An investigation of steady-state velocity overshoot in silicon

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

“…It is well-known that a closure assumption is required in order to have a closed system of evolution equations. In the past, various closure assumptions have been made for the semiconductor transport moment systems, leading to various classes of hydrodynamical models, see e.g., [3][4][5]. However, these various closure assumptions are, at best, only phenomenological and often a consistent physical and mathematical justification is lacking.…”

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

“…If we compare our results with those obtained in [33], where the standard model [20,21] with relaxation times extracted from Monte Carlo data has been employed, one notes that qualitatively the numerical solutions are very similar. There is some quantitative difference in the peak of the energy, which is lower with our model, and the maximum values of the y-component of the velocity, which are lower in the model presented in [33].…”

“…The resulting model, which can be cast in the framework of extended thermodynamics [16,17] or equivalently of Levermore's moment theory [18], comprises balance equations of electron density, energy density, velocity, and energy flux, coupled to the Poisson equation for the electric potential. The presence of a balance equation for energy flux is at variance with the standard hydrodynamical models usually employed, which are based on Navier-Stokes-Fourier like equations [20,21]. Moreover, apart from the Poisson equation, the system is hyperbolic in the physically relevant region of the field variables.…”

Numerical Simulation of Transient Response in 3-D Multi-Channel Nanowire MOSFETs Submitted to Heavy Ion Irradiation

“…In short devices, steep variations of electric field take place in the active area of the devices. Then, nonstationary phenomena (such as velocity overshoot (Baccarani & Wordeman, 1985;Jacoboni & Reggiani, 1983) occur following these rapid spatial or temporal changes of high electric fields. In small devices, non-stationary phenomena play an important role and may dominate the device operation.…”