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Optical characteristics of Tl0.995Cu0.005InS2 single crystals
Physica B 415 (2013) 57–61
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Optical characteristics of Tl0.995Cu0.005InS2 single crystals M.M. El-Nahass a, H.A.M. Ali a,n, F.S.H. Abu-Samaha b a b
Department of Physics, Faculty of Education, Ain Shams University, Roxy, 11757 Cairo, Egypt Department of Physics & Mathematical Engineering, Faculty of Engineering, Port-Said University, 42523 Port-Said, Egypt
a r t i c l e i n f o
abstract
Article history: Received 24 September 2012 Received in revised form 26 January 2013 Accepted 28 January 2013 Available online 4 February 2013
Optical properties of Tl0.995Cu0.005InS2 single crystals were studied using transmittance and reflectance measurements in the spectral wavelength range of 300–2500 nm. The optical constants (n and k) were calculated at room temperature. The analysis of the spectral behavior of the absorption coefficient in the absorption region revealed indirect transition. The refractive index dispersion data were analyzed in terms of the single oscillator model. Dispersion parameters such as the single oscillator energy (Eo), the dispersion energy (Ed), the high frequency dielectric constant (eN), the lattice dielectric constant (eL) and the ratio of free charge carrier concentration to the effective mass (N/mn) were estimated. The third order nonlinear susceptibility (w(3)) was calculated according to the generalized Miller’s rule. Also, the real and imaginary parts of the complex dielectric constant were determined. & 2013 Elsevier B.V. All rights reserved.
Keywords: Tl0.995Cu0.005InS2 Optical band gap Refractive index Dispersion parameters Third order nonlinear susceptibility
1. Introduction
2. Experimental procedures
TlInS2 belongs to the III–III–VI2 family of crystals known as thallium dichalcogenides. Members of this family have both layered (TlGaS2, TlGaSe2, and TlInS2) and chain (TlInSe2, TlInTe2, and TlGaTe2) structures. They have become interesting due to their structural properties and potential optoelectronic applications [1,2]. The crystal lattice of TlInS2 compound consists of alternating two-dimensional layers arranged parallel to the (001) plane. Each successive layer is rotated by a right angle with respect to the previous one. Interlayer bonding is formed between Tl and S atoms while the bonding between In and S atoms is intralayer [3]. Layered ternary crystals TlInS2 are anisotropic crystals whose properties have become the subject of extensive researches [4–10]. The interest in these materials is stimulated not only by their fundamental properties but also by possible practical applications [11]. High photosensitivity in the visible range and high birefringence in conjunction with a wide transparency range of 0.5–14 mm make these crystals useful for optoelectronic applications [12]. Doping of these crystals allows one to tune their physical properties [13]. The aim of this work is to study the effect of partial substitution of thallium by copper atoms on the optical properties, absorption edge and dispersion parameters of TlInS2 single crystals using transmittance and reflectance measurements in the wavelength range of 300–2500 nm.
Single crystals of Tl0.995Cu0.005InS2 and TlInS2 were grown by the modified Bridgman method from a stoichiometric melt of starting materials in evacuated, (10 5 Torr), carbon-coated silica ampoules with a tip at the bottom. To prevent the ampoule from exploding, it was heated in a temperature gradient furnace. The resulting ingots of the crystals had no cracks and voids on the surface. The obtained crystals have a layered structure and were easily split along the cleavage planes with a smooth-mirror surface, thus no further polishing and cleaning treatments were required. Typical sample dimensions were 0.5 0.6 cm2. The sample thickness was 230 mm. The transmittance (T) of the crystals, at normal incidence of light, as well as the reflectance (R), at an incident angle of 51, was measured using a double beam spectrophotometer (JASCO, V-570UV–vis–NIR) in the wavelength range between 300 and 2500 nm. All the measurements were carried out at room temperature.
n
Corresponding author. Tel.: þ201229068680. E-mail address: [email protected] (H.A.M. Ali).
