Semiconductor physics

Which is the Einstein relation between the diffusion coefficient D and the mobility μ of carriers? (k: Boltzmann constant, T: absolute temperature, q: elementary charge)

  1. AD = qμ
  2. BD = μ / (kT)
  3. CD = μkT / q
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Answer: C. D = μkT / q

The Einstein relation is D = μkT/q. How easily carriers diffuse and how easily they drift are both determined by carrier scattering, so the two are proportional. At room temperature kT/q is about 26 mV, so for μ = 1000 cm²/V·s, D ≈ 26 cm²/s.

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