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The primary causes of crystal oscillator aging are mass transfer to or from the resonator's surfaces due to adsorption or desorption of contamination, stress relief in the mounting structure of the crystal, changes in the electrodes, package leaks, and changes in the quartz material.
Contamination Transfer Effects: Adsorption, Desorption, Oxidation and Permeation.
Because the frequency of a thickness shear crystal unit, such as an AT-cut or SC-cut unit, is inversely proportional to the thickness of the crystal plate, and because, for example, a typical 5-MHz 3rd overtone plate is on the order of 1 million atomic layers thick, the adsorption or desorption of contamination equivalent to the mass of one atomic layer of quartz changes the frequency by about 1 ppm. In general, if contamination equal in mass to 1 1/2 monolayers of quartz is adsorbed or desorbed from the surfaces, then the frequency change in parts per million is equal to the resonator's frequency in megahertz. In order to achieve low-aging, crystal units must be fabricated and hermetically sealed in ultraclean, ultrahigh vacuum environments, and into packages that are capable of maintaining the clean environment for long periods.
Fig. 3 shows some data on the oxidation of pure nickel in 76 torr of oxygen at 400 ° C, 450 ° C and 500 ° C. Landsberg  reviewed and summarized a considerable amount of the type of data plotted in Fig. 3. Besides oxidation, data on adsorption and desorption of many types of gases on many types of solid surfaces were reviewed. For most of the reviewed work, the rates of adsorption, desorption and oxidation depended on the logarithm of the time. Some of the parameters of the log-time model depended strongly on the temperature. In studies of the low temperature (i.e., < 400° C) oxidation of metal films, logarithmic kinetics are usually observed . A molecular model of these processes can produce the observed log-time dependence . It was also pointed out that the rates of some particular systems of this type may not depend on log-time.
The adsorption and desorption of contamination is primarily
a function of the nature of the contaminant, the nature of the adsorbing
surface, and the temperature. Included in "the nature of the adsorbing
surface" is the crystallographic nature. For example, the adsorption properties
of an AT-cut surface are likely to be different from that of an SC- or
Leaks into the enclosure, either due to a faulty hermetic seal or to permeation through the enclosure walls, and outgassing of adsorbed and dissolved gases can also result in aging. Even when the hermetic seal is perfect, gases can permeate through the enclosure walls [9,10]. Since most materials used in vacuum and resonator technology exhibit some degree of permeability to gases, maintaining low pressure levels inside the enclosure requires consideration of the permeation characteristics of the enclosure. Hydrogen and helium are notorious for their permeation through metals and glasses, respectively. Even if the permeating gases do not adsorb onto the resonator, if a significant pressure increase occurs, the frequency will change due to the changing hydrostatic pressure in the enclosure [11,12]. When a significant amount of gas leaks into a vacuum sealed resonator, aging can be caused by electrical and mechanical effects caused by changes in the package shape (sometimes called "oil canning," when the package changes with atmospheric pressure changes). Epoxy packages or seals that have been occasionally used in inexpensive resonators are especially susceptible to moisture permeation.
That high amounts of hydrogen permeation can produce aging has been demonstrated . A 5-MHz fundamental mode resonator, which had copper electrodes, was hermetically sealed, in high vacuum, in a nickel HC-6 enclosure. After the aging of this resonator stabilized, it was immersed in one atmosphere of hydrogen and the aging measurements were continued. Three weeks after immersion, the aging had increased 30-fold, to about 3 X 10-9 per day. After the aging stabilized at this higher rate, the hydrogen was removed. Eight weeks later, the aging rate stabilized at a lower rate, but six months after removal of the hydrogen, the rate was still about five times higher than what it was prior to hydrogen exposure.
Thin films of Au, Ag, Al and Cu are commonly used as electrodes on crystal resonators. The stresses in these films depend on the film material and thickness, and other factors. It has been shown  that the film stresses relax with a time constant of a few hours. (The temperature at which the relaxation was measured is not stated explicitly in this reference, but is implied to have been at room temperature. The film thicknesses were 100nm.)
