- Email: [email protected]
Absorption edge and optical constants of Tl2Ga2S3Se crystals from reflection and transmission, and ellipsometric measurements
Physica B 407 (2012) 2229–2233
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Absorption edge and optical constants of Tl2Ga2S3Se crystals from reflection and transmission, and ellipsometric measurements M. Isik a,n, N.M. Gasanly b a b
Department of Electrical and Electronics Engineering, Atilim University, 06836 Ankara, Turkey Department of Physics, Middle East Technical University, 06800 Ankara, Turkey
a r t i c l e i n f o
abstract
Article history: Received 11 February 2012 Received in revised form 29 February 2012 Accepted 1 March 2012 Available online 6 March 2012
The optical properties of Tl2Ga2S3Se layered crystalline semiconductors were investigated from transmission, reflection and ellipsometric measurements. The experimental results of the room temperature transmission and reflection measurements performed in the wavelength range of 400–1100 nm showed the presence of both indirect and direct transitions in the band structure of the crystals with 2.38 and 2.62 eV band gap energies. Spectroscopic ellipsometry measurements on Tl2Ga2S3Se crystals were carried out on the layer-plane (0 0 1) surfaces with light polarization E?cn in the 1.20–4.70 eV spectral range at room temperature. The real and imaginary parts of the dielectric function as well as refractive and absorption indices were found as a result of analysis of ellipsometric data. The Wemple–DiDomenico single-effective-oscillator model was used to study the dispersion of the refractive index in the below band gap energy range. The structures of critical points have been characterized from the second derivative spectra of the dielectric function. The analysis revealed four interband transition structures with 3.14, 3.40, 3.86 and 4.50 eV critical point energies. & 2012 Elsevier B.V. All rights reserved.
Keywords: Semiconductors Energy band gap Ellipsometry Refractive index
1. Introduction Thallium dichalcogenides formulated as TlBX2 (where B¼In or Ga, X¼S, Se or Te) have become essential in the optoelectronic applications owing to their interesting structural, optical and electrical properties [1,2]. The quaternary compound Tl2Ga2S3Se which belongs to the group of semiconductors with layered structure is a structural analog of TlGaS2 [2] in which one quarter of sulfur atoms are replaced by selenium atoms. The optical and electrical properties of TlGaS2, TlGaSe2 and TlGaSeS crystals were studied in Refs. [3–10]. These crystals are useful for optoelectronic applications as they have high photosensitivity in the visible range of the spectra and a wide transparency range of 0.5–14.0 mm [9]. In our previous work, Tl2Ga2S3Se single crystals have been studied in the temperature range of 10–320 K using thermally stimulated current (TSC) technique [11]. The data were analyzed by curve fitting, initial rise and peak shape methods. Experimental evidence was obtained for trapping centers in Tl2Ga2S3Se crystals with activation energies of 11 and 498 meV. Analysis of experimental TSC glow curves registered at different light illumination temperatures revealed the exponential distribution of the shallow traps in Tl2Ga2S3Se crystals.
n
Corresponding author. Tel.: þ90 312 5868715; fax: þ90 312 5868091. E-mail address: [email protected] (M. Isik).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2012.03.004
The transmission, reflection and ellipsometry are non-destructive optical characterization techniques. The analysis of the experimental results obtained from these measurements gives comprehensive information about the electronic band structure of the samples and optical parameters such as refractive index, dielectric constant and absorption coefficients. In this paper, the optical properties of Tl2Ga2S3Se crystal in the photon energy region from 1.20 to 4.70 eV are presented. The studies on the room temperature transmittance and reflectance data in the range of 1.20–3.10 eV were carried out to identify the absorption edge. We report also the results of the spectroscopic ellipsometry measurements of optical constants of Tl2Ga2S3Se crystals. The critical points in the studied crystals were established from the analysis of the dielectric function obtained from ellipsometric measurements.
2. Experimental details Tl2Ga2S3Se semiconductor polycrystals were synthesized using high-purity elements taken in stoichiometric proportions. Tl2Ga2S3Se single crystals were grown by the Bridgman method in evacuated (10 5 Torr) silica tubes with a tip at the bottom. The ampoule was moved in a vertical furnace through a thermal gradient of 30 1C cm 1, between the temperatures 880 and 530 1C at a rate of 1.0 mm h 1. The resulting ingots (yellow-green in color) showed good optical
2230
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
Fig. 2. Spectral dependence of transmittance and reflectivity for Tl2Ga2S3Se crystal. Inset: the dependence of d{ln(ahn)}/d(hn) on photon energy for Tl2Ga2S3Se crystal.
Fig. 1. Energy dispersive spectroscopic analysis of Tl2Ga2S3Se crystal.
quality and the freshly cleaved surfaces were mirror-like. The chemical composition of Tl2Ga2S3Se crystals, shown in Fig. 1, was determined by energy dispersive spectroscopic analysis using a JSM-6400 electron microscope. The atomic composition of the studied samples (Tl:Ga:S:Se) was found to be 26.0:25.8:35.9:12.3, respectively. Room temperature transmission and reflection measurements were carried out in the 400–1100 nm wavelength region using a ‘‘Shimadzu’’ UV-1201 model spectrophotometer. The transmission measurements were carried out under normal incidence of light with polarization direction along the (0 0 1) plane, which is perpendicular to the c-axis of the crystal. We utilized the specular reflectance measurement attachment with 51 incident angle for reflection measurements. The ellipsometric spectroscopy of the Tl2Ga2S3Se crystals was obtained using UVISEL Jobin Yvon variable angle spectroscopic rotating analyzer ellipsometry at room temperature in the 1.20– 4.70 eV spectral range with 0.01 eV increments. The ellipsometer has a high resolution of 0.01 eV. The angle of the incidence of the light beam was 701. The measurements were performed on the layer-plane (0 0 1) crystal surfaces with light polarization E?cn, where cn is the normal to the layer plane. Since the crystal has layered structure, it is very difficult to perform measurements on any other than the sample natural layer plane surfaces.
