JAST 2007 Abstract
Deformation of Bowed Silicon Chips Due to
Adhesion and Applied Pressure
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. 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 the work
of adhesion even after the applied pressure is removed. In high-rate nanomanufacturing intimate contact must be maintained during transfer,
while allowing for easy separation afterwards.
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. In this investigation, a model
is developed to examine the effects of applied pressure, bow radius, and the work of adhesion on the flattening of a
spherically/cylindrically bowed chip. This model uses elastic plate theory and the work of adhesion. An operating window is found
which provides intimate contact while allowing for separation once the pressure is removed.
It is also shown that the effect of adhesion is to produce a discontinuity in the internal bending moment, at the separation boundary,
which is proportional to the square-root of the product of the work of adhesion and the flexural rigidity. This “moment-discontinuity”
method can be applied to other problems involving adhesion of elastic plates.
Andy Pamp and
George G. Adams