Probing anisotropic excitons in mechanically exfoliated Rhenium Disulfide through low temperature reflectance contrast spectroscopy

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Probing anisotropic excitons in mechanically exfoliated

Rhenium Disulfide through low temperature reflectance

contrast spectroscopy

Floris Kienhuis

July 16, 2020

[28]

STUDENTNUMBER 11067381

SUPERVISOR prof. dr. P.(Peter) Schall SECOND EXAMINER dhr. dr. J.(Jorik) van de Groep DAILY SUPERVISOR Marco van der Laan

REPORT Bachelor Project Physics and Astronomy

SIZE 15 EC, conducted between 02-03-2020 and 16-07-2020 INSTITUTE Van der Waals-Zeeman Institute

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1 Popular abstract (Dutch)

Duurzame energie is in de afgelopen jaren van steeds groter belang geworden. Daardoor wordt er ook veel onderzoek gedaan naar zonne-energie en de materialen waarvan dit gemaakt is; de halfgeleiders. Halfgeleiders zijn in principe isolatoren, maar kunnen door externe energie -zoals licht - toch geleiden. Dit komt doordat een elektron in een aangeslagen toestand komt bij toevoeging van energie, bijvoorbeeld in de vorm van photonen, de minimale energie dit hiervoor nodig is heet de bandgap. In dit onderzoek is er gekeken naar een nieuw soort halfgeleiders, de 2D materialen en specifiek Rhenium Disulfide (ReS2). Deze materialen vertonen andere optische eigenschappen wanneer ze van een dikke laag naar slechts één atoomlaag gaan. ReS2 differentieert zich van andere 2D materialen omdat het anisotroop is, dit betekent dat de op-tische eigenschappen kunnen veranderen als functie van de polarizatie. Dit is onderzocht door reflectie metingen uit te voeren en te kijken naar het verschil in absorptie van verschillende polarizaties. Dit leverde twee verschillende absorptie pieken op, die afkomstig zijn van twee verschillende excitonen. Dit is een quasideeltje wat wordt gevormd door een aangeslagen -negatief geladen - elektron en het positief geladen ’gat’ wat het achterlaat. Deze trekken elkaar aan waardoor een quasi-deeltje ontstaat wat dezelfde eigenschappen vertoont als een waterstof atoom. Door dit exciton wordt de energie die een photon nodig heeft om een elektron aan te slaan - en dus de bandgap - kleiner. In dit onderzoek is gekeken naar de bindings energie van zo een exciton, wat vergelijkbaar is met de ionizatie energie van een waterstof atoom.

2 Abstract

Recently, 2D materials have become increasingly important in solar energy conversion. One of these materials is Rhenium disulfide (ReS2), which belongs to the VII transition metal dichalcogenide (TMDC) group. It differentiates from other transition metal dichalcogenides -like MoS2 - due to its anisotropic optical properties. By mechanical exfoliation, flakes with var-ious layer thicknesses were obtained. Through optical contrast analysis, Raman spectroscopy and photoluminescence measurements, the basic optical properties of bulk and few layered ReS2 were established at room temperature. Furthermore, two differential reflection mea-surements were conducted, examining polarization and temperature dependence of bulk ReS2. The polarization measurements exhibit two distinct exciton groundstates with potentially ex-cited states at high energy. The energies of the ground- and exex-cited states of one of the excitons were fitted to a Rydberg series and resulted in an optical bandgap of 1.67 eV and an exciton binding energy of 144 meV. The temperature dependence shows a clear blueshift from room- to low temperature in the central positions of the two groundstates. The temperature dependence

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of these central positions were fitted to the Varshni equation as a function of temperature. The findings partially correspond to the room- and low temperature central values from literature. The discrepancy between the results and existing literature was further discussed.

3 Introduction

In the last couple of decades there has been a transition from fossil fuels to green energy. As more people made this transition, solar panels have become increasingly important. At the same time, there has been a lot of scientific development regarding semiconductors. These are the active components of solar panels, of which Silicon is most widely used. However, the properties of Silicon are far from perfect, problems such as stiffness and loss of efficiency appear due to its thickness [1]. Therefore, in recent years scientists have looked at various alternative materials in order to increase solar cell efficiency.

Semiconductors are materials with a Fermi energy located in a relatively small bandgap (max ±3eV) between the valence band (VB) maximum and conduction band (CB) minimum [16]. For an electron to be excited from the valence band to the conduction band, external en-ergy is needed, which can be provided by a photon. If the enen-ergy of the electron upon absorbing this photon is higher than the bandgap energy, the excess energy will be converted into heat as the excited electron thermalizes to the CB minimum. From this state, the electron will relax back to the VB while emitting light with energy equal to the bandgap energy, this is called pho-toluminescence (PL) [11]. An energy gap is called direct when there is no momentum difference between the CB minimum and VB maximum. For an electron to be excited across an indirect bandgap, a momentum carrier – for instance a phonon - is required [27]. When an electron is excited to the CB, a so-called hole is left in the VB. Furthermore, if the Coulomb interaction between the negatively charged electron and the positively charged hole is larger than their ki-netic energy, or macroscopically the thermal energy, they act as one quasi-particle; this bound state is called an exciton [12]. Because of this Coulomb interaction, the lowest energy states lie below the CB minimum and are directly accessible for optical excitation, which effectively lowers the energy a photon needs in order to be absorbed. These excitons become of special importance in thin materials, because due to the lack of screening from surrounding material, their Coulomb interaction and corresponding binding energy increases.

