Measurement of cantilever vibrations with a new heterodyne laser probe: application to scanning microdeformation microscopy

Abstract

Absolute measurements of cantilever vibrations in scanning probe microscopy are often used to quantify the properties of the investigated sample. Because the standard deflection method must be calibrated, we propose a new heterodyne interferometer which is autocalibrated by the associated electronics. We have applied this interferometer to scanning microdeformation microscopy (SMM), which is a kind of a.c. contact force microscopy, sensitive to variations of the local elastic constants of the investigated material. The connected fiber enables us to probe the vibrations of the cantilever or sample surface locally. The principles and typical features of the new optical probe, as well as applications of displacement probing to a vibrating cantilever, are presented. The results show the effect of the tip-sample interaction on the resonant frequencies of the cantilever in SMM. The data obtained confirm that the proposed probe enables an accurate estimation of the local elastic constants of the sample.Heterodyne interferometry is a useful tool for probing small displacements generated with electrical (e.g., piezoelectric transducer), magnetic, or thermal sources [1][2][3][4][5][6][7][8]. The main advantages of optical probing are the absence of contact or mass loading, wide bandwidth (up to about 1 GHz, limited by the detection electronics and by the spot size), and local measurement. In compact devices, it is also possible to move the optical part of the probe and to use an optical fiber for local probing. In recently developed a.c. force microscopes [9-13] the usual detection method measures the amplitude of the motion of the cantilever in bending mode. For a given excitation, this amplitude depends on the interaction force between the vibrating tip and the sample. In the case of contact, the equivalent spring and dashpot are related to local mechanical properties and the amplitude of vibration is sensitive to the sample stiffness.Our scanning microdeformation microscope (SMM) is a kind of a.c. contact force microscope. Because the investigation of the sample is based on near-field acoustics (the low-frequency vibration source interacts with the sample over a distance shorter than the acoustic wavelength), two interesting aspects can be considered: subsurface defects can be imaged by scanning the sample surface with the vibrating tip, and local elastic constants can be estimated by measuring the resonant frequency of the cantilever versus the contact force. In the first version of SMM [13], the transmitted stress was detected on the opposite face of the sample with a PZT transducer, but the resonant frequency of the cantilever was not easily extracted due to the presence of several resonance peaks. To overcome this limitation we have developed a new laser probe connected to an optical fiber as displacement sensor. Because the interaction stiffness modifies the resonance frequency of the cantilever-tip assembly [14-16], the frequency shift enables an evaluation of the sample stiffness. Consequently, the method allows ...

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