Uncooled IR imaging array based on quartz microresonators

A quartz crystal resonator's resonance frequency is sensitive to temperature. This sensitivity has been exploited in the past in thermometers made of single, macroscopic quartz resonators that can accurately detect temperature changes of μK. Using semiconductor microfabrication techniques, it is now possible to fabricate a large number of microresonators from a single quartz wafer. It is shown that combining the small thermal mass and high thermal isolation capability of such microresonators, the steep frequency versus temperature characteristics of resonators made of certain cuts of quartz and the low-noise characteristics of quartz crystal oscillators can result in high-performance infrared (IR) sensors and sensor arrays. In a microresonator sensor, the temperature change produced by the absorption of IR energy results in a frequency change that can be measured with a resolution that corresponds to a change in the resonator's temperature of less than a μK. Calculation shows that an array of microresonators in the 200 MHz-1 GHz range can be the basis of an uncooled IR imaging system with a noise equivalent temperature difference, NETD, of <0.01 K. The design and fabrication problems to be overcome before such microresonator arrays can be realized are discussed     

High-Q single crystal silicon HARPSS capacitive beam resonators with self-aligned sub-100-nm transduction gaps

This paper reports on the fabrication and characterization of high-quality factor (Q) single crystal silicon (SCS) in-plane capacitive beam resonators with sub-100 nm to submicron transduction gaps using the HARPSS process. The resonating element is made of single crystal silicon while the drive and sense electrodes are made of trench-refilled polysilicon, yielding an all-silicon capacitive microresonator. The fabricated SCS resonators are 20-40 /spl mu/m thick and have self-aligned capacitive gaps. Vertical gaps as small as 80 nm in between 20 /spl mu/m thick silicon structures have been demonstrated in this work. A large number of clamped-free and clamped-clamped beam resonators were fabricated. Quality factors as high as 177000 for a 19 kHz clamped-free beam and 74000 for an 80 kHz clamped-clamped beam were measured under 1 mtorr vacuum. Clamped-clamped beam resonators were operated at their higher resonance modes (up to the fifth mode); a resonance frequency of 12 MHz was observed for the fifth mode of a clamped-clamped beam with the fundamental mode frequency of 0.91 MHz. Electrostatic tuning characteristics of the resonators have been measured and compared to the theoretical values. The measured Q values of the clamped-clamped beam resonators are within 20% of the fundamental thermoelastic damping limits (Q/sub TED/) obtained from finite element analysis.     

Comparison between optically excited vibrations of silicon cantilever and bridge microresonators

A comparison, of the optically excited vibrations, including self-oscillations, of cantilever and bridge silicon microresonators is presented. The theoretical analysis and experimental investigations show that not only has the cantilever microresonator a greater vibration amplitude than the bridge structure, but also its resonance frequency is independent of the strain induced by boron doping and the deformation of the silicon wafer caused by assembly. These advantages could be of great value in achieving practical all-fibre optically addressed silicon microresonator sensors, which are used to measure physical parameters except for force or pressure, such as small masses, chemical components, vibration, temperature, etc.     

Microelectromechanical resonators for radio frequency communication applications

Over the past few years, microelectromechanical system (MEMS) based on-chip resonators have shown significant potential for sensing and high frequency signal processing applications. This is due to their excellent features like small size, large frequency-quality factor product, low power consumption, low cost batch fabrication, and integrability with CMOS IC technology. Radio frequency communication circuits like reference oscillators, filters, and mixers based on such MEMS resonators can be utilized for meeting the increasing count of RF components likely to be demanded by the next generation multi-band/multi-mode wireless devices. MEMS resonators can provide a feasible alternative to the present-day well-established quartz crystal technology that is riddled with major drawbacks like relatively large size, high cost, and low compatibility with IC chips. This article presents a survey of the developments in this field of resonant MEMS structures with detailed enumeration on the various micromechanical resonator types, modes of vibration, equivalent mechanical and electrical models, materials and technologies used for fabrication, and the application of the resonators for implementing oscillators and filters. These are followed by a discussion on the challenges for RF MEMS technology in comparison to quartz crystal technology; like high precision, stability, reliability, need for hermetic packaging etc., which remain to be addressed for enabling the inclusion of micromechanical resonators into tomorrow??s highly integrated communication systems.     

硅谐振微传感器中微弱信号频率的外差式随机共振检测

硅谐振微传感器输出信号的信噪比很低,频率信号往往淹没在噪声之中.论文分析了随机共振系统的功率谱放大率和信噪比特性,提出了外差式随机共振频率检测方法,并将该方法应用于硅谐振微传感器输出信号的频率检测.理论分析和数值仿真结果表明,外差式随机共振能将更多的噪声能量转变为频率信号的能量,通过调节载波信号频率可从共振谱峰的变化中准确测定谐振频率.该方法是可行、有效的.     

