 Acceptor density for a stable Hall sign

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 $1/(e{N}_A)$ 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.