Electrical Properties Of Materials, Seventh Edition

Here we are. We have arrived at last at the transistor, the most famous electronic device of the century. It was discovered at Bell Telephone Laboratories by Bardeen, Brattain, and Shockley in 1948. Since then it conquered the world many times over. It made possible both the pocket radio and the giant computers, to mention only two applications. The number of transistors manufactured is still growing fast from year to year. The figure for 1967, when we first prepared these lectures, was a few times 10 9; that is about one transistor for every man, woman, and child living on Earth. I do not think anyone knows the number of transistors produced nowadays. We are rapidly approaching the stage when a single computer might contain as many as 10 9 transistors (or one of its close relations, namely field-effect transistors or charge-coupled devices).
I am afraid the discussion of the transistor will turn out to be an anticlimax. It will seem to be too simple. If you find it too simple, remember that we have trodden a long tortuous path to get there. It might be worthwhile to recapitulate the main hurdles we have scaled:
Postulation of Schr dinger's equation.
The solution of Schr dinger's equation for a rigid, three-dimensional potential well.
Postulation of Pauli's principle and the introduction of spin.
Formulation of free electron theory, where electrons fill up the energy levels in a potential well up to the Fermi energy.
Derivation of the band structure...