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UNIVERSITY OF CALIFORNIA RIVERSIDE

Investigation of Photoelectric Effect in Transition Metal Dichalcogenides Field Effect Transistors

A Thesis submitted in partial satisfaction of the requirements for the degree of

Master of Science

Materials Science and Engineering

I-Hsi Daniel Lu

September 2017

Thesis Committee: Dr. Ludwig Bartels, Chairperson Dr. Richard Wilson Dr. Sinisa Coh

The Thesis of I-Hsi Daniel Lu is approved:

Committee Chairperson

University of California, Riverside

Acknowledgements

I would like to thank my principal investigator and advisor, Professor Ludwig

Bartels, for his guidance over these past two years. I especially want to thank him for giving me many opportunities to learn and explore the semiconductor field. Over the last two years, I have had a chance to lead and support many projects from the group, collaborators, and national labs. I would like to thank Professor Bartels for sending me to different collaborators and conferences where I excel in developing new skills and presenting my work to the representatives from industries.

I would like to thank Professor Richard Wilson and Professor Sinisa Coh for serving on my master thesis committees. I thank you for your time and support for my thesis defense in such short notice.

I would like to thank all my published co-authorship works in ACS Nano, 2D

Materials, Nano Letters, Nature Communications, ACS photonics, and Applied Physics

Letters. I would like to thank the following professors for the publications: John Mann,

Joshua C. H. Lui, Volker J. Sorger, Hubert J. Krenner, Velveth Klee, and Evan J. Reed.

I would like to thank my family for always being supportive. I would also like to thank my colleagues in Bartels’ group, and in Sorger’s group. Thank you for making my graduate career fun and engaging. Lastly, I want to thank Cindy Merida for always being supportive and helpful during my career.

Table of Contents

Chapter 1: Introduction ...... 1 Overview ...... 1 Introduction to TMDs...... 1 Instrumentation ...... 1 Raman Spectroscopy ...... 2 Photoluminescence Spectroscopy ...... 2

Chapter 2: Materials and Methods ...... 4 Chemical Vapor Deposition ...... 4

Chapter 3: Electrical contacts and Measurements on TMDs .... 7 Electron Beam Lithography ...... 7 MOSFET ...... 9 Electrical Probe Station ...... 9 Scanning Photocurrent Microscopy ...... 10 Chapter 4: Composition-dependent photocurrent in CVD- grown Monolayer MoS2(1-x)Se2x Alloy Devices ...... 14 Introduction ...... 14 Methods ...... 15 Results and Discussion ...... 17 Conclusion ...... 29

Chapter 5: Ferroelectric Control of 2D MoS2 ...... 31 Introduction ...... 31 Methods ...... 32 Results and Discussion ...... 33 Conclusion ...... 43

Chapter 6: Hybrid Field-Effect and Acousto-Electric Devices 45 Introduction ...... 45 Methods ...... 46 Results and Discussion ...... 48

Conclusion ...... 56 Figures ...... 58

Chapter 7: WS2 Band Structure ...... 62 Introduction ...... 62 Methods ...... 63 Results and Discussion ...... 64 Figures ...... 69 Chapter 8: Tunable Properties of CVD Growth of Few-Layer MoTe2 ...... 73 Introduction ...... 73 Methods ...... 74 Results and Discussion ...... 74 Conclusion ...... 78 Figures ...... 79

Chapter 9: Interlayer Breathing and Shear Modes in NbSe2 atomic layers ...... 82 Introduction ...... 82 Methods ...... 83 Results and Discussion ...... 84 Conclusion ...... 87 Figures ...... 89 Chapter 10: Efficacy of Light Emission Enhancement in Nanoscale Antenna ...... 92 Introduction ...... 93 Methods ...... 93 Results and Discussion ...... 95 Conclusion ...... 96 Figures ...... 98 References ...... 102

List of Figures

Figure 1 ...... 4 Figure 2 ...... 5 Figure 3 ...... 8 Figure 4 ...... 11 Figure 5 ...... 12 Figure 6 ...... 13 Figure 7 ...... 18 Figure 8 ...... 20 Figure 9 ...... 21 Figure 10 ...... 22 Figure 11 ...... 25 Figure 12 ...... 29 Figure 13 ...... 35 Figure 14 ...... 37 Figure 15 ...... 40 Figure 16 ...... 58 Figure 17 ...... 59 Figure 18 ...... 60 Figure 19 ...... 61 Figure 20 ...... 70 Figure 21 ...... 71 Figure 22 ...... 72 Figure 23 ...... 79 Figure 24 ...... 79 Figure 25 ...... 80 Figure 26 ...... 81 Figure 27 ...... 89 Figure 28 ...... 89 Figure 29 ...... 90 Figure 30 ...... 91 vii

Figure 31 ...... 98 Figure 32 ...... 98 Figure 33 ...... 99 Figure 34 ...... 100 Figure 35 ...... 101

viii

Chapter 1: Introduction

Overview

One atomically thin 2-D materials, graphene, was brought into the spotlight as an ideal high mobility material for electronics once it was synthesized by Dr. Andre Geim and Dr.

Kostya Novoselov. The two professors found an ingenious way to extract graphene from graphite through a method later known as exfoliation. This opened a gateway for people to learn more about 2-D materials. However, graphene lacks a bandgap due to its single carbon sheet structure. Thus, transition metal dichalcogenides (TMDs) have been studied for their direct bandgap and semi-conductive properties. Two-dimensional materials have then been synthesized through different methods such as exfoliation and chemical vapor deposition (CVD).

Introduction to TMDs

TMDs are materials with the form of MX2 (M= Transition metal; X= Chalcogen). Each different combinations of such materials can provide different properties. As they move from bulk to monolayer, they exhibit a transition from an indirect to direct bandgap. This property allows for functions of optoelectronic devices.

Instrumentation

The TMDs are synthesized by chemical vapor deposition (CVD) to ensure large, uniform monolayer films. The films are characterized through Raman spectroscopy and

1 photoluminescence mapping to ensure uniform quality. The Г-point by a combination of

푑푥푦, 푑푥2−푦2, and 푑푧2orbitals to prominent К-point by the 푑푧2 in single layer forms the direct bandgap. Thus, strong photoluminescence can be detected by light excitation in single layer TMDs. Though there are various TMD materials, MoS2 was a great candidate for measurements due to its strong photo-response, light emission and high field effect mobility, making it an ideal semiconductor for electronics and optoelectronic applications. Metal-oxide-semiconductor field-effect transistors (MOSFET) are fabricated through electron beam lithography (EBL) to measure electron mobility.

Raman Spectroscopy

Raman Spectroscopy is a microscopic technique we use to observe and characterize the vibrational, rotational and other low-frequency modes in our TMD materials. The instrument emits an inelastic light through a 532nm red laser to excite the ground state energy molecules to a higher energy state temporarily. The inelastic light scattered photons cause an energy shift, which is then observed on the spectrum to help us characterize the material. The number of layers in most TMDs can be identified through the separation between the A1g and E2g peaks. For example, for MoS2, if the separation of the two peaks increase, the number of layers increases, too.

Photoluminescence Spectroscopy

Photoluminescence is the light emission from the material through excitation from a light source. The material absorbs the photon from the light and excites its electron to a higher energy state; as it relaxes back to its ground state, the emission of photons can be 2 observed as photoluminescence (PL). This phenomenon can only be observed in direct bandgap materials instead of indirect bandgap. For instance, MoS2 in its bulk crystal form has an indirect bandgap at ~1.3 eV, and in single layer form, it has a direct bandgap that can be observed at ~1.8 eV. The amount of PL we observe shows the quality of the material towards single layer material.

Chapter 2: Materials and Methods

Chemical Vapor Deposition

There are many ways to synthesize TMD islands, such as exfoliation, chemical vapor deposition (CVD), or atomic layer deposition (ALD). However, exfoliation and atomic layer deposition results in lower film quality, which in turn, lowers the optical response of the film. Thus, CVD is the ideal method of choice to synthesize TMD films. CVD allows for the synthesis of many TMD materials utilizing different powder precursors.

The films produced are typically ~20 µm triangular single-crystal islands on commercial

Si/SiO2 substrates.

a) b)

10 µm 10 µm

c) d)

10 µm 10 µm

Figure 1 shows typical single layer islands of my TMD materials as grown via CVD a) MoS2 island grown on 300nm SiO2 b) MoSe2 island grown on 300nm SiO2 c) WS2 island grown on 500nm SiO2 d) MoS2 monolayer film grown on 300nm SiO2 via high vacuum CVD.

For the CVD process, 1-2” quartz tubes are first placed in a single-zone furnace

(Lindberg 55031-S). The furnaces were heated by a controlled programing system

(Honeywell controller UDC3300). Two alumina crucibles were used to hold powder precursors. The Si/SiO2 substrates were first cleaned with an acetone rinse, an IPA rinse and DI water rinse, respectively, then the substrate is treated with a Piranha solution for an hour. The Piranha solution is a mixture of hydrogen peroxide and sulfuric acid at 1:3 ratio. The Piranha was washed off by DI water afterwards.

Once the tube is loaded appropriately as in figure 2, the general growth procedure is listed below.

Figure 2. Shows general CVD growth method in a tube furnace.

Procedure:

1. Purge with high purity N2 at constant rate at 5 Standard Cubic Feet per Hour

(SCFH) to ensure a clean, inert environment in the tube. The flow is held at room

temperature for 15 minutes.

2. Decrease the flow rate of high purity N2 to 0.5 SCFH, then the furnace is

programmed to ramp from room temperature to appropriate growth temperature in

40 minutes. This depends on the melting point of the precursors (typically 650 ºC

for MoS2 growth)

3. Once the temperature reaches the growth temperature, it is held at that

temperature for 10 minutes while keeping the N2 flow at 0.5 SCFH to allow the

growth reaction taking place.

4. The furnace is then cooled off naturally at constant 0.5 SCFH N2 flow below 100

ºC before opening to remove the sample. The slow cooling time is implemented to

avoid grain boundary forming on the TMD films.

The CVD method ensures a controlled growth parameter, while creating high quality, large area TMD films.

Chapter 3: Electrical contacts and

Measurements on TMDs

Electron Beam Lithography

Optical lithography (photolithography) was first used for microfabrication of semiconductor devices. However, to measure the electron mobility of the TMD materials, the field effect transistor devices must be made in nano-scale. This is an impossible task to achieve with photolithography since the resolution is restricted by the diffraction limit of the optics. To achieve nano-scale lithography, electron beam lithography (EBL) was the method of choice to make metal contacts for the TMDs. Since the surface of the CVD grown substrate is covered with debris and oxide precursor, EBL has a high degree of freedom to avoid any contacts landing on top of the debris, which can cause a short in the device.

The TMDs are first CVD grown on top of a Si/SiO2 substrate. A 500nm thick positive photoresist, poly(methyl methacrylate) (PMMA), is layered on top of the substrate by spin coating at 4000 rpm. The substrate is immediately baked at 180 degrees Celsius for 2 minute. The hardened resist is then exposed to an electron beam in EBL to create imprinted structures on top of the sample. The exposed structures are developed and etched away by soaking the substrate in a MIBK/IPA (1:3) solution. The developed electrodes and pads are metalized through e-beam evaporation with a thin adhesion layer

7 follow by a thick gold layer. The structure of the device is normally with electrode contacts placed on top of the TMD film parallelly, then each electrode is connected to a large 100 µm by 100 µm square pads. This structure is used for electrical transport measurements later.

Figure 1. Shows general device fabrication process steps

Figure 3. EBL fabricated device structures on various materials. a) shows MoTe2 contacts with Sc/Au. b) shows interdigital transducer structure with Ti/Au on CVD grown MoS2 on LiNbO3 substrate. c) shows graphene strip with MoS2 CVD grown on top. d) shows vertical pillar device with Ti/Au contact.

MOSFET

MOSFET is one of the most important device for microprocessors and semiconductor memories. It is a type of field-effect transistor that utilizes an insulated gate (normally with an oxide) to connect the source and drain current through a semiconductor. The voltage is first applied at the gate, which generates an electrical field to control the current between drain and source. By controlling the gate, we can turn the transistor on and off at will. This can only be achieved by TMDs due to their direct bandgap property.

In my work, I have demonstrated numerous types of MOSFET devices on various 2-D semiconductor materials; each demonstrates different type of properties and advantage over others.

Electrical Probe Station

Once the device is fabricated, it would be measured by an electrical probe station for its transport properties. Most of the measurements are carried out with a two-probe measurement technique. For example, using a Si/SiO2 wafer, a small portion of top oxide layer was first scratched off to expose the silicon underneath. A gold insulation coated wire was attached onto the scratched surface to apply a gating voltage from silicon through the silicon oxide layer into the TMD device. The two probes are landed onto two separate metal pads connected to a TMD film. A source-drain current is applied to the two metal pads after a gating current is applied to the silicon oxide substrate. The gate voltage generates an electric field that allows the flow of electrons from source to drain.

The source-drain current measured is used to calculate the material’s electron mobility using the following equation:

휇FE=퐿/(푊퐶ox ) ∙ 1/푉sd ∙ (푑퐼sd)/(푑푉g)

(1) where L is the length of channel, W is the width of channel, Vsd is the source-drain voltage, Isd is the source-drain current, Vg is the gate voltage, and WCox is the capacitance per unit length of the oxide.

Scanning Photocurrent Microscopy

Scanning photocurrent microscopy (SPCM) is a microscopic technique that provides a wide range of information such as the charge transport, recombination dynamics and internal electric field. For my measurement, we built a homemade SPCM system with both a green and red laser equipped for excitation of 2D materials. The devices measured using the SPCM are fabricated with three electrodes placed evenly on top of an MoS2 island; the middle electrode is the source current while the other two electrodes are connected to ground (drain). The measurements are done by inputting a source voltage from -2 V to 2V while varying gate voltage from -60 V to 60 V. Two different devices were fabricated with cobalt gold contacts and titanium gold contacts to more closely examine the Schottky barrier effect caused by different metals. The results showed that the device with the titanium gold composition gives out a higher signal. This is attributed to its lower work function.

Figure 4. Transport measurement for Co/Au and Ti/Au contacts on MoS2 a) shows device structure with 3 finger contacts b) shows trend for Co and Ti contacts when applied 2V for source current while varying gate voltage from -60 to 60 V. c) shows trend for measured current for Ti/Au contacts at varying gate voltage. d) shows trend for measured current for Co/Au contacts at varying gate voltage.

After applying equation (1) to the transport measurement results, it showed that the Ti/Au contacts had a mobility of 1.16984 cm2/V·s and the Co/Au contact had a mobility of

0.13264 cm2/V·s.

The device is then excited by a pulsing laser controlled by a shutter system. The laser passes through a spatial filter, then a neutral density filter to have better control on the excitation source. The laser then passes through a beam expander and into a microscope.

The laser is kept at a fixed location, while the sample holder is placed on top of a piezo stage. The piezo stage moves the sample at 1V per scan at a 70 by 70 scanning range. The

11 injected charge carriers will reach the nearby electrodes before they recombine, a photocurrent is measured.

Figure 5. Shows the SPCM set up where a) the laser source b) the optical mirrors c) the optical laser filter d) camera and detector e) piezoelectric sample stage.

Due to the natural oxidation rate of our monolayer TMD islands, the experiments are normally carried out in approximately one week, before the islands become oxidized in air. We investigated how different metal compositions of devices correlate to Schottky barrier effects. Currently, two metal compositions are used (Ti/Au, and Co/Au). The

SPCM scan shows titanium has a lower Schottky barrier than cobalt because it exerts a higher photocurrent than cobalt.

