How to predict the thermal conductivity of multi-layer structures
We were puzzled for a long time, as to why the simulated self-heating of vertical-cavity surface-emitting lasers (VCSELs) is smaller than the measured temperature rise. After checking all the details of model and measurement, we ended up with the suspicion that the thermal conductivity of the GaAs/AlAs distributed Bragg reflectors (DBRs) is much lower than expected. This was eventually confirmed by direct measurements (see picture). Even 100nm thick layers restrict the phonon mean free path that determines the thermal conductivity of GaAs and AlAs. In other words, the typical averaging of bulk thermal conductivities may lead to a serious underestimation of the thermal resistance of multi-layer structures. In fact, the thermal conductivity of such structures could be strongly anisotropic. Unfortunately, I did not find a predictive theory for this effect in the literature – until this paper came out recently. The authors base their model on the Boltzmann transport equation in the relaxation time approximation. They include an effective interface scattering rate, dependent on layer thickness and interface roughness. The latter is the only fit parameter in this model which leads to good agreement with measurements. As stacks of thin layers are an essential part of many optoelectronic devices, this model is of crucial importance for realistic thermal simulations, I think.
PS There now is an online lecture on this model freely available at nanohub.org