Validity of the relation between spontaneous and stimulated emissions in semiconductors

ABSTRACT Validity of the relation between spontaneous emission and stimulated emission (or gain) in a semiconductor isrevisited. It is shown that this relation, while exact for the case of zero-linewidth, is in general not valid for all thecommonly used lineshapes at low excitation levels. At high excitation levels well beyond the transparency density, the validity is almost exact for the Gauss- and Sech-lineshapes. Even at high excitation level, this relation is still not valid for the Lorentzian lineshape. The convoluted Lorentzian lineshape, for which the relation between stimulated and spontaneous emissions is exactly valid, is shown to allow an effective lineshape function which can be expressedexplicitly in terms of elementary functions. 1. INTRODUCTION Spontaneous emission, absorption, and stimulated emission are the most fundamental physical processes in radiation- matter interacting systems. The Einstein relations between the A and B's coefficients established the fundamentallinks among these processes. These relations were originally derived in a simple situation where a thermal photonfield and an ensemble of two state atoms are in thermal equilibrium.1 For solid states and semiconductors inparticular, similar to, or generalization of, these relations were studied2-5 where states of materials are continuumand where scatterings with other subsystems (such as phonons and defects) are important. Most notable were the