Wigner Function Approach

The Wigner function formalism has been introduced with an emphasis on basic theoretical aspects, and recently developed numerical approaches and applications for modeling and simulation of the transport of current carriers in electronic structures. Two alternative ways: the historical introduction of the function on top of the operator mechanics, and an independent formulation of the Wigner theory in phase space which then recovers the operator mechanics, demonstrate that the formalism provides an autonomous description of the quantum world.The conditions of carrier transport in nano-electronic devices impose to extend this coherent physical picture by processes of interaction with the environment. Relevant becomes the Wigner-Boltzmann equation, derived for the case of interaction with phonons and impurities. The numerical aspects focus on two particle models developed to solve this equation. These models make the analogy between classical and Wigner transport pictures even closer: particles are merely classical, the only characteristics which carries the quantum information is a dimensionless quantity affinity or sign.The recent ground-breaking applications of the affinity method for simulation of typical nano-devices as the resonant tunneling diode and the ultra-short DG-MOSFET firmly establish the Wigner-Boltzmann equation as a bridge between coherent and semi-classical transport pictures. It became a basic route to understand the nano-device operation as an interplay between coherent and de-coherence phenomena. The latter, due to the environment: phonon field, contacts or defects, attempts to recover the classical transport picture.