numerical solution (solution of schrodinger equation)

[khaledos]

How can i make a numerical solution for any semiconductor device such as PN junction device then Drawing it by (FEniCS/DOLPHEN) ????

please give an example for it because i'm very needed to it
Thanks

 

[fpgaengineer]

You will hardly be able to use Schrödinger's Equation directly to draw a real semiconductor's UI-behavour in a sensible way. Restrictions and assumptions will have to be applied to propagate the S-equation's solution to band diagrams (wk-diagram) and obtain electron behaviour / occupation statistics and valid values for e.g. the FERMI niveau and such more. Much later you can obtain simplified Shockley-Reed-Hall like models for semicons.

I did that about 20 years ago at university and we found that a full usage of a modelling with more or less 99% accuracy allready required >15min of calculation at a clustor of 4 silicon grafix computer, to find one and only dot in the transmission curve, even when applying most known simplifications.

With nowadays' hardware this is no more than 15 times quicker and even with a GPU cluster (which is actually done by my former collequesm who founded a company for this way of calculation) you will need at least 5-10 sec for one point an this still requires

- fixed doping profiles
- fixed junction temperatures
- fixed voltages between N-I-P
- fixed bulk potential
- fixed geometry
- assumed symmetry

so there are no parameters possible, neither dependencies in voltage, temperature or non square geometry.

Anyway: Happy Calculation. You can find basic equations e.g. in the semiconductor teahing book of "Möschwitzer-Lunze".