Optical properties of (Bi1-xInx)2Se3 thin films

Y. Wang; S. Law

doi:10.1364/OME.8.002570

1. Introduction

Topological insulators (TIs) are a class of materials with unique optical properties. The band structure of TIs comprises a bulk bandgap crossed by linearly-dispersing surface states [1–3]. The electrons in these surface states exhibit spin-momentum locking and have a small mass, leading to a large Fermi velocity and a strong reduction in backscattering. The unique properties of the surface electrons therefore have potential for many optical applications, including THz plasmonics [4–7], optical spin rectifiers [8], and quantum computing [9]. However, in order to create many of the proposed devices, one must use both the TI material as well as a normal, trivial band insulator (BI). Ideally, this BI would have the same lattice constant and crystal structure as the TI, to enable high quality growth of the material stack by molecular beam epitaxy (MBE), similar to how semiconductor lasers and other optical devices are grown. An ideal candidate for this BI is In₂Se₃. In₂Se₃ and Bi₂Se₃ are both layered materials with a crystal structure that is strongly bonded in the a-b plane, but exhibits only weak van der Waals bonding between unit cells (also called quintuple layers, QLs) in the c-direction. The in-plane lattice constants are similar: 0.4nm for In₂Se₃ and 0.414nm for Bi₂Se₃, resulting in a lattice mismatch of only 3.3% [10]. The growth of Bi₂Se₃/In₂Se₃ heterostructures by MBE has been demonstrated previously [11,12]. In addition to the favorable structural properties, In₂Se₃ is also already known as a good optical material that has an extremely high photoresponsivity under visible wavelength illumination [13,14]. The layering of Bi₂Se₃ with In₂Se₃ could therefore lead to a variety of new optoelectronic devices.

In addition to heterostructures comprised of Bi₂Se₃ and In₂Se₃, we can also consider adding the (Bi_1-xIn_x)₂Se₃ (BIS) alloy. In traditional III-V structures, alloying of two binary compounds can lead to more desirable properties than either end member, as well as expanding device design space. We can take a similar approach to the design of TI/BI heterostructures. It has been shown using angle resolved photoemission spectroscopy (ARPES) measurements that for BIS alloy compositions with 0.06<x<0.3, the alloy loses its topological character, while for x>0.3, the alloy behaves like a true band insulator [15]. The BIS alloy has some advantages over pure In₂Se₃ when layering it with Bi₂Se₃. First, the lattice constant should scale with concentration, so alloys with a smaller indium concentration will be more closely lattice-matched to the pure Bi₂Se₃ material and therefore have higher crystalline quality and reduced strain in the heterostructure. Second, the use of the BIS alloy as opposed to pure In₂Se₃ reduces indium diffusion into the Bi₂Se₃ layers, providing shaper interfaces between insulating and conducting material [16]. To date, the primary method of characterizing the BIS alloy has been a combination of electrical and ARPES measurements [12,17]. However, for use in integrated TI/BI optical devices, we must know the optical properties of the BIS alloy both in-plane and out-of-plane in order to choose the correct alloy concentration for specific applications. There have been some previous reports on the optical properties of In₂Se₃ and Bi₂Se₃ in the infrared using both ellipsometry and Fourier transform infrared spectroscopy. However, the work is inconsistent and results are scattershot [18–22]. In addition, we were unable to find any previous reports on the optical properties of the BIS alloy. In this article, we use x-ray diffraction (XRD) and Rutherford backscattering (RBS) measurements to understand how the lattice constant of the BIS alloy depends on indium concentration. We then use a combination of UV-visible spectroscopy and Fourier transform infrared spectroscopy to measure how the bandgap of BIS depends on indium concentration and extract the Drude parameters to model the permittivity of this material in the infrared for both in-plane and out-of-plane directions. With this data, we will be able to construct future BI/TI optical devices.

