Simulation of the stresses produced in large-diameter silicon wafers during thermal annealing

The three-dimensional problem of stress and strain fields in dislocation-free silicon wafers 200 and 300 mm in diameter placed horizontally on three symmetrical supports and subjected to is gravitational forces and thermal stresses formulated and solved in the isotropic approximation. Under the action of gravitational forces, a wafer is shown to have the lowest total stress when the supports are positioned at a distance of 0.6–0.7R from the center of the wafer. The shear-stress fields are calculated for all possible slip systems. The elastic-stress field in a 300-mm wafer is found to be induced mainly by gravitational forces even at a radial temperature gradient of 10 K. At this temperature gradient, the contribution from thermal stresses in a 200-mm wafer is comparable to the contribution from gravitational forces. At radial temperature gradients lower than 5 K, the contribution from thermal stresses can also be neglected for a 200-mm wafer. The maximum shear stresses calculated indicate that one should not neglect possible dislocation generation in the zone of contact between a wafer and the supports during high-temperature annealing of 200-mm and, especially, 300-mm wafers.