0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.01.036
3. Results and discussion 3.1. Spectral distribution of T (l) and R (l) Fig. 1 shows the spectral distribution of T (l) and R (l) for Tl0.995Cu0.005InS2 and TlInS2 crystals of thickness 230 mm, as a representative example, in the wavelength range of 300– 2500 nm. It is seen from the figure that the transmittance of the crystals shows step as the wavelength increases up to 500 nm, then increases by increasing the wavelength. The reflectance
58
M.M. El-Nahass et al. / Physica B 415 (2013) 57–61
0.8
25
0.7
20
0.6
T, R
0.5
R (Tl0. Cu
(αhυ)1/2 (eV/cm)1/2
T (Tl0. Cu0. InS ) InS )
T (TlInS )
0.4
R (TlInS )
0.3 0.2
15
10
5
0.1 0.0
500
1000
1500 λ(nm)
2000
2500
0
2.0
2.2
2.4 hυ (eV)
2.1
2.2 hυ(eV)
Fig. 1. Spectral distribution of transmittance, T(l), and reflectance, R(l) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
3.2. Absorption coefficient (a) The absorption coefficient, a, is calculated at different wavelengths using the following relation [14,15]:
a ¼ ð1=dÞ lnfð1RÞ2 =2T þ ½ðð1RÞ4 =4T 2 Þ þ R2 1=2 g
15
10
5
ð1Þ
where d is the sample thickness in cm. The variation in the absorption coefficient, a, is related to the photon energy (hu) for inter-band transition by the following relation [16]: ðahuÞ ¼ BðhuEg Þr
2.8
20
(αhυ)1/2 (eV/cm)1/2
spectra of the crystals show some peaks lies in the wavelength range of 300–900 nm, then decrease with the increase in wavelength up to 2500 nm. Also, Tl0.995Cu0.005InS2 and TlInS2 crystals become transparent at l 4900 nm, where T þR¼1 and no light is absorbed (non-absorbing region). The inequality TþR o1, at l o900 nm, known as absorbing region, was referred to the existence of absorption.
2.6
ð2Þ
2.0
2.3
2.4
2.5
Fig. 2. Dependence of (ahu)1/2 on the photon energy (hu) (a) for Tl0.995Cu0.005InS2 and (b) for TlInS2 single crystals.
6 Tl
Cu
InS
TlInS
5
4 n
where B is a constant, h is Planck’s constant, Eg is the energy band gap and r is a parameter that takes the values: 1/2, 2, 3/2 and 3 which related to allowed direct, allowed indirect, forbidden direct and forbidden indirect optical transitions, respectively. The analysis of the experimental data revealed that (ahu) was proportional to (hu Eg)r with r ¼2. The dependence of (ahu)1/2 on the photon energy is presented in Fig. 2(a, b) for Tl0.995Cu0.005InS2 and TlInS2 crystals, respectively. Linear dependence is observed for the relation (ahu)1/2 against (hu). The values of indirect allowed band gap energy are found to be Egind. ¼2.29 eV (Tl0.995 Cu0.005InS2), and Egind. ¼ 2.30 eV (TlInS2). The absorption edge was reported to be formed by the indirect transition with energies varying as 2.258 eV [8] and 2.27 eV [9] for TlInS2 single crystals.
0 1.9
3.3. Refractive index (n) The refractive index, n, can be calculated at different photon energy using the following relations [14,15]: 2
n ¼ ½ð1 þ RÞ=ð1RÞþ ½ð4R=ð1RÞ2 Þ2k 1=2
ð3Þ
3
2
where k is the absorption index, k ¼ al=4p
ð4Þ
Fig. 3 represents the dependence of the refractive index, n, on the incident photon energy for Tl0.995Cu0.005InS2 and TlInS2 crystals. The refractive index of Tl0.995Cu0.005InS2 crystal showed
0.5
1.0
1.5
2.0
2.5 hυ (eV)
3.0
3.5
4.0
Fig. 3. Dependence of the refractive index (n) on the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
M.M. El-Nahass et al. / Physica B 415 (2013) 57–61
an increase in its value more than that for TlInS2 crystal. The dispersion curve of (n) shows a normal dispersion at (hu) o1.37 eV, in which a single oscillator model can be applied. While, at (hu) 41.37 eV, the spectrum of (n) shows the anomalous dispersion as well as the appearance of some peaks. This behavior may be attributed to a multi-oscillator model [17]. The energy dependence of the refractive index was analyzed using the relationship based on the single oscillator approximation, suggested by Wemple–DiDomenico [18,19] as: n2 1 ¼ Ed Eo =½ðEo Þ2 E2
ð5Þ
where E is the incident photon energy hu, Ed is the dispersion energy and Eo is the effective oscillator energy. Fig. 4 shows the relation of (n2 1) 1 against (hu)2 for Tl0.995Cu0.005InS2 and TlInS2 crystals. The values of dispersion parameters Ed and Eo are determined from the slope and the intercept of the linear fit portion. The calculated values of Ed and Eo as well as the corresponding high frequency dielectric constant (eN ¼n2) for Tl0.995Cu0.005InS2 and TlInS2 crystals are listed in Table 1. The refractive index can also be expressed as a function of the wavelength (l) by the following equation [20]: n2 ¼ eL 2 ðe2 =pc2 Þ ðN=mn Þl
