next up previous index
Next: Problem: Band Overlap Up: Electronic Band Structure Previous: Problem: Tight-Binding in Dirac-Delta

Problem: Dirac-Delta Potentials

  Atoms are arranged in a one-dimensional chain with a lattice spacing of a. Each atom is represented by the potential tex2html_wrap_inline5943 .

(a) Show that the electron energy E and wavenumber k satisfy the relationship

  equation1617

where tex2html_wrap_inline5957 and tex2html_wrap_inline5959 . Determine the coefficient tex2html_wrap_inline5131 .

   (b) Calculate the energy gaps between the bands for weak potential, tex2html_wrap_inline5963 and compare the result to the gaps obtained in the nearly free-electron approximation.gif

   (c) Calculate the bandwidth of the lowest-energy band for strong potential, tex2html_wrap_inline5965 and compare the result to the bandwidth obtained in the tight-binding approximation.gif  

This document can be accessed on the World Wide Web at "http//:solidstate.physics.sunysb.edu/book/prob/ ".

Laszlo Mihaly
Thu Oct 31 13:23:11 EST 1996

Back to the Small cover of the book Cover Page .