Intrinsic carrier concentration

INTRINSIC CARRIER CONCENTRATION

In an intrinsic semiconductor, the number of electrons in conduction band is equal to the number of holes in valence band.

In general, intrinsic carrier concentration n; is equal to electrons concentration in conduction band (n) or holes concentration in valence band (p).

i.e., n_i = n = p     … (1)

n_i × n_i = n_i² = np   ...(2)

Substituting the expressions of n and p in eqn (2), we have

Taking square root on both sides in eqn (3), we have

The eqn (4) is expression for intrinsic carrier concentration

Limitations of intrinsic semiconductor

Intrinsic semiconductors cannot be directly used to fabricate devices due to the following limitations:

• Electrical conductivity is low. Germanium has a conductivity of 1.67 Ω^-1 m^-1 which is nearly 10⁷ times smaller than that of copper.

•  Electrical conductivity is a function of temperature and increases exponentially as temperature increases.

In intrinsic or pure semiconductors, the carrier concentration of both electrons and holes is very low at normal temperatures.

In order to get sufficient current density through semiconductor, a large electrical field should be applied. This problem is overcome by adding suitable impurities into intrinsic semiconductors.