The film stresses also depend strongly on the substrate material and crystallinity (amorphous, crystal surface orientation, etc.), on the substrate cleanliness, temperature, and chemical state, the gases present in the space around the substrate during the deposition process, the purity of the film material, the deposition rate, and on the deposition process (evaporation, sputtering, etc.) [15-20]. In some films, for example, the stress can be varied from tensile to compressive just by varying the background pressure in the vacuum system during deposition [21-23].
Numerous studies have shown that the properties of thin films change with time subsequent to deposition [24-33]. The stability of the film depends on the deposition conditions, especially the substrate temperature, and deposition rate (lower deposition rates under clean conditions usually result in fewer defects), and on the temperatures subsequent to deposition. For example, the resistivity changes in 700Å to 1650Å gold films deposited onto glass microscope slides were found to depend strongly on the substrate temperature . When the films were deposited at 46° C, significant decreases (up to 8.5%) were observed during resistivity measurements, at room temperature, between the fifth hour and the first few weeks after deposition. When the substrate temperature was 112° C during deposition, which is near the recrystallization temperature of 124° C for gold films, the resistivity decreases were much smaller (0.8 to 1.5%). Films, in general, will tend to be more stable if the substrate temperature during deposition is above the recrystallization temperature of the film material. Deposition at an elevated substrate temperature has a considerably greater stabilization effect than deposition without substrate heating followed by annealing at a later time. The reasons are that diffusion rates are higher at elevated temperatures, and surface diffusion is much faster than bulk diffusion, therefore, the surface atoms have more opportunity to anneal (i.e., move to low energy sites) before they become buried. Similarly, a low deposition rate (under clean conditions) results in a more stable film than a high rate. At very high rates, the surface atoms do not have a chance to anneal before they are buried. High substrate temperatures also contribute to minimizing adsorbed contaminants on the substrate and in the deposited film. If the deposition conditions are not clean, then a slow deposition rate may result in a less stable film due to incorporation of contaminants into the film.
The contribution of electrode stress relief to aging depends on resonator type. SC-cut  and electrodeless (e.g., BVA-type [35,36]) resonators are insensitive to such stress relief. For other types of resonators, electrode stress relief can be a contributor, especially to initial aging.
Other types of changes in the electrodes include diffusion effects and chemical reaction effects. For example, when an adhesion layer (such as Cr) is used under a weakly adhering film (such as Au), the two layers can gradually interdiffuse [37,38]. Chemical reactions can occur between the electrode and the quartz surface , and between the electrode and the gaseous contaminants in the resonator enclosure. Some metals react chemically with a quartz surface. When the heat of oxide formation is higher for the metal oxide than for SiO2, the metal can reduce the SiO2 to form the metal oxide and produce free silicon at the interface. The heat of oxide formation of a -quartz is -201.34 kcal/mol (= 8.73 eV), whereas Al2O3's is -399 kcal/mol and Cr2O3's is -270 kcal/mol. Therefore, Al and Cr, two commonly used materials in resonator fabrication, adhere strongly to quartz by forming metal oxides at the metal-quartz interfaces. The formation of Al2O3 and free Si at the SiO2-Al interface has been demonstrated experimentally [39,40]. Reactions between oxide forming metals and the OH on quartz surfaces also occur.
The properties of thin films can change with time, e.g., the properties of an Al film and of the interface between Al and SiO2 change with time [41,42]. The changes can be enhanced by temperature, temperature cycling, and the presence of an electric field. These changes can result in resonator aging.
Highly reactive metals such as Al or Cr are not the preferred electrode materials for low-aging quartz resonators because thin films of such metals produce aging due to: 1) changes at the metal-quartz interfaces, 2) gettering of oxygen and other residual gases inside the enclosure, 3) changes at high strain gradients that exist at electrode edges , and 4) changes in the high strains that result from temperature cycling due to the strong adhesion and thermal expansion coefficient differences between the metal film and the quartz. Liquid  and plasma  anodization have been used in attempts to minimize aging due to oxide growth on the electrodes.
