I am trying to reproduce the heat conductivity plot originally reported by Carlson (http://dx.doi.org/10.1063/1.1714018), see attached "Carlson data.png". There is a review article by Blakemore (http://dx.doi.org/10.1063/1.331665) in which he discusses Carlson's data. I'm looking for hints about fitting the data points with curves, like Carlson did, but it seems that heat conductivity in semiconductors is a complex phenomenon. Blakemore only says that between 50K and 150K k=A*exp(B/T) (fit.png), but how would you go about fitting the other parts of the data? I'm most interested in 30-250K range.
Article Semiconducting and Other Major Properties of Gallium Arsenide
Article Thermal Conductivity of GaAs and GaAs1-xPx Laser Semiconductors
Hi, you can solve the Boltzmann transport equation for the phonons under the time relaxation approach. A simple way to do that is with the Callaway model, there is quite a lot of literature about that. The term you referred (Blake) for the 50-150 K range comes from the umpklapp anharmonic 3-phonon scattering, being A and B constants of each material (search for example Morelli et al. on the isotopic effect in the thermal conductivity); however, traditionally people leaved this A and B as fitting parameters...less correct but better fitting... To be more accurate the umpklapp is described by (A*T*exp(-DebyeT/(B*T))) ^-1, being at high temperatures the TC proportional to 1\T. At low temperature the thermal conductivity is controlled by the increasing of the phonon population with the temperature, being this modulated by the boundaries and defects/impurities in the lattice (mainly extended defects).
By implementing a full Callaway-Holland including all the phonon scattering events you will be more than capable of getting a very good prediction of the TC of the GAs in the full temperature range, just take a look at the Ziman's book about phonons and electrons or the Srivastava's book on phonons.
Thanks for the answer! Sorry if I come across as ignorant, but I was not really looking for a full theory to predict the TC, I just wanted to fit these data with a function that makes sense from the theoretical point of view. I need to input TC as a (piecewise) function into my solver, so integrating it over the whole range is not a solution for me. Your suggestion about the accurate Umpklapp version was helpful, I got a better fit. What functions would you suggest for lower ranges, especially the 10-50K, where the data look parabolic on the logarithmic plot?
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Semiconductor