Chapter 4 · Visualization 4 of 6 · Sections 4.7 to 4.9
Model Comparison
Put the hand-analysis models side by side with the complete all-region model: the source-referenced strong-inversion model with your choice of α, the α = 1 square law, the weak-inversion exponential and a single-piece interpolation.
Output characteristic at your VGS
Transfer characteristic at VDS = 2 V (dot: your VGS )
Relative error of each simplified model in saturation (VDS = 2 V)
What to look for IDS = (W/L)µC′ox [(VGS − VT )VDS − (α/2)VDS ²] (4.7.24); IDS = I′M e(VGS −VM )/nφt (1 − e−VDS /φt ) (4.8.11)
α = 1 overestimates the current and V′DS : it treats the depletion region as equally deep at the drain as at the source. The strong-inversion model is good above VH but predicts zero current below VT ; the weak model is good below VM and explodes above. The single-piece model is smooth everywhere, but with the physical VT its weak-inversion current is off by a constant factor. Try this Set α = 1.00, then α = α1 , then the 'best α' in the readout. Watch the output plot: which part of the curve does each fit well? Increase tox to 25 nm (larger γ). How much worse is the α = 1 model now? Move the single-piece VT shift until the teal curve sits on the black one in weak inversion. What does it do in strong inversion? Where in VGS does no simple model stay within ±10%? That is moderate inversion.
Model: complete all-region charge-sheet model of Section 4.3, (4.3.13) to (4.3.15), long channel, uniform body, n⁺ polysilicon gate, W = L = 10 µm, µ = 400 cm²/V·s, ni = 10¹⁰ cm⁻³, φ0 = 2ΦF + 6φt , φZ = 4φt , T = 300 K unless set. The same equations are in the Colab notebook. All simplified models use the physical β = (W/L)µC′ox ; no parameter fitting except the sliders. Sections 4.7.3, 4.8.3 and 4.9 of Tsividis and McAndrew, Operation and Modeling of the MOS Transistor .