteristic of Poole-

Frenkel conduction [54, 55, 56]. Fig. 4.8(b) shows a typical J-V trace for the high

conductance state (330 K) of Pillar B. Neither Poole-Frenkel nor direct tunneling only

is able to describe the observed I-V curve as shown in Fig. 4.8(b). A combination of

54

direct tunneling (4.3) and Poole-Frenkel conduction (Jmetallic=JDT+JPF ), is found to

be in good agreement to the data. For the high conductance case, direct tunneling dom-

inates at low voltages, but Poole-Frenkel conduction, which is heavily field dependent,

dominates at higher voltages.

The fitting is performed with with the following approximations. A dielectric con-

stant of 11ε0is approximated from measurements on C-V pads deposited under the same

low temperature conditions and is in good agreement with other reports of low tem-

perature ALD deposition [57, 58].ΦB is estimated by plotting ln(I/V) vs. 1/kBT in the

semiconducting state for fixed voltages, where the slope is(

ΦB −√qE/πε

)and ΦB

is estimated to be 0.52 eV. In the metallic state, the fitting constant K, calculated from

analysis on the semiconducting state tunnel junction is fixed; ΦB for JDT and m* for

JPF are fit and found be 0.48 eV and 0.32m0. The change in ΦB can be understood

as a change in the potential arising from the work function difference between metallic

and semiconducting VO2. Poole-Frenkel analysis can result in barrier heights that are

lower than the Schottky barrier height (SBH) of the metal/insulator and is explained by

the high density of traps, especially at the electrode/insulator interface resulting in a po-

tential well that is lower by the applied bias.[55] The high trap density could be a result

of the low temperature ALD process [57, 58] and the electron beam evaporation of the

electrode, both of which have been shown to increase traps in dielectrics.[59] The fitting

parameters and barrier heights are described in table 1.

55

(b)

(a)

-0.4 -0.2 0.0 0.2 0.410-6

10-5

10-4

10-3

10-2

10-1

100

101

102

J (A

/cm

2 )

Voltage (V)

Data (330 K) Poole-Frenkel Direct Tunneling Total

ON state

-0.4 -0.2 0.0 0.2 0.410-6

10-5

10-4

10-3

10-2

10-1

100

101

102

OFF state

0.45 0.53 0.60 0.67 0.75-26.6

-25.2

-23.8

-22.4

-21.0

ln(I/

V) ln

(S)

sqrt(V) V

J (A

/cm

2 )

Voltage (V)

Data (270 K) Poole-Frenkel

Figure 4.8. (a) Typical J-V off-state curve (pillar B 270 K) in the MIS case and the correspondingfit using Poole-Frenkel conduction. The inset shows a linear relationship of ln(I/V) vs.

√V ,

which is characteristic of Poole-Frenkel conduction. (b) Typical J-V trace (pillar B from 330 K)of an on-state with the device in an MIM case, along with fitting showing the Poole-Frenkel (redcurve) and direct tunneling (green curve) contribution; the total is shown in blue. The parametersused are detailed in table 1

56

Table 4.1. Constants and fitting parameters used for direct tunneling and Poole-Frenkel conduc-tion.

Effective barrier height Φo = 3.5eV

Effective tunneling mass m∗ = 0.32mo

Dielectric thickness d = 2nm

Dielectric constant ε = 11εo

Poole-Frenkel fitting constant k = 2.45x10−4 S/cmEffective trap barrier height ΦB = 0.52 eV (semiconducting), 0.48 eV (metallic)

4.5 Conclusion

In conclusion, VO2 nanoscale tunnel junctions show an abrupt change in conductance

of approximately two orders of magnitude across the MIT. The tunneling transport for

the MIM case is modeled using Poole-Frenkel and direct tunneling. For the VO2 in the

insulating state Poole-Frenkel alone is used to explain the conduction. Without states

to directly tunnel into, the off-state leakage is defined by defect driven conduction and

it stands to reason that higher quality dielectric depositions might further improve the

Ion/Ioff of VO2 tunnel junctions.

Chapter 5

Conclusion

In this thesis, tunneling current modulation in VO2 nanoscale tunnel junctions across

a thermally induced MIT is experimentally demonstrated. A two order of magnitude

change in tunneling conductance is measured, and modeled using Poole-Frenkel con-

duction and direct tunneling.