2. Methods

A set of (Bi_1-xIn_x)₂Se₃ films with five different compositions are grown on c-plane sapphire in a dedicated Veeco GenXplor molecular beam epitaxy (MBE) chamber. A cracking source is used for selenium to improve selenium incorporation and reduce vacancies [23], while bismuth and indium are both evaporated using dual-filament effusion cells. The substrate temperature is monitored with a thermocouple. Sapphire substrates are first outgassed in the loadlock before being heated to 650°C in the MBE chamber to reduce contamination. The substrate temperature is then lowered for film growth.

The selenium flux is held constant for all films, while the bismuth and indium fluxes are adjusted using the effusion cell temperatures to achieve different compositions with a constant growth rate. The In₂Se₃ phase has at least five polytypes: α, β, γ, δ and κ [24,25]. We are interested in growing the β polytype, which has the same crystal structure and similar lattice constant to Bi₂Se₃. Unfortunately, it is difficult to nucleate a single polytype of In₂Se₃. We therefore used a seed layer technique to grow films of a single polytype. We first grow 5QL of Bi₂Se₃ followed by 5QL of In₂Se₃. Upon annealing at a high temperature, the two layers interdiffuse and form a single 10QL (Bi_0.5In_0.5)₂Se₃ layer. We are then able to deposit single-polytype films of any concentration on this seed layer. All films therefore contain a 10QL~10nm layer of (Bi_0.5In_0.5)₂Se₃ followed by a 100QL~100nm layer of (Bi_1-xIn_x)₂Se₃ with varying composition. The crystal quality is monitored in situ by reflection high energy electron diffraction (RHEED). All the films show similar streaky RHEED patterns, indicating single phase and similar crystal quality. Further details of the growth procedure can be found elsewhere [26]. Five films were grown, denoted as A, B, C, D, and E. These films have indium concentrations (and thicknesses) of x = 0, 0.32 (79nm), 0.55 (109nm), 0.73 (116nm), and 1, respectively, as determined by RBS. The thicknesses of pure binary samples are determined by the calibrated growth rate (~1nm/min). After growth, structural properties are characterized using x-ray diffraction (XRD). XRD spectra are taken with a Bruker D8 XRD. Coupled θ-2θ scan mode is used to pick up planes in the c-direction. A Perkin-Elmer Lambda-750 UV-visible-IR spectrophotometer is used for measuring transmission spectra with normal light incidence. A Bruker Fourier transform infrared spectrometer is used for measuring infrared reflection spectra with various incident angles and both TM and TE polarizations. The thickness of pure Bi₂Se₃ and In₂Se₃ are determined by beam flux calibrations.

3. Results and discussion

RBS was used to determine the composition and thickness of films B, C, and D. The data showed slightly asymmetric peaks, indicating a non-uniform composition in the film. The films were modeled as three layers: the seed layer and two bulk layers with differing composition and thickness. In all cases, the top layer had a somewhat higher indium composition than the middle layer. It is difficult to be quantitative using this method, but it is possible that indium exhibits some surface segregation during growth, leading to slightly larger indium concentrations at the top of the film. The concentrations reported here are the total atomic concentrations, which are the most reliable data; these numbers will be used in the rest of this manuscript.

In Fig. 1, we plot the lattice constant in the c-direction of all five films as a function of indium concentration. The lattice constants are calculated using Bragg’s Law. For the pure Bi₂Se₃ and In₂Se₃ end members, the lattice constants are consistent with published results. Pure Bi₂Se₃ has a lattice constant of 2.864nm [27], while the lattice constant of In₂Se₃ is 2.821nm [10,28]. We observe lattice constants of 2.863nm and 2.823nm, respectively, quite close to those reported in the literature. From Fig. 1, we can see that the lattice constant varies linearly with indium concentration, as expected. The dotted line is a linear fit to the data with the equation shown below. The inset shows the [00015] peak for all five samples. We can see that the widths of the peaks are quite similar, indicating a good crystal quality for all samples.

Fig. 1 Lattice constant as a function of indium concentration determined using the [00015] x-ray diffraction peak. Dotted line is a linear fit to the data using the equation. Inset shows the [00015] peak for the five samples.

