Direct Solution Methods for Kinetic Semiconductor Equations

The intention of this project is to create new deterministic methods to solve the Boltzmann transport equations applicable to the mesoscopic system of semiconductor devices in highly integrated circuits. The methods will be based on a partition of the phase space into small cells combined with a representation of the distribution functions in terms of appropriate shape functions in these cells. According to the idea of weighted residuals, the correct balance of a macroscopic quantity can be ensured by choosing a suitable weight function. The first tests have shown that this procedure is faster than Monte Carlo codes and the results are noise-free and agree with measurements. The method is applicable to transient regimes and arbitrary dimensions in real and momentum space. We will break new ground by incorporating the real band structure and all the relevant interaction mechanisms into our transport equations as, for instance, carrier-trap-phonon interactions and carrier-carrier interactions to simulate bipolar transport accurately. This will be achieved by extending our methods to scattering events characterized by two incoming and two outgoing particles within a collision event. Furthermore, we will be able to investigate high field effects and break down phenomena in MOSFETs or other devices, which require the incorporation of carrier-carrier interactions. We will also clarify the influence of minor interaction terms in addition to the dominant scattering mechanism on the dynamics of the coupled Boltzmann-Poisson system. Another topic of special interest is the simulation of low-dimensional systems, in which the electrons and holes are strongly affected by quantum wells at heterojunctions. Typical examples are the modulation doped III-V FETs or high-mobility transistors. Our procedures will allow for a consistent description of degeneracy effects and hot phonon phenomena in modern HFETs. We emphasize that our methods will include a dynamic adaptation of the used time-space resolution regarding the appearing spatio-temporal changes. High order WENO schemes will enable us to work with coarse grids. Moreover, streamline diffusion finite element procedures and characteristic methods will by applied. Based on our experience, we feel confident that our direct solution methods for the Boltzmann transport equations, which govern the dynamics of carriers and phonons in semiconductors, will be a very powerful tool for device simulation.

The intention of this project is to create new deterministic methods to solve the Boltzmann transport equations applicable to the mesoscopic system of semiconductor devices in highly integrated circuits. The methods will be based on a partition of the phase space into small cells combined with a representation of the distribution functions in terms of appropriate shape functions in these cells. According to the idea of weighted residuals, the correct balance of a macroscopic quantity can be ensured by choosing a suitable weight function. The first tests have shown that this procedure is faster than Monte Carlo codes and the results are noise-free and agree with measurements. The method is applicable to transient regimes and arbitrary dimensions in real and momentum space. We will break new ground by incorporating the real band structure and all the relevant interaction mechanisms into our transport equations as, for instance, carrier-trap-phonon interactions and carrier-carrier interactions to simulate bipolar transport accurately. This will be achieved by extending our methods to scattering events characterized by two incoming and two outgoing particles within a collision event. Furthermore, we will be able to investigate high field effects and break down phenomena in MOSFETs or other devices, which require the incorporation of carrier-carrier interactions. We will also clarify the influence of minor interaction terms in addition to the dominant scattering mechanism on the dynamics of the coupled Boltzmann-Poisson system. Another topic of special interest is the simulation of low-dimensional systems, in which the electrons and holes are strongly affected by quantum wells at heterojunctions. Typical examples are the modulation doped III-V FETs or high-mobility transistors. Our procedures will allow for a consistent description of degeneracy effects and hot phonon phenomena in modern HFETs. We emphasize that our methods will include a dynamic adaptation of the used time-space resolution regarding the appearing spatio-temporal changes. High order WENO schemes will enable us to work with coarse grids. Moreover, streamline diffusion finite element procedures and characteristic methods will by applied. Based on our experience, we feel confident that our direct solution methods for the Boltzmann transport equations, which govern the dynamics of carriers and phonons in semiconductors, will be a very powerful tool for device simulation.