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Electronic Transport in Atomically Thin Layered Materials by MASSACHUSETTS INGTIME Britton William Herbert Baugher OF TECHNOLOGY B.A. Physics, Philosophy JUL 0 1 2014 University of California at Santa Barbara, 2006 LIBRARIES Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2014

Signature redacted Author ...... Department of Physics May 23, 2014 Signature redacted Certified by... Pablo Jarillo-Herrero Associate Professor / I Thesis Supervisor Signature redacted

Accepted by ...... Krishna Rajagopal Chairman, Associate Department Head for Education

Electronic Transport in Atomically Thin Layered Materials by Britton William Herbert Baugher

Submitted to the Department of Physics on May 23, 2014, in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Abstract

Electronic transport in atomically thin layered materials has been a burgeoning field of study since the discovery of isolated single layer graphene in 2004. Graphene, a semi-metal, has a unique gapless Dirac-like band structure at low electronic energies, giving rise to novel physical phenomena and applications based on them. Graphene is also light, strong, transparent, highly conductive, and flexible, making it a promising candidate for next-generation electronics. Graphene's success has led to a rapid expansion of the world of 2D electronics, as researchers search for corollary materials that will also support stable, atomically thin, crystalline structures. The family of transition metal diclialcogenides represent some of the most exciting advances in that effort. Crucially, transition metal dichalcogenides add semiconducting elements to the world of 2D materials, enabling digital electronics and optoelectronics. Moreover, the single layer variants of these materials can posses a direct band gap, which greatly enhances their optical properties. This thesis is comprised of work performed on graphene and the dichalcogenides

MoS 2 and WSe 2. Initially, we expand on the family of exciting graphene devices with new work in the fabrication and characterization of suspended graphene nanoelec- tromnechanical resonators. Here we will demonstrate novel suspension techniques for graphene devices, the ion beam etching of nanoscale patterns into suspended graphene systems, and characterization studies of high frequency graphene nanoelectromechanical resonators that approach the GHz regime. We will then describe pioneering work on the characterization of atomically thin transition metal dichalcogenides and the development of electronics and optoelectronics based on those materials. We will describe the intrinsic electronic transport properties of high quality monolayer and bilayer MoS 2 , performing Hall measurements and demonstrating the temperature dependence of the material's resistivity, mobility, and contact resistance. And we will present data on optoelectronic devices based on electrically tunable p-n diodes in monolayer WSe 2 , demonstrating a photodiode, solar cell, and light enmitting diode.

Thesis Supervisor: Pablo Jarillo-Herrero Title: Associate Professor

3 4 Acknowledgments

This thesis had a long, complex, and convoluted life, and its successful completion was only made possible by the ever-present guidance and help of my family, friends, and colleagues.

I would like to thank my advisor, Pablo, for his guidance and patience, my thesis committee for their stewardship of my thesis, my group for all of their insight and assistance, my teammates, Hugh and Yafang, Tchefor and Kevin, and Max, for all their hard work and their direct contributions to this thesis, my family and friends for their encouragement, and my wife, Allie, for her untiring love and support.

5 6 Contents

1 Introduction 15

1.1 M otivation ...... 15

1.2 Outline...... 17

1.3 Graphene ...... 18

1.4 Dichalcogenides ...... 20

2 Fabrication of Electronics Based on Atomically Thin Layered Mate- rials 23

2.1 Introduction . ... . 23

2.2 Graphene Suspension 24

2.3 Current Annealing 28

2.4 Ion Beam Etching. 33

2.5 Acknowledgements 36

3 Etching of Graphene Devices with a Helium Ion Beam 37

3.1 Introduction ...... 37

3.2 Motivation ...... 38

3.3 R esults ...... 39

3.4 Conclusions ...... 42

3.5 Methods ...... 43 3.6 Acknowledgments ...... 43

4 Approaching GHz Resonant Frequencies in Suspended Graphene

7 NEMS Resonators 45 4.1 Introduction ...... 45 4.2 Motivation . 46 4.3 Device Fabrication 46 4.4 Mixing Current 49 4.5 Resonant Modes. 53 4.6 Mode Fitting . 55 4.7 Conclusions ... 58 4.8 Acknowledgments 58

5 Intrinsic Electronic Transport Properties of High Quality Monolayer

and Bilayer MoS 2 59 5.1 Introduction ...... 59 5.2 Motivation ...... 60 5.3 Device Fabrication ..... 61 5.4 Resistivity Measurements. . 62 5.5 Hall Measurements .. ... 65 5.6 Conclusions ...... 68

6 Optoelectronic Devices Based on Electrically Tunable p-n Diodes in a Monolayer Dichalcogenide 69 6.1 Introduction ...... 69 6.2 M otivation ...... 70 6.3 Device Fabrication ...... 72 6.4 Transport in Gate Controlled p-n Junctions ...... 72 6.5 Optoelectronics ...... 76 6.6 Conclusions ...... 80 6.7 M ethods ...... 81

A MoS 2 Supplementary Information 83 A. 1 Fabrication ...... 83

8 A.2 Metal Insulator Transition ...... 86 A.3 Hall Measurements ...... 86 A.4 Mobility ...... 87 A.5 Acknowledgments ...... 89

B WSe 2 Supplementary Information 91 B.1 Device Fabricatioi ...... 91 B.2 M id-Gap Current ...... 94 B.3 Schottky Barriers ...... 95 B.4 Acknowledgements ...... 99

9 10 List of Figures

1-1 Atomically layered materials with diverse electronic and optoelectronic

prop erties ...... 17

1-2 Schematic and electronic band structure of graphene ...... 18

1-3 Overview of a TMD crystal structure and band structure ...... 20

2-1 Suspended graphene structures ...... 24

2-2 Current annealing of suspended graphene devices ...... 30

2-3 Etching suspended graphene with a gallium based focused ion beam

(FIB) and a helium ion beam ...... 33

2-4 Etching suspended graphene by electron beam assisted water etching 36

3-1 Schematic of a graphene device ...... 38

3-2 Etching suspended graphene with a helium ion bean ...... 40

3-3 Electrically isolating suspended graphene with a helium ion beam . . 41

3-4 Etching graphene on SiO 2 with a helium ion beam ...... 42

4-1 Graphene NEMS device schematics, image, and electrical readout .. 48

4-2 Resonance maps, avoided crossings, quality factor, and high frequency

m o d es ...... 53

4-3 Fitting resonance modes and mode softening ...... 57

5-1 MOS2 device schematics, images, and two-ternminmal transport measure-

m en ts ...... 60

5-2 Contact resistance and four-terminal resistivity of monolayer and bi-

layer M oS 2...... 64

11 5-3 Field-effect and Hall mobilities as a function of back-gate voltage and

temperature for monolayer and bilayer MoS 2 ...... 66

6-1 Gate-controlled monolayer WSe 2 p-n junction diodes ...... 71 6-2 Current through the device as a function of doping configuration .. . 75

6-3 Photodetection in monolayer WSe 2 ...... 77 6-4 Photovoltaic response and light emission ...... 79

A-i MoS 2 flake AFM and step heights ...... 84

A-2 Effect of annealing on two-terminal resistance of MoS 2 devices ... . 85

A-3 Hall measurements of MoS 2 ...... 87 A-4 Contact resistance and four-terminal resistivity of monolayer device Mi 88 A-5 Room temperature mobilities and leakage current ...... 88

B-1 Optical micrograph and AFM with step height of the main device . . 92 B-2 Optical micrograph the EL device ...... 93 B-3 Temperature dependence of mid-gap current ...... 94 B-4 Photocurrent and reflected light image ...... 97 B-5 Dependence of photovoltaic power generation on laser power ... .. 98 B-6 Reflected and emitted light image ...... 98

12 List of Tables

A. 1 Device Fabrication Parameters ...... 84 A.2 Metal Insulator Transition ...... 86

13 14 Chapter 1

Introduction

1.1 Motivation

Electronic transport in atomically thin layered materials has been a burgeoning field of study since the discovery of isolated single layer graphene in 2004 [1]. Single layer graphene is a sheet of carbon atoms bonded together in a flat, hexagonal, honeycomb lattice, exactly one atom thick. The inherently two dimensional (2D) nature of graphene, as a one atom thick material, and its highly symmetric honeycomb lattice combine to give it a myriad of new and interesting properties. Graphene is light [2], strong [3], transparent [4], highly conductive [5], and flexible [3]. It has a unique gapless Dirac-like band structure at low electronic energies [6, 7, 8, 9] (see Fig. 1-la).

It has the one of the highest thermal conductivities of any know material [10]. And it has a Young's modulus five tinmes greater than that of steel [3]. Already, since its discovery, many novel and exciting applications have been realized utilizing graphene's unique properties [11, 12, 13].

This thesis will expand on the family of exciting graphene devices with new work in the fabrication and characterization of suspended graphene nanoelectromechanical resonators. Here we will demonstrate novel suspension techniques for graphene devices, the ion beam etching of nailoscale patterns into suspended graphene sys- temus, and characterization studies of high frequency graphene nianoelectromechanical resonators that approach the GHz regime.

15 Graphene's success has led to a rapid expansion of the world of 2D electronics, as researchers search for corollary materials that will also support stable, atomically thin, crystalline structures. Graphene, a semi-metal, is limited in the scope of electronic device applications it can realize. Insulators and semiconductors are needed to complement graphene and to broaden the capabilities of 2D atomically layered materials (ALMs) into a fuller range of electronic devices. Hexagonal boron nitride, an insulator that can be exfoliated down to a single atomic sheet, just as graphene can, was one of the first ALMs to be added into this growing class of materials [14] (see Fig. 1-1b). Structurally, it is very similar to graphene, with the carbon atoms replaced by alternating atoms of boron and nitrogen. This alternating structure breaks the sublattice symmetry of graphene, creating a large band gap of 5.5 eV. The ultra-flat surface, high crystallinity, inertness, and atomic layer control over thickness conspire to make hexagonal boron nitride an outstanding dielectric [15, 14]. More recently, transition metal dichalcogenides (TMDs) were isolated in atomically thin layers, adding semiconducting elements to the world of 2D materials. Semiconducting TMDs, such as

MoS 2 and WSe 2, are made of three atomic sheets: two sheets of chalcogen atoms, such as sulfur or selenium, on the top and bottom, and one sheet of transition metal atoms, such as molybdenum or tungsten, in the middle. This alternating structure of atoms breaks the sublattice symmetry seen in graphene, creating a band gap, and enabling TMDs' use in digital electronics and optoelectronics. What is more, the single layer variants of these materials posses a direct band gap, which greatly enhances their optical properties verses the indirect gap of the bulk (see Fig. 1-1c).

This thesis provides pioneering work into the characterization of these new atomically thin TMDs and into the development TMD based electronics and optoelectronics. First, we will describe the intrinsic electronic transport properties of high quality monolayer and bilayer MoS 2 , performing Hall measurements and demonstrating the temperature dependence of the material's resistivity, mobility, and contact resistance. We will then present data on optoelectronic devices based on electrically tunable p-n diodes in monolayer WSe 2 , demonstrating a photodiode, solar cell, and light emitting diode (LED).

16 Semi-Metal: Insulator: Semiconductor: (a) Graphene (b) Boron Nitride (c) Dichalcogenide

E kX

Figure 1-1: Atomically layered materials with diverse electronic and optoelectronic properties. (a) Graphene, a semi-metal, can serve as a high-mobility conductor and transparent gate electrode. (b) Hexagonal boron nitride is an ultra-flat insulator useful as a gate dielectric with high breakdown voltage. (c) Transition metal dichalcogenides are semiconductors with a direct band gap in their monolayer forms. They also posses a valley degeneracy and a spin-split valence band.

1.2 Outline

Here we present a brief introduction to the world of atomically layered materials (ALMs) and their properties. We will first describe graphene and both its electrical and mechanical properties as they pertain to suspended resonators. Next we will describe the electrical and optical properties of the transition metal dichalcogenides

MoS 2 and WSe 2. Chapter 2 will discuss device fabrication, specifically emphasizing graphene suspension techniques, current annealing suspended graphene, and the etching of suspended graphene devices with ion beams. In chapter 3 we will demonstrate the electrical isolation of suspended graphene by etching it with a helium ion beam. In chapter 4 we present a study of suspended graphene resonators with resonant frequencies approaching the GHz regime. Chapter 5 elucidates the intrinsic electronic transport properties of high-quality monolayer and bilayer MoS 2 . And chapter 6 demonstrates optoelectronic devices based on tunable p-n diodes in monolayer WSe 2 .

17 1.3 Graphene

(a) (b) 1

Zr 0.5 JK

-0.5

-1 -V. -1 -0.5 0 0.5 1 Graphene Lattice kx (T/a)

1.5

0 0 0

-1.5

-3 0 -0.1

Figure 1-2: Schematic and electronic band structure of graphene. (a) Schematic of the 2D hexagonal honeycomb lattice of graphene. (b) An energy contour plot of graphene's conduction band. Energy increases from dark to light. Minima occur at the K and K' points. (c) A construct of the full band structure of graphene. (d) A zoomed in view of the band structure near one of the K points. At low energies the band structure is well described by a Dirac cone. The valence and conduction bands can be seen to meet at the K-points, creating a gapless material.

Graphene, a one atom thick sheet of graphite, is a 2D array of carbon atoms arranged in a honeycomb lattice (Fig. 1-2a). The excitement surrounding its electronic prop-

18 erties stems from its peculiar band structure (Fig. 1-2b and c) [1, 9, 16, 14], which at low energies can be approximated by two non-equivalent conical valleys where the charge carrier dynamics are described by the Dirac equation (Fig. 1-2d) [6, 8]. The symmetric electron arid hole valleys result in charge carriers with linear energy dispersion up to -1eV and a vanishing band gap energy. This peculiar band structure naturally leads to exotic electronic behavior [17, 18, 19, 20, 21, 22].

In addition, single layer graphene has been shown to exhibit unmatched mechanical properties. Recent studies have shown graphene to posses the highest Young's modulus of any existing material at 1 TPa, a third order elastic stiffness of -2 TPa, and an intrinsic stress of 130 GPa [3]. Coupled with its low density, graphene's superior mechanical behavior makes it an ideal material for nanoelectromechanical systems (NEMS), with properties which compare favorably to those of the current state of the art NEMS [23, 24, 25, 26]. Moreover, suspended graphene has a high thermal conductivity of ~4000 W/n-K (exceeding that of diamond and graphite) [10]. This means that graphene resonators may have substantially reduced heat dissipation problems compared to conventional NEMS. Additionally, due to its light mass, graphene resonators can be designed for high frequency applications. This can be achieved, for example, by etching arid suspending subrmicron-sized graphene devices from exfoliated graphene flakes. Such high frequency resonators can be used as ultrasensitive mass, charge, arid chemical sensors. Any extra weight/charge added to such a resonator will appreciably change its mass/doping, arid thus its electromechanical response.

In this thesis we investigate the electromiechanical properties of suspended graphene based nanodevices, probing the coupling between electronic [1, 9, 16] and mechanical [27, 28, 29, 3, 30, 31] degrees of freedom. We fabricate and characterize ultra-high quality devices, demonstrating the mechanical motion of graphene based resonators and probing their electromechanical coupling. The tunability of these resonators prove very useful to explore their potential as ultra-sensitive mass, charge, arid chemical sensors. By changing geometry arid size, graphene resonators with varied resonance frequencies are fabricated. These experiments set the stage for further work

19 aimed at cooling a graphene resonator mechanical mode to its quantum mechanical ground state. We build the foundation for the integration of the excellent properties of graphene into next generation nanoelectromechanical systems and sensors.