Nanoscale X-ray diffraction on tensile strained VO2 revealed that metallic filaments

from an electronically driven transition are R-phase. The channel is analyzed as a net-

work of resistors to determine the filament size and quantify the ratio of M1/R phase

coexistence under varying resistive loads. Time dependent structural evolution of a VO2

oscillator reveal that the oscillation is a result of repeatedly reforming and breaking of

an R filament and structural phase transition from M1 to R and back to M1 plays an

integral role.

5.1 Conclusions on VO2 Nanoscale Tunnel Junctions

200 nm diameter VO2 tunnel junctions were fabricated on a Nb doped TiO2 (001) sub-

strate, with a 2 nm (1 nm Al2O3 + 1 nm HfO2) tunneling dielectric deposited by low

58

temperature ALD. Tunneling transport characteristics across a thermally driven MIT

transition is characterized and modeled. A two order of magnitude change in tunneling

current is measured across the MIT. In the insulating state Poole-Frenkel conduction is

used to explain the conduction. In the metallic state a combination of direct tunneling

and Poole-Frenkel conduction is used to model the measured I-V curves. Without states

to directly tunnel into, the off-state leakage is defined by defect driven conduction and

it stands to reason that higher quality dielectric depositions would reduce the Ioff and

improve the Ion /Ioff of VO2 tunnel junctions.

5.2 Conclusions on Nanoscale Hard X-ray of the Elec-

trically Driven Transition in VO2

In this work, the structural evolution during the electrically driven insulator to metal

transition of tensile strained VO2 is investigated by nanoscale X-ray diffraction. X-ray

diffraction intensity maps of the channel are collected in the HRS and in the LRS. 2-

D mapping of the channel revealed a dynamic R metallic filament in an insulating M1

film during an electrically driven MIT. In the LRS, the filament width is found to be

linearly proportional to the applied current through the device. The ratio of R/M1 phase

coexistence, and subsequently the magnitude of the electrically induced transition can

be controlled by a resistive load. Additionally, the time dependent structural evolution

of a VO2 oscillator reveal that the oscillation is a result of repeated forming and breaking

of an R filament and structural phase transition from M1 to R and back to M1 plays an

integral role.

59

5.3 Future Work

A smaller beamsize such as the 40 nm beam used at ID-26 at the Advanced Photon

Source at Argonne National Labs could be used to probe even smaller structural features,

such as those found at the M1/R boundary. Additionally, other materials which are

suspected of undergoing electrically induced structural transitions can be characterized

using nanoscale XRD with insitu electrical biasing. High speed XRD can be used to

further probe the the structural evolution of VO2 oscillators in the sub /mus time scale

to explore any metastable phases that may form between R and M1.

The VO2 nanoscale tunnel junctions presented in this work are dominated by Poole-

Frenkel conduction, but by developing a low temperature ALD process with fewer traps

on the dielectric the Ion/Ioff may be improved. The MIT based tunnel junction proposed

in this thesis can explored in other materials where the bandgap is modulated through a

metal to insulator transition. Further, if a repeatable mechanism for controlling the MIT

in VO2 by a third terminal is developed a high speed 3-terminal tunnel junction based

off VO2 could be realized.

Appendix A

2-Terminal Process Flow

1. Initial Clean

(a) Remove large Ag particles (used for initial resistivity measurements) using

an acetone spray bottle

(b) Sonicate in acetone for 5 minutes.

(c) Rinse in IPA (15 s)

(d) Rinse in DI water (15 s)

(e) N2 dry

2. MMA/PMMA Bilayer Spin Coat

(a) Dehydrate substrate, by baking at 96 oC for 60 s

(b) Apply MMA EL11 and spin at 4000 RPM for 45 s. This should produce

∼500µm thick coating

(c) Bake at 150 oC for 3 min

(d) Cool for 15 s

(e) Apply PMMA 950A3 and spin at 4000 RPM for 45 seconds. This should

produce ∼150 nm thick coating

(f) Bake at 180 oC for 3 min

(g) Cool for 15 s

3. Source-Drain Level Ebeam: 2-8 µm length devices

61

• Dose = 380 µC/cm2

• Beamsize = 120 nm

4. Source-Drain Level Develop in MIBK/IPA 1:3 for 60 s

5. Source-Drain Metal Deposition

(a) Set Platten cooling to 5 oC for the duration of the deposition

(b) Deposit 20 nm Pd

(c) Deposit 80 nm Au

6. Source-Drain Metal Lift-off in RemoverPG

(a) Heat up RemoverPG from MicroChem to 70 oC

(b) Insert sample for 5 min

(c) Using a pipette, create agitation in the heated RemoverPG bath to until the

most of the metal is lifted off via visual inspection.

