Particle Monte Carlo simulation of quantum phenomena in semiconductor nanostructures

Quantum effects in semiconductor devices are usually described in terms of wave functions obtained from the solution of the Schrödinger equation. However, it is difficult to simulate practical devices where clear semiclassical and quantum features coexist, as is the case for nanoscale devices at normal temperatures. We present here a particle description of quantum phenomena derived starting from Wigner's transport formalism, where the dynamics of particles are treated semiclassically, but with an effective force added to account for quantum effects. The resulting model is solved by using a particle Monte Carlo approach, which we apply to describe transport across a single tunneling barrier. Results of the numerical calculations indicate that size quantization and tunneling effects can be well resolved by the combined Monte Carlo/quantum force approach, yielding quantitative agreement with Schrödinger equation results.