Optical emission of two-dimensional arsenic sulfide prepared by plasma

Optical emission of two-dimensional arsenic sulfide prepared by plasma

Superlattices and Microstructures 114 (2018) 305e313 Contents lists available at ScienceDirect Superlattices and Microstructures journal homepage: w...

2MB Sizes 0 Downloads 25 Views

Superlattices and Microstructures 114 (2018) 305e313

Contents lists available at ScienceDirect

Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices

Optical emission of two-dimensional arsenic sulfide prepared by plasma Leonid Mochalov a, b, c, Aleksey Nezhdanov a, Alexander Logunov a, b, Mikhail Kudryashov a, Ivan Krivenkov a, Andrey Vorotyntsev b, Daniela Gogova d, *, Aleksandr Mashin a a

Lobachevsky University, Nizhny Novgorod, Russia Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia Department of Physics and Optical Science, University of North Carolina at Charlotte, North Carolina, United States d Central Lab of Solar Energy and New Energy Sources at the Bulg. Acad. Sci., Blvd. Tzarigradkso shose 72, 1784 Sofia, Bulgaria b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 December 2017 Accepted 26 December 2017 Available online 2 January 2018

For the first time optical emission of prepared in plasma two-dimensional arsenic sulphide materials “beyond graphene” has been demonstrated. A strong structural photoluminescence exited by continuous wave operation lasers with a laser excitation wavelength of 473 nm and 632.8 nm has been observed. The influence of excitation parameters, chemical composition, structure, and annealing conditions on the intensity of photoluminescence of the chalcogenide materials has been established. Mass-spectrometry and Raman spectroscopy were coupled with quantum-chemical calculations to reveal the fragments which are the building blocks of the 2D As-S materials. A plausible mechanism of formation and modification of the arsenic sulfide luminiscenting structural units has been proposed. The properties of the 2D pole-structured and layered arsenic sulphide could be a key to advancing the 2D photosensitive devices. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Arsenic sulfide films PECVD Structural luminescence Raman spectroscopy

1. Introduction Since the discovery of graphene in 2004 [1], study of 2D materials “beyond graphene” brings about a growing interest of scientists. Among the family of chalcogenide materials, 2D-layered transition-metal dichalcogenides demonstrate excellent electronic and optical properties, outstanding mechanical flexibility, and exceptional catalytic performance. For that reasons, MoS2, WS2, WSe2, etc., are promising candidates to be used in many potential applications, especially in energy-related fields, particularly, in energy storage and conversion systems [2]. Unlike graphene, the two-dimensional layered dichalcogenides possess a forbidden band of 1.2e1.4 eV transforming from indirect-gap bulk semiconductors into direct-band gap ones [3] at thicknesses of 5e7 monolayers. It has been also established that the specific honeycomb structural fragments forming the 2D layered structures of dichalcogenides are responsible for the structural luminescence phenomena [4]. In the same time, chalcogenides like As2S3, As2Se3, etc., have never been considered as materials capable of forming similar structures. It could be due to the limitations of the methods used for those materials preparation. In the present paper, we

* Corresponding author. E-mail address: [email protected] (D. Gogova). https://doi.org/10.1016/j.spmi.2017.12.052 0749-6036/© 2018 Elsevier Ltd. All rights reserved.

