Evaluation of intrinsic film stress distributions from induced substrate deformation

Measuring and controlling intrinsic stress in films deposited on substrates is a basic and essential challenge in micro- and nano-engineering. Indirect measuring methods for determining film stress are commonly used. Generally, commercial tools measure the induced mask shape, and relate it to film stress via the two-dimensional form of Stoney's equation, applied in a point-wise manner. This equation gives incorrect results if the stress distribution is not uniform. As an alternative, a numerical method based upon finite element (FE) analysis has been developed. It contrasts traditional structural FE methods since the out-of-plane displacements, curvatures or cross-section rotations measured on the substrate surface are used as input data. Numerical tests and applications to lithographic masks demonstrated that the FE technique provided accurate film stress even if magnitudes varied from point to point and principal directions changed over the surface.