Some of these thin materials and potentially more optimal semiconductors are the tran-sition metal dichalcogenides (TMDCs). These materials are denoted by MX2 (M: trantran-sition metal, X: S, Se, Te) and are characterized by their unusually weak inter layer and strong intra layer interaction. This allows for the separation of individual or 2D layers of these materials while maintaining a relatively large size [20]. Two of the most intensively studied materials

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are the molybdenum (MoX2) and tungsten (WX2) variants, whose optical properties change when peeled down from bulk to monolayer. A significant change is the transition from indirect to direct bandgap in the monolayer limit. In this limit two other features are of importance, firstly, the exciton binding energy tends to increase. This is because of the decrease of ‘screen-ing’ from the surrounding material [2]. Secondly, because the size along one dimension of the crystal approaches the exciton Bohr radius, quantum confinement comes into play. This re-quires the wavelength of an exciton to be shorter than the size of the material. Due to this, the electronic density of states changes, most notably the lowest energy transition shifts up in energy, e.g. the bandgap increases and a blue shift in PL emission occurs. This shift thus in-creases the energy a photon needs in order to be absorbed. With exciton energy decreasing, and QC increasing the required photon energy, it has been proven difficult to theoretically predict shifts in bandgap energy as a function of layer thickness.

Exciting findings in the Mo- and W-based TMDCs show great promise for future appli-cations as well as deepening fundamental understanding of the behaviour of excitons [20]. However, recent broad theoretical studies predict the existence of several thousand potential layered materials that could potentially be semiconducting [20]. Seeing that already in the last 15 years the discovery of monolayer graphene and MoS2 has led to the birth of a whole new subfield of material science with exciting possibilities, it is certainly worthwhile to investi-gate other promising layered materials for their potential use in future devices or as means to investigate fundamental processes further. The material discussed in this report is Rhenium Disulphide (ReS2). This material differs from the Mo- and W- variants in several respects. For instance, ReS2 has (almost) no transition from indirect to direct bandgap when peeled down from bulk to monolayer. This may be due to the weak interlayer coupling, which excludes sig-nificant interlayer phonons [20]. Furthermore, ReS2 has, opposed to other TMDCs, an in-plane anisotropy. This indicates that optical properties may vary in different directions. Therefore, polarization dependent measurements, such as PL and differential reflection measurements in different polarizations, are of particular interest regarding ReS2. Polarization measurements done in this report will be measured relative to the b-axis, which is the direction in which the Rhenium atoms are aligned (Fig. 1). In Figure 2 various optical properties of ReS2 are shown in a table, where also properties of MoS2 are included for comparison. At room temperature both bulk and monolayer material show a broad PL peak, which has a slight blue shift in the monolayer limit (1.47 to 1.55 eV) [23]. However, at low temperature two distict peaks come forth, both belonging to a groundstate of different excitons [27] [15] [13]. Apart from these groundstates, at higher energies low intensity excited states are found. In analogy to a hydro-gen atom, the exciton binding energy and its excited states can be determined via Rydberg’s formula [15]. In addition, a blue shift in absorption should be observed if cooled down from

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Figure 1: Figure retrieved from Wang et al. [26]. Structure of ReS2 from a top side view. The b-axis is aligned along the Rhenium atoms.

room- to low temperature. This is due to thermal expansion, reducing the interatomic spacing with decreasing temperature. This, in turn, increases the potential of the material and thus increases the energy bandgap [19].

The aforementioned temperature and polarization dependence can be crucial in determin-ing yet unknown properties of ReS2, such as the (in)direct band structure of different layer thicknesses, as well as the exciton binding energy of different excitons. In this thesis, this binding energy has been examined by probing anisotropic excitons in mechanically exfoliated Rhenium Disulfide through low temperature reflective contrast spectroscopy. Firstly, the ma-terial is mechanically exfoliated using different types of tape and/or substrate, a detailed pro-cedure is given in the method section. Subsequently - to establish that the measured material is indeed ReS2 - two well known measurement techniques are conducted, namely Raman scat-tering and PL. For the examination of (anisotropic) exciton behaviour, two different reflection measurements have been conducted, measuring both polarization- and temperature depen-dence of bulk ReS2. In addition to these measurements, the optical contrast of different flakes is determined, as this gives insight into the difference in thickness of each flake.

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Figure 2: Various optical properties of ReS2, MoS2 properties are included as reference. L: measured at low temperature (blue shift)

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4 Theory and equipment

4.1 Reflection optical contrast

In order to have a first impression of the reflection spectrum of ReS2 for different layers, the optical contrast of several flakes was determined. For this analysis an image of both the sub-strate and the flake was taken using white LED light. A portion of this incident light is reflected by both the substrate and the flake. The substrates used in this experiment – sapphire and water-white glass – are both mostly transparent in the visible spectrum, while the ReS2 is not. Therefore, it is expected that the flakes have a higher refractive index than the substrate. Fur-thermore, the substrate can be regarded as a universal background, which is ideal for optical contrast computations using the Weber formula for optical contrast:

R_{f lake}_{− Rsub} Rsub

(1) Where Rf lakeand Rsubare the reflection coefficients of the flake and the substrate respectively. For this report it is assumed that these coefficients correspond to the color intensity of an image. As the refractive index of the flake is higher than that of the substrate, the result is a positive number. A higher number means more optical contrast and thus a thicker material and more layers. This, however, only provides a relative manner to determine the layer thickness. For an absolute number atomic force microscopy (AFM) measurements are required.

