Mott formula: S = −(π²k²T)/(3eE_F) | ZT = S²σT/κ figure of merit
S: — μV/K | ZT: — | ΔV: — mV
The Seebeck effect: a temperature gradient ΔT across a conductor drives electron diffusion, generating voltage ΔV = S·ΔT. For metals, the Mott formula gives S = −(π²k_B²T)/(3eE_F) ∝ T/E_F (typically −10 to −100 μV/K). Phonon drag (Gurevich 1945) enhances S at low T via phonon-electron momentum transfer, adding S_ph ∝ A·T³. The figure of merit ZT = S²σT/κ quantifies thermoelectric efficiency; ZT > 1 needed for practical devices.