Monte Carlo Modeling of Heat Generation in Electronic Nanostructures

2002 ◽  
Author(s):  
Eric Pop ◽  
Sanjiv Sinha ◽  
Kenneth E. Goodson
Keyword(s):  
Monte Carlo ◽  
Electric Field ◽  
Heat Generation ◽  
Microscopic Analysis ◽  
Simulation Method ◽  
Transfer Rates ◽  
Scattering Rate ◽  
Energy Dependent ◽  
Non Equilibrium ◽  
Mc Method

This work develops a Monte Carlo (MC) simulation method for calculating the heat generation rate in electronic nanostructures. Electrons accelerated by the electric field scatter strongly with optical phonons, yet heat transport in silicon occurs via the faster acoustic modes. The MC method incorporates the appropriate energy transfer rates from electrons to each phonon branch. This accounts for the non-equilibrium energy exchange between the electrons and phonon branches. Using the MC method with an electron energy-dependent scattering rate intrinsically accounts for the non-locality of the heat transfer near a strongly peaked electric field. This approach provides more information about electronically generated heat at nanoscale dimensions compared to traditional macroscopic field-dependent methods. The method has applications in any region of high spatial or temporal non-equilibrium between electrons and phonons, and particularly facilitates careful microscopic analysis of heating in a nanoscale transistor.

scholarly journals Monte Carlo Simulation for Economic Analysis of Hydropower Pumped Storage Project in Nepal

2013 ◽  
Vol 12 ◽  
pp. 39-44 ◽  
Author(s):  
Kaspar Vereide ◽  
Leif Lia ◽  
Laras Ødegård
Keyword(s):  
Monte Carlo ◽  
Economic Analysis ◽  
Net Present Value ◽  
Simulation Method ◽  
Construction Costs ◽  
Energy And Environment ◽  
Pumped Storage ◽  
High Degree ◽  
Mc Method

Investments in hydropower pumped storage projects (PSP) are subjected to a high degree of uncertainty. In addition to normal uncertainties in hydropower schemes, the profit of a pumped storage scheme is dependent on the margin between power prices for buying and selling, which is difficult to predict without a power purchase agreement (PPA). A PSP without a PPA and without known construction costs requires quantification of the uncertainties in order to make qualified decisions before investing in such projects. This article demonstrates the advantages of using Monte Carlo (MC) simulations as a tool in the economic analysis of PSPs. The method has been tested on a case study, namely the Tamakoshi-3 Hydropower Project (HPP) in Nepal. The MC method is used to calculate the probability distribution of the net present value of installing reversible units in the Tamakoshi-3 HPP. The calculations show that PSPs may be profitable in Nepal, given a beneficial development of the power market. The MC method is considered to be a useful tool for economic analysis of PSPs. In this case study of installing reversible units in the Tamakoshi-3 HPP, there are many uncertainties, which the MC simulation method is able to quantify. Hydro Nepal; Journal of Water, Energy and Environment Vol. 12, 2013, January Page: 39-44DOI: http://dx.doi.org/10.3126/hn.v12i0.9031 Uploaded Date : 10/29/2013

Detailed Phonon Generation Simulations via the Monte Carlo Method

2003 ◽  
Author(s):  
Eric Pop ◽  
Sanjiv Sinha ◽  
Kenneth E. Goodson
Keyword(s):  
Monte Carlo ◽  
Electric Field ◽  
Heat Generation ◽  
Energy Exchange ◽  
Phonon Mode ◽  
Field Region ◽  
The Monte Carlo Method ◽  
Phonon Generation ◽  
Mc Simulation ◽  
Non Locality

Modeling heat generation at nanometer scales in silicon is of great interest and particularly relevant to the heating and reliability of nanoscale and thin-film transistors. Joule heating is usually simulated as the dot product of the macroscopic electric field and current density [1]. This approach does not account for the microscopic non-locality of the phonon emission near a strongly peaked electric field region. It also does not differentiate between electron energy exchange with the various phonon branches and does not give any information regarding the types of phonons emitted. The present work addresses both of these issues: we use a detailed Monte Carlo (MC) simulation to compute sub-continuum and phonon mode-specific heat generation rates, with applications at nanometer length scales.

X-ray Microanalysis of a Coated Nonconductive Specimen: Monte Carlo Simulation

2004 ◽  
Vol 10 (6) ◽  
pp. 776-782 ◽  
Author(s):  
Hendrix Demers ◽  
Raynald Gauvin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Electric Field ◽  
Charge Density ◽  
Depth Distribution ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
X Ray ◽  
A Charge ◽  
Scanning Electron

The microanalysis of nonconductive specimen in a scanning electron microscope is limited by charging effects. Using a charge density model for the electric field buildup in a nonconductive specimen irradiated by electrons, a Monte Carlo simulation method has been applied to alumina (Al2O3). The results show a change in the depth distribution for characteristic and bremsstrahlung X-ray, φ(ρz) curves, and ψ(ρz) curves (with absorption) for both elements' Kα lines. The influence of the electric field on the measured X-ray intensity is shown. The dependency of this influence by the three parameters, electron energy, X-ray energy, and charge density, is clarified.

