A complete analysis of the laser beam deflection systems used in cantilever-based systems

MIT Media Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States
Ultramicroscopy (Impact Factor: 2.44). 04/2007; 107(4-5):422-30. DOI: 10.1016/j.ultramic.2006.11.001
Source: PubMed


A working model has been developed which can be used to significantly increase the accuracy of cantilever deflection measurements using optical beam techniques (used in cantilever-based sensors and atomic force microscopes), while simultaneously simplifying their use. By using elementary geometric optics and standard vector analysis it is possible, without any fitted or adjustable parameters, to completely and accurately describe the relationship between the cantilever deflection and the signal measured by a position sensitive photo-detector. By arranging the geometry of the cantilever/optical beam, it is possible to tailor the detection system to make it more sensitive at different stages of the cantilever deflection or to simply linearize the relationship between the cantilever deflection and the measured detector signal. Supporting material and software has been made available for download at so that the reader may take full advantage of the model presented herein with minimal effort.

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Available from: P. Grutter, Apr 02, 2014
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    • "When using a cantilever deflection detection system of the Dimension 3100 (which has a measurement bandwidth of 2 MHz), this is, in principle, not easy because both the cantilever and the quadrant photodiode are nonlinear, and not always aligned in the same way. The complexity of obtaining quantitative data from beam deflection systems rather than just using them as a null sensor has been discussed by Beaulieu et al (2007) and Xu et al (2009). Filtering of the HSAFM data to remove higher eigenmode contributions to the deflection signal can significantly affect height data when using a beam deflection system. "
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    Full-text · Article · Jan 2013 · Measurement Science and Technology
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    • "Second, systematic uncertainty in the determination of the sensitivity S in Eq. (4) exists, primarily for two reasons: (i) Silva and Van Vliet [30] invoked the non-linearity of the photodetector voltage–deflection relationship, which may emanate from applying large cantilever deflections [31], and (ii) the assumption of zero indentation into a reference film in Eq. (5) is not satisfied, which is likely the case for stiff AFM cantilevers with k420 N/m, even if the tip-surface interaction only involves purely elastic deformation during calibration. Furthermore, different methods have been proposed to determine the projected area of contact in hardness measurements by AFM nanoindentation, which varies from directly scanning the residual indent [1] [3] [4] [6] [7] [10] [26] to taking the indenter cross-sectional area into account [3] [9]; however, no consensus exists in the literature on the measurement approach resulting in the smallest error. "
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    ABSTRACT: We present a new method to improve the accuracy of force application and hardness measurements in hard surfaces by using low-force (<50 μN) nanoindentation technique with a cube-corner diamond tip mounted on an atomic force microscopy (AFM) sapphire cantilever. A force calibration procedure based on the force-matching method, which explicitly includes the tip geometry and the tip-substrate deformation during calibration, is proposed. A computer algorithm to automate this calibration procedure is also made available. The proposed methodology is verified experimentally by conducting AFM nanoindentations on fused quartz, Si(100) and a 100-nm-thick film of gold deposited on Si(100). Comparison of experimental results with finite element simulations and literature data yields excellent agreement. In particular, hardness measurements using AFM nanoindentation in fused quartz show a systematic error less than 2% when applying the force-matching method, as opposed to 37% with the standard protocol. Furthermore, the residual impressions left in the different substrates are examined in detail using non-contact AFM imaging with the same diamond probe. The uncertainty of method to measure the projected area of contact at maximum force due to elastic recovery effects is also discussed.
    Full-text · Article · Dec 2010 · Ultramicroscopy
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    • "It is a robust detection method with high sensitivity and can be applied to different kinds of cantilevers under different environments. The advantage of the method is its simplicity and well researched principle [4]. Despite its popularity however, the effect of the laser on the resonant cantilever and its mechanical properties is not well examined. "
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    ABSTRACT: Laser beam deflection is a well known method commonly used in detecting resonance frequencies in atomic force microscopes and in mass/force sensing. The method focuses a laser spot on the surface of cantilevers to be measured, which might change the mechanical properties of the cantilevers and affect the measurement accuracy. In this work we showed that the joule heating of the laser, besides other extrinsic effects such as surface contamination, can cause a significant amount of shift in the resonator. The longer and softer the cantilever is, the more significant the effect. We suggest that the laser effects on the resonant response of sensors have to be taken into account.
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