3. Results and discussion 3.1. Absorption edge analysis The transmittance (T) and reflectivity (R) spectra for Tl2Ga2S3Se single crystals were obtained in the wavelength (l) range of 400–1100 nm (Fig. 2). The reflection measurement was performed using specimens with natural cleavage planes and thickness satisfying the condition adb1. However, the thickness of the sample was reduced using adhesive tape for the transmission measurements. The thickness of the sample which gives good transmittance spectra was about 10 mm. The transmittance and reflectivity are related by absorption coefficient (a) and the sample thickness (d) as [12] T¼
ð1RÞ2 expðadÞ ð1R2 Þexpð2adÞ
:
ð1Þ
The absorption coefficient was calculated using Eq. (1) as a function of wavelength. The dependence of absorption coefficient
on photon energy (hn) is analyzed in the high absorption region to get detailed information about the energy band gaps (Eg). The energy band gap values were determined from the relation ðahnÞ ¼ AðhnEg Þp ,
ð2Þ
where A is a constant, which depends on the transition probability and p is an index, which is theoretically equal to either 2 for indirect transitions or 1/2 for direct transitions. Eq. (2) can be also written as [13] d½lnðahvÞ p ¼ : dðhvÞ hvEg
ð3Þ
As a first step of analysis, the value of index p was found to determine the type of optical transition. In order to obtain p value, d{ln(ahn)}/d(hn) vs. hn was plotted (inset of Fig. 2). The figure demonstrates two peaks and the positions of peak’s maximums give optical band gaps of approximately 2.44 and 2.65 eV. The curves of ln(ahn) vs. ln(hn Eg) were plotted with the help of obtained Eg values to determine p values which were found to be about 2 and 1/2 from the slopes of plotted curves. Although the corresponding energies of the peak’s maximums give a foresight about the values of energy band gaps, we determined the more precise values using the graphs of (ahv)1/2 and (ahv)2 as a function of photon energy. These plots give straight lines shown in Fig. 3. The linear dependencies of (ahv)1/2 and (ahv)2 on photon energy suggest that the fundamental absorption edges in Tl2Ga2S3Se crystal are formed by the indirect allowed transitions in the range of 2.42–2.57 eV and direct transitions in the interval of 2.65–2.80 eV. The values of indirect and direct band gap energies were obtained by extrapolating fitted straight lines down to (ahv)1/2 ¼0 and (ahv)2 ¼0 as Egi ¼2.3870.02 eV and Egd ¼2.6270.02 eV, respectively. 3.2. Refractive index analysis It is known, that the structures of TlGaSe2 and TlGaS2 crystals belong to monoclinic symmetry, the space group is C2/c, a¼ 1.0772, b¼1.0771 and c¼1.5636 nm and b ¼100.61 (TlGaSe2); a¼ 1.0299, b¼1.0284 and c¼1.5175 nm and b ¼99.6031 (TlGaS2) [1]. We believe that Tl2Ga2S3Se also crystallizes in monoclinic structure similar to the structure of the constituent TlGaSe2 and TlGaS2 compounds. TlGaSe2 and TlGaS2 crystals having a monoclinic layered structure are optically biaxial. However, biaxiality of these materials at room temperature is very small according to the light figure spectroscopy studies [14]. Therefore, TlGaSe2 and TlGaS2 (as well Tl2Ga2S3Se) at this
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
Fig. 3. The dependencies of (ahv)1/2 and (ahv)2 on photon energy for Tl2Ga2S3Se crystal. Circles represent the experimental data that were fitted to a linear equation (the solid lines) to find the band gaps.
2231
Fig. 4. Spectra of the real and imaginary parts of the dielectric function of Tl2Ga2S3Se crystal.
temperature can be regarded as uniaxial materials with optic axis (cn) normal to the layer plane [15,16]. The refractive (n) and absorption (k) indices of Tl2Ga2S3Se layered crystals were obtained from the ellipsometry measurements in the 1.20–4.70 eV range on the layer-plane (0 0 1) surfaces [i.e., ordinary optical constants (E?cn)]. For these measurements samples with dimensions of about 6 4 1 mm3 were used. The freshly cleaved platelets (along the layer plane (0 0 1)) were mirror-like. That is why no further polishing and cleaning treatments were required. In the spectroscopic ellipsometry measurements, a linearly polarized light beam was irradiated onto a sample and reflected light from the sample was analyzed. The amplitude ratio (C) and phase shift (D) of the parallel (p) and perpendicular (s) components of the reflected light were used to get the complex reflectance ratio of the polarized light given by
r¼
rp ¼ tanðcÞeiD , rs
ð4Þ
where rp and rs are the Fresnel reflection coefficients of the polarized light. The dielectric constant of the material is given for the simple ambient-substrate optical model as [17–19] "
e ¼ e1 þ ie2 ¼ sin2 ðjÞ 1 þ
# 1r 2 tan2 ðjÞ , 1þr
ð5Þ
where j is the angle of incidence. The real and imaginary parts of the dielectric constant as a function of energy of Tl2Ga2S3Se found from this optical model are shown in Fig. 4. The oscillations at low energy region of the spectra are due to the interference from the back-reflected component, since for these thicknesses the crystals are not fully opaque. The refractive and absorption indices are calculated using the real and imaginary parts of the dielectric constant from
Fig. 5. Spectra of the refractive and absorption indices of Tl2Ga2S3Se crystal.
