Characterizing optical and electrical properties of monolayer MoS

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Master Thesis

2020-02-17 to 2020-08-07

Characterizing optical and electrical

properties of monolayer MoS

₂

by

backside absorbing layer microscopy

Nathan Ullberg

supervised by Vincent Derycke

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Nathan Jean Carl Ullberg (ORCID 0000-0002-7264-7992).

To contact author, email to gmail DOT com with the username nathan DOT ullberg.

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Abstract

Nanomaterials are playing an increasing role in novel technologies, and it is important to develop optical methods to characterize them in situ. To that end, backside absorbing layer microscopy (BALM) has emerged as a powerful tool, being capable to resolve sub-nanometer height profiles, with video-rate acquisition speeds and a suitable geometry to couple live experiments.

In the internship, several techniques involving BALM were developed, and applied to study optical and electrical properties of the transition metal dichalcogenide (TMD) monolayer MoS2, a type of 2-dimensional (2D) crystalline semiconductor. A simulations

toolkit was created in MATLAB to model BALM, a workflow to reliably extract lin-ear intensities from the CMOS detector was realized, and 2D MoS2 was synthesized by

chemical vapor deposition followed by transfer to appropriate substrates. BALM data of the 2D MoS2 was acquired and combined with simulations, giving a preliminary result

for its complex refractive index at 5 optical wavelengths. In addition, the first steps to-wards coupling BALM with a gate biased 2D MoS2 field-effect transistor were explored.

To complement BALM measurements, the grown samples were also characterized by conventional optical microscopy, scanning electron microscopy, atomic force microscopy, photoluminescence spectroscopy, and Raman spectroscopy.

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Acknowledgements

Firstly, I would like to thank my supervisor Dr Vincent Derycke. He has devoted a considerable amount of time to help me get on board with the project, in all aspects including scientific, technical, and practical. As the LICSEN team is a part of the UMR 3685 called Nanoscience and Innovation for Materials, Biomedecine and Energy (NIMBE), I want to thank its director DrSerge Palacin. I also thank the administrator of NIMBE, Mme C´eline Delobel. I thank all members of LICSEN, with whom it has been great collaborating with. In regards to photoluminescence and Raman characterization, I thank Dr Arianna Filoramo. I thank the CEA Bottom-up Transverse Program for the funding, in particular Dr Benjamin Gr´evin, coordinator of the Hypothese project. The SMNO

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degree. The internship was full-time in 2020 and took place from February 17 to August 7, with the report due July 10 and the defense on July 17. Additionally, I will be continuing the project as a PhD student starting October 1, thanks to a doctoral MESRI grant, with an affiliation to the EOBE (575) doctoral school of Universit´e Paris-Saclay.

The location of the internship was the Laboratory of Innovation in Surface Chemistry and Nanosciences (LICSEN) which is a part of the French Alternative Energies and Atomic Energy Commission (CEA), where the lab falls within the structure CEA Paris-Saclay/DRF/IRAMIS/NIMBE/LICSEN. The CEA was founded in 1945 with the initial goal of developing nuclear energy, but has since then evolved to encompass other energy sources, as well as other fields of science and technology. LICSEN combines physicists and chemists, with a focus on studying nanomaterials and the chemical functionalization of surfaces, for applications in energy, information and health.

The topic of the project is to study a new class of semiconductors called transition metal dichalcogenide (TMD) monolayers, and how they and their vertical van der Waals heterostructures (vdWHs) can be used for applications in optoelectronics. The project is primarily experimental physics and chemistry, but also involves performing simula-tions.

In the report, I begin by a general scientific introduction on TMD optoelectronics in section 1.2. Then, in section 2 I present and discuss the synthesis of TMD monolayers, specifically that of 2D MoS2 which was a focus in the internship, followed by various

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1.2 TMD optoelectronics

In the field of materials science, nanomaterials have attracted significant attention due to their wide variety of interesting properties both for fundamental research and application. In particular, low-dimensional crystals confined in either 2, 1 or 0 dimensions exhibit behaviors that differ dramatically from their 3D counterparts. The origin of this change in behavior can be attributed in large part to quantum mechanical effects which become more prominent when the physical dimensions of the material are on the scale of atomic radii (< 1 nm). For this reason, nanomaterials are often considered to be a type of quantum material. Furthermore, the nomenclature of “quantum well”, “quantum wire” and “quantum dot” are attributed respectively for 2D, 1D and 0D materials.

The first 2D crystal to have been systematically isolated was a single sheet of graphite, known as graphene, in 2004.1 _{However, low-dimensional systems of carbon had in fact}

previously been explored theoretically by Dresselhaus and others.2 In 2005, the first 2D semiconductor device was realized, using monolayer MoS2,3 although it was only in 2010

and 2011 that such a device was fabricated with more appreciable performance.4–7 _This

marked an important step because since graphene is intrinsically semi-metallic (a zero band gap semiconductor), it is not well suited for applications that require a band gap. Following the realization of 2D MoS2, the discovery of a class of similar crystals quickly

followed, known as transition metal dichalcogenide (TMD) monolayers. These crystals have the general formula M X2, where M is a transition metal and X is a chalcogen atom

(most commonly sulfur or selenium) as shown in Figure 1.

Figure 1: Schematic adopted from A. Kis et al. 20115 of a transition metal dichalcogenide crystal, with multiple monolayers of the trigonal prismatic (2H) phase forming the 3D version of the crystal by vdW stacking.

2D systems exhibit a wide range of interesting properties, but the focus of this report is on optical, electrical, and optoelectronic properties. Furthermore, although other 2D systems than the ones already mentioned exist, such as phosphorene, borophene and silicene, only TMDs will be discussed in detail. It is worthwile to note however that graphene and other 2D materials can play a role of being integrated with TMDs, for instance as a means to lower contact resistance in devices.8

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of the 2D planes bound by weak van der Waals (vdW) bonds out-of-plane, while the in-plane bonds are covalent.

The top-down scotch tape method does not scale however as the flakes obtained are typically only on the order of 10 to 8 × 104 _µm2_{, and only a few are obtained per chip,}

and not in a predictable manner.9 _{Hence, bottom-up approaches of synthesis have been}

widely explored. The most popular synthesis technique for TMDs in recent years has been by chemical vapor deposition (CVD).10,11 _{Other techniques including molecular}

beam epitaxy (MBE) are also being explored as more controlled means to synthesize TMDs.12

The possibility to synthesize a large number of different TMDs with different band gaps and work functions13 allows for band engineering. Furthermore, besides the choice of metal and chalcogen, electrical properties can also be tuned by other means such as binding molecular layers that alter the Fermi level, or by introducing chalcogen vacancies. 2D semiconductors can be combined vertically or laterally, resulting in a junction, often of PN type. When the vertical configuration is used, the stack is called a van der Waals heterostructure (vdWH) and can be used to create a wide variety of novel optoelectronic devices.8,14–17 The idea of band engineering is not new and is already widely employed in optoelectronics by use of other semiconducting systems such as silicon or III-V, however TMDs offer various potential advantages, such as that lattice matching at the interface is not a requirement since the interfacial bonds are of vdW type.

Some devices that can be realized with vdWHs of TMDs include photoemitters,18

photo-voltaics,19,20 _{photodetectors,}21 _{photocatalysts,}22 _{field-effect transistors (FETs)}5 _and

tun-nel FETs.23,24 The first four are optoelectronic devices while the last two are purely electronic, although FETs often play a role in optoelectronics. It is important to note that fabricating a TMD vdWH device such as a FET also serves as a characterization tool allowing extraction of intrinsic material properties like charge carrier mobility and doping, in addition to evaluating device performance.

The benchmark characterization techniques for TMD vdWHs include optical microscopy, scanning electron microscopy (SEM), atomic force microscopy (AFM), photolumines-cence (PL), Raman spectroscopy, photoresponsivity and electrical measurements includ-ing diode and transistor transfer and output curves. Many other characterizations can also be performed such as photoelectron spectroscopy (PES), transmission electron mi-croscopy (TEM), scanning tunneling mimi-croscopy (STM). In the report, I will briefly cover some items of the former enumeration, as well as synthesis aspects and other related topics, but the main focus will be on an optical microscopy based technique known as backside absorbing layer microscopy (BALM),25 _{which I have devoted the majority of my}

time on during the internship.

