scholarly journals A Hydrodynamic Model for Transport in Semiconductors without Free Parameters

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 527-532 ◽  
Author(s):  
P. Falsaperla ◽  
M. Trovato
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Maximum Principle ◽  
Energy Flux ◽  
Hydrodynamic Model ◽  
Entropy Maximum ◽  
Monte Carlo Computation ◽  
Submicron Devices ◽  
Stress Energy ◽  
Free Parameters

We derive, using the Entropy Maximum Principle, an expression for the distribution function of carriers as a function of a set of macroscopic quantities (density, velocity, energy, deviatoric stress, energy flux). Given the distribution function, we obtain, for these macroscopic quantities, a hydrodynamic model in which all the constitutive functions (fluxes and collisional productions) are explicitely computed starting from their kinetic expressions. We have applied our model to the simulation of some onedimensional submicron devices in a temperature range of 77–300 K, obtaining results comparable with Monte Carlo. Computation times are of order of few seconds for a picosecond of simulation.

scholarly journals How Many Monte Carlo Simulations Does One Need to Do? II. Lognormal, Binomial, Cauchy, and Exponential Distributions

2005 ◽  
Vol 23 (6) ◽  
pp. 429-461
Author(s):  
Ian Lerche ◽  
Brett S. Mudford
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Probability Distribution ◽  
General Procedure ◽  
Mean Value ◽  
Distribution Functions ◽  
Considerable Uncertainty ◽  
Free Parameters ◽  
Two Parameters ◽  
Achievable Accuracy

This article derives an estimation procedure to evaluate how many Monte Carlo realisations need to be done in order to achieve prescribed accuracies in the estimated mean value and also in the cumulative probabilities of achieving values greater than, or less than, a particular value as the chosen particular value is allowed to vary. In addition, by inverting the argument and asking what the accuracies are that result for a prescribed number of Monte Carlo realisations, one can assess the computer time that would be involved should one choose to carry out the Monte Carlo realisations. The arguments and numerical illustrations are carried though in detail for the four distributions of lognormal, binomial, Cauchy, and exponential. The procedure is valid for any choice of distribution function. The general method given in Lerche and Mudford (2005) is not merely a coincidence owing to the nature of the Gaussian distribution but is of universal validity. This article provides (in the Appendices) the general procedure for obtaining equivalent results for any distribution and shows quantitatively how the procedure operates for the four specific distributions. The methodology is therefore available for any choice of probability distribution function. Some distributions have more than two parameters that are needed to define precisely the distribution. Estimates of mean value and standard error around the mean only allow determination of two parameters for each distribution. Thus any distribution with more than two parameters has degrees of freedom that either have to be constrained from other information or that are unknown and so can be freely specified. That fluidity in such distributions allows a similar fluidity in the estimates of the number of Monte Carlo realisations needed to achieve prescribed accuracies as well as providing fluidity in the estimates of achievable accuracy for a prescribed number of Monte Carlo realisations. Without some way to control the free parameters in such distributions one will, presumably, always have such dynamic uncertainties. Even when the free parameters are known precisely, there is still considerable uncertainty in determining the number of Monte Carlo realisations needed to achieve prescribed accuracies, and in the accuracies achievable with a prescribed number of Monte Carol realisations because of the different functional forms of probability distribution that can be invoked from which one chooses the Monte Carlo realisations. Without knowledge of the underlying distribution functions that are appropriate to use for a given problem, presumably the choices one makes for numerical implementation of the basic logic procedure will bias the estimates of achievable accuracy and estimated number of Monte Carlo realisations one should undertake. The cautionary note, which is the main point of this article, and which is exhibited sharply with numerical illustrations, is that one must clearly specify precisely what distributions one is using and precisely what free parameter values one has chosen (and why the choices were made) in assessing the accuracy achievable and the number of Monte Carlo realisations needed with such choices. Without such available information it is not a very useful exercise to undertake Monte Carlo realisations because other investigations, using other distributions and with other values of available free parameters, will arrive at very different conclusions.

A generalized hydrodynamic model capable of incorporating Monte Carlo results (LDD MOS devices)

2003 ◽  
Author(s):  
R. Thoma ◽  
A. Emunds ◽  
B. Meinerzhagen ◽  
H. Peifer ◽  
W.L. Engl
Keyword(s):  
Monte Carlo ◽  
Hydrodynamic Model ◽  
Mos Devices

CAT III Autoland Control Laws Design Based on Multi-Objective Optimization

2012 ◽  
Vol 452-453 ◽  
pp. 548-552 ◽  
Author(s):  
Hui Jie Li ◽  
Ling Yu Yang ◽  
Gong Zhang Shen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Multi Objective Optimization ◽  
Control Laws ◽  
Multi Objective ◽  
Automatic Landing ◽  
Simulation Results ◽  
Free Parameters ◽  
Structure Measurement ◽  
Landing Control

The CAT III longitudinal automatic landing control laws based on multi-objective optimization is discussed. Firstly summarized the CAT III airworthiness criteria and transformed into the specifications of control system. The configuration of the longitudinal automatic landing controllers is proposed secondly and multi-objective optimization is used to tradeoff free parameters of the controllers. The Monte Carlo simulation results show the designed control laws fulfill the CAT III requirements, when there are uncertainties of structure, measurement error and disturbances.

Oxygen Vacancy Distribution and Electron Localization on Nanocube CeO2(100)

2021 ◽  
Author(s):  
Weihua Ji ◽  
Na Wang ◽  
Qiang Li ◽  
He Zhu ◽  
Kun Lin ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Pair Distribution Function ◽  
Oxygen Vacancies ◽  
Electron Localization ◽  
Reverse Monte Carlo ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair ◽  
Vacancy Distribution ◽  
Neutron Total Scattering

In this work, the oxygen vacancies distribution in the 5nm CeO2 nanocubes was determined by Reverse Monte Carlo (RMC) simulations for the neutron total scattering atomic pair distribution function (PDF)...

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