Download Full Size | PDF

In Fig. 2(a), we show absorption data as a function of energy across the ultraviolet, visible, and near-infrared ranges. As we move from lower to higher energies, the absorption increases due to absorption across the optical bandgap. We can clearly see that the optical bandgap increases with increasing indium concentration. To quantify this trend, we created Tauc plots for all five samples [29]. For this analysis, we plotted ${(α E)}^{1 / r}$ as a function of E, where E is the photon energy and

α = - \frac{1}{d} \ln (\frac{T}{T_{0}})

where d is the film thickness, T is the transmission through the film and substrate, and T₀ is the transmission through the substrate only. The value of the exponent r depends on whether we expect a direct or indirect transition: r = 1/2 for an indirect transition while r = 2 for a direct transition. When plotted this way, the data should appear linear and the x-intercept determines the optical bandgap. We observed both indirect and direct optical transitions for all samples; the extracted data is shown in Fig. 2(b). The indirect transition occurred at lower energies, while the direct transition occurred at higher energies. For sample A (pure Bi₂Se₃), the lowest energy optical bandgap is an indirect transition at 0.298eV, consistent with other results of ~0.3eV [30]. The higher energy transition occurs at 1.26eV. It should be noted that the precise electronic band structure of Bi₂Se₃ is still under investigation. All calculations put the conduction band minimum (CBM) at the Γ point, but the location of the valence band maximum (VBM) is debated. Some calculations as well as some ARPES measurements put the VBM at the Γ point, leading to a direct electronic gap [31]. However, other calculations put the VBM along the Γ-Z direction, leading to an indirect electronic gap, which is consistent with some scanning tunneling microscopy measurements [32]. In either case, the electronic bandgap is reported as ~0.3eV, reinforcing the idea that the valence band is rather flat along the Γ-Z direction. In our experiments, we are only able to measure the optical band gap, which may or may not be equal to the electronic band gap. These measurements can be unequal for a variety of reasons, including if the direct optical transition is forbidden by symmetry or due to state filling leading to a Burstein-Moss shift.

Fig. 2 (a) Absorption coefficient as a function of energy for all five samples. (b) Extracted indirect (blue squares) and direct (red circles) bandgaps as a function of indium concentration. Dashed lines are a linear fit to the data.

Download Full Size | PDF

For sample E (pure In₂Se₃), we observe an indirect optical bandgap at 1.35eV and a direct optical bandgap at 2.46eV. The lower energy transition is consistent with results for bulk β-In₂Se₃, which has a bandgap of 1.3eV at 523K [21]. Colloidal β-In₂Se₃ sheets have a bandgap of 1.55eV [33], while sheets grown by vapor deposition have bandgaps (for thick sheets) of around 1.44eV [25]. We have been unable to find data for the bandgap of β-In₂Se₃ at room temperature. Again, these are optical bandgaps which may not correspond to the fundamental electronic band gap for this material. In particular, band structure calculations for β-In₂Se₃ indicate that the lowest energy direct transition at the L-point corresponds to a forbidden optical transition, leading to an optical gap much larger than the fundamental gap.

For BIS alloys, we observe a linear increase in both the low energy indirect and high energy direct gaps as the indium content increases, as shown in Fig. 2(b). The dashed lines in Fig. 2(b) are a linear fit to the data, with the following equations: $E_{g, i n d i r e c t} = 0.993 x + 0.358$ , and $E_{g, d i r e c t} = 1.20 x + 1.18$ , where the units of the band gap are given in eV and x is the indium concentration in the films. A linear shift in optical bandgap with alloy concentration is commonly observed in a variety of other semiconductor systems, including AlGaAs and InGaAs.

