Analysis of optical interferometric displacement detection in nanoelectromechanical systems

Abstract

Optical interferometry has found recent use in the detection of nanometer scale displacements of nanoelectromechanical systems ͑NEMS͒. At the reduced length scale of NEMS, these measurements are strongly affected by the diffraction of light. Here, we present a rigorous numerical model of optical interferometric displacement detection in NEMS. Our model combines finite element methods with Fourier optics to determine the electromagnetic field in the near-field region of the NEMS and to propagate this field to a detector in the far field. The noise analysis based upon this model allows us to elucidate the displacement sensitivity limits of optical interferometry as a function of device dimensions as well as important optical parameters. Our results may provide benefits for the design of next generation, improved optical NEMS.

Self-Transducing Silicon Nanowire Electromechanical Systems at Room Temperature

“…This is in contrast to many other transduction schemes in which the voltage signal varies linearly with the displacement. [13][14][15][16][17][18][19][20]25,28 The device can be driven into nonlinear response with application of sufficient drive, as shown for a 22 MHz device of 88 nm thick, 4.9 µm long, 11 kΩ in resistance, with a measured Q ∼ 1200 (Figure 2c). This onset of nonlinearity, characterized by the frequency stiffening and bistability, arises from the effect of increasing tension built up in the wire at large vibration amplitudes.…”

“…At room temperature, optical interferometry detection 16,17 is convenient and ubiquitous; but its sensitivity for very small devices is limited by diffraction. 17,18 Alternatively, near-field optical techniques are also being explored, as recently demonstrated in the readout of NEMS motions utilizing the evanescent-wave coupling between suspended waveguides. 19 Capacitive detection, a common scheme widely used for MEMS resonators, 8 has the advantages of being inherently on-chip and all-electronic.…”

“…In fact, recent demonstrations of optical and capacitive detections have primarily been for <30 MHz beams with >200 nm widths. [17][18][19][20] For very thin SiNW-based NEMS, we seek to develop novel integrated transduction schemes that exploit the unique intrinsic properties of such structures. These must be complementary with realizable device configurations and established growth processes.…”

Spatial mapping of multimode Brownian motions in high-frequency silicon carbide microdisk resonators

“…We have engineered the system to achieve displacement sensitivities at pm Hz À 1/2 to fm Hz À 1/2 levels for devices in various materials and structures 31 , by further advancing the interferometry techniques developed during the last decade [53][54][55][56] . To experimentally determine the displacement sensitivity (resolution, or limit of detection for displacement), we first relate the amplitude of the thermomechanical motion to the measured noise level in the spectrum.…”

Diffractive characterization of the vibrational state of an array of microcantilevers

“…Most of the algorithms are based on the GerchbergSaxton method that iteratively relates two irradiance maps obtained at the plane of interest and also in the far field region. [11][12][13] In the MEMS arena, optical methods are routinely used as the displacement detection mechanism, [14][15][16] with the atomic force microscope probably the simplest and most well-known of these because it is based on the deflection of a light beam reflected by the cantilever itself. 17 The analysis of the stationary status of cantilevers using diffraction has been used previously to understand the individual position of each cantilever.…”