Classification of Materials

Having built the band picture, the chapter classifies every solid -- insulator, conductor, or semiconductor -- purely by the width of its forbidden energy gap $E_g$ and by whether the valence and conduction bands physically overlap, each sub-section below taking one class in turn. Physically, the deciding factor in every case is the same energy-band picture developed in 9.1.1: how wide is the forbidden gap $E_g$ between the valence and conduction bands, and do the two bands even stay separate at all. An insulator's gap is far too wide to cross with any realistic field or temperature; a conductor's bands overlap so there is effectively no gap to cross; and a semiconductor's gap is narrow enough that ordinary thermal energy at room temperature can promote a modest population of electrons across it, which is e …