N. M. Gasanly. Department of Physics, Middle East Technical University, Ankara, Turkey. (Received 21 October 2009, in final form 18 May 2010)

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1 Journal of the Korean Physical Society, Vol. 57, No. 1, July 2010, pp Coexistence of Indirect and Direct Optical Transitions, Refractive Indices, and Oscillator Parameters in TlGaS 2, TlGaSe 2, and TlInS 2 Layered Single Crystals N. M. Gasanly Department of Physics, Middle East Technical University, Ankara, Turkey (Received 21 October 2009, in final form 18 May 2010) The optical properties of TlGaS 2, TlGaSe 2, and TlInS 2 crystals have been investigated through transmission and reflection measurements in the wavelength range of nm. Optical indirect and direct band gap energies of 2.45 and 2.63 ev (TlGaS 2), 1.97 and 2.26 ev (TlGaSe 2), 2.27 and 2.47 ev (TlInS 2) were found by analyzing the absorption data at room temperature. The transmission measurements carried out in the temperature range of K revealed that the rates of change of the indirect band gaps with temperature were γ = , , and ev/k for the TlGaS 2, TlGaSe 2, and TlInS 2 crystals, respectively. The dispersion of the refractive index is discussed in terms of the single oscillator model. The refractive indices, the oscillator and dispersion energies, and the zero-frequency dielectric constants were determined. PACS numbers: Ci, q, Fy Keywords: Absorption edge, Refractive index, Energy band gap, Semiconductors DOI: /jkps I. INTRODUCTION The ternary compounds TlGaS 2, TlGaSe 2, and TlInS 2 belong to the class of layered semiconducting chalcogenides TlBX 2 (where B = Ga or In; X = S or Se). Stacking of the atoms in the crystals is in the form of two twisted anionic layers with weakly bonded Tl 1+ cations located in the trigonal cavities between them. Therefore, the crystals consist of separate layers with strong bonding between atoms within the layer and weak bonding between the layers. Recently, such semiconductor crystals received a great deal of attention due to their optical and electrical properties in view of possible optoelectronic device applications [1 7]. In the past, a large number of studies on the fundamental optical absorption in TlGaS 2, TlGaSe 2, and TlInS 2 crystals were done [8-19]. The experimental data obtained on the indirect and the direct optical transitions remain highly inconsistent and controversial due to differences in the samples qualities and thicknesses, and in the measurement arrangements. Namely, the fundamental absorption edge was reported to be formed by the indirect and the direct transitions with room-temperature energies varying over large ranges: E gi = ev and E gd = ev (TlGaS 2 ), E gi = ev and E gd = ev (TlGaSe 2 ), and E gi = ev and E gd = ev (TlInS 2 ). It should be noted that most transmission measurements were carried nizami@metu.edu.tr; Fax: out on samples with thicknesses in the range of µm. In this paper we present the results of transmission and reflection measurements performed on TlGaS 2, TlGaSe 2, and TlInS 2 layered crystals. As a result, the presence of both optical indirect and direct transitions was revealed in the crystals studied. The rates of change of the indirect band gap with temperature were evaluated from the temperature dependence of the transmission spectra in the K range. Moreover, the refractive index, the oscillator and dispersion energies, and the zerofrequency dielectric constants were identified by means of the room-temperature reflectance and transmittance data. The determination of these optical constants is expected to expand the available physical information. II. EXPERIMENTAL DETAILS Single crystals of TlGaS 