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The quantum hydrodynamic model for semiconductor devices. (English) Zbl 0815.35111
The article under review deals with the quantum hydrodynamic (QHD) equations for the charge transport simulation in quantum semiconductor devices. It is well-known that the behaviour of quantum fluid near thermal equilibrium and in the high temperature limit can be approximated by adding $${\mathcal O} (\hbar^ 2)$$ terms to the classical fluid dynamical equations. These corrections are derived by the author by means of a moment expansion of the Wigner-Boltzmann equation. The corresponding energy density and stress tensor are of the form: $W = {3 \over 2} nT + {1 \over 2} mnu^ 2 - {\hbar^ 2n \over 24m} \nabla^ 2 \log (n) + {\mathcal O} (\hbar^ 4)$ $P_{ij} = - nT \delta_{ij} + {\hbar^ 2n \over 12m} {\partial^ 2 \over \partial x_ i \partial x_ j} \log (n) + {\mathcal O} (\hbar^ 4)$ where $$m$$ and $$n$$ are the electron mass and density respectively, $$u$$ is the particle velocity, $$T$$ is the temperature.
Simulations of a resonant tunneling diode are also represented in the paper. The computed current-voltage characteristics agree quantitatively with experimental results.
Reviewer: I.E.Tralle (Minsk)

##### MSC:
 35Q60 PDEs in connection with optics and electromagnetic theory 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 35Q40 PDEs in connection with quantum mechanics 82C70 Transport processes in time-dependent statistical mechanics
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