Mobility

MOBILITY

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

μn and μp 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.

Table 3.6

Electron and hole mobilities at 300 K

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 vdn. Thus,

where μn is the mobility of electron.

The drift current density Jn 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,

If σn is the conductivity of a semiconductor due to free electrons, the current density Jn 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 σp the conductivity due to the drift of holes, then

where μp is the mobility of holes in the material.

Thus, total conductivity σ due to free electrons and holes

σ = σn + σp

σ = ne μn + pe μp

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 number of free electrons and holes, n = p = ni.

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

From eqn (8)