= MOS inversion threshold
{c}
{title2=$\psi_s\simeq2\phi_F$}
For an ideal <MOSFET> with a nondegenerate <p-type semiconductor> of acceptor density $N_A$, define $\phi_F=(k_BT/e)\ln(N_A/n_i)>0$, where $n_i$ is the <intrinsic carrier concentration>. A positive surface <electric potential> $\psi_s$ lowers the local <conduction band> and <valence band> by $e\psi_s$. The surface <Electron> density is $n_s=(n_i^2/N_A)\exp(e\psi_s/k_BT)$. Equality $n_s=N_A$ gives the conventional onset of strong inversion at $\psi_s=2\phi_F$. The earlier crossover $n_s=p_s=n_i$ occurs at $\psi_s=\phi_F$. Neither condition requires the <Fermi level> to enter the conduction band.
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