Stress tensor mesostructures for freeform shaping of thin substrates

Stress-induced shaping, which deforms thin substrates utilizing stressed surface coatings, has enabled and enhanced a host of applications in past decades. Owing to the touchless fabrication process compatible with modern planar technology, the method has been applied from microscale to macroscale applications such as self-assembled micro-structures and space mirrors. However, the deformations created by existing stress-control schemes are limited to certain classes of geometries (such as sphere, coma and astigmatism) or rely on boundary constraints and hinges because the stress is unary, e.g., equibiaxial stress or uniaxial stress with fixed orientation. Here, we present novel stress tensor mesostructures to spatially control the three required stress tensor components, i.e., two normal stresses and a shear stress, over the surface of thin substrates. Three different mesostructure types have been created, each offering distinct advantages. For demonstration, we patterned these mesostructures on the back sides of silicon wafers for freeform shape generation and correction which are not achievable by conventional methods. Stress tensor mesostructures will unleash the value of fields related to stress-induced bending from microscale to macroscopy, such as thin freeform substrates that will become increasingly important with the rise of wearable and space optics.