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Mechanical behavior of flexible silicon devices curved in spherical configurations

Foldable, stretchable and flexible electronics is of constant increasing interest since the early 2000's. Its applications spread from OLED-based displays, bio-inspired detectors and “epidermal electronics”. Cylindrical curvature is largely studied through many 3 points and 4 points bending variations in electronic devices. However spherical curvature is poorly addressed, especially for monolithic approach. In this paper, a simulation and experiments of the elastic deformation of a thin silicon chip on a spherical holder are presented. The holder can have a concave or a convex shape. The chip is a square of 10 by 10 mm2. Its thickness is 50, 25 or 15 μm. The simulation is performed in 3 steps. First, the use of a shell model is validated by a convergence study and by a comparison with a 3D model and the literature. Then, the influence of the anisotropic elastic behavior (single crystal) is considered. In a given bulge test condition, isotropic and anisotropic silicon simulation gave similar deformations. At the end, the spherical forming is accomplished with a shell model and an anisotropic law. Experimental data is obtained by curving thin silicon plates of various thicknesses on different radii holders in a press. The comparison between experimental and computed results is realized. We found similar macroscopic deformations for both concave and convex shapes. The influence of chip thickness and applied pressure is studied on characteristic folds and flat part amplitudes. A heterogeneous stress distribution with hundreds of MPa variations can explain the difference observed between curved chips and perfect spherical holders. The stress level in electrical and optical active layers of thin curved silicon-based devices may affect their properties. A numerical example on a bolometer gives a stress-induced resistivity variation over 10%.