We investigate temperature dependent thermal conductivity k(T) in a single Ge nanowire (NW) using Optothermal Raman Spectroscopy which utilizes the temperature dependence of Raman lines as a local probe for temperature. The experiment was done from 300 K to above 700 K, a temperature range in which thermal conductivity of single NWs has been explored rarely. The thermal conductivity of Ge NWs (grown by vapor liquid solid mechanism), at around room temperature were observed to lie in the range 1.8 to 4.2 W/m.K for diameters between 50 to 110 nm. The thermal conductivity at a given temperature was found to follow a linear dependence on NW diameter, suggesting that the low magnitude of k(T) is determined by diffused scattering of phonons from the surface of NWs that reduces it severely from its bulk value. k(T) shows approximately 1/T behavior which arises from the Umklapp processes. The quantitative estimation of errors arising from the Optothermal measurement and methods to mitigate them has been discussed. We also suggest a quick way to estimate approximately the thermal conductivity of Ge and Si NWs using the above observations.
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