Noise in microelectromechanical system resonators.

Microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) based resonators and filters, ranging in frequencies from kHz to GHz, have been proposed. The question of how the stabilities of such resonators scale with dimensions is examined in this paper, with emphasis on the noise characteristics. When the dimensions of a resonator become small, instabilities that are negligible in macro-scale devices become prominent. The effects of fluctuations in temperature, adsorbing/desorbing molecules, outgassing, Brownian motion, Johnson noise, drive power and self-heating, and random vibration are explored. When the device is small, the effects of fluctuations in the numbers of photons, phonons, electrons and adsorbed molecules can all affect the noise characteristics. For all but the random vibration-induced noise, reducing the dimensions increases the noise. At submicron dimensions, especially, the frequency noise due to temperature fluctuations, Johnson noise, and adsorption/desorption are likely to limit the applications of ultra-small resonators.

Comments on the effects of nonuniform mass loading on a quartz crystal microbalance.

The Sauerbrey equation can yield incorrect results when the mass and amplitude of vibration distributions are not uniform, and when the mass is not attached rigidly.

A temperature insensitive quartz microbalance.

Mass deposition onto a microbalance is generally accompanied by a temperature change. By measuring a single frequency only, it is not possible to separate the frequency change due to mass change from that due to temperature change. In the temperature insensitive microbalance technique, measurements of two frequencies, the fundamental mode and third overtone frequencies of an SC-cut resonator, yield two equations with two unknowns. This allows the separation of mass change effects from temperature change effects. Dual mode excitation can be used for highly accurate resonator self-temperature sensing over wide temperature ranges. SC-cut resonators are also thermal transient compensated. These unique properties allowed the development of a temperature compensated microbalance that is highly sensitive to mass changes, which can be used in rapidly changing thermal environments, over wide temperature ranges, and which requires neither temperature control nor a thermometer other than the resonator. To demonstrate the performance of this microbalance, SC-cut resonators were coated with thin polymethylmethacrylate (PMMA) photoresist films then placed into a UV-ozone cleaning chamber that initially was at about 20 degrees C. When the UV lamp was turned on, the UV-ozone removed PMMA from the surfaces while the chamber temperature rose to about 60 degrees C. The frequency changes due to mass changes could be accurately determined, independently of the frequency changes due to temperature changes.

Long-term aging of oscillators.

The authors report aging results for more than 40 oscillators, from a variety of sources, for periods ranging from 1 yr to more than 10 yr. The aging data were accumulated with an automated aging facility. The oscillators that have been tested include temperature-compensated crystal oscillators (TCXOs) and oven-controlled crystal oscillators (OCXOs). The TCXOs were maintained in a controlled temperature environment. Several of the TCXOs were built for a gun-launched sensor application and have been shown to be capable of surviving more than 30000-g shock levels of 12-ms duration. The aging results for these ruggedized TXCOs are surprisingly good (<2x10(-10)/d). The better OCXOs exhibit long term aging of a few parts in 10(12 )/d.

Military applications of high accuracy frequency standards and clocks.

The application of frequency control and timing devices in modern military electronics systems is reviewed. The manner in which the stability and accuracy of these devices impact the performance of military communication, navigation, surveillance, electronic warfare, missile guidance, and identification-friend-or-foe (IFF) systems is discussed.

Hysteresis in quartz resonators-a review.

The literature on the frequency versus temperature characteristics of quartz crystal resonators is reviewed. Three papers that deal with frequency versus pressure hysteresis are included, as these may possibly have relevance to frequency versus temperature hysteresis. It is seen that the causes of hysteresis are not well understood. The evidence to date is inconclusive. The mechanisms that can cause hysteresis include: strain changes changes in the quartz, contamination redistribution, oscillator circuitry hysteresis, and apparent hysteresis due to thermal gradients. The results to date seem to indicate that lattice defects are somehow related to thermal hysteresis. Stress relief in the mounting structure can also produce significant hysteresis. As crystal processing techniques have improved. contamination has become less of a problem.

On acoustic sensor sensitivity.

Acoustic sensor sensitivity expressed as frequency change per unit of measurand can result in the erroneous conclusion that higher-frequency sensors are superior to lower-frequency ones. It is argued that, when compared on the bases of reproducibility and resolution capability, good low-frequency sensors are superior to good high-frequency ones.

Modeling resonator frequency fluctuations induced by adsorbing and desorbing surface molecules.

Resonator frequency fluctuations due to adsorption and desorption of molecules on plate electrodes are studied using the principle of mass-loading effects of adsorbed molecules. The study is based on a 525 MHz, AT-cut quartz resonator enclosed in a small crystal holder. Equations relating the surface adsorption rates of the crystal holder to pressure were derived and found to be quadratic polynomial functions of the adsorption rates. Calculations based on these equations show that a contaminant gas with a higher desorption energy creates larger changes in pressure when the temperature is varied. The function describing the frequency fluctuations due to any one contaminant site is a continuous-time Markov chain. Kolmogorov equations and an autocorrelation function for the Markov chain are derived. The autocorrelation and spectral density function of resonator frequency fluctuations are derived. The spectral density of frequency fluctuations at 1 Hz is studied as a function of pressure, temperature, and desorption energy of molecules. The noise levels for a contaminant gas with one type of molecules are found to be lower for lower desorption energies, and higher at lower pressures.

Resonator surface contamination-a cause of frequency fluctuations?

The mass loading effects of adsorbing and desorbing contaminant molecules on the magnitude and characteristics of frequency fluctuations in a thickness-shear resonator are studied. The study is motivated by the observation that the frequency of a thickness-shear resonator is determined predominantly by such mechanical parameters as the thickness of the resonator, elastic stiffnesses, mass loading of the electrodes, and energy trapping. An equation was derived relating the spectral density of frequency fluctuations to: (1) rates of adsorption and desorption of one species of contaminant molecules; (2) mass per unit area of a monolayer of molecules: (3) frequency constant; (4) thickness of resonator; and (5) number of molecular sites on one resonator surface. The induced phase noises were found to be significant in very-high-frequency resonators and are not simple functions of the percentage of area contaminated. The spectral density of frequency fluctuations was inversely proportional to the fourth power of the thickness if other parameters were held constant.