THE PENNSYLVANIA STATE UNIVERSITY

SCHREYER HONORS COLLEGE

DEPARTMENT OF PHYSICS

THE OPTICAL OBSERVATION OF CHARGE CARRIERS IN TUNGSTEN DISELENIDE

JAMES D. O’HARA

SPRING 2017

A thesis

submitted in partial fulfillment

of the requirements

for baccalaureate degrees

in Physics and Mathematics

with honors in Physics

Reviewed and approved* by the following:

Jie Shan

Professor of Physics

Thesis Supervisor

Richard W. Robinett

Professor of Physics

Honors Adviser

* Signatures are on file in the Schreyer Honors College.

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ABSTRACT

Through the use of optical measurements such as Kerr Rotation and Photoluminescence,

the motion of charge carriers in ultrathin Tungsten Diselenide was measured and interpreted. A p-

type semiconductor at the monolayer limit, Tungsten Diselenide is a material of great interest in

the condensed matter community. The optical measurements, along with concurrent electrical

measurements, have led to improvements in the fabrication process for the semiconductor

measured in this thesis, and different fabrication methods are explored and discussed in this thesis.

Assessments and recommendations are made for fabrication methods which could be used to

recognize a unique quantum phenomenon, the Valley Hall Effect, in future Tungsten Diselenide

devices.

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TABLE OF CONTENTS

LIST OF FIGURES ..................................................................................................... iii

LIST OF TABLES ....................................................................................................... iv

ACKNOWLEDGEMENTS ......................................................................................... v

Chapter 1 Experiment Motivation ............................................................................... 1

1.1 Berry Phase and Berry Curvature in 2D Materials .................................................... 4 1.1.1 Symmetry and Berry Curvature ...................................................................... 5 1.1.2 Berry Phase and Charge Carrier Transport in 2D Materials ........................... 6

1.2 Tungsten Diselenide ................................................................................................... 7

Chapter 2 Experimental Methods ................................................................................ 11

2.1 Device Fabrication ..................................................................................................... 12 2.2 Optical Properties Utilized During Experiment ......................................................... 15

2.2.1 Kerr Rotation ................................................................................................... 15 2.2.2 Photoluminescence .......................................................................................... 17

2.3 Electrical and Optical Experimental Setup ................................................................ 18

Chapter 3 “Bottom Up” Fabrication ............................................................................ 21

3.1 Electrical Results ........................................................................................................ 21 3.2 Optical Results ........................................................................................................... 25

Chapter 4 Further Fabrication Processes ..................................................................... 29

4.1 Top Down Fabrication ............................................................................................... 30 4.2 Inverted Device Structure .......................................................................................... 30 4.3 Future Outlook ........................................................................................................... 31

Bibliography ................................................................................................................ 33

ACADEMIC VITA ...................................................................................................... 35

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LIST OF FIGURES

Figure 1 .................................................................................................................................... 1

Figure 2 .................................................................................................................................... 2

Figure 3 .................................................................................................................................... 3

Figure 4 .................................................................................................................................... 3

Figure 5 .................................................................................................................................... 8

Figure 6 .................................................................................................................................... 9

Figure 7 .................................................................................................................................... 10

Figure 8 .................................................................................................................................... 11

Figure 9 .................................................................................................................................... 12

Figure 10 .................................................................................................................................. 13

Figure 11 .................................................................................................................................. 14

Figure 12 .................................................................................................................................. 16

Figure 13 .................................................................................................................................. 17

Figure 14 .................................................................................................................................. 19

Figure 15 .................................................................................................................................. 22

Figure 16 .................................................................................................................................. 23

Figure 17 .................................................................................................................................. 24

Figure 18 .................................................................................................................................. 25

Figure 19 .................................................................................................................................. 26

Figure 20 .................................................................................................................................. 27

Figure 21 .................................................................................................................................. 28

Figure 22 .................................................................................................................................. 31

Figure 23 .................................................................................................................................. 32

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ACKNOWLEDGEMENTS

Many people deserve a shout out for helping me get to this point in my career. Most

importantly, I need to thank my immediate family: my Dad, my Mom, and sister Kaite. Thank you

all for all the early Saturday mornings, helping me out with whatever creative project captivated

us for a weekend. Mom, thank you for making sure I never stopped learning or engaging with the

world; I am the person I am today because of your constant care. Dad, thank you for dedicating all

of your free time to help me grow, from coaching every baseball team to quoting Seinfeld every

chance you get. Of course you are aware… Katie, thank you for always being my sidekick. It is

not easy being a little sister, but I wouldn’t want to have anyone else by my side as we venture

through life.

Secondly, I would like to thank my lab group, headed by Professors Jie Shan and Kin Fai

Mak. I have had the pleasure of working with the hardest working group of scientists on campus,

and as a result have grown immensely as a scientist by trying to emulate all of them. Specifically,

I would like to thank Professor Jieun Lee, who mentored me during my first two years with the

Shan/Mak group, and whose personal work is the starting point for the experimental work for this

thesis. To the graduate students, Egon Sohn, Hongchao Xie, Zefang Wang, and Kaifei Kang,

whom I share an office with and whom have immeasurably helped me as I constantly struggle to

figure out what is going on with my research. To the post-doctoral researchers, Dr. Shengwei Jiang

and Dr. Yi-Hsin Chiu, whose knowledge and experience have aided my research efforts every step

of the way. Finally, thank you to the two professors, Jie and Fai. Dr. Shan has been my advisor for

the past two years, and helped me construct my thesis from beginning to end. Fai was always

available with advice during the research process, and many of his ideas and suggestions are

present in this paper. Again, thank you to the entire lab group for all the help in the world over

these past two and a half years.