(d) Leave in heated RemoverPG for another 5 min

(e) Rinse in Acetone (15 s)

(f) Rinse in IPA (15 s)

(g) Rinse in DI water (15 s)

(h) N2 dry

7. MMA/PMMA Bilayer Spin Coat

(a) Dehydrate substrate, by baking at 96 oC for 60 s

(b) Apply MMA EL11 and spin at 4000 RPM for 45 s. This should produce

∼500µm thick coating

(c) Bake at 150 oC for 3 min

(d) Cool for 15 s

(e) Apply PMMA 950A3 and spin at 4000 RPM for 45 seconds. This should

produce ∼150 nm thick coating

(f) Bake at 180 oC for 3 min

62

(g) Cool for 15 s

8. Active Level Ebeam

• Dose = 380 µC/cm2

• Beamsize = 120 nm

9. Active Level Develop in MIBK/IPA 1:3 for 60 s

10. Active Level etch in Plasmatherm 720

• CF4 = 20 sccm

• Pressure: 20 mT

• Power = 75 W

• Time = 180 s

11. Resist Strip in Remover 1165

(a) Heat up Remover 1165 from MicroChem to 70 oC

(b) Insert sample for 15 min

(c) Sonicate in Remover 1165 for 3 min

(d) Rinse in Acetone (15 s)

(e) Rinse in IPA (15 s)

(f) Rinse in DI water (15 s)

(g) N2 dry

Appendix B

Nanoscale Tunnel Junction ProcessFlow

1. Initial Clean

(a) Sonicate in acetone for 10 minutes.

(b) Rinse in IPA (15 s)

(c) Rinse in DI water (15 s)

(d) N2 dry

2. Tunnel Dielectric Deposition on Cambridge Savannah 200

(a) Al2O3 Deposition Cycle: 0.015 s of H2O, wait 45 s, 0.015 s of Trimethyla-

luminium. Each cycle produces 1 A at 100 oC substrate temperature and the

metal organic precursor at room temperature.

(b) HfO2 Deposition Cycle: 0.015 s of H2O, wait 45 s, 0.15 s of

Tetrakis(Dimethylamido)Hafnium(Hf(NMe2)4). Each cycle produces 1 A at

110oC substrate temperature and a 75oC metal organic precursor tempera-

ture.

Chamber is pre-conditioned by running the above recipe before the sample is in-

serted into the system for 10 cycles of Al2O3 and HfO2.

3. MMA/PMMA Bilayer Spin Coat

64

(a) Dehydrate substrate, by baking at 96 oC for 60 s

(b) Apply MMA EL11 and spin at 4000 RPM for 45 s. This should produce

∼500µm thick coating

(c) Bake at 150 oC for 3 min

(d) Cool for 15 s

(e) Apply PMMA 950A3 and spin at 4000 RPM for 45 s. This should produce

∼150 nm thick coating

(f) Bake at 180 oC for 3 min

(g) Cool for 15 s

4. Top Electrode Level Ebeam: 200 nm diameter nanopillars

• Dose = 440 µC/cm2

• Beamsize = 5 nm

5. Source-Drain Level Develop in MIBK/IPA 1:3 for 300 s

6. Source-Drain Metal Deposition

(a) Set Platten cooling to 5 oC for the duration of the deposition

(b) Deposit 20 nm Pd

(c) Deposit 80 nm Au

7. Source-Drain Metal Lift-off in Remover 1165

(a) Heat up RemoverPG from MicroChem to 70 oC

(b) Insert sample for 5 min

(c) Using a pipette, create agitation in the heated RemoverPG bath to until the

most of the metal is lifted off via visual inspection.

(d) Leave in heated RemoverPG for another 5 min

(e) Rinse in Acetone (15 s)

(f) Rinse in IPA (15 s)

(g) Rinse in DI water (15 s)

(h) N2 dry

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