Radiative and Auger processes in semiconductors

Abstract

Radiative and Auger processes are compared with the main emphasis on five points. 1. (1) It is shown semiempirically that the recombination coefficients for radiative and Auger processes take the form respectively of C r (α 0 a 0) 3/ t 0, C Aug a 0 6/ t 0, where the dimensionless numbers C r , C Aug lie between 1 and 10 10, α 01/137, a 0 is the Bohr radius and t 0 is an atomic unit of time. 2. (2) The method of calculating these coefficients is briefly reviewed, and it is pointed out that the ratios of the radiative to the Auger recombination rates for free-free, free-bound, and bound-bound transitions depend explicitly on the energy E bridged by an electron as E 7/2. (There are implicit dependences on E in addition.) 3. (3) A formal expression for the Auger recombination coefficient in terms of impact ionisation data, corresponding to the van Roosbroeck-Shockley relation is derived. 4. (4) Momentum conservation imposes a threshold energy for Auger and impact ionisation processes which is relaxed if impurities can take up appropriate momenta. This threshold is discussed. 5. (5) In the radiative case occurence of k-selection in relatively pure direct materials leads to lower threshold currents for lasing and to their slower temperature dependence ( T 3/2 instead of T 3). However, the lower density of states in the band tails of impure materials shift the advantage back to impure materials in which impurities take up momentum.