Three-dimensional analysis of dislocation multiplication in single-crystal silicon under accurate control of cooling history of temperature

•3D simulation of dislocation multiplication in single-crystal silicon was studied.•Accurate control of temperature history in furnace was numerically implemented.•Cooling rate in high-temperature region affects dislocations and residual stress.•Slow cooling in high-temperature region is the best choice.

Dislocation multiplication in single-crystal silicon during heating and cooling processes was studied by three-dimensional simulation under accurate control of the temperature history. Three different cooling temperature histories were designed. The results showed that the cooling rate in the high-temperature region has a large effect on the final dislocations and residual stress. The most effective method to reduce dislocations is to use a slow cooling rate in the high-temperature region.