4.2 Differential reflection

For the differential reflectance measurements the reflection of the flake and of the substrate as a function of wavelength were measured. In addition, to measure the noise of the detec-tor, a dark spectrum was acquired. These three measurements combined give the differential reflectance of ReS2 with respect to a substrate using the following equation:

∆R R =

Rf lake− Rsub

R_sub_{− Rdark} (2)

Where ∆R_R is the differential reflection and Rf lake, Rsub, Rdarkare the reflection spectra of the flake, substrate and dark, respectively. Because the transmittance of the substrate is mostly wavelength independent in the visible range a, reflection spectrum that is comparable with the incident light spectrum is expected. The flake, however, absorbs incident light at certain wave-length/energy, therefore less light is reflected and minima occur in the reflection spectrum. We assume that the energy value of these minima correspond to peaks in absorption. To pinpoint these different peaks, the derivative of the reflection spectra is taken, as this narrows the peaks [31].

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Furthermore, the polarization dependence is measured by placing a polarization filter in the detection path, whereas the incident light from a white halogen lamp is unpolarized. To determine the polarization dependence of the absorption peaks, a range around these absorp-tion peaks is integrated. A higher total integral corresponds to a intenser absorpabsorp-tion peak. From literature [15] we know that exciton grounstates and excited states share the same po-larization dependence. By comparing the popo-larization of the exciton groundstates to the higher energy peaks, it can be checked whether they correspond to either groundstate. Since excitons are hydrogen-like, these states can be fitted to a Rydberg series (Eq. 4) and the bandgap and exciton binding energy can be determined.

For these measurements a Witec UHTS 300 Vis spectroscope with a grating of 300 lines/mm was used. This corresponds to an energy domain of 6.54 * 10−1 eV. As each spectrum has 1600 different data points, each data point represents 4.09 * 10−4eV. Because we differentiate the reflection spectra, the downside of this precision is that point-wise differentiation gives a distorted view due to small, insignificant changes. Therefore, before differentiation, the dif-ferential reflection curve was smoothed using the Savitzky-Golay smoothing [21] by averaging 11 data points and connect these points using a polynomial fit of the 3rd order. These values balance between the loss of subtlety due to averaging and noise due the amount of data points.

4.3 Basic optical properties

For the PL measurements a laser with a wavelength of 532 nm is used to excite the sample. Upon absorption of a photon, an electron is excited. This electron loses a portion of its excitation energy – due to conversion into thermal energy – while it relaxes back to the valence band minimum, thus emitting a photon with less energy than the initial one. Therefore, the emitted photon has a longer wavelength (E= hc/λ). To detect it efficiently, this photon is separated from a reflected photon using a filter with a cut off equal to the incident laser light. Both substrates used do not have a PL signal in the energy range important to ReS2 (1.4 to 1.8 eV). So the captured PL signal is only from the ReS2 flake.

Another measurement giving insight into optical properties important to semiconductors is Raman scattering, which arises from inelastic scattering of photons by a material. This means that, in addition to a change in direction, there is an exchange of energy. The photon interacts with the material - for example with phonons - and either gains or loses a discrete amount of energy. Because the energy gain or loss occur equally, the resulting spectrum is symmetrical around the wavelength of the incident light. The energy of the Raman peaks are relatively close the to energy of the incident laser and thus roughly around 2.3 eV as opposed to 1.4 to 1.8 eV for PL. Therefore, in contrast to above mentioned measurements, the Raman scattering is measured as a function of inverse length (rel cm−1) relative to the incident wavelength.

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Figure 3: A schematic overview of the used microscope and further equipment.

5 Method

5.1 Microscope specification

For all three measurements – reflection, Raman and PL – a Customized Witec Alpha 300R Raman system microscope was used. The reflection optical contrast was measured using un-polarized LED light and was detected by a Witec CCD camera. Images were acquired using a Zeiss 5x EC Epiplan objective with numerical aperture (NA) of 0.135, the optical contrast of these images was further analyzed using python. The PL spectra were measured with a Witec 532.345 nm frequency doubled Continuous Wave laser with an incident laser width ofλ/2*NA micrometers, thus depending on the objective used. The signals were filtered using a dichroic mirror and further detected by a Andor Newton 370P back-illuminated EMCCD detector, using three different gratings; 150, 300 and 600 lines/mm. For the PL and Raman measurements, a Zeiss 100x EC objective with NA 0.9 was used. The reflection measurements were conducted using a Zeiss 50X NA 0.55 objective. For a schematic overview of the microscope and further equipment see Figure 3.

The relatively small change in energy for Raman scattering is detected by a CCD detector using a grating of 600 lines/mm, which gives a small but precise energy spectrum. All wave-lengths larger than the incident laser light are filtered, so only scattering with a positive rel

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cm−1_{are measured. The PL - especially at high temperature - usually consists of broad peaks} in a relatively large energy spectrum. Therefore, these measurements are preformed using a 150 lines/mm grating, which gives a relatively large energy spectrum.