Figure 6. SPCM mapping of Co/Au contacts and Ti/Au contacts on MoS2 a) shows the scan at +15 gate voltage. It exhibits higher photocurrent on Ti/Au contacts. b) shows the scan at -15 gate voltage. It exhibits higher photocurrent on Ti/Au contacts.

Chapter 4: Composition-dependent photocurrent in CVD-grown Monolayer

MoS2(1-x)Se2x Alloy Devices

The following is taken from an article published in ACS Nano Letters, in collaboration between Velveth Klee, myself, and other students of Ludwig Bartels, François Léonard and Alec Talin Introduction

We report a way to tune the direct optical gap continuously between the values of single- layer MoS2 (1.87 eV) and MoSe2 (1.55 eV). While the basic optical properties of CVD- grown TMDs have been extensively studied, the optoelectronic response of devices based on such material has not received as much attention, particularly for alloys. Traditional phototransistors are based on mechanically exfoliated single and few-layer MoS2. In contrast, these devices produce a photocurrent that is linearly dependent on laser power at low powers and become sublinear with increasing power. A recent study on few-layer

MoS2 phototransistors also confirms the sublinear dependence of the photocurrent on laser power and attributes the dominant photoresponse to a separation of photoexcited carriers caused by a built-in or external electric field.9 This is contrary to a previous study that reports photocurrent generation in single-layer MoS2 dominated by the photothermoelectric effect (PTE).10 Recent studies report on phototransistors based on

14 single-layers of MoS2 synthesized by CVD; these results also show sublinear dependence of the photocurrent on laser power.11,12 An open question is whether the above results extend to other TMDs and in particular to the recently discovered MoS2(1−x)Se2x alloys grown by CVD. Methods

Single-layer MoS2(1-x)Se2x alloys were grown by CVD in a tube furnace at 650°C on a

SiO2/Si substrate (100 nm thickness of SiO2, heavily doped Si). For MoS2, MoO3 powder and elemental sulfur were used for the metal and chalcogen source, respectively. For

MoSe2 and alloys, the chalcogen sources are thiophenol and diphenyl-diselenide; the amount of each source is varied to adjust the sulfur/selenium ratio, as described in detail in previous publications,. Raman and photoluminescence measurements were used to characterize the alloys (Supporting Information) with regards to their optical bandgap and to confirm the monolayer nature of the material. The photoluminescence peak varies from

1.55 eV for MoSe2 to 1.85 eV for MoS2, with intermediate values attained for intervening alloy compositions. A linear variation of bandgap with composition is assumed throughout this work.

Electronic devices were fabricated by patterning PMMA/MMA bilayer resists using e- beam lithography. Ti/Au (2 nm/ 50 nm) electrodes were deposited by electron beam evaporation. We verified that device fabrication did not affect the material by comparing the photoluminescence before and after fabrication. Devices described throughout this manuscript have channel lengths between 0.5 µm and 5 µm, and they continuously span the compositional space between MoS2 and MoSe2. Dozens of devices were fabricated,

15 characterized, and measured for this study. All devices addressed in this manuscript were fabricated on regular triangular single-layer islands with side lengths around 15 µm, which are typical of single-crystalline material. A representative optical image of a

MoS2(1-x)Se2x device is shown in the inset of Fig. 1a. An AFM linescan in the channel area gives a step height of ~0.85 nm going from the SiO2 substrate to the MoS2(1-x)Se2x island, confirming the monolayer nature of the material (Supporting Information). On all devices, electrical measurements yield very little current for source-drain biases up to ±2 V, even when the devices were gated with up to ±60 Volts through the heavily doped Si substrate

(resistivity 0.005 Ω-cm), the exception being some pure MoS2 devices, as shown in the

Supporting Information. All measurements were performed in ambient.

We use scanning photocurrent microscopy (SPCM) to characterize the optoelectronic properties of the devices. The beam from a red HeNe laser (633nm) was fed into a microscope and focused on the devices using a 50X, NA=0.55 objective, and the current was measured using a DL 1211 current pre-amplifier and a probe station. As shown in the

Supporting Information, the spot diameter at half-maximum is about 1.3 μm. Different beam powers (measured by replacing the sample with a Newport 818 photodetector) were realized by appropriate filters placed between the laser source and the microscope. A computer-controlled stage was used to move the devices in 50 nm steps with respect to the laser beam while the current was recorded. The intensity of the reflected light was collected simultaneously to create spatially-resolved reflection images, in which the metallic electrodes appear bright compared to the moderately reflective SiO2/Si substrate. In

16 addition to regular optical images, the presence of the MoS2(1-x)Se2x island can readily be discerned from the substrate (see insets in Figs 1a,e) by a drop in reflected power of ~6%. Results and Discussion

Figure 1 shows representative SPCM maps taken at zero bias and at biases of ±1 V for two devices consisting of MoS1.6Se0.4 and MoS0.4Se1.6 single-layer islands. We applied a laser power of 1310 μW in a near diffraction-limited spot resulting in a power density of ~80 kW/cm2. At zero bias, very small photocurrent spots typically on the order of hundreds of picoamps are observed which are most often located near the electrodes as in Fig. 1a, but are also sometimes seen in the channel (Fig. 1e). These very small currents could originate from the presence of band-bending at the contacts and/or due to the photothermoelectric effect. Under bias of either polarity, the photocurrent increases by several orders of magnitude to hundreds of nanoamps for S-rich compositions (Fig. 1b,c) and to tens of nanoamps for Se-rich compositions (Fig. 1f,g). While the laser spot size is comparable to the channel length, it is still possible to see in these measurements that the maximum photocurrent is observed in the channel, either closer to the electrode edges (Fig. 1d) or in the middle of the channel (Fig. 1h). Additional SPCM maps for longer channel devices and for MoS2 and MoSe2 can be found in the Supporting Information, and show that for MoS2 and sulfur-rich alloy devices the photocurrent maxima are located near the negatively biased electrode, as would be expected for a system of back-to-back Schottky diodes with band-bending in the channel near the electrodes.

Figure 7. (a-c) Photocurrent images for a single-layer MoS1.6Se0.4 (Eg=1.80 eV) device at (a) Vsd = 0 V, (b) Vsd = -1 V, and (c) Vsd = +1 V. The bottom insets in (a,e) are optical images of the devices, and the top ones are the reflection images. The dotted green lines denote the outline of the TMD island in each plot. The black outlines are the electrode edges extracted from the reflection images. (e-g) Photocurrent images for a MoS0.4Se1.6 device (Eg=1.62 eV). (d,h) Photocurrent line profiles extracted from the photocurrent images. Drain and source electrodes are labeled “D” and “S” respectively. In all panels a red laser is used with a power of 1310 μW, and the voltage is applied to the drain electrode on the left hand side.

The SPCM maps of Fig. 1 were acquired left to right (fast scan direction) and top to bottom

(slow scan direction). We observe some apparent photocurrent even when the excitation beam has passed the area between the electrodes, especially for the S-rich composition.

This artifact is caused by a slow photocurrent response. Fig. 2a shows the time dependence of the photocurrent for a 5μm channel MoS2 device for a bias of +1 V when the laser is focused in the channel near one of the electrodes. The photocurrent dynamics are exceedingly slow, with rise times (90% of maximum current) and decay times (10% of maximum current) of 12 min and 10 min, respectively. Introducing selenium accelerates the photoresponse to a few minutes for MoS1.2Se20.8 (Fig. 2b) until the response exceeds the limit of the pre-amplifier (Fig. 2b inset). The bleeding observed in the SPCM images for the S-rich material originates from the slow photocurrent decay and is observed in the fast scan direction (see Supporting Information for detailed discussion). In addition, a photocurrent outside of the area between the electrodes can originate from fringe fields from the electrodes (experimental results and simulations are presented in the Supporting

Information). Persistent photoconductivity as in Fig. 2a is well-known to arise due to charge traps. In such systems the photocurrent decay can be described with a stretched

 exponential function I( t ) I0* exp t / t ; the inset in Fig. 2a shows an excellent ph ph   fit of this function to the experimental data, giving an exponent   0.52. (Note that a simple exponential decay is not able to describe the photocurrent dynamics.)

Figure 8. (a) Time-dependence of photocurrent for a MoS2 device as a laser focused near the drain electrode is turned on and off. The inset shows a fit of the photocurrent decay to a stretched exponential. (b) Comparison of time-dependent response of MoS2, MoS1.2Se0.8 and MoSe2 devices; the inset highlights the fast photocurrent current decrease for a MoSe2 device, which reflects the limit of our electronics. (c) Current-voltage characteristics under illumination (λ=633 nm) for MoS1.8Se0.2 and MoS0.4Se1.6 (inset) alloy devices of different channel lengths. (d) Dependence of the photocurrent on channel length at 1310μW excitation power. The channel length dependence of the photocurrent (Fig. 2c,d) provides us with important insight into the photocurrent mechanism: for a photoconductive device, the photocurrent is expected to decay exponentially with channel length L for channels longer than the

diffusion length LDD   (where D is the diffusivity and τ is the recombination time),

IILLph0exp / D . From the strong, consistent channel length dependence of the data

20 in Fig. 2d we obtain by least-squares fitting to an exponential function a diffusion length of 0.88±0.06 μm for the sulfur rich material and of 0.45±0.01 μm for the selenium-rich material (the error bars reflect the fit error only). The shorter diffusion length for the selenium-rich material is consistent with the faster photocurrent decay shown in Fig. 2b.

Figure 3 explores the photoresponse at different excitation intensities for a range of MoS2(1- x)Se2x compositions. The samples proved to be stable under prolonged exposure even to the highest laser power shown in this set (see Supporting Information and Fig. 2a). Two trends can readily be discerned: 1) there is an overall decrease of photocurrent as the S content decreases, and 2) the I-V curves become progressively more linear with increasing Se content. Moreover, we also observe a non-linear dependence of the photocurrent on the excitation power that will be discussed later on. (Note that at zero bias, the photocurrent is close to zero in these figures, being due only to the small currents shown in Fig. 1a,e and

Supplementary Figure S5a,d,g).

Figure 9. Current-voltage characteristics at different laser powers (λ=633 nm) for five devices ranging in composition from (a) MoS2 (Eg=1.85 eV) to (e) MoSe2 (Eg=1.55 eV). Laser power labeling is the same for all panels, and all devices have a channel length of 1 μm. The laser position was optimized to give the largest photoresponse at 2V, and kept at that same position as I-V curves were acquired.

We first discuss the origin of the illumination-dependence of the I-V curves (Fig. 3). We note that there is practically no photocurrent at zero bias, and an increasing slope with increasing light intensity. This type of behavior can originate both from photoconductive or bolometric effects but it is inconsistent with a photothermoelectric effect which typically involves a photocurrent at zero bias and no change in slope as the light intensity is increased. A photothermoelectric effect is further ruled out by the magnitude of the current at 1V bias, which even assuming the largest measured Seebeck coefficient for

6 MoS2, would require a temperature gradient on the order of 10 K, an unrealistic value.

The spatial location of the photocurrent maxima near the negative electrodes and the change of this location with inversion of the bias voltage suggests a photoconductive mechanism due to the presence of electric fields in the channel, in contrast to a bolometric effect. To further rule out the latter, we measured

Figure 10. (a) Dark current-voltage characteristics for a 1 micron channel MoS2 device as a function of temperature. (b) Infrared camera image of a single-layer MoS2 film on Si/SiO2 illuminated by a focused red laser at a power of 0.31 W. (c) Profiles of temperature rise extracted from images similar to (b) during laser illumination at different powers. Inset shows the maximum temperature rise as a function of laser power. the temperature dependence of the dark I-V characteristics of a MoS2 device as shown in

Fig. 4a. As expected, the current increases with increasing temperature; however, the

22 increase in current is small. 400K of equilibrium temperature generates a dark I-V current of 80 pA compared to greater than 1 μA measured with the largest laser intensity, i.e. four orders of magnitude difference. An upper bound for the temperature increase during laser illumination can be obtained by assuming uniform illumination and balancing the heat input with the heat dissipation to the substrate. Then a temperature increase TPG/ results where P is the laser power and G is the heat transfer coefficient between the TMD material and the substrate. Values of G 1072 W/m K have been extracted based on studies of heat dissipation in MoS2 transistors, about an order of magnitude lower than for graphene. Using the lower value, we obtain a temperature increase of 80K for the largest laser intensity used in this work, where our equilibrium heating yields less than

10-4 of the photocurrent. To further support the claim that the temperature rise is too small to lead to a significant bolometric effect, we measured the temperature rise during illumination by focusing a red Krypton laser on a region with extended (mm scale) coverage of single-layer MoS2 on Si/SiO2. The laser was focused on the surface, and the temperature profile was measured with an Inframetrics 760 infrared camera with 10 μm resolution. As shown in Figs. 4b,c, the focused laser illumination leads to a temperature rise at the point of excitation which decays over a distance of a few hundred microns.

However, the maximum temperature rise is small, reaching only 4K under illumination with 0.31 W (~2.5 MW/cm2, i.e., more than thirtyfold of that used for the photocurrent measurements). Because most of the optical absorption occurs in the Si substrate (we measured about 6% additional absorption at the location of single-layer MoS2), the IR camera measures predominantly the temperature in the Si substrate. As discussed in the

Supporting Information, because of the heat exchange between the Si and the MoS2, the temperature of the MoS2 is directly linked to that in the Si by the thermal resistances of the SiO2 and the MoS2/SiO2 interface. At the laser power used for the optoelectronic experiments, we estimate a temperature rise of about 7 K in the MoS2, much too small to lead to a significant bolometric effect. Finally, the temperature increase at the laser spot can also be obtained by analyzing Raman spectra as a function of laser power, which gives a temperature increase of 16K for the largest laser intensity (see Supporting Information for details).

Figure 11. Photocurrent measured at a source-drain bias of 2 V as a function of laser power for single- layer MoS2 (Eg=1.85 eV), MoS1.2Se0.4 (Eg=1.74 eV), and MoSe2 (Eg=1.55 eV). The superlinear behavior is observed across compositions. The insets show log-log plots of the photocurrent as a function of laser power. The solid and dashed lines in the insets correspond to linear and quadratic dependence on power. Having established the photoconductive nature of the optoelectronic response, we now discuss the power dependence. Figure 5 shows the photocurrent measured at a bias voltage of 2V as a function of the excitation power for three different alloy compositions.

Remarkably, the photocurrent shows a pronounced and unusual superlinear dependence on

25 the excitation power, a behavior that is also observed for different bias voltages (Fig. S11).

The superlinear dependence on laser intensity is in contrast to previously reported results on exfoliated and CVD-grown MoS2 where the behavior was found to be sub-linear. The difference may be due to the lower optical intensities used in these studies, as well as the properties of the materials.

Indeed, as discussed above, the sensitivity of a photoconductive device is usually determined by a combination of carrier excitation, separation, recombination, and diffusion. Despite all of these processes, the power dependence of the photocurrent is usually simple: it is linear at small power with a cross-over to sub-linear behavior at larger powers. Superlinear photocurrents are relatively rare (see for example Refs ), and few theoretical models exist that predict superlinear behavior even in bulk materials . All of these theories require the presence of recombination centers of different energies and capture cross-sections. A simplified description of the process involves initially empty and filled intragap states close to the conduction band and valence band, respectively. At increased laser intensity, the occupancy of these centers changes due to shifts in the quasi-

Fermi-levels, resulting in an increased carrier lifetime. In our system, the potential origins of the intragap states include different defect types in CVD-grown TMDCs as shown by recent experimental and theoretical analysis,, edges in CVD-grown TMDC islands, which give rise to a metallic (potentially magnetic) edge state that has been discussed in the context of chemical catalysis, or interactions with the substrate, which are known to affect the photoluminescence yield and, thus the exciton dynamics.

