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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 Datta
Professor of Electrical Engineering
Thesis Advisor
Srinivas Tadigadapa
Professor of Electrical Engineering
Kultegin Aydin
Professor of Electrical Engineering
Head 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 and
there is great interest in developing novel low power and high performance switching
mechanisms. Among the various candidates are high speed and abrupt metal insulator
transition based switches.
The metal insulator transition in vanadium dioxide is sub 100 fs and abrupt. Vanadium dioxide has a low mobility and thus is a poor choice as a channel replacement
material. However, modulation of its 0.6 eV bandgap offers a promising method to
enable 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 conductance in nanoscale vanadium dioxide tunnel junctions is shown as a proof of concept
of the proposed device. The large conductance change is modeled using direct tunneling
and Poole-Frenkel conduction.
There exists significant debate on the exact switching mechanism in vanadium dioxide. The structural evolution of tensile strained vanadium dioxide undergoing an electrically 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 an
electronically driven transition, while the majority of the channel area remains in the
monoclinic M1 phase. Further analysis revealed that the width of the R filament can be
tuned externally using resistive loads in series, enabling tunability of the M1/R phase
ratio. Additionally, time resolved X-ray diffraction performed on vanadium dioxide oscillators shows that the oscillations are 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 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
VO2 Transition by External Stimuli . . . . . . . . . . . . . . .
7
Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.2.1
1.3
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
2.3
2.4
Evidence of Peierls Transition in VO2 . . . . . . . . . . . . . .
14
The Mott-Hubbard Transition . . . . . . . . . . . . . . . . . . . . . . .
15
2.3.1
Correlated Electrons and Localization . . . . . . . . . . . . . .
15
2.3.2
Evidence of Mott-Hubbard Transition in VO2 . . . . . . . . . .
18
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
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3.3.1
Two Terminal VO2 Fabrication . . . . . . . . . . . . . . . . . .
26
3.3.2
Nanoscale hard X-ray Setup . . . . . . . . . . . . . . . . . . .
28
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
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.3
3.4
3.5
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
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
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4.4
4.5
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 Transition in VO2
5.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
Appendix A
2-Terminal Process Flow
60
Appendix B
Nanoscale Tunnel Junction Process Flow
vi
63
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] . . . . . . . . . . . . . . . .
1.2
2
Illustration of an Id -Vg curve highlighting the importance of the switching slope to device performance for a fixed Ion /Iof f . 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. . . . . . . . . . . . . . . . . . .
1.3
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. . . . . . . . . . . . . . . . .
viii
4
1.4
Metal insulator transition of various materials. The near room temperature transition and large change in resistivity makes VO2 an attractive material to prototype novel devices utilizing the MIT. VO2 bulk,[2]
V2 O3 & V8 015 ,[3] VO,[4] V9 O17,[5] Ti2 O3 ,[6] NiSe,[7] EuO,[8] LSFO,[9]
Ti3 O5 ,[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
2.3
π
2a
. . . . . . . . . . . . . . . . . .
12
(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
π
.
2a
The avoided crossing phenomenon
at the Brilluion zone lowers the total electronic energy of the system. . .
2.4
13
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] . . . . . . . . . . . .
2.5
15
Experimental correlation between the effective Bohr radius and the critical carrier density of the Mott transition. The solid line represents
n1/3 αo > 0.26. ’e-h’ refers to electron hole photo excitation. Adopted
from [13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6
17
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
18
2.7
Schematic of the hall bar fabricated on VO2 . The hall effect measurements are performed while cooling from 330 K to 270 K across the MIT.
2.8
Resistivity vs. temperature of the 13 monolayer (3.9 nm) VO2 sample
used in the hall measurements. . . . . . . . . . . . . . . . . . . . . . .
2.9
19
22
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
3.4x104 x. (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. . . . . . . . . .
3.1
23
Illustration explaining the derivation of the Bragg equation where the
extra path length seen by the wave reflected from the 2nd layer is determined to be 2dsinθ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
25
(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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
27
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. . . . . . . . .
