Limit cycle in a bound exciton recombination model in non-equilibrium semiconductors

Abstract

A non-equilibrium semiconductor model involving the processes of photogeneration of electron-hole pairs ( e- h) (rate G), stimulated creation of excitons from e- h (rate constant C) and decay of excitons on recombination centres (rate constant k) is analyzed in this paper for steady states and limit cycle behaviour. Considering the exciton decay to be similar to enzymatic processes in chemical reactions obeying a Michaelis-Menten law, and choosing units such that k = 1 = N, where N is the concentration of recombination centres, the model represents a 2-parameter ( C and G) 2-dimensional (exciton and electron-hole concentrations x, n) dynamical system with a unique steady state ( x 0, n 0) which is unstable in the region ( l − G) 3⩾4 C, the equality sign corresponding to the bifurcation curve in parameter space. In the region ( l − G) 3 > 4 C the system displays a unique stable limit cycle which is obtained in analytical form by employing a two-time-scales method for parameters in the neighbourhood of the bifurcation curve. The limit cycles are tilted ellipses with angular frequency \\ ̄ gw of the order of 10 6 s −1. In a realistic semiconductor situation G $ ̃ 10 −3.