306

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

would like to show, how the honeycomb structural fragments are possible to be formed in plasma on the example of the wellknown arsenic sulfide chalcogenide system. Historically speaking, the types and parameters of AseS bonds in the realgar and orpiment structures were studied in detail and reported as early as 1950s [5]. It was shown that realgar and orpiment are built from the same basic (As2S2) structural units, giving rise to similar bond distances and angles in both cases. In the case of the orpiment an additional sulfur atom is added to each As2S2 unit to account for the required stoichiometry, and the realgar consists of discrete As4S4 units, while orpiment is a layered structure. In addition, in 1972 in Ref. [6] it was found that realgar As4S4 shows certain striking structural similarities to orpiment As2S3, although these are not apparent from a cursory inspection of the two structures. Despite of the scientific premises, the synthesis of As-S with a polymer structure, consisting of As2S2 monomers seemed impossible for a long while. Recently, we demonstrated that the 2D (As2S2)n polymeric structure is possible to be obtained when plasma is used as the way of initiation of chemical interaction between As and S precursors [7,8]. Moreover, the chalcogenide materials treated by plasma at low pressures possess a substantial degree of purity that enables gaining insight into their intrinsic properties [9e11]. In the current work we are aiming to demonstrate the conditions of appearance and enhancing of structural luminescence in monochalcogenide (As2S2)n polymeric structure. 2. Experimental 2.1. Deposition As-S samples were prepared by the plasma discharge-based deposition equipment described in Refs. [12,13]. The initial substances - elemental arsenic and sulfur - were loaded into quartz reservoirs with external heaters. The temperatures into the reservoirs were 200  C and 380  C for sulfur and arsenic, respectively. High pure argon was used as a plasma feed gas and as a carrier gas. It was blown at a constant total rate of 30 ml/min through the reservoirs to supply the precursors into the plasma discharge. The plasma chemical rector is a quartz flask with an external inductor. The bottom of the reactor is a stainless steel vacuum flange with a substrate holder cooled by water. The substrate temperature was constantly maintained at 22  C. High-pure quartz glass and sodium chloride were chosen as the substrate materials in terms of different measurements. The samples were the films with the thickness about a few microns. The pressure during the process of deposition was constantly kept 0.1 Torr and the reactor walls temperature was about 150  C. The plasma discharge was excited by an RF generator with a frequency of 40 MHz and power of 50 W. 2.2. Characterization The study of the samples composition was carried out by X-ray microanalysis using a scanning electron microscope JSM IT300LV (JEOL) with an energy-dispersion detector for elemental analysis X-MaxN 20 (Oxford Instruments) under high vacuum and at accelerating voltage of 20 kV. Raman spectra were studied by means of NTEGRA Spectra system for Raman spectroscopy produced by the NT-MDT Company (Zelenograd) using a He-Ne laser with a wavelength of 632.8 nm. The beam was focused by a 100 objective lens with a numerical aperture of 0.95. The unfocused laser power measured by a silicon photodetector 11PD100-Si (Standa Ltd) was in the range 1 mWe1 mW. The Raman spectra of the samples were studied in reflection configuration at room temperature in the range of 50e900 сm1. Photoluminescence study was performed at room temperature employing continuous wave operation lasers with a laser excitation wavelength of 473 nm and 632.8 nm. The arsenic sulfide materials were analyzed by mass-spectrometer DSQII to reveal their main structural fragments. 2.3. Theoretical modeling Quantum-chemical calculations have been performed to gain insight into the plasma synthesized As-S chalcogenide structures. The structural fragments have been proved using the RB3LYP/6-31 þ G(d) method and Gaussian 03 software package [19]. 3. Results and discussion 3.1. Scanning electron microscopy study of the arsenic sulfide Scanning Electron Microscopy (SEM) images typical of the arsenic sulfide with a composition As40S60 are illustrated in Fig. 1 (a) and (b). The striking difference in the surface morphology and structure is due to the very different conditions of the plasma deposition. Both pictures (1a and 1b) illustrate arsenic sulfide structures consisting of (As2S2)n-units (see below) formed in plasma by spherical structural fragments with a diameter of about 100 nm [7]. Fig. 1a shows a pole-structured material and Fig. 1b depicts a 2D layered structure, the theoretical possibility of existence of which has been described in Refs. [5,6]. We have reported quantum-chemical estimations of these structures [8] together with experimental results on the unusually broad

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

307

Fig. 1. SEM images of arsenic sulfide materials prepared by plasma discharge at different conditions: pole-like (a) and layered (b) structures.

transparency window of these materials (0.43e20 mm) [8] in comparison with those of As2S3 (0.6e11 mm), prepared by traditional thermal methods. Judging by the image 1b and taking into account the resolution of the SEM method, we may assume that the thickness of each layer is about a few nanometers. The surface roughness of the layered structure is 3 nm [7]. Thus, Fig. 1 demonstrates the high potential of the plasma discharge method in terms of preparation of chalcogenide materials with diverse structures.

