Table of Contents
In 1879, E. H. Hall observed that when a magnetic field {
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1 References
- [1] A. C. Melissinos, Experiments in Modern Physics (second edition), Academic Press, 2003.
- [2] A. C. Melissinos, Experiments in Modern Physics, Academic Press, 1966.
- [3] C. Kittel, Introduction to Solid State Physics, John Wiley & Sons, New York.
- [4] J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, N. Y., 1972.
- [5] N. W. Ashcroft and N. D. Mermin, Solid State Physics, Thompson Learning, 1976.
- [6] E. H. Hall, American Journal of Mathematics, 2, 287 (1879).
2 Purposes
The purposes of this lab are as follows:
- to familiarize you with the electronic transport properties of semiconductors including the concepts of holes and charge carrier mobility;
- to observe the phenomenon of magnetoresistance and to compare resistivity in and out of a magnetic field;
- to observe the Hall effect and to measure resistivity and the Hall coefficient as functions of temperature; and
- to measure the band gap energy of germanium.
3 Theory
This theory section introduces a number of new condensed matter concepts and includes a lot of derivation. In order to make the main points clear, we have included a SUMMARY list at the end of each section to review the important points.
3.1 Hall effect for one type of charge carrier
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Figure 1: Schematic of the Hall effect for one type of charge carrier (electrons). (Adapted from [5], Fig. 1.3, p 12.)
Let us begin by considering the motion of the free charge carriers of charge q in a conductor (Fig. 1). When an external electric field is applied, these charges feel a force F = qEwhich causes an acceleration, a = qE/m (where m is the mass of the charge carrier). If a particular carrier travels for a _mean free time__τ_before it scatters, – randomly changing speed and direction, – the average velocity over all carriers will be the drift velocity,
| { ${/download/attachments/143560144/eqn_1.png?version=2&modificationDate=1454618327000&api=v2}$ | (1) |
This drift velocity produces a current with current density (current per unit cross-sectional area)