Hl. Grubin et al., DENSITY-MATRIX AND QUANTUM-MOMENT STUDIES OF SINGLE-BARRIER AND MULTIPLE-BARRIER STRUCTURES, Semiconductor science and technology, 7(3B), 1992, pp. 434-438
The time-dependent Liouville equation for the density matrix in the co
ordinate representation, incorporating scattering effects through a qu
asi-Fermi level, and Poisson's equation have been solved numerically f
or a single- and double-barrier structure using algorithms based on 'c
haracteristics', and show significant charge accumulation on the emitt
er side of the barrier, as well as significant charge screening in mul
tiple-barrier structures.