Growth and nanostructure of tellurides for optoelectronic, thermoelectric and phase-change
applications
Vermeulen, Paul Alexander
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Vermeulen, P. A. (2019). Growth and nanostructure of tellurides for optoelectronic, thermoelectric and phase-change applications.
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Chapter 6. Multilevel reflectivity
switching of ultrathin phase change
films.
Multilevel reflectivity tuning of thin-film heterostructures using the strong-interference and Fabry-Perot effects is shown by dynamic ellipsometry.
6.1
Abstract
Optical technology is rapidly increasing in abundance, with applications ranging from display technologies to sensors, and by replacing electric components in favour of faster photonic devices. Several designs techniques for engineering the visible optical and NIR response of a thin film are explored. These designs require optically active and absorbing materials, and should be easily grown on large scale. Switchable chalcogenide phase-change material heterostructures are grown using pulsed laser deposition. Multi-level switching is demonstrated using (dynamic) ellipsometry, and measured reflectance profiles agree well with simulations. The PLD grown films show promise for optical display applications.
6.2
Introduction
Thin optical coatings are used in displays, sensors, and communication- and data transfer devices. While each application has different requirements concerning performance parameters, we may identify several desirable features regardless: systems should be small (or thin), lightweight, give high contrast, and the working wavelength should be tunable. To this end, nanometer-thin coatings with various absorptive, reflective, and even switchable characteristics are being researched.
The field of nanometer thickness absorbing optical coatings was opened in 2012 by Kats et al.1 who demonstrated reflectance color tuning of a coating of a few nm absorbing dielectric layer (Ge) on a metallic reflector (Au). The coatings allowed for a tunable reflection peak throughout the visible spectrum, with decent reflectance peak maxima at 40-80% of incident light. They dubbed this the ‘strong-interference’ effect, since the light is only interfering within the thin lossy dielectric. Due to the far sub-wavelength layer thickness, most phase shift is accumulated on reflection at the interfaces, which makes the reflection profile robust under tilted incidence.1 These thickness determined colours are therefore sometimes referred to as structural colours. Later reports include similar experiments using various substrates (like paper), different absorber layers,2,3 and even phase-change material films.4–7
Hosseini et al.8 showed a different device geometry, using the switchable phase-change material Ge2Sb2Te5 (GST) stacked on a thick oxide layer (ITO) and a bottom reflector (Pt). The thick oxide provides a resonance cavity with effectively zero absorption, which allows phase accumulation and interference due to travel between top (GST) and bottom (Pt) reflectors, commonly dubbed ‘Fabry-Perot’ interference. Similar reflectance intensities can be reached, and importantly, Hosseini et al. show switching the GST to the crystalline state yields a distinct change in the reflectance profile. Using nanopatterning, and by leaving out the bottom reflector, they demonstrate the feasibility of transparent, flexible, electronically switchable displays. While the optical reflectance profiles might exhibit only subtle peak- and intensity-shifts, the human eye is relatively sensitive to these 10-20 nm color shifts. With appropriate choice for a given application, optical displays made from these heterostructures may rival those of OLED displays.
Finally, Yoo et al.9 sought to combine both interference mechanisms, introducing a bottom reflector (Pt), resonant ITO layer, followed by a bilayer of GST, separated by a thermal barrier oxide which should allow for separate switchability of both GST layers. The major reflection resonance tuning is achieved through the ITO thickness (~200 nm). By (partially) crystallizing the bilayer, the resonance peak will shift, similarly to Hosseini. Similar results were obtained by using a bilayer of Sb2Te3 and GeTe, but the authors did not separate the layers by a
6.3 Experimental
diffusion barrier, which is problematic for reversible operation.10 Many authors have followed the path of introducing nanopatterning either within the phase change or reflector layer to make use of plasmon resonance frequencies, but this introduces a still poorly-understood level of complexity, both in terms of analysis and device fabrication.
