Deformation of Single Crystal Wafers of Silicon Caused by Lapping

Two types of deformation of single crystal wafers of silicon introduced by lapping one face of a wafer are observed. There exists a critical thickness, T c , above which the deformation is symmetric with respect to the center of wafers (spherical deformation), and below which the deformation is symmetric with respect to a certain diameter (cylindrical deformation). The plots of the deflection for the spherical deformation at any cross section and for the cylindrical deformation at cross section perpendicular to axis of symmetry coincide with parabolic lines. In the case of {100} wafers, there are two stable modes for the cylindrical deformation and the axes of symmetry coincide with on {100}. Whereas {111} wafers have a single stable mode: some axes of symmetry coincide with and/or but the rest does not coincide with any direction having low indices. It is likely that both types of deformation originate from the plastically deformed layer on the lapped face and that large portion of a wafer is deformed elastically except for the layer.