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

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 slod 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    ...(3)

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

J_n = σ_n E ...(4)

or   σ_n = J_n / E = nev_dn / E  ...(5)

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

σ_n = ne µ_n E / E

σ_n = ne µ_n    ...(6)

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

σ_p = pe µ_p    ...(7)

where µ_p is the mobility of holes in the material.

Thus, total conductivity σ due to free electrons and holes

σ = σ_n + σ_p

σ = ne μ_n + p_e μ_p

σ = e (n μ_n + p (μ_p )   ...(8)

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, electron-hole pairs per unit volume is given by

From eqn (8)

σ_i = e ( n_i µ_n + n_i µ_p)

σ_i = en_i (µ_n + µ_p)   ...(9)

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