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PRACTICE / Intrinsic and doped semiconductors

Doping does not remove the minority carriers

At a fixed temperature, a nondegenerate n-type semiconductor has electron density n = 2.0×10²⁰ m⁻³ and intrinsic carrier density ni = 1.0×10¹⁶ m⁻³.

What is its equilibrium hole density p?

Organize the givens & assumptions
  • n = 2.0×10²⁰ m⁻³
  • ni = 1.0×10¹⁶ m⁻³
  • Equilibrium relation np = ni²

Thermal equilibrium, nondegenerate carrier statistics and uniform bulk sample, no optical injection. Donors supply majority electrons; the crystal remains charge-neutral including fixed ionized dopants.

  1. A1.0×1016 m−31.0\times10^{16}\ \mathrm{m^{-3}}
  2. B2.0×1020 m−32.0\times10^{20}\ \mathrm{m^{-3}}
  3. C0 m−30\ \mathrm{m^{-3}}
  4. D5.0×1011 m−35.0\times10^{11}\ \mathrm{m^{-3}}

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