Springer, 07/06/1990 - 248 من الصفحات
In recent years the mathematical modeling of charge transport in semi conductors has become a thriving area in applied mathematics. The drift diffusion equations, which constitute the most popular model for the simula tion of the electrical behavior of semiconductor devices, are by now mathe matically quite well understood. As a consequence numerical methods have been developed, which allow for reasonably efficient computer simulations in many cases of practical relevance. Nowadays, research on the drift diffu sion model is of a highly specialized nature. It concentrates on the explora tion of possibly more efficient discretization methods (e.g. mixed finite elements, streamline diffusion), on the improvement of the performance of nonlinear iteration and linear equation solvers, and on three dimensional applications. The ongoing miniaturization of semiconductor devices has prompted a shift of the focus of the modeling research lately, since the drift diffusion model does not account well for charge transport in ultra integrated devices. Extensions of the drift diffusion model (so called hydrodynamic models) are under investigation for the modeling of hot electron effects in submicron MOS-transistors, and supercomputer technology has made it possible to employ kinetic models (semiclassical Boltzmann-Poisson and Wigner Poisson equations) for the simulation of certain highly integrated devices.
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CollisionsThe Boltzmann Equation
The Relaxation Time Approximation
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analysis applied approximation assume assumption asymptotic band bias boundary conditions bounded called carrier Chapter characteristic charge classical close collision computed concentration consider constant continuity corresponding current density defined denotes density depends depletion region derived determined device diode discussed doping drift diffusion equations effects electric field electron energy ensemble equilibrium existence expansion field function given gives grad holds implies initial integral introduced inversion layer leads limit linear mathematical means methods Note obtain one-dimensional operator P-N junction p-region parameter particle perturbation physical position potential presented problem quantum Liouville equation quantum mechanical reads reduced refer relation respect reverse satisfies scaled semiconductor semiconductor devices simulation solution solved space steady takes tion transformation transport value problem variable vector Vlasov equation voltage wave zero