egarded as moving positive charges through the crystal with a charge magnitude and ass as that of an electron. Conduction that arises from thermally / optically excited electrons is called intrinsic semiconduction. It usually takes place at elevated temperatures since sufficient thermal agitation is necessary to transfer a reasonable number of electrons from the valence band to the conduction band. At still higher temperatures, the concentration of thermally excited electrons in the conduction band becomes so high that the semiconductor behaves more like a metal. The elements capable of intrinsic conduction are limited, and include: Si, Ge, Sn, Pb, etc.
6 Figure 14-2: Band structure and intrinsic conductivity. In intrinsic semiconductors, the number of holes equals the number of mobile electrons. The resulting conductivity can be expressed as σ = n q. μ + n. q. μ = n. q.( μ + μ )..(12) e. e e h h h e e e h as n e = n h, and both electron and hole possess equal magnitude of charge. The mobility of holes is always less than those of electrons i.e. μ h < μ e. In Si and Ge, the ratio μ e / μ h is approximately three and two respectively. Extrinsic semiconduction: The charge carrier density can also be increased by adding impurities of either higher or lower valence. This addition of impurities is known as doping, and impure atoms in the element are called donor atoms. When a pentavalent substitutional atoms like P, As, or Sb are placed into a covalently bonded tetravalent materials such as Si or Ge, only four of their five valence electrons are required to participate in covalent bonding, while the fifth electron remains weakly bound to the donor atom. However, this binding energy is in order of 0.01 ev, much less than that of a covalently bonded electron. The energy state of this electron is indicated as E d. Energy gap between the donor and conducting bands is much smaller than that between the valence band and conduction band, E g. Thermal agitation, even at room temperature, is good enough to excite this electron to the conduction band, leaving behind a positively charged hole in the donor band. Conductivity is due to motion of negatively charged electrons in the conduction band, and so the material is called n-type semiconductor. Fermi level (E f ) of n-type extrinsic semiconductor is higher than that of intrinsic semiconductor i.e. it shifted upward in the band gap, to within the vicinity of the donor state; and its exact position is a function of both temperature and donor concentration.
7 Figure 14-3: Band structure and n-type semiconductivity. Other possibility of susbstituion involves impurity with lower valence. For example trivalent elements like B, Al, Ga, In, Th doped to Si or Ge. Since the donor atoms are deficient in bonding electrons, one of their bonding orbitals will contain a hole that is capable of accepting an electron from elsewhere in the crystal. Binding energy is small, and promotion of an electron from the valence band to the acceptor band, E a, leaves a positively charged hole in the valence band that can act as a charge carrier. Materials with this p-type extrinsic semiconduction are called p-type semiconductors. Fermi level (E f ) for p-type semiconductors is positioned within the band gap and near to the acceptor level. Figure 14-4: Band structure and p-type semiconductivity. For an n-type semiconductor, electrons in the conduction band are charge carriers and holes participate in bonding, whereas for a p-type semiconductor, the electrons participate in bonding, and the holes are the charge carriers. Conductivity equations for these extrinsic semiconductors are written as: n-type semiconductor: p-type semiconductor: σ n. q. μ.(13) e σ n. q. μ..(14) h
8 In both types of extrinsic semiconductors, the doping elements are chosen so that both acceptor and donor levels are located closer to the corresponding energy bands and only a small energy gap in involved when exciting electrons. Intrinsic semiconductors are pure to the order greater than 10 7, while extrinsic semiconductors are made with impuri