Finally, we obtained infrared reflection spectra for all five samples as a function of polarization and angle from 25° to 55° every 5°. An example of the experimental data for sample B is shown in Figs. 3(a) and 3(b); other samples are similar. In order to extract the optical constants for these samples, we modeled the optical response using a 4 × 4 transfer matrix method [34]. Both the permittivity of the BIS films and Al₂O₃ (0001) substrates were assumed to be anisotropic, with $ε_{x y}$ the permittivity in the x-y plane and $ε_{z}$ the permittivity in the z direction. Here we define the x-y plane as the hexagonally bonded plane in the BIS crystal and the z direction as along the growth direction. The damped harmonic oscillator functions, Eq. (2), were used to model the permittivity of Al₂O₃ (0001) substrates

ε (ω) = ε_{\infty} \prod_{i}^{l} \frac{ω_{L O i}^{2} - ω^{2} - i ω γ_{L O i}}{ω_{T O i}^{2} - ω^{2} - i ω γ_{T O i}}

where

ε_{\infty}

is the high frequency permittivity,

ω_{L O}

and

γ_{L O}

are the frequencies and scattering rates of the longitudinal phonon modes,

ω_{T O}

and

γ_{T O}

are the frequencies and scattering rates of the transverse phonon modes. The parameters used to model the Al₂O₃ (0001) substrates were adopted from M. Schubert [35], and then slightly refined using the 4 × 4 transfer matrix method to fit our reflection data from 5μm to 25μm, at the incident angle of 45°. The correlation coefficients between the fitted curve and the raw data were used as indicators of fitting reliability. The correlation coefficients are 0.9984 and 0.9983 for TE and TM polarization, respectively.

Fig. 3 (a) Reflection spectra for sample B (x = 0.32) with TE polarization and (b) TM polarization. (c) Fitted curve for sample B with TE polarization and (d) TM polarization at different incident angles. Inset in 3(a) shows a schematic of the modelling geometry.

Download Full Size | PDF

The permittivity of BIS films was simulated with a Drude model, as described in Eq. (3).

ε (ω) = ε_{\infty} (1 - \frac{ω_{D}^{2}}{ω^{2} + i γ_{D} ω})

where

ε_{\infty}

is the high frequency permittivity,

ω_{D}

the Drude frequency, and

γ_{D}

the Drude losses. All the BIS films were treated as anisotropic, with different fitting parameters for the x-y plane and z direction. The geometry of the modelling is a layer of BIS film with experimentally-determined thickness and a layer of 0.5mm Al₂O₃(0001) substrate embedded in two semi-infinite air layers. Table 1 shows all the parameters obtained from the data modelling. For each parameter of each sample listed in the table, mean values and the standard deviations (SD) among all seven incident angles were calculated. The units of all the frequencies and losses are cm⁻¹. Again, the correlation coefficients between the fitted curve and the raw data were used as indicators of fitting reliability. We tried to refine the parameters to get the correlation coefficients as close to one as possible. The smallest correlation coefficient we got in the fitting is 0.9906, occurring in Bi₂Se₃ TM 40°. Most of the correlation values lie around 0.998, which means a good agreement between the data and the fitted curve. Examples of the fitted curves are shown in Fig. 3(c) for TE polarization and 3(d) for TM polarization. One may notice larger deviations from the experimental data when the wavelength gets close to 15µm. That is the region over which the sapphire substrate becomes close to 100% reflective. The reflection data in that region is therefore somewhat noisier, leading to a slight deviation from the predicted reflection data.

Table 1. Mean value and standard deviation of all the fitting parameters for all the samples

View Table

In Fig. 4, we show the x-y and z direction high frequency permittivities plotted as a function of the indium concentration. In one case, the error bar is smaller than the size of the data point. As can be seen from Fig. 4, within the error bars the high frequency permittivity decreases linearly with indium concentration for both x-y plane and z direction. We do not see a similar trend for Drude frequencies or Drude losses shown in Table 1. For $ω_{D, z}$ and $γ_{D, z}$ the values are relatively constant across all indium concentrations. For $ω_{D, x y}$ and $γ_{D, x y}$ , however, the values do change with concentration but not with any particular trend. The x-y Drude frequency in particular is quite far away from the fitting range. As such, the model is not very sensitive to the precise values of these parameters.

Fig. 4 The fitted high frequency permittivity as a function of indium concentration. The black and red lines are linear fittings of $ε_{\infty, x y}$ and $ε_{\infty, z}$ , respectively.