I would be remiss if I did not thank my honors advisor, Professor Richard Robinett, who

is probably the sole reason I was able to graduate on time with both of my majors. His advice

throughout the years has been invaluable, and has truly allowed me to have a great and (generally)

stress free college experience.

Finally, I want to send a shout out to my original lab partner, Mike Gade. Whether it was

the Dream Team in AP Chemistry, or the M.U.G. and E.D.P. in AP Physics, we were able to

bungle our way through high school science without any permanent bodily harm. There were

plenty of laughs, as well as plenty of discovery, and as a result I will always have the best of

memories when I think about my high school experience. I miss you buddy. Forever 57.

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Chapter 1

Experiment Motivation

Since the experimental discovery of graphene [1], a class of materials known as two-

dimensional (2D) materials have garnered the attention of the condensed matter community. These

materials are two-dimensional because they are comprised of only one or few layers of atoms,

leading to reduced degrees of freedom in the motion of particles. Along with graphene, another

group of 2D materials known as Transition Metal Dichalcogenides (TMDCs) have been studied

due to their superconducting and semiconducting behavior at the two dimensional limit. A

depiction of the structure of TMDCs is shown in Figure 1. Like graphene, TMDCs have a

honeycomb (hexagonal) lattice structure, which leads to a Brillouin zone similar to that of

graphene. TMDCs also exhibit unique phenomena at the 2D level due to the reduced degrees of

freedom of charge carriers. Unlike graphene, TMDCs have two distinct atoms in a unit cell, a

transition metal and a chalcogenide. As a result, TDMCs have a band gap, visible in Figure 2, on

the same energy scale as visible light, providing the potential for optoelectronic applications.

Figure 1

A depiction of a unit cell of a TMDC monolayer. The yellow atoms represent the chalcogenide group

and the green atoms represent the transition metals. a) A side view of the TMDC. b) A top view of the

TMDC. [2]

2

Looking at the Brillouin Zone of TDMCs, displayed in Figure 3, and the band structure

displayed in Figure 2, the K and K’ points in the momentum space act as momentum valleys. As

Figure 2 shows, the energy of the conduction band is at a global minimum, and the energy of the

valence band is at a global maximum, leading to a direct bandgap for the K and K’ points. As

displayed in Figure 3, the K and K’ points occupy opposite momenta in momentum space, which

will be a key feature for symmetry arguments later on in this thesis.

Over a century ago, then graduate student Edwin Hall discovered an electro-magnetic

phenomenon known now as the Hall effect. The effect arises from the dissimilar motion of positive

and negative charges in the presence of a magnetic field. From the Lorentz equation, changing the

sign of a charge will reverse the direction of the magnetic force exerted by a magnetic field on a

Figure 2

A simplification of the band structure of monolayer WSe2, highlighting the characteristics of the K and

K’ valleys. The orange bands are the conduction bands, with the spin and the azimuthal angular

momentum indicated next to the corresponding band. The blue bands are the valence bands, following

the same labeling conventions for spin and angular momentum. The red vertical arrow indicates optical

excitation, with the rotating blue arrow indicating the preferred handedness for optical excitation. [2]

3

moving charge. As a result, positively charged particles reside on one edge of an electrical device,

while the negatively charged particles reside on the opposite edge. Such an accumulation is

depicted in Figure 4. In 2D materials, discoveries of phenomena similar to the Hall effect have

now been observed. Such phenomena include the spin Hall effect, the quantum Hall effect, and

the fractional quantum Hall effect. One of these is called the Valley Hall Effect (VHE), and will

be the focus of this thesis.

Figure 3

The Brillion Zone with the K, K’, and Γ points marked. The reciprocal space vectors, k1 and k2, are

included as well.

Figure 4

A depiction of the Hall Effect in an electrical device. The V arrow is depicted to show the direction of

the potential bias and motion of charge carriers in the sample.

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1.1 Berry Phase and Berry Curvature in 2D Materials

To begin, the factors leading to the VHE should be examined. We start by expressing the

time dependent wave function as the combination of a dynamic phase and geometric phase [3]

Ψn(𝑡) = 𝜓𝑛exp [𝑖(𝜃(𝑡) + 𝛾(𝑡))]. (1)

Here θ(𝑡) =1

ℏ∫ 𝐸𝑛(𝑡)𝑑𝑡 , called the dynamic phase and equivalent to the common time-dependent

term of the wave function. 𝛾(𝑡) = 𝑖 ∫ ⟨𝜓𝑛|∇𝑅𝜓𝑛⟩𝑑𝑅𝑅2

𝑅1 is the geometric phase, where R can be any

parameter space. 𝜓𝑛 is the time independent wave function. For the case of this investigation, the

momentum space parameter k will take the place of R, In the two dimensional momentum space

of TMDCs, a closed loop integration of the geometric phase around the K or K’ momentum valley

will yield a non-zero value, and this finite value is called the Berry phase.

Often the Berry phase can be expressed intuitively as a surface integration of the flux of a

field, the same way magnetic flux can be expressed as both the surface integral of the magnetic

field through a surface or as a closed loop integration of the vector potential. Equation 1 was the

vector potential representation, and following the magnetic field example, the field-flux

interpretation of the Berry phase takes the form

𝛾(𝑡) = 𝑖 ∫ ∇𝑘 × ⟨𝜓𝑛|∇𝑘𝜓𝑛⟩𝑑2𝑘. (2)

Through this interpretation, many prefer to express the Berry Phase as the measurement of the flux

of the momentum space equivalent of a magnetic field.

