Direct determination of the electron-tunneling escape time from a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well by transient-capacitance spectroscopy

We show that the tunnel emission of electrons out of a single quantum well into an ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As conduction band under a perpendicular electric field can be observed by transient-capacitance spectroscopy in the 0.1–100-ms time range. This has been made possible by the use of a semiconductor-insulator-semiconductor-type structure where the GaAs space-charge probe region is separated from the quantum well by a thin ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As barrier. The variation of the tunneling time with applied electric field is in good agreement with a simple Fowler-Nordheim model. The absolute values of the tunneling time are, however, significantly different from the expected theoretical values. The origin of this discrepancy is briefly discussed.