Effects of doping and free carriers on the refractive index of direct-gap semiconductors

A model for the doping and current dependence of the refractive index of direct-gap semiconductors has been developed and applied to GaAs in order to explain certain properties of single heterostructure injection lasers. The model involves the concept of an effective energy gap which takes account of the effects of doping and free carriers via the Burstein shift, the exchange interaction, and the average screened Coulomb potential of the impurities. This effective gap, together with empirical results for the energy dependence of the refractive index, facilitates the calculation of refractive index changes with doping and current. Numerical results are given for GaAs, and the model is applied particularly to the substrate and active regions of single heterostructure injection lasers. In these devices the refractive index values are particularly important in determining the dielectric waveguide properties. With the aid of our model, this feature can be discussed in detail, with special reference to the breakdown of the waveguide effect which occurs (a) for substrate doping levels below a critical value, and (b) for currents well above threshold ('saturation').