To illustrate the emergence of superlinear photocurrent, we implemented a model based, for reason of simplicity, on the presence of three types of recombination centers, as illustrated in Fig. 6a. This is the simplest model that shows superlinear behavior without invoking divalent centers. We are not implying that all alloys measured here have this particular number and energy-distribution of centers; superlinear behavior can also arise for more general distributions of slow and fast centers, including continuous distributions.

In our model, centers of type 1 (density N1 ) are located near the valence band and have a

large hole capture cross-section ()1h , but a small electron capture cross-section ()1e .

Centers of type 2 and 3 (densities NN23 and ) are considered to have high capture cross- sections for both holes and electrons, and are located near midgap and near the conduction band, respectively. In the dark, the Fermi level is located above centers 1 and 2, but below centers 3 (this is consistent with the low conductivity observed in our devices in the dark).

During illumination, the free hole and electron concentrations increase, and their respective

pn quasi Fermi levels (EEFF and ) move closer to the valence and conduction band edges.

At high enough intensity, the initially empty centers 3 become partially filled and the recombination rate drops rapidly, signaling the onset of superlinearity.

The above model was implemented numerically by solving coupled rate equations for the occupancy of the three types of centers as a function of light intensity, including optical and thermal generation, as well as recombination. The model is presented in detail in the

Supporting Information. Figure 6b shows the calculated photocurrent as a function of light

intensity for the case NNNNN1 2  and 3 /  0.01, assuming

1h  2 h   2 e   3 h   3 e   and varying the ratio 1e /. When the capture cross-

section for centers 1, 2, and 3 are equal (ie . . 1e / 1) , the photocurrent depends linearly on the light intensity; however, as the capture cross-section for electrons in center 1 decreases, a superlinear behavior emerges, which can become quite pronounced. Figures

6c,d show the calculated occupancy of the three centers and the recombination rate as a function of light intensity. For low intensity, centers 3 are mostly empty, while centers 1 and 2 are mostly occupied, and the recombination rate is dominated by centers 3 (barely visible in Fig. 6d, note linear scale). As the light intensity increases, the occupancy of centers 3 increases, while centers 2 become partially empty, and the recombination traffic is mostly through centers 2. In this region the photocurrent is linear with light intensity.

Upon further increase in intensity, the density of empty centers 1 is comparable to those in centers 2 and 3, and the recombination rate drops rapidly with intensity, leading to superlinear photocurrent.

Figure 12. Model to explain the origin of superlinear photocurrent. (a) Illustration of the three different types of recombination centers and their capture cross-sections, as well as the location of the Fermi level in the dark and the quasi Fermi levels under low- and high-intensity illumination. (b) Calculated photocurrent as a function of light intensity for three different values of the ratio of capture cross- sections for centers 1 and 3. (c) Fraction of empty centers as a function of light intensity. (d) Recombination rate as a function of light intensity. Conclusion

In summary, we report on the optoelectronic characteristics of CVD-grown monolayer alloys that span the composition range from MoS2 to MoSe2. Our measurements show significant decrease of the photocurrent at fixed wavelength for Se-rich alloys compared to S-rich ones along with decreased diffusion length of photogenerated carriers. We find a photoconductive response that is characterized by an unusual superlinear dependence of the photocurrent on the illumination intensity. In combination with recent reports of high mobility and high sensitivity of MoS2 , it may suggest potential for optoelectronic application of the films under investigation. Importantly, our results indicate the presence

29 of uncommon non-equilibrium photophysics in these systems, opening a number of intriguing questions regarding the nature and control of such phenomena.

Chapter 5: Ferroelectric Control of 2D

MoS2

The following is taken from an article published in ACS Nano Letters, in collaboration between myself, Ariana Nguyen, and other students of Ludwig Bartels and Peter

Dowben. Introduction

Monolayer transition metal dichalcogenides have been fabricated into nanoscale transistors by electrostatic gating. This has a high on-off ratio not shared by the gapless semiconductor graphene. To develop such nonvolatile ferroelectric gated transistor, the fabrication needs to be scalable. This means the TMD have to be grown in place with chemical vapor deposition (CVD) in a controlled manner. Here, we demonstrate the growth of high-quality single-layer MoS2 films directly onto periodically poled LiNbO3 (PPLN) substrates. We find a significant effect of the ferroelectric polarization on the growth and transport properties of the MoS2 films. The choice of lithium niobate (LiNbO3) as a ferroelectric substrate for this study was motivated by the fact that lithium niobate exhibits a ferroelectric transition temperature well above 1000 °C, thus preserving the ferroelectric domain structure during the deposition of the MoS2 film at a temperature of ∼700 °C.16

Our lithium niobate substrates were cut perpendicular to the c- (polar) axis resulting in a surface of hexagonal symmetry and perpendicular polarization domains.

Methods

CVD growth of single-layer MoS2 [17-21] has been demonstrated on SiO2 and a few other substrates. The resultant films exhibit optical and transport properties that rival those of mechanically exfoliated films. Single-layer MoS2, exfoliated or grown on SiO2/Si, typically shows characteristic n-doped transport [5,6,22-23]. In most cases, an inversion of the MoS2 transport properties to p-type behavior, say through application of a sufficiently strong electrical field, has not been shown feasible except by the use of special materials such as ionic liquids [2,24]. MoS2 on lithium niobate appears to be different.

Complete fabrication and characterization details are given in the SI. Briefly, as substrates we used 5 x 5 x 0.5 mm3 plane-parallel plates (supplementary information, Figure S2) of lithium niobate of congruent composition, with a periodic domain pattern (period of 12~16

μm) made by several approaches. The periodic domain pattern was, in the majority of the samples, prepared by application of 10 kV to a 3-inch LiNbO3 wafer (0.5 mm thick) using liquid electrodes of saturated aqueous LiCl [25,26]. The c+ polar (Z+) surface was covered by a lithographic photoresist pattern whereas the c- polar (Z-) surface was contacted by a continuous liquid electrode, and the photoresist pattern was removed after the poling process by dimethyl sulfoxide and oxygen-plasma dry etching, leaving behind a bare ferroelectric surface. As a result, the lithium niobate substrates exhibit periodic domain stripes of antiparallel 180º ferroelectric domains with spontaneous polarization, oriented either upward or downward along the surface normal. The characteristic dimensions of the domain patterns (supplementary information, Figure S3) were measured in ambient environment by means of piezoresponse force microscopy (PFM) [27-31]. The various

32 approaches to the fabrication of the periodic domain pattern were seen to affect the surface morphology, but without any other significant difference in the results reported here. For the transport measurements, we deposited Ti/Au electrical contacts for transport measurements on the MoS2 single-layer film using electron-beam lithography and a

MMA/PMMA stack as a resist. Our process is optimized to be benign to the MoS2 overlayer, as validated by the absence of significant degradation of the photoluminescence yield.

MoS2(0001) monolayer thin film growth, on the periodically poled lithium niobate, proceeded as described in Ref. [21]. We used alumina boats containing elemental sulfur and MoO3 powder as sources of sulfur and molybdenum, respectively. The boats were placed at different positions in a quartz process tube and inserted into a tube furnace. The comparatively small substrate was supported by means of a molybdenum mesh on the edge of the MoO3-containing alumina boat. The sulfur vapor from the upstream sulfur boat passed over the sample, aided by an N2 carrier gas. Heating of the furnace to 650-700° C at the MoO3 boat position and slow cool-down yielded films with a range of MoS2 coverages from single-layer films to isolated MoS2 islands, depending on the growth temperature and duration. The growth MoS2 overlayers, up to single-layer films under our conditions, was seen to preserve the ferroelectric domain pattern of LiNbO3 substrate. Results and Discussion

We found enhanced MoS2 growth on the domains with polarization oriented “up” compared to domains with polarization oriented “down”. At low coverages of MoS2 deposition, we find the majority of the resultant MoS2 islands on up-domains of the

33 periodically poled LiNbO3 substrate (the SI illustrates an example in Fig. S5). More deposition led to the formation of a continuous MoS2 film on both up- and down-domains.

Under some intermediate deposition conditions, we observed an almost continuous film on the up-domains and practically no film growth on the down domains, as illustrated in

Figure 1 (up-domains). Figure 1a shows an optical micrograph of an area where the MoS2 single-layer film (directly visible as brighter areas) follows the periodic polarization domain pattern of the LiNbO3 substrate (indicated at the bottom of Figure 1a): areas with the substrate dipole moment pointing up out of the surface (up-domains) exhibit MoS2 growth, while areas with down polarization (down-domains) support less or no growth.

The preferential growth of MoS2 on the up-domains and absence on the down-domains is validated by mapping of the photoluminescence (PL) intensity of the A exciton at 1.86 eV photon energy (Figure 1b). The photoluminescence spectra obtained at 100 K on the MoS2 areas (Figure 1c) show the well known A and B exciton peaks, confirming the growth of quality MoS2(0001) single-layer materials on this substrate. Because MoS2 is a direct bandgap semiconductor exclusively at the single-layer limit [32-34], the presence of bilayer or thicker films would result in a significantly reduced and spectrally shifted photoluminescence signal [34]. The strong overlap between MoS2 and LiNbO3 vibrational modes makes Raman spectroscopy less useful.

Figure 13. a) The optical micrograph shows preferential growth of single-layer MoS2 on LiNbO3 domains with a dipole moment pointing up out of the surface, as illustrated in the bottom; (b) spatial mapping of the photoluminescence (PL) intensity (red) of a portion of panel a (same length scale) on the left and (c) spectroscopy validates the single-layer character and quality of the MoS2 single layer film. When a continuous MoS2 film is grown on both ferroelectric domains, only a small difference of the PL yield results (d). While not previously reported for any 2D material, the preferential growth of MoS2 on ferroelectric domains of a particular polarization has considerable precedence. Enhanced adsorption on one polarization domain of a ferroelectric over the opposite polarization has been reported previously [31,35-43] for small molecules, viruses, and metals. The electrically switchable properties of the ferroelectrics can be used to tailor surface reactivity, yet the physico-chemical mechanism of preferred adsorption on one polar surface is not conclusively understood. Inspection of the details of the surface composition of LiNbO3 as a function of temperature [44] indicates that the surface stoichiometry and arrangement of this material differs with polarization under our growth conditions/temperature. At elevated temperatures, as during MoS2 CVD growth, far greater

35 evaporation of Li and especially oxygen has been observed from the up-domains than from the down-domains [44], and thus should facilitate reduction of any ambient compensating charges. This could enhance the existence of free Nb or lithium frontier orbitals and an oxygen poor surface terminal layer for the up-domain compared to a down-domain [45,46].

In the computational studies of poled LiNbO3 surfaces by both Levchenko and Rappe [45] and Sanna et al. [46] the up-domains exhibit less oxygen atoms at the terminal surface layer compared to the down-domain surface thereby facilitating the adsorption/anchoring and reduction of MoO3 during CVD growth. Preferential growth, on one domain over the other, is be mediated by surface chemistry, as has been speculated upon elsewhere [41]. In the case of the preferred MoS2 growth on the up-domain surface, this is likely facilitated by the adsorption/anchoring and reduction of attachment of MoO3-x, thereby seeding MoS2 and leading to preferential growth on this domain. Such terminal layer site occupation

[45,46] occurs in spite of the overall oxygen and lithium rich surface region of the up- domains compared to the negative or down-domain ferroelectric surface, as noted in both experiment [44] and the theory of Levchenko and Rappe [45] and Sanna et al. [46]. We caution that the surfaces of ferroelectrics are complicated and a detailed analysis of the surface composition, under MoS2 growth conditions, is experimentally well beyond the scope of this study.

Figure 14. The PFM amplitude (a) and phase (b) images of the same area of the PPLN substrate covered with isolated single-layer MoS2 islands. Bright and dark contrast in (b) indicates down- and up-domains, respectively. In (a), the MoS2 islands enhance the amplitude of the piezoresponse signal on the up-domains but suppress the force on the down-domains. (c) Kelvin probe force microscopy (KPFM) reveals a change in surface potential, by about 48-52 mV, at the location of single-layer MoS2 islands (dark spots) irrespective of the substrate polarization. The dashed line indicates a ferroelectric domain boundary. d) The cross-sectional profile taken along the red line in (c) indicates a change in surface potential across a MoS2 island. We utilized piezoresponse force microscopy [27-31] to image ferroelectric domains on

LiNbO3 substrates, as seen in Figure 2 and the SI Figure S3. This method exploits as contrast mechanism the fact that ferroelectric behavior implies piezoelectricity.

Consequently, mapping the piezoelectric response of a material provides a direct image of its ferroelectric domain structure. We find that MoS2 monolayers preserve the surface dipoles, as seen in Figure 2. Piezoresponse force microscopy (PFM) and Kelvin probe force microscopy (KPFM) were conducted on a sample exhibiting isolated MoS2 islands, i.e. a

37 reduced CVD coverage compared to that of Figure 1, with growth on the up- and, to a lesser degree on the down-domains. At such MoS2 coverages, we observe that the MoS2 islands on the up-domain frequently touch the substrate domain boundary but generally do not span across the ferroelectric domain boundary into the adjacent ferroelectric polarization domains. The PFM phase image (Figure 2b) indicates the perodic ferroelectric domain stripes (here, darker contrast corresponds to up-domains and brighter contrast indicates down-domains). The PFM amplitude image (Figure 2a) of the same area shows

MoS2 islands on ferroelectric up-domains as bright features meaning that the absolute value of the electric field, which generates the PFM signal at the MoS2/LiNbO3 interface, is greater here than elsewhere. While ambient conditions generally lead to a suppression of the surface polarization charge, this effect is mitigated where the MoS2 islands cover the up-domains, similar to prior experiments on graphene [9,10]. In contrast, the PFM amplitude is reduced over the MoS2 islands on the down-domains. We can reconcile these two findings by invoking a chemically-induced charge transfer from MoS2 to the LiNbO3 substrate whose direction (but not magnitude) is irrespective of the substrate polarization, i.e. MoS2 donates electron charge to both the oxygen rich up domain surface and the down domain surface.

Corroborating evidence of the induced MoS2/LiNbO3 charge transfer and ensuing dipole interactions originates from Kelvin probe force microscopy (KPFM) data (Figure 2c,d)

[47]. The KPFM image of Figure 2c shows two adjacent opposite (180º) ferroelectric polarization domains, with the ferroelectric domain boundary running almost vertically through the image (indicated by dashed line; the supporting information section provides

38 the corresponding PFM image as Figure S4). In each domain, isolated MoS2 islands appear as reduction of the surface potential (i.e. increase of the work function) irrespective of the surface polarization direction. The cross-sectional profile of the relative surface potential, shown in Figure 2d, reveals a reduction by ~50 mV over the MoS2 islands. This local reduction in surface potential is consistent with the direction of a surface dipole that originates from electron transfer from the MoS2 islands to the substrate, as suggested by the PFM results of Figure 2a,b.

We note that the chemically induced dipole of the MoS2 on LiNbO3 (independent of polarization direction) indicates sizeable interaction across the interface. Yet the remnant surface polarization under the MoS2 film offers the possibility for affecting the overlayer transport properties through substrate polarization.

We performed electrical transport measurements (Figure 3) on up-domains (positive boundary charge) and down-domains (negative boundary charge). To this end, we fabricated Ti/Au contacts onto a continuous MoS2 film spanning both substrate polarities.

The transport was measured for a channel length between the contacts of 1 μm aligned with the domain stripes (vertical in Figure 3b). The photoluminescence spectra of Figure 1d were obtained on these ferroelectric domain stripes prior to contact fabrication, with the red/blue spectrum corresponding to the electrode pair marked in the same color in Figure

3b.

