The approaches described so far solve BOLTZMANN's transport equation, but do not take quantum effects into account. These effects can be incorporated by several methods: Coupling a SCHRÖDINGER-POISSON solver to BOLTZMANN's transport equation, solving WIGNER's equation, accounting for quantum effects in simulations, or applying the non-equilibrium GREEN's function2.8 formalism.
A. Gehring: Simulation of Tunneling in Semiconductor Devices