Comparison of the Stress Distribution and Fatigue Behavior of 10- and 25- $\mu\hbox{m}$-Thick Deep-Reactive-Ion-Etched Si Kilohertz Resonators

The stress distribution and fatigue behavior of nominally identical kilohertz fatigue resonators with two different thicknesses, 10 and 25 μm, was compared in this study. The results highlight the non-uniform 3-D stress distribution of the micron-scale notched cantilever beams that depends on the thickness. The areas corresponding to the first principal stress being within 2% of the maximum value are much smaller than the overall notch area and are a function of device thickness. It is also shown that the non-negligible influence of small, nanometer-scale geometrical variations in the dimensions of nominally identical devices on the maximum stress values can be accounted for by measuring the device's resonant frequency (
f
₀
). The observed scatter in the fatigue results of these microresonators is in part associated with the challenge in accurately calculating the local stress amplitudes. Despite that large scatter, the fatigue behavior of the 10 and 25 μm thick devices is similar. Particularly, the overall relative decrease rates in
f
₀
are well related to fatigue life (
N
_f
) and can be used to predict
N
_f
within a factor of 5, for
N
_f
ranging from 10
⁴
to 10
¹⁰
cycles.