Enhanced sensitivity to force gradients by using higher flexural modes of the atomic force microscope cantilever

Abstract

Higher flexural modes of a Si cantilever are used in order to increase the operating frequencies in non-contact mode scanning force microscopy. By recording frequency responses at different tip–sample distances and by using different flexural modes, long-range tip–sample interactions are studied. The experimental results reveal that operating at higher resonant modes makes it possible to improve sensitivity to force gradients and to avoid overlap between hydrodynamic interactions and attractive interactions in the range of 100-nm tip–sample distances. Using the second-harmonic, a sevenfold-enhanced sensitivity is demonstrated. Finally, discussion on the appropriate technique related to force gradient measurement, i.e. slope detection or frequency modulation technique, is reported. During the last decade, atomic force microscopy (AFM) [1] has atttacted a great interest in a wide field of applications including biological living cells [2]. For this kind of application, dynamic mode is the most used operating mode and avoids damage to such samples. There are numerous advantages in developing an AFM operating at high frequencies. Mainly, it allows fast scanning and reduces the thermal noise, and therefore the ultimate sensitivity to force gradients. Imaging systems with true atomic resolution as well as high-speed data storage are the main driving forces in this field. In order to obtain very high operating frequencies, fabrication of nanometric-scale cantilevers of small mass has been already reported [3, 4]. Due to the small size of the cantilever (typically sub-micron size), it requires more complicated detection systems. However, another alternative is to use conventional micromachined AFM cantilevers vibrating at higher flexural modes. Several groups are investigating this possibility. Rabe et al. [5] published a detailed analysis of cantilever vibration mechanisms, detecting more than 10 modes using silicon cantilevers. Recently, tapping mode images were performed by ∗ Permanent address: Laboratoire de Physique et Metrologie des Oscillateurs (LPMO-CNRS UPR 3203) Centre National de la Recherche Scientifique, 32 Avenue de l’Observatoire, 25044 Besancon Cedex, France, Fax: +33-3/8166 6998, E-mail: hoummady@lpmo.univ-fcomte.fr Minne et al. [6] using higher flexural modes. The piezoresistive cantilever that was used was driven at 132 kHz, which corresponded to the second flexural mode of the clamped-free beam. A quantitative analysis of sensitivity enhancement using higher modes has not yet been achieved. In this paper, we will demonstrate the ability of higher modes to enhance sensitivity to force gradients. For our experiments, we used a home-made force microscope with an original detection technique based on a two degrees of freedom optical detection system: interferometry and optical beam deflection [7], and a silicon cantilever driven at higher modes from the first to the fourth flexural mode (up to 6 MHz). By recording the quasi-instantaneous frequency response at different tip– sample distances, the two main long-range interactions were distinguished, i.e. air damping and attractive forces. The results reveal that higher order flexural modes allow us to avoid overlap between these two interactions. For measurement of force gradients, two techniques have been investigated, the frequency modulation technique [8] and slope detection [9]. At a tip–sample distance of 10 nm, the measured sensitivity of the frequency modulation technique was found to be sevenfold-enhanced using the second flexural mode. Therefore, sensitivity in terms of a decrease in amplitude at the initial frequency (corresponding to the slope detection technique), which depends mainly on the quality factor, remains roughly the same [10]. The results reveal also that higher order flexural modes allow us to avoid damping due to frictional forces between the cantilever and sample.