The dimensionless value ZT = S²σT/κ that expresses the conversion performance of a thermoelectric material. It is larger the higher the Seebeck coefficient and electrical conductivity and the lower the thermal conductivity.
Japanese name: 熱電性能指数
Thermoelectric figure of merit appears in 1 practice question across 1 topic, including Battery and energy materials.
Field: Battery and energy materials
S is the Seebeck coefficient, the voltage generated per kelvin of temperature difference; σ is the electrical conductivity, κ the thermal conductivity and T the absolute temperature. S²σ in the numerator is called the power factor and is a measure of how much electrical power can be extracted from the material. The smaller κ in the denominator, the easier it is to maintain the temperature difference between the hot and cold sides. The units in S²σT/κ cancel, so ZT is dimensionless. For example, a material with S = 200 µV/K, σ = 1.0×10⁵ S/m and κ = 1.5 W/(m·K) has ZT = 0.8 at 300 K.
The maximum efficiency of thermoelectric power generation is expressed as the Carnot efficiency, set by the hot- and cold-side temperatures, multiplied by a factor determined by ZT. The larger ZT, the closer the efficiency approaches the Carnot efficiency, but even at ZT = 1 the efficiency is only about 20% of the Carnot efficiency (about 17–24% depending on the temperatures). Bi₂Te₃-based materials near room temperature, PbTe- and Mg₂Si-based materials at intermediate temperatures, and SiGe, silicides and oxides at high temperatures are researched and used, so the materials with high ZT differ by operating temperature range.
S, σ and κ are not independent of one another. Raising the carrier concentration increases σ but lowers S, and the thermal conductivity carried by electrons also increases according to the Wiedemann–Franz law. The optimum carrier concentration therefore lies in the range of heavily doped semiconductors, about 10¹⁹–10²⁰ cm⁻³. Efforts are thus made to lower the lattice thermal conductivity by scattering only the phonons, which carry much of the heat, using nanostructured interfaces, point defects or atoms rattling inside cage-like crystals, while disturbing electron conduction as little as possible.
Answer: C. Scatter phonons with nanostructures or heavy atoms to lower the lattice thermal conductivity while disturbing electrical conduction as little as possible
To make ZT = S²σT/κ large, the Seebeck coefficient S and electrical conductivity σ must be high and the thermal conductivity κ low. However, raising the carrier concentration increases σ but decreases S, and also increases the heat carried by electrons (the Wiedemann–Franz law), so the optimum is a nearly degenerate semiconductor with a carrier concentration of about 10¹⁹–10²⁰ cm⁻³. At metallic levels S becomes too small. A promising strategy is therefore to scatter only the phonons, which carry most of the heat, using nanostructured interfaces or the rattling of heavy atoms, to lower the lattice thermal conductivity; this is described as “phonon glass, electron crystal.” Lowering σ and raising κ moves ZT down.
Metals have high electrical conductivity, but their Seebeck coefficients are small, a few µV/K, and their electronic thermal conductivity is large, so ZT is extremely small. Heavily doped semiconductors are used as thermoelectric materials.
Yes. S, σ and κ all depend on temperature, and the ZT expression itself contains T. Each material has a temperature range where ZT is highest, so materials are chosen to match the operating temperature.
Yes. The coefficient of performance of thermoelectric cooling (Peltier devices) also increases with ZT, so ZT is the index of material performance for both power generation and cooling.
Wiedemann–Franz law Phonon Layered rock salt structure Olivine structure Polymer electrolyte fuel cell Shockley–Queisser limit Solid electrolyte Spinel structure Theoretical capacity