Analysis of the geometry of the growth ridges and correlation to the thermal gradient during growth of silicon crystals by the Czochralski-method

A contactless, non-destructive approach to measure the geometrical parameters of the growth ridge, based on surface topography, is presented and established. It allows a systematic, large scale analysis of growth ridges of single crystals of almost any type. Here, it is applied to Czochralski-grown silicon crystals. Based on the measurement results, Voronkovs theory of the shape of the growth ridge is verified. This theory is used to calculate the temperature gradient at the growth ridge from the geometrical parameters. The presented method gives an easy, direct experimental access to the thermal conditions, both qualitative and quantitative, at the solid-liquid interface during the growth process.