Steps to calculate the band profile of a complex semiconductor heterostructure
Most simulators are just that "simulators", which often do a good job at giving the resulting behavior even if it isn't true to the physics.  BSIM is a good example because it didn't really model the physics until recently with the merger of EKV into the model, it was just a bunch of sweeps that gave a model that worked well enough.  Why not have a model true to the physics?  Well, it takes a LONG time to run, and often we have a lot of the form of X*e^X in there, which requires an iterative approach or the use of a Lambert function.  Most importantly, the perfect model isn't really better than an approximation.

I write my own semiconductor models because I make some non-standard devices, and if you wanted to really get into this, I would suggest the following:
Get Andy Grove's "Physics and Technology of semiconductor Devices" because it is what everyone who wrote a book after read.  From that, you then should read Carver Mead's "Collective Electrodynamics: Quantum Foundations of Electromagnetism".  With those two books, you could then model about everything.  You will quickly see that throwing out the higher order terms makes things much faster, and the 0.01% deviation doesn't really mater to the fact that when you make a junction, you generally are 1% off on your doping, etching, etc anyway.