Band Theory In Solid State 4r5u60

BAND THEORY SOLIDS CAN BE CLASSIFIED ACCORDING TO THEIR CONDUCTIVITIES

CONDUCTORS

INSULATORS

SEMICONDUCTORS  Solids exhibit electrical conductivities, extending over 27 orders of magnitude ranging from 10-20 to 107 Ω-1 m-1 .  The AOs of metal atoms form MOs which are close in energy to each others in energy as to form a band.  In solid-state, the electronic band structure of a solid describes those ranges of energy , called energy bands, that an electron within the solid may have allowed bands and ranges of energy called band gaps (forbidden bands).  Band Theory models the behavior of electrons in solids by postulating the existence of energy bands. It successfully uses a material's band structure to explain many physical properties of solids, such as electrical resistivity and optical absorption.

Although individual atoms have certain permitted energy levels for their electrons, as defined by quantum theory, when large groups of atoms are incorporated into a solid mass those energy levels become reorganised in such a way as to result in bands of possible energy levels. This is known as the tight binding approximation.

Fig. Discrete energy levels within an individual atom (left) and bands of permitted energy levels within a solid (right)

Within an energy band, energy levels can be regarded as a near continuum for two reasons.  The separation between energy levels in a solid is comparable with the energy that electrons constantly exchange with phonons (atomic vibrations).  Second, this separation is comparable with the energy uncertainty due to the Heisenberg uncertainty principle, for reasonably long intervals of time.

Source: http://www.educationscotland.gov.uk/Images/SemiconductorsAndBandTheoryH_tcm4-658243.doc

Why bands occur in materials…???

Basic Concepts  In solids, permitted electron energy levels are organised as bands.  The valence band contains electrons that can be considered to be bound to the atom. In insulators and semiconductors the valence band is full.  The conduction band is a region of permitted energy levels that is empty in insulators and semiconductors, but partially filled in conductors.  Only partially filled bands may permit conduction.  There is a forbidden zone that forms an energy gap between the valence and conduction bands in insulators and semiconductors.  That energy gap must be jumped if an electron is to move to the conduction band, and this is not normally possible in insulators because the gap is too large.  In semiconductors, the forbidden zone is much smaller and electrons can jump the gap to the conduction zone as a result of thermal excitation. Doping of semiconductors can significantly reduce the width of the energy gap.

Fig. Representation of energy bands