Subnanometer Translation of Microelectromechanical Systems Measured by Discrete Fourier Analysis of CCD Images

Abstract

Abstract-In-plane linear displacements of microelectromechanical systems are measured with subnanometer accuracy by observing the periodic micropatterns with a charge-coupled device camera attached to an optical microscope. The translation of the microstructure is retrieved from the video by phase-shift computation using discrete Fourier transform analysis. This approach is validated through measurements on silicon devices featuring steep-sided periodic microstructures. The results are consistent with the electrical readout of a bulk micromachined capacitive sensor, demonstrating the suitability of this technique for both calibration and sensing. Using a vibration isolation table, a standard deviation of σ = 0.13 nm could be achieved, enabling a measurement resolution of 0.5 nm (4σ) and a subpixel resolution better than 1/100 pixel. Microelectromechanical systems (MEMS) comprise integrated devices made by batch-fabrication techniques, like those adopted from silicon-based integrated circuit technology. MEMS sensors and actuators have typical feature sizes ranging from a few tens of nanometers to several hundreds of micrometers. Mechanical transducers fabricated using silicon micromachining technology have to be characterized or even calibrated and possibly trimmed electronically before being used in an instrument. To mention only a few examples, the spring constant of an atomic force microscopy (AFM) cantilever, the voltage-displacement quadratic response of a comb-drive electrostatic actuator, or the sensitivity of a differential capacitive sensor are all parameters that are highly dependent on the microfabrication. Hence, at micro-and nanometer scales, precise and accurate dimensions can be difficult to guarantee because of process limitations. However, there are geometric parameters that are process independent, like the pitch of a periodic micropattern that is determined solely by the design. Thus, the periodicity can be used advantageously for precise and accurate position measurements.Optical measurements are noninvasive in nature and constitute an alternative or a complement to solid-state sensors, which can be challenging to miniaturize and integrate. However, most optical techniques proposed for the characterization of static displacements, motion, and vibrations were developed to quantify the out-of-plane motion of MEMS structures, often relying on complex interferometric techniques [1]. In contrast, only very few approaches were demonstrated for high-resolution in-plane displacement measurements. With continuous illumination, the displacement of the moving part of a We introduce here an extremely simple and robust method for measuring the in-plane linear displacement of MEMS microstructures with a subnanometer resolution. It is applicable to any transducer that shows a translational displacement and features periodic microstructures. Apart from the MEMS device, the setup consists of a charge-coupled device (CCD) camera attached to a bright field optical microscope and a computer for the analysis of th...

Capillary-valve-based platform towards cell-on-chip mechanotransduction assays

“…(A) Two dc power supplies are connected to the left and right fixed combs (UL and UR, respectively), while an ac power supply (UC) drives the central combs (sinusoidal signal of frequency f). The displacement x is measured by "temporally aliased video microscopy" thanks to the periodic patterns [25,26]. (B, C) Typical frequency responses of a MEMS device (B) in air and (C) in water.…”

“…3B and C, we show typical frequency responses of a MEMS device actuated in air and in water. These measurements were performed by "temporally aliased video microscopy" 1 , through analysis of the dynamic motion of periodic patterns etched in the silicon device [25,26]. For comparison purposes, these experiments were performed consecutively on the same packaged chip (see inset in Fig.…”

Modal analysis and modeling of a frictionless electrostatic rotary stepper micromotor

“…An angular speed of 1°/ms could be reached with a driving signal of 600 Hz and 70 V amplitude. The measurements shown in Figures 5 and 6 were performed with a high-speed camera (Mikrotron CMOS high-speed camera, EoSens MC1363), using the algorithm described in [6].…”

Subpixel translation of MEMS measured by discrete fourier transform analysis of CCD images

“…The displacement of the moving structure relative to the reference is simply obtained by subtraction, thereby eliminating common noise sources. For further details on the calculation algorithm, the reader is referred to reference [5].…”

“…Optical techniques that combine digital image processing with stroboscopic video microscopy have been successfully implemented in state-of-the-art instruments for dynamic in-plane characterization of MEMS [1−4]. Here, we propose an in-plane measurement method that does not require any special investment in the measurement equipment and can be used in almost any laboratory, since its implementation only requires a CCD camera and a bright field microscope [5]. Our method is capable of observing in-plane motion with a resolution of 0.5 nm for a pixel size equivalent to 75 nm on the sample.…”