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2 TMD synthesis & characterization

Synthesis

The use of chemical vapor deposition (CVD) to synthesize TMDs is by far the most common, often using powder sources (P-CVD).10,11 _{The configuration usually involves}

a two-zone furnace where a chalcogen powder is placed upstream of a chip boat with a SiO2/Si wafer upside down and the metal powder beneath it, in which a carrier gas such

as Ar or N2 is used. Many variations of this setup exists, such as the use of a TMD bulk

powder upstream which is sublimated and carried downstream to the wafer.26

For the specific case of MoS2 monolayer growths, sulfur is the chalcogen upstream while

MoO3 is placed closer to the wafer, as shown in Figure 2. Furthermore, often a seed

promoter is used to help initiate nucleation of the growth.27 _{As to the physical mechanism}

of the growth, two main descriptions have been proposed: (1) an initial reaction occurs between MoO3 and S which then produces the intermediate volatile MoO3-xSy which by

further sulfurization and reaction of MoO3-xSy on the substrate leads to the formation

of 2D MoS2 grains; (2) MoO3 and S react only in the vapor phase, and MoS2 deposites

directly onto the substrate as nucleation centers from which triangles form.28

Figure 2: Schematic adopted from A. Kis et al. 201729 _{of the CVD growth setup for 2D}

TMDs, used at LICSEN.

At LICSEN, perylene-3,4,9,10-tetracarboxylic acid tetrapotassium salt (PTAS) is used as a seed promoter, with a single-zone furnace, for growth of TMDs. The sulfur powder position is adjusted from the main zone as a means to control its temperature while the boat with the wafer and MoO3 is at the center of the furnace. Prior to growth, the PTAS

powder is diluted in DI water at around 5 mM and spun on the wafer. Although it is possible to perform MoS2 growths without the use of a seed promoter,30 many groups

have reported better yield and sometimes higher quality for promoter-assisted growths. For the specific setup at LICSEN, the use of PTAS for MoS2 growths has always resulted

in better yield.

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Although the use of PTAS and other seeders is widely reported in the literature as being an important growth parameter for MoS2, few microscopic descriptions have been

thoroughly investigated. An exception is a 2020 paper by Ko et al.,31 which thoroughly investigates the atomistic role of crystal violet (CV) seeds for MoS2 growth, both by

experiment and DFT calculations. For the case of CV, they suggest that adsorption of a sulfur atom to the polar part of CV is the origin of the nucleation, while Mo adsorption actually would distort or destroy the CV. Other papers attribute the better growth result to a surface energy effect.27

For the project, we aim to acheive some understanding of the physical mechanisms taking place in the growths that we perform, in order to inform the choices of growth conditions to most efficiently and reliably obtain TMD monolayers for optoelectronic characteriza-tion which is the main focus.

Optical microscopy

Intriguingly, monolayer MoS2 which has a thickness of around 0.65 nm, can be visualized

at relatively high contrast with an optical microscope. This is possible by using an SiO2/Si

substrate where the SiO2 acts as an anti-reflective (AR) coating, enhancing significantly

the contrast of almost any given nanomaterial. An optical micrograph where an 80x magnification lens was used is shown in Figure 3.

Figure 3: Optical micrograph of CVD grown mono- and few-layer MoS2 on SiO2/Si.

Usually, in the world of 2D materials research, an upright microscope with the K¨ohler illumination coming from the objective is used, as in the figure. Since the use of AR coatings to study nanomaterials is the main subject of the report, it will be described in more detail in later sections.

Scanning electron microscopy

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is placed in vacuum, and an electron beam is made to be incident. Most commonly, the secondary electrons are measured and produce a signal. The back-scattered electrons can also be detected. The main drawback to SEM is that it does not resolve axially out of plane, even though axial contrasts are typically resolved but only qualitatively.

An SEM micrograph of mono- and few-layer CVD MoS2 is shown in Figure4.

Figure 4: Scanning electron micrographs of CVD MoS2 on SiO2/Si at (a) 400x

magnifi-cation and (b) 7000x magnifimagnifi-cation, showing nucleative sites on the first monolayer. The beam energy used was 15 kV which is typical, although lower beam energies around say 5 kV produces more surface sensitive results.

Atomic force microscopy

AFM is a type of scanning probe microscopy (SPM), where a tip attached to a cantilever is made to probe the surface, and the changes in tip height are measured by having a laser deflect off the cantilever and directed to a photodiode array which resolves the heights. An AFM micrograph of CVD MoS2 is shown in Figure5.

The advantage of AFM is that in contrast to SEM, it can resolve height profile. However, it is very slow, often by 1000 times. There exist two main modes: contact and tapping. The micrograph shown is tapping, which means that the tip is made to oscillated close to its resonant frequency, and gently taps the surface as it is scanning. As shown in the figure, the heights of the mono and bilayer are close to 0.65 nm which is the typical single layer height. Hence it is confirmed that the synthesized MoS2 is not multilayer.

The slightly larger substrate/monolayer height is typical as the flake is not perfectly adhered to the SiO2 surface which is not perfectly smooth. Furthermore, the halos on

the substrate itself indicate variations in height which also increases the error.

Photoluminescence

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Figure 5: (a) Tapping-mode atomic force micrograph of CVD grown MoS2 on SiO2/Si,

with a (b) trace indicating that the material is indeed monolayer/bilayer.

slowly (phosphorescence). The speed of recombination depends on a number of factors, such as if a particular transition is allowed by quantum selection rules. The process to recombine and luminesce (radiative recombination) is also usually slower than the electron being aided by phonons to travel back to lower energy states (non-radiative process).

Figure 6: Photoluminescence spectrum of CVD 2D MoS2 on SiO2/Si.

Monolayer TMDs have been widely reported to generate brilliant PL spectra, with distinct peaks for the various excitons and charged excitons (trions). A PL spectrum of my CVD synthesized MoS2 is shown in Figure 6. The peak center is at around 678 nm (1.8 eV),

which is the (direct) band gap of monolayer MoS2, while the bulk is known to have an

indirect gap of 1.2 eV. The shape of the PL, as well as its energy, is consistent with what is reported in the literature for 2D MoS2.4,32

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shift between excitation energy and emission is called the Stokes shift, as per Fox p. 5,33 _{which is not to be confused with Stokes Raman scattering.}

Note that excitation wavelength usually does affect the probability of emission, which when quantified is known as excitation spectroscopy. Hence, it is sometimes not sufficient to simply choose an excitation energy above the band gap of the material when probing PL.

Raman spectroscopy

The phenomenon of Raman scattering occurs when light loses or gains energy by creat-ing or absorbcreat-ing phonons/vibrations in a molecule or lattice. The former is called Stokes scattering while the latter is called anti-Stokes scattering. Since phonon energies and dispersions are closely related to the properties of a lattice, Raman spectroscopy is a powerful characterization tool to non-invasively probe the properties of crystals. Fur-thermore, if the incident light used to probe the crystal is in resonance with an electronic (quantum mechanical) resonance, Raman spectra can also provide information on the electronic Brillouin zone (this is called resonant Raman).33

For the experiment: a laser is made incident on the sample, the reflected signal is collected, the predominant elastic scattering (Rayleigh, defined at 0 cm−1) is filtered out as much as possible, and finally a spectrometer resolves the inelastically scattered light. Most often the Stokes signal is measured, as one needs to populate more phonon states (heat the sample) to get a more significant anti-Stokes signal.33

For 2D MoS2, the predominant peaks correspond to the E2g1 and A1g phonon modes. A

Raman spectra of monolayer and bilayer MoS2 that I grew is shown in Figure 7.

Figure 7: Raman spectrum of CVD grown mono- and bilayer MoS2.

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for 1L versus 2L MoS2 samples,34 confirming that the grown MoS2 is indeed mono- and

bilayer.

