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

Young’s modulus ( E ) and Poisson’s ratio ( ν ) are dependent upon the direction on the silicon surface. In this work, E and ν of silicon have been calculated analytically for any crystallographic direction of silicon by using compliance coefficients ( s 11 , s 12 , and s 44 ), 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 °C to +150 °C are presented for (0 0 1) and (1 1 1) silicon wafers.