For the differential reflection measurements a white halogen lamp was used because this re-flection signal gives a high output for wavelengths corresponding to the ReS2 absorption peaks. Furthermore, the focal stop and the aperture of the microscope were maximally shut, to ensure the incident light is perpendicular the the flakes and substrate, this, however, results in a low intensity of the light. The halogen lamp was raised to max intensity as to compensate for this loss of intensity. Because this produces heat, before each measurement we let the system equilibriate for at least 10 minutes to ensure a constant temperature inside the microscope. The measurements were done using a grating of 300 lines/mm with a central point at 1.7 eV. To measure at low temperature (85 K), a cyrostat (Linkam THMS350EV) was installed with liquid nitrogen as cooling element. The cyrostat was first raised to 393 K and evacuated with a Pfeiffer Vacuum Duo 3 Rotary Vane Pump to prevent any water droplets and/or vapor to freeze when cooling down. Moreover, an analyser was placed between the filter and detector (see Fig-ure 3) to enable polarized measFig-urements. The temperatFig-ure dependent measFig-urements varied from 78 K to 303 K and incremented with 25 K. The polarization dependent measurements are conducted at 83 K. The angle of the polarization filter varied between -30° and 150° with respect to the b-axis in steps of 15°.

5.3 Mechanical exfoliation

The ReS2 flakes were fabricated by mechanical exfoliation from bulk ReS2, bought at HQ-Graphene. An exfoliation is done by sandwiching the material in between two strokes of tape and slowly pulling them apart, resulting in two thinner fragments. One of these is again sand-wiched, using a new stroke of tape, while the other one is stored for later use. This process was repeated from bulk 10 to 20 times until only small fragments remained. The last exfoliation was done on the substrate. To minimise the amount of defects and maximise the flake size, it is recommended to separate the pieces of tape perpendicular to each other. For the exfoliation onto the substrate this is even more vital because slow and perpendicular separation reduces the tape residue on the substrate. As thin flakes are desired, more exfoliations should give better results. However, by each exfoliation the flakes get smaller. If the size of the flake is in the same range as the width of the incident laser, measurements become untrustworthy. Therefore, the strategy used in this project is to balance between size and thickness. As this

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balance varies for different tape, substrate and peeling method, it is hard to determine the amount of exfoliations needed. To quantify this, many different attempts must be done. Due to circumstances, this was beyond the scope of this project. In this work, two kinds of tape; M Scotch Magic tape and Nitto SPV-224PR-MJ blue tape were used. Furthermore, two types of substrates were used; Corning Plain water-white glass and Ossila standard sapphire sub-strates (Al2O3). These substrates were prepared by sonicating twice, in between they were cleaned with either ethanol or aceton and afterwards they were cleaned with a plasma cleaner.

6 Results

6.1 Optical contrast

The optical contrast of two images is determined using Eq.1. Figure 4a) shows a reflection of a flake of bulk ReS2 on a non reflecting glass substrate. In the middle of this image a small piece of allegedly thin material is visible. To examine this, a profile plot along the red line (Fig. 4a)) is made. This plot (Fig. 4b)) shows the optical contrast, computed by Eq.1 as a function of position, in which Rsub is the average of the substrate. It provides the profile of a grey scaled image and that for each red-, green-, and blue channels independently. Although there is a clear difference in optical contrast between x = 2.5µm and x = 3.5 µm, this is a continuous increased opposed to the expected discrete increment between different layers.

(a) image (b) profileplot

Figure 4: a) A flake of ReS2 fabricated by mechanical exfoliation, on a glass substrate. Most of the image contains either substrate or bulk material, however, in the middle a thin layer is visible. b) Optical contrast along the red line in a) from left to right. The grey line represents the optical contrast of a grey scaled image, whereas the blue-, , and green lines represent respectively the blue-, red-and green channels of an RGB image.

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Figure 5a) shows a grey scaled image of a triangular shaped flake of ReS2 on a glass sub-strate. The differences in intensity indicate different thicknesses of the material. To determine which is thinner, an optical contrast profile along the blue line is computed. The results are shown in Figure 5b) with the same color code as used in Figure 4b). In contrast to Figure 4 there is a clear, discrete difference between the flake and substrate. In addition, multiple dif-ferent layers can be identified in the red- and green channels, whereas the contrast of the blue channel only clearly changes from substrate to flake. However, for the blue channel a distinc-tion between two layers at approx. y = 20_µm is visible, whereas the green- and red channels are rather flat in this area. This could be because the green- and red channels are at their maximum (measurable) intensity. The sudden drop in intensity for all curves is probably due to a crack in the flake.

(a) image (b) profileplot

Figure 5: a) A triangular flake of ReS2 fabricated by mechanical exfoliation, on a glass substrate. The variety of color indicates different layer thicknesses. b) Optical contrast along the blue line in a) from top to bottom. The grey line represents the optical contrast of a grey scaled image, whereas the blue-, red-, and green lines represent respectively the blue-, red- and green channels of an RGB image.

PL and Raman measurements are preformed on the flake depicted in Figure 4a). This flake is chosen because it contains both clear bulk- and few layered ReS2. Both measurements are done on the same day, at room temperature using a 532 nm laser.

