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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.
Atomistic Simulations of Reliability
06 Jul 2010 | Contributor(s):: Dragica Vasileska
Discrete impurity effects in terms of their statistical variations in number and position in the inversion and depletion region of a MOSFET, as the gate length is aggressively scaled, have recently been researched as a major cause of reliability degradation observed in intra-die and die-to-die...
Band Structure Lab: First-Time User Guide
15 Jun 2009 | | Contributor(s):: Abhijeet Paul, Benjamin P Haley, Gerhard Klimeck
This document provides useful information about Band Structure Lab. First-time users will find basic ideas about the physics behind the tool such as band formation, the Hamiltonian description, and other aspects. Additionally, we provide explanations of the input settings and the results of the...
Bulk Monte Carlo Code Described
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01 Jul 2008 | | Contributor(s):: Dragica Vasileska
In this tutorial we give implementation details for the bulk Monte Carlo code for calculating the electron drift velocity, velocity-field characteristics and average carrier energy in bulk GaAs materials. Identical concepts with minor details apply to the development of a bulk Monte Carlo code...
Bulk Monte Carlo: Implementation Details and Source Codes Download
01 Jun 2010 | | Contributor(s):: Dragica Vasileska, Stephen M. Goodnick
The Ensemble Monte Carlo technique has been used now for over 30 years as a numerical method to simulate nonequilibrium transport in semiconductor materials and devices, and has been the subject of numerous books and reviews. In application to transport problems, a random walk is generated to...
Computational Nanoscience, Homework Assignment 4: Hard-Sphere Monte Carlo and Ising Model
05 Mar 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
In this assignment, you will explore the use of Monte Carlo techniques to look at (1) hard-sphere systems and (2) Ising model of the ferromagnetic-paramagnetic phase transition in two-dimensions. This assignment is to be completed following lecture 12 and using the "Hard Sphere Monte Carlo" and...
Computational Nanoscience, Lecture 10: Brief Review, Kinetic Monte Carlo, and Random Numbers
25 Feb 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
We conclude our discussion of Monte Carlo methods with a brief review of the concepts covered in the three previous lectures. Then, the Kinetic Monte Carlo method is introduced, including discussions of Transition State Theory and basic KMC algorithms. A simulation of vacancy-mediated diffusion...
Computational Nanoscience, Lecture 20: Quantum Monte Carlo, part I
15 May 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
This lecture provides and introduction to Quantum Monte Carlo methods. We review the concept of electron correlation and introduce Variational Monte Carlo methods as an approach to going beyond the mean field approximation. We describe briefly the Slater-Jastrow expansion of the wavefunction,...
Computational Nanoscience, Lecture 21: Quantum Monte Carlo, part II
15 May 2008 | | Contributor(s):: Jeffrey C Grossman, Elif Ertekin
This is our second lecture in a series on Quantum Monte Carlo methods. We describe the Diffusion Monte Carlo approach here, in which the approximation to the solution is not restricted by choice of a functional form for the wavefunction. The DMC approach is explained, and the fixed node...
Computational Nanoscience, Lecture 27: Simulating Water and Examples in Computational Biology
16 May 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
In this lecture, we describe the challenges in simulating water and introduce both explicit and implicit approaches. We also briefly describe protein structure, the Levinthal paradox, and simulations of proteins and protein structure using First Principles approaches and Monte Carlo...
Computational Nanoscience, Lecture 4: Geometry Optimization and Seeing What You're Doing
13 Feb 2008 | | Contributor(s):: Jeffrey C Grossman, Elif Ertekin
In this lecture, we discuss various methods for finding the ground state structure of a given system by minimizing its energy. Derivative and non-derivative methods are discussed, as well as the importance of the starting guess and how to find or generate good initial structures. We also briefly...
Computational Nanoscience, Lecture 7: Monte Carlo Simulation Part I
15 Feb 2008 | | Contributor(s):: Jeffrey C Grossman, Elif Ertekin
The purpose of this lecture is to introduce Monte Carlo methods as a form of stochastic simulation. Some introductory examples of Monte Carlo methods are given, and a basic introduction to relevant concepts in statistical mechanics is presented. Students will be introduced to the Metropolis...
Computational Nanoscience, Lecture 8: Monte Carlo Simulation Part II
14 Feb 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
In this lecture, we continue our discussion of Monte Carlo simulation. Examples from Hard Sphere Monte Carlo simulations based on the Metropolis algorithm and from Grand Canonical Monte Carlo simulations of fullerene growth on spherical surfaces are presented. A discussion of meaningful...
Computational Nanoscience, Lecture 9: Hard-Sphere Monte Carlo In-Class Simulation
19 Feb 2008 | | Contributor(s):: Elif Ertekin, Jeffrey C Grossman
In this lecture we carry out simulations in-class, with guidance from the instructors. We use the HSMC tool (within the nanoHUB simulation toolkit for this course). The hard sphere system is one of the simplest systems which exhibits an order-disorder phase transition, which we will explore with...
From Semi-Classical to Quantum Transport Modeling: Particle-Based Device Simulations
09 Aug 2009 | | Contributor(s):: Dragica Vasileska
This set of powerpoint slides series provides insight on what are the tools available for modeling devices that behave either classically or quantum-mechanically. An in-depth description is provided to the approaches with emphasis on the advantages and disadvantages of each approach. Conclusions...
Generalized Monte Carlo Presentation
17 Jun 2011 | | Contributor(s):: Dragica Vasileska
This presentation goes along with the Bulk Monte Carlo tool on the nanoHUB that calculates transients and steady-state velocity-field characteristics of arbitrary materials such as Si, Ge, GaAs, GaN, SiC, etc. The tool employs a non-parabolic bandstructure.
High Field Transport and the Monte Carlo Method for the Solution of the Boltzmann Transport Equation
21 Jul 2010 | | Contributor(s):: Dragica Vasileska
This set of slides first describes the path-integral solution of the BTE and then discusses in details the Monte Carlo Method for the Solution of the Boltzmann Transport Equation.
Homework Assignment for Bulk Monte Carlo Lab: Arbitrary Crystallographic Direction
20 Aug 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
This exercise teaches the users how the average carrier velocity, average carrier energy and vally occupation change with the application of the electric field in arbitrary crystalographic direction
Homework Assignment for Bulk Monte Carlo Lab: Velocity vs. Field for Arbitrary Crystallographic Orientations
21 Aug 2008 | | Contributor(s):: Dragica Vasileska, Gerhard Klimeck
User needs to calculate and compare to experiment the velocity field characteristics for electrons in Si for different crystalographic directions and 77K and 300K temperatures.
Homework for Monte Carlo Method: High field transport in Bulk Si
06 Jan 2006 | | Contributor(s):: Muhammad A. Alam
This homework assignment is part of ECE 656 "Electronic Transport in Semiconductors" (Purdue University). It contains 10 problems which lead students through the simulation of high-field transport in bulk silicon.
Manual for the Generalized Bulk Monte Carlo Tool
23 Jun 2011 | | Contributor(s):: Raghuraj Hathwar, Dragica Vasileska
This manual describes the physics implemented behind the generalized bulk Monte Carlo tool.