Silicon Resonators Research Articles

Oven controlled N++ [1 0 0] length-extensional mode silicon resonator with frequency stability of 1 ppm over industrial temperature range

This paper presents an oven controlled N++ [1 0 0] length-extensional mode silicon resonator, with a lookup-table based control algorithm. The temperature coefficient of resonant frequency (TCF) of the N++ doped resonator is nonlinear, and there is a turnover temperature point at which the TCF is equal to zero. The resonator is maintained at the turnover point by Joule heating; this temperature is a little higher than the upper limit of the industrial temperature range. It is demonstrated that the control algorithm based on the thermoresistor on the substrate and the lookup table for heating voltage versus chip temperature is sufficiently accurate to achieve a frequency stability of ±0.5 ppm over the industrial temperature range. Because only two leads are required for electrical heating and piezoresistive sensing, the power required for heating of this resonator can be potentially lower than that of the oscillators with closed-loop oven control algorithm. It is also shown that the phase noise can be suppressed at the turnover temperature because of the very low value of the TCF, which justifies the usage of the heating voltage as the excitation voltage of the Wheatstone half-bridge.

Approaching the intrinsic quality factor limit for micromechanical bulk acoustic resonators using phononic crystal tethers.

We systematically demonstrate that one-dimensional phononic crystal (1-D PnC) tethers can significantly reduce tether loss in micromechanical resonators to a point where the total energy loss is dominated by intrinsic mechanisms, particularly phonon damping. Multiple silicon resonators are designed, fabricated, and tested to provide comparisons in terms of the number of periods in the PnC and the resonance frequency, as well as a comparison with conventional straight-beam tethers. The product of resonance frequency and measured quality factor (f×Q) is the critical figure of merit, as it is inversely related to the total energy dissipation in a resonator. For a wide range of frequencies, devices with PnC tethers consistently demonstrate higher f×Q values than the best conventional straight-beam tether designs. The f×Q product improves with increasing number of PnC periods, and at a maximum value of 1.2 × 1013 Hz, approaches limiting values set by intrinsic material loss mechanisms.

Applying laser Doppler vibrometry to probe anchor losses in MEMS AlN-on-Si contour mode resonators

This paper reports the application of high frequency laser Doppler vibrometry to observe the surface profile of waves at the boundaries of contour mode aluminum nitride (AlN) on silicon (Si) resonators. The findings provide better understanding of the nature of the losses at the anchoring regions. These losses set the quality factors of these resonators. We have applied the technique to three groups of resonators to correlate the findings from laser vibrometer measurements to the measured quality factors (and thus also anchor loss). The three groups of resonators differ in their resonant frequencies, which are determined by the resonator dimensions, in order to provide a range of frequencies for enhanced testing reliability. Each group includes a flat-edge resonator and a biconvex resonator of the same resonant frequencies but largely different quality factors (at least by a factor of six: e.g. 12000 vs. 2100) in order to accentuate differences observed by vibrometry. Experimental vibrometer results for all resonators consistently show starkly different surface wave profiles (i.e. out of plane direction) despite the fact that the vibration modes are primarily lateral. The vibrometer wave profiles show strong confinement in the biconvex resonators while the waves in the normal flat edge resonators are spread out uniformly to the boundaries. The vibrometer results match well with the finite-element models. In summary, we find a strong correlation between the out-of-plane displacement profiles and anchor loss, which allows us to verify and consequently exploit the simulations in the course of analyzing anchor losses in AlN-on-Si contour mode resonators. Finally, our results show that varying the support tether length has neither any effect on the wave profile nor the quality factor.

Fabrication and evaluation of capacitive silicon resonators with piezoresistive heat engines

This work reports the design, fabrication and evaluation of capacitive silicon resonators with piezoresistive heat engines. A combination of capacitive transduction and piezoresistive actuation based on a piezoresistive heat engine in the single micromechanical resonator is proposed to achieve a low insertion loss and small motional resistance. Capacitive silicon resonators with single and multiple piezoresistive beams have been demonstrated. In these structures, resonant bodies are divided into many parts that are connected to each other by using small piezoresistive beams to enhance electromechanical transductions by the piezoresistive heat engines. When a bias voltage Vb=7V is applied to the piezoresistive beams, the insertion loss and motional resistance of the capacitive silicon resonator with multiple piezoresistive beams are improved by 20dB (enhanced from −68dB to −48dB) and 90% (reduced from 125.5kΩ to 12.5kΩ), respectively, in comparison to the case without a bias voltage. In addition, the tuning frequency characteristic with the piezoresistive effect is increased by 165 times over that of the structure with only the capacitive effect.

