= Acceptor density for a stable Hall sign
{title2=$N_A>n_i(r_\mu-r_\mu^{-1})$}
For fully ionized uncompensated acceptors, $p-n=N_A$ and $np=n_i^2$. If $r_\mu=\mu_e/\mu_h>1$, the weak-field <two-carrier Hall coefficient> is positive when $p>r_\mu n_i$, giving the displayed sign threshold. A nearly constant Hall coefficient requires a stronger plateau condition. When $N_A\gg n_i$, its relative correction to $1/(eN_A)$ is approximately $-(1+r_\mu)^2(n_i/N_A)^2$. Thus specifying only that the coefficient is approximately constant does not define an exact minimum dopant concentration without a tolerance and mobility assumptions.
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