2, TlGaSe 2, and TlInS 2 were grown by using the Bridgman method from a stoichiometric melt of starting materials sealed in evacuated (10 5 Torr), carbon-coated silica tubes (10 mm in diameter and about 25 cm in length) with a tip at the bottom in our crystal growth laboratory. The resulting ingots of TlGaS 2, TlGaSe 2, and TlInS 2 single crystals (yellow-green, red, and orange in color, respectively) had no cracks and voids on the surface. The chemical compositions of the TlGaS 2, TlGaSe 2, and TlInS 2 crystals were determined by using energy dispersive spectroscopic analyses with a JSM-6400 electron microscope

2 Coexistence of Indirect and Direct Optical Transitions, Refractive Indices, and Oscillator N. M. Gasanly The atomic compositions ratio of the studied samples were estimated as (25.4:25.6:49.0), (25.4:25.2:49.4), and (25.6:25.2:49.2) for TlGaS 2, TlGaSe 2, and TlInS 2, respectively. Analysis of the X-ray diffraction patterns showed that these crystals had a monoclinic structure with the lattice parameters a = , b= , c = nm, and β = (TlGaS 2 ), a = , b = , c = nm, and β = (TlGaSe 2 ), a = , b = , c = nm, and β = (TlInS 2 ). The samples for the optical measurements were taken from the middle parts of the ingots. The freshly-cleaved platelets (along the layer plane (001) were mirror-like. That is why no further polishing and cleaning treatments were required. The transmission and the reflection measurements were carried out in the nm wavelength region with a Shimadzu UV-1201 model spectrophotometer, which consisted of a 20-W halogen lamp, a holographic grating, and a silicon photodiode. The transmission measurements were done under the normal incidence of light with the polarization direction along the (001) plane, which is perpendicular to the c-axis of the crystal [20 22]. For the room temperature reflection experiments, the specular reflectance measurement attachment with 5 incident angle was used. The measured reflectivities were compared with those for a protected silver mirror Thorlabs PF P01. The resolution of the spectrophotometer was 5 nm. An Advanced Research Systems, Model CSW-202 closed-cycle helium cryostat was utilized to cool the sample from room temperature to 10 K. To measure the transmission, we attached the sample on a cold finger of the cryostat. Fig. 1. Spectral dependencies of the transmittance and the reflectivity for the TlGaS 2, TlGaSe 2, and TlInS 2 crystals at T = 300 K. III. RESULTS AND DISCUSSION Figure 1 presents the transmittance (T ) and the reflectivity (R) spectra of the TlGaS 2, TlGaSe 2, and TlInS 2 crystals registered in the wavelength (λ) range from 400 to 1100 nm. The absorption coefficient α and the refractive index n were calculated using the following relations [20]: [ α = 1 d ln (1 R) 2 ( ) (1 R) 4 1/2 ] + 2T 4T 2 + R 2, (1) n = 1 + R 1 R + [ 4R (1 R) 2 ( ) ] 2 1/2 αλ, (2) 4π where d is the sample thickness. The reflection measurements were carried out using specimens with natural cleavage planes and the thicknesses such that αd 1. The sample thickness was then reduced (by repeated cleaving using the transparent adhesive tape) until it was convenient for measuring the transmission spectra. The thickness of the sample was Fig. 2. Dependencies of (αhν) 1/2 and (αhν) 2 on the photon energy for the TlGaS 2, TlGaSe 2, and TlInS 2 crystals at T = 300 K. determined through the transmission interference fringes at wavelengths slightly longer than the intrinsic absorption edge, where the sample has relatively high transmission values (Fig. 1). We evaluated the thickness of the sample by measuring the wavelengths at which two adjacent transmission maxima occur [21], d = λ 1 λ 2 2n(λ 2 λ 1 ). The long-wavelength values of the refractive index, n = 2.55 (TlGaS 2 ), n = 2.82 (TlGaSe 2 ), and n = 2.58 (TlInS 2 ), found from the reflection measurements were used to determine the thickness of the sample, which turned out to be about 10 µm for room-temperature transmission measurements in most cases. An analysis of the experimental data revealed that the absorption coefficient α was proportional to (hν - E g ) p with p = 2 or 1/2 in two different energy regions. The dependencies of (αhν) 1/2 and (αhν) 2 on the photon energy

