1. Introduction

The conversion of heat and solar energy into electrical power could play a significant role in current efforts to develop alternative source energy to reduce the dependence both on fossil fuels and greenhouse gas emissions¹.

For this reason, search for new materials for Thermoelectric (TE) device applications is an active area of research^2,3. Bulk semiconducting materials such as CuGaTe₂^4-8 ternary chalcopyrite and the ordered defect compounds of the Cu₂Te-Ga₂Te₃ pseudo-binary system⁹ such as Cu₂Ga₄Te₇^4,10, Cu₃Ga₅Te₉^4,11, CuGa₃Te₅⁴, and CuGa₅Te₈⁴, have attracted some attention recently as potential candidates for high-temperature TE materials. This is because these compounds have low carrier concentrations^12,13, which reduces their thermal conductivity, a condition required to obtain promising materials for TE applications^1-3. In spite of this, the optical properties of these Cu-Ga-Te ODC’s have not been studied in detail so far. CuGa₃Te₅, a member of these ODC’s, has been studied with some interest and some reports on its electrical^12,14 and optical^14-18 properties have appeared in the literature. However, controversy exists on the nature of its fundamental absorption edge. Although a direct allowed band gap EG, which is of about 1.09-1.15 eV, was originally reported for this material from the analysis of the optical absorption coefficient α at room temperature^14,15, a more recent study suggests that CuGa₃Te₅ has an indirect band-gap, of about EGI≈1.0 eV, followed closely for a direct gap EG≈1.07 eV^16,17. Hence, to further understand the optical properties of this material and to clarify the discrepancy related to the nature of the band gap, in the present article, the optical absorption coefficient spectra of this compound as a function of temperature is studied.

2. Experimental details

Ingot of CuGa₃Te₅ was prepared by heating the stoichiometric mixture of at least 5N pure Cu, Ga, and Te sealed in an evacuated quartz ampoule, by using the vertical Bridgman-Stockbarger technique. Details are described elsewhere¹⁴. The obtained ingot was polycrystalline and black in color with polished surface. Circular shaped void free samples from the central part where cut for optical absorption study by slicing the ingot perpendicularly to the growth direction. X-Ray diffraction data analysis of these samples indicates that they crystallize in a chalcopyrite-related structure with space group P 4¯2c. The unit cell parameters were found to be a=0.59321(8) and c=1.1825(4) nm¹⁴. The optical transmittance spectra were measured with a Cary 17I monochromator using a 170 W tungsten lamp as a light source. The transmitted radiation was detected by a Ge photodiode detector. For the measurements of transmittance spectra, the sample was placed in a He₂ cryostat operating in the range from 10 to 300 K.

3. Results and discussion

3.1 Optical absorption spectra of CuGa₃Te₅

The absorption coefficient 𝛼 was obtained from the measured transmittance through the relation α=1t[lnI0I+2ln1-R]-αR, where 𝑡 is the thickness of the sample, I0 and I the incident and transmitted radiation, respectively, R is the reflectivity and αR a nearly constant residual absorption observed in the low energy region of the spectra. R was estimated from the transmittance in the zero-absorption limit where it is expected that T≈(1-R)/(1+R). Typical values of T in this limit were found to of about 0.60. This gives R≈0.25.

In order to establish the nature of the fundamental energy gap in CuGa₃Te₅, the models for both direct and indirect band gaps should be considered. The theory of interband optical absorption transitions between parabolic bands in semiconductors¹⁹ shows that near the fundamental absorption edge, α varies with the incident photon energy ℎ𝜈 according to the expression,

where AG is a parameter nearly independent of photon energy, EG is the gap energy, and the value of the exponent m depends on the nature of the optical processes involved. This being 2 for allowed direct and 1/2 for allowed indirect transitions¹⁹.

The absorption coefficient spectra (αhν)² at different temperatures from 10 to 300 K of CuGa₃Te₅ are plotted in Fig. 1. Analysis of experimental data shows that αhν)² vs. hν give a straight line for the spectra at each temperature indicating that this compound, like CuGaTe₂ [20], CuIn₃Te₅¹⁵, CuIn₅Te₈[15], and Cu₃In₅Te₉²¹, has a direct band gap. This is shown in Fig. 2, where (αhν)² vs. ℎ𝜈 for representative temperatures 10, 150 and 300 K is plotted.

Figura 1 Absorption coefficient spectra of CuGa₃Te₅ between 10 and 300 K. 

Figura 2 (ahv)₂ vs. hv for CuGa₃Te₅ at representative temperatures 10, 150, and 300 K. 

The value of the energy gap at each temperature was obtained by extrapolating the linear portion of each αhν)² vs >hν curve to αhν 2 = 0. The temperature dependence of the energy gap EG for CuGa₃Te₅, thus obtained, is plotted in Fig. 3. As can be noted, the present value of the energy gap at room temperature, EG=1.090 eV, is in good agreement with the value for this parameter reported in^14-17 which vary from 1.07 to 1.15 eV.

Several models have been employed in the literature to describe the temperature variation of the energy gap.

Varshni has proposed the following empirical expression²²:

where EG(0) is the value of the energy gap at 0 K and b and β are constants, β being of the same order as the Debye temperature θD.

On the other hand, Viña et al.²³ have proposed a more physically justified expression for the EG vs T variation. This, based on Bose-Einstein phonon model, is given by

where EB-ab=EG(0) is the value of the energy gap at 0 K, and θ an average phonon related to the Debye temperature.

Equations (2) and (3) were fitted to the EG(T) data of Fig. 3. Values of different parameters obtained by the fit are EG(0)=(1.189±0.001) eV, b=(4.5±0.5)×10-4 eV/K, and β=(102±18) K from Eq. (2), and EB=(1.213±0.003) eV, ab=(2.5±0.4)×10-2 eV, and θ=(125±20)K from Eq. (3). Theoretical curves from these equations are also shown in the same figure by dotted and continuous lines, respectively. The values of the energy gap at T→0, EG(0)=1.189 and 1.188 eV, predicted by these models, respectively, are in good agreement to each other. Also, as expected, the value of β obtained from Eq. (2) is slightly lower than θ obtained from Eq. (3). This is because these parameters should be related²⁴, according to the expressions β≈(3/8)θD, and θD≈(3/4)θD. The Debye temperature θD of CuGa₃Te₅, as estimated from a semi-empirical model²⁵ that relates θD to the mean atomic weight per lattice site M and the mean atomic volume V, is (208±20) K. By using β≈(3/8)θD and θ≈(3/4)θD, with this value of 𝜃 𝐷 , one gets β=(78±8) and θ=(156±15) K. This in comparable with β=(102±18), and θ=(125±20)K, obtained from the fit of Eqs. (2) and (3), respectively, to the present EG vs. T data.

Figura 3 Variation of the energy gap E_G with temperature in CuGa₃Te₅. Doted and continuous lines represent the fits of Eqs. (1) and (2), respectively, to the E_G versus T data with the parameters E_G (0), b, and β, from Eq. (2), and E_b , a_b , and θ, from Eq. (3), given in the text. 

4. Conclusion

From the analysis of the optical absorption spectra of CuGa₃Te₅ as a function of temperature, it is reconfirmed that this compound has a direct-allowed band gap between parabolic bands which varies from 1.187 to 1.090 eV in the temperature range from 10 to 300 K, respectively. The mean temperature of the phonon involved in the direct band-to-band transition is 3/4 ≈125 K which is comparable with 3/4 θD≈156 K.