2
ð6Þ
where eL is the lattice dielectric constant and N/m is the ratio of carrier concentration to its effective mass. Fig. 5 shows the dependence of n2 on l2 for Tl0.995Cu0.005InS2 and TlInS2 crystals, which shows linear dependence at longer wavelengths. The values of the lattice dielectric constant and the ratio of carrier concentration to its effective mass for Tl0.995Cu0.005InS2 and TlInS2 crystals are calculated from the slope and the intersection with the y-axis of the straight line and listed in Table 1. The Wemple and DiDomenico expression (Eq. (5)) could also be useful for estimating non-linear effects from the linear optical index of refraction, n. According to Wagner et al. [21] and Hemissi and Amardjia-Adnani [22] the Miller rule is very convenient for n
59
visible and near-infrared frequencies, which equalize the third order non-linear polarizability parameter, w(3), the so-called nonlinear optical susceptibility, and the linear optical susceptibility, w(1), from the equation: 4
wð3Þ ¼ Aðwð1Þ Þ4 ¼ AfEd Eo =4p½ðEo Þ2 E2 g ¼ A=ð4pÞ4 ðn2 1Þ4 10
ð7Þ
(3)
(for w in esu). The third order nonlinear where A¼ 1.7 10 susceptibility of Tl0.995Cu0.005InS2 and TlInS2 crystals is calculated using Eq. (7), which is shown in Fig. 6. It can be noticed that the variation of w(3) as a function of photon energy exhibited a consistent behavior with that of the refractive index. The calculated values of w(3) for Tl0.995Cu0.005InS2 crystal are nearly two orders of magnitude higher than those calculated for TlInS2 crystal. This may be due to the partial substitution of thallium by copper atoms in TlInS2 crystal. 3.4. Dielectric constants The complex dielectric constant (e~ ¼ e0 þie00 ) characterizes the optical properties of any solid material. The real, e0 , and imaginary, e00 , parts of dielectric constants are determined by the following relations [23,24]:
e0 ¼ n2 k2
ð8Þ
e00 ¼ 2nk
ð9Þ
Fig. 7 represents the variation of e with the photon energy for Tl0.995Cu0.005InS2 and TlInS2 crystals. As seen from the figure, the real part of the dielectric constant for Tl0.995Cu0.005InS2 crystal shows a higher value than that for TlInS2 crystal. The spectrum of e0 for Tl0.995Cu0.005InS2 crystal is characterized by the existence of two peaks and two shoulders in comparison to one peak for TlInS2 crystals. Fig. 8 shows the variation of e00 with the photon energy for Tl0.995Cu0.005InS2 and TlInS2 crystals. The imaginary part of the 0
0.20
18 Tl0.995Cu0.005InS2 TlInS2
16
Tl
Cu
InS
TlInS
14
n2
(n2 -1)-1
0.15
12 10
0.10
8
0.05 0.0
6 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0
(hυ)2 (eV)2
1
2
3
4
5
6
7
λ2 (μm)2
Fig. 4. Variation of (n2 1) 1 versus (hu)2 for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
Fig. 5. Variation of n2 versus l2 for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
Table 1 Calculated dispersion parameters for Tl0.995Cu0.005InS2 and TlInS2 single crystals. Parameters
Eo (eV)
Ed (eV)
eN
eL
N/mn (cm 3 g 1)
Tl0.995Cu0.005InS2 TlInS2 TlInS2 [8]
3.01 3.03 5.025 77.1 10 5
29.68 17.35 57.85 76.7 10 5
10.87 6.73 12.51 78.7 10 5
11.96 7.62 13.26 70.0065
2.11 1047 2.30 1047 2.4 1047
60
M.M. El-Nahass et al. / Physica B 415 (2013) 57–61
5
15 Tl Cu TlInS
6.0x10
12 9
2
6
1
3
Tl
-4
Cu
InS
2.39
TlInS
5.0x10-4 tanδ
3
χ(3) . 10-11 (esu)
χ(3) . 10-9 (esu)
4
7.0x10-4
InS
2.43
4.0x10-4 3.0x10-4 2.0x10-4 1.0x10-4
0 0.5
1.0
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
0
0.0
Fig. 6. Variation of w(3) as a function of the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
30
Tl
Cu
3.54
InS
25
2.26 1.51
15
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
Fig. 9. Variation of tand as a function of the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
tan d ¼ e00 =e0
ε
20
1.0
The dissipation factor (tand) is a measure of loss-rate of power of a mechanical mode, such as an oscillation, in a dissipative system. For example, electric power is lost in all dielectric materials, usually in the form of heat [25]. The dissipation factor tand can be calculated according to the following equation [26]:
3.26
TlInS
0.5
ð10Þ
The variation of dissipation factor as a function of energy for Tl0.995Cu0.005InS2 and TlInS2 crystals is shown in Fig. 9. This figure shows that the dissipation factor has a sharp peak at 2.39 eV for TlInS2 which is shifted to 2.43 eV for Tl0.995Cu0.005InS2 crystal.
