TABLE OF CONTENTS At room temperature the electrical characteristics of nanoelectronic and highly down-scaled microelectronic devices are influenced simultaneously by semiclassical and quantum mechanical effects. A kinetic equation suitable for describing this mixed transport regime is given by the Wigner equation. This equation can be formulated in such a way that it simplifies to the semiclassical Boltzmann equation in those device regions where quantum effects are negligible. The MC method has proven to be a reliable and accurate numerical method for solving the Boltzmann equation. Therefore, it appears very promising to devise MC techniques also for the solution of the Wigner equation. The advantage of a particle method is that semiclassical scattering from various sources can be included in a straightforward way. The major problem to be overcome originates from the scattering kernel of the Wigner equation, which is, as opposed to the semiclassical case, no longer positive.
A solution to this so-called negative-sign problem is presented in the following for the stationary case [31].
We consider the space-dependent Wigner equation, including semiclassical scattering via the Boltzmann collision operator Q[ f w]
The classical force term q E is separated from the Wigner potential [32]
and thus appears in the Liouville operator on the left-hand side of (140). The kinetic equation (140) has now the form of a Boltzmann equation with an additional term caused by the Wigner potential. Whether the collision operator or the potential operator is dominant depends on the device under consideration.
