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

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

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

Relation to Collision Time

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

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