the relations
e1 ¼ n2 k2
ð6Þ
e2 ¼ 2nk:
ð7Þ
Fig. 5 represents the refractive and absorption indices spectra for Tl2Ga2S3Se obtained by means of Eqs. (6) and (7).
2232
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
Fig. 6. Plot of (n2 1) 1 versus (hv)2. The solid line represents the fit using Eq. (8).
The refractive index in the energy region of hvoEg gradually increases from 2.65 to 2.85 with increasing photon energy in the interval of 1.20–2.35 eV. The analysis of the dispersive refractive index data in the energy region of hvoEg was performed by means of single-effective-oscillator model proposed by Wemple and DiDomenico [20,21]. The photon energy dependence of the refractive index in the suggested model was related to single oscillator energy (Eso) and the dispersion energy (Ed) by the relation n2 ðhnÞ ¼ 1 þ
Eso Ed E2so ðhnÞ2
:
ð8Þ
The oscillator parameters were determined from the plot of (n2 1) 1 versus (hv)2. Fig. 6 shows the linear fitting of the above reported function in the lower energy data range (1.20–2.35 eV). The zero-frequency (hv¼0) refractive index n0 can be deduced from Eq. (8). The values of the optical parameters Eso and Ed were calculated using the slope and the intersection with y-axis of the fitted straight line (Fig. 6) as 5.30 eV and 30.02 eV, respectively. Furthermore, the values of zero-frequency dielectric constant e0 ¼n20 ¼6.67 and refractive index n0 ¼2.58 were evaluated using Eq. (8). The oscillator energy Eso is an ‘‘average’’ energy gap and approximately equal to two times of the lowest direct band gap Egd (Eso E2.0 Egd) [22–24]. In this study, the ratio Eso/Egd for Tl2Ga2S3Se crystal was found to be 2.03.
to 1, 1/2, 0 and þ 1/2 for excitonic, one, two and three dimensional lineshapes, respectively. The second derivative spectra of real (d2e1/dE2) and imaginary 2 (d e2/dE2) parts of the dielectric constant are fitted using Eq. (9) for the consideration of excitonic optical transitions (m¼ 1) as they demonstrate the lowest mean-square deviations (Fig. 7). The smoothing process has been applied for the each step of the analysis without distorting the main experimental curves. The critical point analysis were performed above the band gap energy Eg ¼2.38 eV. Moreover, because the smoothing process strongly deflects the main experimental data in the 1.20–2.80 eV range, we have fitted only the spectra of the dielectric constant for the region above 2.80 eV. In the energy range from 2.80 to 4.70 eV, four critical point lineshapes of 3.14, 3.40, 3.86 and 4.50 eV appeared as a result of least-square fitting program, which are represented by arrows in Fig. 7. At this point, it is worthwhile to make some interpretations on the critical point energies of 3.14 and 3.40 eV. Unfortunately, the band structure of Tl2Ga2S3Se crystal has not been calculated yet. Therefore, we were forced to use the results of the band structure calculation of the relative compound TlGaSe2 which is the constituent of the studied crystal [26]. The authors found that the valence band maximum is located at the G point of the Brillouin zone, while the conduction band minimum occurs along the G–Y direction. The indirect band gap Egi ¼2.0 eV is energetically separated by about 0.1 eV from a direct band gap at G (Egd ¼ 2.1 eV). As shown in Section 3.1, for Tl2Ga2S3Se crystal the energy separation between direct and indirect band gap energies Egd Egi ¼2.62 eV 2.38 eV ¼0.24 eV. For TlGaSe2 crystal, the spin–orbit splitting of the uppermost valence band at point G of the Brillouin zone is about D ¼0.50 eV and the energy separation between the deeper and upper valence bands approximately equals 0.33 eV [26]. Then, assuming for Tl2Ga2S3Se the same value of the spin–orbit separation (D ¼0.50 eV) we may assign the CP structure at 3.14 eV to the transition from spin–orbit separated valence band to the bottom of the conduction band at the Brillouin zone center, which is equal to 3.12 eV. As for CP structure at 3.40 eV we may assign it to the transition from second valence band to the bottom of the conduction band at the Brillouin zone center, which is equal to 3.45 eV. The CP structures in the higher energy region (3.86 and 4.50 eV) were attributed tentatively to the excitations of electrons to either
3.3. Critical point analysis The dielectric property of a material is very close to its band structure. For this purpose, the energy dependence of the dielectric constant obtained from the ellipsometry measurements of Tl2Ga2S3Se crystals was analyzed to get detailed knowledge about its band structure. The critical points in the energy band structure of the crystals were found using the second derivative spectra of the dielectric constant. The second derivative spectra is related to the photon energy (E), amplitude (A), critical point energy (Ecp), phase angle (f) and broadening parameter (G) by the expression [17–19,25] 2
d e dE2
¼ mðm1ÞA expðijÞðEEg þ iGÞm2
ðm a0Þ
ð9Þ
2
d e dE2
¼ A expðijÞðEEg þ iGÞ2
ðm ¼ 0Þ:
ð10Þ
The dimensions of the wave vectors playing a role in the optical transitions determine the value of the parameter m which is equal
Fig. 7. Second-energy derivative of the dielectric function of Tl2Ga2S3Se crystal. Circles and squares represent the second-energy derivative spectra of the real and imaginary parts of the dielectric function, respectively. The solid and dot-dashed curves show the fits to the experimental data.