3 -166- Journal of the Korean Physical Society, Vol. 57, No. 1, July 2010 hν are presented in Fig. 2. The experimental data (triangles, stars, and circles) were fitted to a linear equation (the solid lines) to find the energy band gaps. Linear dependencies were observed for the relations (αhν) 1/2 and (αhν) 2 versus hν. This implies the realization of the indirect and the direct allowed transitions over the ranges and ev (TlGaS 2 ), and ev (TlGaSe 2 ), and ev and ev (TlInS 2 ). Using extrapolations of the straight lines down to (αhν) 1/2 = 0 and (αhν) 2 = 0, we determined the values of the indirect and the direct band gap energies to be E gi = 2.45 ± 0.02 ev and E gd = 2.63 ± 0.02 ev (TlGaS 2 ), E gi = 1.97 ± 0.02 ev and E gd = 2.26 ± 0.02 ev (TlGaSe 2 ), and E gi = 2.27 ± 0.02 ev and E gd = 2.47 ± 0.02 ev (TlInS 2 ). Figures 3(a) - 3(c) show the transmission spectra of the TlGaS 2, TlGaSe 2, and TlInS 2 crystals in the temperature range of K. Thick samples with d 300 µm were used at low temperatures because the thin layered samples broke into pieces at low temperatures due to their high fragility. Therefore, we were only able to analyze the temperature dependence of the indirect band gap energy (E gi ). Technical reasons did not allow us a direct measurement of the reflectivity spectra at low temperatures. Therefore, for the calculation of the absorption coefficient α at low temperatures, the spectral dependence of the room-temperature reflectivity was uniformly shifted in energy according to the blue shift of the absorption edge. The obtained values of the indirect energy gaps decreased in the ranges ev (TlGaS 2 ), ev (TlGaSe 2 ), and ev (TlInS 2 ) as the temperature was varied from 10 to 300 K, as displayed in the insets of Figs. 3(a) - 3(c). The temperature dependence of the energy band gap can be represented by the relation [20] E gi (T ) = E gi (0) + γt 2 T + β, (3) where E gi (0) is the absolute-zero value of the band gap, γ = de gi /dt is the rate of change of the band gap with temperature, and β is approximately the Debye temperature. The experimental data for the dependencies of on the temperature ( K) were fitted using Eq. (3) as shown in the insets of Figs. 3(a) - 3(c) (the solid lines correspond to the theoretical fits). The fitting parameters were found to be E gi (0) = 2.54, 2.06, and 2.44 ev, γ = , , and ev/k, and β = 203, 164, and 160 K for the TlGaS 2, TlGaSe 2, and TlInS 2 crystals, respectively. The Debye temperatures, which were evaluated by using Lindemann s melting rule [23] with the X-ray results and by using the melting temperatures T m = 1155, 1090, and 1050 K, were found to be β = 195, 155, and 153 K, respectively. Figures 4(a) - 4(c) display the dependencies of the refractive indices n on the wavelength, which were determined employing Eqs. (1) and (2). The refractive in- Fig. 3. Spectral dependencies of the transmission in the temperature range of K: (a) TlGaS 2, (b) TlGaSe 2, and (c) TlInS 2. Insets: The indirect band gap energies as a function of temperature. The solid curves represent the fits using Eq. (3). dices in the energy region of hν < E g is observed to gradually decrease from 2.96 to 2.55 (TlGaS 2 ), 2.92 to 2.82 (TlGaSe 2 ), and 2.85 to 2.58 (TlInS 2 ) with increasing wavelength up to 1100 nm. The dispersive refractive index data in the hν < E g range were analyzed according to the single-effective-oscillator model proposed by Wemple and DiDomenico [24,25]. The refractive index

