Spiral microstructures for the measurement of average strain gradients in thin films

Spirals made from LPCVD polycrystalline silicon and sputtered-tungsten films have been observed both to wind up and to curl after etching of underlying sacrificial oxide layers. A theory that identifies the gradient of in-plane residual strain (through the thickness of the film) as the cause of deformation of spiral rings is developed. The angular rotation (wind-up) and lateral contraction of Archimedean spirals are predicted as a function of the average strain gradient in the film. The lateral contraction and rotation can be determined easily and accurately by means of an optical micrograph, making the Archimedean spiral attractive for measurement of average strain gradients. The predicted results are shown to correspond well with the behavior of an experimental sample. Analysis suggests that strain gradients in deposited films may possibly by exploited to extend structures made using surface micromechanics into greater dimensions away from the substrate