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

We present an interface scattering model to describe ballistic-electron-emi ssion microscopy (BEEM) at nonepitaxial metal/semiconductor interfaces. The model starts with a Hamiltonian consisting of the sum of two terms: one te rm, Ho, describes an ideal interface for which the interface parallel compo nent of wave vector is a good quantum number, and the second term, delta H, describes interfacial scattering centers. The eigenstates of Ho consist of an incident and a reflected part in the metal and a transmitted part in th e semiconductor. The three components of each eigenstate have the same inte rface parallel wave vector. Because tunneling preferentially weights forwar d-directed states, the interface parallel component of wave vector is small for the Ho eigenstates that are initially populated with high probability in BEEM. SH scatters electrons between the eigenstates of Ho. The scatterin g conserves energy, but not the interface parallel wave vector. In the fina l state of the scattering process, states with a large interface parallel w ave vector can be occupied with reasonable probability. If scattering is we ak, so that the parallel wave vector is nearly conserved, the calculated co llector current into conduction-band valleys with zero parallel wave vector at the minimum, such as the Gamma valley for GaAs(100), is much larger tha n the calculated collector current into conduction-band valleys with a larg e 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 weightin g varies as the density of final states for the scattering process so that, for example, the calculated L-channel collector current is much larger tha n the calculated Gamma-channel collector current for GaAs(100). Interfacial scattering reduces the overall magnitude of the calculated BEEM current ne ar threshold for GaAs. We generalize the model to describe buried heterostr uctures and apply it to the Au/GaAs(100) interface and GaAs/AlxGa1-xAs hete rostructures buried beneath this interface. Experimental results on these m aterials are presented and compared with the model. Strong scattering is re quired to describe the observed BEEM currents for Au/GaAs(100) and buried G aAs/AlxGa1-xAs heterostructures.