Particle Model of the Scattering-Induced Wigner Function Correction M. Nedjalkov 1,2 , P. Schwaha 1 , O. Baumgartner 1 , and S. Selberherr 1 1 Institute for Microelectronics, TU Wien Gußhausstraße 27-29/E360, A-1040 Vienna, Austria 2 Institute for Parallel Processing, Bulgarian Academy of Sciences Acad. G.Bontchev, Bl 25A, 1113 Sofia, Bulgaria Abstract. The ability of accounting for quantum-coherent and phase- breaking processes is a major feature of the Wigner transport formalism. However, the coherent case is only obtained at significant numerical costs. Therefore, a scheme which uses coherent data obtained with a Green’s function formalism has been developed. This scheme calculates the nec- essary corrections due to scattering using the Wigner approach and the associated Boltzmann collision models. The resulting evolution problem is not only theoretically derived, but simulation results are presented as well. 1 Introduction Modeling and simulation of electronic devices is a part of science where knowl- edge of mathematics, physics, and electrical engineering is required simultane- ously to design, analyze, and optimize these core components of the integral circuits. For the semiconductor industry it appears as the only alternative to the enormously expensive trial-and-error manufacturing approach. By means of device modeling and simulation the physical characteristics of semiconductor de- vices are explored in terms of charge transport and electrical behavior [2]. The progress in this field depends on the level of complexity of the transport models and the application of efficient numerical and programming techniques. Physics provides a hierarchy of charge transport models summarized in Table 1. The ongoing miniaturization of devices forces the use of ever more sophisticated models to be able to capture all relevant effects and correctly calculate device be- havior. The sophistication of the models, which increases from the bottom to the top is also characterized by an increase of the numerical complexity. The analyt- ical models utilized during the infancy of microelectronics for circuit design were replaced by more rigorous drift-diffusion and hydrodynamic formulations, based on the moments of the Boltzmann equation. As these can be solved only numeri- cally, corresponding deterministic methods have been developed. When microelectronic devices enter the sub-micrometer scale, the moment equations fail, while the Boltzmann equation remains relevant. The Boltzmann equation provides a detailed classical picture of carrier evolution, where phys- ical probability functions are associated with the various processes describing I. Lirkov, S. Margenov, and J. Wa´ sniewski (Eds.): LSSC 2009, LNCS 5910, pp. 411–418, 2010. c  Springer-Verlag Berlin Heidelberg 2010