Special CPM Seminar

Charge Transport in a Super-lattice -
A semi-classical model and numerical simulation using moment methods

Yossi Farjoun

MIT

A super-lattice is an artificial, one-dimensional lattice created by alternatively depositing two semiconductors with similar lattice constants and different band-structure. The resulting macroscopic behavior has been seen to produce Gunn-effect type oscillations due to the appearance of a domain with negative electron mobility (as the field increases, the velocity of the electrons decreases). In specific range of parameters choices, this leads to self-sustained current oscillations (in the GHz range) when a potential difference is placed across the sample.

Precise numerical simulations of a model that contains enough terms is difficult since it is nonlinear has hyperbolic (charge transport), elliptic (the Poisson equation), and non-local terms (collisions between k and -k electrons). We present a new approach to the problem using “Moment methods”. This approach is especially relevant in this case since the first three moment end up having a real physical meaning. The method also exhibits spectral convergence in the number of moments thus reduces the computational cost significantly. It allows us to explore the parameter space and find interesting new phenomena, for example evidence of a sub-critical bifurcation in the vicinity of the critical potential and a rapidly oscillating solution that is stable in an overlapping region with the “normal” Gunn-effect solution.