Carrier Concentration in p-Type Semiconductor

CARRIER CONCENTRATION IN p-TYPE SEMICONDUCTOR

For p-type at absolute zero Ep will be exactly between E and E. At low temperatures some electron from valence band fills the holes in the acceptor energy levels as shown in Fig. 2.19.

We know the density of holes in the valence band,

 …….(1)

Let N_a be the number of acceptor energy levels per cm³ which has energy E_a above valence band. If some electrons are accepted by the acceptor energy levels from the valence band, say for example if two electrons are accepted to fill the hole sites in the acceptor levels, then two holes will be created in the valence band as shown in Fig. 2.19.

Therefore, in general the electron density in the acceptor energy level can be written as

N (E_a) dE = Z (E_a) dE • F (E_a)

i.e., n_e = N_a F (E_a) ………(2)

here

Since E_a - E_F >> K_BT

 ………..(3)

Substituting equation (3) in (2), we have

 ……….(4)

At equilibrium condition,

Equating equation (1) and (4) we have

Taking log on both sides

 ………..(5)

At 0K, i.e., when T = 0K, we can write equation (5) as

……(6)

Expression for Density of Holes in Terms of N_a

Substituting equation (5) in (1) we get

 ……..(7)

Here E_a - E_v = ΔE is known as ionisation energy of acceptors i.e., ΔE represents the energy required for an electron to move from valence band (E_v) to acceptor energy level (E_a).

Therefore equation (7) becomes

 ………(8)