Tunneling between density-of-state tails: Theory and effect on Esaki diodes

Abstract

A model for tunneling between conduction and valence band tail states in semiconductors is developed. Localized, lifetime-broadened wave functions originally proposed by Vinogradov [Fiz. Tverd. Tela 13, 3266 (1971)] facilitate the derivation of the microscopic transition rate in a homogeneous electric field of arbitrary orientation. A compact analytical form of the average macroscopic tunnel generation rate is approximately calculated assuming that the Gaussian or exponential band tail represents a ladder of closely spaced single-level densities of states. A fully analytical form yields insight into key quantities like the effective tunnel barrier, the tunneling mass, and the pre-exponential factor in comparison to band-to-band tunneling. Tail-to-tail, tail-to-band, and band-to-band tunneling rates are compared against each other over a broad range of field strengths and characteristic tail energies. The numerical implementation of the model into a commercial device simulator accounts for the inhomogeneous field in pn-junctions and excludes invalid tunnel paths. In the application to a fully characterized InGaAs pin-Esaki diode, all physical processes and parameters that might affect the IV-characteristics are carefully investigated. The value of the bandgap of In0.53Ga0.47As as a function of density, doping, and temperature is revised. It is shown that tail-induced tunneling cannot explain the strong measured valley current of the diode. Besides band-to-band tunneling, zero- and multi-phonon defect-assisted tunneling are the physical mechanisms that allow to reproduce the entire forward characteristics. Whereas tail-to-band tunneling becomes only visible for very large values of the characteristic tail energy in the heavily doped regions, tail-to-tail tunneling remains a completely negligible process.