Optical interferometric displacement calibration and thermomechanical noise detection in bulk focused ion beam-fabricated nanoelectromechanical systems

Abstract

Optical interferometric techniques are used for absolute (calibrated) displacement measurements of focused ion beam (FIB)-fabricated nanoelectromechanical systems (NEMS). FIB nanomachining of bulk Si gives rapidly prototyped cantilever and doubly clamped beam devices. Ion impingement from orthogonal directions allows tailoring of deep, undercut-free gaps between the device layer and the bulk, in turn allowing large amplitude NEMS oscillatory motion, access to a nonlinear readout regime and a new calibration method for optical interferometric displacement detection. The measurements are sensitive enough to determine the thermomechanical noise floor of a bulk FIBed NEMS device with a displacement sensitivity of 166 fm Hz − 1 2 , limited by the combination of optical shot noise and detector dark current. This sensitivity, comparable to the state of the art for free-space optical interferometry of NEMS, validates the robustness of the bulk FIB fabrication technique for rapid prototyping of nanoscale mechanical devices.

Ultrasensitive measurement of microcantilever displacement below the shot-noise limit

“…The results are applicable to any cantilever device operating with minimal back action noise, including optically transduced nano-electro-mechanical-systems (NEMS), which have recently been shown to be shot-noise-limited [9] at frequencies of a few MHz. The 4WM process has approximately 50 MHz of bandwidth within which to demonstrate sub-SNL displacement for NEMS and MEMS structures.…”

“…In many cases, thermal noise, classical laser noise, and quantum mechanical back action can limit the minimum detectable displacement in microcantilevers, but it is possible to work in regimes that evade these noise sources [4,[8][9][10] so that the noise level of the coherent light field, called the photon shot noise limit (SNL), becomes the dominant source. The SNL is determined by the Heisenberg uncertainty relation for minimum uncertainty states, and improvement in sensitivity beyond the SNL is impossible with classical optics [7,11].…”

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.…”

Integrated On-Chip Nano-Optomechanical Systems

“…35,36,37,38,39 Compared with electrical transduction, high-bandwidth operation is easily achieved without signal down-mixing. However, due to natural constrains of the optical wavelength, upon scaling down, physical dimensions of nanomechanical resonators quickly reach the diffraction limit of the laser wavelength in use.…”