Quantization of acoustic-phonon shear modes in a nanowaveguide

Acoustic energy trapping in a thin non-piezoelectric plate is studied. The confinement of resonant acoustic fields is described for the case where energy trapping is caused by thickening the center region of the plate. The elastic continuum mechanics model is used to determine the quantized acoustic-phonon modes in an isotropic nanowaveguide. The acoustic-phonon amplitudes and relative frequency dispersion relations are obtained analytically and presented for both the odd symmetry shear modes and even symmetry shear modes. The acoustic-phonon modes in the non-piezoelectric nanowaveguide are quantized. Furthermore, the limit of the quality factor and frequency (fQ) product achievable by a resonator is theoretically discussed and calculated in silicon resonators for three different orientations.

Effect of thermoelastic damping on silicon, GaAs, diamond and SiC micromechanical resonators

The effect of thermoelastic damping as a main dissipation mechanism in single crystalline silicon, GaAs, diamond, SiC and SiO2 micromechanical resonators are studied. Numerical simulation is performed to compare quality factors of the given materials. Results using Zener’s well-known approximation and recent developments of Lifshitz and Roukes models were used to model thermoelasticity effects. In the later model, the effect of thermal diffusion length is taken into account for determination of thermoelastic damping. Our results show that larger discrepancy is obtained between the two models for SiO2. The difference is pronounced when beam aspect ratio (L/w) is smaller. Such progresses will find potential applications in optimal design of high quality factor micrometer- and nanometer-scale electromechanical systems.

Temperature dependence of resonance characteristics of silicon resonators and thermal stability improvement by differential operation method

In this paper, we describe the mechanism and solution for dominating temperature effects on refractive-index-based Si optical resonator sensors such as ring resonator and photonic crystal resonator sensors. The temperature change affects the silicon refractive index and also the resonator mechanical shape. As a result, it is reported that the refractive index change is marked, whereas the mechanical deformation effect is negligible. We also demonstrated that the differential operation is effective for suppressing the temperature effect for Si ring resonator sensors.

Design and implementation of a 2 μA temperature-compensated MEMS-based real-time clock with ±4 ppm timekeeping accuracy

This paper presents the design and measurements of a temperature-compensated real-time clock based on a silicon resonator. The system exhibits timekeeping accuracy of ±4ppm over the −40 to 85°C temperature range. The current implementation is based on a TIA-based oscillator with a 27kHz MEMS resonator, a differential PTAT temperature sensor and a 2nd order ΣΔ ADC. The temperature compensation is performed by an on-chip DSP block. The system consumes 2μA of current and operates at 1.8V nominal supply. The resonator operates off a 1.2V DC bias without the need for a charge-pump or providing an external higher DC voltage. The integrated electronics interface has been implemented using a standard 0.18μm CMOS process.

Terahertz near-field imaging of dielectric resonators.

As an alternative to metallic resonators, dielectric resonators can increase radiation efficiencies of metasurfaces at terahertz frequencies. Such subwavelength resonators made from low-loss dielectric materials operate on the basis of oscillating displacement currents. For full control of electromagnetic waves, it is essential that dielectric resonators operate around their resonant modes. Thus, understanding the nature of these resonances is crucial towards design implementation. To this end, an array of silicon resonators on a quartz substrate is designed to operate in transmission at terahertz frequencies. The resonator dimensions are tailored to observe their low-order modes of resonance at 0.58 THz and 0.61 THz respectively. We employ a terahertz near-field imaging technique to measure the complex near-fields of this dielectric resonator array. This unique method allows direct experimental observation of the first two fundamental resonances.

Polymer Brush‐Modified Microring Resonators for Partition‐Enhanced Small Molecule Chemical Detection

AbstractSilicon photonic microring resonators have emerged as a promising technology for the sensitive detection of biological macromolecules, including proteins and nucleic acids. However, not all species of interest are large biologics that can be targeted by highly specific capture agents. For smaller organic chemicals, including many toxic and regulated species, a general approach to improving sensitivity would be desirable. By functionalizing the surface of silicon photonic microring resonators with polymer brushes, small molecules can selectively partition into the surface‐confined sensing region of the optical resonators. This in turn leads to response enhancements in excess of 1000% percent, relative to non‐functionalized sensors, for representative targets including 4‐methylumbelliferyl phosphate, a simulant for highly toxic organophosphates, Bisphenol A, an industrial pollutant, as well as other small organic analytes of interest. There are many polymer brush chemistries compatible with silicon resonators, making this a general strategy towards tuning sensor selectivity and specificity by optimizing interactions between the agent(s) of interest and the polymer construct.