4 Coexistence of Indirect and Direct Optical Transitions, Refractive Indices, and Oscillator N. M. Gasanly Fig. 4. Dependencies of the refractive indices on the wavelength: (a) TlGaS 2, (b) TlGaSe 2, and (c) TlInS 2. Insets: Plots of versus (hν) 2. The solid lines represent the fits using Eq. (4). is related to the photon energy through the relationship n 2 (hν) = 1 + E 2 S0 E S0E d (hν)2, (4) where E so is the single oscillator energy and E d is the dispersion energy. Plotting (n 2-1) 1 versus (hν) 2 allows the determination of the oscillator parameters by fitting a linear function to the data in the lower-energy range. The fittings of the above function are presented in the insets of Figs. 4(a) - 4(c). The zero-frequency refractive index n 0 is estimated from Eq. (4), i.e., from the expression n 2 0 = 1 + E d E S0. The values of the parameters E S0 and E d were calculated from the slope and the intersection with the y-axis of the straight line (the insets of Figs. 4(a) - 4(c)) as 4.51 and ev (TlGaS 2 ), 4.96 and ev (TlGaSe 2 ), and 6.02 and ev (TlInS 2 ). Furthermore, the values of the zero-frequency dielectric constants, ε = n 2 0 = 6.35, 7.84, and 6.55, and the refractive indices, n 0 = 2.51, 2.80, and 2.56,were evaluated by means of Eq. (4) for the TlGaS 2, TlGaSe 2, and TlInS 2 crystals, respectively. The oscillator energy E so is an average energy gap and, to a fair approximation, it is associated empirically with the lowest direct band gap, E gd, by the relation E so 2.0 E gd [26,27]. The E so /E gd ratios determined in this study were 1.72 (TlGaS 2 ), 2.19 (TlGaSe 2 ), and 2.28 (TlInS 2 ). At this point, it is worthwhile to compare the dispersive refractive indices presented above with those previously reported for TlGaS 2, TlGaSe 2, and TlInS 2 crystals [28 31]. In this study, the determined values of the refractive indices, corresponding to λ = 700 nm (which was the only common wavelength chosen for the comparison with the results of other studies), were 2.65 (TlGaS 2 ), 2.91 (TlGaSe 2 ), and 2.70 (TlInS 2 ). The values of the refractive indices in the literature for the same wavelength were 2.54 [3] and 2.63 [28] (TlGaS 2 ), 2.82 [3], 2.88 [29], and 2.38 [30] (TlGaSe 2 ), and 2.54 [3] and 2.68 [31] (TlInS 2 ). As a whole, the obtained picture is consistent with the well-known fact that refractive index and the energy gap are inversely related to each other [20]. Particularly, for the TlGaSe 2 crystal, which has the smallest direct band gap energy (E gd = 2.26 ev) among the studied materials, the refractive index has the largest value (2.91). It is possible to observe from Fig. 4(a) that the refractive index of TlGaS 2 crystals increases steeply as the photon energy approaches the energy band gap. A similar, but less pronounceable, behavior of nwith the photon energy is demonstrated by the TlInS 2 crystals (Fig. 4(c)). At the same time, the refractive index of the TlGaSe 2 crystals does not show a strong dispersion, at least to the extent of the obtained data (Fig. 4(b)). IV. CONCLUSIONS The transmission and the reflection spectra of TlGaS 2, TlGaSe 2, and TlInS 2 crystals were measured over the spectral region of nm to derive the absorption coefficient and the refractive index. The analysis of the room temperature absorption data revealed the coexistence of indirect and direct transitions with energy band gaps of E gi = 2.45 and E gd = 2.63 ev (TlGaS 2 ), E gi = 1.97 and E gd = 2.26 ev (TlGaSe 2 ), E gi = 2.27

