Optical properties of Tl2InGaS4 layered single crystal

Optical Materials 29 (2007) 1763–1767 www.elsevier.com/locate/optmat

Optical properties of Tl2InGaS4 layered single crystal A.F. Qasrawi a

a,*

, N.M. Gasanly

b

Department of Electrical and Electronics Engineering, Atilim University, Kizilcasar Koyu, Incek, Golbasi, Ankara 06836, Turkey b Department of Physics, Middle East Technical University, Ankara 06531, Turkey Received 21 February 2006; accepted 30 September 2006 Available online 15 November 2006

Abstract The temperature dependence of the optical band gap of Tl2InGaS4 single crystal in the temperature region of 300–500 K and the room temperature refractive index, n(k), have been investigated. The absorption coefficient, which was calculated from the transmittance and reflectance spectra in the incident photon energy range of 2.28–2.48 eV, increased with increasing temperature. Consistently, the absorption edge shifts to lower energy values as temperature increases. The fundamental absorption edge corresponds to an indirect allowed transitions energy gap (2.35 eV) that exhibits a temperature coefficient of 4.03 · 104 eV/K. The room temperature n(k), calculated from the reflectance and transmittance data, allowed the identification of the oscillator strength and energy, static and lattice dielectric constants, and static refractive index as 16.78 eV and 3.38 eV, 5.96 and 11.77, and 2.43, respectively.  2006 Elsevier B.V. All rights reserved. PACS: 71.23.Cq; 78.20.Ci; 78.66.Jg Keywords: Semiconductors; Optical properties; Band gap; Refractive index; Lattice parameters

1. Introduction Layered semiconductors are of research interest due to their structural properties and potential optoelectronic applications. Their quasi two dimensionality, structural anisotropy, optical and photoconductive properties, and other features attract investigators in an effort to acquire a better insight in the physics of these compounds. Tl2InGaS4 is formed from the TlGaS2–TlInS2 system of layered crystals, which belong to the monoclinic system, and their space group is known as C2/c at room temperature. The lattice structure is composed of two dimensional alternating layers arranged parallel to the (0 0 1) plane; each layer is followed by another layer rotated by 90 with respect to the preceding one [1].

*

Corresponding author. Tel.: +90 312 5868329; fax: +90 312 5868091. E-mail address: [email protected] (A.F. Qasrawi).

0925-3467/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.09.008

Previously, we have studied the temperature-dependent photoluminescence spectra of the Tl2InGaS4 crystal in the temperature region of 10–150 K and wide laser excitation intensity range 0.01–110.34 W cm2 [2]. The study allowed the determination of three emission band energies of 1.754, 2.041 and 2.286 eV. Recently, the thermally stimulated current measurements on this layered crystal have been carried out. Two shallow trapping centers with activation energies of 4 and 10 meV have been detected at low temperatures [3]. The purpose of this work is to study the band gap energy of Tl2InGaS4 crystal as a function of temperature in the high temperature region (300–500 K) to obtain the rate of change of the band gap with temperature. In addition, the room temperature reflectance and transmittance data of this crystal will be analyzed to identify the refractive index, oscillator strength and energy, static and lattice dielectric constants, and static refractive index. The determination of these optical constants is expected to widespread the related available physical information.

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A.F. Qasrawi, N.M. Gasanly / Optical Materials 29 (2007) 1763–1767

2. Experimental Tl2InGaS4 polycrystals were synthesized from the highpurity elements (at least 99.999% pure) prepared in stoichiometric proportions. Single crystal of Tl2InGaS4 was grown by Bridgman method. X-ray powder diffractometer Philips PW1740 (Cu Ka radiation) was used for structural characterization. Fig. 1 shows the X-ray pattern of Tl2InGaS4 crystal. The lattice parameters of the monoclinic unit cell, calculated by a least squares computer program ‘‘Treor 90’’, were found to be a = 1.0639(4), b = 1.0441(4), c = 1.5334(6) nm, and b = 100.12. The obtained parameters are close to the corresponding values reported for TlInS2 (a = 1.0942, b = 1.0484 and c = 1.5606 nm, and b = 100.70 [4]) and TlGaS2 (a = 1.031, b = 1.043 and c = 1.507 nm, and b = 99.60 [5]) as expected. The reported data in Ref. [4] does not match other literature values (ICDD card numbers 74-0030 and 85-0636). At the same time the structure of the two compounds TlGaS2 and Tl2InGaS4 are not solved yet, except ours, in the literature available to us. Hence, the structure

of such compounds needs further study, which can be one of our future interests. The diffraction data: Miller indices (h k l), interplanar spacings (d) and relative intensities (I/I0) of the diffraction lines are listed in Table 1. The samples for optical measurements were prepared by cleaving an ingot parallel to the crystal layer, which is perpendicular to the c-axis, with typical sample dimensions of 5 · 5 · 0.35 mm3. The transmission and reflection spectra were recorded at various temperatures in the temperature range of 300–500 K using a Hewlet Packard 8453 A UV– VIS spectrophotometer. 3. Results and discussion The transmittance (T) and reflectance (R) spectra of Tl2InGaS4 crystal were recorded at different temperatures varying from 300 to 500 K in the photon energy (E = hv) range of 1.5–2.6 eV. From these spectral data, the absorption coefficient (a), illustrated in Fig. 2(a), was calculated using the relation [6] 2

