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  "title": "MOS Capacitor — Band Bending — EDC",
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  "description": "The MOS Capacitor workbench is the heart of every MOSFET. Pick an n-type or p-type substrate, a doping N, a t_ox, and sweep V_GS. Watch the surface potential ψ_s evolve through accumulation (bands bend up), depletion (depletion region forms), and inversion (minority surface layer). Threshold V_T, flat-band V_FB, and body-effect γ are computed live.",
  "keywords": [
    "moscap",
    "mos capacitor",
    "band bending",
    "surface potential",
    "depletion width",
    "flat-band voltage",
    "threshold",
    "accumulation",
    "inversion"
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  "content": {
    "formulas": [
      "Flat-band voltage: V_FB = φ_M − φ_S = φ_M − (χ + E_c − E_F)/q",
      "Threshold: V_T = V_FB + 2·φ_F + √(2·ε_s·q·N·2·φ_F) / C_ox",
      "Body effect: V_T(V_SB) = V_T0 + γ·(√(2·φ_F + V_SB) − √(2·φ_F))",
      "Body coefficient: γ = √(2·q·ε_s·N) / C_ox",
      "Surface potential: ψ_s = 2·φ_F (strong inversion threshold)",
      "Oxide capacitance: C_ox = ε_ox / t_ox"
    ],
    "citations": [
      "Sze, S. M., Ng, K. K., \"Physics of Semiconductor Devices,\" 3rd ed., Wiley, 2006.",
      "Tsividis, Y., \"Operation and Modeling of the MOS Transistor,\" 3rd ed., 2011."
    ],
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        "q": "Why does V_T shift with V_SB?",
        "a": "Body effect: when the source is not at the substrate (V_SB > 0), the source-body junction is reverse-biased, widening the depletion region and increasing V_T. γ·(√(2·φ_F + V_SB) − √(2·φ_F))."
      },
      {
        "q": "What is \"strong inversion\"?",
        "a": "The surface potential ψ_s has reached 2·φ_F, where the minority carrier concentration at the surface equals the bulk doping. Beyond this, further gate voltage creates an inversion layer (minority carriers)."
      }
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  "last_updated": "2026-07-05"
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