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Formulas/physics/Current Electricity/Mobility of Charge Carriers

Mobility of Charge Carriers

Mobility is the drift velocity per unit electric field. SI unit: m² V⁻¹ s⁻¹. Relates to conductivity: σ = neμ. Higher mobility → better conductor at a given carrier density.
Class 12
Derivation

Definition

Mobility μ\mu of a charge carrier is the magnitude of drift velocity per unit electric field:

μ=∣vd∣E\mu = \frac{|v_d|}{E}

From drift velocity vd=eEτ/mv_d = eE\tau/m:

μ=eτm\boxed{\mu = \frac{e\tau}{m}}

SI unit: m2 V−1 s−1\text{m}^2\,\text{V}^{-1}\,\text{s}^{-1}

Relation to conductivity

Current density: J=nevd=neμEJ = nev_d = ne\mu E

From J=σEJ = \sigma E:

σ=neμ\sigma = ne\mu

For a semiconductor with both electrons (nn, mobility μe\mu_e) and holes (pp, mobility μh\mu_h):

σ=e(nμe+pμh)\sigma = e(n\mu_e + p\mu_h)

Physical interpretation

Mobility measures how easily a carrier moves through the material under a given field. High mobility means:

  • Less scattering (longer τ\tau)
  • Lighter effective mass m∗m^*

Typical values

Materialμe\mu_e (m² V⁻¹ s⁻¹)
Copper4.3×10−34.3 \times 10^{-3}
Silicon0.1350.135
GaAs0.850.85
InSb7.87.8

GaAs and InSb have very high electron mobility — hence their use in high-frequency transistors and infrared detectors.

Note
In semiconductors, hole mobility is always less than electron mobility for the same material. Electrons in the conduction band have lower effective mass than holes in the valence band.