Temperature sensitivity of silicon cantilevers’ elasticity with the electrostatic pull-in instability

Abstract

In this paper the temperature effects on the effective Young’s modulus of [1 1 0] silicon cantilevers is analyzed and measured in the range of 25–100 ° C. The quasi-static electrostatic pull-in instability method developed recently for ultra-thin cantilevers [H. Sadeghian, C.K. Yang, J.F.L. Goosen, E. van der Drift, A. Bossche, P.J. French, F. van Keulen, Characterizing size-dependent effective elastic modulus of silicon nanocantilevers using electrostatic pull-in instability, Appl. Phys. Lett. 94 (22) (2009) 221903] is employed to measure the temperature sensitivity of the ultra-thin cantilevers (Dutch Patent App., No. P6027025NL). A temperature sensitivity of 81.3 ° C/V is obtained. The temperature sensitivity is mostly due to the temperature dependence of the effective Young’s modulus of silicon. It is shown that changes in geometrical dimensions due to the change in temperature can be neglected. The changes in the effective Young’s modulus due to the changes in the temperature are extracted using a thermo–electro-mechanical coupled system. The pull-in method showed substantial advantages over other methods used for the study of the thermal effects on micron and sub-micron structures. The method is reproducible for various temperatures and cantilevers’ dimensions and the results demonstrate a new concept for a temperature sensor with ultra-high sensitivity.