Prediction of defect onset conditions in heat cycling based on a thermoelastic wafer model

Abstract

A thermoelastic wafer model is proposed for predicting defect onset conditions during heat cycling in a furnace. This model is formulated for application to the plane stress state under thermal loading. The wafer temperature is calculated by a wafer temperature model proposed in a previous work. Predictions are tested by comparison with the thermal stresses resolved on the slip systems of the silicon crystal under the process conditions (i.e. furnace temperature, insertion velocity, and wafer spacing). When the proposed model is applied to 125-mm diameter and 150-mm-diameter wafers, it is shown that the thermal stress level is reduced to about a half by increasing the wafer spacing by a factor of two or three. Accordingly, the predicted defect onset results based on this model are in reasonable agreement with experiments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>