1.4 Dichalcogenides

(a) side view (b) top view (c) band structure

Figure 1-3: Overview of a TMD crystal structure and band structure. (a) The struc-

ture of a bulk TMD, such as MoS 2 or WSe 2 , consists of layered triangular prisms of a transition metal atoms (grey) and chalcogen atoms (yellow). (b) Top view of a mono-

layer TMD. (c) Schematic band structure of MoS 2 near the K points that are relevant to transport and optical properties at low energy. The hexagonal network of Mo and S atoms gives rise to K and K' valleys as in graphene, but because the structure lacks inversion symmetry, TMDs acquire a band gap and spin-orbit coupling.

The most recent additions to the toolbox of ALMs are the transition metal dichalcogenides, a class of compounds of the form MX 2, where M is a transition metal, such as molybdenum or tungsten, and X is a member of the chalcogen, or oxygen, group of the periodic table, such as sulfur or selenium. The TMDs display an astonishing variety of physical properties, including metals (NbS 2 and VSe2 ), semi-metals (WTe2 and TcTe ), semiconductors 2 (MoS 2, WSe2 , and PdS2 ), and superconductors (NbSe 2 and TaSe2 ) [32]. The most common TMDs have a layered structure in which the transition metal atom is sandwiched between two layers of chalcogen atoms forming a triangular prism (Fig. 1-3a). Viewed from above, each X-M-X monolayer forms a

20 hexagonal lattice with alternating M and X atoms (Fig. 1-3b). The band structure of layered TMDs is similar to that of hexagonal boron nitride, but with a smaller band gap and strong spin-orbit coupling (Fig. 1-3c). Multi-layer TMDs have an indirect band gap with the valence band maximum at the F point. However, the gap changes to a direct band gap for monolayers, with the direct gap at the two inequivalent valleys, K and K' [33, 34, 35]. This indirect-to-direct transition between multi-layer and imonolayer TMDs significantly enhances the optical properties of monolayer TMDs relative to their bulk forms [35].

MoS 2 and WSe2 have been studied in bulk form for several decades [32], but single atomic layers have only been isolated in the past few years with the advent of the mechanical exfoliation technique used to isolate graphene [1]. Initial transport

and optoelectronic measurements on few-layer MoS 2 , MoSe 2, WS2 , and WSe 2 have been done by several groups [36, 37, 38, 39, 40, 41], and field effect mobilities up to 200 cm 2 /Vs for monolayers [36] and 700 cm 2 /Vs for thicker films [42, 43] have been demonstrated. These early results show that TMDs are promising materials with all opportunity to be combined with graphene and hexagonal boron nitride to fabricate high quality electronic TMD devices. We expect that combining the strengths of different ALMs will also be a vital rianotechnology for photonic and optoelectronic applications.

In this thesis we fabricate and characterize ultrahigh quality TMD devices from

MoS 2 and WSe 2. The device technologies demonstrated here integrate ALMs into electronic devices to probe the physics and applications of this family of transparent and flexible materials. This thesis develops the foundation of an ALM-based architecture for next generation electronics and optoelectronics.

21 22 Chapter 2

Fabrication of Electronics Based on Atomically Thin Layered Materials

2.1 Introduction

Here we present studies in the fabrication of nanoscale electronics based on atomically thin layered materials. We discuss various methods of suspending graphene structures including: suspending graphene films on transmission electron microscope

(TEM) grids, deposition of flakes over trenches, transferring flakes over contacts, and etching out the substrate from below. We then describe three techniques for current annealing suspended graphene, and present transport data showing the improvements in conductivity and mobility that can be achieved. Finally, we demonstrate the pat- ternless etching of suspended graphene using a gallium based focused ion beam, a helium ion beam, and electron beam assisted water etching.

23 2.2 Graphene Suspension

(a) 8 (b) 10

-4

-8 -10 -8 -4 0 4 8 -10 0 10 X (pm) X (pm)

3O0000

-2

-4 ' -4 -2 0 2 4 0 1 2 3 4 X (pm) X (pm)

Figure 2-1: Suspended graphene structures. (a) An SEM image of a CVD grown graphene film suspended over an amorphous carbon sheet with 2.5 Pm holes in it. The amorphous carbon sheet is supported by a TEM grid. Inset: A zoomed out SEM image of the sample showing the gold TEM grid. (b) an optical image of a graphene flake deposited on SiO 2 with 1.5 pm holes pre-etched in it. inset: An SEM image of one hole partially covered by the graphene flake, showing the flake is suspended. (c) AFM image of a graphene flake transferred over gold contacts. Inset: A zoomed out optical image of the same device. (d). An SEM image of a device suspended by etching out the SiO 4 substrate from below it. Insets: A zoomed out optical image of the device is shown in the upper left. The resistivity and mobility of the device, both before (blue) and after (yellow) suspension are shown in the upper right. 24 Many promising applications for devices based on suspended graphene have been proposed in the literature: from resonators and mass sensors to nano-sieves and pres- suremeters [30, 2, 5, 27, 44, 28, 29]. Suspending the graphene takes unique advantage of graphene's mechanical, optical, and electrical properties to form devices with such new and interesting functionality. Here we investigate four different ways to fabricate suspended graphene devices and compare their results. We suspend graphene by transferring a chemical vapor deposition (CVD) grown graphene film onto a transmission electron microscope (TEM) grid; we directly deposit exfoliated graphene onto

pre-patterned holes etched in an SiO 2 substrate; we transfer exfoliated flakes on top of gold electrodes; and we etch out the SiO 2 substrate from below contacted graphene flakes.

For strictly mechanical or optical devices, where electrical contact is not neces- sary, it is possible to make a large number of suspended graphene membranes by transferring a CVD grown graphene film onto a TEM grid. For this method we use a gold TEM grid with a lattice of 100 pim wide squares that is covered in an amorphous carbon film with 2.5 pim holes in it. Such TEM grids are commercially available from suppliers such as Structure Probe Instruments.

The graphene film is grown in a CVD oven on a copper substrate. The filn is gently released from the copper below with an acid etch, leaving the graphene to float on the surface of the liquid. We then scoop the film out of the liquid using the TEM grid, thus suspending the film over the grid. A scanning electron microscope (SEM) image of graphene suspended over a TEM grid is shown in Fig. 2-la. And a zoomed out view of the TEM grid, with the graphene film half covering the amorphous carbon, can be seen in the inset to that panel.

This technique produces a large quantity of suspended graphene membranes very quickly and easily. It is ideal for testing further processing or measurement schemes, or obtaining large number statistics. It is also, quite naturally, ideal for TEM studies.

The drawbacks are that it the TEM grid is too delicate for adding electrical contact, CVD graphene is inherently lower quality than exfoliated graphene, many membranes will be rippled, torn, or broken, and there can be significant residue left on the film

25 that is difficult to remove. For our purposes, however, these devices offer an excellent test bed for etching experiments using ion beams.

A second suspension method is to directly deposit exfoliated graphene flakes onto pre-patterned holes etched in an SiO 2 substrate. For this method we use electron beam lithography to pattern holes in the oxide ranging from 1 Pm to 5 Pm in diameter. We then etch out these holes using reactive ion etching. After cleaning the substrate, we deposit exfoliated graphene and scan the wafer under an optical microscope, searching for graphene that happens to cover the holes. An optical image of a graphene flake covering a few holes is shown in Fig. 2-1b and an SEM image of a half covered hole is shown in the inset.

This technique provides us with high quality single crystal graphene sheets that are accessible to mechanical, optical, and electrical measurements. So long as the graphene flake fully covers the hole, the membrane can survive resist spinning, lithography, and metal evaporation to make electrical contact. Unfortunately, this is a very low yield process, as the graphene sticks poorly to the etched substrate and it relies on a significant amount of chance. It also cannot provide unadulterated electrical access to the suspended graphene, as there will always be at least a small portion of the graphene between contacts on the substrate in parallel with the suspended section.

To achieve unfettered electrical access to a suspended graphene sheet, we developed a method to transfer high quality exfoliated graphene flakes onto predefined gold contacts. Our method for transferring graphene onto various substrates was developed by the Jarillo-Herrero group based on a similar technique pioneered at Columbia University [14].

The transfer process begins by depositing exfoliated graphite onto a glass slide covered in a polyvinyl acetate (PVA)- polymethyl methacrylate (PMMA) resist stack. The slide is also framed with a thick edge of tape that serves as a structural support for the resist membrane when the glass slide is removed. The glass slide can be removed leaving the resist membrane intact thanks to the weak structural strength of the sacrificial PVA layer. Once separated the membrane is scanned upside down for candidate graphene flakes under an optical microscope. When a suitable flake is found,

26 a small metal washer (~ 2 mm in diameter) is placed on the back of the membrane surrounding it. When the membrane is fully scanned, a new piece of thick tape is placed over the back side, sealing the washers in place against the membrane. Each individual tape-washer-membrane stack can then be carefully cut out for transfer.

The actual transfer utilizes a flip chip bonder, which aligns a substrate and a transfer object, and then flips the transfer object over onto the substrate in a very precise motion. With this method, we could regularly achieve an alignment accuracy of a few microns. The transfer process has since been improved for simplicity, reli- ability, and higher yield. It is now possible to align transfers within a few hundred nianometers, and to do so with greater yield.

For these devices the graphene is transferred onto 100 nm tall gold electrodes. The electrodes were designed with various gaps between them, ranging from 200 nm to 1 pin. The graphene flake bridges the gaps between the electrodes and remains suspended. An AFM image of a suspended graphene flake prepared in this manner is shown in Fig. 2-1c. A zoomed out optical image of the same device is presented in the inset.

Using this suspension method, electrical contact is made to a suspended device without any of the flake coming contact with the substrate. This method also reduces the number of fabrication steps that the graphene sees, possibly reducing contamination, as the graphene transfer is the final step in the process.

There are significant drawbacks to this method, however. First, the transfer process can be relatively low yield. It is much more difficult to find quality single layer graphene flakes on the transfer slide than it is to find them on an SiO 2 substrate. Transfer can also fail by misalignment, failure of the PMMA to stick to the substrate, or device collapse or tearing. Additionally, even when a device is successfully fabricated, it usually has poor electrical contact to the gold. This can be fixed by annealing the device is forming gas at 250 C. While annealing can lead to very low contact resistance, it tends to cause rippling in the graphene due to the mismatch between the thermal expansion coefficients of graphene and gold. These ripples, as can be seen in the device shown in Fig. 2-1c, can dramatically effect the device's

27 electrical and mechanical properties. Finally, we show data from devices that are suspended by etching the substrate out from below a contacted graphene flake. To build such a device, we begin by exfoliating graphite and depositing it onto an SiO 2 substrate. We scan the wafer for monolayer flakes, then design, pattern, and evaporate contacts onto them, using e-beam lithography and thermal evaporation of gold. With the devices held securely by the gold, we etch out the SiO 2 substrate from below using hydrofloric acid (HF).

Critically the HF will wet through the graphene - SiO 2 boundary but not through the gold - SiO 2 boundary [5]. This means that the HF will etch evenly below the graphene surface, freeing the device, but will not etch below the gold contacts, leaving them as structural support for the graphene membranes. An SEM image of a flake suspended in this manner is shown in Fig. 2-1d. In this image it can be seen that the substrate has been evenly removed everywhere except tinder the gold contacts, where pillars of SiO 2 remain as supporting structure. An optical image of the device is shown in the inset in the upper left of the panel. We have found this suspension method to be the most successful for generating high quality suspended graphene devices with good electrical and mechanical properties. All of the devices described in the graphene nanoelectromechanical resonator chapter were prepared in this manner. A resistivity plot is presented in the inset to Fig. 2-1d, showing the Dirac peak of the device in the main panel both before (blue) and after (yellow) suspension. The mobility of the suspended device is also plotted within the inset showing a peak above 30,00 cm 2 /Vs. This demonstrates the very high quality results that can be achieved with successfully suspended graphene.

2.3 Current Annealing

After fabrication of graphene devices, a significant quantity of residue often remains. Standard graphene fabrication usually involves some kind lithographic resist polymer

(e.g. PMMA, MMA, or SU-8) that will leave contamination behind after processing. Because graphene, as a one atom thick material, has such a severe surface to volume

28 ratio, it is very susceptible to outside contamination. In these situations, graphene's robust thermal stability can be taken advantage of to remove the residue.

One way to do this is to anneal the device in an oven with forming gas. This will successfully remove most residue. Thermal annealing, however, can be limited by the other materials that are around the graphene such as contacts, the substrate, or large amounts of residue in the surroundings. These other materials may limit the temperatures that can be used or the cleanliness of the environment. For instance, it is best to keep temperatures lower than 250 C when annealing devices with gold contacts to reduce migration of the gold. Ideally, only the graphene would be heated and nothing around it. It would also be best to do this process in high vacuum and in the final measurement apparatus where the device will be used. Current annealing is a method that possesses all of these criteria.

Current annealing removes residue by sending a large current through the device.

The graphene's resistance converts the electrical energy into heat, burning off contamination on its surface. The graphene will heat very quickly, due to its minuscule mass, and can survive very high temperatures, due to its thermal stability. These properties allow it to survive what can often be a violent process.

There are three main categories of annealing techniques that are used to clean graphene by various groups: pulse annealing, hold annealing, and wave annealing [45, 46, 47].

In pulse annealing, short pulses of voltage are delivered to the sample driving bursts of current through the device. The sample is then given time to cool before the next pulse. The pulses begin at a low magnitude and are gradually increased. A schematic of this process is shown at the top of Fig. 2-2a in light blue. In theory, the short pulses concentrate the heating to the device itself and reduce excess heating of the contacts or the graphene-contact interface, where over heating may reduce device performance. In practice, it is quite easy to over step and deliver a fatal current spike to the device. The line between a sufficiently powerful pulse that will remove residue, and one that will destroy the graphene is quite narrow. Pulse annealing may be satisfactory on substrate, but is too violent for reliable use on suspended devices.

29 (a)

Hold

Wave

0 1 2 3 4 5 6 7 8 9 t (min)

(b) 60 (c) 60 80,000 200,000

40,000 100,000 E 40 40 0 0 -10 0 10 -10 0 5

20- 20-

S01 -20 -10 0 10 -20 -10 0 10 Vbg M Vbg (V)

Figure 2-2: Current annealing of suspended graphene devices. (a) Schematic time traces of three different current annealing techniques. At the top, in light blue, pulse annealing sends short voltage pulses to drive current through the device. In the middle, in dark blue, hold annealing ramps the voltage up and holds it constant for an extended period of time. At the bottom, in purple, wave annealing ramps the voltage up and back down with one polarity and then does the same with the opposite polarity. (b) and (c) The evolution of the conductivity of suspended graphene devices being current annealed by wave annealing. Early traces are in the lightest blue and progress to later traces in the darkest blue. The final measurement is in yellow. Insets: Mobility data corresponding to the conductivity measurements shown in the main panels. The color coding is the same for the insets as it is in the main panels.

30 For hold annealing, a source voltage is slowly ramped up to a desired value and then held there for an extended period of time, driving a current through the device. The voltage is then ramped back to zero for a resting period, and the processes is repeated at increasing voltage levels. A schematic of hold annealing is shown in Fig. 2- 2a in dark blue. This method has the benefit of increasing the user control during the process. By monitoring the current through the device as the source voltage is ramped, the user can watch for signs that residue is being removed. As contamination is ejected, the current will begin to decrease as the graphene becomes more intrinsic and its Dirac point moves closer to zero. When this signal is seen, the user can stop ramping and hold the voltage at that value until the current stabilizes. The user can then repeat the cycle at high voltages. This also gives the user (or an automated script) control to stop the annealing process if they see a jump in current. For some spikes, if they are mild enough and caught quickly enough, cutting the current can save the device from destruction.

