Frequency-Dependent Piezoresistive Effect in Top-down Fabricated Gold Nanoresistors.

Piezoresistive strain gauges allow for electronic readout of mechanical deformations with high fidelity. As piezoresistive strain gauges are aggressively being scaled down for applications in nanotechnology, it has become critical to investigate their physical attributes at different limits. Here, we describe an experimental approach for studying the piezoresistive gauge factor of a gold thin-film nanoresistor as a function of frequency. The nanoresistor is fabricated lithographically near the anchor of a nanomechanical doubly clamped beam resonator. As the resonator is driven to resonance in one of its normal modes, the nanoresistor is exposed to frequency-dependent strains of ε ≲ 10-5 in the 4-36 MHz range. We calibrate the strain using optical interferometry and measure the resistance changes using a radio frequency mix-down technique. The piezoresistive gauge factor γ of our lithographic gold nanoresistors is γ ≈ 3.6 at 4 MHz, in agreement with comparable macroscopic thin metal film resistors in previous works. However, our γ values increase monotonically with frequency and reach γ ≈ 15 at 36 MHz. We discuss possible physics that may give rise to this unexpected frequency dependence.

Highly sensitive simple homodyne phase detector for ultrasonic pulse-echo measurements.

We have designed and built a modern versatile research-grade instrument for ultrasound pulse-echo probing of the elastic properties of a wide range of materials under laboratory conditions. The heart of the instrument lies in an AD8302 microchip: a gain and phase detector from Analog Devices, Inc. To construct the device, we have implemented a schematic that utilizes the homodyne principle for signal processing instead of the traditional superheterodyne approach. This design allows one to measure phase shifts with high precision and linearity over the entire range of 0°-360°. The system is simple in construction and usage; it makes ultrasound measurements easily accessible to a broad range of researchers. It was tested by measuring the temperature dependence of the ultrasound speed and attenuation in a KTa0.92Nb0.08O3 (KTN) single crystal at a frequency of ∼40 MHz. The tests were performed in the vicinity of the ferroelectric transitions where the large variations of the speed and attenuation demand a detector with outstanding characteristics. The described detector has a wide dynamic range and allows for measuring in a single run over the whole temperature range of the ferroelectric transitions, rather than just in limited intervals available previously. Moreover, due to the wide dynamic range of the gain measurements and high sensitivity this instrument was able to reveal previously unresolvable features associated with the development of the ferroelectric transitions of KTN crystals.

Nanoelectromechanical devices in a fluidic environment.

We present a comprehensive study of nanoelectromechanical systems in pressurized fluids. Resonant responses and quality factors are monitored in five different gases and one liquid, in pressures ranging from vacuum to 20 MPa, in order to evaluate theoretical models of device-fluid interactions at the nanoscale. The traditional Newell picture of microresonator damping in different pressure regimes is found to be inadequate in describing nanoresonators in general. Damping at intermediate pressure ranges is better physically characterized by a Weissenberg number (which compares oscillation frequencies with fluid relaxation rates) than a Knudsen number (which compares mean free paths with device widths) and most adequately described by the Yakhot and Colosqui model. At high-pressure ranges, two models are found to give good agreement with data: the phenomenological model of vibrating spheres and the Sader and Bhiladvala model for the viscous regime. The latter is also successful in explicitly predicting pressure-dependent behavior of the viscous mass load and damping. We observe significant increases in damping due to the squeezed film (SF) of gas between the device and substrate as well as due to undercut (an unavoidable artifact of the standard fabrication technique); correcting the shape of the devices with a focused ion beam allows us to differentiate these two factors. Application of the SF model accounts well for additional damping at high pressures while only qualitatively agreeing at lower pressures. The extensive data collected allow additional insight into fundamental processes underlying fluid damping at the nanoscale, particularly in the intermediate- and high-pressure regimes.

Fiber coupling to BaTiO3 glass microspheres in an aqueous environment.

Compact microspheres with high-quality (Q) whispering gallery modes are required for many applications involving liquid immersion, such as sensing nanoparticles and studying resonant radiative pressure effects. We show that high-index (1.9 and 2.1) barium titanate glass (BTG) microspheres are perfect candidates for these applications due to their high-Q (∼10(4) in the 1100-1600 nm range) resonances evanescently excited in spheres with diameters of 4-15 µm. By reattaching the spheres at different positions along a tapered optical fiber, we show that the coupling constant exponentially increases with thinner fiber diameters. We demonstrate the close to critical coupling regime with intrinsic Q=3×10(4) for water immersed 14 µm BTG spheres.

Pressurized fluid damping of nanoelectromechanical systems.

Interactions of nanoscale structures with fluids are of current interest both in the elucidation of fluid dynamics at these small scales, and in determining the ultimate performance of nanoelectromechanical systems outside of vacuum. We present a comprehensive study of nanomechanical damping in three gases (He, N2, CO2), and liquid CO2. Resonant dynamics in multiple devices of varying size and frequency is measured over 10 decades of pressure (1 mPa-20 MPa) using time-domain stroboscopic optical interferometry. The wide pressure range allows full exploration of the regions of validity of Newtonian and non-Newtonian flow damping models. Observing free molecular flow behavior extending above 1 atm, we find a fluid relaxation time model to be valid throughout, but not beyond, the non-Newtonian regime, and a Newtonian flow vibrating spheres model to be valid in the viscous limit.

A simple cell for the analysis of nanoelectromechanical systems under gas pressure.

A simple yet versatile apparatus for optical microscopy investigations of solid-state devices under high gas pressures is presented. Interchangeable high-grade sapphire windows with different thicknesses allow variable choice of trade-off between the maximum operating pressure and maximum spatial resolution. The capabilities of this compact chamber were tested by performing stroboscopic optical interferometry on nanoelectromechanical systems (NEMSs) under capacitive excitation. With a 1.7 mm thick sapphire window, the cell is safe to operate at pressures ranging from vacuum to 5 MPa. Minimal optical wavefront distortion allows NEMSs with linear dimensions of 0.1x1.6 microm(2) to be explored. For a sapphire window with a maximum thickness of 6 mm, the safe operating pressure increases up to an estimated 60 MPa; however, the increasing distortions inhibit signal from NEMSs smaller than approximately 0.5x1 microm(2). The cell can be used for confocal microscopy, microphotoluminescence and electroluminescence, light scattering spectroscopy, and reflectivity. The light weight and compact design of the chamber allow mounting on a precision piezomotion control stage or inside a volume tight apparatus such as cryostats.