3.4
29
θ/2θ scan at 260 K (red line) and 310 K (blue line) of the R 002 and
M1 402̄ 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. . . . . . . . . . . . . . . . . . . . .
x
30
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 channel. 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. . . . . . . . . . . . . . . . . .
3.6
33
(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. . . . . . . . . . . . . . . . . . . . . . . . . .
3.7
35
(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. . . . . . . . . . . . . . .
xi
37
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 dependence 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 dependence on the current displays a linear relationship until joule heating
increases resistivity, which is not accounted for in this model and incorrectly shows a reduction in filament width.
3.9
. . . . . . . . . . . . . . .
39
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 deficiency 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. . . . . . . . . . . . . . .
4.3
4.4
46
(a) Band diagram of a symmetrical MIM structure in equilibrium. (b)
Symmetrical MIM under bias, where V > φ0 . . . . . . . . . . . . . . .
47
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) Topography scan of the area under investigation. The single pillars are clearly
discernible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . . . . . .
4.7
52
Conductance vs. temperature for 3 nano-pillars showing a tunneling
conductance response to the abrupt MIT in VO2 . . . . . . . . . . . . . .
4.8
51
53
(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 PooleFrenkel 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) contribution; the total is shown in blue. The parameters used are detailed in
table 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiii
55
List of Tables
3.1
Extracted R filament dimensions . . . . . . . . . . . . . . . . . . . . .
3.2
X-ray counts for 20 µs time bins starting at 0, 40, 80, and 120 µs after
37
the rising edge, labeled as B1-B4 respectively. No background subtraction is applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
41
Constants and fitting parameters used for direct tunneling and PooleFrenkel conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiv
56
Acknowledgments
I would like to dedicate this thesis to my parents, who always believed in me and supported 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 assistance 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 measurements and valuable discussions. A big thank you to all the members of the Nanoelecxv
tronic Devices and Circuits Laboratory (NDCL) - Euichul Hwang, Mike Barth, Arun
Thathachary, Matt Hollander, Ashish Agrawal, Nidhi Agrawal, Lu Liu, Bijesh Rajamohanan, Euichul Hwang, Ashkar Ali, Feng Li, Himanshu Madan, Dheeraj Mohata.
xvi
Chapter 1
Introduction
1.1
Introduction to Metal Insulator Transition Based Tunnel 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 followed Dennard’s law,[15] which has reduced voltage by approximately 0.7x each generation. 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 Boltzmann 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
CPU Power (W)
1000
100
10
1990 1995 2000 2005 2010 2015
Year
Figure 1.1. Thermal power dissipation of modern CPUs has stopped increasing and is about 100
W per chip. Adapted from [1]
for a desired Ion /Iof f 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 /Iof f 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
Log (ID)
3
Ideal Switch ~0mV/dec
Steep Slope Transistor < 60mV/dec
Boltzmann Limit 60mV/dec
VG
Figure 1.2. Illustration of an Id -Vg curve highlighting the importance of the switching slope
to device performance for a fixed Ion /Iof f . 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.
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 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.
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 material. 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 (JP F ) conduction and other defect mediated transport. The modulation 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 diagrams in Fig. 1.3 (a) and (b), respectively. This is fundamentally different from conventional 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 o C 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 transition. This thesis explores nanoscale tunnel junctions of 200 nm diameter with a low
temperature ALD dielectric deposition process for the tunneling insulator.