This method does work fairly well on suspended graphene samples, though it can be very labor intensive. It is difficult to fully automate the procedure, as each device will have slightly different thresholds and requirements. Therefore, a user must be present for much of the process, which can take hours depending on the results desired and the risks the operator is willing to take with their device. Ultimately, however, it is simply not the best way to anneal a sample. Wave annealing improves upon the hold annealing method to produce better results.

In wave annealing, the source voltage is ramped slowly up to a given value and then back down. It then performs the same ramps with the opposite polarity. It repeats this cycle with increasing power until the desired annealing is achieved. A schematic of this process is shown in the lower part of Fig. 2-2a in purple. This method is gentle, like hold annealing, but requires much less monitoring, as it does not hold a large voltage for a long period of tine. Wave annealing also has the additional feature of reversing the polarity of the annealing current. Reversing the current significantly improves the annealing process, possibly due to residue migration, uneven heating near the contacts, or other general asymmetries of the device.

31 We were able to write an automatic script to run this annealing process with fairly high yield. After each cycle the program would take a trace of the conductivity of the sample verse back gate voltage and compare its performance to that of the previous round. Based on the comparison, the script would choose the amount to increase the maximal source voltage or whether the annealing was complete. Progressions of conductivity traces are plotted in Figs. 2-2b and c. The corresponding mobilities for these traces is shown in the insets of these panels. The lightest blue traces are the earliest measurements and the darkest blue are the latest. The yellow trace is the final measurement. As the figures show, it can take many iterations to complete an annealing process. In these cases, the annealing took 105 cycles for b and 146 cycles for c. These figures also demonstrate how gains can often come in jumps. It is common that little will happen for many cycles, and then the mobility can double in a single round.

32 2.4 Ion Beam Etching

(a) 1 (b) 4

P 0 2

-1.6 M 0 -1.6 0 1.6 0 1 2 3 4 x (pm) x (Pm)

10 250

E E S 0 C 0

-250 -10

-500 -500 -250 0 250 500 -10 0 10 X (nm) X (nm)

Figure 2-3: Etching suspended graphene with a gallium based focused ion beam (FIB) and a helium ion beam. (a) Four SEM images of suspended graphene structures patterned by FIB. (b) SEM image of a contacted, suspended graphene device etched into a nanoribbon with FIB. (c) An SEM image of a suspended graphene flake etched into a nanoribbon with a helium ion beam. (d) Transmission electron microscope (TEM) image of the edge of a suspended graphene film after etching by a helium ion beam. Inset: A zoomed out TEM image of the slots etched in the suspended graphene filn.

33 Suspended graphene devices can be of supreme quality due to their separation from any substrate or contamination, and their ability to be annealed to pristine levels of cleanliness. Devices to date, however, have been limited in size and shape due to the strains of the suspension process. It would be beneficial to have a process for shaping graphene membranes that are already suspended. In this way, a robust and structurally sound membrane can be suspended safely, and then gently etched into new and interesting shapes and structures, in a clean, dry etching process. Such etching would also avoid problems of hardened residue from reactive ion etching and may be able to create cleaner, straighter etch edges. To investigate the possibilities of this type of patterning, we tested three post suspension etching techniques. First we used a standard gallium based focused ion beam (FIB). Second we used a helium ion beam, a fairly new technology. And finally, we tested the etching of suspended graphene with electron beam assisted water etching.

Gallium based focused ion beams are the most common type of FIB commercially available. They are often found in dual beam configurations, with a complementary SEM that can be used for aligning and imaging of the sample without the destructive effects of using the FIB. The FIB can be programmed to deliver specific doses in a precise pattern to an aligned sample. We use this capability to etch various patterns in suspended graphene samples that would be impossible to etch before suspension. Fig. 2-3a depicts four examples of such structures. In the upper left there is an SEM image of a hexagonal drum head supported by nanoribbons smaller than 100 nm in width. In the upper right is a suspended graphene membrane with the MIT logo etched into it. The nanoribbons that define the logo are as small as 40 nm. In the lower left, a square perimeter is etched into the membrane with the central square shown collapsed on the bottom of the trench. Finally, in the lower right, there is a spiral pattern showing a spiral etched nanoribbon of ~ 100 nm in width. These shapes and structures demonstrate the range of devices that can be fabricated in this method.

The FIB can also be used to etch electrically contacted suspended graphene devices. Fig. 2-3b shows an SEM image of a device after being etched into a ~ 140

34 nm wide nanoribbon. Though the etching was successful, the electrical properties greatly diminished after the process. Most likely this is due to gallium implantation or nanometer scale destruction of the nanoribbon by the outer ions of the beam waist. It seems that etching with a gallium based focused ion beam is best suited for patterning larger scale optical or mechanical structures that would be too delicate to suspend after etching.

The helium ion microscope is a relatively new technology that was only developed commercially in the last few years. This microscope uses helium ions in place of gallium, taking advantage of their lighter mass to produce higher resolution imaging and more delicate etching with less implantation and contamination. Fig. 2-3c shows a suspended graphene nanoribbon that has been successfully etched down to ~ 25 nim wide over a 500 nm length for an aspect ratio of 20:1.

We further characterize the helium ion etching process by observing the edge structure left behind after etching slits in a suspended graphene film. A high resolution transmission electron microscope (TEM) image of such an edge is provided in Fig. 2-3d. The edge is shown to be very clean and well formed with an average roughness of only about 2-3 nmi. A zoomed out image of the slits used in this TEM study is shown in the inset. This work shows the promise of helium ion etching of graphene films as it is a more gentle, higher resolution option compared to standard gallium based focused ion beams. As the technology advances and the commercial machines become more reliable and easier to use, many new and exciting, previously unrealizable, devices may come out.

As a final test, we investigated electron beam assisted water etching of graphene membranes. This process uses a e-bean and a gas injection system to introduce a small amount of water vapor into the SEM environment at the graphene flake. Where the electron beam hits the surface, it locally ionizes the water and the free oxygen selectively etches the carbon of the graphene. This is a well established process for etching graphitic films [48], but is a novel technique for use oii suspended graphene. A nano-constriction etched using this process is shown in Fig. 2-4. The process has some rastering issues as can be seen in the jaggedness of the cut. Because of this the resulting constriction was not as small as designed. However, the process did ultimately succeed in etching the structure into a suspended graphene sample. E-beam assisted water etching shows real merit and warrants further investigation, especially for those without access to a focused ion beam. We believe many interesting structures can be fabricated in this manner.

0 0 1 2 3 X (pm)

Figure 2-4: Etching suspended graphene by electron beam assisted water etching. An SEM image of a suspended graphene film with a nano-constriction etched into it by electron beam assisted water etching. The jagged edges are due to rastering problems with the process.

2.5 Acknowledgements

We would like to thank the Jarillo-Herrero group for help with all the aspects of this research, especially Joel Wang and Javier Sanchez-Yamagishi for their development of the graphene transfer method, Ken Van Tilburg for taking the TEM images, Lewis Stern, Max Lemme, and David Bell for their assistance with the helium ion microscope, Alfonso Reina-Cecco for help preparing CVD graphene on TEM grids, and Monica Allen and Tchefor Ndukum for their help with suspension techniques.

36 Chapter 3

Etching of Graphene Devices with a Helium Ion Beam

with Max Lemme, David Bell, James Williams, Lewis Stern, Pablo Jarillo- Herrero, and Charles Marcus'

3.1 Introduction

We report on the etching of graphene devices with a helium ion beam, including in situ electrical measurement during lithography. The etching process can be used to nanostructure and electrically isolate different regions in a graphene device, as demonstrated by etching a channel in a suspended graphene device with etched gaps down to about 10 nn. Graphene devices on silicon dioxide (SiO 2) substrates etch with lower He ion doses and are found to have a residual conductivity after etching, which we attribute to contamination by hydrocarbons.

'A version of this chapter appeared in the journal ACS Nano [49]

37 VS=OV Vd Graphene

Vg c soc et to trou

Figure 3-1: Schematic of a graphene device. Inset: Photograph of the microscope chamber with installed chip.

3.2 Motivation

Graphene, a stable two-dimensional carbon crystal, has attracted great interest recently as a model system for fundamental physics as well as for possible nanoelectron- ics applications [1, 11, 50]. Many experiments in the field are targeted at graphene devices where artificial confinement in one or two dimensions produces nanoribbons or quantum dots. Typically, such structures are on the ~5-50 nm scale and have been fabricated by electron beam lithography followed by reactive ion etching [51, 52, 53, 54] and by chemical means such as thermally activated nanoparticles [55] or unfolding of carbon nanotubes [56, 57, 58]. While these methods are suitable to produce devices near the atomic limit, they also have significant short- comings. Reactive ion etching typically erodes the resist mask creating disordered graphene edges. Chemical methods can result in irregular shaped and distributed flakes poorly suited for integrated device applications. It has further been proposed to etch graphene at the nanoscale with a focused electron beam [59]. This method, however, requires suspending graphene on specific transmission electron microscope grids, making it difficult to perform simultaneous electrical measurements.

38 Helium ion microscopy (HeIM) has recently been introduced as high-resolution imaging technology for nanoscale structures and materials [60, 61, 62]. In this work, we use a helium ion microscope (Zeiss ORION) as a lithography tool to controllably modify electrical properties of graphene devices. We further demonstrate in situ electrical measurement during lithography. The HeIM is particularly well suited for this purpose because it produces a high-brightness, low-energy-spread, subnanomneter-size beam. The microscope benefits from the short de Broglie wavelength of helium, ~100 times smaller than the corresponding electron wavelength. This gives the beam an ultimate resolution of 0.5 nm or better [61], making it an attractive tool for precision lithography of graphene devices. While process details are published elsewhere [63], this letter focuses on the modification of electrical properties of graphene. Fig. 3-1 shows a schematic of a graphene field effect transistor as used in this work. Note that for some experiments, the SiO 2 substrate was removed prior to measurements to obtain a suspended graphene device (see the Methods). The inset in Fig. 3-1 shows a photograph of a chip carrier inside the HeIM as used for in situ measurements.

3.3 Results

A suspended graphene device with a length of ~150 nmn and a width of ~1.5 im, shown in the HeIM microscope image in Fig. 3-2a, was He ion etched by sequential imaging in high resolution. The graphene was exposed to the He ion beam at a field of view of 2 pim x 2 pin and an image size of 2048 x 2048 pixels, which resulted in a pixel spacing of -1 nmn. The dwell time was chosen to be 50 pis resulting in an effective line dose of 0.8 nC/cn. Fig. 3-2b shows such a high-resolution image, expanded and labeled to distinguish the suspended graphene from the underlying SiO 2 and the chromium (Cr)/gold (Au) contacts. Fig. 3-1c shows a sequence of images taken under these conditions (nos. 1-13, where image 1 is identical to Fig. 3-1b). The red circle indicates the region of the graphene flake where etching occurred initially.

Each scan with the He ion beam resulted in an increase of etched area. After 13 scans, the dwell time, and hence the image quality, was increased to 500 ps, equivalent to a

39 line dose of 8 nC/cm, still not sufficient to completely etch the device (Fig. 3-1c, 14). These images indicate that removal of edge atoms is favorable over atoms within in the graphene crystal.

a) C) a) I) 2 3

iC 11

I I

Figure 3-2: Etching suspended graphene with a helium ion beam. (a) HeIM image of suspended graphene devices. The yellow box indicates the area that was subsequently imaged and etched in high resolution. (b) High-resolution image used to etch graphene. (c) Sequence of images of progressive etching of a suspended graphene sheet. Image 1 corresponds to (b). The red circle indicates the area where etching occurred initially.

The remaining graphene film was etched using live scanning mode with a 100 to 10 nm field of view. Here, etching was confirmed via the live screen image. A resultant cut with minimum feature sizes in the 10 nm range is shown in the HeIM image in Fig. 3-3a. The gap was measured with DesignCAD software after importing the original image.

40 10 before etching .- 8I Vd= 0.5 mV 10"~10 after etching-

12 10 -4-2 02 4 V9 M b)

Figure 3-3: Electrically isolating suspended graphene with a helium ion beam. (a)

HeIM image (with false color) of a suspended graphene device after etching with minimum feature sizes of about 10 nn. (b) Electrical measurement of the device before and after etching.

After a trench was etched across the entire graphene flake, the device was removed from the HeIM and its drain current was measured as a function of back gate voltage

(Fig. 3-3b, Vd = 0.5 mV; note that the gate voltage range is limited in suspended graphene devices [5, 64] and hence, Id changes little with V). The current dropped to about 15 pA, compared to 1 pA prior to etching. While the latter is typical for a

functional graphene device of the given dimensions, the postetching value corresponds

to the noise level of the measurement setup. Adjacent, nonimaged devices made from

the same graphene flake showed conductivity similar to the investigated device prior

to imaging. These results confirni that the graphene was etched successfully using

the He ion beam.

Next, the drain current of a graphene device on SiO 2 substrate was measured

inside the He ion microscope, while part of it was exposed to the ion beam. A field

of view of 1 pim x 1 pim was chosen, indicated by the top yellow box in Fig. 3-4a.

After about 150 s the current saturated, indicating complete etching of the graphene

inside the field of view (Fig. 3-4b). At this point, the imaging window was moved

to the next part of the device in the direction of the white arrow in Fig. 3-4a. The

current was again monitored until it saturated. A beam current of 1 pA, dwell time

of 3 ps, and pixel spacing of ~1 nm allowed us to estimate a suitable He ion line dose

41 for etching graphene on SiO 2 : 1.5 nC/cm. A residual drain current of about 4 nA was measured after etching the entire device, which could not be reduced further by subsequent He ion beam exposure.

We attribute this residual conductivity to contamination of the SiO 2 surface with hydrocarbons.

Id Vd -1.0

-0.8 d=mV V =0V Wg

- -0.4

-0.2-

n.0 0 400 800 1200 m / n time [s] b)

Figure 3-4: Etching graphene on SiO 2 with a helium ion beam. (a) HeIM image of a graphene device. The boxes indicate the field of view used for etching. The window was subsequently moved in the direction of the arrow. (b) Drain current vs time of exposure of the graphene device. The etching window was moved as the current saturated.

3.4 Conclusions

We have demonstrated etching of graphene devices with a helium ion beam. Sus- pended graphene has been etched conclusively, with minimum feature sizes in the

10 nm range. Graphene on SiO 2 was etched with a lower dose compared to suspended graphene. However, these devices showed a residual conductivity attributed to contaminants on the surface. Helium ion etching can be considered an alternative

42 nanofabrication method for suspended graphene devices and, if contamination issues can be solved, graphene on SiO 2 substrates.

3.5 Methods

Graphene was deposited onto ~300 nm of silicon dioxide on degenerately doped silicon by mechanical exfoliation [65] similar to the method described by Novoselov et al. [1] Next, monolayer and few layer graphene akes were identified with an optical microscope. Contacts to the graphene were defined by conventional electron beam lithography, followed by evaporation of chromium/gold (3 nm/150 nin) and titanium/gold (5 nni/40 urn). Suspension of the graphene sheet was obtained by wet etching of the underlying SiO 2 in diluted HF, followed by critical point drying. All devices were measured in a standard field effect transistor (FET)-like configuration, with the evaporated contacts acting as source and drain and the doped substrate as a gate electrode (Fig. 3-1). The drain current Id through the flake was then measured as a function of gate voltage V for a constant drain voltage V. Electrical data of suspended devices were made outside the microscope, before and after He ion etching, using two Keithley 2400 source meters in a Desert Cryogenics probe station at a pressure of ~ 5 - 103 mbar. The second set of graphene devices on SiO 2 substrate were wirebonded to chip carriers and placed in a chip socket inside the Helium ion microscope to enable in situ electrical measurements (inset in Fig. 3-1). These were taken at a pressure of ~1 - 106 inbar with an Agilent 4155B parameter analyzer connected to the device via a vacuum feedthrough. All measurements were taken at room temperature.

