Frequency Tuning of Silicon Micromechanical Cantilevers by Laser Ablation

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The high Q-factor and stability of micromechanical resonators makes them attractive for a range of applications such as R.F. filters [1] and resonant sensors [2]. In many cases, a specific resonant frequency is necessary for optimum performance [3,4], however this cannot be guaranteed as fabrication tolerances, defects and stresses will shift the natural frequencies of the resonator. A tuning method must be employed to re-align the centre frequency of the resonator with the specified band [5]. Permanent tuning using a Nd:YAG laser, which has several advantages over alternative techniques like FIB [6], is examined in this paper. An analytical model of the effect of ablation was developed and includes the contributions from stiffness and mass. The ablation profile was approximated to be hemispherical as indicated by the SEM image shown in figure (1). The predicted frequency shift of the fundamental flexural mode of vibration due to a single laser shot is shown in figure (2) for ablation performed at the fixed and free ends of the cantilever. An optical workstation [7] incorporating a frequency doubled Nd:YAG laser, a laser vibrometer and a CCD camera were employed to perform the tuning and measure the frequency shift. Due to the small frequency shifts expected, the effect of ambient temperature variation on the resonant frequency was monitored during the tuning procedure. A single shot and then three shots were taken at both the fixed end and free end of the cantilever. The measured tuning is shown in figures (3) and (4). For the single and subsequent three laser shots, the model predicts a shift in resonant frequency of -7.3Hz, -29.2Hz (fixed end) and 2.5Hz, 10.2Hz (free end) compared with the measured values of -1.1Hz, -19Hz (fixed end), 0.9Hz, 3.2Hz (free end). Although the model predicts the direction of the shift, there is a large discrepancy in the magnitude, this has been attributed to the redistributed material around the ablation site. Further modelling to incorporate this debris does lead to better agreement however accurately predicting the resulting frequency will remain problematic. Thus for laser tuning it is necessary to monitor the resonant frequency of the device during the tuning process. A microscope objective is currently under development to simultaneously measure and ablate devices.

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Journal: TechConnect Briefs
Volume: 1, Technical Proceedings of the 2003 Nanotechnology Conference and Trade Show, Volume 1
Published: February 23, 2003
Pages: 478 - 481
Industry sector: Sensors, MEMS, Electronics
Topic: Modeling & Simulation of Microsystems
ISBN: 0-9728422-0-9