In this work, we compare reflectance curves of both Fabry-Perot and strong-interference multi-level switchable systems, incorporating three different PCMs with distinctly different crystallization temperatures. We demonstrate the layers crystallize separately using dynamic ellipsometry, and show the reflectance profile changes distinctly for each level, allowing multiple states to be robustly accessed.
6.3
Experimental
Films were grown using Pulsed Laser Deposition (PLD). Thin films of Ge2Sb2Te5 (GST), Sb2Te3 and GeTe were deposited on Si/SiO2 substrates at room temperature yielding amorphous films, confirmed by Reflective High-Energy Electron Diffraction (RHEED). Roughness varied slightly between films but was generally extremely smooth with RMS values below 1 nm. Exact heterostructure stackings are given for all results. Thin (3-4 nm) spacer layers of LaAlO3 (LAO) were used in between and on top of phase-change material (PCM) and metal layers to prevent intermixing and evaporation during heating. Sample composition was verified using an FEI Nova NanoSEM Scanning Electron Microscopy and Electron-Dispersive Spectroscopy (SEM-EDS). Layer thickness was determined by scratching the samples and measuring thickness using a Bruker Veeco Multimode 8 Atomic Force Microscope (AFM). Ellipsometry was performed with a J. Woollam UV-VIS spectroscopic ellipsometer and the VASE software was used to determine optical parameters and verify the thickness of all films and heterostructures. The transparent oxides (LAO and SiO) were fitted using a standard Cauchy model. A 1-oscillator Tauc-Lorentz model was used for amorphous PCMs, a Drude conduction term was added to this to describe metals and PCMs. The models were fitted to the data and low error fits were obtained in all cases. Theoretical multilayer reflection profiles were calculated using an in-house developed script based on the Fresnel equations and a Transfer-Matrix algorithm.11,12 For dynamic ellipsometry in multilevel systems, the observed Ψ and Δ parameters are directly plotted, which can be related to the reflectance according to:
tan
cos
R
p/
R
s, where Ψ gives the amplitude ratio, Δ the phase offset between p- and s- polarized light, and Rp and Rs the reflected intensities of both polarisations.13 All reported reflectance profiles are taken from Rp.6.4
Results
Figure 1a shows the modelled layer system as well as a typical AFM scan of a GST film surface. Using this layer structure for fitting, ellipsometry was performed before, during, and after heating of the films. Figure 1b shows the n and k values of GST before and after crystallization. From the observed dielectric parameters, we immediately see the largest differences may be obtained in the NIR region, but mainly extinction shows a large change within the VIS region as well. Figure 1c shows the change in pseudo n and k values during crystallization. The phase transition is clearly observed as a step, allowing this dynamic ellipsometry to be used to analyze the phase transition temperature. Additional fitting results for other materials are available in D.T. Yimam et al.12 This extensive dataset of PLD-grown films is essential to simulate the optical response and optimize optically functional heterostructures. As mentioned in the introduction, the optical response of a multilayer can be tuned in several ways, which we will demonstrate using two distinct geometries, starting from 2-level systems and expanding toward 2n-level systems.
Figure 1.a) AFM scan (1x1 μm area) of 40 nm GST film with an RMS roughness of 0.8 nm. The inset schematically shows the layer geometry. b) real part n and imaginary or absorptive part of dielectric function k obtained using ellipsometry. c) The pseudo- n and k values during continuous heating of the GST film are obtained using dynamic ellipsometry at 630 nm. The crystallization is clearly observed starting at 120 °C and finishes at 150°C.
Fabry-Perot
Fabry-Perot type interference films were grown on Au, using an LAO spacer layer and GST top absorber (8 nm). A thin LAO capping layer (4 nm) prevents oxidation and evaporation. Figure 2 shows the optical response at perpendicular incidence for three LAO cavity thicknesses, for both amorphous and crystalline GST. Clear differences in the reflection spectra are observed: maxima shift by tens of nanometers, and reflected intensity shifts or drops significantly. An optical
6.4 Results
camera image shows mainly the intensity changes in red/IR are visible. The simulations match the observed data quite well.
