Geometric Model Improves Cantilever-Based Sensing

Richard Gaughan

Micromachined cantilevers in atomic force microscopes and sensors provide precise measurements of everything from molecular binding to acceleration, but their sensitivity can present a problem.

A reflected laser beam typically is used to measure small deflections in the cantilevers, which are a couple of hundred microns long. The location of the reflected beam depends on just about every geometrical relationship in the system, which makes it difficult to provide absolute calibration for cantilever-based instruments.

Micromachined cantilevers are sensitive enough to measure processes such as molecular attachment, but that sensitivity can degrade repeatability. A geometrical model of the laser sensing system has resulted in design rules to improve cantilever sensing accuracy. Courtesy of Luc Y. Beaulieu.

A method developed by Luc Y. Beaulieu of Memorial University in St. John’s, Newfoundland, Canada, along with colleagues from MIT in Cambridge, Mass., and from McGill University in Montreal provides absolute calibration in a robust procedure that promises to extend the applications of cantilever-based devices.

As part of a research program to improve the sensitivity and accuracy of the sensors, Beaulieu developed a mathematical model for the cantilever sensing geometry. The model includes the azimuthal and elevation angles of the laser beam reflected from the micromechanical beam, the cantilever length, the position of the laser spot on the cantilever, the distance from the spot to the position-sensitive detector and the angle of the detector plane relative to the normal to the cantilever surface.

It uses standard vector geometry and geometric optics, and unlike previous approaches, there are no approximations. Approximate methods provide a linear fit for spot position as a function of cantilever deflection, but Beaulieu noted that the new model shows that the deflection curve of the position-sensitive detector versus the cantilever is never perfectly linear.

The investigators verified the model’s predictions by performing measurements using a macroscale, 41-cm-long cantilever. This prompted further investigation of the model, and Beaulieu said that they found that it is possible to “linearize” the position-sensitive detector versus cantilever deflection curve within experimental uncertainties to increase the ease of use of the systems.

The net effect is that a single, comprehensive set of measurements performed on initial installation serves to enhance the sensitivity and accuracy of a cantilever-based instrument. The angles will be measured with accurate mechanical methods, the distance from attachment point to laser spot will be measured with a microscope, and the distance of position-sensitive detector to cantilever will be determined with a method that the scientists are developing.

They are maintaining parallel modeling and experimental programs to accelerate their results, which Beaulieu said is important because he sees cantilever-based instruments as essential elements of improving health care.

Applied Physics Letters, Feb. 20, 2006, 083108