Thermal conductivity of silicon, germanium and silicon-germanium single crystals between 85 K and 300 K

With the aim to improve the reliability of calculating and thus predicting the thermal deformation of cryogenically cooled silicon monochromators for intense synchrotron x-ray beams, we have measured the thermal conductivity of several specimen with different purities: float zone (FZ), Czochralski (CZ) single crystal materials and a Si99.3Ge0.7 (SG) crystal between 85 K and room temperature with 1% accuracy. We have shown by finite element analysis that a measured 30% increase of conductivity between the FZ and the CZ crystals leads to an increase of 30 to 40% of the thermal slope. Whereas the performances of these two materials were just acceptable, the 9 times reduced thermal conductivity of the SG crystal turned out to increase the thermal slope error by a factor 19 to a prohibitive value of 143 mu rad, as compared to 7.6 mu rad for the FZ crystal. Therefore, the application of SG crystals to cryogenic cooling cannot be recommended. In addition, we determined the thermal conductivity of germanium single crystals in the same temperature range. For the silicon FZ and the germanium materials, excellent agreement with recommended values was found. Moreover, we detected a small, but non-negligible dependence of thermal conductivity on the crystallographic direction (a few % at 85 K) that, to our knowledge, has not been published in previous papers.