Non-perturbative macroscopic theory of interfaces with discontinuous dielectric constant
Discontinuity of dielectric constants at the interface is a common feature of all nanostructures and semiconductor heterostructures. Near such interfaces, a charged particle creates a singular self-interaction potential which may be attributed to interaction with fictitious mirror charges. The singularity of this interaction at the interface presents an obstruction to a perturbative approach. In several limiting cases, this problem can be avoided by zeroing out the carrier wave function at the interface. In this paper, we have developed a non-perturbative theory which gives a self-consistent description of carrier propagation through an interface with a dielectric discontinuity. It is based on conservation of the current density propagating through the interface, and it is formulated in terms of general boundary conditions (GBC) for the wave function at the interface with a single phenomenological parameter W. For these GBC, we find exact solutions of the Schrödinger equation near the interface and the carrier energy spectrum including resonances. Using these results, we describe the photo effect at the semiconductor/vacuum interface and the energy spectrum of quantum wells (QWs) at the interface with the vacuum or a high-k dielectric. For a surface of liquid helium, we estimate the parameter W, and match the resulting electron spectrum with the existing experimental data and theoretical analysis.