Deformation of Bowed Silicon Wafers Due to Applied Pressure and Adhesion

One potential method to accomplish high-rate nanomanufacturing is to develop processes which allow for rapid transfer of nano-scaled devices from a template to a device wafer [1]. In order to accomplish this transfer, the device wafer must make intimate contact with the template. A similar situation exists in wafer bonding, except that in that case the two wafers remain in bonded contact due to surface energy even after the applied pressure is removed. We need to maintain intimate contact during transfer, while allowing for easy separation and limiting the contact pressure. Wafers typically have waviness and bow which cause a deviation of many micrometers from flatness over the 15-mm length scale of a typical chip. This non-flatness can be a serious problem in the transfer of nanometer-scale elements. We have developed a model that allows us to examine the effects of applied pressure, bow radius, and surface energy on the flattening of a spherically/cylindrically bowed chip. This model uses elastic plate theory and surface energy. An operating window is found which provides intimate contact while allowing for separation after the pressure is removed. It is also shown that the effect of adhesion is to produce a discontinuity in the internal bending moments at the separation boundary, which is proportional to the square-root of the adhesion energy.