Perspectives on integrated modeling of transport processes in semiconductor crystal growth

The wide range of length and time scales involved in industrial scale solidification processes is demonstrated here by considering the Czochralski process for the growth of large diameter silicon crystals that become the substrate material for modern microelectronic devices. The scales range in time from microseconds to thousands of seconds and in space from microns to meters. The physics and chemistry needed to model processes on these different length scales are reviewed.