Phonon Drag Thermoelectric: Seebeck Coefficient

Debye temp Θ_D (K) 300 Fermi energy E_F (eV) 5.00

e-ph coupling λ 0.50 Impurity rate Γ (K) 10

Seebeck coefficient S = S_diffusion + S_drag
S_diff = −(π²k_B²T)/(3eE_F) (Mott formula for diffusion term)
S_drag ~ λ·T³/Θ_D² · (Θ_D/T)^5·∫ — phonon-drag peak near T ≈ Θ_D/5
At low T: S_drag ∝ T³ (phonon-drag); at high T: S_diff ∝ T dominates. Impurities suppress drag via momentum relaxation.