The Reduced Zone Scheme divides electron energy states into bands and gaps. At the edges of the band gap ( Eg ) the E(k) curve is at its extreme. However little has been said about which states are occupied.
8.2 General Points About Band Structure
The Nearly Free Electron Model suggests that the energy width of the bands increase as the energy increases. We will use statistics later to describe this behaviour however for now we will say that the states fill up to the Fermi Energy.
Figure 8.1 - ???
Any electron which is many kBT away from the nearest empty state can do very little. Visible photons have a wavelength of 400® 800nm which corresponds to an energy level of about 2.5eV .
8.3 Effective Mass
Figure 8.2 - ???
Often we are interested in the region of the E(k) curve within a few kBT of the bandedge. It can be approximated by a parabola. In a classical model the kinetic energy is
E=
p2
2m
Þ E=
2K2
2m0*
where m* is the effective mass, however it can be negative! The electron wave packets in a crystal move under the influence of regions of electric or magnetic fields like charged particles of charge -|e| and mass m* .
8.4 Heterojunctions and Quantum Wells
Hetrojunctions are junctions between two materials with different band gaps but are similar Unit Cells.
Figure 8.3 - A Hetrojuction
At a hetrojunction you get a step in the potential due to the difference in band gaps. The electrons get trapped in the middle layer with K velocities
Figure 8.3 - A Hetrojuction