Figure 2. a) Geometry of a Fabry-Perot type optically tunable system. b.) Photograph of the samples before and after crystallization. The color changes subtly, and the reflected intensity is lower for crystalline phase. ef.) The optical reflection profiles as measured using a reflectometer compare quite well to simulated data (c,e).
Strong Interference
To investigate strong interference a thin film of GST is deposited on Au, with 4 nm LAO on both sides, to prevent intermixing10 as well as evaporation/oxidation.13 Figure 3 shows the optical response of four films, their thickness is tuned to produce apparent reflected colours throughout the visible spectrum. Crystallizing the GST films shows a profound effect on both the spectra maximum wavelength and intensities, which leads to colour and intensity changes easily visible to the eye. As for the Fabry-Perot system, the agreement between experiment and simulation is remarkably good. However, the change in apparent colour upon crystallization is clearly more pronounced.
Figure 3. a) Geometry of a strong-interference type optically tunable system. b.) Photograph of the samples before and after crystallization. The colour changes are quite pronounced. df.) The optical reflection profiles as measured using a reflectometer compare quite well to simulated data (c,e).
Multi-level Switching
Due to the excellent agreement between simulation and experimental data and strong response of the samples to crystallization of one sublayer, a logical next step was to grow heterostructures consisting of multiple phase-change layers. Figures 4ab shows dynamic ellipsometry measurements, which reveal the phase transitions of Sb2Te3, GeTe and GST layers within the heterostructure. The transitions are well separated, which allows for easy discrete switching in three steps, allowing access to 23 = 8 states on reversible switching. The observed values of Ψ are dependent on the exact heterostructure and therefore the curves of figure a and b cannot be directly compared, however, the change in Ψ is an indicator for change of reflectance. Figure 4c shows the optical reflectance of a 2-level Fabry-Perot film that significantly differs in amorphous, crystalline-amorphous, and fully crystallized levels. The reflectance minimum of the film redshifts by 50 nm upon subsequent crystallization of both sublayers. Figure 4d shows the optical reflectance of a 3-layer strong interference film. Crystallization of the bottom Sb2Te3 layer does not significantly change the reflection profile. For the subsequent crystallization of GST and GeTe, a distinct change in reflectance in the 600-800 nm spectral range is observed. When GST and GeTe, respectively, increase and decrease Ψ, they also increase and decrease the reflectivity. While we find that the observed change in Ψ for Sb2Te3 is compensated by a change in Δ, preventing any significant change in reflectance. This is further elucidated in the Appendix.
6.4 Results
Figure 4. a) Dynamic ellipsometry at 630 nm of a Fabry-Perot type system with two PCM layers, and b) strong interference type with three PCM layers. Sb2Te3 crystallizes around 100 °C, Ge2Sb2Te5 around 170 °C, GeTe around 240°C. The crystallization events are distinctly separated, allowing easy switching and access to all sub-states. cd) Reflectance profiles taken with subsequently crystallized sublayers. c) Crystallizing one or both layers redshifts the reflection by ~25 and ~50 nm. d) Crystallizing the bottom Sb2Te3 layer does not significantly influence the reflectance spectrum, but all subsequent crystallization events do show a significantly altered reflection profile, which is red-shifted (GST) or blue-shifted (GeTe) upon crystallization.
Two-PCM-Fabry-Perot
Since from dynamic ellipsometry it seems the two-level Fabry-Perot system shows the largest switching effects, three stacks with different cavity thicknesses and two PCM layers were fabricated. The optical cavity is situated inbetween two phase-change layers. Figure 5 shows the results. Simulation and experiment match
simulation and experiment match quite well, but reflected intensity is quite low, especially for thinner cavities. The phase change is clearly observable.