Download Full Size | PDF

We compared our high frequency permittivity values for pure binary Bi₂Se₃ and In₂Se₃ to those reported in the literature. Different methods have been used to approximate the optical response of these materials, and the optical data were measured with different techniques, making these results inconsistent. In some electrical transport studies, the static dielectric constant of Bi₂Se₃ is taken to be extremely large, approximately 100 [36,37]. Some optical studies have reported 29 [22] and ~25 [19] for $ε_{\infty,x y}$ of Bi₂Se₃, much closer to 22.4 that we observe. While we are reporting a larger value of 26.5 for $ε_{\infty, z}$ , other reports indicate values of ~17.4 smaller than that of $ε_{\infty,x y}$ (~25) [19]. When it comes to indium selenide, discussions of the same phase and polytype (β-type In₂Se₃) as discussed in the present work are limited. There is a publication where $ε_{\infty,x y}$ = 9.53 is extracted from far-IR (>25μm) reflection spectra for α-In₂Se₃ single crystal [38]. Another paper reported values of 9.51, 7.23 and 8.09 for α, β and γ-In₂Se₃ single crystals, respectively [21]. Among all three polytypes, their value for β-In₂Se₃ is the closest to that we observe. This is yet more evidence that we are growing β-type films.

4. Conclusion

In conclusion, we have successfully grown (Bi_1-xIn_x)₂Se₃ films by molecular beam epitaxy with various indium concentrations. Consistent crystal structures for different indium concentrations are shown by XRD. We find a linear relationship between the indium concentration and lattice constant across the composition range. Both direct and indirect optical band gaps of the films are extracted from transmission spectra across the ultraviolet-visible-near IR range. The energy gaps for pure Bi₂Se₃ and β-In₂Se₃ are consistent with theoretical predictions and other experimental measurements. A linear relation between the gap energy and indium concentration is found for both direct and indirect gaps. The infrared reflection spectra are modelled and multiple optical constants are extracted from the model. The high frequency permittivity for both the x-y plane and the z direction show a linear relation with indium concentration. Comparable values can be found in the literature for pure Bi₂Se₃ and β-In₂Se₃. With appropriate optical constants for (Bi_1-xIn_x)₂Se₃, complex optical devices leveraging the unique properties of the topological insulator Bi₂Se₃ can be designed, modeled, and created.

Funding

U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DE-SC0016380).

Acknowledgements

Y. W. and S. L. acknowledge funding from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC0016380. We acknowledge the helpful discussion with W. Li and A. Janotti at the Department of Materials Science and Engineering, University of Delaware. We acknowledge Z. Wang and R. Opila at the Department of Materials Science and Engineering, University of Delaware, for discussions about composition measurement with X-ray Photoelectron Spectroscopy.

References and links

1. Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi₂Te_3.,” Science 325(5937), 178–181 (2009). [CrossRef] [PubMed]

2. M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010). [CrossRef]

3. Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010). [CrossRef] [PubMed]

4. P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013). [CrossRef] [PubMed]

5. J.-Y. Ou, J.-K. So, G. Adamo, A. Sulaev, L. Wang, and N. I. Zheludev, “Ultraviolet and visible range plasmonics in the topological insulator Bi_1.5Sb_0.5Te_1.8Se_1.2.,” Nat. Commun. 5(1), 5139 (2014). [CrossRef] [PubMed]

6. Y.-P. Lai, I.-T. Lin, K.-H. Wu, and J.-M. Liu, “Plasmonics in topological insulators,” Nanomater. Nanotechnol. 4, 13 (2014). [CrossRef]

7. T. P. Ginley and S. Law, “Coupled Dirac plasmons in topological insulators,” Adv. Opt. Mater. 6(13), 1800113 (2018). [CrossRef]

8. I. Appelbaum, H. D. Drew, and M. S. Fuhrer, “Proposal for a topological plasmon spin rectifier,” Appl. Phys. Lett. 98(2), 023103 (2011). [CrossRef]

