Week 10: Phonon transport, windows, ballistic T3 law and ZT

Phonons carry heat too: windows, ballistic T³ law and ZT ≈ (Mλ/A)/(Mλ/A)_ph (Datta Ch. 14)

Phonons obey the same elastic-transport formula as electrons with q → ℏω and Fermi → Bose functions (Eq. 14.6). Left: the two window functions (Fig. 14.1). Right: the ballistic phonon heat conductance per area (Eq. 14.9), with a Debye cut-off. Bottom: thermal conductivity κ_ph = (π²k²T/3h)(Mλ/A)_ph and electrical σ = (q²/h)(Mλ/A) set ZT (Eqs. 14.1–14.4).

Temperature T Sound velocity c_s · Debye temperature θ_D Phonons: M/A (m⁻²) · λ_ph (nm) Electrons: M/A (m⁻²) · λ (nm)

Ballistic G_K/A at T (Debye cut-off) · T³ law–

κ_ph = 284 pW/K × (T/300 K) × (Mλ/A)_ph–

σ = (q²/h)(Mλ/A)–

ZT ≈ 4(k/q)²Tσ/κ_ph (Eq. 14.3) · ratio (Eq. 14.4)–

Phonons carry heat too: windows, ballistic T³ law and ZT ≈ (Mλ/A)/(Mλ/A)ph (Datta Ch. 14)

Phonons carry heat too: windows, ballistic T³ law and ZT ≈ (Mλ/A)/(Mλ/A)_ph (Datta Ch. 14)