2.14
10 5
Conclusion 0.5
1.0
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
Fig. 7. Dependence of e0 on the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
0.005
2.48 Tl
Cu
3.12
3.65
InS
TlInS
0.004
ε
0.003 2.39 0.002
Optical properties of Tl0.995Cu0.005InS2 single crystals were studied. The absorption coefficient and the refractive index were derived from the transmittance and reflectance measurements in the spectral range from 300 to 2500 nm. The analysis of the absorption coefficient data revealed an indirect allowed electronic transition responsible for optical properties. Optical indirect band gap energy was found to be 2.29 eV. The refractive index spectrum showed anomalous dispersion in the absorption region and normal dispersion in the transparent region. According to the analysis of the normal dispersion curve using the single oscillator model, some dispersion parameters were evaluated. Tl0.995Cu0.005InS2 single crystals showed high values of the third order nonlinear susceptibility. It was shown from this study that the partial substitution of thallium by copper atoms has a small effect on the optical properties of TlInS2 single crystals. References
0.001 0.000
0.5
1.0
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
Fig. 8. Dependence of e00 on the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
[1] [2] [3] [4] [5] [6] [7]
dielectric constant for TlInS2 crystal exhibits one peak at 2.39 eV which is shifted to higher energy (2.48 eV) in Tl0.995Cu0.005InS2 crystals. In addition to the previous finding, two peaks at 3.12 and 3.65 eV are observed for Tl0.995Cu0.005InS2 crystal.
[8] [9] [10]
M. Isik, N.M. Gasanly, H. Ozkan, Acta Phys. Pol., A 115 (2009) 732. K.A. Yee, A. Albright, J. Am. Chem. Soc. 113 (1991) 6474. N.M. Gasanly, N.S. Yuksek, Acta Phys. Pol., A 108 (2005) 997. K.R. Allakhverdiev, N.D. Akhmedzade, T.G. Mamedov, T.S. Mamedov, M.Y Seidov, Low Temp. Phys. 26 (2000) 56. M.P. Hanias, A.N. Anagnostopoulos, K. Kambas, J. Spyridelis, Mater. Res. Bull. 27 (1992) 25. B. Abay, H.S. Guder, H. Efeoglu, H.K. Yogurtcu, Phys. Status Solidi B 227 (2001) 469. K.R. Allakhverdiev, T.G. Mammadov, R.A. Suleymanov, N.Z. Gasanov, J. Phys. Condens. Matter 15 (2003) 1291. M.M. El-Nahass, M.M. Sallam, A.H.S. Abdel-Wahab, Curr. Appl. Phys. 9 (2009) 311. N.M. Gasanly, J. Korean Phys. Soc. 57 (2010) 164. A.F. Qasrawi, N.M. Gasanly, J. Mater. Sci. 41 (2006) 3569.
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[11] [12] [13] [14] [15]
S.B. Youssef, Physica A 215 (1995) 176. K.R. Allakhverdiev, Solid State Commun. 111 (1999) 253. S.N. Mustafaeva, N.Z. Gasanov, A.I. Gasanov, Fizika 4 (2007) 95. T.S. Moss, Optical Properties in Semiconductor, Butter Worths, London, 1959. M.M. El-Nahass, A.A. Atta, H.E.A. El-Sayed, E.F.M. El-Zaidia, Appl. Surf. Sci. 254 (2008) 2458. [16] J. Bardeen, F.J. Blatt, L.T. Hall, Photoconductivity Conference, Wiley, New York, 1956, pp. 146. [17] A. Stendal, U. Beckars, S. Wilbrand, O. Stenzel, C. Von Borczskowski, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 2589. [18] S.H. Wempl, M. DiDomenico Jr., Phys. Rev. B 3 (1971) 1338.
