• A resonant cantilevered micro-plate is proved to be a promising candidate that can sequentially detect multiple particles. • The identification of multiple particles is regarded as an optimization problem via genetic algorithm to replace the widely-used least squares method. • Better identification accuracy is illustrated by exquisitely updating the modal shape changes of a micro-plate after each particle adsorption. • An experimental strategy based on focused ion beam and scanning probe microscopy verifies the applicability of the theoretic framework in designing and evaluating micro/nano sensors. The detection of multiple particles has been mainly studied by examining the flexural vibration properties of a one-dimensional Euler-Bernoulli beam under the assumption that the vibration mode shapes are unchanged. In fact, with the torsional vibration of the detector, valuable pieces of information can be derived, while the detection process is facilitated. Besides, the mode shapes of the detector can be easily changed by measuring multiple adsorbates or heavy analytes, which can fundamentally affect the detecting accuracy. To the best of our knowledge, these two issues have not yet been systematically considered in the literature. Along these lines, in this work, a theoretical framework is introduced to detect both the masses and positions of multiple particles absorbed on a two-dimensional micro-plate, where the history of the mass deposition events is sequentially measured from the recorded frequency shifts. The detection of multiple particles was realized by using an optimization process via the genetic algorithm, which circumvents the initial value and the local optimum problems that the widely-used least-squares method could be confronted with. In addition, an improved detection accuracy was ensured by exquisitely updating the modal shape changes of a micro-plate after the adsorption of each particle. To validate the proposed method, the frequency shifts were obtained by running modal analysis, where 20 μ concentrated masses were added sequentially on the top surface of the micro-plate modelling. As was expected, all particles could be effectively identified with enhanced accuracy. Furthermore, experimental validation was performed on Si-based micro-plates cantilevered, which were fabricated by focused ion beam milling and sequentially loaded by carrying out Pt depositions from the measured frequency shifts of the micro-plate structure before and after each sequential Pt deposition, the loaded masses and their positions in both the length and width directions were extracted. The results obtained from the model are in good agreement with the estimation based on scanning electron microscopy. The proposed method is anticipated to be further applied to multiple particle detection applications in many fields including biology, medicine and chemistry.
Read full abstract