Aa. Grinberg, APPROXIMATE DEPENDENCE OF THE SPONTANEOUS EMISSION RATE ON ELECTRON AND HOLE CONCENTRATIONS, IEEE journal of quantum electronics, 30(5), 1994, pp. 1151-1155
The total spontaneous emission rate (R(sp)) is an important quantity,
which is widely used in the particle rate equation of light-emitting d
iodes and semiconductor lasers. It is important to find the explicit d
ependence of R(sp) on electron and hole concentrations. Such an approx
imate analytical expression is proposed both for two- and three-dimens
ional 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.