Charge transport and trapping in the oxides interests many people, when it comes to device engineering, for different reasons. One of them is the variety of device configurations that can exist using thin film oxides.

During my PhD, I worked a lot with simulating such trapping mehanisms using the TCAD software Synopsys Sentaurus. Of course, the main issue with this kind of work was whether it was producing meaningful results. While this can be tested only using experimental output, in order to comare the results of the simulator with the theory, I was using some Mathematica scripts that I am attaching at the end of this post.

This model, is what Sentaurus uses to model transport and trapping in the oxide, and while many calculations can be double checked with the script, some others are impossible, as to derive them solely from the bias applied to the device, would require extensive analytical modelling. Such thing, of course, would be hard if the device is three-dimensional, unless you are willing to write your own code that solves the Drift-Diffusion (DD) equation using the Finite Elements Method.

Instead, I chose to trust the solution of the DD coming from the software, and only test the equations of charge trapping using the values of current and electron density from specific points in the oxide. This was both for current and diffusion enabled trapping, as well as the state transition functionality for the creation of new traps in the oxides (as for example after stress is applied).

DDTrapping calculates the occupational probability and the trapped harge density given constants as well as model parameters from the simulator, taken at a specific location in the device.

StateTransitions similarly calculates the probability of the defect being in a specific state as well as the state transition rates.