Highly efficient damage-free correction of thickness distribution of quartz crystal wafers by atmospheric pressure plasma etching - [letters]

A new finishing method was developed to correct the thickness distribution of a quartz crystal wafer by the numerically controlled scanning of a localized atmospheric pressure plasma. The thickness uniformity level of a commercially available AT-cut quartz crystal wafer was improved to less than 50 nm without any subsurface damage by applying one correction process. Furthermore, applying a pulse-modulated plasma markedly decreased the correction time of the thickness distribution without breaking the quartz crystal wafer by thermal stress.     

Experimental study on the characteristic of the NS-GT cut quartz crystal resonator oscillating in the sub-resonant frequency

We previously reported that the dynamic photo-elastic method was a very effective measuring technique for the stress distribution of vibrating quartz crystal resonators. The existence of a twisted asymmetrical vibration mode has been verified experimentally when the NS-GT cut quartz crystal resonator was vibrating in the main resonant frequency (MRF). A MRF and a sub-resonant frequency (SRF) of the NS-GT cut quartz resonator were defined as follows. If a mechanical standing wave was in the x' or y' direction of the resonator, the former was MRF vibration and the latter was SRF vibration, respectively. In this paper, stress distributions of two samples of the NS-GT cut quartz crystal resonator, one of which had a thickness of 80 mum and the other 150 mum, were measured by the dynamic photo-elastic method when the resonators were vibrating in each SRF. Thereafter, vibration modes of those resonators were estimated by the experimental data of stress distributions. We find that the vibration mode of the 80-mum resonator had a simple mechanical standing wave on the y' direction and the vibration mode of the 150-mum resonator was combined with a shearing mode in the SRF vibration. From the experiment, we decided that vibration modes of the NS-GT cut quartz crystal resonator were composed of the longitudinal stress T(3)' belonging to the z' direction of the plate and of the shearing stress T(5)' when the plate thickness was thickened and the resonator was oscillating in the SRF.     

Quartz resonator frequency shifts computed using the finite element method

A new solution technique has been developed to calculate the frequency shifts arising from mechanical stresses in the case of quartz resonators. This solution technique utilizes finite element analysis as an initial step to calculate mechanical stress distributions in quartz resonators. Output from the finite element solution is used in a recently developed program to calculate resonator frequency shifts as the final step. Frequency shifts are calculated via numerical integration of the perturbation integral derived by Tiersten.³⁶ The solution technique is general in that any combination of mount and resonator geometries may be modelled. Any crystallographic orientation may be chosen and any load or combination of loads may be applied to the resonator. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator centre. Experimental results for AT- and SC-cut quartz resonators subjected to diametric forces and inertial loading verify the accuracy of frequency shifts calculated using the new solution technique.     

Analysis of aging of piezoelectric crystal resonators

Aging of piezoelectric (quartz crystal) resonator has been identified as one of the most important quality control problems of quartz crystal products. Aging is defined as frequency change with time. Aging in quartz resonators can be due to several sources: mass transfer due to contamination inside the resonator enclosure, stress-strain in the resonator blank, quartz defect, etc. In this study, the stress-strain effect, which has been believed as a dominant factor contributing to aging, is studied. The stress-strain effect is caused mainly by the long-term viscoelastic properties of bonding adhesive that attach quartz crystal plate to the ceramic base package. With the available accelerating testing method under elevated temperatures, the stress-strain induced aging in the quartz crystal resonators can be investigated. Because of the miniaturized size of the resonator, a digital image analysis method called image intensity matching technique (IIMT) is applied to obtain deformation patterns in the quartz blank due to thermal load. Our preliminary results showed that the unsymmetric thermal deformations may be a dominant contributing factor to aging. For simulation purposes, finite-element analysis is used to investigate the deformation patterns (i.e., stress-strain distributions) and corresponding natural frequency shift in the piezoelectric resonators. The viscoelastic behavior of mounting adhesives is incorporated into the analysis to show the dominant effect of long-term behavior of stress-strain developed in the crystal resonators. Also, some geometrical aspects-such as uneven mounting supports due to distances, volumes and heights of the adhesives-are simulated in the model.     