3.2. Raman spectroscopy study of arsenic sulfide samples prepared by plasma discharge A typical of the plasma synthesized arsenic sulfide structures Raman spectrum is presented in Fig. 2. Firstly, it should be noted that the whole baseline of the Raman spectrum poses sufficiently higher in comparison with the spectrum of As2S3 prepared by a commonly used thermal method [14]. It includes the AsS3/2 (340 cm1 and 367 cm1) structural unit of the glass-net and the linear modification of sulfur (485 cm1). An analogical abnormal Raman plot was mentioned once in Ref. [15] for realgar with a natural origin. Although, the natural realgar Raman spectrum includes the As4S4 crystal phase (185 cm1, 273 cm1 and 228 cm1 bands), the structural unit of the glass-net AsS3/2 (340 cm1 and 367 cm1), sulfur in the form of S8 rings (475 cm1), and the linear sulfur modification (485 cm1). In general, both spectra of the natural realgar and our plasma discharge-based sample possess the same strong luminescence band.

3.3. Optical emission study of plasma prepared arsenic sulfide 3.3.1. Photoluminescence exited by continuous wave operation lasers with a laser excitation wavelength of 473 nm and 632.8 nm Photoluminescence of the plasma prepared arsenic sulfide was measured with a laser excitation wavelength of 473 nm and 632.8 nm employing continuous wave operation lasers at room temperature (RT, Fig. 3). It has been found that two different mechanisms induce the photoluminescence. When the 632.8 nm laser is used the photon energy (1.9 eV) is not sufficient for transition of electrons from the valence band to the conduction band. The band gap of the As-S samples is approximately 2.4 eV and the photoluminescence process passes through the capture of electrons and holes by recombination centers near the middle of the forbidden band. However, using the laser with the exiting energy 2.6 eV (473 nm) we have observed the photoluminescence bringing about zone-to-zone transitions with a maximum near 2.15 eV. 3.3.2. Dependence of the structural luminescence intensity on the annealing temperature As a next step we have performed annealing of the arsenic sulfide films in the temperature range 50e200  C in a high-pure argon atmosphere. Results on the RT-photoluminescence intensity dependence on the annealing temperature are depicted in Fig. 4 for the laser excitation wavelength of 632.8 nm. The RT-photoluminescence spectrum is a diffuse peak with a width of several tenths of eV. It is assumed that the presence of recombination centres in the structure of plasma prepared arsenic sulfide near the middle of the forbidden band results in luminescence. The authors of [16] associate the peaks at energies of 1.58 eV, 1.65 eV, 1.73 eV and 1.80 eV with the presence of surface donors and acceptors near the forbidden band and with the emission of electrons from deep traps.

308

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

Fig. 2. A typical Raman spectrum of arsenic sulfide prepared by plasma discharge.

Fig. 3. Photoluminescence spectra of the plasma prepared arsenic sulfide excited by continuous wave operation lasers with laser excitation wavelengths of 473 and 632.8 nm at room temperature.

Fig. 4. RT-PL spectra of As-S samples annealed at different temperatures: 50, 100, 150 and 200  C.

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

309

The photoluminescence intensity sharply increases with the increment of the annealing temperature. The growth of the PL intensity is tied with the process of structural modification of chalcogenide materials in result of the ex-situ annealing.

