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. (C) 2014 Elsevier B.V. All rights reserved,