AN ANALYTIC APPROXIMATION WITH A WIDE-RANGE OF APPLICABILITY FOR BAND-TO-BAND RADIATIVE TRANSITION RATES IN DIRECT, NARROW-GAP SEMICONDUCTORS

Good approximations for the radiative transition rates, conduction ban d to heavy-hole band and conduction band to light-hole band, which are continuous over a wide range of temperature and electron and hole Fer mi levels (degenerate and non-degenerate) and in which photon multipli cation may be included, are developed for direct gap III-V semiconduct ors. They are based on the band structure and wavefunctions of the sim ple isotropic three-band approximation to Kane's band structure and de pend solely on the effective masses at the zone centre, the energy gap and the dielectric constant. They are compared with more accurate cal culations based on the diagonalization of the 8 x 8 Ic p matrix of the four-band model with higher and lower bands taken into account by per turbation theory. Application to In1-xAlxSb (0.0 < x < 0.25) and CdxHg 1-xTe (0.17 < x < 0.26) shows that over the whole range of materials, Fermi levels (-0.25 to 0.40 eV) and temperatures (80-400 K) the agreem ent is never worse than 20% and usually considerably better. Results a re given in detail for InSb and Cd0.2188Hg0.7812Te. It is also shown t hat in degenerate material, when the penetration of the hole Fermi lev el into the valence band is greater than that of the electron Fermi le vel into the conduction band, the transition rate to the light-hole ba nd can exceed that to the heavy-hole band. These approximations are em inently suitable for use in modelling semiconductor effects and device s.