Workflow

The above methods and characterizations highlight important and relevant aspects that are necessary to perform prior to taking BALM measurements. The ability to grow 2D MoS2 with some control of morphology and density is not trivial, as there are many

parameters that impact growth outcome. LICSEN has in fact been optimizing the existing growth setup for several years prior, to realize 2D MoS2 such as that shown above.

Following a given synthesis, the first step is always to investigate under an optical micro-scope, giving an idea as to size, density, morphology, and layer number. Due to strong AR conditions of SiO2/Si, it is in fact possible for a trained eye to distinguish between

monolayer and bilayer since the optical properties of MoS2 change so dramatically with

layer number. However, this is not sufficient, and for that reason AFM height profiles can confirm that the material is monolayer, or few-layer. Along with SEM, these microscopies also reveal the kind of features that are present in the MoS2, such as defects, nucleative

sites on the monolayer, grain boundaries, and so on. Depending on the experiment, it may or may not be desirable to have nucleation sites on the monolayer, or isolated tri-angles versus a continuous film. For example, edge effects of the MoS2 can make for a

better catalyst.

In regards to the Raman and PL measurements, peak parameters provided additional confirmation that the grown material is primarily monolayer. By fitting the peaks with Voigt profiles one can also further deduce many properties of the MoS2, such as the extent

to which it is charged by the substrate.

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3 Backside absorbing layer microscopy

In the following sections, the background and theory of the BALM technique will be described, followed by how it was further developed and used during the internship.

3.1 Theory

3.1.1 Thin film interference & AR coatings

The phenomenon of thin film interference is well known in physics. When an EM wave encounters a medium with a different refractive index, part of the wave is reflected. This result is described by one of the Fresnel equations which for normal incidence is

rij =

ni− nj

ni+ nj

(1) where r is called the reflection coefficient (also known as the complex reflection amplitude). The reflectance R is the modulus squared, so R = |r|2 _{= rr}∗_{. For the}

transmitted wave, the transmittance is defined as T = 1 − R.

The principle of thin film interference can be used to create anti-reflective (AR) coatings. Conditions for destructive interference are

2ne = 1₂λ (2m − 1) , _{m ∈ Z}+ (2)

which can also be expressed as

OPL = ne = 1₄λ,3₄λ,5₄λ, . . . (3)

where e is the thickness of the film and ne is the optical path length (OPL). Since the first destructive condition is at a quarter of the incident wavelength, such coatings are called a quarter-wave layer.35

Note that such interference effects are much less prominent in a thick film (a film that is many multiples of the wavelength).36 _{This has to do with the thick film having less}

“angle tolerance” than the thin film. When one looks at a thick film, even a small change in angle between two incident rays will change the number of wavelengths traveled, so the effect tends to average out.

For a more general case of calculating r for an arbitrary number of optical layers, the following formula is used, as explained by Orfanidis p. 187,37 _{Born and Wolf p. 62}38 _and

the SI of Campidelli et al 2017:25 r012...`(`+1) = r012...`+ r`(`+1)e−iδ` 1 + r012...`r`(`+1)e−iδ` (4) where δ` = k0∆`, ∆` = n`2e` and k0 = 2π_λ

0. Note that this formula is compatible with

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contrast to gain which would use a plus sign. This general formula forms the basis of a computational implementation which is discussed later.

Often, multilayer structures are desired when designing AR systems. In particular, al-though single coatings can achieve low reflectance for say a particular wavelength, they cannot achieve low reflectance over a wider span of the visible wavelengths. However, with a multilayer structure such as a Quarter-Half-Quarter coating, this can be much better achieved, as shown in Figure 6.2.3 on p. 192 of Orfanidis.37

In addition to AR structures, there exist also AR absorbing (ARA) structures, which have various applications. For AR structures, the best AR conditions for a structure of incident/AR/emergent media as shown by Orfanidis p. 167-17037 _include

n2_AR= nine (5) with thickness eAR= λ 4nAR (6) For the ARA case, the best conditions for a structure of incident/ARA/emergent media are25,35,39 n2_ARA − κ2 ARA = nine (7) with eARA ≈ λ 4π (ni− ne) nARAκARA (8) 3.1.2 AR microscopy

The use of AR layers on substrates has significantly helped and accelerated the develop-ment of 2D materials research.35 _{By far the most common such substrate is ≈ 0.1 − 0.5}

mm thick, consisting of silicon (with diamond crystal structure, c-Si), with a few hundred nm of amorphous silicon dioxide (a-SiO2) grown by temperature induced oxidation. Prior

to oxidation, one of the sides of the Si is polished to significantly reduce RMS roughness. This results in a mirror-like wafer, of varying color depending on the oxide thickness, as dictated by thin film interference conditions.40 Due to the sensitivity of the system to other optical layers, materials < 1 nm can be visualized under a normal optical micro-scope. Therefore, graphene and other TMDs can be readily identified and studied. Albeit being a relatively simple system, it is important to recognize the incredible throughput, as when compared with for example AFM. Numerous papers have been published on op-timizing the SiO2/Si and wavelength conditions to maximize the contrast of 2D materials,

especially for graphene and graphene oxide (GO) which are less absorbing and thus more transparent than semiconducting 2D materials like TMDs. The most famous publication is from 2007 for graphene,41 _{and the respective color plot indicating the best color filter}

or wavelength to use for different thicknesses is shown in Figure 8. Notably, 90 nm was found to be a favorable thickness for enhancing the contrast in graphene.

The choice of a SiO2/Si substrate also serves the purpose of being an ideal platform to

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Figure 8: Weber contrast color plot for the optical stack of graphene on SiO2/Si with

axes varying the AR (SiO2) layer thicknesses and wavelengths, from Blake et al. 2007.41

a material (with a source electrode) on top of the SiO2 gate oxide, by the electric

field-effect. Fabricating an additional drain electrode results in a field-effect transistor which allows further electrical characterization and evaluation of device performance.42 The configuration is based on the thin-film transistor (TFT) architecture and also resembles silicon-on-insulator (SOI) except that it is “2D material on insulator”.

In principle, it would make sense to show color plots of AR conditions using reflectance R as the parameter, however this does not emphasize the degree to which the visibility of the specimen is enhanced, and furthermore it is difficult to deduce R (which translates to light intensity I) experimentally. For these reasons, either Weber contrast or Michelson contrast43 _{is used. The definitions are}

CW ≡ I − IS IS (9) and CM ≡ I − IS I + IS (10) respectively, where IS is the intensity of the substrate while I is the intensity of the

sample in question. In the literature, both formulations are employed. For example in Figure 8 the authors used the Weber contrast. For this report, the Michelson contrast definition will be used, and is preferred by the author as the values are always between 0 and 1, while with the Weber contrast, the values start to diverge if the substrate signal is very dark, which is not desirable.

Furthermore, AR microscopy allows for extracting the optical properties n and κ of a given specimen, which will be discussed in more detail later.

3.1.3 ARA microscopy

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been explored by various groups, dating back to 2008,44 _{and in various publications since}

then.45–48

In 2014, a particularly interesting ARA system was introduced by Dominique Ausserr´e et al. from Le Mans, France.39 _{The setup uses an inverted microscope geometry as shown}

in Fig. 9, with light incident through immersion oil, glass, thin gold, a nanomaterial, and a final medium of choice such as air, water, or other fluids. The technique is now called backside absorbing layer microscopy (BALM).

Figure 9: Optical stack used in backside absorbing layer microscopy (BALM).35 BALM is particularly powerful as the changes in optical contrasts can resolve as low as < 0.1 nm in the z-direction, which in most cases supersedes that of more conventional AR substrates such as SiO2/Si. Some sample BALM images of the CVD 2D MoS2 that

I synthesized are shown in Figure 14, while an MoS2 on SiO2/Si image is shown in

Figure3. Furthermore, its geometry allows for a variety of in situ experiments at video-rate throughputs. Following its invention, 6 patents have been obtained by D. Ausserr´e and co-workers including 2 co-owned by LICSEN, and the company WATCH LIVE was founded.

