Body Bias

The threshold voltage varies somewhat with the bias between Source and Bulk, V_SB.

V_T = V_T0 + GAMMA [ (2 PHI_F + V_SB)^1/2 - (2 PHI_F)^1/2 ]

where VT0 is the zero-bias threshold voltage, GAMMA is the body-bias factor

GAMMA = (2 q EPSILON_Si N_a)^1/2 / C_ox.

PHI_F is the bulk Fermi potential

PHI_F = (kT/q) ln(N_a/n_i).

N_a is the acceptor, boron, doping density, usually on the order of 10¹⁵ cm^-3.