61
[19] S.H. Wemple, Phys. Rev. B 7 (1973) 3767. [20] J.J. Andre, J. Simon, Molecular Semiconductors, Spring-Verlag, Berlin, 1985. [21] T. Wagner, M. Krbal, J. Jedelsky, Mil Vlcek, B. Frumarova, M. Frumar J. Optoelectron. Adv. Mater. 7 (1) (2005) 153. [22] M. Hemissi, H. Amardjia-Adnani, Dig. J. Nanomater. Biostruct. 2 (4) (2007) 299. [23] O.O. Adewole, A.Y. Suberu, J. Appl. Sci. Res. 2 (11) (2007) 1193. [24] M.M. El-Nahass, H.S. Metwally, H.E.A. El-Sayed, F. Abd El-Salam, H.A. Hassan, Eur. Phys. J. Appl. Phys. 43 (2008) 31. [25] E.M. Assim, J. Alloys Comp 465 (2008) 1. [26] F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 351 (2004) 53.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Optical characteristics of Tl0.995Cu0.005InS2 single crystals M.M. El-Nahass a, H.A.M. Ali a,n, F.S.H. Abu-Samaha b a b
Department of Physics, Faculty of Education, Ain Shams University, Roxy, 11757 Cairo, Egypt Department of Physics & Mathematical Engineering, Faculty of Engineering, Port-Said University, 42523 Port-Said, Egypt
a r t i c l e i n f o
abstract
Article history: Received 24 September 2012 Received in revised form 26 January 2013 Accepted 28 January 2013 Available online 4 February 2013
Optical properties of Tl0.995Cu0.005InS2 single crystals were studied using transmittance and reflectance measurements in the spectral wavelength range of 300–2500 nm. The optical constants (n and k) were calculated at room temperature. The analysis of the spectral behavior of the absorption coefficient in the absorption region revealed indirect transition. The refractive index dispersion data were analyzed in terms of the single oscillator model. Dispersion parameters such as the single oscillator energy (Eo), the dispersion energy (Ed), the high frequency dielectric constant (eN), the lattice dielectric constant (eL) and the ratio of free charge carrier concentration to the effective mass (N/mn) were estimated. The third order nonlinear susceptibility (w(3)) was calculated according to the generalized Miller’s rule. Also, the real and imaginary parts of the complex dielectric constant were determined. & 2013 Elsevier B.V. All rights reserved.
Keywords: Tl0.995Cu0.005InS2 Optical band gap Refractive index Dispersion parameters Third order nonlinear susceptibility
1. Introduction
2. Experimental procedures
TlInS2 belongs to the III–III–VI2 family of crystals known as thallium dichalcogenides. Members of this family have both layered (TlGaS2, TlGaSe2, and TlInS2) and chain (TlInSe2, TlInTe2, and TlGaTe2) structures. They have become interesting due to their structural properties and potential optoelectronic applications [1,2]. The crystal lattice of TlInS2 compound consists of alternating two-dimensional layers arranged parallel to the (001) plane. Each successive layer is rotated by a right angle with respect to the previous one. Interlayer bonding is formed between Tl and S atoms while the bonding between In and S atoms is intralayer [3]. Layered ternary crystals TlInS2 are anisotropic crystals whose properties have become the subject of extensive researches [4–10]. The interest in these materials is stimulated not only by their fundamental properties but also by possible practical applications [11]. High photosensitivity in the visible range and high birefringence in conjunction with a wide transparency range of 0.5–14 mm make these crystals useful for optoelectronic applications [12]. Doping of these crystals allows one to tune their physical properties [13]. The aim of this work is to study the effect of partial substitution of thallium by copper atoms on the optical properties, absorption edge and dispersion parameters of TlInS2 single crystals using transmittance and reflectance measurements in the wavelength range of 300–2500 nm.
Single crystals of Tl0.995Cu0.005InS2 and TlInS2 were grown by the modified Bridgman method from a stoichiometric melt of starting materials in evacuated, (10 5 Torr), carbon-coated silica ampoules with a tip at the bottom. To prevent the ampoule from exploding, it was heated in a temperature gradient furnace. The resulting ingots of the crystals had no cracks and voids on the surface. The obtained crystals have a layered structure and were easily split along the cleavage planes with a smooth-mirror surface, thus no further polishing and cleaning treatments were required. Typical sample dimensions were 0.5 0.6 cm2. The sample thickness was 230 mm. The transmittance (T) of the crystals, at normal incidence of light, as well as the reflectance (R), at an incident angle of 51, was measured using a double beam spectrophotometer (JASCO, V-570UV–vis–NIR) in the wavelength range between 300 and 2500 nm. All the measurements were carried out at room temperature.
n
Corresponding author. Tel.: þ201229068680. E-mail address: [email protected] (H.A.M. Ali).
