Measurement of residual stress in single crystal silicon wafers

The presence of residual stresses in silicon single crystals greatly affects the performance and reliability of the integrated circuits. Residual stresses are developed in silicon wafers during growth of boules as well as in the thermal processing. These stresses can be determined in wafers by analysis of the out-of-plane deformation under transversally axisymmetrically loading. The out-of plane deformation can be used in a model of a modified circular plate theory undergoing large deflections. Shadow Moire interferometry has been used to measure the surface shape contour pattern of a silicon wafer. The phase of the wavefront from the interferogram was obtained. A study of phase stepping and unwrapping technique was used to obtain the out-of-plane displacement of the wafer. A model of thin plates undergoing large deflection is used to extract the radial and tangential residual stresses