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The sign must become positive, so use p-type acceptor impurities, such as boron substituting for tetravalent silicon. Assume uncompensated, fully ionized acceptors of density $N_A$, nondegenerate carriers and equilibrium throughout the interval. Charge neutrality and mass action giveFor a nearly constant hole-dominated Hall coefficient, the dopant plateau must persist up to the highest temperature. Its necessary concentration scale is thereforeThe order-of-magnitude onset is $N_A\sim 4\times 10^{20}{\mathrm{m}}^{-3}$, but equality is not a flat plateau: at $N_A=n_i(500)$, $p/N_A=(1+\sqrt{5})/2=1.618$, changing the hole-only Hall coefficient by about 38 percent. The word approximately does not define a unique sharp minimum without a tolerance.

For $N_A\gg n_i$, $p\simeq N_A[1+(n_i/N_A{)}^2]$, so the hole-only $R_H\simeq 1/(e{N}_A)$ varies by a fraction of order $(n_i/N_A{)}^2$. An illustrative one-percent tolerance in that approximation is obtained with $N_A\simeq 10n_i(500)=4.0\times 10^{21}{\mathrm{m}}^{-3}$. This gives $R_H\simeq +1.56\times 10^{-3}{\mathrm{m}}^3{\mathrm{C}}^{-1}$ and less than one percent hole-density-induced variation. It is an explicit plateau criterion, not an exact minimum deduced from the unspecified word approximately.

At 300 K the minority electron concentration isThus the onset-scale estimate gives about $2.5\times 10^{11}{\mathrm{m}}^{-3}$, whereas the explicit ten-times-larger plateau choice gives $2.5\times 10^{10}{\mathrm{m}}^{-3}$.

The acceptor density for a stable Hall sign can be more restrictive if both carriers matter. With mobility ratio $r_{\mu }={\mu }_e/{\mu }_h>1$, positive Hall sign requires $p>r_{\mu }{n}_i$, or $N_A>n_i(r_{\mu }-r_{\mu }^{-1})$. In the strongly extrinsic limit the full two-carrier Hall correction scales as $(1+r_{\mu }{)}^2(n_i/N_A{)}^2$, not just $(n_i/N_A{)}^2$. Hence a true measured-Hall tolerance can require a larger dopant density than the hole-only illustration. Mobilities and their temperature dependence are not supplied, so they cannot be used to manufacture a unique sharper minimum.