3.4. Structural modification of the plasma prepared arsenic sulfide with increasing of the annealing temperature Raman spectra of the annealed arsenic sulfide films are illustrated in Fig. 5. The spectra were conditionally divided into six sections. Firstly, increasing the annealing temperature leads to decreasing of the peaks intensity in the first region (130170 cm1) related to vibrations of S-atoms in S8 rings and, in parallel, the increasing of the signal intensity of the linear sulfur near 485 cm1 (fifth area). Secondly, the intensity of the signal near (170-200 cm1) in the second region decreases with the rise of the annealing temperature. This peak corresponds to the vibrations of homopolar As-As bonds in the realgar As4S4 unit. In the third region (200-270 cm1) there are two apparent maxima: near 220 and 234 cm1, that are referred to the vibrations of As-As bonds also, however, in two different functional groups - in the realgar As4S4 unit and in the S2As-AsS2 bridges, respectively. It can be seen from this region of the spectrum that with increasing of the annealing temperature, the structural groups from the realgar are rearranged into the form of S2As-AsS2 bridges. Structural modifications taking place in the As2S3 thin films under different annealing conditions have been investigated for a long time. The authors of Ref. [17] prepared arsenic sulfide films of 3 mm thickness by thermal evaporation in vacuum and additionally had annealed them at 180  C. They have assumed that the sharp peaks near 180 and 230 cm1 appearing after annealing refer to the newly formed As4S4 structural units. Besides, the effect of formation of As4S4 structural units in the glass-net of As40S60 thin films, induced by a continuous 488 nm argon-ion laser irradiation, is also discussed in Ref. [14]. It has been established the ex-situ laser beam irradiation causes dissociation of the sulfur atoms in the AsS1/2 bonds, and transformation of the As-S units into realgar As4S4 structures. An explanation of the role of As4S4 in the photoluminescence phenomenon of arsenic sulfide materials was also suggested by Asatryan et al. [18]. They have shown the structures responsible for the PL in amorphous As2S3 thin films must have a disk-like polarizability tensor [18].

3.5. Dependence of luminescence on the chemical composition and structure of As-S films In order to investigate the dependence of luminescence intensity on the chemical composition and structure, an As-S film (5-mm-thick) with a gradually variable chemical composition in depth was synthesized in a plasma deposition process (as discussed above). The As content was gradually increased from 35 to 50 at.% along the sample thickness. In Fig. 6 the crosssection profile of the film, revealed by SEM (6a), the depth distribution of the As concentration (determined by EDX, 6a), the photoluminescence intensity distribution (6b), and the Raman intensity distribution (6c) along the sample cross-section are coupled to observe the impact of the As content on the optical properties of the material investigated. According to the data presented in Fig. 6 (a) the arsenic concentration varied in the range of 30e50 at.% reaching its maximum at about 2.2 mm in depth. We see the As content in the material has a very strong influence on the photoluminescence. For certain compositions the PL intensity is strong, and for others e weak. The PL intensity dependence on the arsenic concentration is shown in Fig. 7 also. Increasing the arsenic content from 30 to 37 at.% leads to the growth of the luminescence intensity. The PL intensity curve has two obvious maxima - near 37 and 34 at.% As.

Fig. 5. Raman spectra of the plasma prepared As-S samples after thermal annealing in the temperature range 50 С-200 С.

310

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

Fig. 6. SEM image and depth distribution of the As concentration (a), photoluminescence intensity distribution (6b), and Raman intensity distribution (6c) along the sample cross-section.

Fig. 7. Dependence of the PL intensity on the As content across the sample depth.

The existence of two luminescence peaks corresponding to two different chemical compositions is probably due to the presence of two different luminescence mechanisms in the structure. Further increasing of the arsenic content up to 50 at.% leads to a sharp quenching of the luminescence intensity. The luminescence through the samples cross-section was excited by a semiconductor laser with a wavelength of 473 nm. The data obtained is illustrated in Fig. 8. Obviously, the distribution of the PL intensity along the sample cross-section has a complex character. However, four characteristic areas can be distinguished. In the first region, photoluminescence is completely absent (the range of arsenic concentrations is 30e35 at.%). When the arsenic concentration reaches about 37 at.% (region 2), intense photoluminescence with a maximum at 620 nm is observed. In region 3, a PL is observed with the maximum at a wavelength of 675 nm at the concentration of arsenic about 37 at.%. If the As concentration is more than 40 at.% PL peaks are not registered (region 4). Raman excitation across the sample depth was carried out by a He-Ne laser with a wavelength of 632.8 nm (see Fig. 9). Similar to the case of annealing, the Raman spectra consist of several areas due to vibrations of different structural units. The regions (130-170 cm1) and (470-490 cm1) are assigned to the vibrations of S atoms in the S8 rings. The region (170200 cm1) includes peaks corresponding to the vibrations of homopolar As-As bonds in the realgar As4S4 units; the region near (200-270 cm1) is referred to the vibrations of As-As bonds in the realgar As4S4 and S2As-AsS2 units, and the region (270430 cm1) is addressed to the vibration of As-S bonds in AsS3 pyramids. It may be concluded that the structures possessing the highest values of the PL intensity include the smallest amount of As4S4 realgar structural units. We may assume that neither As-As bonds in the realgar As4S4 structure nor S2As-AsS2 bridges appear to be the reason of the luminescence in the case of plasma prepared arsenic sulfide.