9. J. E. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010). [CrossRef] [PubMed]

10. S. Popović, A. Tonejc, B. Gržeta-Plenković, B. Čelustka, and R. Trojko, “Revised and new crystal data for indium selenides,” J. Appl. Cryst. 12(4), 416–420 (1979). [CrossRef]

11. Z. Y. Wang, X. Guo, H. D. Li, T. L. Wong, N. Wang, and M. H. Xie, “Superlattices of Bi₂Se₃/In₂Se₃: Growth characteristics and structural properties,” Appl. Phys. Lett. 99(2), 023112 (2011). [CrossRef]

12. Y. Zhao, H. Liu, X. Guo, Y. Jiang, Y. Sun, H. Wang, Y. Wang, H.-D. Li, M.-H. Xie, X.-C. Xie, and J. Wang, “Crossover from 3D to 2D quantum transport in Bi₂Se₃/In₂Se₃ superlattices,” Nano Lett. 14(9), 5244–5249 (2014). [CrossRef] [PubMed]

13. R. B. Jacobs-Gedrim, M. Shanmugam, N. Jain, C. A. Durcan, M. T. Murphy, T. M. Murray, R. J. Matyi, R. L. Moore 2nd, and B. Yu, “Extraordinary photoresponse in two-dimensional In(₂₎Se(₃) nanosheets,” ACS Nano 8(1), 514–521 (2014). [CrossRef] [PubMed]

14. L. Debbichi, O. Eriksson, and S. Lebègue, “Two-Dimensional Indium Selenides Compounds: An Ab Initio Study,” J. Phys. Chem. Lett. 6(15), 3098–3103 (2015). [CrossRef] [PubMed]

15. M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, “Topological-metal to band-insulator transition in (Bi_1-xIn_x)₂Se₃ thin films,” Phys. Rev. Lett. 109(18), 186403 (2012). [CrossRef] [PubMed]

16. H. D. Lee, C. Xu, S. M. Shubeita, M. Brahlek, N. Koirala, S. Oh, and T. Gustafsson, “Indium and bismuth interdiffusion and its influence on the mobility in In₂Se₃/Bi₂Se₃,” Thin Solid Films 556, 322–324 (2014). [CrossRef]

17. M. J. Brahlek, N. Koirala, J. Liu, T. I. Yusufaly, M. Salehi, M.-G. Han, Y. Zhu, D. Vanderbilt, and S. Oh, “Tunable inverse topological heterostructure utilizing (Bi_1-xIn_x)₂Se₃ and multichannel weak-antilocalization effect,” Phys. Rev. B 93(12), 125416 (2016). [CrossRef]

18. M. Eddrief, F. Vidal, and B. Gallas, “Optical properties of Bi₂Se₃: from bulk to ultrathin films,” J. Phys. D Appl. Phys. 49(50), 505304 (2016). [CrossRef]

19. M. Stordeur, K. K. Ketavonc, A. Priemuth, H. Sobotta, and V. Riede, “Optical and Electrical Investigations of n-Type Bi₂Se₃ Single Crystals,” Phys. Status Solidi 169(2), 505–514 (1992). [CrossRef]

20. D. Wu, A. J. Pak, Y. Liu, Y. Zhou, X. Wu, Y. Zhu, M. Lin, Y. Han, Y. Ren, H. Peng, Y.-H. Tsai, G. S. Hwang, and K. Lai, “Thickness-dependent dielectric constant of few-layer In₂Se₃ nanoflakes,” Nano Lett. 15(12), 8136–8140 (2015). [CrossRef] [PubMed]

21. C. Julien, A. Chevy, and D. Siapkas, “Optical properties of In₂Se₃ phases,” Phys. Status Solidi 118(2), 553–559 (1990). [CrossRef]

22. W. Richter, H. Köhler, and C. R. Becker, “A Raman and far-infrared investigation of phonons in the rhombohedra1 V₂-VI₃ Compounds,” Phys. Status Solidi 84, 619–628 (1977). [CrossRef]

