semiconductor A material with resistivity value in between that of good conductor and insulator, that is in the range of 10^-3 to 10^{3 W} .m. The band gap of the semiconductor is ~ 1 to 2 eV. It can be a pure crystal called intrinsic semiconductors, an impurity added crystal called doped or extrinsic semiconductors, a compound consisting of two or more elements.

Intrinsic semiconductor: The fourth group elements (silicon and germanium) have four outermost electrons which form covalent bonds with four neighboring atoms in tetrahedral arrangement. At normal room temperatures, thermal energy breaks a small fraction of the bonds creating free electron and a vacancy site which is called a hole. The band theory of solid can be utilized to better understand the process of conduction. In semiconductors there is a gap between the valance band and the conduction band called the band gap. An electron can jump this gap if its energy is greater than the band gap energy, E_g. The Fermi Dirac function gives the probability of an electron possessing energy E,

f(E) = [exp[(E- E_f)/kT]+1]^-1 (s2)

where E_f is the energy at Fermi level*. The Fermi level for an intrinsic semiconductor is at the middle of the band gap,

E_f = E_g/2

Taking E =0 at the top of the valance band,

f(E) = [exp[E_g/kT]+1]^-1

The value of kT at room temperature is 0.026 eV and E_g =1.1 eV for silicon makes 1 insignificant in the denominator of the above expression. f(E) is then,

f(E) = exp (-E_g/2kT)

The fraction of electrons with energy greater than E_g can be obtained by,

n = N exp(-E_g/2kT) (s3)

where N is the total number of electrons in the valance band, which can be raised to conduction band.

When an electron is raised to the conduction band it leaves a vacant site. Under the influence of external field an adjoining valance band electron can jump on this site, creating a net motion of positive charge in the opposite direction. These vacant sites which acts as charge carriers are called holes. Holes are less mobile compared to the electrons in the conduction band. The conductivity,s of semiconductor is therefore sum of two factors, one due to electrons and the other due to holes.

s = n_e e m _e + n_h e m _h (s4)

where e is the electronic charge, n_e and n_h are the number density of electrons and holes respectively (n_e=n_h for intrinsic semiconductors). The constants m _e and m _h are called mobility for electrons and holes respectively. Mobility is defined as drift velocity acquired under unit field gradient.

Extrinsic semiconductors: The conductivity of pure semiconductor crystal, can be altered by adding impurities. If a Vth group element (P, As, Sb, Bi) is added to a crystal, four outer electrons would form covalent bonds with neighboring atoms leaving one electron free. In such a crystal the number of electrons would be much more than the number of holes. Such semiconductors are called n type semiconductors. The impurity atoms are called donors. The energy of the donor electrons is close to the conduction band. The situation is shown in fig. s1.

Similarly impurity atoms of an element belonging to third group (B, Al, Ga, In) create holes in the valance band, because it has three outermost electrons. These impurity atoms are called acceptors, and the semiconductor is called p type semiconductor. In this case the valance band electrons are transferred to the acceptor level creating holes (see fig. s2).

In a semiconductor the conductivity increases sharply with temperature unlike a conductor where variation is opposite. It happens because at higher temperature more electrons are transferred to the conduction band enhancing the number of charged carriers.

Compound semiconductors: They contain two or more elements, e.g. GaAs. The devices of gallium arsenide have high signal speed, large temperature range and low power consumption. Such devices are used in supercomputers.

Table SI. Properties of some important semiconductors