Constitutive Modeling of Photostrictive Materials and Design Optimization of Microcantilevers QUANTIAN LUO AND LIYONG TONG* School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney, NSW 2006, Australia ABSTRACT: This article presents constitutive models for photo-induced strains in photostrictive materials and an optimal design of microcantilevers driven by light illumination. Behaviors of photo-induced strains in semiconductors and polymeric materials are reviewed first, and then new phenomenological constitutive models are developed that depict two distinctive features of photo-induced strain profile: (a) dependence on variation of light intensity which decreases with the depth measured from the illuminated surface due to light attenuation and energy absorption; and (b) anisotropy or dependence on direction of light polarization. On the basis of the constitutive modeling of photo-induced strain in wafers, design optimization of microcantilevers is then investigated for both geometrically linear and non-linear deformations. Key Words: photo-induced strain, constitutive equation, geometrically non-linear analysis, microcantilever. INTRODUCTION P HOTOSTRICTIVE materials have attracted an increas- ing interest in microsystems as they can be used as actuators and sensors to realize remote operations with noise elimination. When irradiated by specific light, semiconductors such as germanium (Figielski, 1961) and silicon (Gauster and Habing, 1967) deform mechani- cally due to absorbing photons and generating free charge carriers. When exposed to light of some wave- length ranges, mechanical deformation can be induced in a polymer with light-responsive molecules as photon absorption causes molecular order change (Eisenbach, 1980). Absorption of photons by solid generally results in a temperature increase that yields its thermal expansion. Photo-induced deformation in light-responsive mate- rials can be used in sensors for photo detection and in actuators for remote operations. When used as an actuator, the way of delivering energy via light from a non-contact remote source is a superior feature compar- ing to the need of electrical wiring in generating electrical field-induced mechanical deformation in piezo- electric actuators. Photo-induced deformation in a semiconductor or a polymer is a process of transferring light energy into mechanical energy. In this process, when light energy is absorbed by a solid, the crystals of substances or structures of molecules are changed. At the same time, light energy absorption creates thermal strain due to an increase of temperature. In general, the process of energy transformation by light illumination in these materials is very complicated from the viewpoints of physics and chemistry, and it has been investigated by many physicists and chemists. With regards to the applications of photo- responsive materials in micro-electro-mechanical system (MEMS) and micro-opt-mechanical system (MOMS), the establishment of phenomenological models of photo- induced strains is of paramount importance and thus will be mainly considered in this article. It is known that the mechanical strains induced by an electrical field in piezoelectric materials (Crawley and Lazarus, 1991; Hegewald et al., 2008), magnetic field in magnostrictive materials and thermal expansion in heat-conductors (John et al., 2007) have a uniformly distributed profile through the thickness and the materials are transversely isotropic normally. However, the photo-induced strain in photostrictive materials decreases with light penetration depth as light intensity decays with the depth (Warner and Mahadevan, 2004; Guo et al., 2007) depending on the material’s transpar- ency and can also have anisotropic features due to light polarization (Yu et al., 2003; Jiang et al., 2006). In the analysis and design of photo-responsive actua- tors and sensors used in MEMS and MOMS, constitutive equations are needed. In this article, behaviors of photo- induced deformations in semiconductors and poly- meric materials are briefly reviewed in ‘LITERATURE *Author to whom correspondence should be addressed. E-mail: ltong@aeromech.usyd.edu.au Figures 3, 4, 6 and 7 appear in color online: http://jim.sagepub.com JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol. 20—August 2009 1425 1045-389X/09/12 1425–14 $10.00/0 DOI: 10.1177/1045389X09103224 ß SAGE Publications 2009 Los Angeles, London, New Delhi and Singapore