Fundamental suppression of backscattering in silicon microrings.

In this paper we theoretically prove and experimentally demonstrate a novel approach to eliminate the effects of backscattering in silicon ring resonators. Not only the resonance-splitting can be completely suppressed, but also the unwanted light reflected to the in port and directed to the add port can be dramatically reduced. Ring resonators have become one of the most intensively used integrated optical components for various applications. However, in high-index-contrast platforms like silicon photonics, sidewall roughness induced backscattering imposes limits on the performance of ring resonators. It frequently induces resonance-splitting in through and drop ports. At the same time, there will be unwanted light directed to the add port and reflected to the in port. We show that, by putting an intentional tunable reflector inside the ring to compete with the stochastic backscattering, the ring can work under a normal condition. All resonances can be tuned to be non-split with an improved extinction ratio and there will be significantly less light coming out from the in and the add ports.

A simple topology metamaterial blackbody for visible light

Because they can absorb nearly all of the light incident upon them, metamaterial-based blackbodies have many potential applications and have been studied widely. However, the topological structure of most designed metamaterial blackbodies so far is too complicated, at least involving a three-layer structure, to be fabricated and used, especially in the optical band. Here, we designed a simple topology metamaterial blackbody that contains only two layers. The top layer is a periodic arrangement of subwavelength silicon resonators, and the bottom one is a continuous Au film. The simulated results showed that the proposed structure produced a perfect absorption peak in the spectrum because of the Mie resonance of the silicon resonator, the localized surface plasmon resonance of the Au film, and the appropriate losses of the dielectric and metal materials. Furthermore, the impact of the geometrical and material parameters and the incident and polarization angles on the absorption spectrum were studied in depth. Finally, the physical mechanism underlying the blackbody was also studied. All of the results indicate that the designed metamaterial blackbody has many salient features and can be used in devices such as solar cells and bolometers.

Перспективы использования кремниевого резонатора в резонансных преобразователях давления

Перспективы использования кремниевого резонатора в резонансных преобразователях давления

Tunable and Ultra-Small Graphene Integrated Silicon Racetrack Micro Resonator

We have demonstrated ultra-small and tunable graphene integrated racetrack silicon photonic resonators by harnessing the unique optoelectronic properties of graphene layer and the racetrack silicon resonators. Previous studies have been focused on the straight waveguide interacting with a graphene layer. To further explore how to effectively increase the interaction length between graphene layer and silicon photonic devices, this paper employs integrated racetrack silicon resonator interacting with graphene layer within the coupling region . These new configurations will reduce the footprints of the graphene integrated silicon photonics to micron size , instead of hundreds of microns or even millimeter size. We have demonstrated relatively large voltage tuning results and large modulation depth when putting the graphene layer within the coupling region of the racetrack microresonator close to the critical coupling condition. Our work offers flexibility and tunability for hybrid graphene silicon photonic systems, as well as future functional hybrid photonic devices and systems. Potential applications include emerging areas such as active silicon photonic devices for high-performance data processing, tele communications, integrated biophotonics, and low-power energy saving optoelectronic devices.

Resonant silicon nanoparticles for enhancement of light absorption and photoluminescence from hybrid perovskite films and metasurfaces.

Recently, hybrid halide perovskites have emerged as one of the most promising types of materials for thin-film photovoltaic and light-emitting devices because of their low-cost and potential for high efficiency. Further boosting their performance without detrimentally increasing the complexity of the architecture is critically important for commercialization. Despite a number of plasmonic nanoparticle based designs having been proposed for solar cell improvement, inherent optical losses of the nanoparticles reduce photoluminescence from perovskites. Here we use low-loss high-refractive-index dielectric (silicon) nanoparticles for improving the optical properties of organo-metallic perovskite (MAPbI3) films and metasurfaces to achieve strong enhancement of photoluminescence as well as useful light absorption. As a result, we observed experimentally a 50% enhancement of photoluminescence intensity from a perovskite layer with silicon nanoparticles and 200% enhancement for a nanoimprinted metasurface with silicon nanoparticles on top. Strong increase in light absorption is also demonstrated and described by theoretical calculations. Since both silicon nanoparticle fabrication/deposition and metasurface nanoimprinting techniques are low-cost, we believe that the developed all-dielectric approach paves the way to novel scalable and highly effective designs of perovskite based metadevices.

