Electron-impurity tunneling in selectively doped n-type ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs heterostructures

The interaction of the two-dimensional electron gas at the semiconductor interface of a selectively doped n-type ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs heterostructure grown by molecular-beam epitaxy with empty impurity levels in the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As layer is investigated both experimentally and theoretically. The electron subband energy levels in the triangular potential well of the heterostructure are calculated by a new method and are in excellent agreement with other approaches. The calculation of the electron-impurity tunneling process is based on a square-well potential shape to obtain solutions in an analytic and not in a numerical form. For experimental investigations we used time-resolved Hall effect and conductivity measurements combined with excitation by monochromatic illumination of the sample. The decay of the carrier concentration after illumination is monitored for more than 3 days at temperatures ranging from 20 to 150 K and is conclusively found to be nonexponential. Extrapolation of the decay to the dark concentration yields a total lifetime of photoconductivity of more than ${10}^{12}$ s at T<eq77 K. The optical threshold energies of 0.95<${\mathrm{eqE}}_{\mathrm{do}<\mathrm{eq}1.10}$ eV for persistent photoconductivity coincides with the values for transient photoconductivity. This result demonstrates that both parts of the photoconductivity are caused by the same deep Si donor in the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As layer. The relative contributions to persistent photoconductivity of electron excitation from the deep Si donor in the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As layer as well as electron-hole generation in the GaAs layer are determined for a specific alloy composition of ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As. Electron-hole generation in the GaAs layer contributes only a minor part to the observed persistent photoconductivity of the heterostructure for alloy compositions x>eq0.3.