Tunability of bulk acoustic wave solidly mounted resonators using passive elements: Concept,design and implementation

This paper presents the impedance behavior of the bulk acoustic wave solidly mounted resonators (BAW‐SMR). Also, it shows the effects of the addition of passive elements (L, C) to this type of resonators. In addition, this article presents a tunable BAW‐SMR filter realized in a ladder topology used for the 802.11b/g standard (2.40–2.48 GHz). Mainly, the filter fulfills the requirements for the WLAN 802.11 b/g standard, presenting a measured ?3.3 dB of insertion loss, –12.7 dB of return loss and selectivity higher than 33 dB at ±30 MHz of the bandwidth. This tunable BAW‐SMR filter has reduced dimensions (1035 × 1075 μm²). Moreover, we show how to shift the center frequency of this tunable filter toward higher and lower frequencies by adding passive elements. Measured shifts of ?1.3% of the center frequency (2.44 GHz) toward lower frequency and +0.6% of the center frequency toward higher frequencies are obtained. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Acoustoelectronic microwave structures: Principles of operation, similarity with optics

Many technical solutions in microwave acoustics are similar to these in optics. In this paper Bulk Acoustic Wave (BAW) microwave resonators and filters are discussed together with the devices that use the peculiarities of BAW propagation through semitransparent acoustic Bragg structures. An acoustic analogue of the resonator Fabri-Perott and acoustic resonant multilayered structures are considered. The use of a piezoelectric semiconductor resonant layer with electron drift provides the possibility of the amplification and generation of acoustic waves.     

Comparative analysis of a variety of high-Q capacitively transduced bulk-mode microelectromechanical resonator geometries

Microelectromechanical system (MEMS) based on-chip resonators offer great potential for sensing and high frequency signal processing applications due to their exceptional features like small size, large frequency-quality factor product, integrability with CMOS ICs, low power consumption etc. Capacitively transduced MEMS resonators are in general favored than their piezoelectrically transduced counterparts. Also among the former variety of microresonators, bulk acoustic mode of vibration is the preferred option for realizing high frequency of operation. So this study focuses on the design, simulation and optimization of some new as well as previously reported geometries of the particular variety of bulk-mode micromachined resonators based on capacitive transduction. A low motional resistance has been attempted for these resonators, which can make them ideal for use in radio frequency communication circuits like reference oscillators and filters.     

Ladder‐lattice bulk acoustic wave filters: Concepts,design, and implementation

This article presents a study of ladder‐lattice bulk acoustic wave (BAW) filters. First, a review of BAW technology and filters topologies is addressed. Next, a mixed ladder‐lattice BAW filter for application on W‐CDMA reception front‐ends (2.11–2.17 GHz) is presented. An improved solidly mounted resonators (SMR) technology was used for the filter implementation. The filter synthesis methodology is briefly described. Layout guidelines are discussed enabling an optimized filter design. The filter on‐wafer measurement results are as follows: ?3.55 dB of insertion loss, ?8.7 dB of return loss, an isolation higher than ?47 dB at the transmission band (1.92–1.98 GHz) and an improved selectivity (?30 dB at 2.14 GHz ± 60 MHz). Therefore, we can observe that the mixed topology combines the advantages of ladder and lattice networks, having very steep responses and an improved isolation at undesired bands. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

The influence of limit cycle topology on the phase resetting curve

Understanding the phenomenology of phase resetting is an essential step toward developing a formalism for the analysis of circuits composed of bursting neurons that receive multiple, and sometimes overlapping, inputs. If we are to use phase-resetting methods to analyze these circuits, we can either generate phase-resetting curves (PRCs) for all possible inputs and combinations of inputs, or we can develop an understanding of how to construct PRCs for arbitrary perturbations of a given neuron. The latter strategy is the goal of this study. We present a geometrical derivation of phase resetting of neural limit cycle oscillators in response to short current pulses. A geometrical phase is defined as the distance traveled along the limit cycle in the appropriate phase space. The perturbations in current are treated as displacements in the direction corresponding to membrane voltage. We show that for type I oscillators, the direction of a perturbation in current is nearly tangent to the limit cycle; hence, the projection of the displacement in voltage onto the limit cycle is sufficient to give the geometrical phase resetting. In order to obtain the phase resetting in terms of elapsed time or temporal phase, a mapping between geometrical and temporal phase is obtained empirically and used to make the conversion. This mapping is shown to be an invariant of the dynamics. Perturbations in current applied to type II oscillators produce significant normal displacements from the limit cycle, so the difference in angular velocity at displaced points compared to the angular velocity on the limit cycle must be taken into account. Empirical attempts to correct for differences in angular velocity (amplitude versus phase effects in terms of a circular coordinate system) during relaxation back to the limit cycle achieved some success in the construction of phase-resetting curves for type II model oscillators. The ultimate goal of this work is the extension of these techniques to biological circuits comprising type II neural oscillators, which appear frequently in identified central pattern-generating circuits.     

