A simple approximate analytical expression based on an elastic deflection principle is suggested as a design guideline for direct bonding of blank or patterned Si or dissimilar materials of various thicknesses. To achieve the high flatness requirement of the mating surfaces for thick wafer bonding, optical polishing must be employed. With a surface flatness variation of 0.1 wavelength (∼630 Å), two 20 mm thick Si pieces of 100 mm in diam were spontaneously bonded at room temperature. On the other hand, the gaps designed to be formed by patterned surfaces may collapse during the bonding process if the pattern dimensions are not properly selected.
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Tong et al. (1995) studied this question.