Figure 15. (a) Dependence of the corrected source-drain current Isd on an additional voltage Vpol applied to the bottom of the ferroelectric substrate. The red and blue traces correspond to measurement across the 1 μm gaps indicated in panel (b). The approximate location of the domain boundaries are denoted by blue lines. While the left (red) device shows moderate response to negative applied voltage and also for positive Vpol greater than at ~80 V; in contrast the right (blue) device shows higher current under negative Vpol but shows little response for positive Vpol up to Vpol = 200 V. The dotted lines are meant exclusively to guide the eye. The diagrams schematically illustrate the effect of the applied Vpol voltage to the bottom of the ferroelectric LiNbO3 substrate: the left (up) polarization domain corresponds to the left (red) device and vice versa. The current-voltage-measurements were conducted over a source-drain bias (Vsd) range of

±1 V resulting in currents (Isd) in the sub-nanoampere range consistent with typical measurements of MoS2 in the dark and in the absence of means for alleviating the impact of Schottky barriers [17]. We applied an additional voltage (Vpol) of up to ±200 V by means of placing the LiNbO3 substrate on top of a biased metal plate. This is far less than the coercive voltage of the ferroelectric domains, so no domain reversal occurred and no

40 hysteresis was observed. Figure 3a shows the source-drain currents, Isd, for the MoS2 on both up- and down-domains (measured at Vsd = -1 V) as a function of Vpol. The displayed currents, Isd, were corrected for leakage caused by the finite resistance of our substrate. The supporting information shows the raw data.

The remanent surface polarization of the ferroelectric LiNbO3 substrate, under the continuous MoS2 film, offers opportunities for affecting the transport properties of the overlayer. Application of a negative Vpol, along the polarization axis, causes the LiNbO3 substrate to accumulate positive charge at its bottom surface and a negative interface charge at the top surface where the MoS2 film resides (schematic diagrams at the top of Figure 3).

For an up-domain, this reduces the positive boundary charge and, thus, reduces electron transfer from the MoS2 to the substrate. On a down-domain, the applied negative Vpol amplifies the negative boundary charge present from the ferroelectric polarization. This attenuates the electron transfer out of the MoS2 film, indicated by the KPFM measurements. For either substrate polarization domain, i.e. either ferroelectric domain orientation, the application of a negative Vpol voltage increases the electron density remaining in the MoS2 and, hence, is likely to enhance the intrinsic n-doped character. This differs significantly from capacitive gating of a device, while capacitive effects on the channel are minimized by the thickness of the substrate compared to the channel length.

The results of Figure 3 reflect the native n-type character of single-layer MoS2. With increasing magnitude of negative Vpol we observe higher currents, Isd, which is attributed to enhanced n-type carrier concentrations in the MoS2 single-layer conduction channel (left side of Figure 3a). The result is that higher overall conductivities are reached on the down-

41 domain (blue), where a negative boundary charge supports higher electron density in the

MoS2 film in the first place. In contrast, on an up-domain, the positive substrate boundary charge counters the effect of the applied Vpol voltage and reduces overall electron density in the MoS2 film, similar to transistors fabricated with an organic semiconductor on a ferroelectric [48].

More interesting is the application of positive Vpol (right side of Figure 3a), which leads to an increase in positive charge at the top ferroelectric surface, and in turn amplifies the electron transfer from the MoS2 film to the LiNbO3, induced by the MoS2/LiNbO3 interaction. As the MoS2 appears intrinsically n-doped, this reduces the number of its n- type carriers and, hence, reduces the source-drain current Isd. For the case of a down- domain, a positive Vpol is partially compensated by the domain polarization. Consequently, we find that positive Vpol has little effect on the electrical transport of MoS2 on the down- domain. However, transport between the electrode pair on the up-domain (red) goes through a minimum as Vpol reaches ~80 V and increases for higher Vpol. We interpret this as an inversion of the transport character of the MoS2 film and attribute it to the combination of polarization-independent electron transfer from MoS2 to LiNbO3 and the surface charge at the LiNbO3 positive domain interface, which is amplified by application of Vpol..

The change of the MoS2 film conductivity by means of substrate polarization and applied voltage is readily reversible and we observed differences in Isd for up- and down-domains by a factor of >2 for a range of static gate voltages. The 2 µm width contacts, aligned with the domain stripes, are sufficiently narrow to restrict MoS2 transport to material on only

42 one polarization domain, as validated by measurements of the conductance (diagonally) between electrodes on the up- and down-domains.

While for technological application a substantial (i.e., larger than ×2) difference between the transport over up- and down-domains in the absence of an applied voltage is desirable, we wish to point out that in a future nonvolatile transistor based on reversible ferroelectric polarization of the substrate under the MoS2 channel, the ferroelectric interaction and not the applied “gate” voltages

Vpol takes the role of the gate. Moreover, variation of the composition of the transition metal dichalcogenide and the ferroelectric substrate may lead to a material combination that requires a

Vpol only for changing the polarization of the ferroelectric material (write operation) but not for transistor conductance (read operation). Nonvolatile gating by reversible ferroelectric polarization has been observed for p-type organic semiconductors on ferroelectrics [48-54]; and MoS2 top gated by the organic ferroelectric polyvinylidene fluoride with trifluoroethylene (PVDF-TrFE)

[13]. The combination of a ferroelectric gate with a suitable metal dichalcogenides could lead to nonvolatile transistors with appreciably higher mobilities; mobilities as high as 220 cm2/(V·s),

5 with on/off ratios of up to 10 were shown by Lee and coworkers for exfoliated MoS2 [13]. Conclusion

Our transfer-free approach to ferroelectric gated MoS2 transistors utilizes exclusively scalable processing techniques and, hence, has the potential serve as the foundation for large scale device development. In this context we note, that while the coercive voltage in this study is high, much smaller ones are obtained for thin film ferroelectrics [13,48,55].

Also submicron ferroelectric domains in LiNbO3 are known [27-29], so that much smaller ferroelectric domain pattering of MoS2 device structures are certainly within the realms of the possible. We hope that our observations will spark consideration of

43 transition metal dichalcogenide films on switchable ferroelectric substrate as active elements in future nonvolatile microelectronic architectures.

Chapter 6: Hybrid Field-Effect and

Acousto-Electric Devices

The following is taken from an article published in Nature Communications, in collaboration between myself, Edwin Preciado, and other students of Ludwig Bartels and

Hubert Krenner. Introduction

We report millimetre-scale direct chemical vapor deposition (CVD) of monolayer MoS2 onto 128°YX-cut LiNbO3. Field effect transistors (FETs) fabricated on these films exhibit characteristics competitive with established transition metal dichalcogenide (TMD) devices on silicon. The acousto-electric activity of the LiNbO3 substrate permits concomitant control and measurement of the systems electronic and optical properties in a contact-free manner. In our hybrid device, surface acoustic waves (SAWs) excited directly on the LiNbO3 substrate induce a strong acousto-electric effect and sense remotely the photoconductance of an TMD monolayer. SAW photoconductance spectroscopy can be performed at any point along the propagation path of the wave which extends on the millimeter length scale of a chip. This is in strong contrast to contact-based transport measurements, for which only the sample area between the contacts can be probed.

Methods

Sample fabrication:

TMD growth: Single-Layer MoS2 synthesis follows the technique outlined in Ref. : in a typical setup, 25 mg of molybdenum trioxide (MoO3) powder (99.99% Sigma-Aldrich) was placed in an alumina boat and centered in the tube furnace. The LiNbO3 substrate

(128°YX-cut, oxygen reduced and weakly conductive “black” LiNbO3, thickness dsub =

500 µm) was mounted with a molybdenum mesh (Alfa Aesar) on the edge of the boat and

1 g of sulfur was placed upstream at a distance of 25 cm from the center. The furnace was heated at a rate of 12.5 ° C/min, held at ~ 650 °C for 20 minutes, and then allowed to cool naturally to room temperature. N2 carrier gas aided the transfer of the sulfur vapor to the sample region for optimal growth.

Device layout and fabrication: After PL identification of the region with monolayer growth, we fabricated Ti/Au metal contacts and IDTs (21 finger pairs, duty cycle 1:1, aperture 200 µm) for electric and acoustic interfacing to the MoS2 film, respectively. The

IDTs' design wavelength was chosen as λSAW = 25 µm, corresponding to a design frequency of fSAW = 160 MHz. The supporting information shows a micrograph of an IDT. As shown in Fig. 1 (a), the two IDTs are located at opposite ends of the substrate in a delay line configuration (length 5.4 mm) to enable us to launch and record SAWs propagating at vSAW

= 3980 m/s in opposite directions across the chip. The studied FET device features a channel length of L=35 m and a total width of the conducting channel of W=360 µm.

After fabrication of the electrical contacts, in a second lithographic step an oxygen plasma treatment is used to remove the MoS2 single-layer film from the channel area except for a

180 µm wide region across which the SAW propagates. Thus, we ensure correspondence of the electrically and acoustically addressed film area. Fig. 1 (c) shows a PL map of the contact region after electrode deposition and removal of extraneous MoS2 film.

Lithographic Patterning: All lithographic patterning of the IDTs and contact electrodes proceeded in a single exposure step using an electron beam writer and PMMA as resist.

Contacts were fabricated by sequential deposition of 10 nm of Ti followed by 60 nm of Au in an e-beam evaporation tool. Subsequent lift-off defined the active structures. MoS2 was selectively removed in a second e-beam exposure step and subsequent oxygen plasma treatment at a plasma power of 200 W at a pressure of 500 mTorr for 13 s.

Measurement techniques:

SAW excitation and SAW transmission experiments: For measurement of the AEC and

AEV, the output of an RF signal generator was amplified and connected to one of the IDTs.

The RF characteristics of the IDTs and SAW transmission lines were characterized using a vector network analyzer measuring scattering parameters of the RF network, in particular the scattering parameters S11 (reflection) and S21 (transmission, insertion loss).

Electrical characterization: 2-point characterization was performed using a Keithley

K2400 source meter unit (SMU). For 4-point characterization, a K2400 SMU was used only as a constant current source (no measurement probes connected) and the voltage at the potential probes was recorded directly by a K2000 digital multimeter (DMM). The gate voltage was applied by a Keithley K2600 SMU which measured the gate leakage current at the same time. Short-circuit AEC and open-circuit AEV were recorded using a K2400

SMU with VSD = 0 and ISD=0, respectively.

Optical spectroscopy: The photoconductivity experiments relied on red (660 nm) and infrared (850 nm) pulsed semiconductor lasers (Picoquant) with a 80 MHz repetition rate and a pulse duration ≤ 100 ps). Photoluminescence and Raman spectroscopy as well as mapping utilized a Horiba LabRAM HR spectroscopy system using a 532 nm excitation laser and an 1800 line/mm-1 grating. Results and Discussion

Here, we report on two technological advancements: the scalable fabrication of a hybrid

MoS2-LiNbO3 FET/electro-acoustic device that combines FET functionality with response to SAWs and the cross-validation of the respective signals; we demonstrate the versatility and power of this approach by measurement of the photoconductivity of a single-layer

MoS2 film.

A schematic of our hybrid device is shown in Fig. 1a and the fabrication procedure is summarized in the Methods section. The device consists of two components: (i) a SAW delay line formed by a pair of interdigital transducers (IDTs) and (ii) a monolayer MoS2-

FET centred in between the two IDTs. This configuration enables us to probe and manipulate the electrical characteristics of the FET by exciting and detecting SAWs interacting with carriers in the MoS2. IDTs are used for all-electrical excitation and

−1 detection of SAWs. On LiNbO3, SAWs propagate at a velocity vSAW=3,980 m s ; our IDTs are designed for a frequency of fSAW=160 MHz corresponding to a design wavelength λSAW=25 μm. Their arrangement allows measurement of the scattering parameter, S21, that is, the SAW transmission from one IDT to the other. In Fig. 1bwe plot S21 as a function of the RF signal applied to the sending IDT. In this trace, the delay

48 line resonance frequency is resolved as a 40-dB high transmission maximum very close to the nominal design frequency of fSAW=160 MHz. This RF characterization demonstrates high efficiency generation, transmission and detection of SAWs on the LiNbO3 host substrate even after its exposure to the MoS2 growth conditions. FET fabrication was performed on a monolayer region of the as-grown MoS2 film; its single-layer thickness was validated by scanning PL spectroscopy. An overview map demonstrating millimetre-scale growth of monolayer MoS2 onto 128°YX-cut LiNbO3 is presented in Supplementary Fig.

1. After PL characterization, a 4-terminal MoS2 FET is monolithically defined on the

LiNbO3 substrate in the region of maximum emission of monolayer MoS2. The FET is fabricated to be located in between a pair of IDTs. Figure 1c shows a 400 μm × 350 μm spatial map of the characteristic monolayer MoS2 PL emission in the channel region12,13 of the FET. The PL intensity is encoded in colour scale with red/dark regions corresponding to high/low count rates, respectively. PL mapping is used to determine the extent of the monolayer film before device fabrication and it confirms the presence of a monolayer MoS2channel in the completed FET. Intensity variations are likely due to variations in the film domain size as shown in ref. 25. In all other areas, the MoS2 film was selectively removed to avoid any signal contributions from these regions. The four vertical lines indicate reflection from the Au contact lines; the four diffuse spots close to the corners of the panel represent gold alignment marks used during fabrication of the FET channel.

The upper and lower boundaries of the FET channel in Fig. 1c are aligned with the SAW propagation path. Thus, we ensure tight correspondence of the electrically and acoustically addressed film area. The LiNbO3substrates serves as the (휖푟~50) dielectric for back gating

49 to ensure full FET operation and we provide full electrical characterization of this device.

We show the respective wiring diagrams for 4-point and 2-point configuration as insets in

Fig. 1 (a), respectively.

In Fig. 1 (d) we compare normalized PL spectra from MoS2 films grown under nominally identical conditions on LiNbO3 (black) and on a SiO2/Si reference substrate (red). For both samples a PL peak is clearly resolved, corroborating the monolayer nature of the MoS2 (the supplementary material SFig. 2 also provides Raman spectroscopy). However, MoS2 grown on 128°YX-cut LiNbO3, yields PL signal at photon energies larger by 40-50 meV; we attribute this shift to the fivefold larger thermal expansion coefficient of LiNbO3 of

−6 −1 훼LiNbO3 = 12.6 ∙ 10 K compared to that of Si of 훼Si = 2.6 ∙

10−6K−1 near room temperature . These dissimilar values cause a net relative compressive strain of 0.35% for the MoS2-film on LiNbO3 during cool-down from growth temperatures. Compressive strain is expected to give rise to a blue shift of the PL emission.

Extrapolating the data on uniaxial tensile stress reported in Ref. of ∆퐸 = 60 −

70 meV per 1% strain, we expect a blue shift of ~23 meV, about ½ of the observed blue shift. Using the value of ∆퐸 = 300 meV per 1% strain reported by Hui et al. for compressive strain in trilayer MoS2, the expected blue shift amounts to 105 meV, which is larger than the value observed here. Thus, our observation of a blue shift is compatible in magnitude with recent work and corroborates a rigid connection of the MoS2 film to the

LiNbO3 substrate, a precondition for maximum interaction with the SAW.

