Size and Shape Effect in the Determination of the Fracture Strength of Silicon Nitride in MEMS Structures at High Temperatures

Several applications require Micro electro mechanical systems MEMS devices to operate under high temperatures. Previous efforts to study the properties of MEMS materials have shown that an increase in temperature leads to a decrease in the fracture strength. In this paper, three different thin film silicon nitride dog-bone shaped structures suspended on a silicon substrate are used to determine their fracture strength as a function of temperature using tensile strength testing. Analytical modeling is used to determine the elastic resistance of the thin film dog-bones to stresses caused by the forces originated by the difference in coefficient of thermal expansion between the dog-bones and their substrate. The calculated forces incorporate the effect of temperature in these interactions and the mechanical properties of the two materials by considering the temperature dependence of elastic modulus and coefficient of thermal expansion. Analytical results show that the fracture strength of a 175nm silicon nitride thin film decreases from 289MPa to 146MPa as temperatures increase from 250 to 500 degrees Celsius. When compared to other studies, these values show a consistent trend, thus also presenting this as a simple and promising in-situ method for the determination of fracture strength of MEMS devices operating at high temperatures.