3D full hydrodynamic model for semiconductor optoelectronic devices: stability of thermal equilibrium states. (English) Zbl 1542.35380
Summary: In this paper, we study a three-dimensional full hydrodynamic model in a bounded domain with insulating and adiabatic boundary. The model takes the form of nonisentropic Euler-Poisson system and incorporates recombination/generation terms, describing the bipolar transport of hot carriers in semiconductor optoelectronic devices. Of particular concern are the existence, uniqueness and exponential stability of thermal equilibrium states to the model, since these mathematical results are rendered useful in numerical simulation and physical theory of semiconductors. They are rigorously proved by the perturbation argument and energy method.
MSC:
| 35Q81 | PDEs in connection with semiconductor devices |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35Q20 | Boltzmann equations |
| 82D37 | Statistical mechanics of semiconductors |
| 78A35 | Motion of charged particles |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B35 | Stability in context of PDEs |
| 35J61 | Semilinear elliptic equations |
| 35M33 | Initial-boundary value problems for mixed-type systems of PDEs |
Keywords:
semiconductor bipolar transport; recombination-generation phenomenon; nonisentropic Euler-Poisson system; Poisson-Boltzmann equation; perturbation argument; energy estimatesReferences:
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