Following the first publication in 2014, a collaboration begun with LICSEN and a BALM setup was installed at the site. This led to a publication in 2017 by Campidelli et al.,25

where different chemistries of graphene oxide (GO) and reduced graphene oxide (rGO) were explored. This included for example the real time monitoring of Fe3O4nanoparticles

adsorbing on rGO.

Furthermore, LICSEN also hired PhD student K. Jaouen in 2017 specifically to further develop BALM and explore its potential as a tool to study 2D materials.35 _{This also}

resulted in a 2019 publication, which among other things showed how the real time mon-itoring of molecular film depositions in BALM could be resolved with an extraordinary precision of 0.15 nm at the single pixel level, and 10 pm for the 100x100 pixel level (∼ 7 × 7 µm2_).49 _{Jaouen also explored the coupling of electrochemical characterization}

with BALM, for example matching cyclic voltammetry (CV) with grayscale values for ferrocyanide on gold.35

In addition to research by D. Ausserré et al. and that of LICSEN, other groups have also used BALM in their experiments. For example, Frédéric Kanoufi and collaborators have published a number of papers involving BALM,50–55 _{and BALM has also been used to}

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As BALM is relatively new, there are many useful and interesting experiments that can be performed. In the context of my project to study optical and electrical properties of 2D semiconductors and vdWHs, one such experiment is extraction of the complex refractive index ˜n = n − iκ. This is discussed in detail in a later section, and furthermore how this can be extended to monitor the operation of a TMD transistor in real time.

3.2 Simulation

3.2.1 Context

Prior to my arrival, LICSEN had used COMSOL Multiphysics to build a 3D mesh of cells to simulate reflectances and contrasts for the BALM optical stacks, making use of the built-in optics libraries. Although in principle the use of COMSOL for this system would allow for more ambitious calculations such as including the rugosity of the thin gold layer, the drawback was that each computation would usually take several hours. Furthermore, many of the calculations that were desired did not require a high level of 3-dimensional precision as allowed for by COMSOL.

Therefore there was a need to create a model using a more light-weight tool that would be faster and hence make possible a large variety of calculations that cannot be acheived in a COMSOL model since it would take years to compute. The timing of the quarantine due to the COVID-19 pandemic presented an opportunity to develop such a simulations package using MATLAB. The benefit of the simulations are two-fold. Firstly, they help in the design of optimal BALM substrates for specific experiments; as is discussed in section3.2.2 for the case of maximizing the contrast for 2D MoS2 on gold, and in section

3.2.3 for the case of maximizing both contrast and contrast sensitivity for 2D MoS2

on a dielectric layer on gold for electrical transport experiments coupled with BALM. Secondly, simulations are necessary to allow for in-depth analysis of experimental values, as is exemplified by the determination of the optical parameters n and κ for 2D MoS2 in

section 3.3.4.

Finally, it should be noted that for the Campidelli et al. 2017 paper, one of D. Ausserr´e’s collaborators Refahi Abou had in fact carried out simulations in MATLAB for BALM,25

and therefore as I was developing my own model from scratch I was able to compare my results with those of R. Abou.

3.2.2 Foundational calculations

In general, the parameter of interest when performing BALM simulations is to compute the complex reflection amplitude (reflection coefficient) r using equation 4, followed by computing the reflectance R and finally the Michelson contrast CM per equation 9. An

alternative formulation of4 exists where the transfer matrix method (TMM) is used for computing an arbitrary stack, however realizing eq. 4 can be done using a recursive method. Implementing the recursive function in MATLAB was done by forking the code of Orfanidis ewa MATLAB package which contains a script called multidiel.m.37 _A

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function Gamma = multi stack (n,L,lam0) M = length(L); % number of layers

r = n2r(n); % r(i) = (n(i-1)-n(i)) / (n(i-1)+n(i))

Gamma = r(end); % initialize Gamma at right-most interface

L = L.* n(2:end-1); % convert input thicknesses ---> optical path lengths

for l = M:-1:1 % forward layer recursion

D = 2*L(l);

delta = (2*pi/lam0) * D; z = exp(-1i*delta);

Gamma = (r(l) + Gamma.*z) ./ (1 + r(l)*Gamma.*z);

end

The original version by Orfanidis is longer however and can account for other factors like angle and polarization, in addition to the normal incidence case shown above. Since the BALM characterization of monolayer MoS2 is currently a focus in the project before

characterizing other TMDs and vdWHs, the optimal thicknesses and wavelengths for realizing desired levels of CM were performed for that system, as well as for the more

conventional AR stack involving the use of SiO2/Si, for comparison. The following snippet

of code exemplifies how this is achieved:

lam0 = 450e-9; % incident wavelength

nf = 1.0; % final medium in BALM stack = air (1.0) or water (1.33)

r AR = multi stack([1.0 1.5 n Si(lam0)], [e SiO2], lam0); % air/SiO2/Si

r AR M = multi stack([1.0 n MoS2(lam0) 1.5 n Si(lam0)], ...

[e MoS2 e SiO2], lam0); % air/MoS2/SiO2/Si

r ARA = multi stack([1.5 n Au(lam0) n MoS2(lam0) nf], ...

[e Au e MoS2], lam0 ); % glass/gold/[air,water]

r ARA M = multi stack([1.5 n Au(lam0) n MoS2(lam0) nf], ...

[e Au e MoS2], lam0 ); % glass/gold/MoS2/[air,water]

R AR=r AR.*conj(r AR); R AR M=r AR M.*conj(r AR M); % AR reflectances

R ARA=r ARA.*conj(r ARA); R ARA M=r ARA M.*conj(r ARA M); % ARA reflectances

CM AR = (R AR M - R AR ) ./ (R AR M + R AR ); % AR Michelson contrast

CM ARA = (R ARA M - R ARA) ./ (R ARA M + R ARA); % ARA Michelson contrast

Note that for air, water, and amourphous SiO2, the media are essentially non-absorbing

and non-dispersive at optical frequencies, and hence the values 1.0, 1.33 and 1.5 are used, respectiely. However, gold is both absorbing and dispersive in the optical regime, and it is also thickness dependent. The values of n and κ used in the calculations are from Gao et al. 2013 for a 3.96 nm film.57 The data can be found at refractiveindex.info. Regarding silicon, the values from Aspnes et al. 1983 were used,58 _{which is also available}

fromrefractiveindex.info. Regarding the monolayer MoS2 values, the data from Zhang et

al. 2015 were used59 (see refractiveindex.info). Note though that the ˜n dispersion values for 2D MoS2 varies across the literature, and in fact in a later section the extraction of ˜n

will be realized based on the BALM stack.

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results in periodic contrasts as the AR layer (SiO2) is varied, which makes sense since

SiO2 is non-absorbing. For this stack, the use of a ≈ 100 nm oxide gives best contrast

for a wide variety of wavelengths which is similar as for graphene as reported in the previously discussed 2007 paper by Blake et al.41 _{In (b) and (c), which are BALM stacks}

with air and water as the final interface, the desired contrasts are only possible for very thin gold (< 10 nm) which is due to the gold being too absorbing at greater thicknesses. This is consistent based on the values for the penetration depth δp of gold that were

calculated at optical frequencies using the Gao et al. 2011 data.

Figure 10: Color plots of the Michelson contrast for the case of (a) MoS2 on a SiO2/Si

substrate, and MoS2on a BALM substrate with (b) air and (c) water in the final interface.

The axes show incident wavelength and AR/ARA thicknesses.

The δp values are related to extinction coefficient and wavelength by the following:33

α = 2ω c κ ⇒ δp = 1 α = λ 4κπ (11)

where α is the absorption coefficient, and the dispersion relation of light (ω(k) = ck or λf = c) was used. The calculation tells us that for thin gold films, δp ≈ 17.5 nm, 17 nm, 15 nm

for wavelengths of 450 nm, 550 nm, 650 nm respectively. The next noticable result of Figure10is that the use of BALM makes it possible to realize contrast values larger than that of the SiO2/Si substrate. This result is even more clear in Figure 11. The first two

rows of the figure show the resulting reflectance values for the respective stacks of the previous color plots in Figure 10, for the substrate itself and with the MoS2, while the

last row is a cross-section of the color plots for the wavelengths 450 nm, 550 nm, and 650 nm.

