TABLE OF CONTENTS The k p model has become one of the most widely used bandstructure models for describing not only 3-dimensional semiconductors, but lower dimensional systems such as a quantum wells, wires, and dots. It is quite accurate near the bandedges. In the k p method, one starts with the known form of the bandstructure problem at the bandedges and using perturbation theory attempts to describe the bands away from the high symmetry points. Since for the central cell functions, we only expand around the high symmetry points in terms of known functions, the problem is considerably simplified, often leading to analytical results.
Let us consider a semiconductor with a bandedge at k 0. We assume that the eigenvalues and Bloch functions are known for the bandedge; i.e., the equation
| (2.66) |  |
is known. In most applications k 0 is the ?-point (= [000]) in the Brillouin zone. We can expand the general solutions away from the known k = k 0 solutions in the basis set exp[ i( k - k 0) r]. Thus we may write
| (2.67) |  |
where b n are the expansion coefficients, that are to be determined. This general approach is shown in Fig. 2.14. The secular equation has the usual form, formally represented by
| (2.68) |  |
A simple expansion allows us to rewrite this equation for just the central cell part of the Bloch states. Remembering that p
