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Classical solutions of drift-diffusion equations for semiconductor devices: The two-dimensional case. (English) Zbl 1167.35390
Summary: We regard drift-diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes. This evolution equation falls into a class of quasi-linear parabolic systems which allow unique, local in time solution in certain Lebesgue spaces. In particular, it turns out that the divergence of the electron and hole currents is an integrable function. Hence, Gauss’ theorem applies, and gives the foundation for space discretization of the equations by means of finite volume schemes. Moreover, the strong differentiability of the electron and hole density in time is constitutive for the implicit time discretization scheme. Finite volume discretization of space, and implicit time discretization are accepted custom in engineering and scientific computing. This investigation puts special emphasis on non-smooth spatial domains, mixed boundary conditions, and heterogeneous material compositions, as required in electronic device simulation.

MSC:
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35R05 PDEs with low regular coefficients and/or low regular data
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
78A35 Motion of charged particles
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