Semiconductors can be classified as intrinsic and extrinsic semiconductors.

Intrinsic semiconductor is semiconductor material in its extremely pure form. Common examples of such semiconductors are pure germanium and silicon, which have forbidden energy gap of 0.72e V and 1.1eV respectively. The energy gap is so small that even at ordinary room temperature. There are many electrons which possess sufficient energy to jump across the small energy gap between the valence and conduction bands. However it is worth noting that for each electron liberated into the conduction band, a positively charged hole is created in the valence band. When an electronic field is applied to an intrinsic semiconductor at a temperature above 0^oK, conduction electrons move to the anode and the holes in the valence band move towards the cathode. Hence semiconductor current consists of movement of electrons and holes in opposite directions. Electron current is due to movement of electron in the conductor band where as hole current is within the valence band as a result of the holes jumping from one atom to another.

Germanium and Silicon are the two most important semiconductors used in electronic devices. Fig. 2.3 shows the two dimensional structure of a germanium crystal. Germanium has a total of 32 electrons in its atomic structure.

There are four valence electrons in each of its atom. Each of the valence electrons is shared by one of its four nearest neighbours with the result that germanium has low conductivity at very low temperatures. However at higher temperatures say at room temperatures, conduction can occur, because the bonds are easily broken. An electron can break away from the covalent bond (it requires an energy of 0.72 eV) and the point from where it was dislodged represents a hole. Another travelling electron can fill this hole only to break away later. Effectively the hole moves in a direction opposite to that of the electron and this represents a sort of conduction though the electrons are not free. Covalent elements are hard and brittle.

A pure or intrinsic semiconductor is one where the number of holes is equal to the number of free electrons. Here the hole and electron concentrations are equal and is called the intrinsic concentration.

It is given by

'N' is a constant for a given semiconductor

'E_g' is the band gap energy in Joules

'k' is Boltzmann's constant

'T' is temperature in ⁰K

The intrinsic carrier concentration in pure silicon is given by

n_i = N exp (-Eg/2KT)

N = 3 x 10²⁵ m^-3

Eg = 1.1eV

= 1.1 x 1.6 x 10^-19

= 1.76 x 10^-19J

K = 1.38 x 10^-23 J/K, T = 300^oK

n_I = 3 x 10²⁵ (-1.76 x 10^-19 / 2 x 1.38 x 10^-23 x 300)

= 2 x 10¹⁶ m^-3

The current flow in intrinsic semiconductor is due to the movement of electrons and holes in opposite directions. However since their charges are of opposite sign, the current due to each is in the same direction. Even though the number of electrons equals the number of holes, hole mobility m _e is practically half of electron mobility m _n. the total current flow is given by

I = I_e + I_h (2.8)

where I_e is the electron current and I_h is the hole current.

Let V_e = drift velocity of electrons in m/s

V_h = drift velocity of holes in m/s

n_i = density of free electrons in intrinsic semiconductor in per m³ .

P_i = density of holes in intrinsic semiconductors in per m³.

e = electron charge in coulombs

Since in an intrinsic semiconductors n_i = p_i,

since Ev= V/e, where e is the length of the intrinsic semiconductor

V / I = (l / A) x (1 / n_ie (m _e + m _h ) )

= (r l / A)(2.13)

Where r is the resistivity of the semiconductor. It is given by

r =1 / (n_ie(m _e + m _h)) ohm metre (2.14)

The electrical conductivity which is the reciprocal of resistivity i_d given by

s _i = n_ie (m _e + m _h) s/m (2.15)

Now current density J = I/A

\ J = (n_ie + m _h )E = s _i E. (2.16)

Thus, conductivity of semiconductor depends on two factors.

Number of current carriers present per unit volume and

The conductivity of intrinsic semiconductor is given by

s _i = n_ie m _e +n_ie m _h

= 1.41 * 10¹⁶ * 1.6 * 10¹⁹ (0.145 + 0.05)

= 0.437 * 10^-3 S/m