How this calculator works
The classical Einstein relation connects random diffusion with drift under a weak electric field. Thermal energy kBT divided by the carrier charge magnitude gives a voltage scale; multiplying it by electrical mobility gives the diffusion coefficient. Use a positive charge magnitude even for electrons. Degenerate carriers, strong fields and nonequilibrium transport can require a generalized relation.
Formula
D = mu kB T/|q|; mu = D |q|/(kB T).
Worked example
For singly charged carriers at 300 K, D/mu = 0.02585199979 V. Mobility 0.1 m²/(V s) therefore gives D = 0.002585199979 m²/s; at 600 K it gives 0.005170399957 m²/s.
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Frequently asked questions
Should electron charge be negative?
Enter its positive magnitude, 1.602176634e-19 C. Mobility here is also a magnitude.
How do I convert cm²/(V s)?
Multiply by 0.0001 to obtain m²/(V s).
Does this predict mobility from temperature alone?
No. You also need a diffusion coefficient or a separate transport model.