6
1012
VO2 Bulk
1010
VO (001 TiO )
2
ρ(Ω-cm)
8
10
V2O3
106
VO
V8O15
104
V9O17
Ti2O3
This
Work
2
10
2
NiSe
EuO
LSFO
Ti3O5
100
10-2
NdNiO3
-4
10
10-6
0
200
400
600
800
Temperature (K)
Figure 1.4. Metal insulator transition of various materials. The near room temperature transition
and large change in resistivity makes VO2 an attractive material to prototype novel devices utilizing the MIT. VO2 bulk,[2] V2 O3 & V8 015 ,[3] VO,[4] V9 O17,[5] Ti2 O3 ,[6] NiSe,[7] EuO,[8]
LSFO,[9] Ti3 O5 ,[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 varying levels of contribution from a Mott-Hubbard type phase transition and a Peierls-like
structural instability. Significant research efforts are geared towards a better understanding 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 experimentally.
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. furthermore, 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 structural transition is discussed and a method to differentiate M1, M2 and R crystal structures 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)
atom
a
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 =
~2 k 2
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
1
k = ± G = ±nπ/a
2
(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 as
dimerization, leading to a doubling of the lattice parameter to 2a. This shifts the Brilluion zone
π
to 2a
where n is an integer, where n=1 is the first Brilluion zone.
At
π
a
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 completely 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
π
,
2a
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
π
2a
creating a fully filled lower band as shown in Fig. 2.3(b). This phenomenon
13
(a)
(b)
Energy
Energy
EF
EF
-π/a
π/a
Wavevector
-π/a
π/2a
π/2a
π/a
Wavevector
Figure 2.3. (a) E-K diagram for a half filled 1-D crystal of monovalent atoms, with a Brilluion
π
zone at πa . (b) Dimerized crystal of 1-D monovalent atoms result in a new Brilluion zone at 2a
.
The avoided crossing phenomenon at the Brilluion zone lowers the total electronic energy of the
system.
where the Brilluion zone and the Fermi surface lineup is known as Fermi surface nesting. 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
2
λg/2
~2 G
~2 K 2
E'
±U +
1±2
2m 2
2m
U
(2.5)
where G is the reciprocal lattice vector, U is the potential energy of the periodic
potential, λ =
~2 K 2
2m
and K̃ = k − 21 G.
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
π
2a
level of the filled band at
where the avoided crossing phenomenon results in the Fermi
π
,
2a
from the new
a
2
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
(a)
(b)
Dimerization
Low T - Monoclinic
High T - Rutile
Figure 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]
2.3
2.3.1
The Mott-Hubbard Transition
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]
e1 e2
kr2
(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
exp(−qr)
kr
(2.7)
Where q is a screening constant described by the Thomas-Fermi approximation
shown below.
q2 =
4me2 n1/3
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
n1/3 αo > 0.25
Where αo = k~2 /me2 , also known as the Bohr radius.
(2.10)
17
Figure 2.5. Experimental correlation between the effective Bohr radius and the critical carrier
density of the Mott transition. The solid line represents n1/3 αo > 0.26. ’e-h’ refers to electron
hole 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
d1-1
d1
Electron
i-2
t
d1+1
d1
d1
i
Site
i+1
i+2
U
i-1
Figure 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.
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
X
hijiσ
C † jσ Ciσ + U
X
ni↑ ni↓
(2.11)
i
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
(3)
(1)
W =50μm
Contacts
(1)
(4)
L = 400μm
(5)
(2)
(6)
Figure 2.7. Schematic of the hall bar fabricated on VO2 . The hall effect measurements are
performed while cooling from 330 K to 270 K across the MIT.
a Peierls assisted Mott transition where a Peierls instability enhances columbic interactions 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 =
V34 W
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
Vhall q
(2.13)
Once Ns is known µ is calculated from
µ=
1
qNs Rsh
(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 resistivity 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 3.3x104 x, 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
0
10
ρ ( Ω−cm )
-1
10
-2
10
Cooling
Heating
-3
10
-4
10
180
210
240 270 300 330
Temperature (K)
360
Figure 2.8. Resistivity vs. temperature of the 13 monolayer (3.9 nm) VO2 sample used in the
hall measurements.