3.6 Acknowledgments

We would like to acknowledge the support of the Alexander von Humboldt foundation through a Feodor Lynen Research Fellowship. Research also supported in part by the NRI INDEX program. We thank S. Nakaharai for fruitful discussions.

43 44 Chapter 4

Approaching GHz Resonant Frequencies in Suspended Graphene NEMS Resonators

with Tchefor Ndukum, Kevin Fischer, and Pablo Jarillo-Herrero

4.1 Introduction

We report the excitation of suspended graphene NEMS resonators with resonance modes as high as 900 MHz. We successfully suspend high quality graphene resonators with resonance frequencies in the hundreds of MHz, mobilities in the tens of thousands, arid Q values up to 1650. We excite these resonators using a novel mixing circuit that allows for the signal from the high frequency modes to be read with a basic low frequency lock-in amplifier. We then demonstrate the tunability of these modes using a capacitively coupled back gate, and we fit that tunability to a model of a membrane under tension. Finally, we show how this model can lead to capacitive spring softening, and present experimental data that demonstrates this phenomenon.

45 4.2 Motivation

Graphene, a strong [3], light, two dimensional material, exactly one atom thick, em- bodies the ideal properties sought for a nanoelectromechanical system (NEMS) resonator. Its light weight and stiffness [3] make it perfectly suited to mass sensing. And its unbeatable surface to volume ratio at one atom thick, distinguishes it as one of the most promising materials for chemical and biological sensing as well [27. Early incarnations of graphene based NEMS resonators have shown that these devices can achieve microwave resonance frequencies, sensitive mass detection, and frequency tunability [30, 27, 29]. Here we demonstrate devices with resonance modes as high as 900 MHz, furthering development toward graphene NEMS that, beyond acute sensing tasks, can also enter the quantum regime as they are cooled to the ground state, enabling many exotic systems mixing the unique electrical properties of graphene with quantized mechanical modes [12]. In addition we describe the fabrication of high mobility, high Q suspended graphene devices and an actuation circuit used to excite them. We then present data on the tunability of the resonance modes and provide a model to fit the data. Finally we show how capacitive coupling can lead to spring softening and fit data demonstrating that phenomenon.

4.3 Device Fabrication

The devices in this study are all fabricated from graphene exfoliated from naturally forming mined bulk graphite. The graphite is exfoliated using a low tack semiconductor grade tape and then deposited onto highly doped silicon wafers covered in a

285 nm thick layer of thermally grown SiO 2 , as is a standard graphene fabrication process [1]. The wafers are then searched using an optical microscope, and monolayers of graphene are identified by their distinct optical contrast [66]. A circuit is patterned onto the graphene flakes using electron beam lithography and a polymethyl methacrylate (PMMA) mask. 100 nm of gold with a .3 nm sticking layer of chromium is evaporated onto the patterned circuit by thermal evaporation. The gold acts as

46 both the contacts to the graphene and the anchors that will support the membrane after suspension. The device is next released from the substrate by etching out the

SiO 2 under the graphene using hydrofloric acid (HF). The HF preferentially etches along the graphene-SiO 2 boundary and does not etch under the gold-SiO 2 boundary [5]. This phenomenon allows the graphene to be fully suspended while keeping the gold anchors solidly supported. To prevent surface tension forces collapsing the suspended devices, the wafers are dried through critical point drying. A schematic of the device geometry is shown in Fig. 4-la and a scanning electron micrograph of a suspended device is presented in Fig. 4-1b. The completed devices are bonded and placed into a vacuum chamber. All measurements presented here were performed in high vacuum (~ 10-6 torr) and at room temperature. The high vacuum environment helps to eliminate damping effects due to air resistance, which for resonators as light as these, would be substantial. As a final step, the resonators are current annealed to remove fabrication residue and other contaminants and to improve the mobility of the devices [45].

47 (a) (b) raphene

Reference Line

Device - D Lock-in fSource d

40,000 E Mixing Current 9 - 3 20,000 0 -10 0 10 20 z 6 )Vbg(V) 0-

3 -3

o I 1 -6 I -20 -10 0 10 20 -20 -10 0 10 20 Vbg M Vbg (

Figure 4-1: Graphene NEMS device schematics, image, and electrical readout. (a) Upper: A schematic side view of the suspended graphene device, showing the gold electrodes (yellow), graphene resonator (light blue), etched SiO 2 (dark blue), and doped silicon gate (grey). Lower: A diagram of the actuation and measurement circuit. A high frequency source sends an amplitude modulated excitation to the device. The mixed down measurement signal is read at the lock-in amplifier, which is synced to the source by a reference line. A DC voltage is applied to the back gate to capacitively tune the resonator. (b) A scanning electron micrograph of a suspended graphene resonator. (c) Resistivity of a device as a function of back gate voltage, showing the characteristic Dirac peak of graphene. Inset: Mobility of the device shown in (c), demonstrating its high quality. (d) Mixing current of a device away from any mechanical resonance.

48 Suspended graphlene has been shown to benefit greatly from its separation from the substrate [5, 64]. Impurities, residue, and unevenness of the SiO 2 substrate have been shown to limit graphene mobility and conductivity [67]. Substantial improvements can be made by placing the graphene on hexagonal boron nitride [14], but still the best performing graphene devices have been suspended, set apart from all substrates and outside influences. Our experiments have yielded similar results. Devices of mediocre performance on substrate improve in mobility by an order of magnitude better after suspension. We typically find that devices with mobilities of ~ 100 cm 2 /Vs on substrate will increase to mobilities of ~ 1000 cm 2 /Vs.

Once suspended, current annealing of graphene is also extremely effective [64].

With both sides of the material free to expel residue unimpeded, it may be possible to get cleaner results than would be allowed on substrate. The downside, however, is that the device is thermally isolated and far more prone to breakage during the annealing process. While current annealing is very effective, it must be done very carefully. When a device is successfully annealed it can gain an additional order of magnitude in mobility. It is common for our devices to have mobilities in the tens of thousands after annealing. A typical device characteristic is shown in Fig. 4-1c with the conductivity vs. back gate voltage plotted in the main panel and the mobility vs. back gate voltage plotted in the inset.

4.4 Mixing Current

In order to measure the resonance frequency of our NEMS devices we utilize the nonlinear response of the graphene to create a mixing circuit. This scheme is similar to other mixing circuits that have been used to measure graphene and carbon nanotube resonators in the past [68]. A schematic of the circuit is depicted in Fig. 4-la. A high frequency source is connected to the source electrode and a lock-in amplifier is connected to the drain electrode. The source and the lock-in are synced via a reference line that allows their frequency and phase to be matched. Finally, the doped silicon back gate is connected to a DC voltage source. The resonator is excited

49 at high frequency with an amplitude modulated signal provided by the high frequency source. The source signal, V has the form:

V, = VamCOS(Wt)(1 + cos(Awt)) where w is the high frequency signal. w will be swept in order to find the device's resonance frequencies. Aw is the low frequency used for measurement. Aw is matched to the frequency of the lock-in amplifier. Vain is the amplitude of the signal and t is time.

The current, I, that flows through the device as a result of this excitation can be written in a general form as the sum of currents arising at each individual frequency, Wi.

The signal the lock-in amplifier will measure is the current at the measurement frequency, IA.

To find the expected current IA, we can split the source voltage into its component pieces.

V = Van [cos(wt) 1 +- cos((w + Aw)t) 2 +-I COS(( - AW)t) 2

The current will be related to the voltage through Ohm's Law, I = Gj, where G is the conductance of the device. Crucially, the conductance of the device will not be constant; it will vary with frequency. Just as with the current, the conductance can be written in a general form as a sum of conductance arising at each individual frequency, ws.

G GSI + E 6G(w)cos(wt)

From this we see that the current will have two components: a steady state current,

50 ISU, that will be proportional to the sourced voltage by the steady state conductance,

G.., and will not change with frequency or device response, and a dynamic current, 61(w), that will respond to the source frequency as

61(w) = 6G(w)cos(wt)Vanmcos(wt)(1 + cos(Awt))

Expanding this equation yields five components.

6I(w) = G(o)m -aiCos (0t) 21

+~1ICos (2wt)

+ cos((2w Aw)t) 1 4 + cos((2w - Aw)t)

+ cos( Awt) 2

The last component is at the mixed down frequency of the lock-in amplifier. This is the component that we measure.

To complete our analysis we can further describe the change in conductance, 6G, as inversely proportional to the distance, z, between the graphene sheet and the silicon back gate. This is because the conductance is proportional to the charge carriers on the sheet, q, which are proportional to the capacitance, C, which, in turn, is inversely proportional to the distance between the resonator and the back gate, z. That is:

1 G oc q oc C Oc- z

Making simple linear approxinations, the change in conductance, 6G can be expanded as: dG dG dG dC 6G(w) dq-q(w) dq-VC(w) dq-K dz(w) dq dq dq dz

For our purposes the voltage in the capacitor, Vc = Vb9 - V, ca n be simplified to V because the mixing current will only depend appreciably on the direct current voltage

51 applied to the back gate. The alternating current components to V will not produce any significant response at the mixing frequency, Aw. Assembling the measurement current back together, we find:

I dG dC I(W) = - 4 dq dz 6Z (W) V,V,

This current is proportional to 6z the deflection due to the capacitive force between the membrane and the back gate. That deflection will be very small for any value of w off the resonance of the device, and then exponentially larger on the resonance. It is this phenomenon that delivers the signal of a resonance through the mixing current measured at the lock-in. The current will also be proportional to the transconductance, dG/dq. Thus, the signal is expected to be large for high mobility suspended graphene, though it will disappear at the Dirac point. This dependence can be used to calibrate the system and check the functionality of the device. Off resonance, the mixing current should be seen to change sign as it crosses the Dirac point and to peak at the maximal transconductance along a sweep in back gate voltage. A representative mixing current trace is shown in Fig. 4-1d.

52 4.5 Resonant Modes

(a) 130 (b) 125

110 120

90 115 NN

-70 110

50 105

30 100. -12 -6 0 6 12 -10 -9 -8 -7 Vbg (V) Vbg (V)

495

490

485 700L -20 -10 0 10 20 -30 -20 -10 0 10 20 Vbg (V) Vbg (V)

Figure 4-2: Resonance maps, avoided crossings, quality factor, and high frequency modes. (a) A map of resonance modes in frequency and gate space. The modes are seen to be tunable with the back gate voltage. The blue box shows the zoomed in area in (b). (b) A high resolution view of avoided crossings from the same resonator in (a) in the region of the blue box. This shows in greater detail the interaction of the graphene resonance modes with those from the gold contacts. (c) A map of resonance modes from a second device. The vertical blue line shows the location of a cut in frequency space. Inset: the data cut in frequency space showing the sharpness of the resonance peak, giving a quality factor of Q = 1650. (d) A resonance map of a thrid device with modes approaching the GHz regime. Inset: Mode data extracted from the raw data shown in (d). 53 A map of a graphene resonator's resonance modes is shown in Fig. 4-2a. The map depicts the measurement current IA, as a function of frequency and back gate voltage. Multiple resonance modes are seen as here quasi-parabolic signals on the map. These line shapes are due to the tensioning of the the graphene sheet as the magnitude of the back gate voltage is increased. An attractive force is felt between the charges on the back gate and the charges on the graphene sheet, pulling the resonator down and tensioning it. This increases the resonance frequency of the device as the magnitude of the back gate voltage is increased. Such tensioning allows for these resonators to be tuned over a fairly substantial range. In this case the resonator has a maximal tunability of 13 MHz/V.

Also evident in this resonance map are multiple flat resonance modes and avoided crossings. Fig. 4-2b shows a high resolution view of a section of the map containing these features. When the tunable graphene resonance approaches a flat resonance of the system they form a coupled oscillator system that shares energy between the to resonances and forms the avoided crossing. These flat resonances are suspected to come from the suspended portion of the gold electrodes. Because hydrofloric acid will wet under the graphene, the section of the gold electrode over the graphene will be suspended. This suspended electrode will have a mechanical resonance but will be too rigid to be tuned with the back gate voltage. We can model such a resonator as a doubly clamped beam, where the expected resonance frequency is

t E

with t, f, E, and p the thickness of the electrode, the length of the suspended segment, the Young's modulus of gold, and the density of gold respectively. Typical numbers for our devices lead to expected resonance frequencies of around 50 MHz. This matches well with the lowest order modes that we see. Higher modes are also seen on top of those.

We can also take a cut of the resonance map data along the frequency axis to extract the quality factor of the resonance peak. The quality factor of a resonator is

54 defined as the ratio of the resonant frequency to the bandwidth of the resonance peak, Q = fr /Af. This figure of merit quantifies the energy dissipation in the resonator. The inset to Fig. 4-2c shows a cut of the resonance data along the frequency axis. Fitting the resonance peak to a Lorentzian, we find a quality factor of 1650. This is quite a respectable number for a graphene resonator.

Finally, we can look for the highest frequency modes that our system can measure. In Fig. 4-2d we see modes that extend as high as 900 MHz. The resonance peaks of the two modes shown here are extracted and plotted in blue circles in the inset for clarity. These high frequency miodes have ground states that are nearly achievable in traditional dilution refrigerators. Cooling such a mode to the ground state would enable the study of novel physical systems that mix graphene's unique electronic properties with quantized mechanical oscillator. This measurement represents a significant step toward that goal.

4.6 Mode Fitting

We fit a model of tunable resonance modes to our data to further characterize our graphene resonators. Ultimately, the devices can be treated as one dimensional springs [27], though determining the spring constant, k is nontrivial. Their resonant frequency therefore will be

fr = w* where r is the mass of the resonator. Ideally, m would be described simply as m = f -w - t - p, where f, w, t, and p are the length, width, thickness, and density of the graphene sheet. However, this ignores any adsorbates or residues left on the surface of the graphene. Since the resonator's mass is so small, these additions will not be negligible. This sensitivity to adsorbed mass is, in fact, exactly what makes these resonators such promising mass sensors. To account for this, the mass is calculated as the mass of the graphene plus the mass of the residue, = ing + m,. The mass of the residue then, will be one of the two fitting parameter of the model.

55 The spring constant, k, will behave as the spring constant of a tensioned membrane [69].

16 To 128 Ewt 2 _ __2 3 f 3 f3 ze Z3 b

This relation comes from solving the equation of motion of an elastic membrane with some built in tension, To, and added energy from a capacitively couple back gate voltage, Vg. The tension, To, is the second free parameter in the fit. f, w, and t are the length, width, and thickness of the graphene sheet. E and c are the Young's modulus of graphene and the permittivity of the graphene gate capacitor. z is the maximal deflection of the sheet as it is pulled toward the back gate by capacitive forces. And z, is the deflection of the sheet under equilibrium as determined by minimizing the energy of the system. ze has the form

3 -. 870 9 2 + 1.7 4a /3+ 27472 9 1.7 4a3 3 + 27a4 2 2.6a

2 a l 28Eivt 3 16To _ cfw 2 - cw T, 3f Z bg, 2z2 b

The first term in the equation for k is a simple constant, which describes the intrinsic spring hardness of the resonator due to to its built in tension. The second term is dependent on the back gate voltage and is a hardening term. It raises the spring constant with the increase of the magnitude of the back gate voltage. At high values of IVbg this term causes the spring constant to be proportional to Vbg 4/3. The final term in the spring constant equation accounts for a softening effect. Here, as the magnitude of the back gate voltage increases, the spring constant decreases. This effect is due to the increased capacitance of the system at higher back gate voltage. This capacitance acts as a damping mechanism on the resonator, lowering its spring constant. Depending on the initial tension in the resonator, this spring softening term can dominate at low Vg. In frequency space, this would lead to a lowering of the resonance frequency with increasing jVbgI at low values, resulting is a 'W' shape dependence of the resonant frequency with respect to the back gate voltage.

