Mechanical behavior of flexible silicon devices curved in spherical configurations

Abstract

International audienceFoldable, 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

Bending induced electrical response variations in ultra-thin flexible chips and device modeling

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“…Biaxial flexural tests on plates, which have been used to evaluate the strength of ceramics for more than 40 years in various configurations such as ball-on-ring, 111,112 uniform pressure, 113 ring-on-ring, 114 or piston-on-threeballs, 115 have been adapted to investigate the biaxial strain effects in UTCs. 116,117,150 Properties such as phonon or electronic deformation potentials 118,119 are measured through these tests to find the fracture strength 96,[120][121][122] or to investigate the 2D strain effects on the electrical behavior of MOSFETs. 123,124 In the case of thin samples, the fracture strength is influenced by the roughness and morphology of the surface, 125 which in turn are affected by the surface defects introduced through backside grinding, polishing, chemical etching, and edge defects caused by wafer sawing or dicing.…”

“…A compact model which demonstrates the simulations involving elastic deformation of a thin Si chip on a spherical holder is presented in Ref. 117. In this work, the simulation starts with a shell model which is validated through a convergence study and comparison with a 3D model.…”

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