The drive towards miniaturization in polysilicon MEMS industry leads unavoidably to question the hypothesis of homogeneity commonly accepted for continuum mechanics. Silicon grain morphology and orientation eventually influences the mechanical response of MEMS devices, when critical structural components (such as e.g. suspension springs) shrink. Moreover, the deep reactive-ion etching process, leading to the so-called over-etch, whose relevance is more and more increasing when referred to dimensions comparable with the grain size, affects the accuracy of the geometrical layout. Under these conditions, a spread in the working operational behavior of the devices is expected, which is obviously a matter of concern both for MEMS design and reliability. While this consequence is well known and expected, the quantification of the aforementioned spread is far to be under control, both in design practice and theory.
In this work, through Monte Carlo analyses on statistical volume elements we show the effect of the grain morphology and orientation on the elastic effective properties of polysilicon beams constituting critical MEMS components. The extensive numerical investigation is summarized through statistical (lognormal) distributions for the elastic properties as a function of grain size morphology, quantifying therefore not only the expected mean values but also the also the spread around them. These (analytical) statistical distributions represent a simple while rigorous alternative to cumbersome numerical analyses. Their utility is testified through the analysis of a statically indeterminate MEMS structure, quantifying the possible initial offset away from the designed configuration due to residual stresses arising from the production process.