Impurity States in Semiconducting Masers

A formalism is developed for computing negative conductivities for inverted populations involving impurity states in semiconductors. General expressions are obtained for three classes of systems: class (1), transitions between states belonging to the same band edge; class (2), direct transitions between states belonging to two different band edges; and class (3), indirect transitions between states belonging to two different band edges. The expressions for negative conductivities are simplified by using the effective mass approximation. The results are then applied to an example of each of the three classes of processes. Class (2) is represented by a model of the GaAs diode laser. It is concluded for this model that at low temperatures, with an acceptor concentration Na∼1018/cc, and an effective acceptor radius of a∼20 Å, population inversion of donor states relative to acceptor states yields a greater negative conductivity than inversion of donor states relative to the valence band. A brief discussion is presented of the threshold conditions for diode lasers.