Monte Carlo investigation of drift and diffusion in semiconductor superlattices in the Wannier-Stark regime

The high-field behavior of the drift velocity and diffusion coefficient in a SL have been investigated within a Wannier- Stark approach. To this purpose, an ensemble Monte Carlo simulator has been implemented. The drift velocity is found to exhibit a NDM behavior followed by a minimum and a smooth increase coupled with dips and peaks associated with quantum transport effects such as resonance between adjacent wells and intersubband transitions. The longitudinal difusion coefficient is found to exhibit a two-regime behavior. In the NDC region, the diffusion is well described by a generalized Einstein relation which accounts for a fielddependent mobility and diffusivity. In the highest field region, where the drift velocity and the diffusion coefficient start increasing again with the electric field, the results of the simulations are only qualitatively described by an existing WS-hopping model, which is found to represent a too simple model for the system considered here. Remarkably, the superlattice period L is found to represent an intrinsic size parameter for the structure which dominates the behavior of diffusion at high fields. This parameter is replaced, in the case of a more realistic model coupling beyond nearest neighbor and many bands by an effective parameter L*L that can be interpreted as a “mean hopping distance.” In particular, the crossover between the Einstein and the hopping description of diffusion is determined by the condition L*=LE. In the NDM region of low electric fields, the very good agreement between the Einstein relation and the results of the simulation is confirmed by the value of the effective noise temperature, whose negative room-temperature value makes it sensible to refer to the NDM region as an “anti- Ohmic” region. In this region, the application of a semiclassical approach to transport is justified. We want to stress that, in contrast with bulk materials, in SL we predict the possibility of an increase of both drift and diffusion at the highest fields because of the increased efficiency of hopping to further sites. In any case, the values of both drift and diffusion in SLs remain significantly smaller for about three orders of magnitude than those of bulk materials. An experimental validation of the results presented here can profit from the noise conductivity method20 at frequencies high enough to get rid of 1/ f excess noise and/or of the four-wave mixing method as detailed elsewhere.