Week 6: Quantum capacitance and 60 mV per decade

Quantum capacitance and the 60 mV per decade rule (Datta Sec. 7.3.1, Eqs. 7.10–7.14)

Equilibrium (no drain bias). The gate tries to pull the 2D band edge down by qV_G; the electrons that pour in charge the channel and push it back up. Below threshold almost nothing pushes back, so n grows 10× for every kT·ln10 ≈ 60 mV. Above threshold the oxide capacitance C_E and the quantum capacitance C_Q = q²D₀ act in series.

Gate voltage V_G Oxide thickness t_ox (ε_r = 4) Effective mass m/m₀ (sets D₀, hence C_Q) Temperature T

Electron density n–

C_E = ε/t_ox · C_Q here–

Gate efficiency dU/d(−qV_G)–

Subthreshold slope–