Figure 5. a) The geometry of a multilevel Fabry-Perot type optically tunable system. The bottom reflector is now a PCM. b.) Optical photograph of the sample before and after crystallization. The color change is immediately apparent. cdef.) The optical reflection profiles as measured using a reflectometer compare quite well to simulated data.
6.5
Discussion
In this chapter, we have compared single- versus multi-PCM switchable optical devices in two different geometries. Figure 4 shows two device geometries based on two different interference schemes, working in different wavelength ranges, but both capable of accessing multiple reflectance states. The reflectance of the Fabry-Perot device is significantly lower, for comparable layer thickness. The strong-interference systems should be more robust against angle-of-incidence changes. Furthermore, the layers are generally thinner, which improves structural quality and reduces deposition times. The three-level strong interference stack however did not show reflectivity change when the bottom PCM was switched. The changes of Ψ and Δ are consistent both with a crystallizing sublayer, and an unchanged reflectance ratio. Unfortunately the absolute change in reflectance becomes smaller when more sublayers are introduced, effectively limiting the number of switchable layers.
6.6 Conclusions
6.6
Conclusions
We show high-quality multi-level switchable optical reflective heterostructure films. The films were grown using three different phase change materials, using Pulsed Laser deposition without nanopatterning. We observe clear reflected color- and intensity changes upon crystallization of the switchable PCM layers. The phase changes were explicitly observed using dynamic ellipsometry and were well separated, allowing for discrete switching operation. Two optical interference designs were demonstrated, Fabry-Perot and strong interference, and both reproduced the Fresnel- and Transfer Matrix calculations closely. Both multi-PCM designs showed the expected multiple discrete optical permittivity levels, however the reflectivity of the eight-level device did not significantly change upon crystallization of the first layer.
6.7
Literature
1. KATS,M.A.,BLANCHARD,R.,GENEVET,P.&CAPASSO,F.NANOMETRE OPTICAL COATINGS BASED ON STRONG INTERFERENCE EFFECTS IN HIGHLY ABSORBING MEDIA.NAT.MATER.12,20–24(2012). 2. MKHITARYAN,V.K. ET AL.TUNABLE COMPLETE OPTICAL ABSORPTION IN MULTILAYER STRUCTURES
INCLUDING GE2SB2TE5 WITHOUT LITHOGRAPHIC PATTERNS.ADV.OPT.MATER.5,1–7(2017). 3. KATS,M.A.&CAPASSO,F.OPTICAL ABSORBERS BASED ON STRONG INTERFERENCE IN ULTRA-THIN
FILMS.LASER PHOTONICS REV.10,735–749(2016).
4. SCHLICH,F.F.&SPOLENAK,R.STRONG INTERFERENCE IN ULTRATHIN SEMICONDUCTING LAYERS ON A WIDE VARIETY OF SUBSTRATE MATERIALS.APPL.PHYS.LETT.103,(2013).
5. BAKAN,G.,AYAS,S.,SAIDZODA,T.,CELEBI,K.&DANA,A.ULTRATHIN PHASE-CHANGE COATINGS ON METALS FOR ELECTROTHERMALLY TUNABLE COLORS.APPL.PHYS.LETT.109,(2016).
6. MENG,Y. ET AL.DESIGN OF A 4-LEVEL ACTIVE PHOTONICS PHASE CHANGE SWITCH USING VO2 AND GE 2SB 2TE 5.APPL.PHYS.LETT.113,071901(2018).
7. JI,H.-K. ET AL.NON-BINARY COLOUR MODULATION FOR DISPLAY DEVICE BASED ON PHASE CHANGE MATERIALS.SCI.REP.6,39206(2016).
8. HOSSEINI,P.,WRIGHT,C.D.&BHASKARAN,H.AN OPTOELECTRONIC FRAMEWORK ENABLED BY LOW-DIMENSIONAL PHASE-CHANGE FILMS.NATURE 511,206–211(2014).