23
(a)
3
Carrier Density (#/cm )
1E23
1E22
1E21
1E20
1E19
1E18
(b)
260
280
300
320
Temperature(K)
340
260
280
340
8
2
Mobility (cm /V-s)
10
6
4
2
0
300
320
Temperature(K)
Figure 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 3.4x104 x. (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.
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 electrical 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 path
length 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 interference. 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 wavelength, 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 =
X
fj exp [−i2π(ν1 xj + +ν2 yj + ν3 zj )]
(3.2)
j
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 interference produces no diffraction peak.
3.3
3.3.1
Experimental Setup
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
(a)
80nm Au
80nm Au
20nm Pd
20nm Pd
10 nm VO2
500 µm TiO2 (001)
(b)
Figure 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.
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 Photon 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. Twodimensional (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 intensities 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
VO2
DUT
Rload=38 kΩ
RScope
1 MΩ
RScope
1 MΩ
Figure 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.
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 402̄ 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
Normalized Intensity
6
260 K (Insulating/M1)
310 K (Metallic/R)
Detector Position
2θ = 51.714 °
5
R = 4.4
4
3
Expected
M2 Peak = 51.08 °
2
M1 = 1.0
1
0
50.5
51.0
51.5
52.0
52.5
2θ (°)
Figure 3.4. θ/2θ scan at 260 K (red line) and 310 K (blue line) of the R 002 and M1 402̄ 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.
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
3.4.1
Nanoscale X-ray Diffraction
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
R=95.6 kΩ
0V
Normalized Intensity
(a)
6
4
2
0
Length (µm)
(b)
8V
R=49.0 kΩ
10 V
R=5.9 kΩ
12 V
R=5.5 kΩ
6
2.0
1.5
1.0
0.5
0.0
4
2
0
(c)
6
4
2
0
(d)
6
4
2
0
0
2
4
6
8
10
12
14
Width (µm)
Figure 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 channel. 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.
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 simultaneously 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 insulating 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
12
20
30
40
50
60
70
10
20
30
40
50
60
70
Vsource(V)
(a)
8
4
0
Normalized
Intensity
1.6
1.4
1.2
1.0
0.8
(b)
R
5
RVO2(Ω)
10
M1
(c)
10
4
10
3
10
0
Time (s)
Figure 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.
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 incorporating 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 combined 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 rutile 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 )
" ρR Lpara−R ρM Lpara−M #
RV O2 =
ρM Lseries−M
Wseries−M t
+
Wpara−R t
ρR Lpara−R
Wpara−R t
Wpara−M t
(3.3)
ρM Lpara−M
+ W
t
para−M
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 experimental 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 importance of understanding and quantifying the presence and dimensions of R filaments in
the channel.
37
Drain
Rseries-M
1
Rpara-M
Rpara-M=
Rpara-R =
(a) Rutile Filament
Rseries-M=
Source
(c)
(b)
ρ (Ω-cm)
0.1
17x
0.01
571x
571x
1E-3
Width = 9.4 μm
Width = 290 nm
Cooling
Heating
1E-4
240
260
280
300
320
340
0
2
Temperature (K)
4
6
8
10
12
Voltage (V)
Figure 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.
Table 3.1. Extracted R filament dimensions
V
0
8
10
12
R Length (µm)
0.5
3.2
6.0
6.0
R Width (nm)
50
200
270
290
I (µA)
92.0
227.8
275.9
RV O2 (kΩ)
95.6
49.0
5.9
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
(b)
Filament Width, Wpara-R (µm)
(a)
25
Rseries
1:1
3 kΩ
5 kΩ
8 kΩ
20
15
10 kΩ
17 kΩ
27 kΩ
38 kΩ
10
5
0
0
5
10
15
20
25
Patterned Channel Width (µm)
(c)
Filament Width (µm)
4
3
2
ρr increase from
Joule heating
1
0
0.0
0.5
1.0
1.5
2.0
2.5
Current (mA)
Figure 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 dependence 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 dependence on the current displays
a linear relationship until joule heating increases resistivity, which is not accounted for in this
model 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
20
1000
B1 R
800
Vload(V)
600
10
400
5
0
0.0
200
Counts (Arb. Units)
15
M1
B2 B3 B4
0
100.0µ
200.0µ
300.0µ
Time (s)
Figure 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.