0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.01.036
3. Results and discussion 3.1. Spectral distribution of T (l) and R (l) Fig. 1 shows the spectral distribution of T (l) and R (l) for Tl0.995Cu0.005InS2 and TlInS2 crystals of thickness 230 mm, as a representative example, in the wavelength range of 300– 2500 nm. It is seen from the figure that the transmittance of the crystals shows step as the wavelength increases up to 500 nm, then increases by increasing the wavelength. The reflectance
58
M.M. El-Nahass et al. / Physica B 415 (2013) 57–61
0.8
25
0.7
20
0.6
T, R
0.5
R (Tl0. Cu
(αhυ)1/2 (eV/cm)1/2
T (Tl0. Cu0. InS ) InS )
T (TlInS )
0.4
R (TlInS )
0.3 0.2
15
10
5
0.1 0.0
500
1000
1500 λ(nm)
2000
2500
0
2.0
2.2
2.4 hυ (eV)
2.1
2.2 hυ(eV)
Fig. 1. Spectral distribution of transmittance, T(l), and reflectance, R(l) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
3.2. Absorption coefficient (a) The absorption coefficient, a, is calculated at different wavelengths using the following relation [14,15]:
a ¼ ð1=dÞ lnfð1RÞ2 =2T þ ½ðð1RÞ4 =4T 2 Þ þ R2 1=2 g
15
10
5
ð1Þ
where d is the sample thickness in cm. The variation in the absorption coefficient, a, is related to the photon energy (hu) for inter-band transition by the following relation [16]: ðahuÞ ¼ BðhuEg Þr
2.8
20
(αhυ)1/2 (eV/cm)1/2
spectra of the crystals show some peaks lies in the wavelength range of 300–900 nm, then decrease with the increase in wavelength up to 2500 nm. Also, Tl0.995Cu0.005InS2 and TlInS2 crystals become transparent at l 4900 nm, where T þR¼1 and no light is absorbed (non-absorbing region). The inequality TþR o1, at l o900 nm, known as absorbing region, was referred to the existence of absorption.
2.6
ð2Þ
2.0
2.3
2.4
2.5
Fig. 2. Dependence of (ahu)1/2 on the photon energy (hu) (a) for Tl0.995Cu0.005InS2 and (b) for TlInS2 single crystals.
6 Tl
Cu
InS
TlInS
5
4 n
where B is a constant, h is Planck’s constant, Eg is the energy band gap and r is a parameter that takes the values: 1/2, 2, 3/2 and 3 which related to allowed direct, allowed indirect, forbidden direct and forbidden indirect optical transitions, respectively. The analysis of the experimental data revealed that (ahu) was proportional to (hu Eg)r with r ¼2. The dependence of (ahu)1/2 on the photon energy is presented in Fig. 2(a, b) for Tl0.995Cu0.005InS2 and TlInS2 crystals, respectively. Linear dependence is observed for the relation (ahu)1/2 against (hu). The values of indirect allowed band gap energy are found to be Egind. ¼2.29 eV (Tl0.995 Cu0.005InS2), and Egind. ¼ 2.30 eV (TlInS2). The absorption edge was reported to be formed by the indirect transition with energies varying as 2.258 eV [8] and 2.27 eV [9] for TlInS2 single crystals.
0 1.9
3.3. Refractive index (n) The refractive index, n, can be calculated at different photon energy using the following relations [14,15]: 2
n ¼ ½ð1 þ RÞ=ð1RÞþ ½ð4R=ð1RÞ2 Þ2k 1=2
ð3Þ
3
2
where k is the absorption index, k ¼ al=4p
ð4Þ
Fig. 3 represents the dependence of the refractive index, n, on the incident photon energy for Tl0.995Cu0.005InS2 and TlInS2 crystals. The refractive index of Tl0.995Cu0.005InS2 crystal showed
0.5
1.0
1.5
2.0
2.5 hυ (eV)
3.0
3.5
4.0
Fig. 3. Dependence of the refractive index (n) on the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
M.M. El-Nahass et al. / Physica B 415 (2013) 57–61
an increase in its value more than that for TlInS2 crystal. The dispersion curve of (n) shows a normal dispersion at (hu) o1.37 eV, in which a single oscillator model can be applied. While, at (hu) 41.37 eV, the spectrum of (n) shows the anomalous dispersion as well as the appearance of some peaks. This behavior may be attributed to a multi-oscillator model [17]. The energy dependence of the refractive index was analyzed using the relationship based on the single oscillator approximation, suggested by Wemple–DiDomenico [18,19] as: n2 1 ¼ Ed Eo =½ðEo Þ2 E2
ð5Þ
where E is the incident photon energy hu, Ed is the dispersion energy and Eo is the effective oscillator energy. Fig. 4 shows the relation of (n2 1) 1 against (hu)2 for Tl0.995Cu0.005InS2 and TlInS2 crystals. The values of dispersion parameters Ed and Eo are determined from the slope and the intercept of the linear fit portion. The calculated values of Ed and Eo as well as the corresponding high frequency dielectric constant (eN ¼n2) for Tl0.995Cu0.005InS2 and TlInS2 crystals are listed in Table 1. The refractive index can also be expressed as a function of the wavelength (l) by the following equation [20]: n2 ¼ eL 2 ðe2 =pc2 Þ ðN=mn Þl
