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What is the expression of carrier mobility of a semiconductor material? (Where e is electric field, n is carrier density, and σ is conductivity)
1. \(\rm \mu = \frac{\sigma}{ne}\)
2. \(\rm \mu = \frac{ne}{\sigma}\)
3. \(\rm \mu = \frac{1}{\sigma}\)
4. \(\rm \mu = \frac{1}{ne}\)

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Correct Answer - Option 1 : \(\rm \mu = \frac{\sigma}{ne}\)

Concept:

Relation between Current Density and Electric Field:

Current Density:

The amount of electric current travelling per unit cross-section area is called as current density and expressed in amperes per square meter.

Formula for Current Density is given as,

J = I/A

Where,

I = current flowing through the conductor in Amperes

A = cross sectional area in m2.

Consider a conductor of length l and area of cross-section A. Let its two ends be raised to potentials V1 and V2 (V1 > V2).

The electric current density is given by the formula:

j = σE = nevd

The electric current density is given by the formula:

j = σE = nevd

For intrinsic semiconductors (no impurities), the number of electrons will be equal to the number of holes.

\(\sigma = {\rm{ne}}\frac{{{{\rm{v}}_{\rm{d}}}}}{{\rm{E}}} = {\rm{ne\mu }}\)

\(\rm \mu = \frac{\sigma}{ne}\)

For N-type semiconductor, electrons are majority carriers. 

Conductivity, σ ≈ neμ

Resistivity, \(\rho = \frac{1}{\sigma } = \frac{1}{{{{\rm{n}}_{\rm{e}}}{\rm{e}}{\mu _{\rm{e}}}}}\)    

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