Theory of spatially inhomogneous Bloch oscillations in semiconductor superlattices

TL;DR

This paper develops a Boltzmann-Poisson model to analyze inhomogeneous Bloch oscillations in semiconductor superlattices, revealing conditions for their stability and coexistence with other oscillatory phenomena.

Contribution

It introduces a new hydrodynamic framework for inelastic collisions in superlattices, demonstrating persistent inhomogeneous Bloch oscillations under specific parameters.

Findings

Stable inhomogeneous Bloch oscillations occur at long scattering times.

Oscillations vanish when scattering times are short.

Coexistence of Bloch and Gunn oscillations at low temperatures.

Abstract

In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. To demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions is proposed and hydrodynamic equations for electron density, electric field and the complex amplitude of the Bloch oscillations are derived by singular perturbation methods. For appropriate parameter ranges, numerical solutions of these equations show stable Bloch oscillations with spatially inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short. For sufficiently low lattice temperatures, Bloch and Gunn type oscillations mediated by electric field, current and energy domains coexist for a range of voltages. For larger lattice temperatures (300 K), there are only Bloch oscillations with stationary amplitude and electric field profiles.