Warpage of Silicon Wafers

Abstract

High temperature processing of Czochralski grown silicon wafers can create temperature gradients high enough to generate slip. The generation of slip and the slip patterns have been found to depend on three factors: the temperature and the temperature gradient, the amount and form of the precipitated oxygen, and the direction of the initial bow and the wafer diameter over thickness ratio. A model is presented to fit experimental data of critical stress in silicon, temperature gradients, and wafer curvature to predict the critical temperature above which warpage will occur. An important result is that increased wafer diameter over thickness ratio makes the wafers more sensitive to warpage. When this is the case the difference in stresses on both sides of the wafer, because of the bending, makes the area affected by slip on the concave side much larger than on the convex side.