On the semiconductor laser logarithmic gain-current density relation

The simplified relation, α=G₀ In (η _iJ/J₀), between material gain α and current density J is shown to be a very good shape approximation, for quantum wells and bulk materials, essentially independent of the type of recombination processes present. Simulations show that for a given material system, G₀ decreases by only about 30% from pure electron-hole-recombination-dominated to pure Auger-recombination-dominated. A generic quantum-well situation is explored to reveal the density of states and recombination coefficient dependence of G₀ and to formulate simple estimates for G₀. The results were tested against published data for eight quantum-well diode lasers. The predicted values of G ₀ were generally found to be in agreement with experiments only for the wider gap diodes. The discrepancies were attributed in part to carrier induced absorption, and it is shown that the formalism can be modified in selected cases to incorporate this without changing the basic form of the gain. A new expression which relates the temperature dependence of the measured parameters to the characteristic temperature, T₀, is provided