Semiconductors like Germanium and Silicon have crystalline structure . Their atoms are arranged in an ordered array known as crystal lattice. Both these materials are tetravalent i.e. each has four valence electrons in its outermost shell. The neighboring atoms form covalent bonds by sharing four electrons with each other so as to achieve inert gas structure (i.e 8 electrons in outermost orbit). A two dimensional view of the germanium crystal lattice is shown in fig. below, in which circles represent atom cores consisting of nuclear and inner 28 electrons. Each pair of lines represents a covalent bond. The volts represent the valence electrons. It is seen that each atom has 8 electrons under its influence. Each atom shares a valence electron with each of its four neighbors and forms a stable structure.

In case of pure germanium, the covalent bonds have to be broken to provide electrons for condition. There are many ways of rupturing the covalent bond and thereby setting the electrons free. One way is to increase the crystal temperature above 0^oK.

It may be noted that covalent crystals are characterized by their hardness and brittleness. The brittleness is due to the fact that in such crystals adjacent atoms must remain in accurate alignment since the bond is strongly directional and framed along a line joining the atoms. The hardness is due to the great strength of the covalent bond itself.

The shaded region represents the net positive charge of the nucleus. The black dots represent the valence electrons in the atom. These electrons can travel from atom to atom as they are not fixed to any particular atom. These electrons are in continuous motion and since the motion is random, there will be as many electrons passing through unit area in the metal in any given direction as in the opposite direction at any given time. Hence the average current is zero.

If a constant electric field is applied to the metal, the electrons would be accelerated to a finite speed called the drift speed and the velocity is in a direction opposite to the electric field. Thus

V = me (2.1)

This finite speed attained overrides the random characteristic motion of the electrons in the metals and this constitutes directed flow of electrons or current.

Current density J is defined as the current per unit area of the conducting medium.

Where J is in amperes/m², A is the cross sectional area of the conductor in square meter .

The total charge I passing any area is

Therefore J = n q v = r v(2.4)

Here r is the charge density in coulombs per cubic meter and v is the velocity in m/s.

Here s is the conductivity of the metal. Thus the current is proportional to the applied voltage.The power dissipated within the metal is given by

Je or s e ² (2.6)