TABLE OF CONTENTS The pseudopotential is a powerful technique to solve for bandstructures of semiconductors and is often used as a benchmark for comparison of other techniques. We will describe the spirit of the method without going into its details. Like the orthogonal plane wave method, the pseudopotential method makes use of the information that the valence and conduction band states are orthogonal to the core states. However, this information is not just used in the construction of the Bloch states, but is included in an ingenious manner in the Hamiltonian itself. Thus the background periodic potential is replaced by a new "pseudopotential," which is obtained by subtracting out the effects of the core levels. The pseudopotential then has a smooth spatial dependence and yet includes all the relevant information to give the valence and conduction band bandstructure. The following formal equations define the procedure. The Schr dinger equation for the valence or conduction band states is
| (2.63) |  |
with the orthogonality condition
? ? c ? v ? = 0
where ? c are the core states. This condition is explicitly incorporated into the definition of the valence band states by defining new states ? v( k, r) where
| (2.64) |  |
The equation for ? v( k, r) then becomes
where E c are the known core level energies. The Schr dinger equation for ? v( k, r) has the same eigenvalues as the original equation for ? v( k, r)...
