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  "slug": "edc-pn",
  "title": "PN Junction — EDC Workbench",
  "category": "electronic-devices",
  "category_label": "Electronic devices",
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  "description": "The PN Junction workbench is the foundation of all semiconductor devices. Pick a material (Si, Ge, GaAs, SiC), a doping profile (NA, ND), and a temperature T, and see the energy band diagram, the depletion width W, the built-in potential V_bi, the junction capacitance C_j, the I-V curve, and the breakdown voltage. Use it to verify textbook problems, design a diode, or sanity-check a process simulation.",
  "keywords": [
    "pn junction",
    "depletion width",
    "built-in potential",
    "shockley diode",
    "junction capacitance",
    "energy band",
    "edc"
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  "content": {
    "formulas": [
      "Built-in potential: V_bi = V_T·ln(N_A·N_D / n_i²)",
      "Depletion width: W = √(2·ε_s·V_bi·(N_A + N_D) / (q·N_A·N_D))",
      "Junction capacitance: C_j = ε_s·A / W, C_j ∝ 1/√(V_bi + V_R) for abrupt junction",
      "Diode current: I = I_s·(e^{V/V_T} − 1), I_s = q·A·(D_p·n_p0/L_p + D_n·n_n0/L_n)",
      "Thermal voltage: V_T = kT/q = 25.85 mV at 300 K",
      "Intrinsic carrier: n_i² = N_C·N_V·e^{−E_g/kT}",
      "Breakdown voltage: V_BR ≈ (ε_s·E_crit²) / (2·q·N_eff) for one-sided junction"
    ],
    "citations": [
      "Streetman, B. G., Banerjee, S., \"Solid State Electronic Devices,\" 7th ed., Pearson, 2015.",
      "Pierret, R. F., \"Semiconductor Device Fundamentals,\" Addison-Wesley, 1996."
    ],
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        "q": "Why is V_bi higher for Si than Ge?",
        "a": "V_bi ∝ E_g (bandgap) × ln(N_A·N_D / n_i²). Si has E_g = 1.12 eV, Ge has 0.66 eV. So Si has higher V_bi at the same doping."
      },
      {
        "q": "Why does C_j drop with reverse bias?",
        "a": "C_j = ε_s·A / W, and W increases with reverse bias (√(V_bi + V_R)). So C_j decreases."
      }
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  "last_updated": "2026-07-05"
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