Pergamon PII: S0022-3697(96)00231-4 J. Phys. ChemSolids Vol 58, No. 7, pp. 1111- I 114, 1997 © 1997 Elsevier Science Ltd Printed in Great Britain. All fights reserved 0022-3697/97 $17.00 + 0.00 ALLOY COMPOSITION AND TEMPERATURE DEPENDENCE OF THE DIRECT ENERGY GAP IN AlxGal_xAs C. LAREZ and C. RINCON* Centro de Estudios de Semiconductores, Departamento de Fisica, Facultad de Ciencias, Universidad de Los Andes, M&ida, Venezuela (Received 7 September 1996; accepted in revised form 18 November 1996) Abstract--An empiricalmodel is proposed to analyze the variation of the direct energy gap Eo with temperature and alloy composition in the systemAlx Gal_xAs. The Eo (T) curve for pure AlAswas found to be slightlylower than that reported for a high impurity concentration sample. The adjustable parameters obtained for this compound can be related to its average optical phonon energy and lattice thermal dilation coefficient.For the alloys, one of these parameters can also be related to the broadening observed in the line shape of the direct Eo exciton due to electron-phonon interaction. © 1997 ElsevierScienceLtd. All rights reserved. Keywords: A. semiconductors, A. alloys, D. electronic structure, D. optical properties. 1. INTRODUCTION The alloy system AlxGa l_xAs is of practical interest for technological applications in high-speed opto- electronic devices [1]. The lowest direct energy gap Eo at the F point of the Brillouin zone and its dependence on the alloy composition x is one of the most important parameters in AlxGal_xAs. Hence, much attention has been focused recently [2-5] on the study of Eo in the range of low aluminum concentra- tion. Little work has been done, however, on the study of this parameter at x > 0.45 where the lowest band- gap is indirect [2-4]. In particular, to our knowledge, except for the photoluminescence work of Monemar [6], no data on the temperature variation of the direct bandgap have been reported for the compound AlAs. Also, the values of E o at room temperature reported for AlAs differ considerably [7]. This is mainly due to the fact that in an indirect gap material, especially in crystals containing high impurity concentrations, an accurate determination of the lowest direct gap is not easy because impurities cause a broadening of the exciton absorption, and the value of Eo obtained is not the real level in pure AlAs. Another reason for the lack of data is the hygroscopic nature of AlAs, which does not permit the preparation and preservation of good samples [7]. For the AlxGal_xAs alloys the discrepancies between values reported by different authors are mainly due to the reliability of different techniques employed to establish the "tl concentration in alloy samples. Since, for such a system, Eo is a function of both composition and temperature, an analytical expres- sion for Eo(x, T) is essential to interpret the data. Although theoretical analysis of the variation of Eo and x and T has not been reported in these alloys, such an empirical expression was recently proposed to calculate Eo(x, T) for the CuGaxlnl_xSe2 system in terms of the optical properties of the constituent compounds CulnSe2 and CuGaSe2 [8]. Such an ana- lysis is not possible for the AlxGal_xAs system because for AlAs the required parameters are not well known. However, if the interpolation scheme suggested by Adachi [9] is valid for estimating the physical properties of these alloys, the variation of the direct energy gap with temperature and composition in AlAs can be obtained from extrapolation of the corresponding values from AlxGal_xAs alloys. In this article, by analyzing the published data of the temperature variation of the direct energy gap in several alloys, the Eo(T ) curve for AlAs is proposed. Then, using an expression derived in ref. [8], the direct energy gap values for the AlxGal_~As system are calculated. 2. THEORY The variation of the energy gap with temperature in semiconductors is usually described by Varshni's equation, given by [11]: Eg(T) = Eg(0) - AT2/(T -]" fl), (1) * Address for correspondence: CES, Apartado de Correos where Eg (T) is the energy gap at temperature T, and A No. 1, La Hechicera, Merida 5251, Venezuela. and 3 are constants. 1111