A thermoelectric material that turns a temperature difference into electricity is ranked by a single dimensionless number, ZT = α²σT/κ. Move the sliders for the Seebeck coefficient α, electrical conductivity σ, thermal conductivity κ and the hot- and cold-side temperatures, and watch the power factor, Carnot limit and real conversion efficiency all update at once.
Parameters
Seebeck coefficient α
μV/K
Voltage per K of temperature difference. Positive for p-type, negative for n-type.
Electrical conductivity σ
S/cm
Carrier mobility × density. Bi₂Te₃ is around 1000 S/cm.
Thermal conductivity κ
W/(m·K)
Sum of electronic and phonon contributions. Lower is better for ZT.
Operating temperature T_op
K
Representative temperature at which α, σ and κ are evaluated.
Hot side T_h
K
Heat-source temperature. 600–900 K is typical for waste-heat recovery.
Cold side T_c
K
Heat-sink temperature. About 300 K with room-temperature water cooling.
Results
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Power factor (μW/cm·K²)
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ZT (at T_op)
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ZT_avg (at T_avg)
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Carnot efficiency (%)
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Real efficiency (%)
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Commercialisation tier
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Thermoelectric leg module — conceptual animation
Heat flowing in at the hot side passes through the p-type and n-type legs and drives a DC current through the external load. Red arrows: incoming heat Q_h, blue arrows: rejected heat Q_c, yellow arrows: current I.
At ZT = 1 the real efficiency is about 15% of Carnot, at ZT = 2 about 30%, and only at ZT → ∞ does it reach the Carnot limit (separating electron and phonon transport is the technical challenge).
The power factor PF measures the maximum electrical power per unit ΔT² and per unit volume. It ignores κ and is therefore the "electrical figure of merit" of the material on its own.
Thermoelectric figure of merit ZT
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I heard "thermoelectric" materials can make electricity from a temperature difference. Is that the opposite of a Peltier element?
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Exactly. The same element acts as a Peltier cooler when you push current through it, or as a Seebeck generator when you apply a temperature difference instead. It has no moving parts, so as long as you have a ΔT you get DC power. NASA's deep-space probes — Voyager, Curiosity on Mars, New Horizons — all run on radioisotope thermoelectric generators (RTGs) using exactly this effect.
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OK, so how do we rank one material against another? People keep mentioning "ZT".
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ZT = α²σT/κ is a single dimensionless number that captures the whole story. Big voltage per K (large α), low electrical resistance (large σ) and a poor thermal conductor (small κ) all push ZT up. The famous "ZT ≈ 1 wall" held for decades — Bi₂Te₃ was stuck around 1. Since the 2000s nanostructuring has cracked it: SnSe now reports ZT ≈ 2.6. Drag the sliders here and you'll get a feel for the trade-offs.
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Wait — if I just need big α, big σ and small κ, that sounds easy. Why is it so hard?
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Because the three are not independent — they are all functions of carrier concentration and they fight each other. More carriers means higher σ but lower α, and the extra electrons also carry heat, so κ goes up too. So a ZT-vs-carrier curve always shows a peak around 10¹⁹–10²⁰ cm⁻³. The modern winning strategy is "phonon glass, electron crystal" (PGEC): let electrons flow freely, but scatter phonons heavily with nanoparticles, alloying, rattling atoms or layered structures so that κ_lattice drops without hurting σ.
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My current numbers show ZT = 0.8 and real efficiency 11%. Is that good or bad?
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A typical commercial Peltier module sits at ZT ≈ 1, so 0.8 is "close but not quite". The 11% is pulled out of a Carnot ceiling of 57% — about a fifth of Carnot — because you set a big ΔT of 400 K. The hard lesson is that doubling ZT does not double the efficiency: the √(1+ZT) form means going from ZT 0.8 to 2.0 only lifts you from roughly 11% to 20%. So thermoelectrics rarely compete with combined-cycle gas turbines (30–40%). They win where nothing else can run — on waste heat from car exhaust, on dim sunlight in deep space, on body heat for wearables, in cryogenic cooling with no moving parts.
Frequently Asked Questions
ZT is a single dimensionless number that summarises how good a thermoelectric material is, defined as ZT = α²σT/κ. α is the Seebeck coefficient (voltage produced per K of temperature difference), σ is the electrical conductivity, κ is the thermal conductivity and T is absolute temperature. A material that gives a large voltage, conducts electricity well but blocks heat has a high ZT. For decades ZT ≈ 1 was the practical ceiling; modern nanostructured materials such as Bi₂Te₃ and SnSe now report ZT > 2.
The real efficiency of a thermoelectric generator is the Carnot efficiency η_C = (T_h−T_c)/T_h multiplied by a ZT-dependent term: η = η_C·(√(1+ZT)−1)/(√(1+ZT)+T_c/T_h). At ZT = 1 the device runs at about 15% of Carnot, ZT = 2 gives about 30%, and only ZT → ∞ recovers the full Carnot limit. Doubling ZT does not double the efficiency, which is the most counterintuitive feature of the formula.
