Информационная система "Конференции"

Вычислительные и информационные технологии в науке, технике и образовании

Усть-Каменогорск, Казахстан, 11-14 сентября 2003 года

Тезисы докладов

Асимптотическая устойчивость состояния равновесия для моментных уравнений переноса заряда в случае "длинного" полупроводника

Блохин А.М., Бушманов Р.С.

Институт Математики СО РАН (Новосибирск),
Новосибирский государственный университет (Новосибирск)

Modelling modern submicron electron devices requires an accurate description of energy transport in order to cope with high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. These phenomena cannot be described satisfactorily within the framework of the drift-diffusion equations and the simplest hydrodynamic models.

As known in the hierarchy of approximate macroscopic models beyond the drift-diffusion equations one finds the hydrodynamical models which are obtained from the infinite set of moment equations of the Boltzmann Transport Equation (BTE) by a suitable truncation procedure. It is well-known too that moment systems require a closure assumption in order to lead to closed system of evolution equations. In [1] by using the maximum entropy ansatz for the closure one obtains explicit constitutive relations for the stress tensor and the flux of energy flux tensor.

One dimensional problem for the model proposed in [1,2] is considered. This problem describes a bulk semiconductor, in other words we suppose that the doping density is uniform.

The dynamics of the charge carriers depends on the applied potential (the bias voltage). When the applied voltage is negligible one expect that the situation of global thermodynamical equilibrium is reached: the charge are at rest with the same temperature of the crystal.

The stability of the equilibrium state in an essential condition to be satisfied for any model. Usually for the models described by means of hyperbolic systems the previous property is investigated by constructing an appropriate entropy function. However in our case is not easy to get an explicit form of the entropy and a special analysis is required.

Using the technique of a priori estimates it is proved in the linear approximation that for the model under consideration the equilibrium solution is asymptotically stable in the sense of Lyapunov.

[1] Anile A.M., Romano V. Non parabolic band transport in semiconductors: closure of the moment equations// Cont. Mech. Thermodyn. 1999. Vol. 11
[2] Romano V. Non parabolic band transport in semiconductors: closure of the production terms in the moment equations// Cont. Mech. Thermodyn. 2000. Vol. 12.

Примечание. Тезисы докладов публикуются в авторской редакции

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