Characterization of Young’s modulus of silicon versus temperature using a ‘‘beam deflection” method with a four-point bending fixture

Abstract

Young’s modulus (E) and Poisson’s ratio (m) are dependent upon the direction on the silicon surface. In this work, E and m of silicon have been calculated analytically for any crystallographic direction of silicon by using compliance coefficients (s11, s12, and s44), and the values of E are confirmed experimentally by using a ‘‘beam deflection” method with a four-point bending fixture. Experimental results for E as a function of temperature from -150 ℃ to +150 ℃ are presented for (001) and (111) silicon wafers.