Semiconductor EquationsSpringer, 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. |
المحتوى
Kinetic Transport Models for Semiconductors | 3 |
The Initial Value Problem | 9 |
Magnetic Fields | 16 |
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عبارات ومصطلحات مألوفة
approximation assume asymptotic analysis band Boltzmann equation boundary conditions boundary value problem Brillouin zone carrier densities classical computed consider constant continuity equation current density denotes density matrix depletion region derived differential equations dimensional diode doping concentration doping profile drift diffusion equations Eeff effects electric field electron ensemble given grad holds implies initial integral inversion J₁ lattice layer term linear Markowich mathematical MOSFET n₁ nonlinear number density obtain Ohmic contacts one-dimensional P-N junction p-region parameter particle Poisson equation position potential quantum Liouville equation quantum Vlasov equation recombination recombination-generation reduced problem reverse bias satisfies saturation scaled Schrödinger equation Section semi-classical semiconductor devices simulation singular perturbation solution solved space charge stationary thermal equilibrium tion U₁ unscaled V₁ variable vector velocity Vlasov equation voltage-current characteristic Wigner function x₁ zero ΘΩΝ μη