While the BALM substrate can allow for an impressive CM = 1 at certain conditions,

the conventional SiO2/Si substrate can only realize a maximum of CM = 0.4. The higher

contrast levels attainable by BALM can be used to image features at the ˚A or even pm scale out-of-plane, as was initiated by previous student K. Jaouen.35,49

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Figure 11: Optical stacks for (a) MoS2 on a SiO2/Si substrate, and MoS2 on a BALM

substrate with (b) air and (c) water in the final interface. Each case shows the reflectances and Michelson contrasts for the wavelengths 450 nm, 550 nm and 650 nm.

the cases of air and water, but in fact other fluids could be used. In particular, varying glycerol concentrations in water allows for tuning the refractive index between 1.0 and 1.33. Furthermore, an effect observed in BALM but not in SiO2/Si is the of positive

contrast values for MoS2, as seen in the last row of Figure11(c), meaning that the MoS2

is brighter than the substrate. Therefore, the same stack can reveal very strong contrast inversions, from -1 to 0.4 (change in 1.4) in the example shown, meaning the sensitivity is high.

3.2.3 FET on BALM

A BALM experiment of interest that the lab is currently working on, is to monitor in real time changes in optical contrast due to electric field induced charge accumulation in 2D MoS2. For this experiment, the gold ARA layer would also act as a back gate, and an

additional layer of insulating dielectric would be needed on top of the gold to act as the gate oxide. This also requires a ground electrode (source) on top of the MoS2, completing

the capacitor circuit and allowing for application of Vgs. Note that the oxide also is part

of the optical stack, which needs to be taken into account. Finally, addition of a drain electrode would allow for application of Vds, and a field-effect transistor (FET) would be

realized.42

The gate oxide being investigated is amorphous alumina (AlOx). When deposited on top

of the thin gold layer, this forms a bi-layer ARA system. The notion of using a second layer on top of the absorbing layer in BALM was explored for the case of PMMA, by K. Jaouen et al. and published in 2019.49 _{As application of V}

gs would make the 2D

MoS2 more conductive, its extinction coefficient κ should increase slightly for various

wavelengths.33 _{This alters the interference conditions of the optical stack and may give}

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MoS2 by application of a gate bias has been explored by Newaz et al. 2013 through

alternative methods, where changes in photoluminescence spectra, absorption spectra, and fluorescence microscopy images were clearly observed.60

Based on an understanding of the mechanism to which contrast changes would result from the gate bias, it is possible to simulate what the ideal gold thickness, alumina thickness, and wavelengths should be for the “FET on BALM” experiment. Note that in this case it is not simply the contrast values themselves which are important, but rather how readily the contrast will change as κMoS2 is changing. The results of the simulations are shown

in Figure 12.

Figure 12: Simulations of Michelson contrasts (first row) and contrast sensitivity (sec-ond row) due to changes ∆κMoS2 = 1 for different gold and alumina thicknesses and

wavelengths.

A change ∆κ = 1 was simulated, and the values for alumina dispersion are from Boidin et al. 201661 (see refractiveindex.info). The resulting changes in contrast per the figure vary around −0.6 to +0.6 depending on the thicknesses chosen, providing an indication that the system may be sensitive enough to show contrast changes as a function of Vgs.

Note in the figure that the optimal contrast sensitivities as shown in the bottom row are not appreciably overlapping with the actual contrast values as in the top row. Hence some kind of balance between the two needs to be accounted for, although it is not a significant drawback as the wavelength dependence can allow for selection of the desired contrast or contrast sensitivity even after the layers have been evaporated.

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MoS2 on such substrates. This data is also being used to extract optical parameters of

monolayer MoS2 as described in a later section.

3.3 Experiment

3.3.1 BALM microscope

A BALM microscope is essentially an inverted microscope with a few modifications. This includes the use of an immersion oil lens (and immersion oil), a cell where the BALM substrate can be clamped down such that liquids or gases can be added without leaks, and other mechanical parts that make it convenient to do the experiment.

In particular, this includes the ability to insert color filters into the beam path, in order to choose what wavelength should be incident from the objective. Furthermore, field and condenser diaphragms need to be present in order to reduce stray and angular light beams which would cause deviations from expected contrast values. The field diaphragm controls the width of the incident beam, and is usually visible upon closing since it reduces the field of view, while the condenser diaphragm controls the angle or “dispersion” of the beam. And finally, the presence of a linear photodetector is vital in order to be able to extract accurate grayscale values.

3.3.2 BALM substrate

To fabricate a BALM slide, thin glass slides of about 2 cm diamater are first purchased. Then, a thermal evaporator is used to create the ARA layer and other layers. A thin Cr layer (usually ≈ 0.5 nm) is first evaporated, followed by a few nm of gold (depending on the experiment). The purpose of the Cr is for adhesion, since gold does not adhere well to glass. For the case of an alumina layer, pure aluminum is evaporated in a succession of steps, where between each step the vacuum is vented so that oxygen can oxidize the aluminum. For the gold, the evaporation parameters have been tested and calibrated to allow precision to about 1 nm, as characterized by AFM measurements.

3.3.3 Linearity of BALM photodetector

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When CMOS sensors initially came to the market, a drawback was that their performance did not match that of the CCD. Therefore, for many years CCD cameras were still a standard in scientific instruments as they are highly linear and not as plagued by noise. In more recent years however, CMOS cameras have improved to the point that they too can provide a clean enough signal for scientific purposes where photon intensity values (which translate to grayscale) need to be accurate. The camera model used in our lab is the Canon EOS 6D, which has a CMOS sensor. Since extracting reliable contrast values is of utmost importance, I characterized the degree to which the sensor response was linear. To do this, I followed a procedure created by astrophotographer Blair MacDonald to test linearity of a different Canon model (60Da).63 The procedure involves directing the camera out of focus to a white surface in manual mode with a constant ISO sensitivity, and taking a series of images with varying shutter speed (exposure time).

Furthermore, a significant challenge was to obtain the sensor image of the photograph taken with the camera. As in most cameras, the Canon allows saving photos either as already processed JPG files, or the so-called RAW format which is typically different for each camera manufacturer. In the case of Canon models, the format is called CR2. However even with the RAW image available, care must be taken as many softwares that can read RAW formats do not readily output the actual sensor data, but rather apply multiple processing steps by default which result in a non-linear image. Various processing steps that render the sensor data non-linear include gamma correction, conversion from a linear color space to sRGB or other color spaces, and application of channel multipliers to alter the color temperature (white balance). Furthermore there is the demosaicing of the Bayer image (which interpolates RGB values to fill in the empty spaces) but this does not really affect the grayscale values.64,65

In order to convert the RAW images into TIFF files whose gray values were processed for analysis, a free and open-source software (FOSS) called dcraw (pronounced “dee-see-raw”) written primarily by David Coffin, was used.66 This software is licensed with the GNU General Public License version 2+ (GPLv2+), and is used as the back-end of about a dozen GUI front-end FOSS for RAW image processing. As the software is available to use as a command-line utility, it is possible to design a custom shell script to batch process multiple CR2 files and export them as TIFFs that closely resemble the sensor image, using for example GNU Bash on a GNU/Linux distribution like Ubuntu:

#!/usr/bin/env bash

dcraw -v -r 1.0 1.0 1.0 1.0 -q 0 -o 0 -W -g 1 1 -T *

(Note that two particularly helpful resources that explain the use of dcraw and MATLAB to work with the RAW sensor image, include a student lab exercise written by course staff from Brown University,67 _{and a guide by R. Sumner from UC Santa Cruz.}68_{) Each}

parameter as specified in the above code is explained in Table 1.

