I have a question regarding the numerical simulation of semiconductor devices. Many commercial and open-source software packages, such as DEVSIM, Genius, and COMSOL, use the finite volume method (FVM) to discretize the semiconductor drift-diffusion equations. However, when I look into academic papers and textbooks, the focus seems to be primarily on the finite difference method (FDM) and finite element method (FEM). This is evident in works like the review “On the History of the Numerical Methods solving the Drift Diffusion Model” and in Selberherr’s textbook Analysis and Simulation of Semiconductor Devices.

I’m curious: why does it seem like the finite volume method is less discussed in academic literature when it comes to semiconductor simulations?

Additionally, if anyone knows of any textbooks or papers that focus on using FVM for numerical analysis in semiconductor devices, I would greatly appreciate your recommendations.

I’m sure a lot of the reason is that the method is based on intuition on conservation of flow, and not always on rigorous nomenclature. Finite difference is very close to finite volume. Names I have seen:

Control Volume

Box Integration

Finite Difference

Finite Volume (node or vertex centered)

I have seen some papers, in other disciplines, using cell centered finite volume as opposed to node centered, but for the most part most TCAD codes are using node centered FVM, no matter what they are calling it.

The advantage of all of these methods is the application of Sharfetter Gummel (SG) to calculate currents. There are now may papers where researchers are adapting the SG to FEM, or just using FEM directly.

However

the success of SG in handling the nonlinear relationship between potential and current

FVM is formulated to conserve current

It is relatively easy to develop an intuition for how it works

makes it likely that FVM will continue to be dominant for device simulation for a while longer.