Which properties of the materials we have to focus on for probing the temperature dependence , as Figure of merit involve the Thermopower , electric resistivity/conductivity and as well as thermal conductivity,
Also I have confusion related to the phonon contribution at higher temperature, while at higher temperature large number of phonons are generated while the graph of thermopower varies linearly i.e it seems that only electronic part contribution is there.
The contribution of phonons is complex. If we discuss the Figure of merit, we must consider their contribution to the resistance, the Seebeck coefficient and the thermal conductivity.
Thermal conductivity: In metals, the electronic contribution dominates (silver, copper). In semiconductors the contribution of phonons is important. The phonon contribution of the thermal conductivity is proportional to the velocity of sound and the specific heat of the lattice - increasing with temperature.
Seebeck coefficient S: S increases directly with T but furthermore the scattering processes (mobility of charge carriers) influence S. At high T dominate electron-phonon scattering processes. At low T we have additionally to consider the phonon drag.
Resistivity: the resistance is proportional to the mobility. At high T the scattering of electrons to phonons reduces the electrical conductivity. Therefore the Figure of merit reduces with increasing T (so far it is due to the increasing resistance).
I recommend the answer from Mitdank
for more understanding particularly for thermal conductivity in semiconductors you may read the following articles
Nanoscale Size Dependence Parameters on Lattice Thermal conductivity of
Wurtzite GaN Nanowires
S. M. Mamand, M. S. Omar and A. J. Muhammed Materials Research Bulletin 47, 1264(2012)
Effect of Parameters on Lattice Thermal Conductivity in Germanium Nanowires S. M Mamand and M S Omar
Advanced Material Research, 832, 33 (2014)
Trans Tech Publications, Switzerland
Thanks Dr Mitdank and Omar for your suggestion. Key points mention by Mitdank are really helpful.
Hello !, maybe I can add something here;
The ZT (FOM) itself depends on the temperature, so all its parameters (S, sigma and k) does too.
So, to evaluate/characterize the thermal performance of a thermoelectric material you need to measure the thermoelectric properties related to a certain applied temperature (usually the temperature these materials will operate in a thermoelectric device at an actual thermal-electric conversion system's application).
You can see the temperature dependence on the material's performance in any of these properties. S, sigma or k.
The percentage of phonons contribuiting to the total thermal conductivity depends fundamentally on the DOS (density of States for phonons, and for electrons) as well as the free carrier concentration within the material, macroscopically we can see this as the material being, insulator, metal, semi-metal or semiconductor.
Then, there are phonons of all frecuencies in a material, contribuiting to the lattice thermal conductivity, low frecuency, medium frecuency and high frecuency phonons, and that now, is related with the temperature (more accurately, with a temperature gradiente), which is function of a range of energy of the phonons.
I hope this can help
Regards !
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