Lastly, following the export of the sensor image into TIFF files, they were batch processed in ImageJ, a public doman software that is used to analyze and process images, primarily written by a former employee of the National Institutes of Health (NIH) agency.69 _With

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Option Explanation

-v verbose output

-r 1.0 1.0 1.0 1.0 channel multipliers set to 1.0 to avoid color temperature (white balance)

-q 0 choose interpolation type [0-3] for bilinear, VNG, PPG, AHD respectively

-h alternative to -q 0, it is the same except it halves the number of pixels

-o 0 specify color space [0-6], where 0 is the camera native RGB which is the same as CIE XYZ -g 1 1 specify the toe slope and gamma values

-W use a fixed white level

-T output as TIFF file

Table 1: Input parameters for dcraw.

Having established a workflow to accurately extract raw sensor data from the photographs of the BALM setup and extracting the grayscale values, a calibration sample was created to test for which intensity ranges the contrasts do not change as a function of sensor signal. For the sample, a thermal evaporater with a shadow mask was used to evaporate 2 nm, 4 nm and 6 nm of gold onto a BALM slide. Then, an image series with varying shutter using a 550 nm color filter was obtained, and the results are shown in Figure

13.

13(a) of the figure is a representative image of the calibration sample, with the field diaphragm of the microscope almost fully closed to reduce stray light from the optical path. 13(b) shows the desired linear response curve of the RAW images compared with the nonlinear JPG, and13(c) gives an idea of the intensity values that the CMOS sensor would require to give accurate contrast values. Namely, at around < 5% of saturation (≈ 13/255 gray scale) the sensor does not respond sufficiently linearly to give accurate contrasts, while the upper threshold is at around 90%.

3.3.4 Extracting optical properties

Having established in the previous sections a reliable means to measure and extract contrasts from BALM data, as well as the methods to simulate BALM conditions, the following deals with how one can combine data with the model to compute the optical properties of monolayer MoS2.

The complex refractive index ñ = n − iκ of a medium, also known as the optical pa-rameters, are of utmost importance for understanding how electromagnetic (EM) waves interact and travel in the medium. Furthermore, all media exhibit a dispersive ñ (λ), although certain ranges of wavelengths may not exhibit significant dispersion. It is im-portant to note the connection between ñ and the relative permittivity ˜εr, which are

related by33

˜

n2 = ε0ε˜r (12)

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Figure 13: (a) BALM calibration sample with 2/4/6 nm gold evaporations, (b) signal intensities of CMOS sensor for the 2/4/6 nm regions for JPG and RAW data, and (c) the three Michelson contrasts for JPG and RAW data.

impacted in a similar manner to which EM waves are as they travel through a medium. Having said this, it is worthwhile to review the microscopic origins of ˜n and εr.

Ultimatily, it is the way that the medium is absorbing energy which determines ˜n. The absorption of the medium is characterized by extinction coefficient κ (where α = (2ω/c) κ is the absorption coefficient). There are two main ways in which the medium can absorb energy. The first is known as dielectric loss, and can be described by a rather classical treatment. The idea is that dipoles of various forms will oscillate as they are influenced by an electric field, and in this process due to phase delays from trouble keeping up with the oscillating electric fields, there is a power loss that occurs. The dipoles can be either due to atomic polarizability, ionic (lattice) polarizability, or dipolar polarizability.70 The response times go from fast to slow in the order stated. The first is due to electron shells of atoms becoming polarized, the second is due to the lattice becoming polarized, and the last is typically only present for liquids or gases where molecules are free to move. (In fact, the dielectric loss due to dipolar polarizability is the mechanism by which we use microwaves to heat food in a microwave oven.71₎

The second cause of absorption is quantum mechanical transitions of the medium. These include electronic excitations, which are typically at optical or UV wavelengths for semi-conducting and insulating crystals, and vibrational and rotational transitions which are more typically at IR wavelengths. For the real part n of the refractive index ˜n, it is in fact intimatily connected to κ by the Kramers–Kronig relations.33 _{Hence, by}

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Figure 14: White-light BALM images of monolayer MoS2 for 4 different optical stacks.

been described. Finally, it is evident that power loss associated with operation of an AC capacitor follows the same principle.

There exist a large number of techniques to measure the optical parameters of materials at different wavelengths. One way is to use reflectance spectroscopy, where one measures R and hence can extract κ, and then compute n from the Kramers–Kronig relations. This was done by Beal et al. in 1979 for bulk MoS2.72 Furthermore, there exist publications

where reflectance spectroscopy was used to calculate ˜n for monolayer MoS2 and other

TMDs.73 _{In recent years, the use of spectroscopic ellipsometry has become more}

common, as explained by M. Fox 2010 on p. 86.33 There are a number of papers in the literature that use this technique to measure ˜n of MoS2.74–79

Finally, there is a technique known as contrast spectroscopy, where expected contrasts from a model optical stack are fitted to contrast data to compute the optical parameters. This technique was used in fact in the early days of graphene for instance,80,81 _{and more}

recently for monolayer MoS2.59,82,83 A specific setup as used by Zhang et al. 2015 is

shown in Figure 15. In the setup of the figure, white light is incident and collected to a spectrometer to resolve contrast versus wavelength, and followed by deducing ˜n (λ) from the model. Similar methods were used by Hsu et al. 201982 _{and Khadir et al. 2017.,}83

also using the SiO2/Si based AR system.

It is of interest to apply contrast spectroscopy in BALM to extract ˜n (λ) for 2D MoS2,

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Figure 15: Extraction of n and κ for monolayer MoS2 using contrast spectroscopy with

SiO2/Si as the AR substrate, from Zhang et al. 2015.59

The ability to acheive CM closer to 1 also can minimize uncertainties.

During the internship, CVD 2D MoS2was transferred to BALM slides with approximatily

0.5 nm Cr/3 nm Au/18 nm AlOx. The alumina was deposited such that there was still

a region with only the Cr/Au exposed. Therefore, photographs of both 2D MoS2 on

glass/gold and glass/gold/alumina stacks were available for data acquisition. White-light images are shown in Figure14. Although the use of a spectrometer to resolve the reflected white signal may be done in the future, this data set consisted of a series of photographs with the color filters 450, 500, 550, 600, 650 nm; as shown in Figure 16.

To extract ˜n (λcolor filters), it is necessary to simulate the expected contrasts of the optical

stack, and to adjust ˜n such that for each wavelength the difference between data contrasts and model contrasts are minimized. In principle and for the future it would make sense to use a standard fitting of least squares function, such as the built-in lsqcurvefit in MATLAB. However as the data of 16 is the first ever obtained with linear values using BALM, a first order approach was employed. Namely, a UI based fitting program was created as a means to “brain-fit” the data, which is shown in Figure 17.

The UI includes the use of slider objects, two for each n, κ at each wavelength. As the user changes the sliders, the model contrasts are updated in real time, in addition to the n, κ values on the right. Additionally, 8 of the previously cited 2D MoS2 optical

parameter curves from literature were placed in the background for comparison. The scattered points are from bulk MoS2 values. Note the large variation in the parameters

from literature, up to 2.5 in the real part, and 3 in the imaginary part.

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Figure 16: BALM data of monolayer CVD MoS2 in 4 different optical stacks, with 5

different wavelengths, acquired for the purpose of extracting optical parameters.

the microscope needs further investigation as it influences resulting contrast values, and model parameters may need to account for more details.

Despite the work that remains, the UI that was developed and is further being developed can be useful for extracting optical parameters beyond that of 2D MoS2, with a degree

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Figure 17: BALM simulator UI allowing for a “brain-fit” of model contrasts to data contrasts in real time, resulting in 2D MoS2 n, κ values being updated against existing

curves from literature as the sliders are altered for best fit.

4 Conclusions

A 6-month master thesis project has been reported, on the use of backside absorbing layer microscopy (BALM) to study optical and electrical properties of monolayer (2D) MoS2.

In the first part of the report, the state of the art for transition metal dichalcogenide (TMD) based optoelectronics was reviewed, and relevant methods and characterizations that accompanied the use of BALM were presented.