In a periodic lattice, like those of TMDCs, the wave function can be expressed as a Bloch

function, which is a periodic wave function of the form 𝜓(𝑥 + 𝑎) = 𝜓(𝑥)𝑒𝑖𝑘𝑎, where a is the

lattice constant. When only the periodic portion of the wavefunction, written as u(k) in momentum

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space, is used in the Berry phase calculation from Equation 2, the resulting quantity is known as

Berry curvature. Looking at the flux quantity from Equation 2,

∇𝑘 × ⟨𝑢(𝑘)|∇𝑘𝑢(𝑘)⟩, (3)

one can understand how this quantity would take on equal and opposite values at the K and K’

points in momentum space, as they occupy equal and opposite locations in the space. From this,

the Berry curvature and Berry phase of the K and K’ points are equal and of opposite sign.

1.1.1 Symmetry and Berry Curvature

Examining Berry Phase through the perspective of flux and Berry Curvature, the

importance of symmetry comes to the forefront. Two types of symmetry affect the Berry

Curvature: time reversal symmetry and inversion symmetry. If a system has time reversal

symmetry, then moving forward or backward in time are indistinguishable. The macroscopic

universe normally does not exhibit such behavior due to the second law of thermodynamics, but

some ideal systems can exhibit this behavior, such as a ball with an elasticity of one bouncing up

and down. When observing such a system, it is impossible to distinguish which direction in time

this system is moving.

Inversion symmetry occurs when the inversion of all spatial coordinates results in an

identical system. Mathematically, this can be expressed as [ x , y , z ] = [ -x , -y , -z ]. When a

system has inversion symmetry, the momentum space Berry Curvature behaves like an even

function to preserve the inverted relation. Because of this, the Berry Phase of the K and K’ points

would be equivalent. In the presence of time reversal symmetry, the K and K’ carriers have the

same wave functions, since the K point is the time reversal of the K’ point, and these equivalent

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wave functions preserve the symmetry. This gives the Berry curvature the behavior of an odd

function, which gives the K and K’ points opposite Berry phase. Therefore, in a system with both

time reversal symmetry and inversion symmetry, Berry curvature vanishes.

1.1.2 Berry Phase and Charge Carrier Transport in 2D Materials

The behavior of Berry phase and curvature is important, because the two are incorporated

in the orbital magnetization (M) calculation [4], taking the general form of

𝑀 ∝ 𝛾(𝑡)𝜖(𝑡) + ∫ 𝑑2𝑘 𝐻(𝑘). (4)

Here, ε(t) is the energy of the system and H(k) is the Hamiltonian of the system. Furthermore, the

integrated term is also proportional to Berry Phase [4], so the Berry Phase of the system determines

the total orbital magnetization. In the presence of inversion symmetry breaking and time reversal

symmetry, the odd behavior of Berry Curvature leads to opposite phases for the K and K’ points,

and thus opposite orbital magnetizations. This, in turn, creates an antisymmetric motion in a

TMDC sample. When a voltage bias is applied across a TMDC such as WSe2, the K carriers will

be pushed to one end of the device, and the K’ carriers will be pushed to the other end of the device.

This antisymmetric motion of valley charge carriers is known as the valley Hall effect.

In 2014, Mak et al. [5] electronically observed the VHE in monolayer Molybdenum

Disulfide (MoS2), using an electrode geometry which was able to measure the Hall voltage of the

MoS2 device. Specific parameters (quarter-wave modulation excitation, broken inversion

symmetry, response to circularly polarized light) were used to conclude the observed Hall effect

was in fact the VHE. In 2016, Lee [6] was able to optically observe the VHE in bilayer MoS2 with

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optical measurements used in this thesis. Lee was able to break inversion symmetry of the bilayer

with an out of plane electric field resulting from the bottom gate effect.

Looking at the symmetry arguments and the methods used by these two experiments, one

can see the importance of both time reversal symmetry and the breaking of inversion symmetry.

By the nature of layer stacking in TMDCs, inversion symmetry is broken in odd numbered layers

and preserved in even-numbered layers. Monolayer devices, therefore, have broken inversion

symmetry and will exhibit the VHE. However, the presence of an out-of-plane magnetic field will

break time reversal symmetry and disturb the VHE. In bilayer devices, the presence of an out-of-

plane electric field will break inversion symmetry but not time reversal symmetry, allowing for

the VHE to occur.

The band structure and Berry Curvature of 2D materials has been manipulated using other

methods. Geim and Novoselov [7] were able to induce a bandgap in graphene through the creation

of a lattice potential mismatch by intentionally misaligning hBN and graphene atoms. Mak et al.

[8] were able to induce a bandgap in bilayer graphene through the application of an external,

perpendicular electric field. Yeh et al. [9] believe their straining processes on monolayer graphene

samples lead to the observation of the VHE in single-layer graphene samples. Fortunately, WSe2

monolayers have broken inversion symmetry and a direct bandgap at the K and K’ points, so the

VHE should readily occur in WSe2.

