Universal Limits of Thermopower and Figure of Merit from Transport Energy Statistics

The search for new thermoelectric materials aims at improving their power and efficiency, as expressed by thermopower S and figure of merit ZT.
By considering a very general transport spectral function w(ε), expressions for the S and ZT can be derived, which contain the statistical weights of an effective distribution function only, see Ref. [1]. The assumption of a Lorentzian shape with width kBT resulting from the electron-phonon coupling allows to estimate an upper limit of S and ZT regardless the microscopic mechanisms of the transport process.
The limit of |S| is given by 1.88 in units of kB/e, which is about 160 μV/K, and the limit for ZT is about 1.11 (red dots in the figure).
The work was partially supported by the Initiative and Networking Fund of the German Helmholtz Association, International Helmholtz Research School NanoNet (VH-KO-606), the Helmholtz Exzellenznetzwerk cfaed (ExNet-0026), and the DFG Priority Program 'Nanostructured Thermoelectrics' (ZA264/3-2). We thank S. Gemming for helpful discussions.