Thermoelectric Materials and the Seebeck Effect

The Seebeck effect: charge carriers driven by heat

When one end of a conductor is hotter than the other, the charge carriers at the hot end have more thermal energy and diffuse toward the cold end. This pile-up of carriers builds an internal electric field that opposes further diffusion; at steady state a measurable open-circuit voltage appears across the sample. The proportionality constant between that voltage and the temperature difference is the Seebeck coefficient, S = −ΔV/ΔT, reported in microvolts per kelvin (µV/K).

The sign of S reveals the dominant carrier. In an n-type material electrons carry the charge and S is negative; in a p-type material holes dominate and S is positive. This is why a practical device pairs an n-type leg and a p-type leg electrically in series but thermally in parallel — the two Seebeck voltages add rather than cancel. Good thermoelectrics have |S| in the range of 150–300 µV/K, far larger than ordinary metals (copper is only about +1.8 µV/K), which is why heavily doped semiconductors, not metals, are used.

The figure of merit zT: three properties in tension

Device efficiency is set by the dimensionless figure of merit zT = S²σT/κ, where σ is electrical conductivity and κ is thermal conductivity (the sum of an electronic part κ_e and a lattice/phonon part κ_L). The numerator S²σ is called the power factor. A material is efficient only if it behaves like a good electrical conductor but a poor thermal conductor — a combination nature rarely supplies.

• Raising carrier concentration n increases σ but decreases |S| and raises κ_e (they are coupled through the Wiedemann–Franz law).
• The optimum carrier concentration for most thermoelectrics sits near 10¹⁹–10²⁰ carriers/cm³ — degenerate-semiconductor territory.
• The only property that can be tuned somewhat independently is κ_L, by scattering the heat-carrying phonons without scattering the electrons.

A zT of 1 corresponds to a device converting roughly 5–10% of the heat it receives into electricity; reaching zT ≈ 3 would make thermoelectrics competitive with conventional heat engines for many niches.

Materials chemistry: doping, alloying, and the phonon-glass idea

The workhorse near room temperature is bismuth telluride, Bi₂Te₃, a layered chalcogenide first exploited in the 1950s (notably by H. Julian Goldsmid, who demonstrated Peltier cooling with it in 1954). Native Bi₂Te₃ is tuned by doping: excess Te or SbI₃ additions give n-type material, while forming solid solutions with Sb₂Te₃ (i.e. Bi_0.5Sb_1.5Te₃) gives high-performance p-type legs. Alloying introduces mass and strain disorder that scatters phonons and lowers κ_L.

Glen Slack articulated the guiding principle in 1995 as the “phonon-glass, electron-crystal” (PGEC) concept: the ideal thermoelectric conducts electrons like a crystalline semiconductor but scatters phonons like an amorphous glass. Real strategies to approach it include:

• Cage compounds — skutterudites (CoSb₃) and clathrates hold loosely bound “rattler” atoms (e.g. Yb, Ba) inside structural voids that rattle and scatter phonons.
• Nanostructuring — grain boundaries and nanoprecipitates ~1–100 nm across scatter mid- and long-wavelength phonons; this pushed PbTe–SrTe to zT > 2.
• Intrinsic low conductivity — single-crystal SnSe has extremely soft, anharmonic bonding that gives ultralow κ_L, yielding a record bulk zT ≈ 2.6 at ~923 K (Zhao et al., 2014).

The Peltier and Thomson effects: running heat pumps in reverse

The Seebeck effect has two thermodynamic siblings. In 1834 Jean Charles Peltier found the converse: pass a current through a junction of two materials and heat is absorbed at one junction and released at the other. The Peltier effect makes solid-state refrigeration possible — the same Bi₂Te₃ couples used for power generation, driven electrically, become CPU coolers, portable fridges, and infrared-detector chillers. The rate of heat pumped is Q = ΠI, where the Peltier coefficient Π = S·T links the two effects (the Kelvin relation, derived by William Thomson, Lord Kelvin, in 1854).

Thomson also predicted a third effect that bears his name: a current-carrying conductor with a temperature gradient absorbs or releases heat continuously along its length. The three effects together (Seebeck, Peltier, Thomson) are unified by Onsager’s reciprocal relations in irreversible thermodynamics, which is why a single coefficient S governs both generation and cooling.

Applications: from deep space to your wristwatch

Thermoelectrics win wherever reliability and silence matter more than raw efficiency. Their marquee application is the radioisotope thermoelectric generator (RTG): the heat from decaying ²³⁸Pu drives SiGe or PbTe legs to power spacecraft. Voyager 1 and 2 (launched 1977), the Cassini orbiter, and the Curiosity and Perseverance Mars rovers all run on RTGs, which supply steady power for decades with zero moving parts.

• Peltier cooling — laser diodes, PCR thermal cyclers, wine coolers, and camping refrigerators use Bi₂Te₃ modules.
• Waste-heat recovery — skutterudite and PbTe generators are being fitted to automotive exhaust manifolds and industrial furnaces to reclaim heat that would otherwise be lost; a car engine dumps roughly 60% of its fuel energy as heat.
• Micro-power — body-heat-driven modules power wearable sensors and self-charging smartwatches, harvesting the few kelvin of gradient between skin and air.

The chief limitation remains cost and efficiency: bulk device efficiencies of 5–8% and the reliance on scarce, toxic elements (Te, Pb) confine thermoelectrics to specialty roles rather than grid-scale power.

Scope, limitations, and where research is heading

No single material spans all temperatures. Bi₂Te₃ degrades above ~450 K, PbTe and skutterudites cover the mid-range (600–800 K), and SiGe alloys serve above 900 K, so real generators use segmented legs that stack different materials along the temperature gradient. Mechanical and chemical stability — sublimation of Te, oxidation, and contact-resistance growth at hot junctions — often limits device lifetime more than zT does.

Current research pushes three fronts: (1) earth-abundant, non-toxic replacements such as Mg₃Sb₂, half-Heusler alloys, and copper selenide superionic conductors; (2) band-structure engineering — convergence of multiple valleys and resonant doping levels to raise the power factor, as demonstrated by Tl-doped PbTe; and (3) organic and hybrid thermoelectrics based on conducting polymers like PEDOT:PSS for flexible, low-temperature harvesting. The goal that would transform the field is a cheap, stable, non-toxic material with zT > 3 across a wide temperature window.

Common thermoelectric materials and their working temperature ranges

Material	Type	Peak zT	Optimal T range	Typical use
Bi₂Te₃ (doped)	p and n	~1.0	300–450 K	Peltier coolers, wearables
PbTe (doped)	p and n	~2.0	600–800 K	Deep-space RTGs, auto exhaust
SnSe (single crystal)	p	~2.6	800–900 K	Research / high-T generation
SiGe alloy	p and n	~1.0	900–1200 K	Radioisotope generators
Skutterudites (CoSb₃)	n	~1.4	700–800 K	Automotive waste heat