T ¼ ð1  RÞ expðadÞ;

2

where d = 350 lm is the sample thickness. It is clear from the figure that the absorption coefficient of Tl2InGaS4 crystal sharply increases with increasing photon energy in the region of 2.35–2.48 eV. It also exhibits higher numerical values and an absorption edge shift with increasing temperature. To obtain a detailed information about the energy band gap as a function of temperature, the a–E dependencies are analyzed in the sharp absorption region where a can be represented by the relation [6]

10

Intensity (a.u.)

5

9 11 13

6

3

1

8

4

10

12

7

20

30

40

50

ð1Þ

14

60

15

ðaEÞ ¼ BðE  Eg Þp :

70

2 θ (degrees)

Fig. 1. X-ray diffraction pattern of Tl2InGaS4 powder sample.

Table 1 X-ray powder diffraction data for Tl2GaInS4 crystal No.

h

k

l

d (nm)

I/I0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

2 4 0 3 4 5 4 3 5 1 1 1 6 3 1

0 0 3 2 2 2 0 4 4 4 5 6 0 6 3

0 0 1 2 2 2 4 2 0 4 3 2 4 2 7

0.7468 0.3735 0.3346 0.3182 0.2820 0.2493 0.2338 0.2078 0.1989 0.1870 0.1762 0.1674 0.1664 0.1561 0.1332

3 100 4 2 15 4 2 2 5 16 4 3 4 2 2

ð2Þ

In this equation, B is a constant that depends on the transition probability and p is an index that characterizes the optical absorption process and is theoretically equal to 2, 1/2, 3 or 3/2 for indirect allowed, direct allowed, indirect forbidden and direct forbidden transitions, respectively. The best linear plot that covers the widest range of data in accordance with Eq. (2) was obtained for the (aE)1/2–E dependence. Some of these plots for different temperatures are presented in Fig. 2(b). The extrapolation of straight lines down to (aE)1/2 = 0 give the values of indirect band gap energy. As illustrated in Fig. 2(b), the value of indirect allowed transition energy gap decreases with increasing temperature. Namely, it shifts from 2.35 to 2.28 eV as temperature increases from 300 to 500 K. Moreover, the Eg–T dependence is linear above 420 K. Below which, the Eg–T dependence slightly diverts from linearity. The temperature dependence of the energy band gap can be represented by the relation [6] Eg ðT Þ ¼ Eg ð0Þ þ

cT 2 : T þb

ð3Þ

A.F. Qasrawi, N.M. Gasanly / Optical Materials 29 (2007) 1763–1767

1765

16 80

(αE (cm eV))

1/2

12

-1

α (cm )

-1

60 300 K 340 380 420 460 500

40

20 2.28

2.33

8 300 K 340 380 420 460 500

4

2.38

2.43

0 2.25

2.48

2.30

2.35

2.40

2.45

2.50

E (eV)

E (eV)

Fig. 2. (a) Temperature dependence of the absorption coefficient for Tl2InGaS4 crystal. (b) The (aE)1/2–E plots at selected temperatures.

Here, Eg(0) is the absolute zero value of the band gap, c = dEg/dT is the rate of change of the band gap with temperature and b is approximately the Debye temperature. The Debye temperature for Tl2InGaS4 crystal b = 279 K was estimated by Lindemann’s melting rule [7] using X-ray results reported in the previous section. The data of the Eg–T dependence (Fig. 3(a)) are fitted using Eq. (3). The fitting of Eq. (3), which is represented by the solid line in the figure, revealed fitting parameters of Eg(0) = 2.42 eV and c =  4.03 · 104 eV/K. The room temperature indirect allowed transitions band gap being 2.35 eV, calculated through this study for the Tl2InGaS4 crystal, is higher than the values 2.26 and 2.28 eV of the indirect allowed transitions band gaps reported for TlInS2 crystals [8,9]. On the other hand, as expected this value is lower than that which was estimated

as 2.45 eV for TlGaS2 crystal [10]. The temperature dependence of the band gap of the Tl2InGaS4 crystal in the high temperature region (300–500 K)-up to our knowledge- is not studied yet. The behavior of the Eg–T dependence is similar to that reported for TlInS2 crystal [9]. For TlInS2 crystal the Eg–T dependence revealed a c value of 8.40 · 104 eV/K and Eg(0) = 2.45 eV. For TlGaS2 crystal, c and Eg(0) are reported to exhibit the values of 4.38 · 104 eV/K and 2.48 eV, respectively [11]. The reflectivity (R), the extinction coefficient (K) and the refractive index (n) of crystalline solid at certain constant wavelength (k) are related through the two equations [6] K¼

ak ; 4p

ð4Þ

3. 0 2.41 Eq. (3)

2. 9

Eg (eV)

n

2.36

2. 8

2.31

2.26 0

100

200

300 T (K)

400

500

2. 7 600

650

700 λ (nm)

750

800

Fig. 3. (a) The energy band gap as a function of temperature. The solid line represents the theoretical fit using Eq. (3). (b) The refractive index – wavelength variation for Tl2InGaS4 crystal.

