Nanostructured Thermoelectric Generator

Nanostructuring

Grain size d 50 nm

Carrier concentration n 3.0 ×10¹⁹ cm⁻³

Temperature Split

Hot side T_h 500 K

Cold side T_c 300 K

Live Readouts

Seebeck coeff. S

-- μV/K

Elec. conductivity σ

-- S/cm

Thermal cond. κ

-- W/m·K

κ_lattice / κ_electronic

-- / --

Figure of merit ZT

Output power P

-- mW

electrons (charge current)

phonons (heat current)

How it works

A thermoelectric leg converts a temperature gradient directly into electricity via the Seebeck effect. Its efficiency is set by the dimensionless figure of merit:

ZT = S²σT / κ
κ = κ_e + κ_lat   (electronic + lattice/phonon)
κ_e = L·σ·T        (Wiedemann-Franz law, L = Lorenz number)
1/κ_lat(d) grows as grain size d shrinks below the
   phonon mean free path Λ  →  boundary scattering

Doping sets the carrier concentration n, which trades off two quantities in opposite directions — this is the classic thermoelectric bottleneck:

S(n)  ∝ n^(-2/3)     (Mott/degenerate-semiconductor formula: more carriers → less entropy per carrier → lower Seebeck voltage)
σ(n)  ∝ n             (more carriers → higher electrical conductivity)

The nanostructuring trick: grain boundaries scatter heat-carrying phonons (mean free path ~100–300 nm in most semiconductors) far more strongly than they scatter the much shorter-wavelength electrons. Shrinking the grain size d below the phonon mean free path collapses κ_lat while leaving S and σ almost untouched — a "phonon-glass, electron-crystal." That is exactly what the animation shows: electrons (blue) drift smoothly hot→cold, while phonons (orange) zig-zag and lose forward progress as the grains get smaller.

Grain size — sets how often phonons scatter at a boundary; smaller grains ⇒ lower κ_lat ⇒ higher ZT, down to the amorphous limit.
Carrier concentration — the Seebeck/conductivity trade-off; there is an optimum n that maximizes the power factor S²σ.
T_h / T_c — the driving temperature difference ΔT; output power scales with ΔT².

Real-world relevance: this phonon-glass/electron-crystal strategy (nanograined Bi₂Te₃, SiGe superlattices, skutterudites) is how modern thermoelectric generators recover waste heat from engines, spacecraft radioisotope generators, and industrial exhaust.

HOT ▸◂ COLD

Electron current Phonon (heat) current

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