9. YOO,S.,GWON,T.,EOM,T.,KIM,S.&HWANG,C.S.MULTICOLOR CHANGEABLE OPTICAL COATING BY ADOPTING MULTIPLE LAYERS OF ULTRATHIN PHASE CHANGE MATERIAL FILM.ACSPHOTONICS 3,1265–1270(2016).
10. LU,L.,DONG,W.,BEHERA,J.K.,CHEW,L.T.&SIMPSON,R.E.INTER-DIFFUSION OF PLASMONIC METALS AND PHASE CHANGE MATERIALS.(2018). AT <HTTP://ARXIV.ORG/ABS/1808.08682> 11. MCGEHEE.TRANSFERMATRIX SCRIPT STANFORD GROUP. AT
<HTTPS://WEB.STANFORD.EDU/GROUP/MCGEHEE/TRANSFERMATRIX/INDEX.HTML>
12. D.T.YIMAM.OPTICAL PROPERTIES OF PULSED LASER DEPOSITED TELLURIDE HETEROSTRUCTURES. (UNIVERSITY OF GRONINGEN,2018). AT <HTTP://FSE.STUDENTTHESES.UB.RUG.NL/18477/> 13. FUJIWARA,H.SPECTROSCOPIC ELLIPSOMETRY PRINCIPLES AND APPLICATIONS.SPECTROSCOPIC
ELLIPSOMETRY PRINCIPLES AND APPLICATIONS (2007). DOI:10.1002/9780470060193 14. PERUMAL,M.T.K.EPITAXIAL GROWTH OF GE-SB-TE BASED PHASE CHANGE MATERIALS.THESIS
6.8
Appendix A- Optical Reflectivity in an
8-level device
Dynamic ellipsometry
While for most reflectance systems the dynamic ellipsometry intuitively matched the actual reflection profile, for the 3-PCM strong interference system no reflectance change was observed on crystallization of Sb2Te3, while a clear Ψ change was observed. The mechanism is elucidated by also showing the Δ parameter and reflectance ratio (Figure S1). All relevant parameters are related according to
tan
cos
R
p/
R
s. In figure S1, the crystallization events are clearly observed. Strikingly, the Δ and reflectance ratio changes are an order of magnitude smaller for the crystallization of Sb2Te3 than for the GST and GeTe layers. This is consistent with the absence of a significant reflectance in figure 4d.Figure S1.a) The Δ change during dynamic ellipsometry at 630 nm of the system shown in figure 4bd. The Δ changes during the crystallization of each sublayer. Like for Ψ, the change is smallest for Sb2Te3 and largest for GeTe. Interestingly, for GeTe Δ goes up while Ψ goes down. This immediately reveals the reflectance must have changed. b) The reflectance ratio is calculated for all temperatures. The change in reflectance for crystallization of Sb2Te3 is an order of magnitude smaller than for GST and GeTe.
6.8 Appendix A- Optical Reflectivity in an 8-level device
simulation
The 8-level (3 PCM) device was also simulated based on the grown layer thicknesses, assuming zero roughness. The reflection profile is shown in figure S2. A larger change is expected for this system based on an initial simulation than observed in the experiment. We hypothesize this deviation from the simulations is due to large number of layers increasing the roughness, and reducing the effective layer thickness of the individual layers as well as increasing the amount of incoherently scattered light.
Figure S2. The simulated reflection profile for the system shown in figure 4bd. Distinct changes are predicted for every crystallized layer.
6.9
Appendix B- Hyperbolic Dispersion in
textured single-layer vdWaals materials
Abstract
The anisotropic structure and bonding of 2D materials is expected to affect their optical properties. More specifically, light dispersion within a 2D material may become hyperbolic, only allowing light propagation at specific angles, which allows applications such as hyperlensing and plasmonic imaging. We investigate textured thin film tetradymites (Bi2Te3 and Sb2Te3), using ellipsometry to fit dielectric permittivities. No conclusive evidence of hyperbolicity is found based on fitting, but a reflectivity experiment is proposed which may show the hyperbolic nature of these tetradymite thin films.