1.2 Tungsten Diselenide

WSe2 is different from graphene and MoS2. Due to naturally occurring impurities the Fermi

level of WSe2 is located closer to the valence band as opposed to MoS2 and graphene. It should

8

also be noted that graphene has no band gap, with a Fermi level at the intersection of the conduction

and valence band. Thus, graphene is considered a zero-gap semiconductor. Since the Fermi level

is closer to the valence band in WSe2, the material is more susceptible to p-doping, sometimes

called hole-doping. Because of this, it is easier to observe the motion of holes in WSe2, as opposed

to other materials. Additionally, the p-n junction is the hallmark of semiconductor physics, used

in both diodes and transistors, which collectively make up a large portion of circuitry in modern

electronics. If TMDCs are to one day be used in actual electronic devices, then having both a p

type and n type semiconductor is essential. The n type already has been well studied with MoS2

[5], [6], and this thesis as well as many other research groups are discovering more about WSe2

[10], [11].

However, measuring the VHE in WSe2 has proven quite difficult, for numerous reasons.

For one, the conduction and valence bands of WSe2 are higher in energy than that of MoS2. This

requires higher work function metals to be used as electrical contacts, to insure a more Ohmic

contact with the WSe2 sample. Because of this, our initial tests on gold (Au) electrodes and a WSe2

Figure 5

An energy diagram of Platinum and WSe2. From left to right, the energies depicted are the work function

of Pt, the valence band energy, the channel energy, and the conduction band energy of WSe2.

9

sample provided discouraging results. However, platinum (Pt) has a higher work function than Au,

so Pt electrodes were used to observe a much more conductive WSe2 sample [12]. Figure 5 shows

how the Valence and Conduction energies for WSe2 compare to the work function of Pt, and Figure

6 displays the Shockey barrier at an Au/WSe2 junction, and the less extreme barrier at the Pt/WSe2

junction.

Additionally, the back gating technique commonly used by our lab insufficiently tunes the

Fermi level of WSe2 samples. With only the back gate, the Fermi level still resides above the

valence band, significantly reducing the hole conductivity in the sample. To assist the back gate,

a solid state top gate was fabricated above the sample, separated by a few-layer hexagonal Boron

Nitride (hBN) sample. Since the separation of the top gate and WSe2 sample was on the order of

20 nm, as opposed to the 300 nm separation of the back gate and WSe2 sample, the resulting gating

effect is much more significant. This can be explained by the inverted relationship between

capacitance and distance.

Figure 6

A depiction of the Shottky barrier in the heterojunctions between a) Pt and WSe2 and b) Au and WSe2.

Here EFm is the Fermi Energy of the metal, EC is the conduction band energy of WSe2, ECh is the Fermi

Energy of intrinsic WSe2, and EV is the valence band energy of WSe2.

10

With sufficient top gating, the WSe2 sample could be conductive to both electrons and

holes. With mobile charge carriers, the VHE should be observed with the proper optical setup. If

the VHE was present, then there should be an observation of an “edge signal”, with K carriers

located on one edge of the sample and K’ carriers located on the other edge of the sample. This

has been observed by our group in MoS2 [6], and is depicted in Figure 7.

Figure 7

Valley Hall effect in bilayer MoS2 under an out-of-plane electric field imaged by the Kerr rotation

method [6]. The red edge indicates the accumulation of K carriers, and the blue edge indicates the

accumulation of K’ carriers.

11

Chapter 2

Experimental Methods

The initial experiments intended to observe the VHE in bilayer WSe2 samples. The top and

back gate voltages created an electric field, which in turn broke inversion symmetry and allowed

the VHE to occur in our bilayer samples. Figure 8 shows the cross section of our device, and the

subsequent section details the fabrication of such a device.

Section 2.2 will describe the theory behind the optical methods used to observe the motion

of charge carrier. Section 2.3 will describe how the experimental setups were able to measure and

determine the electrical transport properties of the WSe2 device. Both the electrical and optical

methods will be detailed.

Figure 8

A cross section of the device used in experiments detailed in Chapters 3 and 4.1

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2.1 Device Fabrication

The samples measured were assembled in our lab, and were exfoliated from a bulk crystal

using what is commonly referred to as the “scotch-tape” method. Due to the relative strength of

the covalent bonds holding together the intra-layer tungsten and selenium atoms, and the relative

weakness of the van Der Waals forces holding together the multiple layers of WSe2, scotch tape

can sufficiently exfoliate single layers of WSe2 off of a bulk crystal. This method was used for the

hBN samples as well.

Exfoliated WSe2 samples on the scotch tape were transferred onto a clean substrate, in this

case 300 nm silicon dioxide (SiO2). A 20X scanning microscope was then used to identify

monolayer samples on the SiO2 substrate based on their optical contrast. Due to the thin nature of

these samples (~0.5 Å), WSe2 samples with different layer numbers reflect light of different colors

as a result of thin film interference. Thus, it is easier and more effective to characterize layer

number by optical contrast, as opposed to atomic force microscopy, which is not accurate for such

thin materials. Since the hBN samples were also only a few layers in thickness, optical contrast

Figure 9

An image of few-layer hBN sample on a 300 nm Si chip.

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was used to identify the appropriate flakes of hBN. Figure 9 shows a few-layer hBN sample on the

300 nm Si substrate.

The process of picking up the samples required hBN to be obtained first, because using

only one slide to transfer the samples is the cleanest way to transfer all of these materials onto the

electrodes. Since hBN is the capping layer on the top, it must be picked up first. For an ideal top

gate effect, the thickness of the hBN should be 15-20 nm, and should be 20 x 20 um to sufficiently

cover the WSe2 sample. After identifying an appropriate hBN sample, an adhesive Polypropylene

Carbonate (PPC) slide was used to pick up the flake. The hBN remained on this slide until it was

transferred onto the electrodes.