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 B2B4 are approximately equal and significantly lower than B1, indicating M1 phase for the
Bin
B1
B2
B3
B4
Counts (Arb. Units)
917
605
595
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 modulation 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 tunneling 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 Al2 O3 followed
by 1 nm thick HfO2 is then deposited by atomic layer deposition (ALD) at 100 o C
44
200 nm
Nano‐pillar
Au
80 nm
Pd
HfO2
Al2O3 VO2
20 nm
Nb‐TiO2 (001)
1 nm
1 nm
10 nm
500 μm
Figure 4.1. Illustrated cross-section of the fabricated nano-pillars.
and 110 o C, respectively. Trimethylaluminium and tetrakis (dimethylamino) hafnium
metal organic precursors are used for the Al2 O3 and HfO2 respectively, with H2 O as the
oxygen source. Previous studies have shown that annealing VO2 at temperatures as low
as 150 o C 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. Stepby-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 metalinsulator-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 (JP F ) 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
(b)
JPF
E
2.8eV
Hybrid Upper
Hubbard Band
3d||/3dπ
EF
Pd
3d||
Lower Hubbard
Band
Al2O3
HfO2
JPF
Pd
JDT
4.2eV
E
ON
Al2O3
HfO2
OFF
2.8eV
(a)
3d||/3dπ
VO2
(Metallic)
2pπ
VO2
(Insulating)
Figure 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 deficiency 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.
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
(a)
d*
(b)
d
qφ0
qφ0
EF
EF
EF
qV
EF
M1
I
M2
Figure 4.3. (a) Band diagram of a symmetrical MIM structure in equilibrium. (b) Symmetrical
MIM under bias, where V > φ0
ZEm
J=
D(Ex )ξdEx
(4.1)
0
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
4πm2 q
ξ1 =
h3
ξ2 =
4πm2 q
h3
Z∞
f (E)dEr
0
Z∞
(4.2)
f (E + eV )dEr
0
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
V
Φo −
2
s
exp −C
V
Φo −
2
!
−
V
Φo +
2
s
exp −C
V
Φo +
2
!#
(4.3)
Where,
q2
2πhd2
√
4πd 2mq
C=
h
Jo =
4.3.2
(4.4)
(4.5)
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
r
∆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
−ΦB
∝ exp
kB T
(4.7)
Where U0 is the ionization energy, k is Boltzmanns constant and T is temperature.
49
ΦB
EF
Oxide
EF
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
−(U0 − ∆U )
∝ exp
kB T
(4.8)
Resulting in the Poole-Frenkel conduction equation
"
JP F = KE · exp −
where K is a constant.
q
kB T
r
ΦB −
qE
πε
!#
(4.9)
50
4.4
Conductive Atomic Force Microscopy of VO2 Tunnel 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 mechanical 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
(a)
(b)
198 nm
300 nm
(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 investigation. 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 nanopillar 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
(b) 1E-8
Pillar A
1E-9
1E-9
1E-10
1E-10
Current (A)
Current (A)
(a) 1E-8
1E-11
1E-12
1E-13
1E-11
1E-12
1E-13
-0.4
-0.2
0.0
0.2
0.4
Voltage (V)
(c) 1E-8
Pillar C
1E-11
1E-12
1E-13
-0.2
-0.2
0.0
0.2
0.4
Temperature (K)
1E-10
-0.4
-0.4
Voltage (V)
1E-9
Current (A)
Pillar B
0.0
Voltage (V)
0.2
0.4
260
265
270
275
280
285
290
295
300
305
310
315
320
325
330
335
340
Figure 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.
