A hydrodynamic model for silicon semiconductors including crystal heating

2015 ◽  
Vol 26 (4) ◽  
pp. 477-496 ◽  
Author(s):  
GIOVANNI MASCALI
Keyword(s):  
Transition Rate ◽  
Evolution Equations ◽  
Kinetic Equations ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Macroscopic Model ◽  
State Variables ◽  
Silicon Devices ◽  
Electron Distributions ◽  
Entropy Principle

We present a macroscopic model for describing the electrical and thermal behaviour of silicon devices. The model makes use of a set of macroscopic state variables for phonons and electrons that are moments of their respective distribution functions. The evolution equations for these variables are obtained starting from the Bloch–Boltzmann–Peierls kinetic equations for the phonon and the electron distributions, and are closed by means of the maximum entropy principle. All the main interactions between electrons and phonons, the scattering of electrons with impurities, as well as the scattering of phonons among themselves are considered. In particular, we propose a treatment of the optical phonon decay directly based on the expression of its transition rate (Klemens 1966Phys. Rev.148 845; Aksamija & Ravaioli 2010Appl. Phys. Lett.96, 091911). As an application of the model, we evaluate the silicon thermopower.

A new stochastic analysis method for mechanical components

2012 ◽  
Vol 227 (8) ◽  
pp. 1818-1829 ◽  
Author(s):  
YL Zhang ◽  
YM Zhang
Keyword(s):  
Finite Element ◽  
Dimension Reduction ◽  
Probability Density ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Entropy Principle ◽  
Input Variables ◽  
First Four Moments

Univariate dimension-reduction integration, maximum entropy principle, and finite element method are employed to present a computational procedure for estimating probability densities and distributions of stochastic responses of structures. The proposed procedure can be described as follows: 1. Choose input variables and corresponding distributions. 2. Calculate the integration points and perform finite element analysis. 3. Calculate the first four moments of structural responses by univariate dimension-reduction integration. 4. Estimate probability density function and cumulative distribution function of responses by maximum entropy principle. Numerical integration formulas are obtained for non-normal distributions. The non-normal input variables need not to be transformed into equivalent normal ones. Three numerical examples involving explicit performance functions and solid mechanic problems without explicit performance functions are used to illustrate the proposed procedure. Accuracy and efficiency of the proposed procedure are demonstrated by comparisons of the estimated probability density functions and cumulative distribution functions obtained by maximum entropy principle and Monte Carlo simulation.

Maximum entropy principle and classical evolution equations with source terms

2007 ◽  
Vol 374 (2) ◽  
pp. 573-584 ◽  
Author(s):  
J-H. Schönfeldt ◽  
N. Jimenez ◽  
A.R. Plastino ◽  
A. Plastino ◽  
M. Casas
Keyword(s):  
Maximum Entropy ◽  
Evolution Equations ◽  
Maximum Entropy Principle ◽  
Source Terms ◽  
Entropy Principle ◽  
Classical Evolution

Maximum Entropy Principle for Lattice Kinetic Equations

1998 ◽  
Vol 81 (1) ◽  
pp. 6-9 ◽  
Author(s):  
Iliya V. Karlin ◽  
Alexander N. Gorban ◽  
S. Succi ◽  
V. Boffi
Keyword(s):  
Maximum Entropy ◽  
Kinetic Equations ◽  
Maximum Entropy Principle ◽  
Entropy Principle

Statistical Mechanics and Information Theory for Complex Systems

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Complex Processes ◽  
Entropy Principle ◽  
Path Dependent ◽  
Statistical Systems ◽  
Dependent Processes

Most complex systems are statistical systems. Statsitical mechanics and information theory usually do not apply to complex systems because the latter break the assumptions of ergodicity, independence, and multinomial statistics. We show that it is possible to generalize the frameworks of statistical mechanics and information theory in a meaningful way, such that they become useful for understanding the statistics of complex systems.We clarify that the notion of entropy for complex systems is strongly dependent on the context where it is used, and differs if it is used as an extensive quantity, a measure of information, or as a tool for statistical inference. We show this explicitly for simple path-dependent complex processes such as Polya urn processes, and sample space reducing processes.We also show it is possible to generalize the maximum entropy principle to path-dependent processes and how this can be used to compute timedependent distribution functions of history dependent processes.

Continuum equations in the dynamics of rarefied gases

1959 ◽  
Vol 6 (4) ◽  
pp. 523-541 ◽  
Author(s):  
Max Krook
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Gas Dynamics ◽  
Kinetic Equations ◽  
Distribution Functions ◽  
State Variables ◽  
Moment Equations ◽  
Characteristic Temperatures ◽  
Equivalent Continuum ◽  
The Continuum

A procedure is given for translating boundary-value problems of gas dynamics from microscopic form into approximately equivalent continuum form. The continuum formulations involve state-variables that are either half-space moments, or complete moments of the molecular distribution functions. Moment equations derived from the kinetic equations are reduced to a determinate set by representing the distribution functions as sums of ‘modified Maxwellian functions based on various characteristic temperatures and velocities’. The particular choice of such a representation depends on the Knudsen number and on the nature of the microscopic boundary conditions.

scholarly journals A hierarchy of hydrodynamic models for silicon carbide semiconductors

2017 ◽  
Vol 8 (1) ◽  
pp. 251-264
Author(s):  
Orazio Muscato ◽  
Vincenza Di Stefano
Keyword(s):  
Silicon Carbide ◽  
Hydrodynamic Model ◽  
Energy Transport ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Maximum Entropy Principle ◽  
Hydrodynamic Models ◽  
Drift Diffusion ◽  
Transport Models ◽  
Entropy Principle

Abstract The electro-thermal transport in silicon carbide semiconductors can be described by an extended hydrodynamic model, obtained by taking moments from kinetic equations, and using the Maximum Entropy Principle. By performing appropriate scaling, one can obtain reduced transport models such as the Energy transport and the drift-diffusion ones, where the transport coefficients are explicitly determined.

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