Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices

Abstract

Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric field domains, pinning or propagation of domain walls, self-sustained oscillations of the current and chaos. Theories of these effects use reduced descriptions of transport in terms of average charge densities, electric fields, etc. This is simpler when the main transport mechanism is resonant tunnelling of electrons between adjacent wells followed by fast scattering between subbands. In this case, we will derive microscopically appropriate discrete models and boundary conditions. Their analyses reveal differences between low-field behaviour where domain walls may move oppositely or parallel to electrons, and high-field behaviour where they can only follow the electron flow. The dynamics is controlled by the amount of charge available in the superlattice and doping at the injecting contact. When the charge inside the wells becomes large, boundaries between electric field domains are pinned resulting in multistable stationary solutions. Lower charge inside the wells results in self-sustained oscillations of the current due to recycling and motion of domain walls, which are formed by charge monopoles (high contact doping) or dipoles (low contact doping). Besides explaining wave motion and subsequent current oscillations, we will show how the latter depend on such controlling parameters as voltage, doping, temperature, and photoexcitation.

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

“…This is a typical boundary condition that yields Gunn type self-sustained oscillations of the current in drift-diffusion SL models [17,18,22,23]. …”

Self-Sustained Spin-Polarized Current Oscillations in Multiquantum Well Structures

“…. , N − 1, provided that scattering-induced broadening of energy levels is much smaller than sub-band energies and chemical potentials [17,18]. The spin-dependent 'forward tunneling velocity' v ( f )± is a sum of Lorentzians of width 2γ (the same value for all sub-bands, for simplicity) centered at the resonant field values…”

Miniband transport and oscillations in semiconductor superlattices

“…The second term accounts for impurity elastic collisions with frequency ν i . Equation (2) is the Poisson equation and equation (3) relates electron density with exact and FD distribution functions, thereby preserving charge continuity as in the BGK model [12]. Equation (4) is the 1D Fermi-Dirac model, (5) is the tight-binding dispersion relation and (6) is the group velocity.…”