Metals have free charge carriers. With increase in temperature, the resistivity of a metal increases.
Pure (intrinsic) semiconductors are very similar to insulators. For a semiconductor, the resistivity decreases with
increase in temperature.
Metals have partially occupied band which allow charge carriers to move even when a small amount of energy is
supplied. Semiconductors have occupied valence band and unoccupied conduction band. Carriers can be thermally excited from valence band to conduction band.
Insulators are similar to semiconductor in their band structure. However, the band gap is much larger than in a
semiconductor.
Behaviour of simple metals can be described by a free electron theory in which an electron is taken to move in a
constant potential. At zero temperature the electron states are occupied from the lowest energy state to a state of maximum energy, known as Fermi energy.
Density of state is the number of states per unit volume of a substance per unit energy interval. For free electrons
the density of state is proportional to the square root of energy.
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