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On steady-state carrier distributions in semiconductor devices. (English) Zbl 0621.35047

The object of the paper is to prove the existence of a solution of van Roosbroeck’s system of partial differential equations for the transport of mobile charge carriers in spatially homogeneous semiconductor devices under some general conditions. The physically important ones are: (i) The relation between the carrier densities and the chemical potential is general, where the Fermi-Dirac statistics is a special case, (ii) carrier mobilities may depend on the gradient of the corresponding electrochemical potential, apart from the electrical field. The existence of a solution is proved via Schauder’s fixed point theorem. With further restrictions that the driving forces for flows vanish at the boundary, it is shown that the flows vanish throughout the device for the unique steady-state solution.
Reviewer: N.D.Sengupta

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
78A35 Motion of charged particles
82C70 Transport processes in time-dependent statistical mechanics
78A55 Technical applications of optics and electromagnetic theory
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:

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