Once a WSe2 monolayer sample of sufficient size and shape was observed, the sample was

picked up with the PPC slide. Now the WSe2 sample and hBN are on the sample PPC slide and

ready to be placed on a cleaned SiO2 chip with patterned Pt electrodes. A microscope with a

computer monitor attachment is used to properly place the two samples onto the electrodes. Then

the PPC is heated and removed, leaving the WSe2 and hBN on the electrodes, with some PPC

Figure 10

A WSe2 sample capped by a few-layer hBN sample. Here the sample outlined in blue is the WSe2

monolayer, and the sample outlined in green is the thin hBN sample.

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residue. This residue can be removed with an Anisole treatment, leaving behind little organic

residue on the sample.

With the WSe2 sample on the electrodes, capped by an insulating hBN layer as depicted in

Figure 10, the device is brought to the cleanroom to fabricate a 15 nm layer of Palladium (Pd) on

top of the hBN. This served as a top-gate. First, a photoresist layer was spin-coated onto the SiO2

chip. Then electron beam lithography was used to cut out the pattern for the Pd electrode.

Afterwards, an electron beam evaporator was used to deposit a thin film of Pd onto the SiO2 chip.

Finally, a chemical solution was used to remove the photoresist from the chip, leaving only the Pd

deposited on the lithographed portion of the chip. Figure 11 is an image of a fully fabricated device.

Figure 11 An image of a complete device after the evaporation of Pd. The section outlined in pink is the bilayer

sample of WSe2.

15

2.2 Optical Properties Utilized During Experiment

2.2.1 Kerr Rotation

By utilizing the optical selection rules for WSe2, we were able to observe the distribution

of K and K’ carriers in a TMDC sample. The Kerr Rotation (KR) of a polarized laser source was

used to make such a detection. Through conservation laws and lifting of spin degeneracy in the

valence carriers around the K and K’ points of WSe2, charge carriers are preferential to excitation

by a certain helicity of light, either right circularly polarized or left circularly polarized [12].

Because of this, K carriers absorb mostly left circularly polarized light and K’ carriers absorb

mostly right circularly polarized light. In return, the reflected signal possesses a polarized

handedness, opposite of the absorbed light. This rotated polarization of the reflected light signal is

measured from our experimental setup, and in turn allows us to map the distribution of K and K’

carriers.

16

Figures 12 and 13 show how the optical setup is able to determine the polarization of the

reflected beam. Figure 12 depicts a laser beam which underwent no KR. Because of this, the

photodetector at the end of the apparatus measures light beams of equal intensity. Figure 13

demonstrates the other case, where the reflected beam has undergone KR to some degree. Due to

the rotation of the polarization, the photodetector will measure unequal intensities. What is more,

the greater the rotation, the greater the difference in intensity, allowing for the photodetectors to

measure the rotation of the reflected beam simply by observing the difference in intensities of the

two beams.

Figure 12

A schematic of the Kerr rotation measurement a) The polarization of a non-rotated laser after it exits

the test chamber. b) The beam rotated by 45 degrees by the half-wave plate, so the x and y components

are equal as depicted by the red arrows. c) The intensity of the two beams received by the two

photodetectors, after being split by the Wollaston Prism.

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2.2.2 Photoluminescence

Photoluminescence (PL) is the second optical method used in this experiment. The purpose

is to measure the excition energy of the sample. To do this a 532 nm laser was shone directly onto

the WSe2 sample. The energy of the 532 nm laser is significantly greater than the energy gap of

WSe2, allowing for the excitation of many charge carriers from the valence band to the conduction

band. When conduction carriers drop back down to the unoccupied valence band, conservation of

energy dictates that they emit light at a wavelength equivalent to the energy drop from conduction

to valence band. This is the light our apparatus detects. Once the carriers emit this light, the light

is directed, via mirrors, to a spectrometer with a Charge Coupled Device (CCD). Inside the

spectrometer, the light is diffracted, allowing us to measure the intensities of different wavelengths

Figure 13

A schematic of the Kerr Rotation measurement a) The polarization of a laser after it exits the test

chamber having underwent KR. b) The beam rotated by 45 degrees by the half-wave plate, so the x and

y components are unequal as depicted by the red arrows. c) The intensity of the two beams received by

the two photodetectors, after being split by the Wollaston Prism.

18

of light. This, in turn, allows us to determine the peak wavelength of light and the corresponding

energy gap.

This information will later be utilized in the KR measurements. To utilize the optical

selection properties of the K and K’ valleys, light equivalent to the energy gap should be directed

toward the WSe2 sample.

2.3 Electrical and Optical Experimental Setup

After a device was fabricated, it was placed in the Montana Cryogenic chamber. Due to the

cryogenic nature of the cooling chamber, most experiments were conducted near liquid helium

temperatures (4 Kelvin), and the conditions were near-vacuum. A window at the top of the

chamber allowed for optical experiments on the device.

First, the electrical properties of the WSe2 device was measured. There were three main

electrical parameters which could be controlled with the experimental setup: top gate voltage, back

gate voltage, and source drain voltage. These tests allow for a characterization of the electrical

behavior of the device before further tests. For example, if the device was non-conducting, there

is no need for optical measurements, as there would be no charge carriers to observe. Since the

importance of this particular experiment involves observing the motion of holes in TMDCs, if the

device is more n-doped than p-doped, then it would be more difficult observe such a phenomenon.

19

After the electrical measurements, PL experiments were conducted to determine the

excitation energy of WSe2. Once the excitation energy was determined, KR measurements began.

Figure 14 displays the optical setup used for such tests. First, the linearly polarized red laser was

tuned to closely to match the energy of the photoluminescence peak. This was directed through a

polarizer, giving a linearly polarized beam. Due to the optical selection rules for the K and K’

momentum valleys, the polarization of the reflected light can be rotated if there is a population

difference between the K and K’ valleys.

