Theoretical Concepts and Methods

Abstract

Of the many options for broadly classifying solids, electrical resistivity has proved to be the most useful. The grouping of materials into insulators, semiconductors, semimetals, and metals involves a parameter with a range of order 10¹⁰. The resistivity boundaries between the classifications are not very sharp, but they are sharp enough to make the separation for most practical purposes. For the semiconductor regime, the resistivity is betwen 10⁹ and 10⁻³ ohm -cm, but we will also discuss insulators with resistivities above 10⁹ ohm-cm and doped semiconductors and semimetals with resistivities below 10⁻³ ohm-cm. The distinction at the boundary between semiconductors and insulators will be made on the basis of the size of the fundamental (minimum) band gap. Semiconductors are assumed to have band gaps from 0 to ∼4eV, insulators >4eV, and semimetals ≤0. Gray Sn (α-Sn) is an example of a borderline material which has zero band gap. It has been called a zero-gap semiconductor; it has also been called in ideal semimetal.