Question

Define and write the formula of mobility.

Hint:

Mobility is drift velocity per unit electric field; recall \( \mu = v_d/E = e\tau/m \).

Answer 1

Step 1: Definition.
The mobility of a charge carrier is defined as the magnitude of the drift velocity acquired by the carrier per unit applied electric field. In other words, it tells us how easily a charge carrier (an electron in a metal) moves through the material under an external electric field.

Step 2: Formula.
If \( v_d \) is the drift velocity of the charge carrier and \( E \) is the applied electric field, then mobility \( \mu \) is
\[ \mu = \frac{v_d}{E} \]

Step 3: Alternative form and SI unit.
Since the drift velocity for electrons is \( v_d = \dfrac{eE\tau}{m} \) (where \( e \) is the electronic charge, \( \tau \) is the average relaxation time and \( m \) is the electron mass), substituting this gives
\[ \mu = \frac{e\tau}{m} \]
The SI unit of mobility is \( \text{m}^2\,\text{V}^{-1}\,\text{s}^{-1} \) (metre squared per volt per second).

\[\boxed{\ \mu = \dfrac{v_d}{E} = \dfrac{e\tau}{m}\ }\]