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I am an EE undergraduate with a lot of interest in semiconductors. I took an introductory semiconductors course which was helpful but left me with some holes in my understanding, as the course (rightfully) assumed that the EE students had not yet had quantum or solid state physics. As I dig deeper into the topic, I find many papers that will give a complex layer structure (not exactly complex, just a "stack" of parameters) and then show the conduction band profile of the device, which is probably calculated using some simulator.

I have looked at many, many books to find the steps involved in calculating such a thing given a layer structure, but most explain the pn junction, metal metal junction, and then a heterojunction, and stop there without showing any concrete examples. What I have learned is that there is both a classical (I'm assuming extending the junction problem and electrostatics) and quantum way ("introducing new long-wavelength boundary conditions")

I am simply interested in the steps a simulator would go through, classically or otherwise, to take a stack of semiconductor layers and spit out a conduction band profile. Answers like "it iteratively solves such and such equation" is fine/what I'm looking for, or a direct reference that will explain to me what I am looking for is also great, as I have been searching hard for a clear answer.

As a bonus, I am mostly interested in III-V materials, how all of this relates to quantum wells, wires, and dots. I also understand the complexity behind this, things like strain and lattice matching and the electrostatics involved, and would also appreciate knowing under what assumptions your answer applies to.

Thank you!

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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.

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  • \$\begingroup\$ Thank you very much, this was a useful answer in general and i will immediately check out the mentioned texts. You say, however, that it just "simulates" the behavior, but what does that mean? I can draw any stack of "thin layers of semiconductor material of different bandgaps" and it will give me a band profile, how is it doing this? What is this model? Thank you again for your reply! \$\endgroup\$ Feb 18 '16 at 20:46
  • \$\begingroup\$ Right, but the simple band diagram are in there and that's your start. Grove's book has the reference for the original work for everything. There's not a "band diagram for dummies", if you'll excuse the reference, that I know of. I usually start by making a 2-D diagram and then use Carver's stuff to make a 3-D diagram. Brad Minch at Olin is very "pro student" and might actually help you if you email him. Jennifer Hasler would be another person and she lives for band diagrams of complex structures, but she's less available. Sorry that I couldn't help you more. \$\endgroup\$
    – b degnan
    Feb 19 '16 at 13:48
  • \$\begingroup\$ You were very helpful, another day of looking and I'm starting to grasp the big picture. I believe I just need more familiarity as well. I will keep at it. Thanks again \$\endgroup\$ Feb 19 '16 at 19:38

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