No. They are all functions of carrier concentration and trade against each other. Adding more carriers raises σ but lowers α and also raises κ through the electronic contribution. There is therefore an optimum carrier concentration, typically in the 10^19–10^20 cm⁻³ range. Modern designs follow the phonon-glass / electron-crystal concept: enhance phonon scattering with nanostructuring, alloy scattering or rattling atoms to lower κ_lattice without hurting electron transport.
Operating temperature dictates the material. Room temperature to 450 K: Bi₂Te₃ family (Peltier cooling and small generators, ZT ≈ 1). 450–850 K: PbTe and skutterudites (automotive waste-heat recovery, ZT ≈ 1.5). 850–1200 K: SiGe alloys (spacecraft RTGs, ZT ≈ 1). Emerging candidates include SnSe (ZT > 2.5 thanks to ultralow κ in its layered structure), half-Heusler alloys (non-toxic, mechanically robust) and Mg₂Si (light, low cost).
Real-world applications
Spacecraft RTGs (radioisotope thermoelectric generators): Voyager 1 and 2 (still transmitting since 1977), the Curiosity Mars rover and New Horizons all rely on RTGs as their primary power source for missions where solar power is impractical. The decay heat of plutonium-238 (hundreds of °C) and the cold of deep space drive SiGe thermoelectric stacks with no moving parts and a 30–50 year lifetime. Reliability, not efficiency, is what sells thermoelectrics here.
Automotive and industrial waste-heat recovery: A gasoline engine is roughly 30% efficient, and about 30% of the remaining energy leaves through the exhaust at 600–900 K. BMW, Ford and GM have run demonstrators wrapping PbTe and skutterudite modules around the exhaust pipe to harvest 500–1000 W during driving, targeting a 3–5% fuel-economy gain. Steel mills, glass furnaces and cement kilns are similar high-grade waste-heat sources.
Peltier coolers (thermoelectric cooling, TEC): Reverse the current in the same module and one side cools while the other heats. Used to stabilise laser-diode wavelength, lower dark current in CCD/CMOS image sensors, drive PCR thermal cyclers, run small wine cellars and provide auxiliary CPU cooling. Maximum ΔT is around 70 K and COP is 0.5–1.5 — worse than vapour-compression — but the simplicity, lack of refrigerant and silent, vibration-free operation win in many niches.
Wearable and IoT energy harvesting: The few-K difference between skin and air can drive tens to hundreds of microwatts into a smartwatch or a battery-less sensor. Flexible Bi₂Te₃ thin-film modules are the front-runner, enabling self-powered IoT that never needs a coin-cell change. The figures of merit that matter here are not ZT alone but power density per cm² and the mechanical flexibility to follow body curvature.
Common misconceptions and pitfalls
The first trap is assuming that a higher-ZT material always delivers more power. Output is a function of both ZT and ΔT. A Bi₂Te₃ (ZT ≈ 1) module run across ΔT = 200 K often beats an SnSe (ZT ≈ 2.5) module run across ΔT = 50 K. ZT is also a strong function of temperature: every material has a "peak temperature" outside which its performance collapses. The ZT-vs-T chart in this tool is flat by construction; real materials show U-shapes or peaks.
The second pitfall is looking only at the power factor PF = α²σ. PF is a convenient figure of merit for a single bulk material, but the module efficiency is decided by ZT, which has κ in the denominator. Papers that report "record" PF without also measuring κ should be read carefully. The carrier concentration that maximises PF is not the same as the one that maximises ZT either. Real device design ranks materials on ZT, temperature dependence, mechanical strength, machinability, toxicity and raw-material cost together.
Finally, the ZT in the efficiency formula is not a single-temperature value; it is the average across the leg. That is why this tool shows both ZT at T_op and ZT_avg at T_avg = (T_h + T_c)/2. Strictly, ZT_avg is the temperature integral of the local ZT(T). On top of that, real modules lose 20–40% of their ideal efficiency to electrical and thermal contact resistance, leg-to-leg shorting and ΔT lost in the heat exchangers. Always distinguish the textbook efficiency from the assembled-module efficiency.
How to Use
Input Seebeck coefficient (μV/K) for your material—typical range 100–300 μV/K for bismuth telluride, higher for skutterudites
Enter electrical conductivity (S/cm): 100–1000 S/cm for Bi₂Te₃, lower for organic thermoelectrics
Specify thermal conductivity (W/m·K): 1–2 W/m·K for optimized Bi₂Te₃, up to 10 W/m·K for unoptimized bulk
Set operating temperature (K): 300K ambient, 573K for automotive waste heat recovery
Simulator calculates power factor, ZT at operating and mean temperatures, real efficiency versus Carnot limit