Introduction
In most materials, the (complex) index of refraction is isotropic. Light will propagate similarly through these materials, regardless of the orientation of the crystal axes with respect to the incident light. Some crystals however, display significant birefringence: due to a difference in optical impedance for light propagating in different directions, or with different polarizations, an image is ‘duplicated’ when viewed through such a crystal, and s- and p-polarised waves will be split. Even more exotic phenomena occur when the electric permittivity becomes negative along one crystal axis, while staying positive along another: the resulting dispersion relation becomes hyperbolic. The dispersion relation for p-polarized waves in crystals with z-axis anisotropy is given by equation A1:
2 2 2 2 2 x y z z x
k
k
k
c
(6.A1) Where the k is the wavevector of light propagation within the crystal, ε the dielectric permittivity, ω the wavelength and c the speed of light.1 Refraction from a normal into a hyperbolic crystal occurs negatively, and due to the hyperbolic shape of the dispersion only occurs along certain narrowly defined angles. The normal and hyperbolic dispersions are shown in figure 1. While a fully negative permittivity might sound exotic, this simply implies reflection, and is quite common in materials such as metals.6.9 Appendix B- Hyperbolic Dispersion in textured single-layer vdWaals materials
Figure 1. Dispersion relations for different permittivity combinations. Most materials are isotropic (a). Hyperbolic dispersion type 1 and 2 (b and c) may occur at various wavelengths within one material. Total external reflection occurs for (d).
Hyperbolic dispersions have been observed by several authors in thick hBN crystals as well as thin films on graphene.2–4 These 1-atom-layer materials are only hyperbolic in the far IR regime. However, TMDCs and tetradymites are predicted to have hyperbolic dispersion in the other optical regimes.1,5 Recently Esslinger et al.6 reported hyperbolic dispersion in Bi2Se3 and Bi2Te3 bulk single-crystals, within the visible wavelength regime. The dispersion was determined based on standard ellipsometry measurements and fitting. The authors proposed and simulated depositing a thin film structure to take advantage of the hyperbolicity to create a so-called hyperlens which overcomes the optical diffraction limit (figure 2). Since the hyperbolic dispersion only supports propagation of p-polarised light along highly specific angles (See formula 1), a small (sub-wavelength) structure under a hyperbolic film may be imaged by exciting and probing with a well-defined wavelength. The sub-wavelength structure produces plasmonic reflections, which travel along the hyperbolic angle to the film surface. Consequently, the sub-wavelength structure is projected enlarged on the film surface and can be detected by a spatially scanning light microscope.7,8
To our knowledge, no experimental proof of such a hyperbolic dispersion within a tetradymite thin film exists in literature. It seems reasonable to assume the vdWaals materials such as Bi2Te3 would possess anisotropic permittivities; after all bonding character is significantly different in the c- direction compared to the basal plane (chapter 1). It seems also reasonable to assume that, since the in-plane conductivity is higher, the basal plane might behave more like a metallic reflector with negative permittivity, while the c-axis plane still acts as a nonconducting positive permittivity. We describe an attempt to grow, characterize, and test tetradymites for their hyperbolic properties.
Figure 2. a.) A single layer of Bi2Se3 is deposted on top of a patterned gold film. The gold edge features in the heterostructure act as plasmon sources when irradiated. The Bi2Se3, due to its supposed hyperbolic dispersion, will transmit these plasmons at the hyperbolic dispersion angle (fig 1), effectively working as a lens to display the gold corners at a larger separation on the surface of the film. Since the dispersion is wavelength dependent, the peak maxima can be more or less resolved by tuning the photon energy. Adapted from Esslinger et al.6
Experimental
Several out-of-plane textured thin films of Sb2Te3, Bi2Te3 and Ge2Sb2Te5 (GST) were grown on Si-SiO2 wafers using Pulsed Laser Deposition. The properties of these films have been reported elsewhere (chapter 2,3,4). Ellipsometry was performed within the Vis-NIR regime and data was fitted using Woollam Software. The films were modeled using a Tauc-Lorentz model with one oscillator. The fit quality is indicated by the Mean Square Error estimator (MSE).