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6.2.1 Photoluminescence

Figure 6a) shows a colormap of the integrated PL intensity from 1.33 eV to 1.48 eV. Apart from the substrate (purple), three distinct regions are visible. The red and turquoise regions correspond to the bulk and thin layered material shown in Figure 4 a) and b). Where red corre-sponds to high contrast bulk ReS2 and turquoise to low contrast few layered ReS2. The spectra visible in Figure 6b) show peaks at 1.40 and 1.53 eV, as determined by Lorentzian fitting (Eq.6). Each spectrum also contains a higher energy shoulder, indicating additional absorption peaks. These peaks were fitted at 1.48 and 1.79 eV for the bulk and few layered material respectively. These higher energy peaks are of significant lower intensity and might indicate the presence of exciton excited states. In the differential reflectance spectroscopy further analysis of these higher energy states will be preformed through polarization dependent measurements.

(a) Colormap (b) Fit

Figure 6: a) Integrated PL intensity from 1.33 eV to 1.48 eV. The heatmap depicts a zoomed-in version of Figure 4. The red and turquoise regions are isolated as two different layers. b) PL intensity as a function of energy. The PL intensity of the two regions is averaged and fitted to Eq. 6. The central values are shown in the figure, at 1.40 eV and 1.48 eV for bulk and few layered material respectively. The blue and red curves represent the turquoise and red regions respectively. A slight blue shift from bulk to few layered material is visible. In both the spectra a second, low intensity peak is visible at higher energy.

6.2.2 Raman spectroscopy

Figure 7a) depicts a colormap of Raman intensity of the same area used as the PL measure-ments, integrated between 120 rel cm−1_{and 500 rel cm}−1_{. In contrast to the PL intensity, the} Raman signal shows a relative high intensity for few layered ReS2 in comparison to its bulk counterpart. Therefore, the colors of the different regions are opposite to its PL counterpart. Several characteristic peaks are observed (Fig.7b)), which were then fitted using Lorentzian

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functions. The main peaks of few layered material are at 159.4, 209.9, 304.0 and 343.9 cm−1_, whereas bulk has 159.5, 209.6, 304.2 and 344.0 cm−1 as its main peaks. Since these peaks do not differ more than 1 cm−1 _{- which is the precision of the equipment - these changes are} regarded as nonsignificant.

(a) Colormap (b) Spectra

Figure 7: a) Integrated Raman intensity from 120 rel cm−1 _{to 500 rel cm}−1_{. The colormap depicts a} zoomed-in version of Figure 4. The red and turquoise regions are isolated as two different layers. Note that the intensity of bulk and thin material - and the corresponding color - is flipped relative to the PL counterpart. b) Raman intensity as a function of relative inverse length. The Raman intensity of the two regions is averaged and fitted to Eq. 6. The blue and red spectra represent the red and turquoise regions respectively.

Two different measurements are taken regarding differential reflectance. One of these is polarization-dependent reflection at low temperature (83 K), whereas the other one is unpo-larized temperature-dependent reflection, in a range from 78 K to 303 K. Figure 8 depicts the flake on which both measurements are done. It shows a homogeneous, high contrast flake, which indicates a flat piece of bulk material.

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Figure 8: Image of a homogeneous, high contrast flake, which indicates a flat piece of bulk material. On a background of a sapphire substrate.

6.3.1 Temperature dependence

For each temperature, a reflection spectrum of the flake and the substrate and a dark spectrum was obtained. Differential reflection combines these spectra using equation 2. For an exam-ple of the obtained spectra, Figure 9 is included, note that both spectra are already derived once. The orange spectrum belongs to an unpolarized measurement at 78 K and shows various oscillations throughout the spectrum, these oscillations represent absorption peaks. The two most intense of these absorption peaks are further investigated as a function of temperature. All measured temperature spectra are plotted in Figure 10a), the black and red lines roughly trace these two most intense oscillations for different temperatures, which we hypothesize to be two distinct exciton groundstates. Figure 10b) shows a more precise curve of the energy of these groundstates, as a function of temperature. For both states a clear blue shift from high to low temperature is visible, which results in two energy values at E₁ = 1.53 eV and E₂= 1.57 eV, obtained through a Varshni fit (Eq. 5). For both states the low temperature energies seem to not correspond to literature [13] [15], a further analysis of this difference will be done in the discussion.

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Figure 9: Comparison between two measurements under the same circumstances. Derivative of differ-ential reflectance as a function of energy. The blue line represents a averaged summation of all detected polarization measurements at 83 K, the orange line represents a reflectance measurement at 78 K with-out an polarization filter in the detection path. Below 1.60 eV the two measurements are approximately equivalent. At higher energies, however, the unpolarized spectrum shows more fluctuations.

(a) all temperatures (b) peak shift exciton groundstates

Figure 10: a) Derivative of differential reflectance as a function of energy for different temperatures from 78 K to 303 K. The reflection intensity lowers as a function of temperature. Also a blue shift is visible for both exciton groundstates, depicted by the black and red dashed lines. b) Energy as a function of temperature. Both blue shifts of the exciton groundstates are fitted to the Varshni equation (Eq. 5). Exciton groundstate energies from literature ([2], [13], [15], [10]) are plotted as well, these will be further compared in the discussion.

