Learning Resources
In addition to the tutorial model in the last section of the Introduction to the Semiconductor Module book (Tutorial Example: DC Characteristics of a MOSFET), there are many examples in the Application Libraries. Every example is accompanied by a PDF documentation with step-by-step instructions and useful comments. The examples can be accessed either online (https://www.comsol.com/models/semiconductor-module) or within the software by going to the File Menu>Application Libraries>Semiconductor Module.
For users interested in the drift-diffusion type of formulations, we recommend to start with the simple model of a p-n junction with user-defined generation for a silicon solar cell: https://www.comsol.com/model/si-solar-cell-1d-35661. This gives a quick introduction to building a semiconductor model from scratch.
Next, the 1D heterojunction model demonstrates standard techniques to achieve convergence (see comments in the accompanying PDF documentation):  https://www.comsol.com/model/heterojunction-1d-14617.
The tutorial in the last section of the Introduction to the Semiconductor Module book shows a simple 2D model. More 2D models can be found in the Application Libraries.
To model the oxide domain explicitly, use the Charge Conservation domain condition, as shown in this example of an EEPROM:  https://www.comsol.com/model/programming-of-a-floating-gate-eeprom-device-18075.
3D models require swept mesh:  https://www.comsol.com/model/3d-analysis-of-a-bipolar-transistor-19699.
For users interested in the Schrödinger Equation, you may find the following blog post and examples useful:
https://www.comsol.com/blogs/computing-the-band-gap-in-superlattices-with-the-schrodinger-equation/
https://www.comsol.com/model/double-barrier-1d-47041
https://www.comsol.com/model/superlattice-band-gap-tool-45281