= Conductivity ratio of doped and intrinsic semiconductors
An <intrinsic semiconductor> has electron and hole densities $n=p=n_i$, so $\sigma_i=en_i(\mu_e+\mu_h)$. In a fully ionised, uncompensated n-type sample with $N_D\gg n_i$, $n\simeq N_D$, $p\simeq n_i^2/N_D$, and
$$
\frac{\sigma_d}{\sigma_i}\simeq\frac{N_D\mu_{e,d}}{n_i(\mu_{e,i}+\mu_{h,i})}.
$$
Thus a carrier-density ratio alone is not generally the <electrical conductivity> ratio. If <electron mobility> is unchanged and electron transport dominates the intrinsic conductivity, it reduces to $N_D/n_i$; equal electron and hole mobilities instead give $N_D/(2n_i)$. Ionised-impurity scattering can change the doped mobility.
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