Physics · Ch 14 — Electronic Devices
Energy Bands in Solids
Energy Bands in Solids
From discrete atomic levels to continuous bands. In a single, isolated atom, each electron occupies one of a set of sharply defined, discrete energy levels. When a very large number of such atoms -- of the order of Avogadro's number, in even a small piece of solid -- are brought close enough together to form a crystal, the electrons of neighbouring atoms interact, and each formerly sharp atomic level splits into a great many extremely closely spaced sub-levels, one for every atom in the crystal. Packed this closely together, the sub-levels merge, for all practical purposes, into a continuous range of allowed energies called an energy band. Between two neighbouring bands, there may remain a range of energy values that NO electron in the crystal can ever have -- a forbidden energy gap, .
Valence band and conduction band. Of the several bands a real solid has, only the two nearest the electrons' actual energies matter for its electrical behaviour: the valence band, the highest energy band that is normally (wholly or mostly) occupied by electrons at low temperature, and the conduction band, the next higher band, normally empty (or nearly so). Only an electron that has been promoted INTO the conduction band -- and left the valence band mobile enough to carry current -- can actually contribute to electrical conduction; an electron confined to a completely full valence band cannot move into a new energy state at all (every nearby state is already occupied by another electron, forbidden by the Pauli exclusion principle), and so contributes nothing to conduction. …
What this figure shows. Three vertical energy-axis diagrams are drawn side by side, each showing two shaded rectangular bands -- a lower VALENCE BAND (shown fully or mostly shaded/filled with electrons) and an upper CONDUCTION BAND (shown empty, unshaded) -- separated by a blank gap region labelled the FORBIDDEN ENERGY GAP . In the LEFT panel (a CONDUCTOR, e.g. copper), the valence and conduction bands are drawn OVERLAPPING, with no gap at all between them (), so the shading of the two bands runs together continuously. In the MIDDLE panel (an INSULATOR, e.g. diamond), a very WIDE blank gap (several eV, drawn as the largest of the three gaps, roughly eV) separates a completely full valence band from a completely empty conduction band. In the RIGHT panel (a SEMICONDUCTOR, e.g. silicon or germanium), a NARROW blank gap (about 1 eV, drawn visibly smaller than the insulator's gap but still a real gap, unlike the conductor's) separates the two bands, with a few small dots shown just above the gap in the conduction band and a few small circles (holes) just below it in the valence …