Silicon as an anisotropic mechanical material a （硅的各向异性力学材料）.pdfVIP

Silicon as an anisotropic mechanical material - a tutorial Ville Kaajakari This tutorial covers the calculation of silicon Young’s modulus and Poisson’s ratio from elastic constants in any crystal orientation. The algebra is the same for any elastic material with cubic symmetry but I am mostly interested in silicon as I have used it to make micromechanical compo- nents. The tutorial assumes knowledge of matrix algebra and some elementary mechanics concepts such as stress and strain. The material in this tutorial is mainly based on the paper by Wortman and Evans [ 1] with some concepts not familiar for a typical engineer briefly explained. Figure 1 below shows how Young’s modulus Y is defined: the bar is stretched in the x-direction while simultaneously it is allowed to move freely in y- and z-directions. The Young’s modulus is then defined as the ratio of stress to strain in the direction of the stretching (Y = T11/ε11). The Pois- son’s ratio is defined as ratio of length extension to sideways contraction (ν = −ε22 /ε11). Different directions are referred with numbers and letters interchangeably with numbers 1, 2, and 3 used to indicate x , y, and z axes respectively. F deformed 1 T shape 11 F T = 1 11 A F =F = 0 2 3 slope ≡ Y T = T = 0 22 33 x