Scattering theory of ballistic-electron-emission microscopy at nonepitaxial interfaces

Abstract

We present an interface scattering model to describe ballistic-electron-emission microscopy (BEEM) at nonepitaxial metal/semiconductor interfaces. The model starts with a Hamiltonian consisting of the sum of two terms: one term, ${H}_{0},$ describes an ideal interface for which the interface parallel component of wave vector is a good quantum number, and the second term, $\ensuremath{\delta}H,$ describes interfacial scattering centers. The eigenstates of ${H}_{0}$ consist of an incident and a reflected part in the metal and a transmitted part in the semiconductor. The three components of each eigenstate have the same interface parallel wave vector. Because tunneling preferentially weights forward-directed states, the interface parallel component of wave vector is small for the ${H}_{0}$ eigenstates that are initially populated with high probability in BEEM. $\ensuremath{\delta}H$ scatters electrons between the eigenstates of ${H}_{0}.$ The scattering conserves energy, but not the interface parallel wave vector. In the final state of the scattering process, states with a large interface parallel wave vector can be occupied with reasonable probability. If scattering is weak, so that the parallel wave vector is nearly conserved, the calculated collector current into conduction-band valleys with zero parallel wave vector at the minimum, such as the \ensuremath{\Gamma} valley for GaAs(100), is much larger than the calculated collector current into conduction-band valleys with a large parallel wave vector at the minimum, such as the L valleys for GaAs(100). However, if scattering is strong, the injected electron flux distribution is redistributed and valleys with zero interface transverse wave vector at their energy minimum are not preferentially weighted. Instead, the weighting varies as the density of final states for the scattering process so that, for example, the calculated L-channel collector current is much larger than the calculated \ensuremath{\Gamma}-channel collector current for GaAs(100). Interfacial scattering reduces the overall magnitude of the calculated BEEM current near threshold for GaAs. We generalize the model to describe buried heterostructures and apply it to the Au/GaAs(100) interface and ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures buried beneath this interface. Experimental results on these materials are presented and compared with the model. Strong scattering is required to describe the observed BEEM currents for Au/GaAs(100) and buried ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures.