Electrical model of the injection laser

The simplest electrical model of the injection laser assumes that the active layer, the layer in which spontaneous and stimulated radiative recombination take place, is a homogeneous layer. The only parameters of such an electrical model are the thickness of the active layer, and the electron and hole concentrations and quasi-Fermi levels. If such a model is combined with an optical model with no -selection rule, one obtains reasonable agreement with experimental threshold current densities, particularly if energy band tails are taken into account. The theory, however, predicts a superlinear relation between gain constant and current density near room temperature, while the observed relation is linear. An alternative electrical model by Pikus assumes that the quasi-Fermi levels of electrons and holes are constant in the active layer. This model, when combined with an optical model having a -selection rule, gives a strong superlinear dependence of gain on current and is therefore also in disagreement with experiment. A realistic electrical model of the injection laser requires a knowledge of the impurity concentration at each point and solution of the equations governing the motion of electrons and holes. We are carrying out such calculations, using a method of solution developed by J. W. Cooley and G. Hachtel. Preliminary results show that at room temperature the spontaneous emission rate and the stimulated emission rate may have substantially different spatial dependences. The calculations will give information about the effect of different impurity profiles on injection laser performance and on the effect of different current densities on the electron and hole distributions. A detailed account of this work Will be submitted for publication later.