56 (a) 130 (b) 13 !0 To = 100 nN 110 11 0 - Mr=150 m

90 C0- N -I 70 70 - -

50 50 --

30 3n -12 -6 0 6 12 -12 -6 0 6 12 Vbg M Vbg (

235 235

2301 2301

225 IN 225 L -12 -6 0 6 12 -12 -6 0 6 12 Vbg M Vbg (

Figure 4-3: Fitting resonance modes and mode softening. (a) A map of resonance modes in frequency and gate space. The tunability of the graphene modes is evident. (b) Extracted mode data (light blue circles) from the map in (a) are fit using our model (dark blue lines), showing excellent agreement. (c) A resonance mode map of a second device showing capacitive mode softening. (d) Extracted mode data (light blue circles) from the map in (c) are fit using our model (dark blue line), showing excellent agreement.

Fits to our resonator data are shown for two devices operating in the two different regimes. One in the low To regime where the resonant modes rise monotonically with increasing IVlbg (data in Fig. 4-3a and fits in Fig. 4-3b). And one in the high To regime where the mode has a 'W' shape (data in Fig. 4-3c and fits in Fig. 4-3d).

57 The three modes fit in the low To case are three sequential harmonics of the system. The fits give an initial tension of 100 nN and a resonator mass 150 times that of pristine graphene. The high tension device gives an initial tension of 450 nN and a resonator mass 81 times that of pristine graphene. It is clear from these fits that contamination is still a significant problem and that attempts at developing higher frequency resonators and resonators that can be cooled to their ground state should focus on reducing fabrication residue and improved cleaning processes.

4.7 Conclusions

In conclusion, we successfully suspend high quality graphene resonators with microwave resonance frequencies approaching the GHz range, high mobilities in the tens of thousands, and high Q values in the thousands. We have demonstrated the tunability of the modes in these devices using a capacitively coupled back gate, and we have fit that tunability to a model of a membrane under tension. Finally, we have show how this model can lead to mode softening, and presented experimental data that demonstrates this phenomenon. These are promising results for the future of graphene NEMS resonators.

4.8 Acknowledgments

We would like to thank Monica Allen for her help with device fabrication techniques and Adrian Bachtold and especially Joel Moser for their hospitality and incredible helpfulness showing us their actuation and measurement systems. We would also like to thank Hadar Steinberg for many thoughtful discussions.

58 Chapter 5

Intrinsic Electronic Transport Properties of High Quality

Monolayer and Bilayer MoS 2

with Hugh Churchill, Yafang Yang, and Pablo Jarillo-Herrero'

5.1 Introduction

We report electronic transport measurements of devices based on nonolayers and bilayers of the transition-metal dichalcogenide MoS 2. Through a combination of in situ vacuum annealing and electrostatic gating we obtained ohmic contact to the MoS 2 down to 4 K at high carrier densities. At lower carrier densities, low temperature four probe transport measurements show a metal-insulator transition in both monolayer and bilayer samples. In the metallic regime, the high temperature behavior of the mobility showed strong temperature dependence consistent with phonon dominated transport. At low temperature, intrinsic field-effect mobilities approaching 1000 cm 2 /Vs were observed for both monolayer and bilayer devices. Mobilities extracted fromn Hall effect measurements were several times lower and showed a strong dependence on density, likely caused by screening of charged impurity scattering.

'A version of this chapter appeared in the journal Nano Letters [70]

59 (a) Top View Si de View (b) Monolayer (c) Bilayer MO 1 ,-

(e) 106 (d) (f) 10-6 fVxxq Vds = 0.1 V Vds = 0.1 V 10-8 10O Vds, Ids - ? 10 U, 1OF 10 10 300K _. 300K 200K 200K 10- 100K 1OF2 1OOK 5OK 50K 14 5K K 1 ( V)45 Vbg 10 -50 0 50 1- 50 0 50 Vbg (V) Vbg M)

Figure 5-1: MoS 2 device schematics, images, and two-terminal transport measurements. (a) Structure of a single sheet of MoS 2 from both a top and side view, showing the locations of molybdenum (black) and sulfur (yellow) atoms. (b) and (c) Color en- hanced AFM height images of six-terminal monolayer (Ml) and bilayer (Bi) devices. Scale bars are 2 pm. (d) Device schematic and measurement setup. (e) Two-terminal drain-source current, Is, of monolayer MoS 2 as a function of back-gate voltage, Vg. Temperatures from 300 K to 5 K are denoted with traces colored from red to black in (e) and (f). (f) Id, of bilayer MoS 2 as a function of Vg. The DC drain-source voltage, Vds, was 0.1 V for both (e) and (f).

5.2 Motivation

Molybdenum disulfide (MoS 2 ), a layered transition-metal dichalcogenide (TMD) semiconductor, is attracting increasing interest for its novel nanoelectronic and optoelectronic properties [71]. Bulk MoS 2 is a stack of atomic trilayers composed of a single atomic layer of molybdenum between two layers of sulfur [Fig. 5-1a]. Strong intralayer covalent bonds lead to high mechanical strength in plane [721, while weak Van der Waals bonds between layers render the material chemically inert with robust electrical properties [73]. As with graphite, this weak inter-layer coupling also allows individual layers to be isolated and studied [9]. Monolayer MoS 2 (one S-Mo-S unit) is of partic- ular interest as a large (1.8 eV), direct-gap semiconductor [35] with strong spin-orbit interaction leading to a spin- and valley-split valence band [74, 32]. These qualities

60 could lead to novel physics such as an unconventional quantum Hall effect, combined spin Hall and valley Hall effects [75], and new devices such as high-performance, ultra-low power transistors [76] and devices integrating spin- and valley-tronics [77].

Further, MoS 2 is compatible with standard semiconductor manufacturing [71], can be grown in large-scale by chemical vapor deposition [78, 79, 80], and integrated with other two-dimensional, flexible, and transparent materials [77].

Few-layer MoS2-based devices in field-effect transistor geometries have demonstrated the promise of these materials [36, 71, 81, 82, 83, 84]. However, in a two- terminal contact configuration mobilities are underestimated by including contact resistance. This point is illustrated by measurements of imulti-terininal devices based on

2 thick MoS2 with mobilities up to - 500 cmn /Vs, whereas two-terminal measurements showed mobilities on the order of 10-50 cnm2 /Vs [73, 85, 86, 87, 88]. Encapsulating monolayer MoS 2 in high-k dielectric or a polymer electrolyte improved device performance in several ways: increasing miobilities for imonolayer devices from r 15 cm 2 /Vs up to r 160 cm 2 /Vs [36, 42, 78, 41, 77, 89], increasing the on/off current ratio to

108 [76], and enabling observation of a metal-insulator transition [89]. Nevertheless, investigation of the novel quantum transport phenomena expected for TMDs will require further improvements in device quality. Here we report mnulti-terminal devices based on monolayer and bilayer MoS 2 with sufficiently transparent contacts at high density to enable access to the intrinsic mobility of MoS 2 at low temperatures. These measurements highlight the potential for observing novel quantum transport phenomena in TMDs.

5.3 Device Fabrication

Devices based on monolayer and bilayer MoS 2 were fabricated from bulk MoS 2 (SPI Supplies) that was exfoliated on highly doped silicon substrates with 285 urn of thermal oxide using the micronechanical cleavage process standard for graphene [1]. Monolayer and bilayer flakes were identified by optical contrast [90] and confirmed with AFM measurements (see Appendix A). We present data from two nimonolayer and

61 two bilayer devices, denoted Mi, M2, B1, and B2. Device contacts were patterned using PMMA masks and e-beam lithography. To optimize fabrication procedures, we investigated a number of process variations. Titanium/gold contact metal was evaporated in thicknesses of 0.3-4 nm for Ti and 50-100 nm for Au. Some devices were annealed in an Ar/H 2 atmosphere at 350 'C for 3 hours, both before and after con- tacting. All of the devices were annealed in situ at high temperatures (- 120 0C) for up to 20 hours in vacuum (~10-6 mbar) before measurement. Variations in contact metal thickness and whether devices were annealed in Ar/H 2 were not found to have a substantial effect on mobility or contact resistance. In contrast, vacuum annealing caused a substantial drop in two-terminal resistivity (see Appendix A) and the nearly complete elimination of Schottky behavior in the contacts, even at 4 K (Fig. 5-2).

Vacuum annealing substantially doped the sample with n-type carriers, shifting the threshold gate-voltage for conductance by as much as 100 V toward negative values. The formation of S vacancy donors would cause n-doping [91], but this scenario

0 is unlikely given the thermal stability of MoS 2 up to 1000 C in vacuum [92]. We speculate that this effect points to intrinsic doping of mined, natural MoS 2 [93]. The result is a large increase in carrier density and conductivity, and a significant decrease in contact resistance. After vacuum annealing, both monolayer and bilayer devices displayed stable, smooth field-effect transistor characteristics with on/off current ra- tios up to 106 (Fig. 5-1). Two-terminal measurements such as these reiterate the viability of MoS 2 as a transistor material, but contact resistance ultimately obscures the intrinsic material properties.

5.4 Resistivity Measurements

To investigate the intrinsic properties of MoS 2 , we further annealed our devices to reduce contact resistance, allowing us to use standard current-biased lockin techniques to measure four-probe resistivity for a second set of monolayer and bilayer devices. Without vacuum annealing, two-terminal I-V measurements showed evidence of large Schottky barriers. After sufficient annealing, two-terminal I-V measurements remain

62 nearly linear at small drain-source bias, low back-gate voltage, and low temperature, with a clear positive slope across zero bias at 5 K and zero Vg (insets to Fig. 5-2 a and b). Non-linearities indicating small residual Schottky barriers begin to appear at zero

Vbg, but are small enough to allow reliable four-terminal measurements of resistivity in the regimes studied here.

To measure the contact resistance, the devices were connected as shown in Fig. 5-1 with the outer contacts serving as the current drain and source and two inner contacts as voltage probes. These measurements, combined with the two-probe measurements like those shown in Fig. 5-1, allowed for the separation of the MoS 2 resistivity and the device contact resistance (both shown in Fig. 5-2). Contact resistance was calculated from the resistivity as R, = VdjIdS - p. l/w, where / and w are the full sample length and width, respectively, and p = (Vx/Ids) - (lm,/w), with lj, the length between the inner contacts. Even after annealing, contact resistance makes up a significant portion of the total device resistance. Contact resistances of 5-50 kQ could be reliably achieved at higher densities, though Rc increases to greater than 1 MQ at low temperature and low density (Fig. 5-2).

The temperature dependence of the resistivity provides useful information such as whether a sample is metallic or insulating and provides a means of distinguish- ing nobility-liniting scattering mechanisms. At high gate voltages, p monotonically decreases with decreasing temperature, showing a consistent metallic state for both monolayer and bilayer MoS 2 (Fig. 5-2). In an intermediate range, p is non-monotonic but ultimately increases at low temperature. At the lowest gate voltages, p mnono- tonically increases with temperature, characteristic of insulating behavior. These observations indicate the presence of a imetal-insulator transition in the samples with critical resistivities p = 0.8 h/c 2 for the monolayer sample and 0.3 h/e 2 for the bilayer, consistent with previous observations for monolayer MoS2 [89] and theoretical expectations [94]. Other imonolayer and bilayer samples we measured also showed critical resistivities of order h/e 2 (see Appendix A).

63 Monolayer Bilayer (a) 107 (b) 10 7 O.3 5K 20 5K 0 -0 106 106 -20 0 Vbg a -1 0 ( a 5 -1 0 1 1 Vds(VM 0. 10 5K 5K VSV 4 50K 10 100K 10 lOOK 200K 200K 300K, 3 300,K 10 3 10o -25 0 25 50 75 -50 0 50 Vbg M Vbg (V) (c) 10 7 (d) 10 7 5K 5K 50K 50K 1061 100K 106 100K 200K100K 200K 300K 300K 1o5 1 CL CL 300

10 4 1

103 10 3 -25 0 25 50 75 -50 0 50 Vbg M Vbg ( (e) 107 10 -75 Vbg -50 Vbg -25 Vbg 10 6 106 0OVbg

50 Vbg 5 75 V 0. 10 10 5 0-

4 -20 Vbg 10 0 Vbg 50 Vbg 75 Vl 10 10 - 10 100 300 10 100 300 T(K) T(K)

Figure 5-2: Contact resistance and four-terminal resistivity of monolayer and bilayer MoS 2. (a) Contact resistance, Rc, to monolayer MoS 2 as a function of Vg. Curves colored from red to black show measurements at 300, 200, 100, 50, and 5 K, respectively, across panels (a) through (d). Inset: Two-terminal Ids vs. V, at 5 K and Vbg = 0 V for the monolayer. (b) Contact resistance, Rc, to bilayer MoS 2 as a function of Vg. Inset: Two-terminal Ids, vs. Vd at 5 K and Vbg = 0 V for the bilayer. (c) Four-terminal resistivity of a monolayer device as a function of Vbg. (d) Four-terminal resistivity of a bilayer device as a function of Vg. (e) Resistivity of a monolayer device as a function of temperature. The curves, from purple to yellow, correspond to Vbg = -20, 0, 25, 50, and 75 V. (f) Resistivity of a bilayer device as a function of temperature. The curves, from black to yellow, correspond to Vbg = -75, -50, -25, 0, 25, 50, and 75 V. Data from devices M2 and B2.

64 5.5 Hall Measurements

Hall effect measurements were used to determine carrier density, n, as a function of

Vb,. The Hall coefficient, RJ = 1/ne, was calculated by fitting the slope of the transverse resistance, Rx, as a function of magnetic field up to 1 T (see Appendix A). We note here that for the full gate voltage and temperature ranges of the Hall inea- surenents, contact resistances of both the monolayer (Ml, with further annealing relative to data shown in Fig. 5-1) and bilayer (B2) devices remained below 500 kQ.

The nearly linear dependence of rt On V corresponds to a capacitance per unit area of c = 10 ± 2 nF/cm2 for the monolayer and 13 + 1 nF/cm 2 for the bilayer sample (Fig. 5-3 a, b, and insets). These values are in rough agreement with the capacitance expected for a parallel plate geometry, 12 nF/cm2 , which we expect to underestimate the true capacitance by about 10% due to finite size effects for an MoS 2 flake only a few times wider than the oxide thickness due to the contribution from fringing fields [95, 96]. At fixed Vbg, the density varied with temperature significantly for the monolayer, though not for the bilayer. The monolayer density decreased by a factor of 1.5 from 300 K to 5 K, whereas the density change in the bilayer was negligible. A reduction in density is expected in inhonogeneous samples due to localization of charge carriers at low temperatures. Inhonogeneities in electric potential from different sources such as the substrate, charged impurities, or defects will trap more charge carriers as the device cools and the ability of carriers to be thermally excited out of these potential wells decreases.

