Mass determination and sensitivity based on resonance frequency changes of the higher flexural modes of cantilever sensors

Micro-and nanocantilevers are increasingly employed as mass sensors. Most studies consider the first flexural mode and adsorbed masses that are either discretely attached or homogeneously distributed along the entire length of the cantilever. We derive general expressions that allow for the determination of the total attached mass with any mass distribution along the cantilever length and all flexural modes. The expressions are valid for all cantilevers whose flexural deflection can be described by a one-dimensional function. This approach includes the most common types of microcantilevers, namely, rectangular, picket, and V-shaped. The theoretical results are compared with experimental data up to the fourth flexural mode obtained from thermal noise spectra of rectangular and V-shaped cantilevers.