Analysis of resonant silicon bridges

The aim of this work is to compare dynamic and static methods of measurement for the determination of Young´s modulus (E) and the internal stress (σ) caused by fabrication of micromachined structures. These data are essential far accurate modelling of resonant microstructures. Quoted values of E for boron doped silicon are between 122 and 220 Gpa for the (110) direction, 131 Gpa for the (100) direction and between 90 and 190 Gpa for polysilicon. For other materials, such as silicon dioxide and silicon nitride, there is also uncertainty. For these films we have used both resonant and indent type tests to attempt to evaluate E. We wish to ultimately measure both E for all these materials and also the pre-stress σ caused by fabrication of clamped structures. Comparison is made between the results of dynamic tests, in which the resonant frequencies were measured accurately for transverse modes up to about 200 kHz, and static tests in which the point compliance was determined. Measurements were made on two bridges. Both were 200 μm wide and about 3 μm thick. One had a length of 2.2 mm and the other was 3.6 mm long