Combining the measurements of n and p, we extract Hall mobility IH = /nc as a function of n, where -= i/p is the conductivity and c is the electron charge (Fig. 5-3 a and b). The Hall mobilities increased with density, reaching 250 cm 2 /Vs for the monolayer and 375 cn 2 /Vs for the bilayer at high n. Another method commonly used to estimate carrier mobility is to calculate the field-effect mobility upFE = du/dVbg -1/c, where c = creo/d is the gate capacitance per unit area (12 nF/cm 2 for 285 nm of

SiO 2 ). The large carrier density of these highly doped samples leads to very high field effect mobilities. Both devices show I'FJ1 1000 Cm2 /Vs (Fig. 5-3 a and b),

65 Mo~nol-aer (a)1000 . . N~nn~k~,I~r(b)1000 Bilayer1.5x10iIlav.er 13 . 21.5x1*

750 2 E 750 1E V 0. 5 1FE 0 50 1 0 50 500- v v E 500 Vg(V) E 50500 Vbg(V(M PH 250 250

0 T=10K 0 T=5K -25 0 25 50 -25 0 25 50 75 Vbg (V) Vbg(V) (C) 500 (d) 500 y=1.1

100 y=1. 7 100 EE 2 50 n=1.9x10 cm - 50 n=1.3x10 cm' 1.8x10 13 1.1x10 13 i 7' 20 1.6x10 13 20 0.7x10 13 3 10 100 300 3 10 100 300 T(K) T(K)

Figure 5-3: Field-effect and Hall mobilities as a function of back-gate voltage and temperature for monolayer and bilayer MoS 2. (a) Field-effect mobility, PFE, (yellow) and Hall mobility, pH, (blue) of a monolayer device as a function of back-gate voltage, Vbg, at 10 K. Inset: Density of a monolayer device as a function of Vbg at 10 K. Solid lines in the insets to (a) and (b) are fits to n = mVbg + b, where the slope, m, and the intercept, b, are free parameters. (b) PEE (yellow) and pH (blue) of a bilayer device as a function of Vg at 5 K. Inset: Density of a bilayer device as a function of Vbg at 5 K. (c) pH as a function of temperature for a monolayer device. The curves, from 2 blue to yellow, correspond to n = 1.6, 1.7, 1.8, and 1.9 . 1013 cm- . The black line is a power law fit, PH oc T-7, with y = 1.7 for the high density data from 150-300 K. (d) Pm as a function of temperature for a bilayer device. The curves, from blue to yellow, correspond to n = 0.7, 0.9, 1.1, and 1.3- 1013 cm- 2 . The black line is a power law fit, Pm oc T-1, with -y = 1.1 for the high density data from 150-300 K. Data from devices MI and B2.

66 the highest field-effect mobilities reported to date for either monolayer or bilayer

MoS 2 . Encapsulating MoS 2 in a high-k dielectric has shown substantial mobility improvements [36, 42, 78, 41, 77, 89]. The devices reported here are not in a high-k environment, however, suggesting the possibility of further mobility improvement in future devices.

The discrepancy between pH and PFE evident in Fig. 5-3 a and b can be explained by the density dependence of the Hall mobility. Substituting O- = nepH and nc CVbg into the field effect mobility formula, we find PFE = pHn pH+n dpH /dn. Thus, the field effect mobility can differ significantly from the Hall mobility if the Hall mobility changes with density. Within this model a linear trend of pH with density would lead to a field effect mobility trend with twice the slope (see Appendix A).

Conversely, when dpH /dn approaches zero, the two mobility values should nearly match. These two behaviors roughly match the data: in the gate range where PH is nearly independent of density, pEE approaches PH (Fig. 5-3b). And where PH increases with density, PFE does so at about twice the rate. Additionally, we note that the devices were not operated in a regime of saturated current with drain-source bias, a situation which would lead to a similar overestimation in the calculation of

PFE.

For high densities in the metallic regime, Hall mobilities at constant density increase rmonotonically from 300 K to 5 K for both the imonolayer and the bilayer saul- ples (Fig. 5-3 c and d). At high temperatures (above 100 K), PH approximately follows a power law in temperature, PH oc T--,, with Y= 1.7 for the monolayer device and 1.1 for the bilayer. It is expected that MoS 2 devices with mobilities limited by hioriopolar, optical phonons should follow this form in this temperature range, with 'l = 1.69 for monolayer [97] and y = 2.6 for bulk MoS 2 [98]. The nonolayer value agrees well with the prediction, though we note that the fit was obtained over a limited temperature range. The power law for the bilayer sample is significantly lower than the prediction. This is similar to a previously reported value where a suppressed ' = 1.4 was attributed to phonon quenching by a top-gate dielectric [89].

Such quenching, however, is not expected in our case.

67 The monolayer and bilayer mobilities begin to saturate below 100 K, a temperature by which scattering from optical phonons is expected to become negligible [97]. At lower temperatures, scattering from phonons should be dominated by acoustic modes with a linear dependence of mobility on temperature [98], in contrast with the near saturation we observe (Fig. 5-3 c and d). Another candidate explanation is mobility limited by long-range Coulomb scattering. This picture is consistent with our observation of p-H being roughly linear with carrier density [99], which is not expected for phonon scattering [97]. Whether the temperature dependence we observed can be mostly described by long-range Coulomb scattering awaits further experimental and theoretical study.

5.6 Conclusions

In conclusion, we have demonstrated high quality MoS 2 devices that may open oppor- tunities for measuring novel quantum transport phenomena at low temperature. We showed that in situ vacuum annealing can dope devices and significantly reduce Schot- tky barriers and contact resistance, allowing for ohmic contact to MoS 2 down to 4 K at high densities. A clear metal-insulator transition was evident in both monolayer

2 and bilayer samples at p ~ h/c , showing that high density MoS 2 devices remain conducting at low temperature. Additionally, the field effect mobilities were quite high, indicating good sample quality. Finally, Hall mobilities calculated from density measurements gave relatively high values, though the field effect equivalents are still several times larger due to the density dependence of the Hall mobility. Based on the temperature and density dependence of the mobilities, we infer a crossover from a regime limited by optical phonon scattering at high temperature to one likely limited by long-range Coulomb scattering below 100 K.

68 Chapter 6

Optoelectronic Devices Based on Electrically Tunable p-n Diodes in a Monolayer Dichalcogenide

with Hugh Churchill, Yafang Yang, and Pablo Jarillo-Herrerol

6.1 Introduction

The p-n junction is the functional element of many electronic and optoelectronic devices, including diodes, bipolar transistors, photodetectors, light emitting diodes, and solar cells. In conventional p-n junctions, the adjacent p- and n-type regions of a semiconductor are formed by chemical doping. Materials with ambipolar conductance, however, allow for p-n junctions to be configured and modified by electrostatic gating. This electrical control enables a single device to have multiple functionali- ties. Here we report ambipolar monolayer WSe 2 devices in which two local gates are used to define a p-n junction within the WSe 2 sheet. With these electrically tunable p-n junctions, we demonstrate both p-n and n-p diodes with ideality factors better than 2. Under optical excitation, the diodes show photodetection responsivity of 210 nmA/W and photovoltaic power generation with a peak external quantum efficiency of

'A version of this chapter appeared in the journal Nature Nanotechnology [100]

69 0.2%, promising values for a nearly transparent monolayer material in a lateral device geometry. Finally, we demonstrate a light emitting diode based on monolayer WSe 2. These devices provide a building block for ultra-thin, flexible, and nearly transparent optoelectronic and electronic applications based on ambipolar dichalcogenide materials.

6.2 Motivation

Next generation photodetectors and photovoltaic devices, as well as sensors, displays, and light emitting diodes, will require new optoelectronic materials with characteristics superior to those currently in use. Candidate materials must be flexible for wearable devices, transparent for interactive displays, efficient for solar cells, and robust for broad distribution. Monolayer semiconducting transition metal dichalcogenides (TMDs) such as tungsten diselenide (WSe 2 ) are flexible [72], nearly transparent [35, 101], high strength [72], direct band gap [35] materials with the potential to meet all of these criteria. The crystal structure of tungsten diselenide comprises stacks of sheets, each made of one atomic layer of tungsten encapsulated by two layers of selenium. This structure leads to strong intralayer and weak interlayer bonding [72].

Such bonding allows the exfoliation of bulk crystals down to a single Se-W-Se layer, similar to graphene [9].

Monolayer WSe 2 is a direct gap semiconductor with a band gap of -1.65 eV [102], a complement to other two-dimensional materials [103] such as graphene, a gapless semimetal, and boron nitride, an insulator. The direct band gap distinguishes monolayer WSe 2 from its bulk and bilayer counterparts, both indirect gap materials with smaller band gaps [32, 102]. This sizable direct band gap in a two-dimensional layered material enables a host of new optical and electronic devices. Thin film TMDs have already demonstrated novel nanoelectronic and optoelectronic devices such as ambipolar and high quality field effect transistors [73, 89, 70], electric double-layer transistors [104], integrated circuits [77], and phototransistors [105] with high responsivity [106]. In addition, photoluminescence [35] and electroluminescence [93, 107]

70 (a) (b) 200 PN NN

100 PP NP

0 V

Vds WSe 2 ids -100

Hf02 -200 2 -1 0 1 2 V19 Vrg VdsM

S VD S"D

10' 10'

PN NP 1012 n=1.9 1012 n=1.9

-2 -1 0 1 2 -2 -1 0 1 2 Vd ( VdS (M

Figure 6-1: Gate-controlled monolayer WSe 2 p-n junction diodes. (a) Optical micrograph of a monolayer WSe2 device controlled by two local gates. The WSe 2 is contacted with Au electrodes. The flake and contacts are insulated from the gates by 20 uni of HfO2. The scale bar is 2 pm. Below is a schematic side view of the device including electrical connections. (b) Current-voltage (Id-V,) curves showing transport characteristics of four doping configurations of the device, NN, PP, PN, and NP. Both gates were set to 10 V for the NN configuration and -10 V for PP. Vig was set to ±10 V and V, to -F10 V for PN/NP. The NN and PP configurations (yellow and black curves respectively) are ohmic at low Vd5, while the PN and NP configurations (blue and green curves, respectively) strongly rectify current in opposite directions. (c) and (d) Semi-log plots of Ids through the PN (blue circles) and NP (green circles) diodes as a function of Vd8 , with fits in yellow (see text). The fits give a diode ideality of n = 1.9 for both the PN and NP configurations. Insets: Schematic band diagram of the device in forward bias for PN and NP configurations.

71 have revealed effects including giant spin-valley coupling [108] and optical control of valley polarisation [109, 110 and coherence [111]. P-n junctions in TMDs have, to date, been less explored than field effect transistors. Junctions of p- and n-doped bulk WSe 2 were reported over 30 years ago [91]. More recently, p-n devices have been constructed of low-dimensional semiconductors [112] and thin-film TMDs, such as an ionic-liquid gated bulk MoS 2 device [104], an InAs/bulk WSe2 heterojunction [101], and a doped silicon/monolayer MoS 2 heterojunction [107]. Unfortunately, bulk TMDs and heterostructures involving other materials lack many of the most appealing properties of monolayer TMDs: direct band gap, flexibility, and transparency. Here we characterise monolayer WSe2 p-n junctions defined and controlled by electrostatic gates, demonstrating devices with diverse functionality, including current rectifying diodes, a photodetector, a photovoltaic device, and a light-emitting diode.

6.3 Device Fabrication

Device fabrication uses exfoliated natural crystals of WSe 2 , with monolayer flakes transferred [14, 113] onto substrates with a pre-patterned pair of local back gates separated by 100 nm and covered by 20 nm of HfO 2. An optical image and schematic of the device used for all measurements except electroluminescence are shown in Fig. 6- la. Comprehensive fabrication details are provided in Appendix B. All measurements were performed at room temperature and in vacuum (~ 10- torr), with a voltage bias, Vd,, applied to the source contact and the DC current through the device, Ids, measured at the drain.

6.4 Transport in Gate Controlled p-n Junctions

The voltages on the two gates, V, for the left gate and Vg for the right gate, independently control the carrier density in the left and right sides of the monolayer. In this way the device can be electrostatically doped into various conducting regimes

72 (Fig. 6-1). With both sides of the device n-doped (Vg = ,.g = 10 V, denoted NN) or both sides p-doped (V. = ._, = -10 V, denoted PP), the device shows a nearly ohmic current-voltage relation at low V, (Fig. 6-1b). The device has a significantly higher conductance in NN, most likely due to lower contact resistance between gold and n-type WSe 2 , as observed in MoS 2 [36]. The current-voltage relations in these configurations are slightly nonlinear, due to Schottky barriers that likely dominate the contact resistance.

By oppositely biasing the two gates, the device rectifies current as a diode. Current measurements for the two diode configurations (V = -10 V, V. 9 = 10 V, denoted PN and VIg = 10 V,/.g = -10 V, denoted NP) are shown in Fig. 6-1b. At low Vd8, current in both PP and NN is substantially larger than in NP and PN, demonstrating that the p-n junction dominates transport in this regime rather than Schottky barriers at the contacts. The effect of Schottky barriers is discussed further in Appendix B. Ids versus V, for PN and NP are fit (Figs. ic and id) to the Shockley diode equation [114], extended [115] to include a series resistance, R,:

n/ Io R Vds +Io Rs Ids = W xp -UV0

where VT = kBT/q is the thermal voltage at temperature T, with kB the Boltzmann constant and q, the electron charge. 1 o is the reverse-bias current, and n is the diode ideality factor (n = 1 is ideal). W is the Lambert W function [116].

The rapid increase in current under forward bias defines an ideality factor n

1.9 for both PN and NP, indicating current mostly limited by recombination rather than diffusion [114]. Investigating this recombination, including contributions from

Shockley-Read-Hall or Auger processes, will be a focus of future work. The roll-off of

Ids at high bias constrains R, = 3 MQ for PN and R, = 5 MQ for NP due to contact resistances. Environmental conditions such as substrate and fabrication residue most likely determine the contact resistance and the asymmetry between the PN and NP configurations. An increase in current at high reverse bias indicates a 0.5 TQ shunt resistance across the junction. This large shunt resistance indicates a high quality

73 p-n interface and is an expected advantage of a lateral device geometry. Though our data do not strongly constrain the value of Io, because it is below the 1 pA noise floor of the measurement, uncertainty in 1o has an insignificant effect on the fits to the slope and roll-off of the current and does not impact the values of n and R,. Both diodes have rectification factors of 105 and reverse bias currents less than 1 pA up to IVdI = 1 V, promising characteristics for low-power electronics.

A more complete view of transport through the device is shown in a map of current as a function of V1, and Vg (Fig. 6-2). The four corners of the map show the extremes of the four doping configurations (NN, PP, PN, and NP). The off state of the device can be seen in the dark blue region in the centre of the map, separating the four conducting regions. Though mid-gap states, most likely due to disorder, form a conducting region between the NN and NP quadrants, current through these states is thermally activated and can be eliminated by cooling the device (see Appendix B).

Along the diagonal line defined by Vbg = Vig = Vg, line cuts show the device operating as an ambipolar field effect transistor (Fig. 6-2c). Along the off-diagonal, line cuts show gate-controlled rectifying behaviour (Fig. 6-2d) as a function of the asymmetric gate voltage, V1 = , = -Vg, which defines a junction between the p- and n-type regions. We note a decrease in device performance between the datasets presented in Fig. 6-1 and Fig. 6-2. We suspect that this decrease stems from local

Joule heating at the contacts when the device is operated at high Vds.

