In the last 25 years a number of solid state devices have come in to use. Most of these devices use semiconductor crystals. Field of electronics has now been revolutionized since the discovery of transistor in 1948. The vacuum tubes have now been largely replaced by solid state devices. Technological development, such as invention of integrated circuits, has further increase the dependence on semiconductor materials. From the point of band theory of electrical conductivity, semiconductors and insulators in that they have narrow forbidden energy gap. We have seen that in metal addition of impurities as well as rise of temperature result in decrease in the electrical conductivity whereas in semiconductors, in contrary to the conductors the electrical conductivity increases. Of all the elements in the periodical table, eleven elements are semiconductors. Germanium and silicon are important semiconductors which are widely used in the manufacturing of diodes and transistors.

Elemental Intrinsic semiconductor-Germanium and silicon possess diamond cubic crystalline structure. The tetrahedral bonding of the basic diamond structure. The space lattice of diamond is face centered cube. The diamond lattice is formed by inter-penetration of two fcc lattice along the body diagonal. One sub lattice has its origin at the point (0, 0, 0) and the other at a point quarter of the way along the body diagonal,(a/4,a/4,a/4).

Each atom has four nearest neighbors’ and there are eight atoms in the unit cube. The diamond lattice is relatively empty with a low filling of space, 34% of the germanium and grey tin crystallize in the diamond structure with lattice constants a=3.56, 5.65 and 6.46 Armstrong respectively. The diamond structure is the result of directional covalent bonding.

Covalent bonding- The covalent bond is the strong classical electron pair bond. It act between neural atoms and has strong directional properties. The covalent bond is usually formed between two electrons, one from each atom participating in the bond. The electrons forming the bond tend to be partly localized in the region between two atoms joined by the bond. The spins of the two electros in the bond are anti parallel. Most of the covalent bonds do not conducts electricity because of the non availability of free charge carriers. Depending on the number of electron shared, bond length and bond energy vary. When the number of electron shared is more, the bond length between the atoms decreases and bond energy increases. The property of covalent crystals is the lack in the sensitivity of their physical properties. The property of covalent crystals is the hardest substance and a very high melting point (3280k). The hardness and melting point then decrease as we proceed to other elements in column4 of the periodic table from silicon to lead. The variation in the electrical properties is also pronounced. Diamond is a very good insulator; silicon and germanium are well known semi-conductors while lead is a good conductor.

Germanium has 32 electrons and silicon has 14 electrons in their atomic structures. Since each of them has 4 valence electrons, they are tetravalent atoms. The neighboring atoms form covalent bonds by sharing four electrons with each other. Since all the four valence electrons are covalently bound to the four neighbouring atoms the crystal acts as a perfect insulator at 0k. since the bond is strongly directional and formed along a line joining the atoms, the adjacent atoms remain in accurate alignment and hence these crystals possess brittleness. The great strength of the covalent bond provides hardness. Thus at 0k all the bonds are intact and hence the crystal acts as a perfect insulator. I order to provide conduction electrons, covalent bond are to be broken. The energy required to break such a covalent bonds are to be broken. The energy required to break such covalent bonds. When a covalent bond are to be broken. The energy required to break such a covalent bond is about 0.72eV for germanium and 1.1eV for silicon. At room temperature the thermal energy is sufficient to break covalent bond. When a covalent bond is broken an electron escapes to the conduction band leaving behind an empty space in the valence band called hole. It is relatively for a valence electron in a neighbouring atom to leave the covalent bond to fill this hole thereby leaving a hole in its original position. Thus the hole effectively moves in the opposite to that of electrons. Hence the conduction of electricity is due to the motion of the free electron in one direction and holes in the opposite direction. Therefore in semiconductors both the hole and the electrons are charge carriers and the current transformation is also taking place by holes and electrons. Since these charge carriers are due to breaking of covalent bonds the numbers of holes is equals to the number of free electrons. Due to thermal agitation new electron holes pairs are generated continuously while as a result of recombination already present electron-hole pairs disappear. Duping recombination a free electron is converted into a bound electron and a covalent bond is created. In a intrinsic semiconductor the Fermi energy level lies midway in the forbidden gap.

Carrier concentration in intrinsic semiconductor- We know that in intrinsic semiconductors the charge carriers are nothing but electrons in the conduction band and holes in the valence bonds, since these carriers are generated due to breaking of covalent bonds, we have equal number of electrons and holes. At 0k, since the entire bond is intact, the semiconductors act as an insulator. With increase of thermal energy the covalent bonds are broken and electron-hole pairs are created. Now we have to calculate the carrier’s concentration namely number of electrons in the conduction band per unit volume of the material (n) as well as number of holes in the valence band per unit volume of the material (p).