= Solution
Let $e>0$ denote the <elementary charge>, so an <Electron>'s charge is $-e$. In the relaxation-time <Drude model> with positive transport <effective mass>,
$$
m^*\frac{d\mathbf v_d}{dt}=-e\mathbf E-\frac{m^*\mathbf v_d}{\tau}.
$$
The steady <drift velocity> is $\mathbf v_d=-e\tau\mathbf E/m^*=-\mu\mathbf E$, defining positive <electron mobility> $\mu=e\tau/m^*$. The <current density> is opposite to the <Electron> drift:
$$
\mathbf J=-ne\mathbf v_d=ne\mu\mathbf E.
$$
By the definition of <electrical conductivity>, $\mathbf J=\sigma\mathbf E$, so
$$
\boxed{\sigma=ne\mu}.
$$
Its units are $(\mathrm{m^{-3}})(\mathrm C)(\mathrm{m^2\,V^{-1}\,s^{-1}})=\mathrm{S\,m^{-1}}$. The mobility definition alone establishes the result in the scalar linear-response regime; the relaxation-time equation supplies a microscopic approximation for $\mu$.
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