Chapter 2 · Visualization 4 of 6 · Section 2.6
Regions of Inversion
On a log scale the inversion charge is exponential in weak inversion and linear in strong inversion. Between them, in moderate inversion, neither simple formula works.
Inversion charge versus gate voltage: exact curve and the two approximations
What to look for weak: Q′I ∝ exp(ψS /φt ) strong: Q′I ≈ −C′ox (VGB − VT )
Weak inversion: a straight line on the log plot. The swing is n φt ln 10, about 60 mV per decade times n. Strong inversion: Q′I = −C′ox (VGB − VT ) with VT = VFB + ψ0 + γ√ψ0 ; a curve that bends away from it near VT . Moderate inversion is only a few tenths of a volt wide, yet circuits for low supply voltages often operate in it. Try this Drag the marker across the three regions and read the error of each approximation in the panel. Raise the temperature to 400 K. How does the weak-inversion swing change? Thicken the oxide to 10 nm and watch the slope factor n and the swing grow.
Model: exact one-dimensional Poisson solution for a p-type MOS capacitor with Boltzmann statistics, following Chapter 2 of Tsividis and McAndrew, Operation and Modeling of the MOS Transistor . ni = 1010 cm⁻³ at 300 K, εs = 11.7 ε0 , εox = 3.9 ε0 , Q′o /q = 10¹⁰ cm⁻² unless a slider changes it. Values are for teaching and are not a process simulation.