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6.3.2 Polarization dependence

Figure 11 shows the spectra obtained by measurements with polarization directions of 90° (blue) and 15° (red). In these spectra two distinct high intensity absorption peaks can be iden-tified (X1, X2). We hypothesise these two peaks to be exciton groundstates. To test this, further analysis of these states combined with higher energy states (Xex1, Xex2, Xex3) were conducted. The 15° polarization maximizes the first peak at EX1 = 1.521 eV. The 90° polarization

max-imises the second peak, at Ex2=1.563 eV. Full polar plots depicting the polarization dependence

over the full angular range are shown in Figure 12. This plot also shows the presence of two polarized absorption peaks, with main polarizations at 14(5)° and 92(5)°, obtained through fit-ting (Eq. 3). Henceforth, these absorption peaks will be identified as exciton groundstate 1 (red) and 2 (black). The margins of error (5°) are mainly caused by determining the direction of the b-axis and aligning it with the 0° axis direction.

Figure 11: Derivative of the differential reflectance plotted as a function of energy. The spectra corre-spond to polarizations of 90° (black line) and 15° (red line) with respect to the b-axis. These polarizations correspond to the maximum reflectance of either exciton groundstate. The rising points of inflection at Ex1=1.521 eV and Ex2=1.563 eV are taken as the central position of the exciton groundstates. The higher

energy states are presumably due to excited excitonic states. This can be tested by analysing whether the polarization of these states correspond to either of the groundstates. For the 15° polarization three higher energy states are defined.

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Figure 12: Polar plots of the derivative of the differential reflectance (for spectra see Fig. 11) for each exciton groundstate, integrated over a range of 10 meV around the absorption peak positions Ex1=1.521

eV and Ex2=1.563 eV. Fits according to Eq.3, are represented by the solid black and red lines. The angle

of the polatization filter varied between -30° and 150° with respect to the b-axis, with a 15° interval. Further datapoints were mirrored along the -30 to 150 axis.

Furthermore, the polarization of the higher energy peaks is examined. We hypothesize that if these higher energy states have a similar polarization as either of the aforementioned grounstates, these higher energy states are excited states of the corresponding groundstate. Although for reflectance spectra close to the second groundstate polarization, clear higher en-ergy peaks are visible, these could not be isolated from groundstate 1 polarized states. How-ever, higher energy peaks corresponding to the exciton 1 groundstate (EX1= 1.52 eV) could be

isolated, as shown in Figure 13a). The red data and connections represent the groundstate, whereas the yellow, green and cyan datapoints represent integrals over higher energy peaks, namely 1.631, 1.648 and 1.657 eV. We thus fit these peaks - together with the correponding grounstate - to a Rydberg series (Eq: 4), as shown in Figure 13b). The resulting bandgap is computed at 1.666 eV with a exciton binding energy of 0.144 eV. The margins of error is 0.004 eV for the central position of the states, as derived from the Savitzkt-Golay smoothing, in which we average over 11 points, this corresponds to a range of 0.004 eV.

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(a) exciton 1 states (b) Rydberg series

Figure 13: a) Polarplot of exciton 1 groundstate Ex1=1.521 eV (10 meV range) and higher energy states

with polarization corresponding to the groundstate. The higher energy peak positions are at 1.631, 1.648 and 1.657 (Fig. 11) with a 4 meV range integration window. b) Experimentally obtained absorption peaks with excited 1 polarization, fitted to a Rydberg series (Eq. 4).

7 Discussion

7.1 Optical contrast

The profile plots of Figures 4 and 5 both show that the monochromated optical contrast closely resembles that of the green channel. In addition, according to Wang et al. [25], the green channel optical contrast shows less fluctuations due to noise in comparison to monochromated images. Therefore, it can be fitted more easily. However, a clear differentiation between differ-ent layers should be visible [25] [2], which is not the case in Figures 4 and 5. Instead of a clear, discrete function, Figure 4 shows a slow and continuous increase in the supposed few layered material. It could be possible that the few layered material is actually a slowly thickening flake. Therefore, AFM measurements could provide a solution by precise measurement of this flake. Furthermore, the triangular flake shows plenty of differentiation in the flake, partly con-tinuous, partly discrete. This is especially interesting for AFM measurements, because many different layers can be identified. The optical contrast of these layers could then be fitted, as to achieve a reference for optical contrast of ReS2 with respect to a glass substrate.

The Raman and PL measurement are not conclusive on the thickness of different layers, as there is no difference in bulk and few layered material for the Raman measurements, while