A Semi-Analytical Interpretation of Transient Electron Transport in Gallium Nitride, Indium Nitride, and Aluminum Nitride

1998 ◽  
Vol 512 ◽  
Author(s):  
B. E. Foutz ◽  
S. K. O'Leary ◽  
M. S. Shur ◽  
L. F. Eastman
Keyword(s):  
Monte Carlo ◽  
Gallium Nitride ◽  
Electric Field ◽  
Aluminum Nitride ◽  
Monte Carlo Simulations ◽  
Field Effect Transistors ◽  
Indium Nitride ◽  
Relaxation Times ◽  
Transient Effects ◽  
Energy Dependent

ABSTRACTThe energy dependent momentum and energy relaxation times, and the effective single valley energy dependent effective mass, are extracted from Monte Carlo simulations of gallium nitride, indium nitride, and aluminum nitride. A simple semi-analytical energy model, which uses these dependencies, is in good agreement with the results of transient Monte Carlo simulations. Both the Monte Carlo and the semi-analytical simulations show that the overshoot effects are most pronounced when the electric field abruptly changes from a value below a critical field to one above. This is attributed to the relatively large difference between the effective energy and momentum relaxation times for such a variation of electric field. Our calculations indicate that gallium nitride and indium nitride should have the most pronounced transient effects. A calculation of the transit times as a function of the gate length shows that an upper bound for the maximum expected cut-off frequencies are 260 GHz and 440 GHz for 0.2 μm gallium nitride and indium nitride field effect transistors, respectively.

Monte Carlo Calculation of Hole Transport in Bulk Zincblende Phase of GaN including a Pseudopotential Calculated Band Structure

1995 ◽  
Vol 395 ◽  
Author(s):  
I. H. Oguzman ◽  
J. Kolnik ◽  
K.F. Brennan ◽  
R. Wang ◽  
P. P. Ruden
Keyword(s):  
Monte Carlo ◽  
Electric Field ◽  
Drift Velocity ◽  
Monte Carlo Calculation ◽  
Average Energy ◽  
Hole Transport ◽  
Ensemble Monte Carlo ◽  
Scattering Rate ◽  
Valence Bands ◽  
Field Strengths

ABSTRACTIn this paper, we present ensemble Monte Carlo based calculations of the steady state hole transport properties, i.e. average energy, drift velocity, and band occupancy of zincblende GaN. The Monte Carlo calculation includes the full details of the valence bands and a numerically determined scattering rate derived from an empirical pseudopotential calculation. Calculations are made for electric field strengths up to 1000 kV/cm. It is found that the average hole energies are much lower than the corresponding electron energies at comparable electric field strengths, and that some anisotropy in the drift velocity and average energy appears at the higher fields examined here.

scholarly journals Monte Carlo Investigations of Non-Equilibrium Effects at High Values of E/p in Swarm Experiments in Hydrogen

1970 ◽  
Vol 23 (5) ◽  
pp. 847 ◽  
Author(s):  
MA Folkard ◽  
SC Haydon
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Electric Field ◽  
Constant Electric Field ◽  
Monte Carlo Computer Simulation ◽  
Spatial Growth ◽  
Non Equilibrium

The results of a Monte Carlo computer simulation of the properties of electrons in a gas at pressure p sUbjected to a constant electric field E are presented for E /p = 350 V cm -1 torr-1 in hydrogen. Evidence is provided that the spatial growth of ionization is essentially non-equilibrium in these circumstances and that the general form of the predicted growth of currents is consistent with experiment.

QMC integration errors and quasi-asymptotics

2020 ◽  
Vol 26 (3) ◽  
pp. 171-176
Author(s):  
Ilya M. Sobol ◽  
Boris V. Shukhman
Keyword(s):  
Monte Carlo ◽  
Error Estimate ◽  
Numerical Experiments ◽  
Probable Error ◽  
Quasi Monte Carlo ◽  
Integration Error ◽  
Asymptotic Error ◽  
Dimensional Cube ◽  
Integration Errors ◽  
Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

scholarly journals Uncertainty Cost Functions in Climate-Dependent Controllable Loads in Commercial Environments

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2885
Author(s):  
Daniel Losada ◽  
Ameena Al-Sumaiti ◽  
Sergio Rivera
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Method ◽  
Electricity Sector ◽  
Cost Functions ◽  
Density Estimator ◽  
Monte Carlo Simulation Method ◽  
Commercial Building ◽  
Complementary Method ◽  
The Cost

This article presents the development, simulation and validation of the uncertainty cost functions for a commercial building with climate-dependent controllable loads, located in Florida, USA. For its development, statistical data on the energy consumption of the building in 2016 were used, along with the deployment of kernel density estimator to characterize its probabilistic behavior. For validation of the uncertainty cost functions, the Monte-Carlo simulation method was used to make comparisons between the analytical results and the results obtained by the method. The cost functions found differential errors of less than 1%, compared to the Monte-Carlo simulation method. With this, there is an analytical approach to the uncertainty costs of the building that can be used in the development of optimal energy dispatches, as well as a complementary method for the probabilistic characterization of the stochastic behavior of agents in the electricity sector.

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