The temperature distribution in nanowires due to Joule heating is studied analytically using a continuum model and a Greens function approach. We show that the temperatures reached in nanowires can be much lower than that predicted by bulk models of Joule heating, due to heat loss at the nanowire surface that is important at nanoscopic dimensions, even when the thermal conductivity of the environment is relatively low. In addition, we find that the maximum temperature in the nanowire scales weakly with length, in contrast to the bulk system. A simple criterion is presented to assess the importance of these effects. The results have implications for the experimental measurements of nanowire thermal properties, for thermoelectric applications, and for controlling thermal effects in nanowire electronic devices.
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