The concentration of minority carriers in an extrinsic semiconductor under equilibrium is

The concentration of minority carriers in an extrinsic semiconductor is given by the law of mass action, according to which:

n.p = n_i²

n = concentration of electrons in the conduction band

p = concentration of holes in the valence band

n_i = intrinsic carrier concentration

Cases:

In an n-type semiconductor, the minority hole concentration is given by:

\(p = \frac{{n_i^2}}{{{N_D}}}\)

N_D = Concentration of Donor impurity

In a p-type semiconductor, the minority electron concentration is given by:

\(n = \frac{{n_i^2}}{{{N_A}}}\)

N_A = Concentration of Acceptor impurity

Observations:

Thus the minority carriers concentration is:

1) inversely proportional to the doping concentration

2) directly proportional to the square of intrinsic concentration and not to the intrinsic concentration.