Kelvin probe force microscopy

Kelvin probe force microscopy (KPFM) is the method, which allows to map work function of materials with high spatial resolution. It relies on operation of Atomic force microscope (AFM). In this thesis Cypher AFM (Asylum research) was used to perform both AFM and KPFM. We skip revision of AFM, as soon as it is a standard imaging technique for materials science, and concentrate on commenting the KPFM mode.

In KPFM one measures a contact potential difference (VCPD) between a conducting tip

inside AFM and a surface under investigation. It can be written in the following way [93]:

VCPD=φt− φs

3.4. Material characterization

b

a

c

Figure 3.6 – Electronic energy levels of the sample and AFM tip for three cases. (a) Tip and sample are separated by distance d with no electrical contact. (b) Tip and sample are in electrical contact. (c) External bias VDCis applied between tip and sample to nullify the

CPD and, therefore, the tip–sample electrical force. Ev is the vacuum energy level. Ef sand

Ef t are Fermi energy levels of the sample and tip, respectively. Reprinted from W. Melitz, J. Shen, A.C. Kummel, and S. Lee, "Kelvin probe force microscopy and its application",

Surface Science Reports, vol. 66, no. 1, pp. 1-27, © (2011), with permission from Elsevier.

Whereφtandφscorrespond to workfunction levels of tip and sample respectively. On

Figure 3.6 electronic levels of the sample and conductive AFM tip are discussed. Without electrical contact tip and sample, each having certain work function level, are isolated from each other (Figure 3.6a). When tip and sample are put into electrical contact due to

work function mismatch the CPD is created. In KPFM one compensates VCPDby applying

external voltage VDCto the tip. Typical KPFM maps represent the spatially resolved surface

potential maps.

The measurements are performed in the following way. Alternating signal is applied to the tip VAC, which creates electrostatic force, while VDCis used to minimize this force. The

electrostatic force can be written in the following way:

Fes(z)= −

1 2ΔV

2dC (z)

d z (3.3)

WhereΔV is the difference between VCPDand voltage applied to the tip anddC (z)_{d z} is the

gradient of effective capacitance between the tip and the specimen. We further develop Equation 3.3 taking into account DC and AC components of voltages applied to the tip:

Fes(z)= − 1 2 dC (z) d z [(VDC±VCPD)+VACsin(ωt)] 2 _(3.4)

Equation 3.4 can be further divided on 3 parts: FDC(z)= − dC (z) d z [ 1 2(VDC±VCPD) 2 ] (3.5) F_ω(z)= −dC (z) d z (VDC±VCPD)VACsin(ωt) (3.6)

b

a

Figure 3.7 – Example of graphene work function imaging. (a) Topography of the graphene Hall bar is superimposed with surface potential maps on a 3D image. (b) Plots show characteristic profiles, i.e. surface potential on top and topography on bottom along the horizontal line in the center of the image (not shown). Adapted from V. Panchal, R. Pearce, R. Yakimova, A. Tzalenchuk, and O. Kazakova, "Standardization of surface potential measurements of graphene domains", Scientific Reports, vol. 3, p. 2597, © (2013), Rights Managed by Nature Publishing Group .

F2ω(z)= − dC (z) d z 1 4V 2 AC[cos(2ωt) − 1] (3.7)

Equation 3.6 is used to measure VCPD. There are several types of KPFM modes. Similar to

3.4. Material characterization

surface. First run is the standard tapping mode to determine the topography of our sample, during the second run we lifted the tip and performed work function measurement of the

surface, zeroing the potential difference VCPD. This is so-called amplitude modulation

(AM) mode of measurement. We refer to comprehensive review on the topic in Ref. [93] for further information.

4

Electrical Transport Properties of Single-

Layer WS

₂

4.1 Introduction

Monolayer MoS2 was the first to attract significant attention of scientific community

partially due to the fact that high quality single crystals of this material are abundant in nature. Other members of TMDCs materials family however appear to be also very promising both for electronics and optics. Monolayer WS2has identical crystal structure to

MoS2and a direct bandgap of at least 2.0 eV [95]. Due to the presence of heavier tungsten

atoms in this material spin-orbit coupling is more pronounced [96] than in MoS2case and

thus valence band spin splitting reaches the value of 400 meV. This in principle should allow easier observation of the valley Hall effect [29, 97] in WS2than in MoS2. In this

chapter we are going to discuss electrical transport properties of monolayer and bilayer WS2. This chapter is based on the article published in ACS Nano, 2014, 8 (8), pp 8174–8181,

where Dmitry Ovchinnikov was the first author. There is significant overlap between this chapter and the above mentioned paper.

Our initial interest to this material was based on the lack of fundamental knowledge on electrical transport properties of monolayer WS2at the time. One of the early theoretical

transport studies [98] indicated that among monolayers of TMDCs WS2has the lowest

effective mass, which leads to improved ON current and mobility according to calculations. In fact recent experimental study [99] of "clean" samples encapsulated in h-BN partially

support this hypothesis, where WS2samples have higher mobility than MoS2. Although

mobility depends not only on effective mass, but also on defects [100, 101], dielectric environment [16, 102] and device fabrication procedure [16, 103], it was important to

show devices in simple geometry similar to studied at that time monolayer MoS2samples

[75, 102, 104, 105]. Monolayer MoS2lacks p-type conduction, while monolayer WS2was

reported to have ambipolar carrier injection [85], which was possible using ionic liquid

are shown on Figure 4.1. Ionic liquid gating, however, is known to provide low contact resis- tances even for such intrinsic materials as monolayer WSe2[58], [60] and thus performance

of devices with solid gate can be remarkably different. For practical applications solid gated devices are preferred, where contact resistance has never been studied for mono- layer WS2. Efficient carrier injection with solid gate, as well as information on temperature

dependent transport properties was missing. Although some reports found insulating behaviour of transport in mono- and multilayers of WS2[106], band-like transport was not

demonstrated. On the other hand one would intuitively expect to have band-like transport and metallic state due to similarities with MoS2[75, 102, 104, 105].

b

a

Figure 4.1 – Ionic liquid gating of WS2. (a) Ambipolar transport in monolayer WS2for

different Vds. Adapted with permission from S. Jo, N. Ubrig, H. Berger, A.B. Kuzmenko, and

A.F. Morpurgo, "Mono- and bilayer WS2light-emitting transistors", Nano Letters, vol. 14,

no. 4, pp. 2019-2025, © (2014) American Chemical Society. (b) Ambipolar transport in

multilayer WS2with quantitative determination of bandgap. Adapted with permission from

D. Braga, I. Gutiérrez Lezama, H. Berger, and A.F. Morpurgo, "Quantitative Determination of the Band Gap of WS2with Ambipolar Ionic Liquid-Gated Transistors", Nano Letters, vol.

12, no. 10, pp 5218–5223, © (2012) American Chemical Society.

In this chapter we demonstrate simple devices - mono- and bilayer WS2FET, which

are fabricated on SiO2substrates with global back gate underneath. Our devices show

n-type behaviour and Ion/Ioffcurrent ratio in the order of 106. These samples have channel

exposed to atmosphere and we demonstrate, that by careful annealing we are able to modulate both doping level of the channel and contact resistance. We find that initially our samples are quiet resistive, but long annealing in vacuum can restore band-like transport and relatively low contact resistances. Field-effect mobilities at room temperature even

in non-optimized geometry show values, comparable to state of the art monolayer MoS2

transistors. Furthermore, we turn our attention to temperature-dependent measurements. We observe metal-insulator transition and explore both metallic and insulating states.