Numerical Simulation of Transport Processes during Growth of Single Crystal using Czochralski Crystal Growth Technique

Abstract

newline quotSemiconductor revolution that forms the backbone of present day technological develop- newlinements is based on ability of mankind to grow large diameter semiconductor crystal having newlinedesired distribution and concentration of different chemical species, in an industrial scale newlinesetup. Oxygen species concentration and its radial distribution along the length of silicon newlinecrystal is one of the key parameter that dictate the use of a crystal for making a semiconduc- newlinetor based device for a required application. The ever increasing demand of higher processing newlinepower has lead to consistent increase in size of silicon crystal grown leading to present day newlinesilicon crystal of 450 mm diameter. newlineMajor chunk of the semiconductor device rely on silicon crystal that are grown using the newlineCzochralski (CZ) technique. The Czochralski method essentially consists of solidification of newlineliquid melt filled inside a crucible, onto a seed crystal attached to a pull rod. Both, the crystal newlineas well as crucible are rotated in opposite direction while the solid crystal is gradually pulled newlineout resulting in drop of melt height inside the crucible. The crucible and crystal are housed newlineinside a closed container with inert gas used as purging medium in space above the free melt newlinesurface. An external magnetic field is imposed to control the melt motion inside the crucible newlinevia the action of Lorentz force. newlineExperimental investigation of Czochralski process presents unique challenges owing to newlinehigh melt temperature and space constraint inside the crystal growth setup. Flow field mea- newlinesurement at temperature as high as 1685 K makes the experimental investigation even dif- newlineficult. Hence, numerical simulation is still the industry norm for investigation of different newlineaspects related of growth of crystal using Czochralski method. In fact, dedicated commer- newlinecial software like Crystal Growth Simulator (CGSim) are available that deal specifically with newlinesimulation of crystal growth using Czochralski method. newlineA numerical simulation approach has been adopted to simulate