Thursday,
September 16, 1999, 12:15 p.m. in GWC Room 604
Heather Loechelt
Department of Mathematics
A Green's Function Approach to Electron Energy Calculations in
Crystals
Abstract
Green's functions are an effective technique for calculating the
electron energy levels and density of states in a crystalline material.
They are particularly useful in a perturbation analysis of localized
defects once the Green'’s function for a perfect crystal and the
Hamiltonian for the defect are known. This seminar will discuss an
application of Green'’s functions to the energy calculations of one
dimensional silicon chains and a three dimensional silicon crystal,
using a tight binding model for the Hamiltonian and overlap matrices. A
matrix representation of the Green'’s function is developed using a non
orthogonal basis. Unlike an orthogonal basis, a non orthogonal one
retains the localized character of the perturbation in the elements of
the Hamiltonian matrix. However, it also complicates the calculation of
quantities of interest such as the energy spectrum and the density of
states. A formalism for the proper treatment of Green'’s functions with
a non orthogonal basis will be covered, along with a comparison of
different numerical algorithms for calculating the Green'’s function for
a perfect crystal.
