Patterning and modeling of mechanically bent silicon plates deformed through coactive stresses V. Guidi a, ⁎, L. Lanzoni b , A. Mazzolari a a INFN Sezione di Ferrara, Dipartimento di Fisica, Università di Ferrara, Via Saragat 1, 44124 Ferrara, Italy b Facoltà di Ingegneria Civile, Università degli Studi di San Marino, Via Salita alla Rocca 44, 47890 Repubblica di San Marino abstract article info Article history: Received 28 March 2011 Received in revised form 25 August 2011 Accepted 2 September 2011 Available online 10 September 2011 Keywords: Patterning Silicon nitride Silicon plates Stress Crystal deformation In the present work a technique to impart a controlled deformation to a substrate through deposition of a thin film is shown. Such a technique allows film–substrate systems to be tailored with a desired shape for various applications. An analytical model has been applied to calculate the displacements and stresses of a patterned crystalline substrate. Analytical results have also been validated via Finite Element simulations. Si substrates have been patterned with Si 3 N 4 and measurements of the transverse displacement were found to agree with the theoretical predictions. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Bent crystals are increasingly used by the scientific community as a powerful tool for many technological and scientific applications. A bent crystal is a method to excite coherent interactions between par- ticles or photons with the crystal in a different manner than a rectilin- ear crystal would do. As an example, a properly tailored bent crystal can be given the shape of a parabola and, as a result of Bragg diffrac- tion of photons, be used for focusing/defocusing X-rays within the range of some tens of keV. Typical structures of this kind are the so- called Göbel mirrors [1], which are commonly used components in X-ray diffractometry. Bent crystals have also been proposed to be part of the components of hard X-ray concentrators (from 100 keV on) to collect the radiation from cosmic sources for focusing onto a detector [2]. Here the Laue scheme is preferred to Bragg geometry due to higher penetration of such radiation. A bent crystal offers the capability to concentrate X-rays over a wide photon energy range as compared to a traditional straight crystal and also gives the opportu- nity of a broader visual angle for observation [3]. Hard X-ray radiation such as that emitted by decaying Tc 99m atoms in single-photon emis- sion computer tomography, if properly focused by a bent crystal, could be used to determine the emitting area in the body under anal- ysis with no need for a gamma camera, i.e., such a scheme could work with better resolution and/or lower dose imparted to the patient [4]. More recently, interaction of high-energy charged particles was intensively investigated because of the possibility of steering the tra- jectory of a particle beam in the same way as a traditional magnetic- field structure would do [5, 6]. Bent silicon crystals underwent strong technological development that raised deflection efficiency from a few percent up to the maximum theoretical limit [6]. Based on that, a project has been started aimed at collimating beam halo in the large hadron collider at CERN to protect supermagnets from quench- ing due to too strong an irradiation [7]. Normally, bent crystals are deformed via mechanical stress imparted by an external device to a rectilinear crystal. Either primary or secondary deformation (e.g. anticlastic deformation) can be used for bending. This second option ensures a leverage of the strain, more homogeneous deformation and the possibility to bend to a de- sired curvature via mechanical action far from the area of interest [8, 9]. However, there are situations where an external mechanical de- vice cannot be afforded. As an example, X-ray observation of celestial sources requires satellite-borne experiments to avoid the adsorption of target radiation by the atmosphere. For such missions, weight con- straint is a mandatory issue and an alternative for crystal bending should be sought. Even in the field of accelerators, the usage of sec- ondary curvatures to maintain bending devices far from the area of interaction with the beam is not always possible. For instance, the re- alization of a crystalline undulator [10] requires the deformation of a crystal to take a quasi-sinusoidal shape and that cannot be done by direct application of any mechanical devices. The need for a reliable methodology to bend a silicon crystal to the wanted shape with the aid of deposition of tensile or compressive thin films, i.e., by “internal forces” in contrast to “external forces” of Thin Solid Films 520 (2011) 1074–1079 ⁎ Corresponding author. Tel.: + 39 0532974284; fax: + 39 0532974210. E-mail address: guidi@fe.infn.it (V. Guidi). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.09.008 Contents lists available at SciVerse ScienceDirect Thin Solid Films journal homepage: www.elsevier.com/locate/tsf