As we discussed in class, for Thursday your HW is to calculate x_0 so that the following constraints are all satisfied:
1) a constant chemical potential (independent of x),
2) an appropriate relationship between mu and the CB and VB edges based on the doping should be maintained in the "bulk" regions far from the interface, and
3) no discontinuities in either the CB or VB (edges) as a function of x.
This is all in the context of an all or nothing ansatz: i.e., at a given value a x, either all the CB electrons escape to the VB on the other side, or none do...
Steps probably involve graphs of, and relationships between, charge, electric field, potential and energy...
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