A.F. Qasrawi, N.M. Gasanly / Optical Materials 29 (2007) 1763–1767 0.16

9.1

0.15

8.7

2

0.14

n

(n2-1)-1

1766

0.13

0.12 2.5

8.3

7.9

7.5 3.5

4.5

3.5

4.0

4.5

5.0

5.5

λ2 (10-13 m2)

E2 (eV2)

Fig. 4. (a) The (n2  1)1  E2 variation. (b) The n2 versus k2 plot. 2

R¼

ðn  1Þ þ K 2 2

ðn þ 1Þ þ K

2

:

ð5Þ

Using these relations, the values of K and n were calculated from the R and T data. The obtained refractive index as function of photon energy in the region where E < Eg is displayed in Fig. 3(b). As could be seen from the figure, the refractive index sharply decreases with increasing wavelength (decreasing photon energy) down to 720 nm (1.72 eV). Below which the refractive index decrement is less pronounced. The data of the dispersive refractive index, n(E), may be analyzed using the single-effective-oscillator model [12]. This model is widely used for analyzing the refractive index of crystalline materials like TlGaS2, ZnSe, GaAs, CdTe and ZnTe [10,12]. The model suggests that the data could be described by n2 ðEÞ ¼ 1 þ

E1 Eo ; E2o  E2

ð6Þ

where E1 is the oscillator strength or dispersion energy and Eo is the oscillator energy. Plotting (n2  1)1 as function of E2 allows the determination of the oscillator parameters, by fitting a linear function to the lower energy data range (1.7–2.1 eV). The fitting of the above reported function is illustrated in Fig. 4(a). The values of E1 and Eo calculated from the slope and the intersection with the y-axis of the straight line in Fig. 4(a) are found to be 16.78 eV and 3.38 eV, respectively. The values of static dielectric constant, es = n2(0), and the static refractive index, n(0), are also calculated using Eq. (6) and found to be 5.96 and 2.43, respectively. The energy-dependent refractive index variation displayed in Fig. 3(b) is consistent with that reported for TlInS2 and TlGaSe2 [13,14] and TlGaS2 [10] single crystals.

The authors employed the same method of calculation used there to obtain the refractive index data. The refractive index for TlInS2 [13] studied in the energy range of 1.55– 4.14 eV increased from 2.7 at 1.55 eV to 3.7 at 4.14 eV. Consistently, the refractive index of TlGaS2 [10] increased from 2.6 at 1.10 eV to 3.6 at 2.50 eV. In addition, the static dielectric constant, which was calculated (in this work) from the refractive index data for Tl2InGaS4 crystal are close to that reported as 6.4 for TlInS2 crystal and as 6.25 for TlGaS2 crystal [10,12]. The relation between the lattice dielectric constant (eL) and the refractive index (n) is given by [15] n2 ¼ eL  Ak2 ;

ð7Þ

where A is a constant which depends on the ratio of the carrier concentration to effective mass [16]. The plot of n2 versus k2 shown in Fig. 4(b) is also linear verifying Eq. (7). The value of eL = 11.77 is determined from the intercept of the solid line (Fig. 4(b)) of the n2 versus k2 plot in accordance to Eq. (7). The disagreement between the values of the static and lattice dielectric constants can be explained by recalling that the slope (A) in Eq. (7) depends on the ratio of the carrier concentration to effective mass. The slope identifies the n2-axis interception. Thus, the larger the free carriers concentration in the sample, the steeper the straight line is and the larger the difference between the lattice and static dielectric constants [15]. 4. Conclusions In this work, the optical properties of Tl2InGaS4 crystal have been investigated. The absorption edge was observed to shift toward lower energy values as temperature increases. The data are used to calculate the energy band gap of the crystal as function of temperature. The rate of

A.F. Qasrawi, N.M. Gasanly / Optical Materials 29 (2007) 1763–1767

change of the band gap with temperature is 4.03 · 104eV/K. The absolute zero value of the band gap energy Eg(0) = 2.42 eV. The transmittance and reflectance data analysis allowed the identification of the optical dispersion parameters. Particularly, the oscillator strength, oscillator energy, the static and lattice dielectric constants and the refractive index are found to be 16.78 eV, 3.38 eV, 5.96, 11.77 and 2.43, respectively. References [1] K.A. Yee, A. Albright, J. Am. Chem. Soc. 113 (1991) 6474. [2] K. Goksen, N.M. Gasanly, H. Ozkan, J. Korean Phys. Soc. 47 (2005) 267. [3] Nader A.P. Mogaddam, N.S. Yuksek, N.M. Gasanly, H. Ozkan, J. All. Comp. 417 (2006) 23. [4] N.M. Gasanly, A. Aydinli, A. Bek, H.I. Yilmaz, Solid State Commun. 105 (1998) 21.

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