FET characterization

We expect our hybrid device to exhibit FET properties. Due to the very large dielectric

50 constant εr ~ 50 for this cut of LiNbO3, moderate electric fields D = εrVGS /dsub = ±40 kV/cm can be achieved by applying VGS = ±40V between the LiNbO3 backside (thickness dsub =

500 µm) and the MoS2 layer. We test FET-operation of our hybrid device by measurement of its transport characteristics as a function of a back gate voltage (VGS) across the LiNbO3 substrate. In Fig. 2 (a) we plot a set of output characteristics (ISD vs. VSD), recorded in 4- point configuration, for different back gate voltages ranging between VGS = ±40V. As VGS is tuned from negative to positive polarity, we observe the expected reduction of the sheet resistance due to accumulation of electrons in the MoS2 monolayer. This observation clearly demonstrates FET operation in our hybrid device in the linear regime and the formation of an n-type transport channel, in agreement with prior work. Transfer characteristics (ISD vs. VGS) recorded in 2-point configuration are plotted in Fig. 2 (b) for different VSD. Again, the increase of ISD as VGS is tuned to positive bias at constant VSD is consistent with n-type character. We note that in the data a small leakage current through the substrate was subtracted for clarity; the supplementary Fig. 3 (a) contains the graphs prior to subtraction of gate leakage. The transfer characteristics exhibit a small hysteresis, which may arise from poling effects of LiNbO3 at the interface to the MoS2 layer. We note that MoS2-based FETs on dielectric Si/SiO2 substrates have been found to be sensitive to the local environment, and in particular to the surrounding gas atmosphere. Adsorption and desorption of impinging gas atoms and molecules have been suggested as an origin of an hysteretic I-V characteristics. From the turn-on behavior we are able to derive the threshold voltage Vth, marked in Fig. 2(b). From this analysis we can determine the field effect

퐿∙푑푠푢푏 1 푑퐼푆퐷 mobility in our device given by 휇퐹퐸 = ∙ ∙ , with L and W being the length and 푊휖푟휖0 푉푆퐷 푑푉퐺푆

51 width of the channel, respectively and dsub denotes the thickness of the LiNbO3 substrate.

An example analysis is presented in SFig. 3 (b) and the VSD-dependence of the values Vth and µFE are presented in SFig. 3 (c) and (d), respectively. From the output characteristics set we are able to extract the channel’s electrical properties as a function of VGS. Fig. 2 (c) depicts the channel resistance and conductance extracted from 2-point output characteristics evaluated at VDS = 0 and plotted versus VGS.. Moreover, from a linear fit of the conductance for VGS > 20 V, we can determine µFE and Vth from the slope and from the intersection at ISD = 0, respectively. We performed an analogous analysis on the 4-point output characteristics that is presented in SFig. 4 of the supplementary information. Table

1 summarizes the results for µFE and Vth; the error estimates originate from the accuracy of the linear fit and from the standard deviation of twelve VGS up- and down-sweeps for output and transfer characteristics, respectively. The values for µFE and Vth derived from these independent sets of data are in good agreement. We note that the values obtained on our highly piezoelectric architecture are competitive with back-gated devices fabricated by exfoliation on the Si/SiO2 platform.

Acousto-electric effect

Having established the electrical functionality of our hybrid device, we validate its acousto- electric transport properties. Acoustoelectric effects are expected within the transmission band of the SAW delay line. The frequency dependence of the corresponding scattering parameter S21 is plotted in Fig. 3a. First, we measure the short-circuit (VSD = 0) acousto- electric current (AEC) (Fig. 3b) in a 2-probe configuration as a function of an RF signal of varying frequency and power PRF applied to each of the two IDTs. For a forward

52 propagating SAW excited by constant PRF, we observe that the AEC exhibits a characteristic frequency dependence. This dependence faithfully reproduces the S21 data.

As the propagation direction of the SAW is reversed, the polarity of the AEC reverses: this finding indicates that the propagation direction of the SAW determines the direction of the carrier flow between the two contacts (i.e., momentum transfer between the SAW and the mobile carriers in the MoS2 film). The observed polarities provide an independent verification of n-type majority charge carriers in the MoS2 film. We note that the different

AEC levels measured for the two IDTs at constant PRF arise from a combination of variations in their absolute conversion efficiencies, different distances from the location of our measurements, and different SAW attenuation along the propagation path. The lower amplitudes of the AEC compared to reports on graphene on LiNbO3 are expected due to the lower carrier concentrations in our MoS2 films compared to zero-bandgap graphene.

Second, we explore the PRF power-dependence of the acousto-electric effect for both SAW directions in a complementary experiment by measuring the open circuit voltage in a 4- point configuration (Fig. 1 (b)) with open connection to the back contact. Here, the total current between the two outer contacts is set to ISD = 0 and the acousto-electric voltage

(AEV) is picked up between the two inner contacts. In Fig. 3 (c) we plot the measured AEV as a function of PRF (in mW) applied for a forward (black) and reverse (red) propagating

SAW. We observe the expected linear power dependence of the acousto-electric effect. We note that the acousto-electric current and voltage represent sound-driven constant current and voltage sources, respectively. Such an “acoustic battery” is remotely driven by the

SAW.

Contact-free Photoconductivity Probe

Having established the functionality of our hybrid device, we proceed by applying it to the measurement of the photoconductivity of the MoS2 layer. MoS2 single-layer material exhibits a pronounced photoconductive response to optical (above bandgap) irradiation.

SAWs provide an extremely sensitive and fast conductivity (σ) probe and are particular suitable to the characterization of poorly conductive films. The SAW attenuation coefficient is given by

퐾2 ∙푘 휎 푒푓푓 SAW ⁄휎푚 Γ = ∙ 2 (1) 2 (휎 ) 1+ ⁄휎푚

2 In this expression 퐾푒푓푓 = 0.056 is the electromechanical coupling efficiency, kSAW the

−6 1 SAW wavevector and 휎푚 = 푣SAW ∙ 휖0(1 + 휖푟) = 1.8 ∙ 10 the characteristic sheet Ω□ conductivity. This value corresponds to a characteristic channel conductance of 퐺푚 = 휎푚 ∙

푊 ~ 18.5 µS in our device. This value is larger than the measured channel conductance 퐺 < 퐿

1.2 µS derived from FET the characteristics of Fig. 2.

To characterize the SAW transmission along the delay line, we measured the S21 scattering parameter, that is, the transmitted SAW intensity from one IDT to the other. In the upper panel of Fig. 4a, we plot the variation of S21 as a function of time. At t=6 s, a diffraction- limited spot in the centre of the hybrid device is irradiated for Δt=5 s by either a red

(hν=1.87 eV) or an infrared laser (hν=1.46 eV) source at 1 mW power. The red laser is resonant with the fundamental optical transition of MoS2 on LiNbO3, while the photon energy of the infrared laser is less than the optical bandgap of MoS2. We resolve a pronounced photoresponse for the red laser, manifesting itself in a reduction of the

54 transmitted SAW signal (ΔS21 <0). Such an increase of the attenuation is expected from equation (1) since photogeneration of electrons and holes leads to an increase of G, while still remaining in the G<0) is clearly resolved.

The agreement of the global features of ΔS21 and ΔG is remarkable: both channels show quasi-instantaneous responses as the laser is switched on and off, which is attributed to the presence or absence of photogenerated carriers in the MoS2 layer. The associated processes occur on a timescale faster than the acquisition time of each data point of 250 ms. In addition to this fast contribution, a response on longer (seconds to minutes)50 timescales is resolved clearly.

In Fig. 4b, we present a detailed optical pump power series. In this experiment, the laser source is repeatedly switched on for 5 s every minute. The optical pump power is initially increased in ΔPlaser=0.1 mW steps from Plaser=0.1–1 mW and then reduced to Plaser=0. The corresponding optical power pattern is plotted in the lower panel of Fig. 4b. The upper and centre panels compare the measured SAW (ΔS21) and current (ISD) responses for VSD=+100 mV and −100 mV, respectively. Clearly, both the SAW attenuation and the

FET current scale with the laser power in a nonlinear manner similar to the observations of Yin et al.49 and Lopez-Sanchez et al.51 but different from the short-channel devices of ref. 50. While the sign of ISD depends on the polarity of VSD, ΔS21decreases irrespective of the VSD polarity. Furthermore, the amplitude of ΔS21 only depends on Plaser and is independent of the applied VSD. These facts prove that electro-acoustic and

FET operation do not interfere. The component of the photoresponse with the longer time constant50 leads to the accumulation of higher sheet conductivity over the full 20-min duration of the experiment. Such processes are frequently observed in 2D materials and are typically attributed to traps at the interface to the substrate or in the material itself. In ref. 50, we demonstrate the composition dependence of this phenomenon for MoS2(1- x)Se2x alloys. Conclusion

Direct growth of MoS2 onto the 128°YX-cut of LiNbO3 permits acousto-electric spectroscopy on the TMD overlayer as validated by the hybrid device assembled in this work. This finding opens many new avenues of research: while our hybrid device relied on metal contacts to the TMD film so as to validate congruence between electric transport and

SAW-based conductivity measurements, subsequent experiments may dispense with the contacts, thereby allowing entirely contact-free transport measurements on TMD films.

Moreover, the tight coupling of the TMD film to the underlying substrate as being indicated by the blue-shift of the PL signal suggests that not only acousto-electric but also acousto- mechanic spectroscopy on TMD films may be possible. In such experiments the SAW exerts tensile or compressive strain allowing measurement of the coupling of the dynamic deformation to the electronic degrees of freedom of the TMD material. Spin and charge excitations in recently discovered TMD-based quantum dots could also be controlled dynamically by SAW-driven deformation potential coupling and Stark effect. The rigid connection of the TMD layer to the LiNbO3 is crucial for such acousto-mechanically driven approaches, since it ensures close coupling of the SAW to the film. We also highlight that our device fabrication used exclusively scalable techniques avoiding transfer or exfoliation steps. This paves the road toward the incorporation of TMD films as, e.g., optically-active elements, into conventional and inexpensive LiNbO3-based SAW devices of a type similar to those currently used e.g., as frequency filters in cell phones. As a consequence, we foresee that the fundamental device concept introduced in this manuscript will attain widespread application both in the fundamental study of the properties of TMD films and in the technological realm where optically-active thin, inorganic and durable films are desired: our SAW device remained functional for 9 months in air withstanding multiple intermittent thermal cycles of heating to temperatures as high as > 450 K and cooling to as low as < 10 K in vacuum in the meantime. Measurements on different TMD materials show promising initial results and will be reported on once completed.

Figures

ISD ISD (a) VGS VGS VGS VGS VSD VSD ISD ISD + - - + + - + -- + + - Micro+ scope + V V MoS2 - SD MoS2 MoS2 - SD MoS2 1 2 3 4 1 o2 b3j e1 4ct 2 ive3 4 1 2 3 4

LiNbO3 LiNbO3 LiNbO3 LiNbO3

SAW

IDT LiNbO3 Electrical contacts (b) (c) (d) Energy (eV) 1.97 1.94 1.91 1.88 1.85 1.82 1.80 1.77 SAW Transmission

-30 50 meV MoS2 on

1.0 LiNbO3 -40

SiO2

y t

i 0.8 )

-50 s

(

1 0.6

-60 .

m r

o 0.4

-70 N

0.2 -80

120 140 160 180 200 0.0 630 640 650 660 670 680 690 700 Frequency (MHz) 100 mm Wavelength (nm)

Figure 16 (a) – Sample – (a) Schematic representation of our hybrid MoS2-LiNbO3 device. Four Ti/Au electrodes form the contacts of a FET fabricated on CVD-grown MoS2. Two opposing, non-impedance matched IDTs are used to excite SAWs propagating across the MoS2 FET. The insets show the electrical wiring configurations for 4-point (left) and 2-point (right) measurements. The sample was excited optically using a 50x microscope objective with a numerical aperture of NA = 0.55. (b) SAW transmission between the IDTs across the FET device shows a pronounced 40 dB maximum at the design frequency fSAW = 160 MHz. (c) PL map of the active FET region (scale bar: 100 µm). Monolayer MoS2 PL intensity (color coded: red high intensity, black low intensity) is detected only in the channel region. Reflection from the FET contacts and alignment marks is clearly visible. (d) Comparison of single point PL spectra obtained on SiO2 (red) and our 128°YX-cut LiNbO3 substrate (black) reveals a blueshift attributed to compression of the MoS2 film.

(a) 1.0 (b) 0.8 (c) 1.2 V (V) V (mV) 2-point GS SD 125 40 0.6 600 1.0 V 0.5 20 300 th

0 0.4 100 ) 0 )

0.8 S W

-20 -300 m

(

-40 0.2 ( )

) -600 e

A A

0.0 e 0.6

(

0.0 t

I u

s 50 i

0.4 d s

-0.2 n e

-0.5 o R 25 C -0.4 0.2 4-point 2-point -1.0 -0.6 0 0.0 -1.0 -0.5 0.0 0.5 1.0 -40 -20 0 20 40 -40 -20 0 20 40 V (V) V (V) V (V) SD GS GS

Figure 17 – FET operation of hybrid MoS2-LiNbO3 device – (a) Output characteristics (ISD vs. VSD) for different gate voltages VGS recorded in 4-point configuration. For large negative VGS the device is weakly conducting; an n-type channel is formed for positive VGS. (b) Transfer characteristics (ISD vs. VGS) for different source-drain voltages VSD recorded in 2-point configuration shows pronounced increase of |ISD| at positive VGS due to formation of an n-type channel. (c) Channel resistance (red) and conductance (blue) as a function of VGS extracted from 2-point output characteristics at VSD=0. 2 For positive VGS a linear fit indicates a mobility µFE = 33±5 cm /Vs and a threshold voltage Vth = 5.5±1.5 V. The latter agrees well with that derived from the data in panel (b), as summarized in Table 1.

(a) -20

-40

)

( -60

1 2 S -80 SAW transmission

(b) 15 dBm Forward 10 dBm propagating 3 5 dBm VSD = 0

) 2

(

n e

r 1

u C

5 dBm 10 dBm Reverse -1 15 dBm propagating

150 155 160 165 170 Frequency (MHz)

ISD = 0 15

)

m (

t l

o 0 V

-5 Forward propagating Reverse propagating -10 0 50 100 150 RF Power (mW)

Figure 18 – Acousto-electric spectroscopy – (a) Frequency band of the SAW transmission between IDTs plotted as the scattering parameter S21. (b) Acousto-electric current (AEC) as a function of radio frequency applied to the IDTs for different RF power levels PRF. Current measurements were performed in a 2-point short circuit (VSD = 0) configuration. The forward and reverse propagating SAWs were excited by either of the two opposing IDTs. They yield acousto-electric currents of opposite sign. (c) Acousto-electric voltage (AEV) as a function of PRF measured in 4-point, open circuit configuration (ISD = 0). For both SAW propagation directions the expected linear dependence is well reproduced. The signs of the acousto-electric currents and voltages correspond to n-type conductivity of the film.

(a)

0.0 )

B -0.2

(

2 -0.4

S SAW Transmission D -0.6 Red Laser -0.8 Infrared Laser 0.4 P hotoconductance 0.3 V = 100 mV

) SD S

m Red Laser

0.2 ( Infrared Laser

G 0.1 D 0.0 0 10 20 30 40 50 60 Time (s) (b) 0.19 V = +100mV 0.0 SD

0.18 -0.2

0.17 )

A )

-0.4 m

(

r r

S -0.6 0.16

D C

-0.8 0.15

-1.0 V = -100mV 0.0 SD -0.14 -0.2

-0.15 )

A )

-0.4 m

(

e 2

-0.16 r r

S -0.6

D C

-0.8 -0.17 SAW Electrical

-1.0 -0.18 )

1.0

W m

( 0.8

e 0.6

o 0.4

a 0.2

i t

p 0.0

O 0 300 600 900 1200 Time (s) Figure 19 – Photoconductance spectroscopy – (a) Comparison of the time-dependent photoresponse detected by the change of the transmitted SAW intensity (ΔS21) with the change of the 2-point conductance (ΔG) of the FET. Red and black traces were recorded for Plaser=1 mW excitation by a red and infrared laser, respectively. These lasers are switched on for Δt=5 s at t=6 s. Both the instantaneous and persistent features of the photoresponse are consistently resolved by both measurement techniques. For excitation with an infrared laser, no photoresponse is detected, proving that the signal detected for the red laser indeed stems from the MoS2 monolayer. (b) Comparison of ΔS21 with ISD under photoexcitation using a red laser. The laser is switched on every 1 min for Δt=5 s. Each successive minute Plaser is increased by 0.1 mW until Plaser=1 mW is reached. Subsequently, Plaser is decreased to 0 mW in steps of ΔPlaser=100 μW as shown in the lower panel. Upper and centre panel compare the SAW transmission (ΔS21, red) and photocurrent (ISD, black) for VSD=+100 mV and −100 mV, respectively. Direct correspondence between ΔS21 and ISD is confirmed: while ΔS21 reduces irrespective of voltages, the sign of ISD is determined by the polarity of VSD.