5 -168- Journal of the Korean Physical Society, Vol. 57, No. 1, July 2010 and E gd = 2.47 ev (TlInS 2 ). The absorption edge was observed to shift toward lower energy values as the temperature was increased from 10 to 300 K. The data were used to calculate the indirect energy band gap of the crystal as a function of the temperature. The rates of change of the indirect band gaps with temperature were γ = ev/k (TlGaS 2 ), ev/k (TlGaSe 2 ), and ev/k (TlInS 2 ). The absolute zero values of the band gap energies were found to be E gi (0) = 2.54, 2.06, and 2.44 ev for the TlGaS 2, TlGaSe 2, and TlInS 2 crystals, respectively. The refractive index dispersion data were analyzed using the single oscillator model. As a result, the oscillator and the dispersion energies, and the zero-frequency refractive index were determined. ACKNOWLEDGMENTS The author is grateful to K. Goksen and I. Guler for their assistance. REFERENCES [1] K. A. Yee and A. Albright, J. Am. Chem. Soc. 113, 6474 (1991). [2] K. R. Allakhverdiev, Solid State Commun. 111, 253 (1999). [3] Y. Shim, W. Okada, K. Wakita and N. Mamedov, J. Appl. Phys. 102, (2007). [4] A. Kato, M. Nishigaki, N. Mamedov, M. Yamazaki, S. Abdullaeva, E. Kerimova, H. Uchiki and S. Iida, J. Phys. Chem. Solids 64, 1713 (2003). [5] T. D. Ibrahimov and I. I. Aslanov, Solid State Commun. 123, 339 (2002). [6] I. M. Ashraf, M. M. Abdel-Rahman and A. M. Badr, J. Phys. D: Appl. Phys. 36, 109 (2003). [7] Y. Rud, V. Rud, M. Morohashi-Yamazaki, H. Uchiki and N. Mamedov, Inst. Phys. Conf. Ser. 152, 967 (1998). [8] C. S. Yoon, S. J. Chung, S. J. Nam and W. T. Kim, Cryst. Res. Technol. 31, 229 (1996). [9] M. Hanias, A. Anagnostopoulos, K. Kambas and J. Spyridelis, Physica B 160, 154 (1989); Mat. Res. Bull. 27, 25 (1992). [10] N. Kalkan, M. P. Hanias and A. Anagnostopoulos, Mater. Res. Bull. 27, 1329 (1992). [11] S. Duman and B. Gurbulak, Phys. Scr. 72, 82 (2005); ibid 77, (2008). [12] V. Grivickas, V. Bikbajevas and P. Grivickas, Phys. Status Solidi B 243, R31 (2006). [13] I. M. Ashraf, J. Phys. Chem. 108, (2004). [14] O. Karabulut, M. Parlak and G. M. Mamedov, J. Alloys Compd. 429, 50 (2007). [15] S. Kashida, Y. Yanadori, Y. Otaki, Y. Seki and A.M. Panich, Phys. Status Solidi A 203, 2666 (2006). [16] S. R. Samedov, O. Baykan and A. Gulubayov, Int. J. Infrared Millimeter Waves 25, 735 (2004). [17] A. M. Akhmedov, A. E. Bakhyshov, A. A. Lebedev and M. A. Yakobson, Sov. Phys. Semicond. 12, 299 (1978). [18] H. Uchiki, D. Kanazawa, N. Mamedov and S. Iıda, J. Lumin , 664 (2000). [19] G. A. Gamal, Semicond. Sci. Technol. 13, 185 (1998). [20] J. I. Pankove, Optical Processes in Semiconductors (Prentice-Hall, New Jersey, 1971). [21] T. S. Moss, G. J. Burrell and B. Ellis, Semiconductor Opto-electronics (Butterworth, London, 1973). [22] C. H. Ho and S. L. Lin, J. Appl. Phys. 100, (2006). [23] J. R. Drabble and H. J. Goldsmid, Thermal Conduction in Semiconductors (Pergamon, Oxford, 1961), p [24] S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 (1971). [25] S. H. Wemple and M. DiDomenico, Phys. Rev. Lett. 23, 1156 (1969). [26] K. Tanaka, Thin Solid Films 66, 271 (1980). [27] F. Yakuphanoglu, A. Cukurovali and I. Yilmaz, Physica B 351, 53 (2004); Physica B 353, 210 (2004). [28] A. F. Qasrawi and N. M. Gasanly, Phys. Status Solidi A 202, 2501 (2005). [29] J. A. Kalomiros, N. Kalkan, M. Hanias, A. N. Anagnostopoulos and K. Kambas, Solid State Commun. 96, 601 (1995). [30] M. M. El-Nahass, M. M. Salam, S. A. Rahman and E. M. Ibrahim, Solid State Sci. 8, 488 (2006). [31] J. A. Kalomiros and A. N. Anagnostopoulos, Phys. Rev. B 50, 7488 (1994).