A high-accuracy working standard for absolute pressure from 5 kPa to 130 kPa

We describe a calibration device for absolute pressure ranging from 5 kPa to 130 kPa whose relative uncertainty contribution (k = 1), including stability, repeatability and linearity is better than 1 Pa. The device is composed of a capacitance diaphragm gauge (CDG) and a resonant silicon gauge (RSG). The good long-term stability of the calibration slope of the RSG disseminated to the CDG which in turn allows one to master the offset of the RSG, is the reason for such a low uncertainty contribution. The metrological characterisation of this working standard is presented.

Enhancement and Inhibition of Spontaneous Photon Emission by Resonant Silicon Nanoantennas

Substituting noble metals for high-index dielectrics has recently been proposed as an alternative strategy in nanophotonics to design broadband optical resonators and circumvent the ohmic losses of plasmonic materials. In this report, we demonstrate that subwavelength silicon nanoantennas can manipulate the photon emission dynamics of fluorescent molecules. In practice, it is showed that dielectric nanoantennas can both increase and decrease the local density of optical states (LDOS) at room temperature, a process that is inaccessible with noble metals at the nanoscale. Using scanning probe microscopy, we analyze quantitatively, in three dimensions, the near-field interaction between a 100 nm fluorescent nanosphere and silicon nanoantennas with diameters ranging between 170 nm and 250 nm. Associated to numerical simulations, these measurements indicate increased or decreased total spontaneous decay rates by up to 15 % and a gain in the collection efficiency of emitted photons by up to 85 %. Our study demonstrates the potential of silicon-based nanoantennas for the low-loss manipulation of solid-state emitters at the nanoscale and at room temperature.

Long-range all-dielectric plasmonic waveguide in mid-infrared

In this paper, we introduce the modal analysis of hybrid plasmonic waveguides in the mid-infrared region. In our plasmonic waveguide, the metal is replaced by doped silicon allowing for low-loss, subwavelength confinement of optical modes that can be easily integrated with standard silicon technology. In addition, our waveguide characteristics can be easily tuned along the wavelength by changing the doping concentration of the doped silicon layer. Manipulating the dimensions of the waveguide, we can effectively change the propagation distance and the mode confinement. The simulation results show a maximum propagation distance of 220 µm and modal area of 5–500 times smaller than the diffraction limit area. Moreover, the wavelength dependence of the effective indices of the hybrid structures modes around the doped silicon resonance was investigated. Our results showed that our structures exhibit anomalous dispersion and can support slow and fast light. Also, a comparison has been made between our hybrid structure and the conventional insulator–metal–insulator (IMI) waveguide with metal replaced by our doped silicon. This comparison shows that our hybrid structure is a compromise between the modal area and the propagation distance of the IMI structures.

Disperse-and-Collect Approach for the Type-Selective Detection of Matrix Metalloproteinases in Porous Silicon Resonant Microcavities.

We report on the design and testing of photonic biosensors for the type-selective detection of different types of matrix metalloproteinases (MMPs). The ability to detect a panel of different MMP types has important implications for prognosis of wound healing. We combine the immunocapture of MMPs on dispersed magnetic nanoparticles modified with antibodies specific for target MMPs (immuno-magNPs) with subsequent MMP detection upon fluorogenic peptide cleavage in porous silicon resonant microcavity (pSiRM) architectures. We report fast, sensitive, and type-selective detection of MMPs directly in wound fluid. This study sets the scene for downstream developments of multiparametric biosensors as point-of-care (POC) prognostic tools that may step-change chronic wound management.

Mode selection for electrostatic beam resonators based on motional resistance and quality factor.

An analytical comparison between the fundamental mode and higher modes of vibration for an electrostatic beam resonator is presented. Multiple mode numbers can be matched to a desired resonance frequency through appropriate scaling. Therefore, it is important to determine which mode yields the best performance. A dynamic model of the resonator is derived and then used to determine the motional resistance for each mode. The resulting equation provides the basis for comparing performance between modes using motional resistance and quality factor. As a demonstration of the approach, a quality factor model that has been previously validated experimentally is introduced. Numerical results for silicon resonators indicate that the fundamental mode can provide a lower motional resistance and higher quality factor when the resonators under comparison have the same aspect ratio or the same stiffness.