Semiconductor physics

With electron density n, hole density p, electron mobility μn, hole mobility μp and elementary charge q, which expression gives the conductivity σ of a semiconductor?

  1. Aσ = q(nμn − pμp)
  2. Bσ = (nμn + pμp) / q
  3. Cσ = q(nμn + pμp)
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Answer: C. σ = q(nμn + pμp)

Both electrons and holes contribute to current, with conductivities q n μn and q p μp. These add together, giving σ = q(nμn + pμp). The resistivity is its reciprocal, ρ = 1/σ.

  • A. Holes move opposite to electrons but also have the opposite charge, so their currents flow in the same direction and add rather than subtract.
  • B. Conductivity is proportional to q, so dividing by q is wrong.
  • C. Correct. The electron and hole contributions are added.
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