Chapter 7: WS2 Band Structure

The following is taken from an article published in Applied Physics Letter, in collaboration between myself, Iori Tanabe, and other students of Ludwig Bartels and

Peter Dowben. Introduction

Transition metal dichalcogenides (TMD) have attracted keen interest as novel 2- dimensional (2D) semiconductor materials because they combine a direct band gap and a spin-orbit split valence band, thus providing a mechanism for the magneto-electric control of any hole carriers. Several groups have reported fabrication of transistors with WS2 as the semiconductor channel [1-6], with a high (roughly 105) on/off current ratio observed at room temperature [5]. In comparison, exfoliated MoS2, the archetypical 2D TMD

2 semiconductor, has achieved room-temperature mobilities of at least 200 cm /(V·s) (and much more at low temperatures [7]) as well as on/off ratios of 108 [8]. Even higher room-

2 temperature values of up to 500 cm /(V·s) have been reported for CVD grown MoS2 [9] as well as for WSe2 [10]. In these reports, TMD devices exhibit n-type behavior with the exception of WSe2, which shows p-type behavior.

Prototypical devices have been manufactured by exfoliation of bulk TMD materials, yet for technological applications a reliable method for producing films of the desired monolayer or few-layer thickness is required. Here we describe measurements that validate the material quality of few-layer WS2 thin films grown by chemical vapor deposition

(CVD) and reveal properties of the band structure near the valence band edge. Our

62 approach combines CVD growth, optical characterization, synchrotron band-mapping at sub-micron spatial resolution, transport measurements, and accompanying DFT based calculations. We focus on the electronic structure of the material at the band edges because the valence band maximum and conduction band minimum determines transport properties and imposes limits on the maximum attainable performance.

Methods

The samples were grown by CVD, utilizing WO3 and elemental sulfur as precursors. In order to provide sufficient chemical potential of the tungsten precursor during growth, a high temperature of 1000 ◦C was chosen. Otherwise, the film growth followed the procedure for MoS2 outlined in Ref. [11]. Films intended for transport measurements were grown on 300 nm SiO2/Si substrates, whereas samples for angle resolved photoelectron spectroscopy (ARPES), utilize Si substrates with a very thin (<1 nm) oxide film, so as to allow for reliable charge neutralization during measurements. Before and after ARPES measurements, the samples were characterized utilizing photoluminescence and Raman spectroscopy, as well as atomic force microscopy and optical imaging (see Supplementary

Fig. 1 [12]).

The ARPES experiments were performed at the 3.2 L spectromicroscopy undulator beamline of the Elettra light source at a temperature of 110 K using a photon energy of 74 eV. The incident radiation was linearly polarized (along the horizontal direction) and focused to a ~0.6 µm diameter spot by means of a Schwarzschild objective [13]. An incident angle of 45◦ with respect to the sample surface was used to optimize surface sensitivity. The ARPES data were acquired using a hemispherical electron energy analyzer 63 with a combined energy resolution of ~50 meV and angular resolution of ±0.33◦. The sample was mounted onto a scanning stage, which enabled positioning and raster imaging with respect to the fixed photon beam. Photoelectron intensity distribution maps I(kx, ky,

E) were taken from microscopic areas of the WS2 sample by rotating the electron energy analyzer with respect to the sample using a two-axis goniometer. This approach matches the one we used to obtain the band structure of single layer WSe2 in Ref. [14].

Results and Discussion

Figure 1(a) shows the experimental band structure of multilayer WS2(0001) obtained from the second-derivative of the ARPES display plots. The valence band maximum is located at the Brillouin zone center (Γ̅ point) and not the zone edge (K̅ point), in contrast to the monolayer (Figure 2). This finding agrees with theoretical predictions [16] and results of our calculated DFT band structure shown in Figure 1(b). We attribute the shift of the valence band maximum from the K̅ point to the Γ̅ point to the increasing width or greater interlayer splitting at the Γ̅ point in multilayer WS2, [15,16]. Our measurements find the energy difference between the top of the valence band at the Γ̅ point and at the K̅ point,

ΔΓ→Κ, to be 380±20 meV.

As in our joint experimental and theoretical investigation of single layer WSe2 [14] and

MoS2(0001) [17], we performed DFT calculations using the super cell method. We employed a plane-wave basis set at a cutoff energy of 500 eV and the projector-augmented wave (PAW) [18,19] technique as implemented in the Vienna ab-initio Simulation Package

(VASP) [20,21]. The generalized gradient approximation (GGA) in the form of Perdew-

Burke-Ernzerhof (PBE) functional [22] was applied to describe the exchange-correlation of the electrons together with the pairwise DFT-D3 correction [23] to account for van der

Waals (vdW) interactions. The Brillouin zone was sampled on a (15 × 15 × 1) k-point mesh. Our calculations were performed on for supercells comprised of 1, 2, 3, 4, and 5 repetitions of the WS2 trilayer separated by sufficient vacuum (15 Å ) to decouple the layer stacks in adjacent periodic supercells. The calculated layer thickness dependent band structures for WSe2 are shown in Figure 2. As expected, the valence band maximum is found to be at the K̅-point for the single-layer material and at the Γ̅ point for the bilayer and higher thicknesses. This is consistent with our experimental band structure (Figure 1b).

The experimental width of the valence band in the vicinity of the center of the Brillouin zone increases from 0.3 eV for bilayer WS2, to 0.8 eV for the trilayer, and 1.1 eV for the pentalayer, which is in good agreement with results from our DFT calculations as seen in

Figure 2d. Thus, the WS2 film thickness affects the bandwidth in addition to the location of the valence band maximum and the relative binding energy positions of the local band maxima at these two locations, i.e. the energy difference between the top of the valence band at the Brillouin zone center and zone edge, ΔΓ→Κ . Our results confirm the computational predictions of Ref. [16]. Our DFT calculations show that the valence band at Γ̅ is derived mainly from the chalcogen pz and W dz2-r2 orbitals. As the transition metal dichalcogenide thickness increases from the single layer to the bulk, the interaction between the stacked WS2 layers first gives rise to a sequence of bands near Γ̅ (dispersing in the plane) near the top of the valence band. As the material becomes thicker than the few layers investigated in this study, these sub-bands merge into a bulk band that disperses

65 along the Γ-L direction (i.e., perpendicular to the (0001) plane), as soon as the film is thick enough to support a Bloch like wave function. Because the valence band maximum is located at the Γ̅-point in our multilayer film, the spacing and effective hole mass of this sequence of bands is important for determining the overall electronic properties of layered

WS2. Our calculated effective masses of the different sub bands presented in

Supplementary Fig. 2 [12] show the top of the valence band at Γ̅ (blue in Supplementary

Fig. 2) to be characterized by a hole effective mass of a few times -1 me and lower with increasing film thickness.

For spintronic applications of WS2, one of the most crucial properties is the spin-orbit splitting (soc) at the top of the valence band, which is dominated by the W dxy and dx2-y2 weighted bands near the Brillouin zone edge at K̅. Our experimental value of 420±20 meV and DFT result of 422 meV for soc at K̅ are in close agreement with previously reported measurements of soc of 425±18 meV [24]. The spin-orbit splitting can in principle depend on film thickness, but it does not vary much, as indicated in Table 1: values between 425 meV [25-27] and 577 meV [15] were reported for the single-layer limit. The soc for bulk

WS2 is modestly smaller than that for WSe2, which was reported to lie between 450±10 meV [28] and 500 meV [28-31]. This includes our own experimental determination of

490±10 meV [47]. In contrast, soc is much smaller for MoS2 (Table 1), because the energy level splitting is determined mainly by the spin-orbit coupling which increases with the atomic number Z and depends primarily on the transition metal species, as the top of the valence band derives predominantly from the latter.

∗ ̅ The hole effective mass 푚ℎ at the top of the valence band at the K point is obtained from

ℏ2 푘2 the dispersion of the experimental band mapping according to 퐸 = − ∗ . Values for the 2 푚ℎ

∗ ∗ hole effective masses, 푚ℎ,푢푝 = -0.35±0.02 me and 푚ℎ,푑표푤푛 = -0.43±0.07 me , for the upper and the lower spin-orbit components, respectively, were extracted from the experimental band structure. These values agree very well with our DFT calculations for the pentalayer

∗ ∗ slab, which result in 푚ℎ,푢푝 = -0.35 me and 푚ℎ,푑표푤푛 = -0.48 me, respectively. For single- layer WS2, computational predictions of similar values of -0.31 me [32], -0.339 me [33] and

∗ -0.35 me [26] for 푚ℎ,푢푝 and -0.31 me [32], -0.339 me [33] and -0.49 me [26] for

∗ 푚ℎ,푑표푤푛have also been reported.

We now turn to the location of the Fermi level, which is of particular importance for the operation of devices. Our ARPES measurements place the valence band maximum at a considerable binding energy, indicating n-type character for our CVD-grown WS2. We find the top of the valence band at a binding energy of 1.4-1.6 eV, which is comparable to the band gap of bulk WS2, for which values range from 1.4 eV in various transistor [1] and optical studies [34], to values of 1.2 eV [35] obtained from other measurements of the indirect band gap of bulk WS2(0001). These values are on average slightly larger than the calculated band gap of 1.3 eV [16]. Prior photoelectron spectroscopy on bulk single crystal

WS2 has shown a similarly large values for the binding energy of the top of the valence band (1.1 eV) [24], although Ref. [36] placed the valence band much closer to the Fermi level. These prior values may be affected by band bending, which decreases the observed binding energy of the top of the valence band. We note that although our film is multilayer,

67 it is too thin to be affected significantly by band bending in the region of the surface.

Consequently, the ARPES measurements suggest that our CVD WS2 film is robustly n- type, although photoemission is not an explicit test for the majority carrier type. To address this question, we investigated the transistor properties utilizing the same kind of material.

Simple field-effect transistors (FET) were fabricated using a single platelet of monolayer

WS2 grown on SiO2/Si, with the doped substrate functioning as the gate. The 300 nm SiO2 layer acted as the gate oxide and source-drain contacts were fabricated with alumina tunneling barriers. A micrograph of a typical device is shown in the inset of Figure 3.

The source-drain current current-voltage characteristics, shown in Fig. 3 for many different gate voltages, indicate n-type conduction, as a current is observed only a for a sufficiently large positive gate voltage. Supplementary Fig. 3 [12] shows similar findings for multilayer

WS2 and demonstrates explicitly the absence of appreciable current at negative gate voltages, similar to literature results for exfoliated WS2 transistors.

In summary, we find from angle resolved photoemission that multilayer WS2, grown by chemical vapor deposition, is robustly n-type. This finding is in agreement with literature transport measurements on exfoliated material as well as transport measurements on the same CVD material as reported here. The band structure of CVD-grown multilayer WS2 demonstrates the material’s high quality and its suitability for any WS2 application envisioned. The hole effective masses are consistent with expectations, and the experimentally determined spin orbit splitting soc for multilayer WS2(0001), is found to be 420±20 meV at K̅, which is consistent with density functional theory.

Figures

MoS2 WS2 WSe2 monolayer 145±4 [45] ~400 [36] 400 [37] (expt.) 404 [38] 412 [39] 430 [40] 460 [41] 510 [42] 513±10 [14] monolayer 146 (GW) [48] 425 (PBE)[25] 456 [27] (theory) 147 (PBE) [15] 425 (PBE) [26] 463 [15] 148 [27] 426 [27] 462-466 [26] 202 (HSE) [15] 429 (HSE) [26] 461 [33] 202 (HSE) [46] 430 [9] 454-469 [14] 433 [15] 501 [25] 435 (PBE) [15] 500 [43] 440 [32] 630 [44] 456 (GW) [25] 461 [33] 521(HSE) [25] 577 (HSE) [15] bulk (expt.) 196 + 22 meV [24] 420 ± 20a 450±10 [28] 425 ± 18 [24] 490±10 [47] ~450 [36] 500 [29] 500 [30] 500 [31] bulk (theory) 422a 470 [30] 410-466 [24] 480 [47] 570 [24] 540 [43]

TABLE I. The spin-orbit splitting, SOC, near the top of the valence band at the 퐊̅ point of monolayer and bulk MoS2, WS2 and WSe2 Brillouin zone both theoretically calculated and experimentally measured. (a) indicates this work.

Figure 20. (a) The second-derivative image of the experimental band structure of multilayers of WS2 obtained by ARPES along the 횪̅-횱̅ high symmetry direction and (b) the comparison with theoretical calculations for pentalayer WS2 overlaid as dashed green lines. The photon energy is 74 eV. The splitting due to the spin-orbit coupling in the valence band near the 횱̅ point is found to be 420 ± 2 meV.

Figure 21. The DFT calculated band structure of monolayer (a), bilayer (b), trilayer (c), tetralayer (d), and pentalayer (e) WS2, respectively. The reference zero energy level was set to the top of the valance band at 횱̅. For monolayer material, the top of the valence band is located at the 횱̅ point but for 2+ layers it is found at the 횪̅ point. The bandwidths at the 횪̅ point are shown in panel (d). Blue points indicate the calculated positions of the largely tungsten dz2-r2 weighted bands at the 횪̅ point, which increase in number with the number of layers within the slab. Red is the experimental band width at the 횪̅ point, from photoemission, for comparison. For visualization purpose, the center of the band is set to zero.

Figure 22. The characteristics of a gated WS2 monolayer transistor. The source drain currents (Isd vs. Vsd curves) were recorded for different gate voltages Vg ranging from 0 to 70 V. The top inset shows the corresponding transfer characteristics. The bottom inset shows the device as fabricated on the 300 nm SiO2/Si growth substrate. The doped substrate acts as a backgate.

Chapter 8: Tunable Properties of CVD

Growth of Few-Layer MoTe2

The following is taken from an article published in ACS Nano, in collaboration between myself, Thomas Empante, and other students of Ludwig Bartels and Evan Reed. Introduction

The optical band gap of single-layer Mo-based 2H TMDs decreases from 1.87 eV for

MoS2 to 1.55 eV for MoSe2 and 1.1 eV for MoTe2, suggesting the potential for silicon- based photonic applications of the latter.2,3,15 Various reports indicate switching of

MoTe2 between its semiconducting 2H and metallic 1T′ structures exploitation as a phase change material.16−19 Yet while MoS2 and, to a lesser degree, MoSe2 and their

MoS2(1−x)Se2x alloys have been investigated intensively, MoTe2 has found less prolific experimental exploration largely because of its limited stability in air. From the perspective of a field of researchers accustomed to graphene, limited environmental stability is a severe shortcoming, yet we note that the surface of MoTe2 is no less oxidation resistant than that of bare silicon, the premier industrial semiconductor.20,21 A number of schemes for the passivation of MoTe2 surfaces have been proposed; in this work, we cover our films either with a layer of poly methyl methacrylate (PMMA) or by repeated deposition of ∼1 nm of aluminum followed by brief oxidation in air.

Methods

Molybdenum-based TMDs consist of a hexagonal transitionmetal layer sandwiched between two chalcogen layers. In the 2H phase, both chalcogen layers are in registry with each other as well as with a single set of hollow sites of the central Mo layer (Figure 1c).

