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

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.