23. T. P. Ginley and S. Law, “Growth of Bi₂Se₃ topological insulator films using a selenium cracker source,” J. Vac. Sci. Technol. B 34(2), 02L105 (2016). [CrossRef]

24. J. Ye, S. Soeda, Y. Nakamura, and O. Nittono, “Crystal structures and phase transformation in In₂Se₃ compound semiconductor,” Jpn. J. Appl. Phys. 37(1), 4264–4271 (1998). [CrossRef]

25. N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In₂Se₃ nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016). [CrossRef]

26. Y. Wang, T. P. Ginley, and S. Law, “Growth of high-quality Bi₂Se₃ topological insulators using (Bi_1-xIn_x)₂Se₃ buffer layers,” J. Vac. Sci. Technol. B 36(2), 02D101 (2018). [CrossRef]

27. Landolt-Bornstein, “Bismuth selenide (Bi₂Se₃) crystal structure, chemical bond, lattice parameter (including data of related compounds),” in Non-Tetrahedrally Bonded Elements and Binary Compounds I, O. Madelung, U. Rossler, and M. Shulz, eds. (1998), vol. 41C.

28. X. Tao and Y. Gu, “Crystalline-crystalline phase transformation in two-dimensional In₂Se₃ thin Layers,” Nano Lett. 13(8), 3501–3505 (2013). [CrossRef] [PubMed]

29. J. Tauc, “Optical properties and electronic structure of amorphous Ge and Si,” Mater. Res. Bull. 3(1), 37–46 (1968). [CrossRef]

30. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009). [CrossRef]

31. I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi₂Se₃ from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013). [CrossRef]

32. S. Kim, M. Ye, K. Kuroda, Y. Yamada, E. E. Krasovskii, E. V. Chulkov, K. Miyamoto, M. Nakatake, T. Okuda, Y. Ueda, K. Shimada, H. Namatame, M. Taniguchi, and A. Kimura, “Surface scattering via bulk continuum states in the 3D topological insulator Bi₂Se₃,” Phys. Rev. Lett. 107(5), 056803 (2011). [CrossRef] [PubMed]

33. G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In₂Se₃ nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017). [CrossRef] [PubMed]

34. J. Hao and L. Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: generalized 4×4 transfer-matrix method,” Phys. Rev. B 77(9), 094201 (2008). [CrossRef]

35. M. Schubert, T. E. Tiwald, and C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61(12), 8187–8201 (2000). [CrossRef]

36. D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, “Two-dimensional surface charge transport in topological insulators,” Phys. Rev. B 82(15), 155457 (2010). [CrossRef]

37. D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi₂Se₃,” Nat. Phys. 8(6), 459–463 (2012). [CrossRef]

38. K. Kambas and J. Spyridelis, “Far Infrared optical study of α-In₂Se₃ compound,” Mater. Res. Bull. 13(7), 653–660 (1978). [CrossRef]

Optical properties of (Bi_1-xIn_x)₂Se₃ thin films

Abstract

1. Introduction

2. Methods

3. Results and discussion

4. Conclusion

Funding

Acknowledgements

References and links

Cited By

Figures (4)

Tables (1)

Equations (3)

Optical Materials Express

	Bi₂Se₃		(Bi_0.70In_0.32)₂Se₃		(Bi_0.49In_0.55)₂Se₃		(Bi_0.26In_0.73)₂Se₃		In₂Se₃
	Mean	SD	Mean	SD	Mean	SD	Mean	SD	Mean	SD
$ε_{\infty, x y}$	22.4	0.6	15.3	0.8	12.3	1.5	9.7	0.8	5.0	0.2
$ω_{D, x y}$	315	32	277	38	201	48	111	13	207	63
$γ_{D, x y}$	696	183	799	93	897	37	346	125	548	90
$ε_{\infty, z}$	26.5	2.0	24.2	1.8	23.2	1.1	17.8	1.9	16.9	1.4
$ω_{D, z}$	914	18	908	10	906	8	918	16	918	13
$γ_{D, z}$	67	38	60	27	55	23	67	23	54	19