Effect of nonequilibrium deep donors in heterostructure modeling

The deep donors (DX centers) which supply carriers in many GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructures are known to be metastable at low temperatures, maintaining a nonequilibrium state because of a microscopic barrier to recombination if ionized. Earlier modeling by three of us [Kumar, Laux, and Stern, Phys. Rev. B 42, 5166 (1990)] incorrectly assumed the donors in the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As to be in equilibrium with the electrons in the GaAs channel. We present data on the threshold voltage of heterostructures cooled under bias and results of calculations which assume that the deep donor charge is locked at the value attained at 100 K when the sample is cooled with a bias voltage applied. The revised calculations account for part of the discrepancy between the calculated threshold voltage for the quantum dot structure used in experiments by Hansen et al. [Phys. Rev. Lett. 62, 2168 (1989)] and the observed value. Part of the remaining discrepancy may be due to processing damage.