硅酸镓镧晶体谐振器的高频振动分析

利用Mindlin板理论分析了硅酸镓镧晶体板强耦合的厚度剪切振动和弯曲振动，获得了硅酸镓镧晶体板高频振动的色散关系、频谱关系和振动模态位移图。数值计算结果表明，Mindlin板理论可以获得硅酸镓镧晶体板厚度剪切振动的一阶精确截止频率，无需修正系数。基于石英晶体谐振器设计晶片最佳长厚比的选取方法，确定了硅酸镓镧晶片的最佳尺寸，避免了厚度剪切振动模态和弯曲振动模态的强耦合。通过绘制硅酸镓镧晶体板在最佳尺寸时的各振动模态位移图，发现厚度剪切振动模态是主振模态，具有很好的能陷效应。Mindlin板理论在硅酸镓镧晶体板高频振动的应用分析可以指导硅酸镓镧晶体谐振器的实际研发。     

Acoustic Wave Flow Sensor Using Quartz Thickness Shear Mode Resonator

A quartz thickness shear mode (TSM) bulk acoustic wave resonator was used for in situ and real-time detection of liquid flow rate in this study. A special flow chamber made of 2 parallel acrylic plates was designed for flow measurement. The flow chamber has a rectangular flow channel, 2 flow reservoirs for stabilizing the fluid flow, a sensor mounting port for resonator holding, one inlet port, and one outlet port for pipe connection. A 5-MHz TSM quartz resonator was edge-bonded to the sensor mounting port with one side exposed to the flowing liquid and other side exposed to air. The electrical impedance spectra of the quartz resonator at different volumetric flow rate conditions were measured by an impedance analyzer for the extraction of the resonant frequency through a data-fitting method. The fundamental, 3rd, 5th, 7th, and 9th resonant frequency shifts were found to be around 920, 3572, 5947, 8228, and 10 300 Hz for flow rate variation from 0 to 3000 mL/min, which had a corresponding Reynolds number change from 0 to 822. The resonant frequency shifts of different modes are found to be quadratic with flow rate, which is attributed to the nonlinear effect of quartz resonator due to the effective normal pressure imposing on the resonator sensor by the flowing fluid. The results indicate that quartz TSM resonators can be used for flow sensors with characteristics of simplicity, fast response, and good repeatability.     

Voltage-controlled narrowband and wide, variable-range four-segment quartz crystal oscillator

In this work, our goal is to develop a voltage-controlled variable-frequency quartz crystal oscillator with narrowband response, wide, variable frequency range and the capacity to oscillate across the series resonance frequency using a four-segment configuration of a quartz crystal oscillator. In conventional quartz oscillators, the quartz resonator is inserted in the feedback loop between the input and the output of the active circuit, providing sufficient gain and the phase relation. In the oscillator developed here, the quartz crystal resonator is inserted between the loop circuit and the ground potential. The performance of the voltage-controlled variable-frequency oscillator is demonstrated across the series resonance frequency.     

Lam e-mode miniaturized quartz temperature sensors

Lam e-mode is very useful for realization of a miniaturized quartz crystal resonator because its resonant frequency principally depends only on the contour dimensions. Because the heat capacitance for the miniaturized quartz crystal resonator is small and the frequency response versus temperature is very rapid, the quartz crystal resonator is useful for application in temperature sensors. In addition, because a Lam e-mode quartz crystal resonator has zero temperature coefficients, designated LQ(1) cut and LQ(2) cut, and, particularly, the resonator for LQ(1) cut has a comparatively large value of the second-order temperature coefficient beta, a Lam e-mode quartz crystal resonator can be obtained with the large first-order temperature coefficient or when beta=0. In this paper, when cut angles phi=45 degrees and theta=45 degrees , alpha has a value of 44.6x10(-6)/ degrees C in the calculation and 39.9x10(-6)/ degrees C in the experiments with beta=0; when phi=51.5 degrees and theta=45 degrees , alpha=68.1x10(-6)/ degrees C in the calculation and 62.0x10(-6)/ degrees C in the experiments with a value of beta larger than that of phi=45 degrees and theta=45 degrees . For both cut angles, the calculated frequency change vs. temperature is found to be sufficiently large and slightly larger than the measured one.     

Design and evaluation of an antiparallel coupled resonator for chemical sensor applications

In this paper, a new type of quartz crystal resonator in which the electrodes are located on one side has been developed for chemical sensing. The resonator has two electrodes for exciting thickness shear mode (TSM) vibrations on one side of the crystal and a conductive layer on the other side. These electrodes are capacitively coupled with the electric fields in opposite directions, forming an antiparallel coupled resonator (ACR). The resonant characteristics of the ACR were evaluated as a function of gap width between the two electrodes used to excite the TSM. The conductance value was observed to increase with decreasing gap width. We also discovered that the gap should be parallel with the crystallographic x-axis to obtain the highest sensitivity. The frequency response to a viscous loading was almost same as that of a standard quartz crystal microbalance (QCM). The ACR sensor is an attractive alternative to a QCM chemical sensor because it can be easily integrated into packaging and film coatings.     

