# Questions about Discretization Methods in the Paper

Hello Juan,

Thank you for the material on semiconductor simulation you provided last week; it has been very helpful. However, I have some questions about a different approach I’ve encountered.

In the textbook, “Analysis and Simulation of Semiconductor Devices”, semiconductor device simulation involves discretizing the Poisson Equation and Carrier Continuity Equations using the finite difference or finite volume method, resulting in a large system of nonlinear algebraic equations that are solved using the Newton Method.

However, in the paper “Element Edge Based Discretization for TCAD Device Simulation,” the method of assembling the equations seems different from the textbook approach, and I’m a bit confused about it.

Thank you.

Best regards,

Wong

And in the paper, the terms C_a and A_a are all in the divergence operator. Why are they different that one is edge quantity while the other is element edge quantity?

Please focus on the “edge quantity” as that is the most useful for general purpose simulation. For example the “electric field” is an edge quantity. The main focus of the paper is the “element edge quantity”, it is useful when you want the “electric field normal to current flow” or some other vector based quantiy.

The textbook approach is similar to our approach. They are all based on control volumes and integration of fluxes along edges. However, our approach uses triangular meshes, whereas the book covers meshes with rectangle. The idea is similar in that you are doing a surface integral along the edges.

For a triangular mesh, the surface area for an edge is between the centers of the 2 triangles sharing the edge. For a rectangular mesh, the surface area is between the centers of the 2 rectangles bordering the edge.

This paper may be helpful to understanding the triangular discretization:
http://www.jommpublish.org/p/61/