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a clear difference is visible in the PL measurements. The absorption peaks obtained through PL spectroscopy are centered at 1.40 eV and 1.53 eV for bulk and 1.48 eV and 1.79 eV for few layered material. These peaks do not correspond with existing literature, which observed a single broad peak at 1.47 eV [10] and excitonic peaks at 1.47 eV [2] (X1) and at 1.51 eV [2] (X2). In the monolayer regime, literature observes peaks at 1.55 eV [29] [10], 1.61 eV [2] and 1.67 eV [2]. These last two peaks correspond once again to exciton 1 and 2. The relatively low energetic peaks obtained in this project might be due to a relatively high laser intensity. As these measurements were done at the beginning of the project, the resulting red-shift of high laser intensity measurements was yet unknown. If we assume that the impact of the high laser intensity is relatively equal for the different regions, some comparisons can still be useful. The difference between the two high intensity peaks of bulk and thin material is 0.08 eV, which corresponds to the broad peaks observed by Friemelt et al. [10] and Zhang et al. [29]. The excitonic peaks observed by Aslan et al. [2] are measured by differential reflection spectroscopy. Since these measurements tend to have slimmer peaks than PL measurements, this could be the reason why we did not observe a distinction between the two excitonic states. Furthermore, it can be stated that the few layered region is in the regime in which the effects of reduced screening and dimensionality come into play. This reduced screening causes a larger exciton binding energy for the few layered material, which could also explain the higher energy of the few layered second peak as opposed to its bulk counterpart. However, in room temperature the peaks overlap too much for a robust statement about potential excited states. In order to do this, low temperature polarization dependent measurements are needed. The reason for this is that the PL peaks show less broadening at low temperature, thus differently polarized peaks can be isolated more easily. These could then be fitted to a Rydberg series, which is done for the reflection measurements.

In contrast to the PL measurements, no difference between bulk and few layered material is observed for Raman scattering. Although the two regions have a different average intensity, the peak positions do not vary significantly. As each of the characteristic peaks do not vary more than 1 cm−1, which is roughly the difference between each datapoint of the spectrum. In literature the difference between multiple peaks was measured and shifts of at least 3 cm−1 were observed [5] [9] between the regions. As the maximum difference between the bulk and thin material did not exceed 1 cm−1, this was not the case in this research. Most of the peaks correspond to bulk peaks obtained by Feng et al. [9], however some differ more than 10 cm−1 from either bulk or monolayer. This is strange because Raman scattering is a highly repro-ducible measurement which should always give roughly the same spectrum. As there is no apparent reason for this difference, this experiment should be repeated.

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The PL measurements show - apart from a main peak at relatively low energy - a broad shoulder at higher energies. To determine the connection between these peaks, polarization-dependent reflection measurements are analysed. These result in two polarized exciton ground-states at low energy and three excited ground-states of exciton 1 at higher energies. Furthermore, temperature-dependent measurements show a blue shift in these exciton groundstates from high to low temperatures, as expected from the thermal expansion of the material [19].

7.3.1 Temperature dependence

In Figure 10a) the red and black dotted lines give a rough approximation of the temperature dependence of the energy of the groundstates of exciton 1 and 2 respectively. As discussed, according to literature [2] [6], these are represented by the rising point of inflection. The precise fit to these points in Figure 10b) show good correspondence to both exciton groundstates, and high temperature absorption peaks found in literature [2] [10]. The data is extrapolated to 0K as to compare the results with literature which measured absorption of ReS2 at 7K [15] [13]. Their results are also plotted in Figure 10b) and show higher energy values for both exciton groundstates than our data. This discrepancy between literature and our data may be due to the difference in temperature of the cyrostat and the flake. Since the precise thermal conductivity between the cyrostat and the flake is unknown, it could have occurred that the temperature of the flake lagged behind the temperature of the cyrostat. Therefore, for the lowest temperature measurement the temperature of the flake could have been warmer than expected. This would cause a lower energy value than expected at 78K for both groundstates. This, in turn, flattens the curve and causes lower extrapolated energies. This is strengthened by the fact that the energy values found in the polarization dependent measurements are in fact higher (±0.005 eV) while conducted at a slightly higher temperature (78K to 83K). However, the discrepancy between data and literature could also be due to other, unknown effects. These effects could for example be due to a difference in doping of the material or the amount of defects in the material.

For further research extensive waiting in between measurements is proposed as to mini-mize the difference in temperature between material and cyrostat. In addition, a similar mea-surement could be preformed probing the higher energy absorption peaks (±1.65 eV). Since these peaks are less intense, a longer measurement time and a smaller grating (600 lines/mm) are proposed.

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7.3.2 Polarization dependence

To give greater insight in the relation between the exciton groundstates and the higher energy states, polarization measurements at low temperature were conducted. For clarification, unpo-larized incident light was used, so the discussed polarization only applies to the detected light, due to the analyser shown in Figure 3.

The central positions of the exciton groundstate (Fig. 11) are determined at 1.52 and 1.56 eV. Since the temperature dependence of the energy peaks and the fact that in literature few measurements are conducted at this temperature, no real comparison can be made. However, the PL measurements on bulk ReS2 conducted by Nella [18] (see Fig. 14 in Appendix) are preformed at roughly the same temperature and using the same setup. These show central values of the exciton groundstates at 1.54 and 1.57 eV. The difference between our results and these values might be due to the high halogen lamp intensity that was used, causing a red shift in the energy values of the reflection measurements. Another explanation might again be the difference in temperature between the flake and the cyrostat. Although both measurements used the same material, it could have happened that the thermal conductivity between the flake an cyrostat was different for each measurement.

Further analysis of the data resulted in a polar plot showing two differently polarized ab-sorption peaks with maximum intensity at 14(5)° and 92(5)° with respect to the b-axis (Fig. 12). Although the angle may differ due to the rough approximation of the b-axis position, the difference between the two states (±78°) shows similarity to the polarized excitons in bulk ReS2 found in literature [15] [2]. This further indicates that these states are in fact exciton groundstates. Furthermore, Aslan et al. [2] found different polarization dependecies in few layered mateial. Therefore, in further research polarization dependence of such few layered materials is proposed, as this gives more insight into the change in anisotropic properties for few layered material.

