Optical evaluation of the flexural rigidity and residual stress in thin membranes: Picosecond transient grating measurements of the dispersion of the lowest-order Lamb acoustic waveguide mode

This article describes a convenient, noncontacting technique for determining the flexural rigidity and residual stress in thin membranes. The method was based on transient grating photoacoustics, also known as impulsive stimulated thermal scattering. Crossed laser pulses provided a coherent source of wavelength tunable acoustic modes in the membranes. Diffraction of a probe laser revealed the time dependence of these motions. The measured dispersion of the lowest-order Lamb mode at small acoustic wavevectors, coupled with classical plate theory, allowed the flexural rigidity and the residual stress to be determined. The technique, its accuracy, and spatial mapping capabilities were demonstrated through analysis of membranes designed for masks in next-generation lithography systems based on projected beams of electrons.