Measurement of the Anisotropy of Young's Modulus in Single-Crystal Silicon

Abstract

In (100) silicon wafers, the most commonly used in microelectromechanical systems (MEMS) fabrication, the value of Young's modulus of a MEMS structure can vary by over 20%, depending on the structure's orientation on the wafer surface. This anisotropy originates from the crystal structure of silicon. We have directly measured the anisotropy of Young's modulus in the (100) plane of silicon from the measured resonance frequencies of a “wagon-wheel” test structure comprising an arc of identical microcantilevers fabricated in the structural layer of a (100) silicon-on-insulator wafer. The direction of the principal axis of the cantilevers increased from 0° to 180 ° in 10° steps with respect to the [110] direction, allowing the angular dependence of Young's modulus to be experimentally mapped out. The Young's modulus was measured to have a value of 170 GPa ± 3 GPa at 0° and 90 ° to the [110] direction and a value of 131 GPa ± 3 GPa at ±40° and ±50° to the [110] direction. The measured values of Young's modulus and their angular dependence agree very well with the theoretical values that were recently reported, thereby experimentally verifying the theoretical calculations.