TABLE OF CONTENTS The free electrons in metals and semiconductors carry charge and are responsible for their electrical conductivity and for some important magnetic effects. They also carry energy and therefore contribute to thermal conductivity. In metals, their concentration is so high that electrons are the major contributors to thermal conductivity. It is therefore important to study the response of free electrons to external electric and magnetic fields and to temperature gradients.
When a system of free electrons is at equilibrium, the number of electrons in any volume element is statistically constant and there is no net flow. This means that macroscopic measurements will find the electron concentration to be independent of time. Of course, the electrons are constantly moving and there will be microscopic fluctuations in the number of electrons in a volume element, but on the average, just as many will be entering as leaving the volume element per second. If an electric or magnetic field acts on the system, however, the electrons will accelerate in a direction determined by the field. A drift motion will thereby be superimposed on the random movements of the electrons, giving rise to a directional net flow.
Consider an electron with velocity v in a state labeled by the wave number vector k. Its energy and momentum are given by
At a time t = 0, switch on an electric field E. The field exerts a force ? e E on...