In the main portion of the report, the theory of BALM was described, followed by details on the MATLAB toolkit developed by the author, which was used to simulate BALM both for general cases where the optical contrast of a nanomaterial is maximized by appropriate choice of thicknesses and wavelengths, as well as for the specific optical stack of an upcoming experiment that involves coupling electrical measurements to changes in optical contrast. Relevant technical information for obtaining correct grayscale values from the CMOS detector was reported, and served as a foundation in the first steps towards extracting the optical parameters (˜n = n − iκ) of 2D MoS2. Estimations of ˜n

were realized in a first order manner, by creation of a BALM simulator that enables a “brain-fit” of simulated contrast curves to data, comparing the results with literature values in real time.

The internship served as a prelude to a 3-year-long PhD that the author will begin on October 1, 2020 for the same topic. Future work will involve refining of ˜n extraction of 2D MoS2, by more analysis, more data, and coupling of a spectrometer to the setup in place of

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Future work may also involve synthesis and study of other TMDs with different work func-tions, and combining them to form vertical van der Waals heterostructures (vdWHs). To that end, SnS2 is a promising candidate as it has a work function that is higher than

MoS2 by about 1.36 eV,84 and has been reported by a few dozen publications. BALM

is well suited to reveal various properties of such heterostructures, with other measure-ments equally important, such as photoluminescence mapping (where quenching at the interface would indicate efficient charge separation by the built-in field Vbi), diode and

transistor measurements, and photoelectron spectroscopy. Furthermore, electro/photo-catalytic properties could be probed as well, building on previous work by LICSEN on electrochemical activity of 2D MoS2 by scanning electrochemical microscopy.85

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Bibliography

[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science, vol. 306, no. 5696, pp. 666–669, 2004.

[2] M. S. Dresselhaus and G. Dresselhaus, “Intercalation compounds of graphite,” Ad-vances in physics, vol. 51, no. 1, pp. 1–186, 2002.

[3] K. S. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proceedings of the National Academy of Sciences (PNAS), vol. 102, no. 30, pp. 10451–10453, 2005.

[4] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a

new direct-gap semiconductor,” Physical review letters, vol. 105, no. 13, p. 136805, 2010.

[5] B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, “Single-layer MoS2 transistors,” Nature nanotechnology, vol. 6, no. 3, pp. 147–150, 2011.

[6] M. S. Fuhrer and J. Hone, “Measurement of mobility in dual-gated MoS2transistors,”

Nature nanotechnology, vol. 8, no. 3, pp. 146–147, 2013.

[7] B. Radisavljevic and A. Kis, “Reply to Measurement of mobility in dual-gated MoS2

transistors’,” Nature nanotechnology, vol. 8, no. 3, pp. 147–148, 2013.

[8] Liu, Yuan and Weiss, Nathan O and Duan, Xidong and Cheng, Hung-Chieh and Huang, Yu and Duan, Xiangfeng, “Van der Waals heterostructures and devices,” Nature Reviews Materials, vol. 1, no. 9, pp. 1–17, 2016.

[9] Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano, vol. 9, no. 11, pp. 10612–10620, 2015. [10] Y. Zhang, Y. Yao, M. G. Sendeku, L. Yin, X. Zhan, F. Wang, Z. Wang, and J. He, “Recent progress in CVD growth of 2D transition metal dichalcogenides and related heterostructures,” Advanced Materials, vol. 31, no. 41, p. 1901694, 2019.

[11] R. Lv, J. A. Robinson, R. E. Schaak, D. Sun, Y. Sun, T. E. Mallouk, and M. Terrones, “Transition metal dichalcogenides and beyond: synthesis, properties, and applica-tions of single-and few-layer nanosheets,” Accounts of chemical research, vol. 48, no. 1, pp. 56–64, 2015.

(34)

nitride heterostructures grown by molecular beam epitaxy,” Microelectronic Engi-neering, vol. 147, pp. 306–309, 2015.

[13] F. A. Rasmussen and K. S. Thygesen, “Computational 2D materials database: elec-tronic structure of transition-metal dichalcogenides and oxides,” The Journal of Physical Chemistry C, vol. 119, no. 23, pp. 13169–13183, 2015.

[14] A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature, vol. 499, no. 7459, pp. 419–425, 2013.

[15] K. Novoselov, A. Mishchenko, A. Carvalho, and A. C. Neto, “2D materials and van der Waals heterostructures,” Science, vol. 353, no. 6298, 2016.

[16] X. Zhou, X. Hu, J. Yu, S. Liu, Z. Shu, Q. Zhang, H. Li, Y. Ma, H. Xu, and T. Zhai, “2D Layered Material-Based van der Waals Heterostructures for Optoelectronics,” Advanced Functional Materials, vol. 28, no. 14, p. 1706587, 2018.

[17] R. Frisenda, A. J. Molina-Mendoza, T. Mueller, A. Castellanos-Gomez, and H. S. van der Zant, “Atomically thin p–n junctions based on two-dimensional materials,” Chemical Society Reviews, vol. 47, no. 9, pp. 3339–3358, 2018.

[18] F. Withers, O. Del Pozo-Zamudio, A. Mishchenko, A. Rooney, A. Gholinia, K. Watanabe, T. Taniguchi, S. Haigh, A. Geim, A. Tartakovskii, et al., “ Light-emitting diodes by band-structure engineering in van der Waals heterostructures,” Nature materials, vol. 14, no. 3, pp. 301–306, 2015.

[19] J. Ahn, P. J. Jeon, S. R. A. Raza, A. Pezeshki, S.-W. Min, D. K. Hwang, and S. Im, “Transition metal dichalcogenide heterojunction PN diode toward ultimate photovoltaic benefits,” 2D Materials, vol. 3, no. 4, p. 045011, 2016.

[20] L. Wang, L. Huang, W. C. Tan, X. Feng, L. Chen, X. Huang, and K.-W. Ang, “2D photovoltaic devices: progress and prospects,” Small Methods, vol. 2, no. 3, p. 1700294, 2018.

[21] M. Long, P. Wang, H. Fang, and W. Hu, “Progress, challenges, and opportunities for 2D material based photodetectors,” Advanced Functional Materials, vol. 29, no. 19, p. 1803807, 2019.

[22] B. Luo, G. Liu, and L. Wang, “Recent advances in 2D materials for photocatalysis,” Nanoscale, vol. 8, no. 13, pp. 6904–6920, 2016.

[23] T. Roy, M. Tosun, M. Hettick, G. H. Ahn, C. Hu, and A. Javey, “2D-2D tunneling field-effect transistors using WSe2/SnSe2 heterostructures,” Applied Physics Letters,

vol. 108, no. 8, p. 083111, 2016.

[24] H. Ilatikhameneh, Y. Tan, B. Novakovic, G. Klimeck, R. Rahman, and J. Appen-zeller, “Tunnel field-effect transistors in 2-D transition metal dichalcogenide materi-als,” IEEE Journal on Exploratory Solid-State Computational Devices and Circuits, vol. 1, pp. 12–18, 2015.

(35)

[26] D. Lloyd, X. Liu, J. W. Christopher, L. Cantley, A. Wadehra, B. L. Kim, B. B. Goldberg, A. K. Swan, and J. S. Bunch, “Band gap engineering with ultralarge biaxial strains in suspended monolayer MoS2,” Nano letters, vol. 16, no. 9, pp. 5836–

5841, 2016.

[27] X. Ling, Y.-H. Lee, Y. Lin, W. Fang, L. Yu, M. S. Dresselhaus, and J. Kong, “Role of the seeding promoter in MoS2 growth by chemical vapor deposition,” Nano letters,

vol. 14, no. 2, pp. 464–472, 2014.

[28] D. Zhou, H. Shu, C. Hu, L. Jiang, P. Liang, and X. Chen, “Unveiling the growth mechanism of MoS2 with chemical vapor deposition: from two-dimensional planar

nucleation to self-seeding nucleation,” Crystal Growth & Design, vol. 18, no. 2, pp. 1012–1019, 2018.