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
the second or the third group of conduction bands present in the band structure of the studied crystals.
4. Conclusions The optical characterization of the Tl2Ga2S3Se crystals was performed by means of transmission, reflection and ellipsometry measurements. The analysis of absorption data obtained from transmittance and reflectivity spectra revealed the presence of both optical indirect and direct transitions with band gap energies of 2.38 and 2.62 eV, respectively. The real and imaginary parts of the dielectric function, refractive and absorption indices of Tl2Ga2S3Se crystals were obtained using the spectroscopic ellipsometry measurements for light polarization E?cn in the 1.20–4.70 eV spectral region. The refractive index dispersion data in the energy region of hvoEg were analyzed using the Wemple–DiDomenico single-effective-oscillator model. The refractive index dispersion parameters: oscillator and dispersion energies, and zero-frequency refractive index were found to be 5.30 eV, 30.02 eV and 2.58, respectively. The critical point analysis of the second derivative spectra of the dielectric constant in the above band gap region revealed the presence of four critical points with energies of 3.14, 3.40, 3.86 and 4.50 eV.
Acknowledgment The authors are grateful to Dr. S.S. Cetin for her assistance.
2233
References [1] A.M. Panich, J. Phys.: Condens. Matter 20 (2008) 293202. [2] K.A. Yee, A. Albright, J. Am. Chem. Soc. 113 (1991) 6474. [3] M. Hanias, A. Anagnostopoulos, K. Kambas, J. Spyridelis, Mater. Res. Bull. 27 (1992) 25. [4] I.M. Ashraf, M.M. Abdel-Rahman, A.M. Badr, J. Phys. D: Appl. Phys. 36 (2003) 109. [5] A. Kato, M. Nishigaki, N. Mamedov, M. Yamazaki, S. Abdullaeva, E. Kerimova, H. Uchiki, S. Iida, J. Phys. Chem. Solids 64 (2003) 1713. [6] M.M. El Nahass, M.M. Sallam, S.A. Rahman, E.M. Ibrahim, Solid State Sci. 8 (2008) 488. [7] V. Grivickas, V. Bikbajevas, P. Grivickas, Phys. Status Solidi (b) 243 (2006) R31. [8] B. Gurbulak, S. Duman, Phys. Scr. 77 (2008) 025702. [9] K.R. Allakhverdiev, Solid State Commun. 111 (1999) 253. [10] I. Guler, N.M. Gasanly, J. Korean Phys. Soc. 51 (2007) 2031. [11] T. Yıldırım, N.M. Gasanly, Solid State Sci. 11 (2009) 1562. [12] J.I. Pankove, Optical Processes in Semiconductors, Prentice-Hall, New Jersey, 1971. [13] F. Yakuphanoglu, J. Phys. Chem. Solids 69 (2008) 949. [14] N. Mamedov, Y. Shim, N. Yamamoto, Jpn. J. Appl. Phys. 41 (2002) 7254. [15] Y. Shim, W. Okado, K. Wakita, N. Mamedov, J. Appl. Phys. 102 (2007) 083537. [16] N. Mamedov, Y. Shim, H. Toyota, K. Wakita, N. Yamamoto, S. Iida, Phys. Status Solidi (b) 203 (2006) 2873. [17] M. Cardona, Modulation Spectroscopy, Academic, New York, 1969. [18] D.E. Aspnes, Handbook on Semiconductors, vol. 2, North-Holland, Amsterdam, 1980. [19] J.W. Garland, C. Kim, H. Abad, P.M. Raccah, Phys. Rev. B 41 (1990) 7602. [20] S.H. Wemple, M. DiDomenico, Phys. Rev. B 3 (1971) 1338. [21] S.H. Wemple, M. DiDomenico, Phys. Rev. Lett. 23 (1969) 1156. [22] K. Tanaka, Thin Solid Films 66 (1980) 271. [23] F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 351 (2004) 53; F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 353 (2004) 210. [24] E. Marguez, A.M. Bernal-Oliva, J.M. Gonzalez-Leal, R. Pricto-Alcon, A. Ledesma, R. Jimenez-Garay, I. Martil, Mater. Chem. Phys. 60 (1999) 231. [25] S.G. Choi, D.H. Levi, C. Martinez-Tomas, V.Munoz Sanjose, J. Appl. Phys. 106 (2009) 053517. [26] S.G. Abdullaeva, N.T. Mamedov, Phys. Status Solidi (b) 133 (1986) 171.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Absorption edge and optical constants of Tl2Ga2S3Se crystals from reflection and transmission, and ellipsometric measurements M. Isik a,n, N.M. Gasanly b a b
Department of Electrical and Electronics Engineering, Atilim University, 06836 Ankara, Turkey Department of Physics, Middle East Technical University, 06800 Ankara, Turkey
a r t i c l e i n f o
abstract
Article history: Received 11 February 2012 Received in revised form 29 February 2012 Accepted 1 March 2012 Available online 6 March 2012
The optical properties of Tl2Ga2S3Se layered crystalline semiconductors were investigated from transmission, reflection and ellipsometric measurements. The experimental results of the room temperature transmission and reflection measurements performed in the wavelength range of 400–1100 nm showed the presence of both indirect and direct transitions in the band structure of the crystals with 2.38 and 2.62 eV band gap energies. Spectroscopic ellipsometry measurements on Tl2Ga2S3Se crystals were carried out on the layer-plane (0 0 1) surfaces with light polarization E?cn in the 1.20–4.70 eV spectral range at room temperature. The real and imaginary parts of the dielectric function as well as refractive and absorption indices were found as a result of analysis of ellipsometric data. The Wemple–DiDomenico single-effective-oscillator model was used to study the dispersion of the refractive index in the below band gap energy range. The structures of critical points have been characterized from the second derivative spectra of the dielectric function. The analysis revealed four interband transition structures with 3.14, 3.40, 3.86 and 4.50 eV critical point energies. & 2012 Elsevier B.V. All rights reserved.
