I. Introduction
Several near-field microscopies use resonant cantilevers. The first one is the scanning microdeformation microscopy. It is used in the microscopic range [1], [2]. Atomic force microscopy has also been modified to use a resonant cantilever [3] to achieve atomic resolution. Presently, frequency modulation atomic force microscopy is the preferred method to obtain atomic resolution in vacuum. The force-sensing cantilever is the most important component. It can be characterized by the three following parameters: stiffness eigenfrequency and quality factor . The spring constant and the quality factor of quartz tuning forks have initiated the attempt to achieve atomic resolution [4]. Piezoelectric tuning forks have the advantage of being self-sensing. The use of optics is thus not necessary and operations in ultrahigh vacuum and at low temperatures are easily implemented. Quartz length-extension resonators (LER) have already been used to obtain atomically-resolved imaging by frequency-modulation atomic force microscopy [5], [6]. The tip used to obtain atomic resolution is obtained by means of sharpened tungsten wire glued onto the LER. This point constitutes a technological difficulty which considerably increases the cost of the devices.