Nanowire Thermoelectric Power Factor Lab

Confinement dimensionality

Wire cross-section d 14 nm

Fermi level E_F 0.50

Temperature gradient ΔT 40 K

Live readouts

Seebeck coeff. S

0 µV/K

Conductivity g(E_F)

0.00

Power factor S²·g(E_F)

0.00

How it works

Squeezing a conductor down to a nanowire (1D) or thin film (2D) turns its smooth bulk density of states g(E) ∝ √E into a staircase of subbands, each opening with a van Hove singularity g(E) ∝ 1/√(E−E_n) in 1D. That reshaping is the whole trick behind nanostructured thermoelectrics.

Subband energies:  E_n = n² · E1,  E1 ∝ 1/d²  (particle-in-a-box confinement)
3D bulk DOS:       g(E) ∝ √E
2D well DOS:       g(E) = Σ_n step(E − E_n)          (a staircase)
1D wire DOS:       g(E) = Σ_n 1/√(E − E_n)            (van Hove spikes)

Mott formula:      S(E_F) = (π²/3)(k_B²T/e) · d[ln g(E)]/dE |_E=E_F
Power factor:      PF = S² · g(E_F)

Dimensionality — switches which g(E) shape drives the Mott formula; the electron stream in the nanowire visualizes the resulting drift.
Wire cross-section d — smaller d pushes the subbands E_n = n²E1 further apart (E1 ∝ 1/d²), sharpening the DOS steps/spikes that boost S.
Fermi level E_F — where the electron gas sits on the DOS curve; placing it right where g(E) rises steeply maximizes |d ln g/dE|, hence |S|.
Temperature gradient ΔT — the hot→cold electron drift shown in the wire (open-circuit Seebeck voltage V ≈ S·ΔT); it also sets the drift speed here.

Real-world relevance: this is the Hicks–Dresselhaus mechanism used to design nanostructured thermoelectric materials (nanowires, superlattices, quantum-dot arrays) that convert waste heat into electricity or run solid-state Peltier coolers with a higher figure of merit ZT than any bulk crystal of the same composition.

Hot end Cold end Drifting electron

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