MOS Capacitor — Energy Bands & Surface Potential

← EDC

Standard M | SiO₂ | Semiconductor structure (Al gate, SiO₂ oxide, user-picked substrate). Vary the substrate doping N_A/N_D and the gate voltage V_GS to sweep the three regimes — accumulation (bands bend up at the surface), depletion (bending down, depletion region forms), and inversion (bending past E_i = E_f, minority layer).

Substrate

Material

Substrate type

N_A / N_D (cm⁻³)

t_ox (nm)

Temperature (K)

Gate voltage

V_GS (V) — 0.00 (slider range −5 to +5)

Default gate: Al (φ_M = 4.10 eV) on SiO₂. Sweep V_GS to cross V_FB and V_T; the band diagram re-bends live. The number box accepts any value; out-of-range values still calculate (slider just visually pins at the edge). …

E_c E_v E_i E_f E_vac M SiO₂

✍ Derivation — click to expand ▶