Semi-empirical descriptions of temperature dependences of band gaps in semiconductors

• Published in: Physica Status Solidi (b) Vol. 236; no. 3; pp. 710 - 728
• Main Author: Passler, R
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01-04-2003; WILEY‐VCH Verlag; Wiley
• Subjects: 71.20.Mq; 71.20.Nr; 71.35.-y; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron density of states and band structure of crystalline solids; Electron states; Elemental semiconductors; Exact sciences and technology; Physics; Semiconductor compounds; Temperature dependence; Gallium arsenides; Inorganic compounds; Semiconductor materials; Quantum dots; Luminescence; Self consistency; Theoretical study; Binary compounds; Energy gap; Phonon dispersion; Silicon; Semiempirical method; Least square fit
• ISSN: 0370-1972; 1521-3951
• DOI: 10.1002/pssb.200301752

Starting from general foundations of the semi‐empirical theory of monotonic temperature dependences of band gaps in semiconductors, we devote ourselves in this article to further analytical development and applications of the power function model. On the basis of a detailed analytical study of asymptotic low and high temperature behaviors, including numerical comparisons for intermediate temperatures, we devise a novel analytical (higher order root) expression. Applications to least‐mean‐square fittings of fundamental band gap data available for a variety of group IV, III–V, and II–VI materials are shown to provide, both for regimes of moderate and large phonon dispersion, self‐consistent values for basic dispersion‐related parameters. This is essential for detailed comparisons of the power function model with other elaborate semi‐empirical models developed in last years, which differ above all by qualitatively different types of low temperature asymptotes. An exemplification for bulk samples of Si and GaAs shows that it is rather difficult to distinguish clearly between T → 0 asymptotes, [E(0) – E(T)] ∝ T p, that are controlled by system‐specific fractional exponents (2 < p < 3) and other dispersion‐related descriptions that admit exclusively quadratic asymptotes (p = 2). Novel high‐precision data for single quantum dot luminescence peak positions are found to give us better chances for distinguishing between qualitatively different types of low temperature asymptotes.