In contrast, in the 1T phase, the top and bottom chalcogen layers are in registry with different Mo-layer hollow sites (Figure 1a). The 1T′ phase represents a 2 × 1 reconstruction of the 1T phase leading to slight buckling of each atomic plane (Figure

1c). The overwhelming majority of prior publications on MoTe2 have used exfoliated films often utilizing crystals grown by chemical vapor transport22−27 (refs 28−30 indicate exceptions). Exfoliated films can be of very high quality, and they lend themselves to a wide range of exploratory research, yet this procedure lacks a direct pathway to technological realization and produces films exclusively in the phase adopted by the original crystal. A number of methods for postexfoliation phase change have been described utilizing chemical and physical treatment of the MoTe2 film.16−19 In this manuscript, we utilize chemical vapor deposition (CVD) for the preparation of singleand few-layer MoTe2 films,29,30 which allows us access to all three phases. CVD is a process well-established in semiconductor processing, compatible with current tool sets, and eminently scalable.

Results and Discussion

Three MoTe2 phases: Figure 2 shows Raman spectra and optical micrographs of the

MoTe2 films in all three phases. The growth procedure differs only by the cooling rate,

74 and the formation of 1T phase films requires the presence of CO2 in addition to H2.

While we can obtain extended (>10 μm) singlelayer films of 2H MoTe2, we find the growth of uniform singleor few-layer thickness films of 1T and 1T′ MoTe2 to nucleate frequently in a circular fashion around growth seeds. Figure 2 also shows atomic force microscopy profiles revealing the layer thickness of our MoTe2 samples. CVD growth of molybdenum and tungsten disulfides and diselenides reliably leads to triangular islands with straight edges in our lab.31,32 In contrast, MoTe2 films generally do not adopt straight edges, so that the edge shape cannot be used to indicate crystallographic orientation. We found that 1T MoTe2 shows the highest propensity for straight edges.

We discuss the origin of this phenomenon below.

Using density functional theory (DFT), we calculated the phonon spectrum for each structure by means of 3 × 3 supercell, while neither the 2H nor the 1T′ exhibited negative phonon frequencies (see Supporting Information Figure S1), a band of negative frequencies was found for the 1T structure when expanded to a 3 × 3 supercell. This indicates that this phase requires stabilization by extrinsic effects that will be discussed in the following section. Raman spectroscopy is used to identify and characterize the

MoTe2 phases. Samples not quenched during the growth process exhibit Raman peaks at

171 and 233 cm−1 , as shown in Figure 2a. These features agree well with peaks predicted from DFT calculations of the 2H phase at 170 and 230 cm−1 , at a deviation of

0.59% and 1.30%, respectively. Our values also corroborate published results on exfoliated17,22−27 and CVDgrown28−30 2H:MoTe2. Quenching at ∼350 °C leads to an

MoTe2 film (Figure 2b) that exhibits a number of Raman features that are typically

75 associated with the 1T′ phase of MoTe2. Because of the expanded supercell and lower symmetry of this structure, the set of Raman-active modes is wider. In particular, we observe pronounced features at 80 cm−1 , 85 cm−1 , 102 cm−1 , 112 cm−1 , 126 cm−1 , and 162 cm−1 . These match our DFT predictions within an error of 1.25%, 4.49%,

2.00%, 0.90%, 1.61%, and 3.18%, respectively. The Raman modes observed in these films also correspond well to literature values. Quenching the film growth at 450 °C, we observe a Raman spectrum that is clearly distinct from the 1T′ phase (Figure 2c). It is significantly simpler consisting of two prominent modes only at 155 and 242 cm−1 , each of which is slightly broader than is the counterpart in the 2H phase. Comparison to our computational work reveals good agreement of the two experimental Raman modes with the Raman modes of 1T MoTe2, which we predict at 159 and 240 cm−1 , respectively.

Based on this finding, we assign this phase to be 1T MoTe2. We note that the higher- energy mode is consistently broader in the spectral signature. We are not aware of prior experimental observation of this phase.

Band Structure and Semimetallicity. Figure 3 shows the band structure of 1T MoTe2 and compares it to the 2H (left) and 1T′ (center) phases. 1T MoTe2 is metallic; an electronic feature resembling a valence band crosses the Fermi level at the K point by a very small amount; and a feature resembling a conduction band crosses below the Fermi level by a similar, very small amount at a low-symmetry point along Γ- K. The amount of

Fermi level crossing is properties of a semiconducting film including comparatively low conductivity as well as a ready response to an applied bottom gate. Our measurements corroborate this (Figure S6) at a resistance of 570 MΩ at zero gate and VSD = 0.5 V

76 corresponding to a resistivity of 168 Ω cm. Our film shows a mobility μ of 0.03 cm2 /(V s) under gating through 300 nm of SiO2, in line with prior work on CVD films.12,24,29

The 1T′ phase reveals metallic behavior with electrode-to-electrode resistances in the upper kΩ regime. For the 1T material, we find an electrical response with significant sample to sample variation (see below); the conductivity of few-layer 1T MoTe2 films can exceed that of our best single-layer 1T′ devices. The resistivities of the 1T and 1T′ phases of Figure 4 are 2.0 Ω cm and 0.17 Ω cm, respectively. Neither the 1T nor the 1T′ devices of Figure 4a show an appreciable response to back gating. However, the 1T phase exhibits a decreasing resistance with temperatures (inset of Figure 4a) as expected for a semimetal.

Hybrid Phase Films. Slight variation in the MoTe2 growth parameters, such as the temperature or the rate at which the quench occurs, results in uniform films that exhibit

Raman spectra of a combination of two (or all three) MoTe2 phases within a diffraction limited sample spot. We have observed every which pairing and focus on a device that combines the 1T and 2H phases. The Raman spectrum and micrograph of such a film is shown in Figure 2d. The film is 3 layers thick, and the Raman spectrum is practically constant across the entire film region. Figure 4b shows the transport properties between electrodes at successive separation (see inset for device image); a linear fit results in a contact resistance of 17 MΩ (or 0.75 Ω cm2 ) and a channel resistance of 14 MΩ/μm (or

2.7 Ω cm). The Figure S5 shows the device resistance as measured in a 4-point configuration; the values agree with the ones obtained here. 1T MoTe2 has a significantly stronger Raman response than the 2H material. Despite the dominant 1T character of the

77 material’s Raman spectrum, the device exhibits a semiconducting behavior and responds to gating just like the 2H phase, yet the total conductivity exceeds that of our 2H MoTe2 devices by 2 orders of magnitude while lacking by a similar factor compared to the pure

1T device. This finding suggests that judicious tuning of the 1T-2H mixture allows tailoring the conductivity and gate-response of MoTe2-based devices at will.

Conclusion

CVD growth of MoTe2 can provide a material with tunable semiconducting and metallic properties. Hybrid/mixed phases can yield low-resistance gate-able semiconducting 2D films.

Figures

Figure 23. MoTe2 phases and overview of preparative technique. (a− c) Top view onto a sheet of 1T, 1T′, and 2H MoTe2, respectively. The unit cells are indicated. (d,e) CVD growth of few-layer MoTe2 in a tube furnace. The temperature (indicated) at which the growth is quenched determines the resultant MoTe2 phase.

Figure 24. Comparison of the experimental (black) Raman spectra for each phase of MoTe2 with computational predications (colored lines): (a) 2H continuous film, (b) 1T′ island, (c) 1T island, and (d) mixed phase film, as indicated by the presence of 2H Raman peaks in an otherwise 1T film. The AFM line scans indicate the film thicknesses.

Figure 25. Band structures calculations of monolayer films. Left: Semiconducting 2H-MoTe2; center: metallic 1T′-MoTe2; and right: semimetallic 1T′-MoTe2. Spin−orbit coupling effects are included in all calculations.

Figure 26. Transport measurements. (a) source-drain current ISD as a function of source-drain voltage VSD across two-terminal devices fabricated on the MoTe2 materials of Figure 2: 2H MoTe2 (blue, right y-axis) exhibits p-type semiconducting behavior (for gating response, see Figure S6). 1T′ (black) and 1T (green) show metallic, ohmic behavior and significantly increased currents (left yaxis) that correspond to resistances of 0.67 MΩ and 0.14 MΩ, respectively. The inset shows the temperature dependence of the resistance of a 0.5 μm channel of 1T MoTe2 measured in a 4-probe setup. (b) ISD−VSD curves as a function of channel length (measured electrode center to center) for a MoTe2 device with a mixture of 1T and 2H phases: The response is semiconducting despite the low Raman contribution of the 2H phase.

Chapter 9: Interlayer breathing and

shear modes in NbSe2 atomic layers

The following is taken from an article published in IOP Science, in collaboration between myself, Rui He, and other students of C H Lui. Introduction

Atomically thin transition metal dichalcogenide (TMD) niobium diselenide (NbSe2) has recently stimulated strong scientific interest due to its distinctive electronic and magnetic properties. In contrast to the more-studied group-VI TMD semiconductors, such as MoS2,

MoSe2 WS2, and WSe2, bulk NbSe2 is a conductor, which exhibits charge density waves

(CDWs) and superconductivity at transition temperature of TCDW = 33.5 K and TC = 7.2

K, respectively [1, 2]. Two-dimensional (2D) NbSe2 inherits these features, but their properties change significantly as the layer thickness approaches the monolayer (1L) limit. Recent research has reported distinct electronic band structure [3], strongly enhanced CDW order [4] and suppressed superconductivity in 1L NbSe2 compared to the bulk [3, 5]. Superconducting 1L NbSe2 also exhibits Ising pairing of spins due to broken inversion symmetry [5]. These thickness-dependent phenomena indicate that the interactions between the NbSe2 layers play a crucial role for a diverse set of material properties. It is therefore important to study the detailed characteristics of interlayer coupling in NbSe2 to thoroughly understand its rich physics.

The interlayer interactions in 2D materials are closely related to the layer stacking order.

In this respect, the crystallographic structure of NbSe2 crystals is generally different from the common structure of MoS2, MoSe2, WS2 and WSe2 [6, 7]. According to the convention by Wilson and Yoffe [6], the position of the atoms in each TMD atomic plane can be specified by three points in a triangular lattice (a, b, c or A, B, C). The upper

(lower) case denotes the chalcogen (metal) atoms. 1L NbSe2 has the same trigonal prismatic (H) structure as 1L MoS2(denoted as AbA or equivalently AcA) (figure 1). As the layer number increases, however, the stacking order of NbSe2 layers differs subtly from that of MoS2. Multilayer MoS2 exhibits the so-called 2Hc structure, which can be represented as (AbA BaB). In contrast, NbSe2 exhibits the 2Ha structure (AcA BcB), in which the Nb atoms in all the layers are aligned vertically but the Se sublattice is rotated by 60° with respect to that of the neighboring layer [6, 7] (figure 1). It would be interesting to examine how this subtle stacking difference and the metallic nature of

NbSe2 may influence the interlayer interactions. Methods

We prepared NbSe2 samples with layer number N = 1–15 (denoted as 1L–15L) by mechanical exfoliation of high-quality bulk 2H-NbSe2 crystals. Atomically thin samples were first deposited on silicone elastomer polydimethylsiloxane (PDMS) stamps, and afterward transferred onto Si/SiO2 substrates [4]. The sample thickness was identified by the optical contrast (figure 2(a)) and further confirmed by the frequency of the interlayer

Raman modes. To minimize the environmental effects, we covered some samples with hexagonal boron nitride (BN) flakes (thickness 10–20 nm) and stored all the samples in

83 vacuum. We measured Raman spectra using a commercial Horiba LabRam Raman microscope, which provides a frequency range down to 5 cm−1 and a spectral resolution

−1 of 0.5 cm . The NbSe2 samples were mounted inside a helium-cooled optical cryostat with controllable temperature T = 8–300 K. The samples were excited with a linearly polarized 532 nm laser through a 50×objective lens. The incident laser power is kept below 5 mW with a spot diameter of ~2 μm on the samples. The Raman signal was collected in a backscattering geometry and analyzed by the spectrometer. Results and Discussion

−1 Figure 2(b) displays Raman spectra of 1L and 2L NbSe2 in the range of 10–50 cm , measured at room temperature in vacuum conditions. The 1L spectrum does not display any noticeable Raman feature in this range, but the 2L spectrum exhibits two distinctive

−1 peaks at 19.5 and 33 cm . Because of their absence in the spectrum of 1L NbSe2, we deduce that these two peaks arise from the interaction between the two NbSe2 layers.

Similar interlayer Raman features have been reported in graphene and other TMD bilayers [11, 23, 34]. According to these prior studies, we attribute the 19.5 cm−1 peak to the doubly degenerate interlayer shear (S) mode, and the 33 cm−1 peak to the interlayer breathing (B) mode. These frequencies allow us to extract the coupling strengths between two NbSe2 layers, which are important material parameters for the thickness-dependent superconductivity and CDW phenomena. In a simple model of two coupled layers, the interlayer mode frequency (ω) is related to the monolayer mass density (μ) and the interlayer force constant (κ) as ω2 = 2κ/μ. From our measured frequencies, we estimate

18 −3 that κ = 27 and 78 × 10 N m for the shear and breathing modes in 2L NbSe2,

18 −3 respectively. These values are very close to those in MoS2 (κ = 28 and 87 × 10 N m for the shear and breathing modes, respectively) [23, 25, 26]. Therefore, the interlayer van der Waals forces are similar for the metallic NbSe2 and the semiconducting MoS2.

Figure 3(a) compares the Raman spectra of NbSe2 samples with N = 2–15 layers to that of bulk NbSe2, all measured at room temperature. In order to reveal the breathing modes more clearly, we used uncapped samples in all these measurements. For clarity, we removed the broad background by subtracting a smooth baseline for each spectrum. The multilayer samples exhibit two sets of interlayer modes: one shear mode that blueshifts with increasing N, and one layer breathing mode that redshifts with increasing N. Their thickness-dependent frequencies can be well described by a coupled-oscillators model with only nearest-layer coupling. In this simple model, the layers are treated as a linear chain of N masses connected by constant springs. An N-layer system possesses N − 1 normal modes with frequencies [11]:

Here n = 1, 2, ... N − 1 is the mode index from high to low frequency, and ωo is the shear

(breathing) mode frequency of bulk NbSe2 at the Brillouin zone center. For the shear

−1 mode, the bulk frequency can be directly measured to be ωo = 28 cm (see the bulk spectrum in figure 3(a)). For the breathing mode that is Raman inactive in the bulk, we can deduce the bulk frequency to be from the 2L frequency A direct comparison between theory and experiment shows that these modes correspond to the highest-frequency shear branch (n = 1) and the lowest- frequency breathing branch (n = N − 1) (figure 3(b)). 85

In addition to the thickness-dependent frequency, we have also examined the line width of the interlayer modes as a function of layer number (figure 3(c)). As the NbSe2 sample thickness increases from N = 2 to 15 layers, the breathing mode narrows from a line width of 5 cm−1−1 cm−1. A major factor is the change of phonon lifetime [11]. The breathing mode redshifts dramatically from 34 to 5 cm−1 as N increases from 2 to 15

(figure 3(b)). The reduced phonon energy at higher layer number suppresses the anharmonic decay into the acoustic phonons of lower energy. Consequently, the breathing-mode phonons have a longer lifetime and hence sharper Raman line for thicker

NbSe2 samples. Similar narrowing behavior of breathing modes has been observed in few-layer graphene and TMDs [11, 23]. On the other hand, one may expect an opposite

(slightly broadening) behavior for the shear mode that blueshifts moderately as N increases, similar to that occurs in few-layer graphene [11]. However, our shear- mode spectra show a decrease of line width from 2.7 to 1 cm−1 as Nincreases from 2 to 15 layers. This unexpected narrowing behavior is attributed to environmental effects and sample degradation. As shown in figure 2(c), exposure to air broadens considerably the shear mode of uncapped 2L NbSe2 samples. As the external environment predominantly affects the surface layer, its overall influence diminishes in thicker samples. To fully account for the line width of the interlayer Raman modes, we have to consider the competing contribution of phonon lifetime and surface degradation.