74 V =2V VdS=-2V I (a) 10 ds(b) 10 V s1 pA

1nA

5 5 1 pA

0 - 0

-5 -5

-10 N 1P -10 -5 0 5 10 -10 -5 0 5 10 Vg (V) Vg (V)

Vds= 2 V Vds- 2 V Vds = -2 V Vds = -2 V 10 -

- 1010

10 -1

0-12- PN ------NP 10-1 10~12 1 1 -10 -5 0 5 10 -10 -5 0 5 10 Vbg M VJ (V)

Figure 6-2: Current through the device as a function of doping configuration. (a) and (b) Current magnitude through the device, Ids , as the drain-source bias, Vda, is held at 2 V (a) and -2 V (b), and the two back gates are varied independently. The colour scale is logarithmic from 1 pA to 1 pA. (c) Diagonal cuts of U1dJ where both gates are swept together as one back gate, V, - V1, = V,,, for V, = 2 V (yellow curve) and -2 V (blue curve). These curves are characteristic of an ambipolar field-effect transistor. (d) Off-diagonal cuts of hiasl where the two gates are swept with opposite polarity, showing the dependence of the current on the asymmetric gate voltage, Vj = V -- -- Vg, that defines the junction. The current was measured at V, = 2 V (yellow curve) and -2 V (blue curve), demonstrating rectification of current in opposite directions for p-n (Vj < 0) and n-p (Vj > 0) gate configurations.

75 6.5 Optoelectronics

The optoelectronic properties of monolayer WSe 2 p-n diodes were investigated with scanning photocurrent microscopy (Fig. 6-4a), in which Ids is measured as a laser spot (~ 2 pm diameter) is scanned over the sample. With the gates in the NP configuration, photons impinging on the junction create electron-hole pairs that are separated to opposite contacts by the electric field at the junction, generating a photocurrent. Scanning the beam (power 75 jpW, wavelength 830 nm) over the sample and measuring Ids at V, = 0 yields a spatial map of the photoresponse of the device (Fig. 6-4b). Calibrating the photocurrent map with a simultaneously acquired image of reflected light from the sample (Fig. B-4), we overlay the positions of the contacts and gates to demonstrate that maximum photocurrent arises when light is incident on the junction. A line cut through the centre of the photocurrent map is shown in Fig. 6-4c with the positions of the contacts and the junction illustrated for reference. The photocurrent is symmetric and centred on the junction, demonstrating that the photoresponse is dominated by the p-n junction and not Schottky barriers at the contacts (see Appendix B).

At relatively large V, in the NP configuration, a substantial photocurrent is generated when the junction is illuminated with laser light at 532 nm. The Id,- Vd, curves at laser powers 0-10 pW are shown in Fig. 6-4d. The photocurrent,

Iph = Ids,light - Ids,dark, at Vds = -2 V and a linear fit of I,, up to 8 PW are shown in the inset. The slope from the fit gives a responsivity of 210 mA/W, which is comparable to commercial silicon photodetectors for green light. We note that phototransistors based on monolayer dichalcogenides can achieve even higher respon- sivities [106], though the principle of operation and device geometry differ significantly from the photodiodes presented here.

In addition to photodetection, monolayer WSe 2 p-n diodes are also capable of photovoltaic power generation. With the device in the NP configuration, current is measured as a function of V. for various laser powers from a 700 nm band-pass filtered supercontinuum white-light source. Figure 4a depicts a zoomed-in view of the Ids-Vds

76 Iph (nA) (a) Photodiode (b) 4 8

4 laser 2 0 beam splitter

V V -,piezo =S 0 lenses mirror >-

Vds ds -2

-4 -2 0 2 4 V9 Vrg X (pm)

(d) i (c) 8 Junc. 1 w 2Vds= 1.5 8 pW

*9 1 - ,' - 6 4pW nph 2pW t~ OpW , 0 4- 0 5 10 4 0.5 SIaser (pW) -

2- Contacts 0 M.... 0 -2 -1 0 1 2 -4 -2 0 2 4 Vds (V X(Pm)

Figure 6-3: Photodetection in monolayer WSe 2 . (a) Schematic of the scanning photocurrent microscopy setup and the device. The laser (solid red line) is focused onto the sample through a microscope objective at a position set by a piezo-controlled mirror. As the laser is scanned over the sample (represented by the dashed red line), photocurrent is recorded simultaneously with the reflected laser power measured by a photodiode. (b) Photocurrent, 'ph, as a function of laser position (75 puW, 830 nm diode laser), with the device in the NP configuration and V, = 0 V. The peak in current corresponds to the location of the junction. Outlines of the contacts (orange lines) and gates (red lines) are overlaid on the current map based on the reflected image (see Fig. B-4). (c) Line cut from (b) at Y=0 (blue curve). Outlines of the contacts (orange rectangles) and the position of the junction (red dashed line) are shown based on the reflected image. (d) Id,-V, characteristics with the device in the NP configuration at laser powers 0-10 pW from a 532 nm diode laser. Inset: I.,, (green dots) at Vd, = -2 V as a function of laser power. A linear fit (black dashed line) to 'ph for powers 0-8 pW gives a responsivity of 210 mA/W.

77 curve, focusing on the quadrant of photovoltaic power generation. The short-circuit current, I, which is the zero-bias current through the illuminated device, increases linearly with power up to at least 10 /uW (Fig. 6-3a inset). The power generated by the photovoltaic device, P = Id Vd, is shown for laser powers 0-10 puW in Fig. 6-3b. The photovoltaic power generation also has a linear dependence on laser power (see Fig. B-5).

Varying Vj, the asymmetric gate voltage that defines the junction, at different laser powers, we observe a saturation in the short-circuit current when Vj - t5 V (Fig. 6-3c). The current is higher for NP than for PN due to a difference in contact resistances between the two contacts. We also note that the photocurrent due to the photovoltaic effect in these WSe 2 diodes is approximately an order of magnitude larger than photothermoelectric currents observed at the contacts of a monolayer

MoS 2 field-effect transistor [117].

To obtain spectrally resolved photocurrent in the NP configuration, we measure 1', as a function of excitation wavelength. To quantify the efficiency of light conversion into current, we extract the external quantum efficiency, EQE = (Isc/Paser)(hc/eA), as a function of wavelength, A, at constant laser power, Piaser, where h, c, and e, are Planck's constant, the speed of light, and electron charge, respectively. We observe three peaks in the spectrally resolved photocurrent at 755, 591, and 522 nm (Fig. 6-3d), corresponding to energies of 1.64, 2.10, and 2.38 eV, respectively. These energies match well with the values observed via photoluminescence [102], differential reflectance [108], and optical absorption spectroscopy [118] for the A, B, and A' transitions of monolayer WSe 2, as depicted in the band diagram in the inset to Fig. 6-3d. We measure a maximum EQE of 0.2% at 522 nm. This number does not take into account the low absorption of monolayer WSe 2 or the narrow cross-section of the p-n junction relative to the size of the laser spot, which together suggest an internal quantum efficiency at least an order of magnitude larger than the EQE reported here.

Finally, we measure the electroluminescence spectrum of a second monolayer WSe 2 p-n diode (Fig. 6-3d). To improve hole injection, this device was fabricated with Pd instead of Au to contact the p-type WSe 2 (see Fig. B-2). In the PN configuration

78 (a) 2 (b) 400

10' 700 nm 10 p-4w e,,' -1.5 8 pW 300 4 pW 2 pW

1 0- () 200 - 0 5 10 PIaser (pW) 0 10 VV 8 pW 100

4pW / 2 pW 0 0 1 -0.75 -0.5 -0.25 0 -1 -0.75 -0.5 -0.25 0 Vds M Vds (

Cn Cb0 - 4 -WE 1 5 - A C -1 PN NP a) NP NN PP w 0 0 -2 PN - - -- - NP -10 -5 0 5 10 500 750 10 0)0 Vj (V) A (nm)

Figure 6-4: Photovoltaic response and light emission. (a) Ids as a function of V, in the NP configuration for laser powers 2 - 10 pW (wavelength 700 rim). Positive Ids and negative Vds in this regime reflects photovoltaic power generation. Inset: Short- circuit current, 'Sc (green dots), versus laser power with a linear fit (black dashed line). (b) Power, P = Ids - V,, produced by the device as a function of Vd. for different incident laser powers, calculated from the data in (a). (c) IU, as a function of the the asymmetric gate voltage, Vi, for different laser powers. I,, is nearly linear with power up to 10 piW in the NP configuration, though it saturates in the PN configuration beyond 6 pW. As a function of gate voltage, the current saturates in both configurations for V ~ ±5 V. (d) External quantum efficiency as a function of wavelength at a constant laser power of 2 pW in the NP configuration (purple line). Peaks in the external quantum efficiency correspond to exciton transitions A, B, and A', as labeled. Right axis: Electroluminescence (EL) intensity from a second monolayer WSe 2 device with one Au and one Pd contact. Vd, = 2 V in the PN (blue trace), NN (yellow trace), aid PP (black trace) configurations, and Vd =-2 V in the NP (green trace) configuration. NN and PP traces are offset vertically for clarity. Inset: Diagram of the band structure around the K and Q points, with arrows indicating the lowest energy exciton transitions for monolayer WSe 2.

79 (VS = 2 V, Ids = 100 nA), the device behaves as a light-emitting diode (LED). The emitted light spectrum peaks at 752 un, corresponding to the direct-gap exciton transition seen in the photocurrent spectrum (Fig. 6-3d). Using a blackbody source for calibration, we estimate the electroluminescence efficiency, defined as optical output power divided by electrical input power, to be approximately 1%. Light emission and a peak at ~ 750 nm are also seen in the NP configuration (Vd, = -2 V, Is, = 4 nA), with a peak height smaller in proportion to Is. No emission is seen in either

NN (with V, = 2 V and Ids = 300 nA) or PP (with V, = 2 V and Ids = 500 nA), confirming that the gate-defined p-n junction generates the electroluminescence. A spatial image of light emission from a third device is shown in Fig. B-6. Based on the device performance presented here, we anticipate a prominent role for diodes and optoelectronic devices based on monolayer dichalcogenide p-n junctions. Taking into account the three-atom thickness and low optical absorption of monolayer

WSe 2 [118, 119] the responsivity and EQE reported here are quite substantial. Fur- ther, the device geometry could be optimised to significantly enhance photoresponse. We expect that vertical junctions based on transfer-aligned exfoliated flakes [14] or large-area dichalcogenides grown by chemical vapour deposition [118] could increase responsivity and external quantum efficiency by more than an order of magnitude. Additionally, improved contact resistance, particularly for holes, should dramatically improve device performance.

6.6 Conclusions

In conclusion, we have demonstrated electrically tunable p-n diodes based solely on monolayer WSe 2. These diodes strongly rectify current, in a direction selectable by the two gates controlling the device. Both the PN and NP configurations have diode ideality factors of n = 1.9 and a rectification factor of 10'. With laser light incident on the junction, these diodes produce a large photocurrent with a responsivity of 210 mA/W at high bias. At low bias, the diodes generate power via the photovoltaic effect, with a peak external quantum efficiency of 0.2% at 522 un. The spectral

80 response of the photocurrent from visible to near infrared wavelengths showed peaks corresponding to the three lowest excitonic transitions expected for monolayer WSe 2 . Finally, these devices also function as light-emitting diodes with an electrolunines- cence peak at 752 urn. These p-n diodes demonstrate the potential of monolayer

WSe 2 , in addition to other direct gap semiconducting dichalcogenides, for novel electronic and optoelectronic applications. As device quality improves, they also lay the foundation for more fundamental quantum transport experiments [120].

Note added: During the final preparation of this manuscript we became aware of similar work on p-n diodes inimonolayer WSe2 [121, 122].

6.7 Methods

Device fabrication begins with exfoliation of bulk, natural WSe 2 (Nanosurf Inc.) down to few-layered sheets using the mechanical cleavage method pioneered for graphene [9].

The thin flakes are deposited onto a transfer slide made as a stack of glass, a poly- muer (polydimethylsiloxane [PDMS]), and a resist (methyl methacrylate [MMA]), as described for graphene-boron nitride device fabrication [14, 113]. Single molecular layers are identified by optical contrast. Layer number is later confirmed with atomic force microscopy and either photocurrent spectroscopy or electroluminescence (see the

Device Fabrication section of Appendix B). These monolayers are transferred onto a pair of split gates covered by 20 nm of HfO2 (grown by atomic layer deposition at 80

C). The gates are separated by a 100 nm gap, patterned using e-beam lithography on a highly doped Si substrate covered in 285 nm of thermally grown SiO 2 . They are made from e-beam evaporated gold and are 20 nim thick. The two back gates are capacitively coupled to the device through the HfO 2 dielectric, which has a dielectric constant, Er~ 15. The WSe 2 is contacted by two gold electrodes, each approximately

1 /-mt wide and 25 nmi thick with a 0.3 nm chromium sticking layer.

All measurements were performed at room temperature and in vacuum (- 10- torr) to avoid device degradation from adsorbates present in air, which could be imitigated by encapsulation of the WSe 2 . Electrolumirnescence (EL) was measured

81 using a liquid nitrogen cooled charged-coupled device with an integration time of 60 seconds. A background measured at Vd, = 0 was subtracted from all four EL traces in Fig. 6-3d.

82 Appendix A

MoS 2 Supplementary Information

A.1 Fabrication

The devices presented here were fabricated starting from mined, naturally-grown, flake MoS2 acquired from SPI Supplies. MoS 2 was exfoliated from the bulk material down to atomic layers using a mircomechanical cleavage process standard for graphene [1]. The flakes were deposited onto highly doped silicon substrates with a 285 urn, thermally-grown, silicon-oxide dielectric layer. Monolayers and bilayers were identified by optical contrast [90] using a Zeiss Axio-Inager microscope. Op- tical identification was calibrated and checked with AFM measurements (Fig. A-1). Step heights fron the substrate to the flake were often found to be slightly larger than the predicted inter-layer spacing for MoS 2 (0.62 nmi) [123]. As is common with graphene depositions on SiO 2 , the discrepancy was reduced after thermal annealing in Ar/H 2, though the step would still remain marginally higher than expected. Layer to layer measurements, however, match very well with predicted inter-layer spacing (Fig. A-1). Once identified, candidate flakes were contacted using PMMA masks patterned with e-beam lithography and developed in cold (- 5 'C) MIBK:IPA, 1:1. Contacts were then deposited using either e-beam or thermal evaporators, with gold contacts 50-100 num thick, and titanium sticking layers 0.3-3.5 nm thick (Table A.1). After annealing, device B2 was annealed in an Ar/H 2 environment at 350 'C for 3 hours,

83 AFM Step Height (a) 2 nm (b) 2 Bilayer 1.5 , 1.5 E 0.67 nm 1.0 .

.5 0.5 0 0.85 nm

0 0 0 0.2 0.4 0.6 0.8 1 Distance (pm)

Figure A-1: MoS 2 flake AFM and step heights. (a) Atomic force micrograph of an MoS 2 flake containing both monolayer and bilayer regions deposited on an SiO 2 substrate. The light blue (monolayer) and dark blue (bilayer) lines added show the position of the step heights in (b). Scale bar is 2 Am. Inset: Optical image of the flake in (a) showing the color contrast change with layer number. Scale bar is 2 Pm. (b) Step height for monolayer (light blue) and bilayer (dark blue) regions of an MoS 2 flake. though this procedure did not seem to have a substantial effect on quality. Device B2 was also etched into a Hall bar pattern using oxygen plasma. All other devices reported on in chapter 5 were unetched. All of the devices were annealed in situ at high temperatures (- 120 'C) in vacuum (~10-6 mbar) for 5-20 hours. This procedure caused a substantial drop in two terminal resistivity (Fig. A-2) and the elimination of Schottky behavior in the contacts down to 4 K.