Results
To rigourously analyze the optical properties of the textured films, several model fittings were compared, using either full isotropy, in-plane, or out-of-plane anisotropy. Negative permittivities were allowed to be fitted in all cases. The fits are
6.9 Appendix B- Hyperbolic Dispersion in textured single-layer vdWaals materials
shown in figure 3. Fits for more materials, showing similar trends as Sb2Te3 are available from D.T. Yimam et al.9 The isotropic and in-plane anisotropy fits yield highly similar optical properties, which strongly suggests no in-plane anisotropy is present (which is as expected). When comparing to the out of plane anisotropy, the c-axis index of refraction shows a large deviation from the in-plane parameters. Most interestingly k is effectively zero in the out-of-plane direction indicating no absorption, which is consistent with isolator characteristics across the vdW gaps and higher conduction within the plane. It is important to note those values were not used as input to the fitting model. The fitting however is not conclusive, since similar MSE values are reached for all fits.
Figure 3. Fitting results for Sb2Te3sample grown with z-axis texture. a) Result
extracted with isotopic data analysis assuming isotopic material. b) Analysis result gathered assuming similar optical property in x and y axes but different in z. c) Analysis done with assumption of similar optical property in the x and z axes but different in y axis.
Assuming the out-of-plane anisotropy model fitted in figure 3 is correct, we plot the permittivities of textured Bi2Te3 films and compare them to the plots given by Esslinger for single crystals (figure 4). The permittivities look highly similar, which is encouraging, since it indicates the thin films show similar behaviour to the bulk. We have now established that thin films and bulk crystals look similar when investigated using ellipsometry, but we should stress again that when the isotropic fits are used, the permittivities would look rather different.
Figure 4. Imaginary and real parts of the permittivity for Bi2Te3. The top row shows our data for an out-of-plane textured 210 nm film, the bottom row shows shows bulk crystal data from Esslinger et al.6 In-plane (black) and out-of-plane (red) permittivities are shown. Reasonable agreement between bulk and thin film is observed. The material is hyperbolic in the range where the sign of real permittivity is opposite for both crystal axes.
6.9 Appendix B- Hyperbolic Dispersion in textured single-layer vdWaals materials
An experiment to verify the hyperbolic nature of thin films is now proposed. The reflectivity profile for p-and s-polarised light is modelled using a method similar to that used for the study of hyperbolic dispersion in hBN.3,4,10 Since hyperbolicity introduces a single allowed propagation angle, at this angle all reflection should vanish and the light should propagate into the material. Figure 5 shows the theoretical reflectance profile for both s- and p-polarized light incident on a semi-infinite slab of Bi2Te3. A clear, very sharply defined minimum is observed around 900-1100 nm. If the crystal is flat, and no out-of-plane misalignment of the c-axis is present, a sharp reflectance minimum should be observed in a very narrow, angle-dependent, wavelength range.
Figure 5. Reflected intensity of p- and s-polarized light from a Bi2Te3 sample using the fitted anisotropic dispersion shown in figure 3. A sharp, well-defined minimum is observed between 900-1100 nm.
Several complications prevented us from performing this experiment. Firstly, all light coupled into the film should be absorbed by the film, without being reflected off the substrate-film interface and coupling out again. This requires relatively high absorbance, and films of several 100 nm in thickness. Furthermore, the texture should be extremely sharp throughout the film to observe full absorption. Finally, the light source and wavelength resolution used should be sufficiently stable within the 800-1100 nm range, which unfortunately was outside the range used in this research project.
