Second-order sound field during megasonic cleaning of patterned silicon wafers: Application to ridges and trenches

We report calculations of first-order pressure and second-order pressure gradient fields in the neighborhood of patterned silicon wafers. The patterned wafers consist of a single ridge and two parallel ridges separated by a trench on a planar substrate. The efficacy of megasonic waves for cleaning patterned wafers contaminated with micron to submicron silica particles is discussed by comparing a removal force arising from the second-order pressure gradient to a van der Waals adhesion force. The calculated second-order pressure gradient fields show that acoustic energy may be concentrated in small volumes in the vicinity of pattern features with dimensions significantly smaller than the wavelength of the incident acoustic wave. The angle the incident acoustic wave makes with the planar substrate has a strong impact on the second-order pressure gradient field. Grazing incident waves appear to provide a more efficient way of cleaning inside a trench. Excitation of a trench resonant vibrational mode enhances the magnitude of the first-order pressure, the second-order pressure gradient, and therefore the removal force.