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 current 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
(b) 1E-8
Pillar A
Conductance (S)
Conductance (S)
(a) 1E-8
1E-9
1E-10
1E-11
260
280
300
320
340
1E-10
1E-11
260
280
300
Pillar C
Voltage
260
-0.5
-0.4
-0.3
-0.2
-0.1
1E-9
1E-10
1E-11
1E-12
280
300
320
320
340
Temperature (K)
Temperature (K)
Conductance (S)
1E-9
1E-12
1E-12
(c) 1E-8
Pillar B
340
0.5
0.4
0.3
0.2
0.1
Temperature (K)
Figure 4.7. Conductance vs. temperature for 3 nano-pillars showing a tunneling conductance
response to the abrupt MIT in VO2 .
4.4.3
Modeling
The transport before and after the MIT transition is modeled using Poole-Frenkel conduction 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, JP F conduction (4.9) superimposed 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 PooleFrenkel 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 +JP F ), is found to
be in good agreement to the data. For the high conductance case, direct tunneling dominates 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 constant of 110 is approximated from measurements on C-V pads deposited under the same
low temperature conditions and is in good agreement with other reports of low temperature ALD deposition [57, 58].ΦB is estimated by plotting ln(I/V) vs. 1/kB T in the
p
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 J D T and m* for
JP F 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 potential 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
(a)
102
ln(I/V) ln(S)
101
J (A/cm2)
100
-1
10
-21.0
-22.4
-23.8
-25.2
-26.6
0.45
0.53
10

0.60
sqrt(V)
-2

0.67
V
0.75
10-3
10-4
10-5
10-6
(b)
OFF state
-0.4
-0.2
Data (270 K)
Poole-Frenkel
0.0
0.2
0.4
Voltage (V)
10
2
101
J (A/cm2)
100
10-1
10-2
10-3
Data (330 K)
Poole-Frenkel
Direct Tunneling
Total
10-4
10-5
10-6
ON state
-0.4
-0.2
0.0
0.2
0.4
Voltage (V)
Figure 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) contribution; the total is shown in blue. The parameters
used are detailed in table 1
56
Table 4.1. Constants and fitting parameters used for direct tunneling and Poole-Frenkel conduction.
Effective barrier height
Effective tunneling mass
Dielectric thickness
Dielectric constant
Poole-Frenkel fitting constant
Effective trap barrier height
4.5
Φo = 3.5eV
m∗ = 0.32mo
d = 2nm
= 11o
k = 2.45x10−4 S/cm
ΦB = 0.52 eV (semiconducting), 0.48 eV (metallic)
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 /Iof f 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 conduction 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 network 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) substrate, with a 2 nm (1 nm Al2 O3 + 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 Iof f and
improve the Ion /Iof f of VO2 tunnel junctions.
5.2
Conclusions on Nanoscale Hard X-ray of the Electrically 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. 2D 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 PooleFrenkel conduction, but by developing a low temperature ALD process with fewer traps
on the dielectric the Ion /Iof f 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 o C 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 o C 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 o C 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 o C 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 o C
(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 o C 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 o C 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 o C 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 o C
(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 Process
Flow
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) Al2 O3 Deposition Cycle: 0.015 s of H2 O, wait 45 s, 0.015 s of Trimethylaluminium. Each cycle produces 1 Å at 100 o C substrate temperature and the
metal organic precursor at room temperature.
(b) HfO2 Deposition Cycle: 0.015 s of H2 O, wait 45 s, 0.15 s of
Tetrakis(Dimethylamido)Hafnium(Hf(NMe2 )4 ). Each cycle produces 1 Å at
110o C substrate temperature and a 75o C metal organic precursor temperature.
Chamber is pre-conditioned by running the above recipe before the sample is inserted into the system for 10 cycles of Al2 O3 and HfO2 .
3. MMA/PMMA Bilayer Spin Coat
64
(a) Dehydrate substrate, by baking at 96 o C 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 o C 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 o C 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 o C 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 o C
(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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