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The Relationship between the Bending Stress in Silicon Wafers and the Mechanical Strength of Silicon Crystals

Silicon wafers horizontally stacked in a vertical furnace bend downward due to their weight. Using a linear elastic theory, we calculated the shear stress caused by the wafer bending and investigated the mechanical strength by comparing the shear stress with the upper yield stress of silicon crystals. We concluded that the maximum shear stress increased with the increase in the wafer diameter, 0.20, 0.30, and 0.55 MPa for 6, 8, and 12 inch wafers. In bending the 12 inch wafers, oxygen precipitates, lowering the upper yield stress, caused serious wafer warping because the shear stress exceeded the lowered yield stress.