Chemical sensor based on quartz microresonators

A novel chemical sensor is proposed that consists of an array of quartz microresonators. It is shown that a microresonator can act as a quartz crystal microbalance and as a calorimeter, simultaneously, because quartz resonators can be highly sensitive to both mass and temperature changes. By applying a variety of thin-film adsorbers to the different resonators in an array and observing the pattern of frequency changes due to an unknown that is admitted into the resonator array enclosure, one can detect and identify chemical and biological agents. The total frequency change of an individual resonator will be the sum of the frequency change due to mass loading and the frequency change due to the change in temperature resulting from the heats of adsorptions or reactions. It is shown that the proposed sensor is capable of detecting on the order of 10^-6 monolayer of a material deposited onto the resonators' surfaces     

Low phase noise design of microwave oscillators (invited article)

Time domain methods for numerical nonlinear analysis of the steady state solution as well as the spectral behavior of microwave oscillators are discussed. In addition, a method to minimize the phase noise of oscillators by numerical optimization is outlined and applied to the design of a low phase noise oscillator. Computer simulations are compared with measurement results of the fabricated oscillators. © 1996 John Wiley & Sons, Inc.     

A Microresonator Design Based on Nonlinear 1 : 2 Internal Resonance in Flexural Structural Modes

A unique T-beam microresonator designed to operate on the principle of nonlinear modal interactions due to 1 : 2 internal resonance is introduced. Specifically, the T-structure is designed to have two flexural modes with natural frequencies in a 1 : 2 ratio, and the higher frequency mode autoparametrically excites the lower frequency mode through inertial quadratic nonlinearities. A Lagrangian formulation is used to model the electrostatically actuated T-beam resonator, and it includes inertial quadratic nonlinearities, cubic nonlinearities due to midplane stretching and curvature of the beam, electrostatic potential, and effects of thermal prestress. A nonlinear two-mode reduced-order model is derived using linear structural modes in desired internal resonance. The model is used to estimate static pull-in bias voltages and dynamic responses using asymptotic averaging. Nonlinear frequency responses are developed for the case of resonant actuation of a higher frequency mode. It is shown that the lower frequency flexural mode is excited for actuation levels above a certain threshold and generates response component at half the frequency of resonant actuation. The effects of damping, thermal prestress, and mass and geometric perturbations from nominal design are thoroughly discussed. Finally, experimental results for a macroscale T-beam structure are briefly described and qualitatively confirm the basic analytical predictions. The T-beam resonator shows a high sensitivity to mass perturbations and, thus, holds great potential as a radio frequency filter–mixer and mass sensor.$hfill$ [2008-0107]      

Air-damped microresonators with enhanced quality factor

It is known that the dissipative damping force due to the air film trapped between the bottom of surface micromachined resonators and the substrate on which they are fabricated decreases in magnitude as the separation between the two increases. The practical outcome of this is that microresonators located close to a substrate will have higher damping and a lower quality factor Q. In order to further investigate this effect and compare experimental findings with theory, a new test device that enables modulation of the damping interaction between a surface micromachined resonator and the substrate has been fabricated. The device consists of a surface micromachined polysilicon microresonator, which is self-elevated out of the plane of the substrate using a bimorph beam. A second, identical microresonator lying parallel to the plane of the substrate has also been fabricated. Both devices have been fabricated using the polysilicon multiuser microelectromechanical systems (MEMS) processes (polyMUMPs). The resonator-to-substrate separation of the elevated resonator is varied by changing the temperature of the bimorph beam, and the Q factors for different separations have been measured. Experimental results show that the elevated microresonators have Q values which are 65% higher than the in-plane microresonators. These experimental findings show good agreement with the theoretical model of damping used.     

Design of silicon micro-resonators with low mechanical and optical losses for quantum optics experiments

The interaction of the radiation pressure with micro-mechanical oscillators is earning a growing interest for its wide-range applications and for fundamental research. In this contribution we describe the fabrication of a family of opto-mechanical devices specifically designed to ease the detection of ponderomotive squeezing and of entanglement between macroscopic objects and light. These phenomena are not easily observed, due to the overwhelming effects of classical noise sources of thermal origin with respect to the weak quantum fluctuations of the radiation pressure. A low thermal noise background is required, together with a weak interaction between the micro-mirror and this background (i.e. high mechanical quality factors). In the development of our opto-mechanical devices, we heve explored an approach focused on relatively thick silicon oscillators with high reflectivity coating. The relatively high mass is compensated by the capability to manage high power at low temperatures, owing to a favourable geometric factor (thicker connectors) and the excellent thermal conductivity of silicon crystals at cryogenic temperature. We have measured at cryogenic temperatures mechanical quality factors up to 10⁵ in a micro-oscillator designed to reduce as much as possible the strain in the coating layer and the consequent energy dissipation. This design improves an approach applied in micro-mirror and micro-cantilevers, where the coated surface is reduced as much as possible to improve the quality factor. The deposition of the highly reflective coating layer has been carefully integrated in the micro-machining process to preserve its low optical losses.     

