A quasi-particle model of the electron–Wigner potential interaction

The Wigner equation was used for the calculation of carrier transport in mesoscopic devices. The carrier transport has a coherent part determined by the Wigner potential Vw and a dissipative part accounting for the interaction with phonons. Models have been developed which solve the equation by using quasi-particles evolving over pieces of classical Newton trajectories. In a backward evolution approach [1], the interaction with the Wigner potential is interpreted as a scattering process. The quantum information is carried by the particle weight. In the ensemble model proposed in [2], the quantum information from Vw is included by the particle affinity. Both weight and affinity are artificial numerical quantities. We propose a model which interprets the Wigner equation with a Boltzmann scattering term as a Boltzmann equation with a generation term. The quantum information is carried by the sign of the quasi-particles. In all other aspects quasi-particles behave as classical particles. The sign has a physical meaning since particles of opposite sign can annihilate. The model ensures a seamless transition between classical and quantum regions. Negative values of the Wigner function are explained in a direct way.