While in bulk ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As there is some agreement that persistent photoconductivity (PPC) is related to the photoionization of deep levels that have a recombination barrier, a diverse collection of models has been proposed to explain the interplay between macroscopic (band bending and tunneling) and microscopic (deep levels) contributions to PPC and related phenomena in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures. One of these related effects is transient photoconductivity (TPC) whereby the PPC-enhanced carrier density (or conductivity) undergoes a long-term decay. In this work a model based on phonon-assisted tunneling through a realistic barrier is developed for TPC, and predictions for the apparent capture energies and lifetime prefactors are presented. The model self-consistently accounts for the changes in the conduction-band profile and tunneling barrier due to the transfer of charge during this process. By using the derivative of conductivity or carrier number density with respect to the logarithm of time during decay, e.g., dN/d(lnt), phonon-assisted tunneling may be identified from other PPC-associated decay mechanisms in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures. This method of analysis is applied to experimental data showing TPC decay of carrier density and conductivity. The DX-center capture energies obtained from phonon-assisted-tunneling data in this work agree with results from other direct-capture studies.

• Received 27 June 1988

DOI:https://doi.org/10.1103/PhysRevB.39.13276