Selective measurement of hole tunneling times through AlGaAs barriers based on the quantum confined Stark effect

Abstract

We demonstrate a method able to measure selectively and over a wide dynamic range the tunneling time of electrons or holes through a given potential barrier in a semiconductor heterostructure. The method relies on appropriate band gap engineering of the intrinsic region of a $p\text{\ensuremath{-}}i\text{\ensuremath{-}}n$ diode, and on the quantum confined Stark effect. As an example, the hole tunneling time through thick ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ potential barriers has been measured over six orders of magnitude in $\mathrm{In}\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ structures. For $x=0.6$, ultralong hole tunneling times are demonstrated in fair agreement with a semiclassical tunneling model. This model however turns out to be inapplicable for $x\ensuremath{\leqslant}0.4$, overestimating the tunneling times by several orders of magnitude. This suggests the formation of intrinsic leakage current paths through the AlGaAs barriers at these concentrations.