[29] S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, “2D transition metal dichalcogenides,” Nature Reviews Materials, vol. 2, no. 8, p. 17033, 2017. [30] P. Gnanasekar, D. Periyanagounder, A. Nallathambi, S. Subramani, M. Palanisamy,

and J. Kulandaivel, “Promoter-free synthesis of monolayer MoS2by chemical vapour

deposition,” CrystEngComm, vol. 20, no. 30, pp. 4249–4257, 2018.

[31] H. Ko, H. S. Kim, M. S. Ramzan, S. Byeon, S. H. Choi, K. K. Kim, Y.-H. Kim, and S. M. Kim, “Atomistic mechanisms of seeding promoter-controlled growth of molybdenum disulfide,” 2D Materials, vol. 7, no. 1, p. 015013, 2019.

[32] J. W. Christopher, B. B. Goldberg, and A. K. Swan, “Long tailed trions in monolayer MoS2: Temperature dependent asymmetry and resulting red-shift of trion

photolu-minescence spectra,” Scientific Reports, vol. 7, no. 1, pp. 1–8, 2017. [33] M. Fox, “Optical properties of solids,” 2010.

[34] C. Lee, H. Yan, L. E. Brus, T. F. Heinz, J. Hone, and S. Ryu, “Anomalous lattice vibrations of single-and few-layer MoS2,” ACS Nano, vol. 4, no. 5, pp. 2695–2700,

2010.

[35] K. Jaouen, Backside absorbing layer microscopy: a new tool for the investigation of 2D materials. PhD thesis, Universit´e Paris-Saclay, France, 2019.

[36] H. C. Ohanian and J. T. Markert, Physics for Engineers and Scientists. 2007. [37] S. J. Orfanidis, “Electromagnetic Waves and Antennas,” 2016.

[38] M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Elsevier, 2013.

[39] D. Ausserr´e, A. R. Khachfe, L. Roussille, G. Brotons, L. Vonna, F. Lemarchand, M. Zerrad, and C. Amra, “Anti-reflecting absorbing layers for electrochemical and biophotonic applications,” Journal of Nanomedicine & Nanotechnology, vol. 5, no. 4, p. 1, 2014.

(36)

[41] P. Blake, E. Hill, A. Castro Neto, K. Novoselov, D. Jiang, R. Yang, T. Booth, and A. Geim, “Making graphene visible,” Applied physics letters, vol. 91, no. 6, p. 063124, 2007.

[42] S. M. Sze and K. K. Ng, Physics of semiconductor devices. John wiley & sons, 2006. [43] A. A. Michelson, Studies in Optics. Courier Corporation, 1927.

[44] G. Teo, H. Wang, Y. Wu, Z. Guo, J. Zhang, Z. Ni, and Z. Shen, “Visibility study of graphene multilayer structures,” Journal of applied physics, vol. 103, no. 12, p. 124302, 2008.

[45] M. A. Kats, R. Blanchard, P. Genevet, and F. Capasso, “Nanometre optical coatings based on strong interference effects in highly absorbing media,” Nature materials, vol. 12, no. 1, pp. 20–24, 2013.

[46] F. F. Schlich and R. Spolenak, “Strong interference in ultrathin semiconducting layers on a wide variety of substrate materials,” Applied Physics Letters, vol. 103, no. 21, p. 213112, 2013.

[47] M. Velick`y, W. R. Hendren, G. E. Donnelly, J. M. Katzen, R. M. Bowman, and F. Huang, “Optimising the visibility of graphene and graphene oxide on gold with multilayer heterostructures,” Nanotechnology, vol. 29, no. 27, p. 275205, 2018. [48] I. Wlasny, P. Dabrowski, and Z. Klusek, “Optical contrast of single-and multi-layer

graphene deposited on a gold substrate,” arXiv preprint arXiv:1102.4953, 2011. [49] K. Jaouen, R. Cornut, D. Ausserr´e, S. Campidelli, and V. Derycke, “Ideal

opti-cal contrast for 2D material observation using bi-layer antireflection absorbing sub-strates,” Nanoscale, vol. 11, no. 13, pp. 6129–6135, 2019.

[50] J.-F. Lemineur, J.-M. No¨el, D. Ausserr´e, C. Combellas, and F. Kanoufi, “ Combin-ing Electrodeposition and Optical Microscopy for ProbCombin-ing Size-Dependent SCombin-ingle- Single-Nanoparticle Electrochemistry,” Angewandte Chemie, vol. 130, no. 37, pp. 12174– 12178, 2018.

[51] J.-F. Lemineur, T. J. Stockmann, J. M´edard, C. Smadja, C. Combellas, and F. Kanoufi, “Optical nanoimpacts of dielectric and metallic nanoparticles on gold surface by reflectance microscopy: adsorption or bouncing?,” Journal of Analysis and Testing, vol. 3, no. 2, pp. 175–188, 2019.

[52] T. J. Stockmann, J.-F. Lemineur, H. Liu, C. Cometto, M. Robert, C. Combellas, and F. Kanoufi, “Single LiBH4 nanocrystal stochastic impacts at a micro water—ionic

liquid interface,” Electrochimica Acta, vol. 299, pp. 222–230, 2019.

[53] J.-F. Lemineur, J.-M. No¨el, C. Combellas, and F. Kanoufi, “Optical monitoring of the electrochemical nucleation and growth of silver nanoparticles on electrode: From single to ensemble nanoparticles inspection,” Journal of Electroanalytical Chemistry, p. 114043, 2020.

(37)

[55] J.-F. Lemineur, J.-M. No¨el, C. Combellas, and F. Kanoufi, “Revealing the sub-50 ms electrochemical conversion of silver halide nanocolloids by stochastic electrochem-istry and optical microscopy,” Nanoscale, vol. 12, no. 28, pp. 15128–15136, 2020. [56] “Hydroxide Ions Stabilize Open Carbon Nanotubes in Degassed Water,,”

[57] L. Gao, F. Lemarchand, and M. Lequime, “Comparison of different dispersion models for single layer optical thin film index determination,” Thin Solid Films, vol. 520, no. 1, pp. 501–509, 2011.

[58] D. E. Aspnes and A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Physical Review B, vol. 27, no. 2, p. 985, 1983.

[59] H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the refractive index of highly crystalline monolayer MoS2 with high confidence,”

Scientific reports, vol. 5, p. 8440, 2015.

[60] A. Newaz, D. Prasai, J. I. Ziegler, D. Caudel, S. Robinson, R. F. Haglund Jr, and K. I. Bolotin, “Electrical control of optical properties of monolayer MoS2,” Solid

State Communications, vol. 155, pp. 49–52, 2013.

[61] R. Boidin, T. Halenkoviˇc, V. Nazabal, L. Beneˇs, and P. Nˇemec, “Pulsed laser de-posited alumina thin films,” Ceramics International, vol. 42, no. 1, pp. 1177–1182, 2016.

[62] D. Durini, High performance silicon imaging: fundamentals and applications of CMOS and CCD sensors. Woodhead Publishing, 2020.

[63] “Canon 60Da Linearity Testing.” http://www.nightanddayastrophotography. com/PDFs/Canon%2060Da%20Linearity%20Testing.pdf. Accessed 2020-07-06. [64] C. A. Poynton, A technical introduction to digital video. John Wiley & Sons, Inc.,

1996.

[65] C. A. Poynton, “Rehabilitation of gamma,” in Human Vision and Electronic Imaging III, vol. 3299, pp. 232–249, International Society for Optics and Photonics, 1998. [66] “DCRAW - Decoding raw digital photos in Linux.” https://www.dechifro.org/

dcraw. Accessed 2020-06-23.

[67] “Lab RAW debayering.” https://cs.brown.edu/courses/csci1290/labs/lab_ raw/index.html. Accessed 2020-07-06.

[68] R. Sumner, “Processing RAW images in MATLAB,” Department of Electrical En-gineering, University of California Sata Cruz, 2014.

[69] “ImageJ - Image Processing and Analysis in Java.” https://imagej.nih.gov/ij. Accessed 2020-07-07.

[70] P. Hofmann, Solid state physics: an introduction. John Wiley & Sons, 2015.

Characterizing optical and electrical properties of monolayer MoS

Master Thesis