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Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating physical and mathematical systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is unfeasible or impossible to compute an exact result with a deterministic algorithm.
Learn more about quantum dots from the many resources on this site, listed below. More information on Monte Carlo method can be found here.
Multilevel Markov Chain Monte Carlo for Uncertainty Quantification in Subsurface Flow
04 Feb 2016 | | Contributor(s):: Christian Ketelsen
The multilevel Monte Carlo method has been shown to be an effective variance reduction technique for quantifying uncertainty in subsurface flow simulations when the random conductivity field can be represented by a simple prior distribution. In state-of-the-art subsurface simulation the...
High Dimensional Uncertainty Quantification via Multilevel Monte Carlo
04 Feb 2016 | | Contributor(s):: Hillary Fairbanks
Multilevel Monte Carlo (MLMC) has been shown to be a cost effective way to compute moments of desired quantities of interest in stochastic partial differential equations when the uncertainty in the data is high-dimensional. In this talk, we investigate the improved performance of MLMC versus...
Study of the Interface Roughness Models using 3D Finite Element Schrödinger Equation Corrected Monte Carlo Simulator on Nanoscaled FinFET
25 Jan 2016 | | Contributor(s):: Daniel Nagy, Muhammad Ali A. Elmessary, Manuel Aldegunde, Karol Kalna
IWCE 2015 presentation. Interface roughness scattering (IRS) is one of the key limiting scattering mechanism for both planar and non-planar CMOS devices. To predict the performance of future scaled devices and new structures the quantum mechanical confinement based IRS models are essential....
Sensitivity Analysis of Multiscale Reaction Networks with Stochastic Averaging
25 Jan 2016 | | Contributor(s):: Araz Ryan Hashemi
We shall show how stochastic averaging may be employed to speed computations and obtain estimates of mean values and sensitivities with respect to the steady state distribution. Further, we shall establish bounds which show the bias induced by the averaging method decays to zero as the disparity...
Anisotropic Schrödinger Equation Quantum Corrections for 3D Monte Carlo Simulations of Nanoscale Multigate Transistors
05 Jan 2016 | | Contributor(s):: Karol Kalna, Muhammad Ali A. Elmessary, Daniel Nagy, Manuel Aldegunde
IWCE 2015 presentation. We incorporated anisotropic 2D Schrodinger equation based quantum corrections (SEQC) that depends on valley orientation into a 3D Finite Element (FE) Monte Carlo (MC) simulation toolbox. The MC toolbox was tested against experimental ID-VG characteristics of the 22 nm gate...
Atomistic Modeling: Past, Present, and Future, MGI, ICME, etc.
03 Nov 2015 | | Contributor(s):: Paul Saxe
I will present a perspective on atomistic modeling — tools using quantum methods such as DFT, as well as molecular dynamics and Monte Carlo methods based on forcefields — over the past 30 years or so. While we are all caught up in the present, it is important to remember and realize...
Lecture 3: The Wigner Monte Carlo Method for Density Functional Theory
18 Nov 2014 | | Contributor(s):: Jean Michel D Sellier
In this lecture, Dr. Sellier discusses the Wigner Monte Carlo method in the framework of density functional theory (DFT).
ECE 695A Lecture 14a: Voltage Dependent HCI I
19 Feb 2013 | | Contributor(s):: Muhammad Alam
Outline:Background and Empirical ObservationsTheory of Hot Carriers: Hydrodynamic ModelTheory of Hot Carriers: Monte Carlo ModelTheory of Hot Carriers: Universal ScalingConclusionAppendices
ECE 695A Lecture 14b: Voltage Dependent HCI II
[Illinois] CSE Seminar Series: Advances in First-principles Computational Materials Science
20 Nov 2012 | | Contributor(s):: Elif Ertekin
Title: Advances in first-principles computational materials scienceSubtitle: Things we can calculate now, that we couldn't when I was in grad school.The capability to rationally design new materials with tailored properties and functionality on a computer remains a grand challenge whose success...
Particle Simulations of Ion Generation and Transport in Microelectromechanical Systems and Micropropulsion
29 May 2012 | | Contributor(s):: Venkattraman Ayyaswamy
The first part of the talk deals with use of the PIC method with Monte Carlo collisions (MCC) between electrons and the ambient neutral gas to develop models to predict charge accumulation, breakdown voltage, etc. for various ambient gases, gap sizes, cathode material, and frequency of applied...
ECE 656 Lecture 41: Transport in a Nutshell
21 Feb 2012 | | Contributor(s):: Mark Lundstrom
ECE 656 Lecture 34a: Monte Carlo Simulation I
OutlineIntroductionReview of carrier scatteringSimulating carrier trajectoriesFree flightCollisionUpdate after collisionPutting it all togetherSummary
ECE 656 Lecture 34b: Monte Carlo Simulation II
ECE 656 Lecture 32: Balance Equation Approach III
19 Jan 2012 | | Contributor(s):: Mark Lundstrom
Outline:Review of L31Carrier temperature and heat fluxHeterostructuresSummary
Discussion about Ion Channels Using Reduced Model Approaches
21 Sep 2011 | | Contributor(s):: James Fonseca
The seminar will cover the reasons how the channels are able to selectively permit the flow of certain species of ions while blocking other physiological cations.
ECE 656 Lecture 31: Monte Carlo Simulation
01 Dec 2009 | | Contributor(s):: Mark Lundstrom
Outline:IntroductionReview of carrier scatteringSimulating carrier trajectoriesFree flightCollisionUpdate after collisionPutting it all togetherSummary
ECE 656 Lecture 30: Balance Equation Approach III
OutlineCarrier Temperature and Heat FluxBalance equations in 3DHeterostructuresSummary
Illinois PHYS 466, Lecture 18: Kinetic Monte Carlo (KMC)
04 May 2009 | | Contributor(s):: David M. Ceperley, Omar N Sobh
Quantum and Thermal Effects in Nanoscale Devices
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18 Sep 2008 | | Contributor(s):: Dragica Vasileska
To investigate lattice heating within a Monte Carlo device simulation framework, we simultaneously solve the Boltzmann transport equation for the electrons, the 2D Poisson equation to get the self-consistent fields and the hydrodynamic equations for acoustic and optical phonons. The phonon...