Approximate dependence of the spontaneous emission rate on electron and hole concentrations

The total spontaneous emission rate (R/sub sp/) is an important quantity, which is widely used in the particle rate equation of light-emitting diodes and semiconductor lasers. It is important to find the explicit dependence of R/sub sp/ on electron and hole concentrations. Such an approximate analytical expression is proposed both for two- and three-dimensional systems. Accuracy of the approximation is within 15% for undoped and 25% for doped semiconductors. Dependence of the relative error on the electron-hole concentrations and a quantitative comparison of the approximate, and exact expressions are illustrated.<
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