The theoretical model and novel analytical solution are of interest in the design of micro-diaphragm-based biosensing devices.
A simple and theoretical model using the flexural and torsional vibrations of micro-plates was proposed to simultaneously identify the mass and position of the attached particle by the vibration of a micro-plate.It is found that our strategy offers the unique specialty in the two-dimensional position (in width and length directions) detection, and is of wide adaptability for microcantilevers with arbitrary aspect ratios.
The results indicate that the mode shape change due to adsorption of a relatively large particle can influence the performance of the nanomechanical resonator considerably.
The investigation proves that it is necessary to adopt exact mode shapes, instead of approximate mode shapes, to ensure the accuracy in the theoretical evaluation of the vibration of the diaphragm in the fluid. Furthermore, the quality factor associated with acoustic radiation losses is mode dependent, and its dependency on the mode number shows plate, membrane, and plate-membrane transition behaviors as pre-stress varies.
This finding is verified numerically in finite element modeling using a freestanding circular diaphragm with and without an added particle, and it proves that the method resolves the particle position and mass with high accuracy.
The results obtained employing this method are in excellent agreement with those obtained numerically in finite element modelling when tested using freestanding circular SiC diaphragms with residual tensile stress. The stress and modulus values are also in reasonably good agreement with those obtained from nanoindentation and wafer curvature measurements, respectively.
By measuring the resonant frequencies of cantilever beams without and with thin films deposited and with the use of the Euler–Bernoulli beam theory, elastic modulus and density of thin films can be determined simultaneously. This simple resonant method was validated using a sputtered Ni film/Si substrate system. The elastic modulus of the Ni film obtained from this method was in excellent agreement with that measured by use of nanoindentation.