Mechanical FEM simulation of sampled nanomembranes for mass detection

Abstract

This thesis investigates the applicability of mechanical finite element (Finite Element Method (FEM)) simulations to predict the tensile stress and mass of chemical samples deposited on perforated nanomechanical membranes, as used for nanoelectromechanical systems-based infrared spectroscopy. The membranes are modeled as prestressed elastic structures, and their eigenfrequencies are computed and compared with experimental measurements for different deposited materials and masses. A calibration of the simulation framework was performed using unsampled membranes from various manufacturers and with different prestresses and sizes, demonstrating agreement within the error bounds of the measurement (< 1% with experimental data across a broad parameter range. For sampled membranes, systematic measurements of eigenfrequencies were carried out with polystyrene (PS) and polypropylene (PP)deposits spanning masses from 625 pg to 40 ng. The results reveal a strong material dependence: PS samples induce measurable frequency shifts consistent with mass loading and negligible prestress, whereas PP samples show almost no shifts, which can be explained only by introducing an internal prestress in the deposited material. Quantitative agreement between simulation and experiment was achieved for most cases; however, the predictive power of purely mechanical modeling is not testable for small sample masses below 10 ng. In this regime, the frequency shifts are smaller than experimental uncertainties. Nonetheless, the developed simulation framework enables reliable estimation of membrane prestress and offers a basis for future extensions, such as constructing simulation databases to infer mass distributions from frequency response data. A challenge in modeling these thin membranes are different length scales in the thickness and width of the membrane. Previous modeling attempts in Comsol have shown problems with high aspect ratios of the finite elements. This was solved by using a 2D simulation. Overall, this work demonstrates both the potential and the limitations of Finite Element Method (FEM)-based modeling of nanomechanical membranes with deposited samples, providing insights for further development of quantitative analysis methods in nanomechanical spectroscopy.