Hydrodynamic methods for calibrating the normal spring constant of microcantilevers

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

Micro- and nanocantilevers are employed in atomic force microscopy (AFM) and in micro- and nanoelectromechanical systems (MEMS and NEMS) as sensing elements. They enable nanomechanical measurements, are essential for the characterization of nanomaterials, and form an integral part of many nanoscale devices. Despite the fact that numerous methods described in the literature can be applied to determine the static flexural spring constant of micro- and nanocantilever sensors, experimental techniques that do not require contact between the sensor and a surface at some point during the calibration process are still the exception rather than the rule. We describe a noncontact method using a microfluidic force tool that produces accurate forces and demonstrate that this, in combination with a thermal noise spectrum, can provide the static flexural spring constant for cantilever sensors of different geometric shapes over a wide range of spring constant values (≈0.8-160 N/m).

Calibration of the torsional and lateral spring constants of cantilever sensors

A method suitable for the calibration of the spring constants of all torsional and lateral eigenmodes of micro- and nanocantilever sensors is described. Such sensors enable nanomechanical measurements and the characterization of nanomaterials, for example with atomic force microscopy. The method presented involves the interaction of a flow of fluid from a microchannel with the cantilever beam. Forces imparted by the flow cause the cantilever to bend and induce a measurable change of the torsional and lateral resonance frequencies. From the frequency shifts the cantilever spring constants can be determined. The method does not involve physical contact between the cantilever or its tip and a hard surface. As such it is non-invasive and does not risk damage to the cantilever. Experimental data is presented for two rectangular microcantilevers with fundamental flexural spring constants of 0.046 and 0.154 N m(-1). The experimentally determined torsional stiffness values are compared with those obtained by the Sader method. We demonstrate that the torsional spring constants can be readily calibrated using the method with an accuracy of around 15%.

Determination of the spring constants of the higher flexural modes of microcantilever sensors

A method for the simultaneous calibration of the spring constants of all flexural modes of microcantilevers is presented. It is based on a flow of gas from a microchannel that interacts with the microcantilever. The gas flow causes a measurable shift in the resonance frequencies of thermal noise spectra of the flexural modes. From the magnitude of the frequency shifts of the individual modes the spring constants can be determined with high accuracy and precision. The method is non-invasive and does not risk damage to the cantilever. Experimental data are presented for several V-shaped and rectangular cantilevers with nominal fundamental spring constants in the range of 0.03-1.75 N m(-1). The spring constants of the fundamental modes compare favorably to those obtained using the Sader method. The higher modes of oscillation are readily calibrated with experimental uncertainties of 5-10%.