Calculation of the temperature profile in nanowhiskers growing on a hot substrate

We propose a model for calculating the temperature profile along nanowhiskers bound perpendicularly to a hot substrate, taking into account the heat conduction and radiation. We first derive an exact implicit relationship between the distance from the substrate and the local temperature. We then give a simple analytical approximation of the temperature profile, valid even for the slenderest semiconductor whiskers fabricated so far. We study analytically how the temperature profile changes when the total whisker length increases during growth. Finally, we discuss the validity of various assumptions of our model and their effects upon our results.