Dear all,
One of researcher said that " The relaxation time for lattice thermal conductivity is totally different from that for electronic part of thermal conductivity." that is, phonon relaxation time is totally different from electron relaxation time. Is it true?(as should be) If so, why many authors calculate electrical conductivity and electronic thermal conductivity by using phonon relaxation time? Nanoscale, 2012,4, 4348-4369 , EPL (Europhysics Letters). 2017 Apr 6;117(4):47002.
If I use phonon relaxation time in that case of electronic part, how much error will appear? How can I calculate electron relaxation time? From electron self-energy by using EPW method, it can be calculate for low temperature, but I need for high temperature.
Thanks in advances !
A phonon is a common vibrational excitation of atoms (i.e. atomic nuclei) in a solid; an electron is a part of of single atom, its excitation depending on the atomic structure of that specific atom as well as its bonds to other atoms in a solid; so you talk about fundamentally different excitations .If you want to measure or model relaxation times you first need to define the type of excitation you consider.
Dear Thomas Walther,
Thank you. Can you tell me why authors (mentioned above papers) use phonon relaxation time to calculate electrical conductivity? What is the condition behind this to be equal?
Hi Enamul,
I am not an expert on the theory here, but I suspect that one may get away with equating the phonon relaxation time with the electron relaxation time when at and just above the Bloch-Gruneisen temperature, because this is where there are just enough phonons that the electron-phonon scattering becomes a dominant mechanism. But I think that is only for certain types of materials, like ones exhibiting 2D gas-like electronic structures.
For all conducting materials, it gets even more complicated than that, as the electronic contribution to the thermal conductivity is not even that straight forward. Weidemann-Franz relation breaks down (kappa/[sigma*T] is not equal to L0) at low temperatures (well below the Debye temp of the material). This has to do with the fact that randomizing an electrons net momentum may not happen on the same time scale as randomizing its excess thermal energy. And at any temperature where you have both holes and electrons contributing to the conduction (bipolar conduction), W-F grossly underestimates the electronic contribution to the thermal conduction.
Two books I recommend to anyone interested in electronic and thermal transport:
Band Theory and Electronic Properties of Solids (ISBN: 978-0-19-850644-7)
Thermal Conductivity: Theory, Properties, and Applications (ISBN: 0-306-48327-0)
Dear Tim C. Holgate,
Thank you very much for your important information! Actually, I have calculated lattice thermal conductivity and the relaxation time from phonon-self energy. The electrical and thermal conductivity calculated by using BolzTraP in the form sigma/tau, and kappa/tau, respectively. To calculate electrical and thermal conductivity, I have to multiply the obtained data by relaxation time. In this case, can I use the relaxation time calculated from phonon self-energy or deformation potential (Bardeen and Shockley formula)? Or, How can I calculate the electron relaxation time?
Thank you in advances!
An electron is considered a fermion, while phonon is considered a boson. An electron, unlike phonon, follows the principle of Pauli exclusion principle and Fermi–Dirac statistics, While Phonon follows the Bose–Einstein statistics. Hence their behaviors and equations are different and you may find your answer from quantum topics.
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