This light was then sent through a half wave plate to rotate the polarization of the reflected

beam by 45 degrees. Then a Wollaston prism separated the x and y components of the rotated

beam onto two photodetectors, one measuring the x component and the other measuring the y

component. If the reflected beam is still linearly polarized, implying an equal population of K and

K’ carriers, then the measured x and y components should be equal, as portrayed in Figure 12. If

Figure 14

A birds-eye view of the optical setup for the KR measurement. The Red arrows indicate the direction

of the light beam. The inset (depicted with the dashed lines coming from the “Test Chamber” icon) is

a front view of the vertical optical setup directing the light beam into and out of the test chamber.

20

the reflected beam is now elliptically polarized, then there should be an imbalance in the x and y

components when measured by the photodetectors, as depicted in Figure 13. This is indicative of

a population imbalance of the K and K’ carriers, and the polarization is indicative of which valley

has more carriers.

As the laser was swept over the surface of the WSe2 crystal, this difference between the x

and y components was measured and recorded, which in turn was able to map the distribution of

K and K’ electrons imbalances. If the VHE was observed, then there will be an accumulation of

excess K carriers on one edge of the device and an accumulation of excess K’ carriers on the other

end of the device.

21

Chapter 3

“Bottom Up” Fabrication

This first round of results comes from devices fabricated using the “bottom up” fabrication

process, with the device cross section of that seen in Figure 8. Additionally, the device was

fabricated using an adhesive known as polydimethylsiloxane (PDMS). Unlike PPC, PDMS is

known to leave a significant amount of residue on the sample. The effect of the residue will become

apparent with the optical tests. After conducting tests with such a fabrication method, it became

clear that a cleaner fabrication method was required to observe the VHE in WSe2.

3.1 Electrical Results

The first results presented are the preliminary electrical experiments. There were three

major parameters to be adjusted during experimentation: the top gate voltage (VTG), the bottom

gate voltage (VBG), and the source drain voltage (VDS). The response to changes in these

parameters will allow for further characterization of the WSe2 device.

The doping capacity of the device was the first characteristic to be tested. As noted in

Chapter 1 Section 2, the Fermi energy of crystal WSe2 lies in between the conduction and valence

band. Therefore, an un-doped WSe2 sample should not be conductive to either holes or electrons.

However, doping through the top gate and bottom gate should tune the Fermi Level of the sample,

and thus the conductivity of the WSe2 device. This can be observed by sweeping the back gate and

top gate voltage.

22

Starting with Figure 15, the device appears to be more easily hole-doped than electron-

doped. The negative current associated with a negative source-to-drain bias, as seen in Figure 15,

occurring when the VTG is positive indicates a hole current. A positive VTG will place the Fermi

Energy in the valence band of WSe2, allowing for hole conductivity. With a positive source-to-

drain bias, visible in Figure 16, the device appears to be more conductive to electrons, because the

current is higher when VTG is negative and tuning the Fermi Energy to the conduction band of

WSe2.

While initially confusing, this can be explained by the combined gating effect on the

device. The total gating effect on the sample is a combination of all three voltages: VTG, VDS, and

Figure 15

Drain-source current as a function of top gate voltage VTG of a WSe2 device described in Sect. 3.1. Here

a negative VDS is used.

23

VBG. Sweeping the VTG will affect the Fermi Energy, and so will changing the VDS. Therefore the

trials described by Figure 15 are not undergoing a gating effect equivalent to that of the trials

described by Figure 16. This is why Figure 16 describes a WSe2 device which is less p-doped than

the WSe2 device with a negative VDS, as in Figure 15. With all this said, the magnitude of the

currents for both positive and negative VDS show a favorability towards hole doping.

Looking at Figure 17, the superiority of the top gate becomes apparent. Figure 17 depicts

a sweep of the VBG, which appears to only mildly effect the conductivity of the WSe2 device. The

different colored curves show top gates of different voltages. From this, the top gate appears to

Figure 16

A plot of Current vs. VTG. Here a positive VDS is used.

24

have a greater effect on the conductivity than the back gate, since the ten-volt sweep has a minor

effect on the current compared to the ten-volt changes in top gate. This occurred for both positive

and negative VDS.

Finally, looking at the sweep of VDS, the Shottky nature of the WSe2 device is still apparent.

Figure 18 shows the current versus voltage curve is non-linear, a characteristic of the Shottky

barrier. If the contacts were Ohmic, then the current versus voltage curve should be linear. This

brings to light problems in the fabrication process, which will be addressed at the end of the

chapter.

Figure 17

A plot of Current vs. VBG. Here a positive VDS is used. The distinct curves are indicative of different

VTG, labeled in the upper inset.

25

3.2 Optical Results

After the electrical tests, photoluminescence (PL) and Kerr Rotation (KR) experiments

were conducted to probe the properties of the K and K’ carriers in the WSe2 device. Looking at

Figure 19 and the PL results, the effect of the top-gate is visible in the blue shift of the PL peak.

The different curves represent the different top gate voltages applied to the device, and an increased

VTG appears the blue shift the PL peak of the sample (except for the final curve with VTG = 10 V).

Figure 18

A plot of Current vs. VDS with a positive VTG = 10V.

– A plot of Current vs. VDS with a positive VTG = 10V.

26

Additionally, the PL experiments show the excitation energy to be around 2.69 and 2.73 eV (using

the PL peak between 720 and 730 nm).

