Derive the equation of mobility in terms of relaxation time $(\tau)$. Write its unit.
(N/A) The drift velocity $v_d$ of an electron in the presence of an external electric field $E$ is given by the relation: $v_d = -\frac{eE}{m} \tau$,where $e$ is the charge of an electron,$m$ is the mass of the electron,and $\tau$ is the relaxation time.
Taking the magnitude,we have $|v_d| = \frac{eE}{m} \tau$.
Mobility $\mu$ is defined as the magnitude of drift velocity per unit electric field: $\mu = \frac{|v_d|}{E}$.
Substituting the expression for $|v_d|$,we get $\mu = \frac{eE\tau}{mE} = \frac{e\tau}{m}$.
The $SI$ unit of mobility is $\frac{m/s}{V/m} = m^2 V^{-1} s^{-1}$.
Taking the magnitude,we have $|v_d| = \frac{eE}{m} \tau$.
Mobility $\mu$ is defined as the magnitude of drift velocity per unit electric field: $\mu = \frac{|v_d|}{E}$.
Substituting the expression for $|v_d|$,we get $\mu = \frac{eE\tau}{mE} = \frac{e\tau}{m}$.
The $SI$ unit of mobility is $\frac{m/s}{V/m} = m^2 V^{-1} s^{-1}$.
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