## How to Simulate the Carrier Dynamics in Semiconductor Devices

##### Chien Liu December 27, 2018

Learn how to simulate carrier dynamics in semiconductor devices with 2 examples: reverse recovery and forward recovery PIN rectifier models.

Read More##### Chien Liu October 20, 2015

The shortest route between two points isn’t necessarily a straight line. If by shortest route, we mean the route that takes the least amount of time to travel from point A to point B, and the two points are at different elevations, then due to gravity, the shortest route is the brachistochrone curve. In this blog post, we demonstrate how to use built-in mathematical expressions and the Optimization Module in COMSOL Multiphysics to solve for the brachistochrone curve.

Read More##### Chien Liu August 24, 2015

Today we continue our discussion on the weak formulation by looking at how to implement a point source with the weak form. A point source is a useful tool for idealizing the situation where a source is concentrated in a very small region of the modeling domain. We will find that it is very convenient to set up such a point source using the weak form.

Read More##### Chien Liu April 16, 2015

Previously in our weak form series, we discretized the weak form equation to obtain a matrix equation to solve for the unknown coefficients in our simple example problem. Following the same procedure as in this previous blog post, we will implement the equation in the COMSOL Multiphysics® software with additional steps included to examine the matrices. We will find it more convenient to use a COMSOL® software application to display all relevant matrices at once, arranged logically on one screen.

Read More##### Chien Liu April 1, 2015

Over half a century ago, Mark Kac gave an interesting lecture on a question that he had heard from Professor Bochner ten years earlier: “Can one hear the shape of a drum?” He focused on the (then undetermined) uniqueness of the set of eigenvalues given the shape of a vibrating membrane. The eigenvalue problem has since been solved and here we explore the “hearing” part of the question by considering some interesting physical effects.

Read More##### Chien Liu February 9, 2015

This post continues our blog series on the weak formulation. In the previous post, we implemented and solved an exemplary weak form equation in the COMSOL Multiphysics software. The result was validated with simple physical arguments. Today, we will start to take a behind-the-scenes look at how the equations are discretized and solved numerically.

Read More##### Chien Liu January 6, 2015

This blog post is part of a series aimed at introducing the weak form with minimal prerequisites. In the first blog post, we learned about the basic concepts of the weak formulation. All equations were left in the analytical form. Today, we will implement and solve the equations numerically using the COMSOL Multiphysics simulation software. You are encouraged to follow the steps with a working copy of the COMSOL software.

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