Five-mode frequency spectra of x3-dependent modes in AT-cut quartz resonators

We study straight-crested waves and vibration modes with variations along the x(3) direction only in an AT-cut quartz plate resonator near the operating frequency of the fundamental thickness-shear mode. Mindlin's two-dimensional equations for anisotropic crystal plates are used. Dispersion relations and frequency spectra of the five relevant waves are obtained. It is found that, to avoid unwanted couplings between the resonator operating mode and other undesirable modes, in addition to certain known values of the plate length/thickness ratio that need to be avoided, an additional series of discrete values of the plate length/thickness ratio also must be excluded.     

Low Frequency Noise Quartz Crystal Oscillator

For years, engineers and scientists have been plagued by an extremely undesirable property of the quartz crystal unit-its significant frequency shift as a function of drive level for drive levels in excess of 10 to 100 ?W. This fact was reported by Hammond [1]. As a result, all precision and moderate precision quartz oscillators have been operated at low drive in an effort to avoid the phenomena. The author has discovered, however, that this unique property of the quartz resonator can be effectively utilized in the design of the quartz oscillator with the result of substantial improvement in oscillator short-term frequency stability. Futhermore, since the crystal frequency-drive characteristic is repeatable, maintenance of moderately high crystal drive in the oscillator circuit will not result in long-term frequency instability in excess of that required for the majority of radar and communication systems [2].     

HF and VHF Source Stabilization Technique Incorporating Q-Multiplied Quartz Crystal Resonator

A new approach is described for the desiga of HF/VHF crystal-controlled frequency sources exhibiting theoretical short-term stability unattainable through the use of conventional quartz oscillator design. The signal generator design uses the concept of AFC stabilization of a conventional quartz oscillator (VCXO) by means of a crystal-controlled highly selective active frequency reference. The AFC reference is a phase-shift type frequency discriminator that employs a product detector and an active Q-multiplied quartz crystal resonator. The extremely selective transmission response, large group delay, and power gain exhibited by the resonator, together with resonator phase noise levels comparable to that exhibited by the oscillator-maintaining circuit, provide the principal means for prediction of superior output signal spectral purity. Models of the resonators have been designed and constructed at 30 and 80 MHz, exhibiting 3-dB bandwidths of 30 and 160 Hz, respectively. Based on actual measurement of VHF Q-multiplied crystal resonator performance characteristics, approximately 16 dB improvement in VHF crystal-controlled frequency source spectral purity at low and moderate modulation rates is possible, compared to that attainable using the best available VHF quartz oscillator circuit designs.     

Doubly rotated contoured quartz resonators

Doubly rotated contoured quartz resonators are used in the design of temperature-compensated stable clocks and dual-mode sensors for simultaneous measurements of pressure and temperature. The design of these devices is facilitated by models that can predict frequency spectra associated with the three thickness modes and temperature and stress-induced frequency changes as a function of crystalline orientation. The Stevens-Tiersten technique for the analysis of the C-mode of a doubly rotated contoured quartz resonator is extended to include the other two thickness modes. Computational results for harmonic and anharmonic overtones of all three thickness modes of such resonators help in optimizing the radius of curvature of the contour and electrode shape for suppression of unwanted modes and prevention of activity dips. The temperature and stress-induced changes in thickness-mode resonator frequencies are calculated from a perturbation technique for small dynamic fields superposed on a static bias. The static bias refers to either a temperature or stress-induced static deformation of the resonator plate. Phenomenological models are also used for calculating the temperature and stress-induced changes in resonant frequencies as a function of crystalline orientation. Results for the SBTC-cut quartz plate with a spherical convex contour of 260 mm indicate that normal trapping occurs for the third (n=3) and fifth (n=5) harmonic of the A-mode, the fundamental (n=1) and third (n=3) harmonic of the B-mode, and the fundamental (n=1) and fifth (n=5) harmonic of the C-mode     

Is an oscillator-based measurement adequate in a liquid environment?

Oscillator-based measurements with quartz crystal resonators are analyzed. The investigations have shown that classical thickness monitors as well as many chemical vapor sensors based on a quartz crystal microbalance (QCM) work properly, even with simple oscillators. It was demonstrated that, for applications in a liquid environment, more sophisticated electronics are necessary. Also a comparison between the experimental results in liquids and the theoretical predictions is hardly possible without the knowledge of the oscillator behavior. As our solution, we present an automatic gain-controlled oscillator with two output signals, the oscillator frequency, and a signal that represents the damping of the quartz resonator. A calibration method is introduced, which allows one to calculate the series resonance frequency f/sub s/ and the series resistance R/sub s/ from these oscillator signals.     