2
ð6Þ
where eL is the lattice dielectric constant and N/m is the ratio of carrier concentration to its effective mass. Fig. 5 shows the dependence of n2 on l2 for Tl0.995Cu0.005InS2 and TlInS2 crystals, which shows linear dependence at longer wavelengths. The values of the lattice dielectric constant and the ratio of carrier concentration to its effective mass for Tl0.995Cu0.005InS2 and TlInS2 crystals are calculated from the slope and the intersection with the y-axis of the straight line and listed in Table 1. The Wemple and DiDomenico expression (Eq. (5)) could also be useful for estimating non-linear effects from the linear optical index of refraction, n. According to Wagner et al. [21] and Hemissi and Amardjia-Adnani [22] the Miller rule is very convenient for n
59
visible and near-infrared frequencies, which equalize the third order non-linear polarizability parameter, w(3), the so-called nonlinear optical susceptibility, and the linear optical susceptibility, w(1), from the equation: 4
wð3Þ ¼ Aðwð1Þ Þ4 ¼ AfEd Eo =4p½ðEo Þ2 E2 g ¼ A=ð4pÞ4 ðn2 1Þ4 10
ð7Þ
(3)
(for w in esu). The third order nonlinear where A¼ 1.7 10 susceptibility of Tl0.995Cu0.005InS2 and TlInS2 crystals is calculated using Eq. (7), which is shown in Fig. 6. It can be noticed that the variation of w(3) as a function of photon energy exhibited a consistent behavior with that of the refractive index. The calculated values of w(3) for Tl0.995Cu0.005InS2 crystal are nearly two orders of magnitude higher than those calculated for TlInS2 crystal. This may be due to the partial substitution of thallium by copper atoms in TlInS2 crystal. 3.4. Dielectric constants The complex dielectric constant (e~ ¼ e0 þie00 ) characterizes the optical properties of any solid material. The real, e0 , and imaginary, e00 , parts of dielectric constants are determined by the following relations [23,24]:
e0 ¼ n2 k2
ð8Þ
e00 ¼ 2nk
ð9Þ
Fig. 7 represents the variation of e with the photon energy for Tl0.995Cu0.005InS2 and TlInS2 crystals. As seen from the figure, the real part of the dielectric constant for Tl0.995Cu0.005InS2 crystal shows a higher value than that for TlInS2 crystal. The spectrum of e0 for Tl0.995Cu0.005InS2 crystal is characterized by the existence of two peaks and two shoulders in comparison to one peak for TlInS2 crystals. Fig. 8 shows the variation of e00 with the photon energy for Tl0.995Cu0.005InS2 and TlInS2 crystals. The imaginary part of the 0
0.20
18 Tl0.995Cu0.005InS2 TlInS2
16
Tl
Cu
InS
TlInS
14
n2
(n2 -1)-1
0.15
12 10
0.10
8
0.05 0.0
6 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0
(hυ)2 (eV)2
1
2
3
4
5
6
7
λ2 (μm)2
Fig. 4. Variation of (n2 1) 1 versus (hu)2 for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
Fig. 5. Variation of n2 versus l2 for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
Table 1 Calculated dispersion parameters for Tl0.995Cu0.005InS2 and TlInS2 single crystals. Parameters
Eo (eV)
Ed (eV)
eN
eL
N/mn (cm 3 g 1)
Tl0.995Cu0.005InS2 TlInS2 TlInS2 [8]
3.01 3.03 5.025 77.1 10 5
29.68 17.35 57.85 76.7 10 5
10.87 6.73 12.51 78.7 10 5
11.96 7.62 13.26 70.0065
2.11 1047 2.30 1047 2.4 1047
60
M.M. El-Nahass et al. / Physica B 415 (2013) 57–61
5
15 Tl Cu TlInS
6.0x10
12 9
2
6
1
3
Tl
-4
Cu
InS
2.39
TlInS
5.0x10-4 tanδ
3
χ(3) . 10-11 (esu)
χ(3) . 10-9 (esu)
4
7.0x10-4
InS
2.43
4.0x10-4 3.0x10-4 2.0x10-4 1.0x10-4
0 0.5
1.0
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
0
0.0
Fig. 6. Variation of w(3) as a function of the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
30
Tl
Cu
3.54
InS
25
2.26 1.51
15
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
Fig. 9. Variation of tand as a function of the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
tan d ¼ e00 =e0
ε
20
1.0
The dissipation factor (tand) is a measure of loss-rate of power of a mechanical mode, such as an oscillation, in a dissipative system. For example, electric power is lost in all dielectric materials, usually in the form of heat [25]. The dissipation factor tand can be calculated according to the following equation [26]:
3.26
TlInS
0.5
ð10Þ
The variation of dissipation factor as a function of energy for Tl0.995Cu0.005InS2 and TlInS2 crystals is shown in Fig. 9. This figure shows that the dissipation factor has a sharp peak at 2.39 eV for TlInS2 which is shifted to 2.43 eV for Tl0.995Cu0.005InS2 crystal.
