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Physics · Ch 3 — Current Electricity

Mobility

3.5.1

Mobility

Mobility: The Ease of Charge Carrier Motion

Mobility quantifies how quickly a charge carrier (like an electron or ion) can drift through a material when an electric field is applied. It is a measure of the "ease" with which the carrier moves.

Definition

Mobility (μ\mu) is defined as the magnitude of the drift velocity per unit electric field.

μ=∣vd∣∣E∣\mu = \frac{|\mathbf{v}_d|}{|\mathbf{E}|}

  • vd\mathbf{v}_d is the drift velocity of the charge carrier.
  • E\mathbf{E} is the applied electric field.

The SI unit of mobility is m2/Vs\text{m}^2/\text{Vs}. A commonly used practical unit is cm2/Vs\text{cm}^2/\text{Vs}, where 1 m2/Vs=104 cm2/Vs1 \, \text{m}^2/\text{Vs} = 10^4 \, \text{cm}^2/\text{Vs}. Mobility is always a positive quantity.

Relation to Collision Time

From the expression for drift velocity (vd=eEτm\mathbf{v}_d = \frac{e \mathbf{E} \tau}{m}), we can substitute into the definition of mobility:

μ=∣vd∣∣E∣=eτm\mu = \frac{|\mathbf{v}_d|}{|\mathbf{E}|} = \frac{e \tau}{m}

  • ee is the magnitude of the charge on the carrier (e.g., 1.6×10−19 C1.6 \times 10^{-19} \, \text{C} for an electron).
  • τ\tau is the average collision time (or relaxation time) for the charge carrier.
  • mm is the mass of the charge carrier. …