Chapter 6:Energy Band Theory

Energy Band Theory

Semiconductors Si, Ge, GaAs, InP, CdTe.. - all are crystalline solids.

This is a 3D regular arrangement of atoms called the lattice. Some elemental semiconductors such as Si & Ge have only one kind of material at the lattice sites, where as GaAs, InP,.are compound semiconductors and are composed of two interpenetrating 3D lattices.

  • phycomp.technion.ac.il/~sshaharr/nonbravias.html
  • www.chem.lsu.edu/.../MERLO/flattice/20zns.html

There may be defects in the lattice and each atom in a lattice vibrates.

  • http://simple-semiconductors.com/

Defects and vibrations are second order phenomenon which would be discussed separately.

If we have a charged ion at x = 0 and an electron outside the attractive force between the ion and the electron is

The PE of the   and PE =0 at

Fig. 3.1

If we consider two ions separated by 'a', the potential profile in on shown in Fig.3.2

Fig.3.2

To get a feel for the electron energies in a crystal semiconductor let us consider an electron in a 1D lattice of atoms. The simplest lattice structure is a 1 D lattice.

A regular array of atoms placed periodically.

Fig.3.3

At each lattice site (x = 0, a, 2a, ..) there exists an ion with some net charge