Keywords: Semiconductors Energy band gap Ellipsometry Refractive index
1. Introduction Thallium dichalcogenides formulated as TlBX2 (where B¼In or Ga, X¼S, Se or Te) have become essential in the optoelectronic applications owing to their interesting structural, optical and electrical properties [1,2]. The quaternary compound Tl2Ga2S3Se which belongs to the group of semiconductors with layered structure is a structural analog of TlGaS2 [2] in which one quarter of sulfur atoms are replaced by selenium atoms. The optical and electrical properties of TlGaS2, TlGaSe2 and TlGaSeS crystals were studied in Refs. [3–10]. These crystals are useful for optoelectronic applications as they have high photosensitivity in the visible range of the spectra and a wide transparency range of 0.5–14.0 mm [9]. In our previous work, Tl2Ga2S3Se single crystals have been studied in the temperature range of 10–320 K using thermally stimulated current (TSC) technique [11]. The data were analyzed by curve fitting, initial rise and peak shape methods. Experimental evidence was obtained for trapping centers in Tl2Ga2S3Se crystals with activation energies of 11 and 498 meV. Analysis of experimental TSC glow curves registered at different light illumination temperatures revealed the exponential distribution of the shallow traps in Tl2Ga2S3Se crystals.
n
Corresponding author. Tel.: þ90 312 5868715; fax: þ90 312 5868091. E-mail address: [email protected] (M. Isik).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2012.03.004
The transmission, reflection and ellipsometry are non-destructive optical characterization techniques. The analysis of the experimental results obtained from these measurements gives comprehensive information about the electronic band structure of the samples and optical parameters such as refractive index, dielectric constant and absorption coefficients. In this paper, the optical properties of Tl2Ga2S3Se crystal in the photon energy region from 1.20 to 4.70 eV are presented. The studies on the room temperature transmittance and reflectance data in the range of 1.20–3.10 eV were carried out to identify the absorption edge. We report also the results of the spectroscopic ellipsometry measurements of optical constants of Tl2Ga2S3Se crystals. The critical points in the studied crystals were established from the analysis of the dielectric function obtained from ellipsometric measurements.
2. Experimental details Tl2Ga2S3Se semiconductor polycrystals were synthesized using high-purity elements taken in stoichiometric proportions. Tl2Ga2S3Se single crystals were grown by the Bridgman method in evacuated (10 5 Torr) silica tubes with a tip at the bottom. The ampoule was moved in a vertical furnace through a thermal gradient of 30 1C cm 1, between the temperatures 880 and 530 1C at a rate of 1.0 mm h 1. The resulting ingots (yellow-green in color) showed good optical
2230
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
Fig. 2. Spectral dependence of transmittance and reflectivity for Tl2Ga2S3Se crystal. Inset: the dependence of d{ln(ahn)}/d(hn) on photon energy for Tl2Ga2S3Se crystal.
Fig. 1. Energy dispersive spectroscopic analysis of Tl2Ga2S3Se crystal.
quality and the freshly cleaved surfaces were mirror-like. The chemical composition of Tl2Ga2S3Se crystals, shown in Fig. 1, was determined by energy dispersive spectroscopic analysis using a JSM-6400 electron microscope. The atomic composition of the studied samples (Tl:Ga:S:Se) was found to be 26.0:25.8:35.9:12.3, respectively. Room temperature transmission and reflection measurements were carried out in the 400–1100 nm wavelength region using a ‘‘Shimadzu’’ UV-1201 model spectrophotometer. The transmission measurements were carried out under normal incidence of light with polarization direction along the (0 0 1) plane, which is perpendicular to the c-axis of the crystal. We utilized the specular reflectance measurement attachment with 51 incident angle for reflection measurements. The ellipsometric spectroscopy of the Tl2Ga2S3Se crystals was obtained using UVISEL Jobin Yvon variable angle spectroscopic rotating analyzer ellipsometry at room temperature in the 1.20– 4.70 eV spectral range with 0.01 eV increments. The ellipsometer has a high resolution of 0.01 eV. The angle of the incidence of the light beam was 701. The measurements were performed on the layer-plane (0 0 1) crystal surfaces with light polarization E?cn, where cn is the normal to the layer plane. Since the crystal has layered structure, it is very difficult to perform measurements on any other than the sample natural layer plane surfaces.