Table A.1: Device Fabrication Parameters

Device Length Width Sticking Layer (Ti) Metal (Au) Vacuum Annealing M1 4.0 pm 2.6 pm 0.3 nm 100 nm 120 0C, 20 hours M2 3.5 pm 4.2 pm 0.3 nm 60 nm 120 'C, 10 hours M3 3.5 pan 3.2 pm 0.3 nm 60 nm 120 'C, 10 hours B1 4.6 jim 5.1 Am 0.3 nm 100 nm 120 0C, 10 hours B2 5.0 pim 0.6 pm 3.5 nm 50 nm 100 OC, 5 hours

84 Annealing Monolayer (a) 107 (b) 1012 T=1200C 50 Vbg 10 9 Before

- 106 After Bilayer 106

5 Monolayer T=20 C 10 10 0 3 6 9 12 0 10 20 30 40 50 Time (hours) Vbg (

Figure A-2: Effect of annealing on two-terminal resistance of MoS 2 devices. (a) Two-terminal resistance change over time for monolayer (yellow) and bilayer (blue) devices being annealed at 120 'C in vacuum. (b) Back-gate sweeps of a monolayer device before and after vacuum annealing. Data from devices Mi and Bi.

85 A.2 Metal Insulator Transition

The Ioffe-Regel condition for two-dimensional semiconductors states that kF *A - 1 at a metal-insulator transition [124], for the Fermi wave vector, kF \/2w7n and the mean free path, A = hkF u/nc2 . This leads to the expectation that the critical resistivity, pc, will be of order h/c 2 . Our results match this condition, though the mean, h/2e2 , is slightly below the predicted value.

Table A.2: Metal Insulator Transition

Device Critical Resistivity, pC (h/e 2 ) M1 0.9 M2 0.8 M3 0.7

B1 0.4

B2 0.3

Table A.2: Resistivity of monolayer and bilayer MoS 2 at the metal insulator transition. Four-terminal critical resistivity, pc, of monolayer and bilayer devices. The values mark the resistivity at which the lowest tem-

perature traces of p vs. Vbg cross.

A.3 Hall Measurements

Density, n, and Hall mobility, I'H, were calculated from Hall measurements performed in a magnetic field. The current was sourced longitudinally along the device from one of the outer contacts. The transverse voltage, Vy, was then measured across the sample. The Hall resistance was calculated as R I/Voy. Fitting a linear trend to RY as it varies with magnetic field yields the Hall coefficient, RH= dR '/dB. (Fig. A-3). There was a non-zero transverse resistance at zero field due to imperfec-

86 tions in contact alignment and sample inhomogeneities. This offset was subtracted from the data as it was small and irrelevant to our fit of the slope.

Monolayer Density (a) (b) 3 25 -/ Monolayer 2 25 V 0 [ 75 Vb. E o Vbg 0: 1

Bilayer 25 V -251 T=10K- o5 Vbg n -1 0 1 00 100 200 300 B (T) T (K)

Figure A-3: Hall measurements of MoS 2 . (a) Hall resistance of a monolayer MoS 2 device. Hall resistance, Rx, of a monolayer device as a function of magnetic field, B, measured at 10 K. Traces shown are at back-gate voltages of 25 (blue) and 75 (yellow). The dotted lines show linear fits to the traces. (b) Density as a function of temperature for monolayer and bilayer MoS 2 at 0, 25, and 50 Vbg, colored from dark to light. Data from devices M1 and B2.

A.4 Mobility

If pH varies linearly with density, the field-effect mobility will vary with density with twice the slope. To show this, we write pH = A -n + C, where A and C are constants. Then PFE PH + n dtH/dn = A -n + C + n - (A) = 2A . n + C. Then dp-rE;/dn 2A 2 - dpH/dn, as stated in chapter 5.

87 Monolayer Monolayer (a) 10 (b) 105 106 T=5K -50 Vbg -25Vbg 0 Vbg 4 ,-- 10 0 10 0C 101K

200K 300K 10 103 -50 -25 0 25 50 3 10 100 300 Vbg (V) T (K)

Figure A-4: Contact resistance and four-terminal resistivity of monolayer device M. (a) Four-terminal resistivity of device M1 as a function of Vbg. Curves colored from red to black show measurements at 300, 200, 100, 50, and 5 K, respectively. Inset:

Contact resistance, Rc, to device M1 as a function of Vb, at 5 Kelvin. (b) Resistivity of device M1 as a function of temperature. The curves, from black to orange, correspond to V, = -50, -25, 0, 25, and 50 V.

Room Temp. Mobility Leakage (a) 150 (b) 4 T=20 0 C 2 1001 '0' C E CU 50 PF -2 PH M B Monolayer M2 B2 Oh -4 -25 0 25 50 75 -50 0 50 Vbg (V) VbgV)

Figure A-5: Room temperature mobilities and leakage current. (a) Hall and field effect mobilities for monolayer and bilayer devices at room temperature. Data from devices M1 and B2. (b) Representative leakage currents measured for each device presented in the text.

88 A.5 Acknowledgments

We would like to thank Lili Yu and Han Wang for their help with early device fabrication and measurements, and Andrea Young for many fruitful discussions. This work was funded by the ONR GATE MURI and a Packard Fellowship. This work made use of the MRSEC Shared Experimental Facilities supported by NSF under award No. DMR-0819762 and of Harvard's CNS, supported by NSF under grant No. ECS-0335765.

89 90 Appendix B

WSe 2 Supplementary Information

B.1 Device Fabrication

Devices for this paper were fabricated from a natural crystal of WSe 2 from Nanosurf. The bulk crystal was exfoliated down to few-layered sheets by mechanical cleavage using a semiconductor grade low-tack tape. The thin flakes were then deposited onto a glass/PDMS/MMA transfer slide. The transfer slide is built as a stack of a glass slide, PDMS ~ 2 mm thick, a piece of clear packing tape (the tape improves smooth MMA adhesion), and a bilayer of MMA. The transfer slide is then searched using an optical microscope, and single molecular layers are identified by optical contrast [90]. Flake thickness is later confirmed with AFM (see Fig. B-1) and either photocurrent spectroscopy or electroluminescence spectroscopy. The gates were patterned using e-beam lithography onto a highly doped Si substrate covered in 285 urn of thermally grown SiO 2. The gates are Au for the main device used for most measurements and AuPd for the electroluminescence (EL) device

(see Fig. B-2). They were evaporated in an e-beam evaporator 20-30 nm thick with a 0.7 nin Cr sticking layer, and are separated by a 100 inmi gap for the main device and a 300 rim gap for the EL device. They are both covered in 20 nim of HfO 2 grown by atomic layer deposition at a terriperature of 80 C.

Monolayer WSe2 was transferred onto the gates using a mnicromianipulator and a microscope with a long working distance objective. The WSe2 sits on top of the

91 Height (nm) (a) (b) 5 20

t~~ 10 0.9 nm -- 2.5 . -.~

-2.5

-5 -5 -2.5 0 2.5 5 X (pm)

Figure B-1: Optical micrograph and AFM with step height of the main device. (a) Optical micrograph of the main device after transfer to pre-patterned split gates. The consistent faint color of the flake is indicative of a monolayer. The scale bar is 2pm. (b) Atomic force micrograph of the right side of the device. This AFM image was taken after the left side of the device was destroyed by electrostatic shock. Inset: Step height of the WSe 2 flake showing a step of 0.9 nm, which is consistent with one molecular layer of WSe 2 with some fabrication residue on an uneven surface.

HfO 2 and is contacted by two Au contacts for the main device and one Au and one Pd contact for the EL device. The contacts are each approximately 1 pm wide. The main device contacts are 25 nm thick with a 0.3 nm chromium sticking layer, and the EL device contacts are 50 nm thick with a 0.7 nm chromium sticking layer. Fig. B-1 shows an optical micrograph of the main device on the split gates after transfer. An atomic force micrograph of the right side of the device is also shown along with the step height of the WSe 2, confirming that it is a monolayer. The measured thickness of 0.9 nm is consistent with a monolayer with some fabrication residue on an uneven surface and is appreciably less than the 1.4 nm thickness of a bilayer. Pho- tocurrent spectroscopy and electroluminescence spectroscopy also corroborate this identification.

92 EL Device

Figure B-2: Optical micrograph the EL device. Optical micrograph of the device used to measure electroluminescence. The WSe 2 flake sits on two AuPd split gates separated by 300 nm and covered in 20 nm of HfO2 . It is contacted by Pd on the left and Au on the right. The scale bar is 2pm.

93 B.2 Mid-Gap Current

It is expected that the band gap of WSe2 will create an insulating state between the four conducting quadrants in gate-voltage space (NN, PP, PN, and NP). In Fig. 6-2 of the main text, however, current through the device does not drop to zero between NN (upper right corner) and NP (lower right corner) at room temperature. By cooling the device to 200 K, the conducting states disappear and the gap region becomes fully insulating (see Fig. B-3). We speculate that this behavior reflects thermal activation of mid-gap states created by disorder in the sample.

Vds=-2V l-2s (a) 10 (b) 10 (C) 10 pA 2K22KInA 5 5 lpA

2, 0 > E 0 > e 0

-5 -5

-10 -10-10 -10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10 V (V) V" (V) V9 V (d) 10-6

10"

270 K 10 200 K

-10 -5 0 5 10

Figure B-3: Temperature dependence of mid-gap current. (a) A logarithmic color plot of Ids at V, = -2 V as the two back gates are varied independently. The map was taken at room temperature (290 K), and mid-gap current is visible connecting the NP and NN quadrants with a conducting region. (b) and (c) The same measurement as in (a), at 270 K in (b) and 200 K (c), showing the diminishing conductance of the mid-gap states. (d) Line cuts along Vg with Vg fixed at 10 V. By 200 K, the mid-gap current is completely suppressed.

94 B.3 Schottky Barriers

In this section we discuss the role of Schottky barriers on the performance of the p-n diodes presented in chapter 6. Schottky barriers likely dominate the current through the device near zero gate voltage. However, the measurements presented in this paper were almost all obtained near the maximum gate voltage allowed before dielectric breakdown, minimizing the effects of any barriers present. In this regime of high electrostatic doping, several aspects of our measurements demonstrate that the transport characteristics of these devices are dominated by the p-n junction defined by the gates and not by residual Schottky barriers:

First, Figure lb shows that nearly ohmic contact is achievable at high carrier density for both contacts at both n-type and p-type doping (NN and PP configurations). The Id,-V, curves for the NN and PP configurations are slightly asymmetric, indicating the presence of residual Schottky barriers even at high carrier density, but it is important to note that the currents for both the PP and NN configurations are much larger at low source-drain bias than the NP and PN configurations. This demonstrates the dominant role of the p-n junction. For instance, at Vds = 0.5 V we see that the relatively weak PP current is four orders of magnitude larger the the current in either PN or NP (~20 nA vs. 1 pA). Because of the small cross-coupling of gate capacitances (which can be seen in Fig. 6-2 of the main text), the widths of the Schottky barriers in the PN and NP configurations are expected to be the same as in the PP and NN configurations for the same gate voltage magnitudes. Thus, current through the device in PN and NP is dominated by the junction.

In addition to this, the presence of a strong photocurrent signal in the PN and NP configurations further supports the conclusion that Schottky barriers at the contacts have only a weak influence on the device characteristics. Though band bending from Schottky barriers generally produces photocurrent, the addition of a p-n junction between the contacts suppresses the photocurrent contribution from the Schottky barriers [125]. In such a configuration, the carriers generated at the contacts are blocked by the depletion region at the p-n junction. A p-n junction capable of blocking

95 photocurrent from the contacts is certainly formed in our devices, as demonstrated by the suppression of the drain-source current at low bias, presented in Fig. 6-1 of the main text. Similarly, photocurrent generated by the p-n junction could be blocked by Schottky barriers at the contacts. If Schottky barriers dominated the flow of current through our devices, we would expect little or no photocurrent in the PN and NP configurations, contrary to what is observed.

Finally, the emission of light in the PN and NP configurations and not the NN and PP configurations (Figure 4d) provides another indication that the p-n junction and not residual Schottky barriers dominates the performance of these devices. We note in chapter 6 that asymmetric contacts (one Au, one Pd) were used specifically to reduce the influence of contacts on the performance of the device. If the device behavior were, nevertheless, Schottky-dominated, we would expect light emission from the Schottky barriers for all four doping configurations [93], in contrast with our observations. In principle, some electroluminescence from the residual Schottky barriers in our devices should still be observable for NN and PP. But the fact that these emissions are below the sensitivity of our measurement indicates that they are at least two orders of magnitude weaker than the electroluminescence peak in the PN configuration.

Contact resistance is expected to reduce the magnitude of photocurrent generated by the p-n junction, negatively impacting the photovoltaic EQE and the maximum current that limits electroluminescence yield. For the photovoltaic performance of the device, we note in chapter 6 that the EQE of 0.2% is limited by the two dominant factors of the 10% light absorption by monolayer WSe2 and the narrow p-n junction formed by our lateral gate geometry. Both of these effects reduce the efficiency of the device by approximately a factor of 10. Further losses may be limited by the residual Schottky barriers, recombination of electron-hole pairs, or other factors, but are not the dominant effects presently limiting PV efficiency.

96 Iph (nA) Vph (MV) (a) 4 8 (b) 4 30

4 15 2 10 2 0

0 =0

-2 -2

-4 -4 -4 -2 0 2 4 -4 -2 0 2 4 X (pm) X (pm)

Figure B-4: Photocurrent and reflected light image. (a) Color plot of the photocurrent, Iph, as the laser spot (power 75 pW, wavelength 830 nin) scans over the device.

The peak in current corresponds to the location of the p-n junction. Outlines of the contacts and gates taken from the reflected image are overlaid for context. The scan was taken with the device in the NP configuration (ig = 10 V, V1 g = -10 V) at zero bias. (b) The corresponding reflected image taken simultaneously with the photocurrent map. The outlines of the contacts and gates are drawn over the image.

97 PV Power Annfl

300 - ~0 Si

0. 0/ 200 -

0 0~ 0'

100 -

0 .. 0 2 4 6 8 10 Plaser (pW)

Figure B-5: Dependence of photovoltaic power generation on laser power. Plot of the maximum power output from the device as a function of laser power. The data is plotted in green circles and the black dashed line shows a linear fit to the data. Laser wavelength: 700nm.

Figure B-6: Reflected and emitted light image. A third monolayer WSe2 device, configured as an LED (PN configuration. V = 2 V, Id, = 25 nA) and simultaneously illuminated with a halogen lamp. The emitted and reflected light are imaged with a liquid nitrogen cooled CCD (integration time 10 s, color scale represents counts recorded by the monochrome CCD). This device has one Au and one Pd contact. The scale bar is 5 pym.

98 B.4 Acknowledgements

We would like to acknowledge experimental assistance from Kaiphol Akkaravara- wong, Trond Andersen, Nathaniel Gabor, Qian Lin, Qiong Ma, Wenjing Fang, and Javier Sanchez-Yamagishi and discussions with Patrick Brown. This work has been primarily funded by ONR Young Investigator Award N00014-13-1-0610, and partly by the ONR GATE MURI and a Packard Fellowship. This work made use of the MRSEC Shared Experimental Facilities supported by the NSF under award No. DMR-0819762 and of Harvard's CNS, supported by the NSF under grant ECS-0335765.

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