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

311

Fig. 8. Distribution of the PL intensity in the sample depth.

Fig. 9. Depth distribution of the Raman spectra.

Moreover, the appearance of As4S4 fragments in the structure of the glass-net causes the quenching of the luminescence. 3.6. Mass-spectrometry study of arsenic sulfide plasma prepared materials The arsenic sulfide materials prepared by plasma were analyzed utilizing the mass-spectrometry method to reveal and to gain insight into the main structural fragments affecting the luminescence intensity. For this purpose the thin film with the weakest luminescence intensity (Fig. 10 a) and the film with the strongest luminescence (Fig. 10 b) have been investigated. Several micrograms of the investigated substances have been placed in a microtube of direct injection system and introduced via the vacuum lock directly into the ion source of the mass spectrometer. The tube was heated from 50 to 450  C with a rate of 100 K/min. The mass spectra shown in Fig. 10 have been recorded in the mass number range 32e600 at an energy of the ionizing electrons equal to 70 eV. Obviously, the units with chemical formulas: AsS, As2, AsS2, and As4S4 are the common basic elements of the glass-net of both samples. As4S5 fragment presents in the structure with the strong luminescence only. Besides, the intensity of the As4S4 line in the mass-spectrum of the As-S structure with the strongest PL is substantially greater. According to quantum-chemical estimations, these particles are result of the initial interaction of the precursors in the plasma discharge. The structural fragments have been proved using the RB3LYP/6-31 þ G(d) method and Gaussian 03

312

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

Fig. 10. Mass-spectrum of arsenic sulfide plasma prepared material with the lowest (a) and the highest (b) PL intensity. In (b) fragments calculated by quantumchemistry modeling are inserted.

software package [19]. The geometric parameters of the discovered units correspond to the minimum energies that were found by the methods chosen. Verification of our quantum-chemical calculations has been performed by comparing the results of the perarealgar structure calculations, done by these methods, with the literary data for the pararegal structure. The mass-spectroscopy data presented clarify the main structural fragments affecting the PL intensity of arsenic sulfide prepared by plasma. Based on the experimental results and theoretical modeling and taking into account the point of view formulated in the work [18] we may assume that the main reason of appearance and enhancing of the luminescence in arsenic sulfide materials, prepared by plasma, is the (As2S2)n cyclic structure unit playing the role of a “disk-like polarizability tensor”.