3. Results and discussion 3.1. Absorption edge analysis The transmittance (T) and reflectivity (R) spectra for Tl2Ga2S3Se single crystals were obtained in the wavelength (l) range of 400–1100 nm (Fig. 2). The reflection measurement was performed using specimens with natural cleavage planes and thickness satisfying the condition adb1. However, the thickness of the sample was reduced using adhesive tape for the transmission measurements. The thickness of the sample which gives good transmittance spectra was about 10 mm. The transmittance and reflectivity are related by absorption coefficient (a) and the sample thickness (d) as [12] T¼
ð1RÞ2 expðadÞ ð1R2 Þexpð2adÞ
:
ð1Þ
The absorption coefficient was calculated using Eq. (1) as a function of wavelength. The dependence of absorption coefficient
on photon energy (hn) is analyzed in the high absorption region to get detailed information about the energy band gaps (Eg). The energy band gap values were determined from the relation ðahnÞ ¼ AðhnEg Þp ,
ð2Þ
where A is a constant, which depends on the transition probability and p is an index, which is theoretically equal to either 2 for indirect transitions or 1/2 for direct transitions. Eq. (2) can be also written as [13] d½lnðahvÞ p ¼ : dðhvÞ hvEg
ð3Þ
As a first step of analysis, the value of index p was found to determine the type of optical transition. In order to obtain p value, d{ln(ahn)}/d(hn) vs. hn was plotted (inset of Fig. 2). The figure demonstrates two peaks and the positions of peak’s maximums give optical band gaps of approximately 2.44 and 2.65 eV. The curves of ln(ahn) vs. ln(hn Eg) were plotted with the help of obtained Eg values to determine p values which were found to be about 2 and 1/2 from the slopes of plotted curves. Although the corresponding energies of the peak’s maximums give a foresight about the values of energy band gaps, we determined the more precise values using the graphs of (ahv)1/2 and (ahv)2 as a function of photon energy. These plots give straight lines shown in Fig. 3. The linear dependencies of (ahv)1/2 and (ahv)2 on photon energy suggest that the fundamental absorption edges in Tl2Ga2S3Se crystal are formed by the indirect allowed transitions in the range of 2.42–2.57 eV and direct transitions in the interval of 2.65–2.80 eV. The values of indirect and direct band gap energies were obtained by extrapolating fitted straight lines down to (ahv)1/2 ¼0 and (ahv)2 ¼0 as Egi ¼2.3870.02 eV and Egd ¼2.6270.02 eV, respectively. 3.2. Refractive index analysis It is known, that the structures of TlGaSe2 and TlGaS2 crystals belong to monoclinic symmetry, the space group is C2/c, a¼ 1.0772, b¼1.0771 and c¼1.5636 nm and b ¼100.61 (TlGaSe2); a¼ 1.0299, b¼1.0284 and c¼1.5175 nm and b ¼99.6031 (TlGaS2) [1]. We believe that Tl2Ga2S3Se also crystallizes in monoclinic structure similar to the structure of the constituent TlGaSe2 and TlGaS2 compounds. TlGaSe2 and TlGaS2 crystals having a monoclinic layered structure are optically biaxial. However, biaxiality of these materials at room temperature is very small according to the light figure spectroscopy studies [14]. Therefore, TlGaSe2 and TlGaS2 (as well Tl2Ga2S3Se) at this
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
Fig. 3. The dependencies of (ahv)1/2 and (ahv)2 on photon energy for Tl2Ga2S3Se crystal. Circles represent the experimental data that were fitted to a linear equation (the solid lines) to find the band gaps.
2231
Fig. 4. Spectra of the real and imaginary parts of the dielectric function of Tl2Ga2S3Se crystal.
temperature can be regarded as uniaxial materials with optic axis (cn) normal to the layer plane [15,16]. The refractive (n) and absorption (k) indices of Tl2Ga2S3Se layered crystals were obtained from the ellipsometry measurements in the 1.20–4.70 eV range on the layer-plane (0 0 1) surfaces [i.e., ordinary optical constants (E?cn)]. For these measurements samples with dimensions of about 6 4 1 mm3 were used. The freshly cleaved platelets (along the layer plane (0 0 1)) were mirror-like. That is why no further polishing and cleaning treatments were required. In the spectroscopic ellipsometry measurements, a linearly polarized light beam was irradiated onto a sample and reflected light from the sample was analyzed. The amplitude ratio (C) and phase shift (D) of the parallel (p) and perpendicular (s) components of the reflected light were used to get the complex reflectance ratio of the polarized light given by
r¼
rp ¼ tanðcÞeiD , rs
ð4Þ
where rp and rs are the Fresnel reflection coefficients of the polarized light. The dielectric constant of the material is given for the simple ambient-substrate optical model as [17–19] "
e ¼ e1 þ ie2 ¼ sin2 ðjÞ 1 þ
# 1r 2 tan2 ðjÞ , 1þr
ð5Þ
where j is the angle of incidence. The real and imaginary parts of the dielectric constant as a function of energy of Tl2Ga2S3Se found from this optical model are shown in Fig. 4. The oscillations at low energy region of the spectra are due to the interference from the back-reflected component, since for these thicknesses the crystals are not fully opaque. The refractive and absorption indices are calculated using the real and imaginary parts of the dielectric constant from
Fig. 5. Spectra of the refractive and absorption indices of Tl2Ga2S3Se crystal.