Discussion
While the effect of hyperbolic dispersion has been conclusively shown in thin films of hBN, the existence of this dispersion in chalcogenides is not strongly supported by the difference in fit quality between isotropic and anisotropic behaviour. We expect this is due to the small thickness of the films and the
relatively small anisotropy compared to true 2D materials such as hBN.11 As figure 5 shows, a sharp minimum should exist in the NIR region for a specific incidence angle. This effect will need careful experimentation and high-quality film growth. Firstly, all light coupled into the film should be absorbed by the film, without being reflected off the substrate-film interface and coupling out again. This requires relatively high absorbance, and films of several 100 nm in thickness. Furthermore, the texture should be extremely sharp throughout the film to observe full absorption. Finally, the light source and wavelength resolution used should be sufficiently stable within the 800-1100 nm range, which unfortunately was outside the range used in this research project.
Conclusion
We have shown that, from ellipsometry, there is no conclusive evidence from fitting that dispersion is hyperbolic in thin-film chalcogenides, but their behaviour does seem to match that of high-quality bulk crystals. Nevertheless, since the anisotropy is smaller than in true 2D materials, the effect will be subtle. A simulation of a reflectivity experiment is provided, which should verify the hyperbolic nature of these materials. The existence of hyperbolicity is still an open question.
6.9 Appendix B- Hyperbolic Dispersion in textured single-layer vdWaals materials
Literature
1. NARIMANOV,E.E.&KILDISHEV,A.V.METAMATERIALS:NATURALLY HYPERBOLIC.NAT.PHOTONICS 9,214–216(2015).
2. CALDWELL, J.D. ET AL.SUB-DIFFRACTIONAL VOLUME-CONFINED POLARITONS IN THE NATURAL HYPERBOLIC MATERIAL HEXAGONAL BORON NITRIDE.NAT.COMMUN.5,1–9(2014).
3. BARANOV, D. G., EDGAR, J. H., HOFFMAN, T., BASSIM, N. & CALDWELL, J. D. PERFECT INTERFERENCELESS ABSORPTION AT INFRARED FREQUENCIES BY A VAN DER WAALS CRYSTAL.PHYS. REV.B-CONDENS.MATTER MATER.PHYS.92,1–6(2015).
4. WU,J. ET AL.TUNABLE PERFECT ABSORPTION AT INFRARED FREQUENCIES BY A GRAPHENE-HBN HYPER CRYSTAL.OPT.EXPRESS 24,17103(2016).
5. GJERDING,M.N.,PETERSEN,R.,PEDERSEN,T.G.,MORTENSEN,N.A.&THYGESEN,K.S.LAYERED VAN DER WAALS CRYSTALS WITH HYPERBOLIC LIGHT DISPERSION.NAT.COMMUN.8,(2017). 6. ESSLINGER, M. ET AL. TETRADYMITES AS NATURAL HYPERBOLIC MATERIALS FOR THE NEAR
-INFRARED TO VISIBLE.ACSPHOTONICS 1,1285–1289(2014).
7. DAI,S. ET AL.SUBDIFFRACTIONAL FOCUSING AND GUIDING OF POLARITONIC RAYS IN A NATURAL HYPERBOLIC MATERIAL.NAT.COMMUN.6,1–7(2015).
8. LI, P. ET AL. HYPERBOLIC PHONON-POLARITONS IN BORON NITRIDE FOR NEAR-FIELD OPTICAL IMAGING AND FOCUSING.NAT.COMMUN.6,1–9(2015).
9. D.T.YIMAM.OPTICAL PROPERTIES OF PULSED LASER DEPOSITED TELLURIDE HETEROSTRUCTURES. (UNIVERSITY OF GRONINGEN,2018). AT <HTTP://FSE.STUDENTTHESES.UB.RUG.NL/18477/> 10. LOW,T. ET AL.POLARITONS IN LAYERED TWO-DIMENSIONAL MATERIALS.NAT.MATER.16,182–194
(2017).
11. WUTTIG, M., DERINGER, V. L., GONZE, X., BICHARA, C. & RATY, J. INCIPIENT METALS : FUNCTIONAL MATERIALS WITH A UNIQUE BONDING MECHANISM.