L. Mochalov et al. / Superlattices and Microstructures 114 (2018) 305e313

313

4. Conclusions For the first time optical emission of synthesized in plasma two-dimensional “beyond graphene” arsenic sulphide has been studied. Chalcogenide materials were synthesized via interaction of elemental arsenic and sulfur in a low-temperature non-equilibrium plasma discharge at low pressure. It was found out that the samples possess intense structural luminescence. The photoluminescence intensity strongly depends on the structural units forming the glass-net and on the chemical content. The experimental results obtained prove the main reason of appearance and enhancing of the structural luminescence in arsenic sulfide materials, prepared by plasma, is the (As2S2)n cyclic structure unit playing the role of a “disk-like polarizability tensor”. Acknowledgement The reported study was supported by the basic part of the State Task of the Ministry of Education and Science of Russia N 3.6507.2017/8.9. The X-ray microanalysis and scanning electron microscopy were carried out on the equipment of the Collective Usage Center “New Materials and Resource-saving Technologies.” (Chemistry Research Institute of Lobachevsky State University of Nizhny Novgorod). Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.spmi.2017.12.052. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films, Science 306 (5696) (2004) 666e669. [2] A. Eftekhari, Tungsten dichalcogenides (WS2, WSe2, and WTe2): materials chemistry and applications, J. Mater. Chem. 5 (2017) 18299e18325. [3] K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Atomically thin MoS2: a new direct-gap semiconductor, Phys. Rev. Lett. 105 (2010) 136805. [4] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.Y. Chim, G. Galli, F. Wang, Emerging photoluminescence in monolayer MoS2, Nano Lett. 10 (4) (2010) 1271e1275. [5] T. Ito, N. Morimoto, R. Sadanaga, The crystal structure of realgar, Acta Crystallogr. 5 (1952) 775e782. [6] D.J.E. Mullen, W. Nowacki, Refinement of the crystal structures of realgar, AsS and orpiment, As2S3, Z. Kristallogr. 136 (1972) 48e65. [7] L.A. Mochalov, M.A. Kudryashov, A.A. Logunov, S.V. Zelentsov, A.V. Nezhdanov, A.I. Mashin, D. Gogova, G. Chidichimo, G. De Filpo, Structural and optical properties of arsenic sulfide films synthesized by a novel PECVD-based approach, Superlattice. Microst. 111 (2017) 1104e1112. [8] L.A. Mochalov, D. Dorozh, M.A. Kudryashov, A.V. Nezhdanov, D. Usanov, D. Gogova, S.V. Zelentsov, A. Boryakov, A.I. Mashin, Infrared and Raman spectroscopy study of As-S chalcogenide films prepared by plasma-enhanced chemical vapor deposition, Spectrochim. Acta Mol. Biomol. Spectrosc. 193 (2018) 258e263. [9] L.A. Mochalov, A.S. Lobanov, A.V. Nezhdanov, M.A. Kudryashov, A.I. Mashin, A.N. Stepanov, A.I. Korytin, A.V. Vorotyntsev, V.M. Vorotyntsev, Comparison of optical properties and impurities content of Ge-Sb-S-I glasses prepared by different methods, Opt. Mater. Express 6 (12) (2016) 3759e3765. [10] L.A. Mochalov, A.S. Lobanov, A.V. Nezhdanov, A.I. Mashin, M.A. Kudryashov, A.V. Strikovskiy, A.V. Kostrov, A.V. Vorotyntsev, V.M. Vorotyntsev, Influence of the preparation technique on the optical properties and content of heterophase inclusions of As2S3 chalcogenide glasses, Opt. Mater. Express 6 (11) (2016) 3507e3517. [11] L.A. Mochalov, A.S. Lobanov, A.V. Nezhdanov, A.V. Kostrov, V.M. Vorotyntsev, Preparation of Ge-S-I and Ge-Sb-S-I glasses by plasma-enhanced chemical vapor deposition, J. Non-Cryst. Solids 423e424 (2015) 76e80. [12] A.V. Vorotyntsev, L.A. Mochalov, A.S. Lobanov, A.V. Nezhdanov, V.M. Vorotyntsev, A.I. Mashin, PECVD synthesis of As-S glasses, Russ. J. Appl. Chem. 89 (2) (2016) 179e184. [13] L.A. Mochalov, D. Dorosz, A.V. Nezhdanov, M.A. Kudryashov, S.V. Zelentsov, D. Usanov, A.A. Logunov, A.I. Mashin, D. Gogova, Investigation of the composition-structure-property relationship of AsxTe100x films prepared by plasma deposition, Spectrochim. Acta Part A: Molecular Biomolecular Spectroscopy 191 (2018) 211e216. [14] S.H. Messaddeq, O. Boily, S.H. Santagneli, M. El-Amraoui, Y. Messaddeq, As4S4 role on the photoinduced birefringence of silver-doped chalcogenide thin films, Opt. Mater. Express 6 (5) (2016) 1451e1464. [15] http://rruff.info/chem¼As,S/notchem¼all/display¼default/R060107. [16] M. Popescu, Disordered chalcogenide optoelectronic materials: phenomena and applications, J. Optoelectron. Adv. Mater. 7 (4) (2005) 2189e2210. [17] S. Solin, G. Papatheodorou, Phys. Rev. B 15 (1977) 2084. e, Phenomenological model of anisotropic microstructures in a-As2S3 chalcogenide glass, Phys. Rev. B 67 [18] K.E. Asatryan, B. Paquet, T.V. Galstian, R. Valle (1) (2003) 014208. [19] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian 03, Revision A.1, Gaussian, Inc., Pittsburgh PA, 2003.