the relations
e1 ¼ n2 k2
ð6Þ
e2 ¼ 2nk:
ð7Þ
Fig. 5 represents the refractive and absorption indices spectra for Tl2Ga2S3Se obtained by means of Eqs. (6) and (7).
2232
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
Fig. 6. Plot of (n2 1) 1 versus (hv)2. The solid line represents the fit using Eq. (8).
The refractive index in the energy region of hvoEg gradually increases from 2.65 to 2.85 with increasing photon energy in the interval of 1.20–2.35 eV. The analysis of the dispersive refractive index data in the energy region of hvoEg was performed by means of single-effective-oscillator model proposed by Wemple and DiDomenico [20,21]. The photon energy dependence of the refractive index in the suggested model was related to single oscillator energy (Eso) and the dispersion energy (Ed) by the relation n2 ðhnÞ ¼ 1 þ
Eso Ed E2so ðhnÞ2
:
ð8Þ
The oscillator parameters were determined from the plot of (n2 1) 1 versus (hv)2. Fig. 6 shows the linear fitting of the above reported function in the lower energy data range (1.20–2.35 eV). The zero-frequency (hv¼0) refractive index n0 can be deduced from Eq. (8). The values of the optical parameters Eso and Ed were calculated using the slope and the intersection with y-axis of the fitted straight line (Fig. 6) as 5.30 eV and 30.02 eV, respectively. Furthermore, the values of zero-frequency dielectric constant e0 ¼n20 ¼6.67 and refractive index n0 ¼2.58 were evaluated using Eq. (8). The oscillator energy Eso is an ‘‘average’’ energy gap and approximately equal to two times of the lowest direct band gap Egd (Eso E2.0 Egd) [22–24]. In this study, the ratio Eso/Egd for Tl2Ga2S3Se crystal was found to be 2.03.
to 1, 1/2, 0 and þ 1/2 for excitonic, one, two and three dimensional lineshapes, respectively. The second derivative spectra of real (d2e1/dE2) and imaginary 2 (d e2/dE2) parts of the dielectric constant are fitted using Eq. (9) for the consideration of excitonic optical transitions (m¼ 1) as they demonstrate the lowest mean-square deviations (Fig. 7). The smoothing process has been applied for the each step of the analysis without distorting the main experimental curves. The critical point analysis were performed above the band gap energy Eg ¼2.38 eV. Moreover, because the smoothing process strongly deflects the main experimental data in the 1.20–2.80 eV range, we have fitted only the spectra of the dielectric constant for the region above 2.80 eV. In the energy range from 2.80 to 4.70 eV, four critical point lineshapes of 3.14, 3.40, 3.86 and 4.50 eV appeared as a result of least-square fitting program, which are represented by arrows in Fig. 7. At this point, it is worthwhile to make some interpretations on the critical point energies of 3.14 and 3.40 eV. Unfortunately, the band structure of Tl2Ga2S3Se crystal has not been calculated yet. Therefore, we were forced to use the results of the band structure calculation of the relative compound TlGaSe2 which is the constituent of the studied crystal [26]. The authors found that the valence band maximum is located at the G point of the Brillouin zone, while the conduction band minimum occurs along the G–Y direction. The indirect band gap Egi ¼2.0 eV is energetically separated by about 0.1 eV from a direct band gap at G (Egd ¼ 2.1 eV). As shown in Section 3.1, for Tl2Ga2S3Se crystal the energy separation between direct and indirect band gap energies Egd Egi ¼2.62 eV 2.38 eV ¼0.24 eV. For TlGaSe2 crystal, the spin–orbit splitting of the uppermost valence band at point G of the Brillouin zone is about D ¼0.50 eV and the energy separation between the deeper and upper valence bands approximately equals 0.33 eV [26]. Then, assuming for Tl2Ga2S3Se the same value of the spin–orbit separation (D ¼0.50 eV) we may assign the CP structure at 3.14 eV to the transition from spin–orbit separated valence band to the bottom of the conduction band at the Brillouin zone center, which is equal to 3.12 eV. As for CP structure at 3.40 eV we may assign it to the transition from second valence band to the bottom of the conduction band at the Brillouin zone center, which is equal to 3.45 eV. The CP structures in the higher energy region (3.86 and 4.50 eV) were attributed tentatively to the excitations of electrons to either
3.3. Critical point analysis The dielectric property of a material is very close to its band structure. For this purpose, the energy dependence of the dielectric constant obtained from the ellipsometry measurements of Tl2Ga2S3Se crystals was analyzed to get detailed knowledge about its band structure. The critical points in the energy band structure of the crystals were found using the second derivative spectra of the dielectric constant. The second derivative spectra is related to the photon energy (E), amplitude (A), critical point energy (Ecp), phase angle (f) and broadening parameter (G) by the expression [17–19,25] 2
d e dE2
¼ mðm1ÞA expðijÞðEEg þ iGÞm2
ðm a0Þ
ð9Þ
2
d e dE2
¼ A expðijÞðEEg þ iGÞ2
ðm ¼ 0Þ:
ð10Þ
The dimensions of the wave vectors playing a role in the optical transitions determine the value of the parameter m which is equal
Fig. 7. Second-energy derivative of the dielectric function of Tl2Ga2S3Se crystal. Circles and squares represent the second-energy derivative spectra of the real and imaginary parts of the dielectric function, respectively. The solid and dot-dashed curves show the fits to the experimental data.