After the excitation energy was determined, KR measurements probed for the movement

of K and K’ carriers in the device. Figure 20 shows a two-dimensional mapping of the KR

measurements on the WSe2 sample. For this trail the VTG is set to a constant 8V, the VBG is set to

zero, and the VDS is an oscillating 10V signal, with a frequency of 4.3 kHz. There is no clear edge

signal, going against expectations. This again exposes problems with the fabrication process.

Looking at the pockets of K’ electrons observed in the device, it appears as if the WSe2 was

680 690 700 710 720 730 740 750 760

80

100

120

140

160

180

200

220

240

PL

Wavelength (nm)

W12_10K_532nm_230uW_20sec_Vtg-10V_Vbg0V.dat

W12_10K_532nm_230uW_20sec_Vtg-5V_Vbg0V.dat

W12_10K_532nm_230uW_20sec_Vtg0V_Vbg0V.dat

W12_10K_532nm_230uW_20sec_Vtg5V_Vbg0V.dat

W12_10K_532nm_230uW_20sec_Vtg10V_Vbg0V.dat

Figure 19

A plot of the PL measurements of Intensity vs. Wavelength, with the different color curves representing

different VTG.

27

adversely affected by straining created during the fabrication process. This is hindering the VHE,

which is why no clear edge signal is observed.

There is another source to the unclear VHE signal, known as source-gate coupling. Figure

21 shows how, in the absence of a source to drain bias, there is still an observed KR signal due to

a modulating VTG. This is because the VTG is too high, and as a result a KR signal occurs. Looking

back at the initial electrical tests, one can see the VTG has to exceed 5V before there is any

noticeable increase in voltage, and only in the 8 to 10V range is there an significant amount of

current in the WSe2 device. Therefore, a large VTG is needed to have a conductive sample, which,

as Figure 21 shows, effects the KR signal.

Figure 20

A two dimensional (x,y) mapping of the KR signal from a WSe2 device. The coloration depicts the measured

rotation of the polarization. The inset provides a Reflection measurement to provide an image of the sample,

meant to provide an image of the sample.

28

Figure 21

A two dimensional (x,y) plot of KR measurements with a modulating VTG, with VDS equal to zero.

29

Chapter 4

Further Fabrication Processes

Referring to Figures 20 and 21, there are a few apparent problems with the “bottom-up”

device. While this device was more conductive than previously fabricated WSe2 devices, the

contacts were still Shottky in nature. This is probably due to the use of PDMS as a substrate. The

organic residue resulting from the use of PDMS limited to mechanical and electrical contact

between the Pt electrodes and WSe2 sample. Additionally, this organic residue may have strained

the WSe2 when the hBN flake was placed on top. Looking at Figure 20, there appears to be pockets

of false signals in the form of circular anomalies. Induced strain creates a KR signal, and the KR

measurements displayed in Figure 20 appear to be indicative of strain as opposed to the VHE, due

to the location of the signals on the device. Compounding with the false KR signal is the impaired

motion of charge carriers in a strained sample. The K and K’ electrons probably did not have the

opportunity to exhibit the motion of the VHE because our bilayer sample incurred to much intrinsic

straining.

All of these factors lead to the electrical shortcomings of the device, such as the Shottky

contacts and the need for a high VTG to properly dope the device. As Figure 21 demonstrates, the

high top gate voltage is detrimental to the device and subsequent KR measurements. The simple

top gate voltage modulation created a KR signal, indicative of source-gate coupling. The gate

voltage was too high, and as a result coupled to the bias voltage, which is unideal for a device.

After this was realized, the fabrication process was revised to that of the “top down”

method detailed in Chapter 2. Such a process will limit the organic residue on the device,

improving the electrical contacts and limiting the straining of the sample.

30

4.1 Top Down Fabrication

After the flaws of the Bottom-Up, PDMS dependent fabrication process became apparent,

a cleaner method was proposed. To limit the organic residue on the WSe2 sample, the methodology

detailed in Chapter 2, Section 1 was used. The PPC pickup process minimizes the amount of

organic residue on the device because most of the PPC can be removed from the use of anisole

treatment.

Other lab members were able to test WSe2 devices made using this Top Down fabrication

process. With a 50nm thick Pd top gate, the device preformed optimally, with transport properties

comparable to that of other groups. However, a top gate with such a thickness leaves the WSe2

inaccessible to optical measurements. We cannot optically observe the VHE with such a thick

layer of Pd on top of the WSe2 sample. A new method must be used.

4.2 Inverted Device Structure

Because such a thick Top Gate is required, the device geometry must be inverted. This is

the current method used by the group, and separate parts of this fabrication methodology have

been utilized by our group to a positive outcome. Figure 22 depicts the device cross section, and

Figure 23 has a microscopy image of a completed device.

Silicon chips with large, rectangular Pt are already fabricated, and this is will act as the

“top gate”, now located below the sample. Thin hBN will separate the top gate and WSe2 sample,

allowing for a similar gating effect as the bottom up fabricated devices. Pt will be evaporated on

top of the sample, which has been done before to success.

31

While the inverted process will have experimental benefits, allowing for proper gating

without limiting the optical access for KR measurements, there are still some drawbacks to this

method, especially in the cleanroom. Top fabrication of Pt electrodes has proven to be difficult in

the cleanroom. Platinum requires much more heating by the electron beam evaporator, relative to

other elements like Gold and Titanium. As a result, the liftoff process for the photoresist is

imperfect, to put it lightly. Therefore, there is no dependable liftoff process with Pt electrodes.

