### PHYSICS OF SEMICONDUCTOR DEVICES - REVISION OF SEMICONDUCTOR BAND THEORY

Kamis, 05 Mei 2011 ·

In the previous unit we discussed the concept of the band-structure of a crystalline material, using a diagram showing the relationship between an electron’s energy E and its momentum kph=(usually we drop the factor and just talk of E-k diagrams). This enabled us to distinguish between metals, insulators, and semiconductors, depending on how many of the bands are occupied, and the fraction of the occupation, h. In this unit we will now go on to examine the band-structure of real semiconductors, and discuss various experimental techniques that can be used to measure the semiconductor’s band-gap.

After studying this unit you will be able to
1.      1  Explain the concept of the effective mass in semiconductors.
2.      2  Relate the effective mass to the semiconductor band-structure.
3.      3  Explain the concept of “holes” as positively charged particles in the valence band.
4.      4  Describe the difference between direct and indirect band-gap materials.
5.      5  Describe the key features of the band-structure of real semiconductors.
6.      6  Describe three different techniques for measuring the band-gap.

THE EFFECTIVE MASS

In Unit 1 we derived an ideal band diagram for a crystalline solid with a simple cubic lattice structure, using the nearly free electron model. Although we said that the electron interacts only weakly with the crystal lattice, now it is time to quantify how this interaction affects the electron. The detailed form of the E(k) curve (which is different for different materials) determines the electron velocity and momentum – so it determines the electrical properties of the material.
Schematic of the direct band-gap, conduction band, and valence bands. The curves in the valence band are called heavy hole, light hole, and split-off hole states, respectively. [reproduced from Kittel, Introduction to Solid State Physics (7th Edition), (Figure 8.13), Wiley 1995].