Quartz crystal resonator g sensitivity measurement methods and recent results

A technique for accurate measurements of quartz crystal resonator vibration sensitivity is described. The technique utilizes a crystal oscillator circuit in which a prescribed length of coaxial cable is used to connect the resonator to the oscillator sustaining stage. A method is provided for determination and removal of measurement errors normally introduced as a result of cable vibration. In addition to oscillator-type measurements, it is also possible to perform similar vibration sensitivity measurements using a synthesized signal generator with the resonator installed in a passive phase bridge. Test results are reported for 40 and 50 MHz, fifth overtone AT-cut, and third overtone SC-cut crystals. Acceleration sensitivity (gamma vector) values for the SC-cut resonators were typically four times smaller (5x10(-10) per g) than for the AT-cut units. However, smaller unit-to-unit gamma vector magnitude variation was exhibited by the AT-cut resonators. Oscillator sustaining stage vibration sensitivity was characterized by an equivalent open-loop phase modulation of 10(-6) rad/g.     

On the accuracy of Mindlin plate predictions for the frequency-temperature behavior of resonant modes in AT- and SC-cut quartz plates

The frequency spectra of resonant modes in AT- and SC-cut quartz plates and their frequency-temperature behavior were studied using Mindlin first- and third-order plate equations. Both straight-crested wave solutions and two-dimensional plate solutions were studied. The first-order Mindlin plate theory with shear correction factors was previously found to yield inaccurate frequency spectra of the modes in the vicinity of the fundamental thickness-shear frequency. The third-order Mindlin plate equations without correction factors, on the other hand, predict well the frequency spectrum in the same vicinity. In general, the frequency-temperature curves of the fundamental thickness-shear obtained from the first-order Mindlin plate theory are sufficiently different from those of the third-order Mindlin plate theory that they raise concerns. The least accurately predicted mode of vibration is the flexure mode, which results in discrepancies in its frequency-temperature behavior. The accuracy of other modes of vibrations depends on the degree of couplings with the flexure mode. Mindlin first-order plate theory with only the shear correction factors is not sufficiently accurate for high frequency crystal vibrations at the fundamental thickness-shear frequency. Comparison with measured resonant frequencies and frequency-temperature results on an AT-cut quartz plate shows that the third-order plate theory is more accurate than the first-order plate theory; this is especially true for the technically important fundamental thickness shear mode in the AT-cut quartz plate.     

Linear frequency tuning of SAW resonators

Frequency tuning in SAW (surface acoustic wave) resonator-stabilized oscillators is normally accomplished via utilization of a voltage-controlled phase shifter. The design of abrupt junction varactor diode-inductor networks which employ impedance transformation techniques to obtain linear frequency tuning of two-port SAW resonators is reported. The approach is similar to that previously developed for linear tuning of bulk wave, quartz crystal resonators. This technique uses varactor diode parallel inductance to provide a linear reactance versus voltage network, which is effectively connected in series with the resonator motional impedance in order to tune the effective resonator center frequency. Typical tuning ranges are significantly larger than those achievable using the phase shifter approach, and are on the order of 400 ppm for the 320-MHz resonator used.     

A Frequency-Lock System for Improved Quartz Crystal Oscillator Performance

The intrinsic noise of the best quartz crystal resonators is significantly less than the noise observed in oscillators employing these resonators Several problem areas common to traditional designs are pointed out and a new approach is suggested for their solution. Two circuits are described which frequency lock a spectrally pure quartz crystal oscillator to an independent quartz crystal resonator. The performance of the composite system is predicted based on the measured performance of its components.     

Long-term performance of precision crystal oscillators in a near-Earth orbital environment

The Navy Navigation Satellite System (NNSS) uses precision quartz crystal oscillators to provide time and frequency in the orbiting spacecraft. The frequency changes for multiple oscillators, which were observed for 28 years of operational service in the orbital environment, are discussed. The primary frequency changes are believed to be caused by mass transfer to and from the resonator, stress relief in the resonator mounting structure and electrodes, and ionizing radiation of the quartz resonator. Observations to a resolution of 10- 13 have been made from 1963 to 1991 on 20 operational satellites in near-Earth orbit. No oscillator failures have occurred during the entire program life of nearly 30 years. One oscillator provided continuous operational service for over 21 years, and several have served more than 15 years. No oscillator changed frequency more than two parts in 107 while in operational service. One of the best performing oscillators had a predictable drift rate of 9x10(-13)+/-1x10(-13) per day after three years of service.     

石英晶体微天平质量检测量研究

基于石英晶体微天平质量检测原理,通过分析石英谐振器表面的振动位移,得出决定其电极表面每一点处质量灵敏度的物理量为该点处的振动加速度。在此基础上,基于石英谐振器的巴特沃斯-范·戴克等效电路模型提出一种计算石英晶体谐振器表面振荡幅度的方法,最终得到石英晶体微天平在整个检测过程中能检测到的平均质量。用10MHz的石英晶体微天平进行了数值验证,计算值与其理论上能达到的pg级检测限基本相吻合。