MOS electrostatics · 300 K · Si / SiO₂ / high-k

Dual-Poly Gate Explorer

Why does CMOS use an n⁺⁺ polysilicon gate on the NMOS and a p⁺⁺ polysilicon gate on the PMOS, and what replaced them after 45 nm? Move each gate's workfunction or add an interface dipole, and watch the energy band diagram and the threshold voltage respond. Pick a technology node to load a typical gate stack from 180 nm to 2 nm.

VT has a fixed costTo invert the surface you always pay 2φF + Qdep/Cox, about 1.3 V for N = 3×10¹⁷ cm⁻³ and tox = 5 nm. The gate material cannot change that part.
The gate sets VFB = Φm − ΦsA p-body has a large Φs (≈ 5.06 eV). An n⁺⁺ gate (Φm ≈ 4.05 eV) gives VFB ≈ −1 V, which cancels most of the fixed cost and leaves a small positive VT.
The PMOS is the mirror imageAn n-body has a small Φs (≈ 4.16 eV), so a p⁺⁺ gate (Φm ≈ 5.17 eV) gives VFB ≈ +1 V and a small negative VT. Swap the gates and |VT| jumps to ≈ 1.4 V.
A dipole adds ΔVdip directlyA La₂O₃ or Al₂O₃ layer at the high-k/SiO₂ interface creates a potential step. VFB and VT shift one-for-one: La moves both down (helps NMOS), Al moves both up (helps PMOS). The step does not depend on tox.
Quick setups: technology nodeillustrative values

Gate pairing
Gate stack
Diagram view

Threshold voltage for every gate choice

Model: ideal MOS capacitor with Qox = 0, ni = 10¹⁰ cm⁻³, kT/q = 25.85 mV, χSi = 4.05 eV, Eg = 1.12 eV (Ei at mid-gap), χSiO₂ = 0.95 eV, χHfO₂ ≈ 2.0 eV, εSi = 11.7ε₀, εox = 3.9ε₀ (high-k entered as EOT). Degenerate poly has EF at the band edge: n⁺⁺ Φm = 4.05 eV, p⁺⁺ Φm = 5.17 eV. VFB = Φm − Φs + ΔVdip. The band diagram solves the 1-D Poisson charge relation for ψs; the VT formula uses the depletion approximation (ψs = 2φF). In thin-body mode the depletion charge is capped at qN·Tsi and the gate is treated as single-sided; real FinFET/GAA devices are multi-gate and define VT by a current criterion, so treat those numbers as trends. Node presets are textbook-typical stacks, not any foundry's actual process; poly depletion, quantum confinement and short-channel VT roll-off are ignored. The oxide is drawn wider than scale.