M. Isik, N.M. Gasanly / Physica B 407 (2012) 2229–2233
the second or the third group of conduction bands present in the band structure of the studied crystals.
4. Conclusions The optical characterization of the Tl2Ga2S3Se crystals was performed by means of transmission, reflection and ellipsometry measurements. The analysis of absorption data obtained from transmittance and reflectivity spectra revealed the presence of both optical indirect and direct transitions with band gap energies of 2.38 and 2.62 eV, respectively. The real and imaginary parts of the dielectric function, refractive and absorption indices of Tl2Ga2S3Se crystals were obtained using the spectroscopic ellipsometry measurements for light polarization E?cn in the 1.20–4.70 eV spectral region. The refractive index dispersion data in the energy region of hvoEg were analyzed using the Wemple–DiDomenico single-effective-oscillator model. The refractive index dispersion parameters: oscillator and dispersion energies, and zero-frequency refractive index were found to be 5.30 eV, 30.02 eV and 2.58, respectively. The critical point analysis of the second derivative spectra of the dielectric constant in the above band gap region revealed the presence of four critical points with energies of 3.14, 3.40, 3.86 and 4.50 eV.
Acknowledgment The authors are grateful to Dr. S.S. Cetin for her assistance.
2233
References [1] A.M. Panich, J. Phys.: Condens. Matter 20 (2008) 293202. [2] K.A. Yee, A. Albright, J. Am. Chem. Soc. 113 (1991) 6474. [3] M. Hanias, A. Anagnostopoulos, K. Kambas, J. Spyridelis, Mater. Res. Bull. 27 (1992) 25. [4] I.M. Ashraf, M.M. Abdel-Rahman, A.M. Badr, J. Phys. D: Appl. Phys. 36 (2003) 109. [5] A. Kato, M. Nishigaki, N. Mamedov, M. Yamazaki, S. Abdullaeva, E. Kerimova, H. Uchiki, S. Iida, J. Phys. Chem. Solids 64 (2003) 1713. [6] M.M. El Nahass, M.M. Sallam, S.A. Rahman, E.M. Ibrahim, Solid State Sci. 8 (2008) 488. [7] V. Grivickas, V. Bikbajevas, P. Grivickas, Phys. Status Solidi (b) 243 (2006) R31. [8] B. Gurbulak, S. Duman, Phys. Scr. 77 (2008) 025702. [9] K.R. Allakhverdiev, Solid State Commun. 111 (1999) 253. [10] I. Guler, N.M. Gasanly, J. Korean Phys. Soc. 51 (2007) 2031. [11] T. Yıldırım, N.M. Gasanly, Solid State Sci. 11 (2009) 1562. [12] J.I. Pankove, Optical Processes in Semiconductors, Prentice-Hall, New Jersey, 1971. [13] F. Yakuphanoglu, J. Phys. Chem. Solids 69 (2008) 949. [14] N. Mamedov, Y. Shim, N. Yamamoto, Jpn. J. Appl. Phys. 41 (2002) 7254. [15] Y. Shim, W. Okado, K. Wakita, N. Mamedov, J. Appl. Phys. 102 (2007) 083537. [16] N. Mamedov, Y. Shim, H. Toyota, K. Wakita, N. Yamamoto, S. Iida, Phys. Status Solidi (b) 203 (2006) 2873. [17] M. Cardona, Modulation Spectroscopy, Academic, New York, 1969. [18] D.E. Aspnes, Handbook on Semiconductors, vol. 2, North-Holland, Amsterdam, 1980. [19] J.W. Garland, C. Kim, H. Abad, P.M. Raccah, Phys. Rev. B 41 (1990) 7602. [20] S.H. Wemple, M. DiDomenico, Phys. Rev. B 3 (1971) 1338. [21] S.H. Wemple, M. DiDomenico, Phys. Rev. Lett. 23 (1969) 1156. [22] K. Tanaka, Thin Solid Films 66 (1980) 271. [23] F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 351 (2004) 53; F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 353 (2004) 210. [24] E. Marguez, A.M. Bernal-Oliva, J.M. Gonzalez-Leal, R. Pricto-Alcon, A. Ledesma, R. Jimenez-Garay, I. Martil, Mater. Chem. Phys. 60 (1999) 231. [25] S.G. Choi, D.H. Levi, C. Martinez-Tomas, V.Munoz Sanjose, J. Appl. Phys. 106 (2009) 053517. [26] S.G. Abdullaeva, N.T. Mamedov, Phys. Status Solidi (b) 133 (1986) 171.