2.14
10 5
Conclusion 0.5
1.0
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
Fig. 7. Dependence of e0 on the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
0.005
2.48 Tl
Cu
3.12
3.65
InS
TlInS
0.004
ε
0.003 2.39 0.002
Optical properties of Tl0.995Cu0.005InS2 single crystals were studied. The absorption coefficient and the refractive index were derived from the transmittance and reflectance measurements in the spectral range from 300 to 2500 nm. The analysis of the absorption coefficient data revealed an indirect allowed electronic transition responsible for optical properties. Optical indirect band gap energy was found to be 2.29 eV. The refractive index spectrum showed anomalous dispersion in the absorption region and normal dispersion in the transparent region. According to the analysis of the normal dispersion curve using the single oscillator model, some dispersion parameters were evaluated. Tl0.995Cu0.005InS2 single crystals showed high values of the third order nonlinear susceptibility. It was shown from this study that the partial substitution of thallium by copper atoms has a small effect on the optical properties of TlInS2 single crystals. References
0.001 0.000
0.5
1.0
1.5
2.0 2.5 hυ (eV)
3.0
3.5
4.0
Fig. 8. Dependence of e00 on the photon energy (hu) for Tl0.995Cu0.005InS2 and TlInS2 single crystals.
[1] [2] [3] [4] [5] [6] [7]
dielectric constant for TlInS2 crystal exhibits one peak at 2.39 eV which is shifted to higher energy (2.48 eV) in Tl0.995Cu0.005InS2 crystals. In addition to the previous finding, two peaks at 3.12 and 3.65 eV are observed for Tl0.995Cu0.005InS2 crystal.
[8] [9] [10]
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S.B. Youssef, Physica A 215 (1995) 176. K.R. Allakhverdiev, Solid State Commun. 111 (1999) 253. S.N. Mustafaeva, N.Z. Gasanov, A.I. Gasanov, Fizika 4 (2007) 95. T.S. Moss, Optical Properties in Semiconductor, Butter Worths, London, 1959. M.M. El-Nahass, A.A. Atta, H.E.A. El-Sayed, E.F.M. El-Zaidia, Appl. Surf. Sci. 254 (2008) 2458. [16] J. Bardeen, F.J. Blatt, L.T. Hall, Photoconductivity Conference, Wiley, New York, 1956, pp. 146. [17] A. Stendal, U. Beckars, S. Wilbrand, O. Stenzel, C. Von Borczskowski, J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 2589. [18] S.H. Wempl, M. DiDomenico Jr., Phys. Rev. B 3 (1971) 1338.
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[19] S.H. Wemple, Phys. Rev. B 7 (1973) 3767. [20] J.J. Andre, J. Simon, Molecular Semiconductors, Spring-Verlag, Berlin, 1985. [21] T. Wagner, M. Krbal, J. Jedelsky, Mil Vlcek, B. Frumarova, M. Frumar J. Optoelectron. Adv. Mater. 7 (1) (2005) 153. [22] M. Hemissi, H. Amardjia-Adnani, Dig. J. Nanomater. Biostruct. 2 (4) (2007) 299. [23] O.O. Adewole, A.Y. Suberu, J. Appl. Sci. Res. 2 (11) (2007) 1193. [24] M.M. El-Nahass, H.S. Metwally, H.E.A. El-Sayed, F. Abd El-Salam, H.A. Hassan, Eur. Phys. J. Appl. Phys. 43 (2008) 31. [25] E.M. Assim, J. Alloys Comp 465 (2008) 1. [26] F. Yakuphanoglu, A. Cukurovali, I. Yilmaz, Physica B 351 (2004) 53.