Finally, we comment on the possible influence of CDWs on the interlayer phonon modes in NbSe2. NbSe2 hosts robust in-plane CDWs with 3 × 3 supercells at low temperature

(TCDW = 33.5 K) [1, 3, 39]. The origin and characteristics of these CDWs are an on-going

86 research topic. We have examined the influence of CDWs on the interlayer phonons by measuring the Raman spectra of 2L NbSe2 from T = 300 to 8 K (figure 4). In this experiment, we used a BN-capped 2L sample to ensure high sample quality. In our

Raman results, the breathing mode is weak but observable at T > 100 K (figures 4(a) and

(b)). At T < 100 K, the breathing mode is overshadowed by a broad Raman band (>30 cm−1). The shear mode remains prominent at all temperatures. It exhibits a slight blue shift in frequency as well as a decline of line width and intensity as the temperature decreases (figures 4(d)–(f)), which we attribute to the lattice contraction and the decrease of thermal fluctuation and phonon population at lower temperature, respectively.

Notably, we observe the shear mode to evolve smoothly from T = 300 to 8 K, i.e., well below the bulk TCDW (33.5 K)—CDW formation does not cause a discontinuity in the frequency, line width, or intensity of the shear mode. Similar results are also found in the

4L and bulk NbSe2, which are less sensitive to any surface degradation (figures S2 and

S3 in the supporting information), as well as in a prior Raman study of few-layer

NbSe2 that displays broader shear mode features [4].

Conclusion

In conclusion, we have investigated the interlayer breathing and shear modes in

NbSe2 atomic layers by ultralow-frequency Raman spectroscopy, group-theory analysis and DFT calculations. Although the layer stacking order of NbSe2 differs from MoS2,

MoSe2, WS2 and WSe2, it exhibits the same symmetry and Raman selection rules, as well as similar interlayer coupling strength and thickness dependence of interlayer phonon

87 modes. These interlayer phonons in NbSe2 are found to be insensitive to CDW transition.

The information gained in our research should be useful to understand the thickness- dependent properties of NbSe2. Moreover, the experimental technique established here can be applied to study a broad set of further properties of NbSe2 and other TMDs, such as the superconducting phase at low temperature.

Figures

Figure 27. Comparison of the crystal structure of bilayer NbSe2 and MoS2. (a) The schematic 2Ha structure of NbSe2, with both the top and side views. The atom location can be specified by the a, b, c (or A, B, C) points of a triangular lattice, as denoted in the top view. The 2Ha structure can thus be represented as (AcA BcB), where the upper and lower cases denote the chalcogen and metal atoms, respectively. (b) The schematic 2Hc structure of MoS2, as in panel a. Similar 2Hc structure also exists for MoSe2, WS2 and WSe2.

Figure 28. (a) Optical image of an exfoliated NbSe2 sample on a Si/SiO2substrate. The sample is partially covered by a boron nitride (BN) flake. The 2L and 3L NbSe2 regions and the BN-capped region are denoted by red, yellow, and black dashed lines, respectively. (b) Low-frequency Raman spectra of 1L and 2L uncapped NbSe2. A dashed baseline is added to the 2L spectrum to highlight the weak breathing mode. The inset displays the schematic interlayer shear (S) and breathing (B) modes. (d) Comparison of the shear mode of 2L NbSe2 with and without the BN cap layer.

Figure 29. (a) Low-frequency Raman spectra of NbSe2 with layer number N = 2–15 and bulk NbSe2. For clarity the spectra are vertically displaced with the broad background removed by subtracting a smooth baseline. The green and red dashed lines highlight the shear (S) and breathing (B) modes, respectively. The 2L breathing mode is magnified by a factor of three for clarity. The orange curves in the 3L spectrum denote the fitted shear and breathing modes that overlap with each other. (b) Frequency of the shear and breathing modes as a function of layer number. The solid lines are the predicted phonon frequencies from the linear-chain model. The open triangles are the predicted phonon frequencies from DFT calculations. (c) The full width at half maximum (FWHM) of the shear and breathing Raman modes as a function of layer number.

Figure 30. (a) Temperature dependent color map of the low-frequency Raman spectra of a BN- capped 2L NbSe2 sample at T = 8–300 K. The shear (S) and breathing (B) modes are denoted. (b) Selected spectra at T = 8, 30, 100, 200 and 294 K from panel (a). (c) Schematic side-view configurations of 2L NbSe2 without (top) and with (bottom) charge density waves (CDW) at high and low temperature, respectively. The dash boxes denote the unit cell of each structure. (d)–(f) The frequency, full width at half maximum and integrated intensity of the shear Raman mode as a function of temperature. The dash lines in (d) and (e) are guides for the eye. The dashed line in (f) is the predicted (1 + n) temperature dependence according to the shear-mode phonon population (n).

Chapter 10: Efficacy of Light Emission

Enhancement in Nanoscale Antenna

The following is taken from an article published in ACS photonics, in collaboration between myself, Mohammad Tahersima, and other students of Ludwig Bartels, Evan

Reed, and Volker Sorger. Introduction

The structural, chemical, and electronically similar monolayer semiconducting TMDs

MoS2, MoSe2, WS2, and WSe2 provide light emission in the visible and near-infrared spectral regions (1.1−2.0 eV).1−4 The spatial confinement of carriers to a three atom-thin physical plane and the weak dielectric screening in atomically thin materials lead to high oscillator strengths and strong Coulombic interactions between the excited electron− hole pairs. This results in strong binding energies allowing for observation of excitons at room temperature.11−18 In addition to neutral excitons, charged trions can also be excited in the presence of residual excess charge carriers. These quasi particles consist either of two electrons and one hole (A−) or one electron and two holes (A+ ). Therefore, electrostatic gating modifies the spectral weight of charge-neutral excitonic species in TMDs.14−17

Moreover, given the large binding energy of the excitons, the formation of states consisting of two excitons (biexciton) is possible in TMDs, whose photoluminescence

(PL) emission is red-shifted due to the additional binding energy.

Plasmonic nanoantennae fall into the former category, and they can synergistically (a) increase the absorption cross-section, thereby enhancing the pump efficiency, (b) accelerate the internal emission rate via the Purcell effect through the nanoscale optical mode of the antenna, and (c) improve emission out-coupling to free space via impedance matching (transformer action). As such, optical antennae increase the excitation rate while simultaneously enhancing the local density of states (DOS) in the emission process, which modifies (here accelerates) the spontaneous emission rate known as the Purcell effect.25 Hence, these optical antennae behave as electromagnetic cavities that strongly modify spontaneous emission of fluorescence in the spatial and spectral proximity.

Methods

Our work uses WS2 single-layer islands prepared by chemical vapor deposition (CVD).

CVD offers an, in principle, scalable source of TMD material for future technological implementation of this approach. Samples studied here consist of WS2 monolayer flakes grown directly by CVD on 100 nm of thermal SiO2 on a Si wafer. The bright-field microscopy image in Figure 1a shows the bare substrate appearing purple, the single- layer material as dark blue, and thicker material regions as lighter blue areas. To characterize our emitter material, micro-Raman, micro-PL, and differential reflectance spectra were taken on WS2 flakes on a SiO2/Si substrate at room temperature. We confirm the thickness of the WS2 material by the appropriate difference in the intensity of the interlayer phonon mode A1g between material identified as multilayer and single- layer (Figure1b) as well as a corresponding difference in PL intensity.42,43 We further

93 analyze the Raman signal by a multi-Lorentzian fitting of all recognizable features in both monolayer and few-layer WS2 (Figure 1b). The PL emission spectrum of a monolayer WS2 flake is dominated by the A exciton peak at 633 nm (∼1.96 eV) wavelength. After deposition of an Al2O3 spacer layer, the PL emission spectrum of monolayer WS2 slightly red-shifts from the pristine value of 633 nm (∼1.96 eV) to 637 nm (∼1.95 eV) (Supporting Information). We attribute this red-shift to a combination of strain imparted by the electron beam evaporation of Al2O3 and weak electronic interaction with the Al2O3 film. Following the deposition of the antennae, we find an enhancement of the PL emission of monolayer WS2 flakes. The 75 nm dimer cavity exhibits the largest increase by a factor of 3.2 (2.7) in peak intensity (in integrated PL count) relative to emission of the reference sample (bare monolayer WS2 flake) at the same excitation power density (Figure 2). In contrast, monomer and dimer antennae with a radius of 200 nm do not substantially alter the PL peak or intensity of monolayer WS2.

We note that some fluctuations of the enhancement values and spectral response shifts can be expected, because the optical properties of the WS2 monolayer are strongly influenced by the nanoantenna surface plasmon that can alter the effective pumping of

WS2, generation rate of Figure 2. Collected photoluminescence (PL) emission from monolayer WS2 is enhanced when it is placed under a plasmonic monomer or dimer antenna cavity with a resonance close to that of the emission wavelength. Electron beam lithography (EBL) has been used for fine-tuning of the optical antenna dimensions on the scale of 10’s of nanometers (see Methods). (a) PL intensity of CVD-grown monolayer

WS2 before and after fabrication of four different optical antennae. Insets are SEM

94 images of each type of optical cavity; the scale bar is 400 nm. (b) Full width at halfmaxima (fwhm) and enhancement of integrated PL emission from the as-grown sample and for each optical antenna. (c) Dark-field optical image of the 637 nm PL emission from a monolayer WS2 under an optical excitation of 532 nm. Fitting the beam intensity profile shows that 90% of the Gaussian beam power is within an 800 nm beam spot size. Our modeling of the monomer antenna with a 75 nm radius reveals a scattering efficiency of about 1.8 and 6.3 at an excitation wavelength of 532 nm and emission wavelength of ∼640 nm, respectively, in which the emission of the WS2 is in resonance with the resonance of the cavity (Figure 3b). Since the monomer is electromagnetically a simple dipole under excitation, we observe the expected monotonic resonance redshift with increasing dimension of the monomer particle (dashed lines), while the discrepancy from a linear trend can be explained by dispersion. Results and Dicussion

Regarding the internal photon generation enhancement process of the TMD−cavity system, we focus on the near- field enhancement and Purcell product in eq 2. The overall fluorescence enhancement of monolayer WS2 by the plasmonic optical antenna can be expressed as the product of excitation rate enhancement, the spontaneous emission probability enhancement (Purcell effect), and the outgoing portion of the spontaneous emission. We calculate the spatial distribution of the electromagnetic field profile at the location of the monolayer WS2 and, for comparison, at the cross-section of the optical antenna for both the excitation and emission wavelengths (Figure 4) (see Methods). The dimer metallic nanoparticles separated by a small gap (4 nm in Figure 4b) support

95 hybridized plasmon resonances because of the capacitive coupling between the plasmon modes of each nanoparticle. Thus, the often-cited high-peak-field enhancement (here

60×) is observed only if a few-atom small point emitter would be positioned precisely inside the gap center (Figure 4c). Even if this is achieved (e.g., using dye molecules), the signal could not be collected from this hot-spot only, because even the highest resolution near-field light collector such as a NSOM averages its signal over an area of hundreds of square nanometers.46 Since the 2-D TMD cannot be placed. Inside the gap nor right underneath the metal nanoparticle (to avoid quenching), the only logical position would be to place it below or above the antenna, separated by a thin spacer (Figure 4a). Thus, when we measure the field enhancement at the position of a TMD flake residing at an optimized length of 8 nm beneath the metal nanoparticle, the peak field enhancement is only 3.4-fold (Figure 4c). We observe a similar trend for the 100 and 200 nm radius dimer antennae (Supporting Information).

Conclusion

In conclusion, we have demonstrated that optical nanoantennae can be used to control the emitting properties of monolayer TMDs. This control was achieved using two types of metallic cavities (monomer vs dimer) at four different sizes. These emission dynamics were also supported by numerical calculations. In particular, we have demonstrated the fluorescent enhancement of 2-D materials, and unlike quantum dots there is an areal average effect that has to be taken into account. We have also observed band narrowing of the emission response when the resonance of the cavity corresponds to the emission

96 wavelength of monolayer WS2. Both monomer and dimer nanoantenna architectures are scalable to emission resonances of other members of the TMD family as well including

MoTe2, which emits at a telecommunication wavelength in the near-infrared. The demonstrated nanoantenna-controlled emission from a monolayer WS2 flake could open a pathway to visible light sources based on lithographically fabricated nanoantennae supporting a variety of optoelectronic applications

Figures

Figure 31. Optical characterization of CVD-grown WS2 at room temperature. (a) Optical images of as-grown WS2 on 100 nm SiO2 on a silicon substrate. (Inset) Comparison of PL emission of monolayer and multilayer WS2. (b) Room-temperature Raman spectra from a monolayer WS2 flake, including Lorentzian peak fits for the 532 nm laser excitation.

Figure 32. Collected photoluminescence (PL) emission from monolayer WS2 is enhanced when it is placed under a plasmonic monomer or dimer antenna cavity with a resonance close to that of the emission wavelength. Electron beam lithography (EBL) has been used for fine-tuning of the optical antenna dimensions on the scale of 10’s of nanometers (see Methods). (a) PL intensity of CVD-grown monolayer WS2 before and after fabrication of four different optical antennae. Insets are SEM images of each type of optical cavity; the scale bar is 400 nm. (b) Full width at halfmaxima (fwhm) and enhancement of integrated PL emission from the as-grown sample and for each optical antenna. (c) Dark-field optical image of the 637 nm PL emission from a monolayer WS2 under an optical excitation of 532 nm. Fitting the beam intensity profile shows that 90% of the Gaussian beam power is within an 800 nm beam spot size. White scale bar = 5 μm.

Figure 33. Cold cavity response. Absorption loss (Qabs) (a) and far-field scattering efficiency (Qscat) (b) mapping of monomer nanodisc antennae for a radius range of 50 to 200 nm. (The black and white points represent our fabricated antennae for emission and excitation wavelengths, respectively.) Absorption loss (c) and far-field scattering efficiency (d) for a dimer nanoantenna of single 75 nm radius and in a gap sweeping range from −150 nm (overlapping charge transfer mode) to 150 nm (gap plasmon mode). The points represent our fabricated 75 nm dimer antenna. The scale bar shows the ratio for absorption or scattering cross-section to geometrical cross-section of each type of antenna. The dashed lines are guides to the eye.

Figure 34. Electric field intensity enhancement (|E|/|E0|) comparison of dimer and monomer antennae showing comparable enhancement at the TMD position, which is separated by a spacer layer to avoid quenching. (a) Schematic of the proposed optical antenna types for PL enhancement of monolayer TMDs. (b) Side view of the electric field intensity magnitude enhancement distribution in a 4 and 25 nm gapped 75 nm radii dimer antenna and a 75 nm radius monomer antenna, respectively, from top to bottom. (c) Comparison of electric field intensity enhancement for the same antennae shown in top view and two different z-normal plane positions at the midpoint of the antenna and at the z-normal plane where the TMD layer is positioned. The maximum value, the averaged value over the area of the beam spot size of the simulation, and the averaged value over the area of geometrical antenna cross-section of (|E|/|E0|)2 is reported for each case.

100

Figure 35. Photon generation rate. Spatial map of the quantum efficiency (a, c) and enhancement in the total radiative rate of Fp × QE (b, d) for a dipole emitting at a z normal plane corresponding to the position of the TMD in the fabricated device. The dashed white lines represent the position of the dimer antennae.

101

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