Bending of silicon plate crystals through superficial grooving: Modeling and experimentation

Permanent and reproducible deformation of silicon mono-crystals has been experimentally attained by mechanical grooving of one of its surfaces. The method produces uniform deformation that can be controlled by proper choice of the parameters of grooving. The strain in silicon plates was modeled analytically in terms of a superficial compression occurring in the material between the grooves. The superficial grooved region acts as if it were like a tensile film with the strain propagating deep into the bulk, which results in spherical and homogeneous curvature of the whole crystal plate. Thereby, the classic Stoney's formula was reconsidered and adapted for explanation of the experimental behavior. Minimum radius of curvature experimentally achieved was about 3 m. Curved crystals are the basis for many applications, e.g. for x-ray optics to manipulate high energy photons for the construction of very sensitive instruments for x-ray astronomy.