Mobility

MOBILITY

If E = 1 V/m then µ = v_d Thus, mobility μ is defined as the velocity of a charge carrier per unit electrical field strength.

µ_n and µ_p denote electron mobility and hole mobility respectively.

Since the types of drift of electrons and of holes are different, the mobility of an electron at any temperature is different from (greater than) that of the hole.

Table 3.6 gives the values of electron and hole mobilities at 300K.

Expression for Electrical conductivity

If the density of free electrons in the material is n, the net charge available per unit volume of the material for the conduction is equal to ne, where e is the charge of the electron.

When an external electrical field E is applied, the electrons move with a drift velocity v_dn Thus,

V_dn = µ_n E .................(2)

where μ_n is the mobility of electron.

The drift current density J_n due to electrons is defined as the charge flowing across unit area of cross-section per unit time due to their drift under the influence of an electrical field E. It is given by,

J_n = nev_dn

If σ_n is the conductivity of a semiconductor due to free electrons, the current density J_n is related to the applied electric field E by

Substituting eqn (2) in eqn (5), we have

If p is the number of holes per unit volume and σ­_p the conductivity due to the drift of holes, then

where µ_p is the mobility of holes in the material.

Thus, total conductivity o due to free electrons and holes .

where σ is the total conductivity of the material and it is generally expressed in mho/m.

For the intrinsic semiconductor which contains the same (8). number of free electrons and holes, n = p = n_i.

Therefore, the electrical conductivity σ_i of an intrinsic semiconductor having n_i electron-hole pairs per unit volume is given by