Due to the similarities in work function of Pd and Pt, Pd may take the place of Pt as the electrodes

of choice, since the evaporation process for Pd requires the normal heating level of electron beam

heating.

4.3 Future Outlook

At the present moment, the inverted device structure appears to possess the greatest

potential for the observation of the VHE. Further devices will be fabricated, and Pd electrodes may

take the place of Pt electrodes if the electron beam evaporator proves to be unable to properly

deposit the Pt electrodes. Additionally, new electrodes may have to be fabricated to allow for a Pd

bottom gate. Other group members have received similar results with both Pt and Pd gates;

Figure 22

The device cross section for the inverted structure, with proper electrical connections labeled in the figure.

32

thickness appears to be the more important, as this effects the work function of the metal and thus

the doping ability of the gate.

Due to the success that other members have had with printed-on electrodes, a properly

fabricated device using the inverted structure should have comparable electrical performance to

the bottom-up and top-down samples. With the thin hBN top layer to protect the device, the WSe2

sample will be accessible to optical measurements, allowing for a high performing electrical device

to be open to KR measurements, and the possibility of observing the VHE.

Figure 23

A microscope image of a fully fabricated inverted device. Here the WSe2 sample is outlined in blue, the top

hBN layer is outlined in black, and the bottom hBN layer is outlined in green.

33

Bibliography

[1] Novoselev, K. and Geim, A. Electric Field Effect in Atomically Thin Carbon Films.

Science. 10, 666-669 (2004)

[2] Mak, K.F. and Shan, J. Photonics and optoelectronics of 2D semiconductor

transition metal dichalcogenides. Nature Photonics 10, 216-226 (2016)

[3] Griffiths, D.J. “Section 10.2: Berry Phase,” in Introduction to Quantum Mechanics,

Upper Saddle River, NJ, Prentice Hall, 333-349 (1995)

[4] Xiao, D. Yao, W. and Niu, Q. Valley-Contrasting Physics in Graphene: Magnetic

Moment and Topological Transport. Physical Review Letters. 99, 236809 (2007)

[5] Mak, K.F. McGill, K. Park, J. and McEuen, P. The valley Hall effect in MoS2

transistors. Science, 344, 6191, 1489-1492 (2014)

[6] Lee, J. Mak, K.F. and Shan, J. Electrical control of the valley Hall effect in bilayer

MoS2 transistors. Nature Nanotechnology. 11, 421-425 (2016)

[7] Woods, C. et. al. Commensurate–incommensurate transition in graphene on

hexagonal boron nitride. Nature Physics. 10, 451-456 (2014)

[8] Mak, K.F. Lui, C.H. Shan, J. and Heinz, T. Observation of an Electric-Field-

Induced Band Gap in Bilayer Graphene by Infrared Spectroscopy. Physical Review Letters

102, 256405 (2009)

34

[9] Yeh, N. et. al. Nano-scale strain engineering of graphene and graphene-based

devices. Acta Mechanica Sinica. 3, 32, 497-509 (2016)

[10] Wang, Z. Shan, J. and Mak, K.F. Valley- and spin-polarized Landau levels in

monolayer WSe2. Nature Nanotechnology. 12, 144-149 (2017)

[11] Movva, H.C. High-Mobility Holes in Dual-Gated WSe2 Field-Effect Transistors.

ACS Nano. 10, 9, 10402-10410 (2015)

[12] Mak, K.F. He, K. Shan, J. and Heinz, T. Control of valley polarization in

monolayer MoS2 by optical helicity. Nature Nanotechnology. 7, 494-498 (2012)

ACADEMIC VITA

Academic Vita of James Daniel O'Hara jdo511@psu.edu

Education Majors: Physics and Mathematics Honors: Physics Thesis Title: The Optical Observation of Charge Carriers in Tungsten Diselenide Thesis Supervisor: Jie Shan Work Experience Summer 2013 and 2014 Engineering Intern Worked with electrical engineers tasked with designing systems to test commercial communication devices. Focused on system configuration and troubleshooting. Communications Test Design Inc. Matthew Parsons Summer 2015 to Present Undergraduate Research Assistant Working with Profs. Jie Shan and Kin Fai Mak in their Experimental Condensed Matter group at PSU, using optical and electrical measurements to observe properties of charge carriers in two dimensional Transition Metal Dichalcogenides. Shan/Mak Group at Penn State University Professor Jie Shan 2013 – 2015, 2016 – 2017 Eco Rep Peer leader tasked with promoting sustainability in the East Residence Halls through peer-to-peer engagement. Served as mentor and area coordinator in subsequent years (2014 – 2015, 2016 – 2017, respectively). Penn State Housing David Manos Grants: 2016

PPG Undergraduate Research Fellowship: Summer research fellowship granted to 6-10 PSU students each year, funded by PPG and administered by the Materials Research Institute at Penn State. Awards: 2016 J & E Teas Scholarship: Trustee scholarship awarded by the Eberly College of Science for outstanding academic performance. 2014 President’s Freshman Award: Award given to Freshman students having completed 18+ credits with a 4.00 GPA.

Professional Memberships:

Sigma Pi Sigma Physics Honor Society

Phi Sigma Phi Honors Society

Phi Eta Sigma Honors Society

Community Service Involvement:

2015

Springfield Fundraising Chair: One of five fundraising chairs in charge of

organizing fundraising for a volunteer organization of over 200 members. Dedicated

approximately 20 hours a week to organize and manage fundraising efforts which

resulted in $270,000 raised in a six-month period, to benefit the families and

children in the pediatric cancer ward of Hershey’s Children’s Hospital.