23 - The electrical properties of materials

Summary

In this chapter, we use quantum statistics to help us understand the distinctive electrical properties of conductors, semiconductors, and insulators. We have previously learned that although the occupation number has the same form for all systems, the spectrum of accessible states varies from one to the next. For this reason, we begin this chapter with a brief and simplified overview of band structure.

Band structure

The splitting of levels

As atoms are brought close together, the overlapping of their electron clouds allows electrons to move from one atom to another. These interactions with their neighbors cause shifts in the allowed electron energies. What were initially states of identical energies in isolated identical atoms turn into “bands” of very closely spaced states for the shared electrons in groups of atoms.

Band widths and structure

In general, the outer states of higher energy experience greater overlap, which usually results in greater splitting and wider bands (Figure 23.1). Within any band, the density of states usually is largest near the middle and falls off near the edges (Figure 23.2). Electrons preferentially fill the lowest energy states, so at low temperatures the lower bands are full and the higher bands are empty.

The highest completely filled band in the T → 0 limit is called the “valence band.” Because it is full, there are no empty states into which these valence electrons can move. (Although pairs could trade places, they are identical particles, so it is the same as staying put.)