Multistability of conductance in doped semiconductor superlattices

Abstract

We use a simple nonlinear Kronig-Penney model to study multistability and discontinuity in the currentvoltage characteristics of doped semiconductor superlattices in a homogeneous electric field. Nonlinearity in our model enters through a self-consistent potential used to describe the interaction of the effective electrons with charge accumulation in the doped layers. We show that the process of Wannier-Stark localization is slowed down by the nonlinear effect in the doped layers, and that the shrinking and destruction of minibands in the superlattice by the nonlinearity is related to the occurrence of discontinuity and multistability in the transport of electrons.The electric-field-induced Stark-ladder effect, WannierStark (WS) localization, and the electro-optical properties and device applications in the semiconductor superlattices (SL), such as GaAs-A1, 6ai,As, have been studied extensively in recent years.Quantum effects become significant in such systems because the electron wavelength is of the same order as the superlattice constant. Recently, there has been renewed interest in the study of multistability and discontinuity in the current-voltage (I V) chara-cteristic of doped semiconductor superlattices, both theoretically ' and experimentally.The charge domain theory for multistability is based on the idea that the charges of the carriers cannot move continuously as the biased voltage is increased; instead, they accumulate in one well for a certain time and, for larger fields, move spontaneously to the next well. Microscopic theories so far have not been able to take a complete account of the quantum mechanical wave nature of the carriers.As a step toward the direction of considering the wave nature of the carriers, we propose a simple quantum mechanical model based on self-consistent potentials, and study the transport of ballistic electrons in terms of transmissions of quantum mechanical waves in a SL heterostructure. We neglect the scattering of the waves by impurities and phonons. Our emphasis here is not to build a complete model that takes everything into account, but rather gain an insight into the nature of electronic wave coherence and interferences by considering the interwell coupling and the interactions of an electron with a self-consistent potential, while neglecting scattering and other effects. By solving a tunneling and transmission problem for the electrons in the quantum well (QW) heterostructure, we avoid making the usual assumption of strong barriers and weak interwell coupling.We demonstrate that multistability and discontinuity in the transport of carriers are related to the shrinking and destruction of the miniband structure by the nonlinearity in the doped layers. We assume, for simplicity, that the longitudinal and transverse degrees of freedom are decoupled, thus resulting in an effectively one-dimensional problem. The interaction of an electron with charge accumulation in a doped layer is represented by a nonlinear term, that is seen to arise from a self-consistent potential i...

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