Chapter 3 · Visualization 5 of 6 · Section 3.5
Pinch-off Voltage and Control From Terminal C
Fix the gate and use VCB as the control. The inversion charge falls almost linearly, would reach zero at the pinch-off voltage VP , and then decays exponentially instead.
Inversion charge versus VCB at fixed VGB (Fig. 3.16); amber line: VP
Pinch-off voltage versus VGB (dot: your VGB )
What to look for VP = ψsa (VGB ) − φ0 , ψsa = (−γ/2 + √(γ²/4 + VGB − VFB ))²
Linear axis: in strong inversion |Q′I | falls almost linearly with VCB ; extrapolated to zero it gives VP . Log axis: past VP the charge does not vanish; it falls by 10× per 60 mV of VCB (slope 1/φt , not 1/nφt ). VP grows with VGB with slope about 1/n: this VP is the one used in Chapter 4 for saturation. Try this At VGB = 2 V, read VP . Set VCB = VP : what fraction of the VCB = 0 charge is left? Switch to log scale and measure how much VCB reduces the charge by one decade in weak inversion. Find the VGB at which VP = 0. What is that voltage called? Double tox . Does the slope of VP versus VGB increase or decrease? Relate it to n.
Model: exact charge-sheet equations of Chapter 3 (3.2.8), (3.2.21), with hole, acceptor and electron terms, Boltzmann statistics, ni = 10¹⁰ cm⁻³, φ0 = 2ΦF + 6φt , Q′o /q = 10¹⁰ cm⁻², T = 300 K. The same equations are in the Colab notebook. Section 3.5 of Tsividis and McAndrew, Operation and Modeling of the MOS Transistor .