Adaptive stabilization of non-linear oscillators using direct adaptive control

Direct adaptive controllers developed for linear systems are applied to non-linear oscillators. A wide range of nonlinearities are considered, including stiffness non-linearities, input non-linearities, limit cycle oscillations and friction. Numerical results suggest that by increasing the speed of adaptation, these direct adaptive controllers are highly effective when applied to non-linear plants.     

Experimental verification of frequency decoupling effect on acceleration sensitivity in tuning fork gyroscopes using in-plane coupled resonators

The effect of in- and anti-phase mode decoupling on the frequency response of coupled in-plane resonators was examined, experimentally, to suppress the acceleration sensitivity (acceleration output) in tuning fork gyroscopes (TFGs). Finite element simulations, conducted in our recent works, show that the origin of acceleration sensitivity for the sensing resonators in TFGs lies in the transduction of linear (in-phase) acceleration to anti-phase resonant vibration of the sensing resonators in TFGs. We further revealed that the frequency decoupling of the in- and anti-phase vibration modes is effective in suppressing the transduction. To experimentally validate this, two types of coupled resonators (one coupled with a frame and the other with a spring) to represent the sensing resonators of TFGs were fabricated on silicon-on-insulator wafer. Different resonant frequencies were used to evaluate the frequency decoupling effect on the coupled resonators, i.e., the coupling from in-phase mode oscillation to the anti-phase mode vibration. The vibration amplitude of the anti-phase mode increased in the coupled resonators with small frequency decoupling (decoupling ratio, DR) value. Additionally, the two types of coupled resonators exhibit similar output after considering the effect of decoupling ratio, anti-phase frequency and different stiffness unbalances. Our results reveal that TFG can be designed with lower acceleration sensitivity by utilizing sense resonators with large decoupling ratio, higher anti-phase frequency, and possessing structures which are insensitive to fabrication imperfections.     

Quality factors in micron- and submicron-thick cantilevers

Micromechanical cantilevers are commonly used for detection of small forces in microelectromechanical sensors (e.g., accelerometers) and in scientific instruments (e.g., atomic force microscopes). A fundamental limit to the detection of small forces is imposed by thermomechanical noise, the mechanical analog of Johnson noise, which is governed by dissipation of mechanical energy. This paper reports on measurements of the mechanical quality factor Q for arrays of silicon-nitride, polysilicon, and single-crystal silicon cantilevers. By studying the dependence of Q on cantilever material, geometry, and surface treatments, significant insight into dissipation mechanisms has been obtained. For submicron-thick cantilevers, Q is found to decrease with decreasing cantilever thickness, indicating surface loss mechanisms. For single-crystal silicon cantilevers, significant increase in room temperature Q is obtained after 700°C heat treatment in either N₂ Or forming gas. At low temperatures, silicon cantilevers exhibit a minimum in Q at approximately 135 K, possibly due to a surface-related relaxation process. Thermoelastic dissipation is not a factor for submicron-thick cantilevers, but is shown to be significant for silicon-nitride cantilevers as thin as 2.3 μm     

Temperature Dependence of Quality Factor in MEMS Resonators

The temperature dependence of the quality factor of microelectromechanical system (MEMS) resonators is analyzed and measured. For silicon MEMS resonators, there are several energy loss mechanisms that determine the quality factor. These include air-damping, thermoelastic dissipation, and anchor and surface losses. For resonators operating at a low pressure in hermetic wafer-scale encapsulation, the effect of each energy loss mechanism is discussed. The temperature dependence of each mechanism and their contribution to the total quality factor is investigated. MEMS resonators can be designed to have either strong or weak dependence of on temperature, which is if the effects of the temperature on the dominant loss mechanisms are well understood. The sensitivity of up to 1% changes in quality factor per degree Celsius change of temperature was demonstrated by experiment. By using as the thermometer for temperature compensation, a preliminary experiment demonstrated less than 4-ppm resonant frequency variation over the 0 -70 temperature range. This indicates that the quality factor can be used as an absolute intrinsic thermometer for temperature compensation in the MEMS resonators.     

Energy conservation in the transient response of nonlinear beam vibration problems subjected to pulse loading—a numerical approach

The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.