These polarized exciton groundstates are further compared to the polarization of different higher energy peaks, as to determine if these are possible excited states of either exciton. For the polarization of the low energy exciton groundstate, three distinct higher energy peaks are identified (Fig. 13) and - together with the goundstate - fitted to a Rydberg series (Fig. 13b). This resulted in a bandgap of 1.666 eV and a exciton binding energy of 0.144 eV. The result-ing bandgap is slightly lower than expected from literature [15] [14] which agree on a 1.672 bandgap. This difference may in part be due to the low temperature (8K and 25K respectively) at which these measurements were conducted. The literature [15] [14] does, however, not agree upon the exicton binding energy, which is determined to be 0.118 eV and 0.157 eV respectively. Because the difference of these binding energies is rather large, it is hard to place this projects’

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results into perspective.

A Rydberg series for the second exciton was unfortunately not possible because for this corresponding polarization only two distinct higher energy peaks were determined, which is regarded insufficient to fit to a Rydberg series. Therefore, in further research more precise measurements of these higher energy peaks are suggested. By taking a smaller grating of 600 lines/mm and focus on the energy range of these higher energy states, a better distinction between the different states can be made. Moreover, a longer measurement time is suggested, while measurement time in this research (averaging 100 measurements of 0.1 seconds) was sufficient for the groundstate energies, the signal-to-noise ratio for the higher energy states was rather low. Furthermore, measurements at low temperature (83K) are suggested as this tightens the absorption peaks.

8 Conclusion

In this research four different measurements of few layered and mostly bulk Rhenium Disulfide were conducted. These contain PL and Raman spectroscopy at high temperature, temperature dependent differential reflection spectroscopy and low temperature polarization dependent re-flectance spectroscopy. In addition, an optical contrast analysis of different layers was deter-mined. The PL measurements show a clear sign of difference between bulk and few layered material in both the main absorption peak and the higher energy shoulder. This higher energy shoulder was of higher energy for the few layered material as opposed to its bulk counterpart. This may indicate the presence of exciton excited states. However, for further analysis, low temperature measurements are required. In contrast, the Raman measurements showed no significant change in the two different regions, the reason for this remains unclear. In line with the PL recommendation, low temperature measurements could further identify the difference in absorption peaks of different layers. The temperature dependent reflection measurements showed a blue shift in energy from high to low temperature. The results were fitted to the Varshni equation and extrapolated. This corresponds roughly to measurements at high and low energy in literature. The relatively small difference could be due to difference in temper-ature of the flake and the cyrostat. In further research the tempertemper-ature dependence of the higher energy peaks could be compared. The low temperature polarization-dependent reflec-tion measurements resulted in two differently polarized exciton groundstates. One at 14(5)° and one at 92(5)°, which roughly corresponds to literature. Furthermore, a Rydberg series of equally polarized states was taken. Which resulted in a 1.666 eV bandgap with a exciton binding energy of 0.144 eV, corresponding to exciton 1. For further research a more precise measurement of the alleged excited states is suggested, using a grating with higher resolution

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and a longer time to measure.

9 Acknowledgements

Thanks to the University of Amsterdam and the Van der Waals-Zeeman Institute for providing the workplace. Special thanks to prof. dr. Peter Schall for his support and knowledge in the weekly sessions and dhr. dr. Jorik van de Groep for his support and granted access to his microscope and further equipment. Also great thanks to Marco van der Laan for the daily support and various tips.

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10 Appendix

Figure 14: PL measurements conducted by Nella [18]. X1and X2denote the groundstates of exciton 1 and 2 respectively.

10.1 Various fits

To determine the polarization dependence of the integrated intensities, these intensities were plotted as the radius of a polar plot and fitted to the following equation:

I(θ_{) = I0}+ I1cos2(θ−θmax) (3) Where I_θ is the intensity at angle_θ, I₀ is the minimal radius, I₁ is the maximum growth of the radius constants andθmaxis the angle at maximum radius.

By comparing the polarization of the exciton groundstates to the higher energy peaks, it can be checked whether they correspond to either groundstate. To determine the exciton bind-ing energy an exciton, the higher energy peaks with correspondbind-ing polarization to the exciton groundstate, were fitted to a Rydberg series using the following equation:

E(n)_b _{= Eg}₋R y ∗

n2 (4)

Where E(n)_b is the binding energy at the nth excitation, Eg is the energy bandgap, R y∗ is the effective Rydberg constant and n is the number of excited state, n = 1 being the ground state.

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In the temperature dependence measurements the energy of the two exciton groundstates as a function temperature were measured. The resulting blue shift from high to low tempera-ture was fitted to the Varshni equation [22]:

E_{g(T) = E}_{g(0) −} αT 2

T +β (5)

Where Eg(T) is the groundstate energy at temperature T, Eg(0) is the supposed energy at 0 K andα,βare constants.

The PL and Raman spectra consist of several absorption peaks as a function of energy. To distinguish and identify them, they are fitted to a linear combination of Lorentzian functions. The Lorentzian function is of the form:

A γ

2

γ2_{+ (x − x0)}2+ c (6)

Probing anisotropic excitons in mechanically exfoliated Rhenium Disulfide through low temperature reflectance contrast spectroscopy