Gold has been the preferred electrode material in the fabrication of low-aging resonators. The reasons for this are that: 1) gold is not highly reactive, it does not form an oxide under normal conditions (clean gold will getter organic contaminants from the air , however, such contaminants can be readily removed by UV/ozone cleaning ); 2) gold adheres weakly to quartz, the adhesion is strong enough for the electrodes not to be detached by a 36,000 g shock of 12 millisecond duration  but is weak enough not to support strain gradients that would show up on X-ray topographs (Cr, Al and Ni films produce strain in the quartz that can be readily seen in X-ray topographs) ; and 3) the stresses in pure gold films anneal rapidly . These properties are probably the reason for the fact that the aging of the best long term aging AT-cut resonators with gold electrodes is about the same as that of the best SC-cut and BVA resonators, i.e., a few parts in 1012 per day. That the initial aging of the best SC-cut resonators is better than that of the best AT-cuts [49,50] is probably due to the superior insensitivity of the SC-cut to some important types of stresses, such as the stresses due to the electrodes.
It is also possible to make low-aging resonators with copper electrodes , however, in one unpublished study , although copper plated resonators exhibited low initial aging, the long term aging was poorer than that of similarly fabricated resonators with gold electrodes.
It is well known that, under the influences of high temperatures and high electric fields, electrode materials such as gold and silver will diffuse into the dislocations in quartz . Although diffusion of gold and other electrodes into the quartz has been reported in high-temperature processed resonators [54,55], it is unlikely that such diffusion occurs at normal processing and operating temperatures without the presence of an electric field. If such diffusion did occur, then the adhesion of, for example, gold on quartz would improve as the resonator ages. Such improved adhesion has not been observed. When five high precision glass enclosed resonators with gold electrodes, which had been fabricated 18 years earlier, were tested, it was found that the gold electrodes could be readily removed with the "Scotch-tape test." Even the weakly adhering "3M Post-it Self-Stick Removable Notes" readily removed these gold electrodes . After removal of the electrodes, with either method, a narrow strip of very thin gold that outlines the perimeter of where the electrodes had been, remained (the strip can be scratched off with tweezers). This strip appears to be the "shadowing" that occurs when an evaporation mask is a finite distance from the quartz plate. The reason for the stronger adhesion of the strip is under investigation. A preliminary analysis of the quartz that had been under the center portion of the electrodes did not indicate the presence of any gold in the quartz. The analysis was performed using SIMS (secondary ion mass spectroscopy).
It has been shown that a DC voltage between the electrodes of a resonator can dramatically increase the initial aging, presumably because of electric field driven diffusion of impurities and electrodes . Although oscillator designers often design circuits which (sometimes inadvertently) place a small DC voltage across the electrodes, one can readily minimize the DC voltage, without lowering the effective Q of the resonator, by placing a capacitor in series and a few megohm resistor in parallel with the resonator .
Surface catalytic reactions at silver electrode surfaces, accompanied by the emission of silver atoms, have also been reported to be an aging mechanism in silver-plated resonators .
Powerful tools to determine the possible aging contributions of stresses in films associated with particular film fabrication technologies are the form, values, and temperature dependence of the stress relaxation process. Since these parameters of the films are not too difficult to measure directly on actual resonator materials, it is surprising that very few results of this type have been reported for resonator fabrication technologies in current use. Powerful surface analytical tools for detecting diffusion and chemical reaction effects are also available.
Strain/Stress in the Resonator.
Radial forces applied at the perimeter of AT and SC plates shift the frequency . Since the forces applied to the crystal wafer by the mounting clips and bonding materials are difficult to control and probably change (i.e., relax) with time, resonator aging will depend, to some extent, on the mounts' type, material, and location, on the crystal orientation, and on departures from the design in real resonators. When the bonding process is carried out at high temperatures, the structure is likely to be in equilibrium at a temperature higher than the normal operating temperatures of the resonator. In this case, mismatches in the thermal expansion coefficients of the various materials in the structure will cause stress-induced frequency shifts. When these stresses change with time, aging can result. Bonding materials, such as silver-filled epoxies and polyimides, change dimensions upon curing. This results in further stress changes. The clip forming and welding operations produce residual stresses which are also subject to stress relief.
X-ray topographs can be used to demonstrate the strains caused by a particular mounting clip structure [60,61]. If the strains change with time, aging can result. Radial and tangential thermal coefficients of linear expansion for AT-cut quartz wafers depend on direction. Thermal expansion coefficient differences between the crystal plate and the mounting structure (including the enclosure base) usually result not only in radial stresses on the crystal plate, but also tangential (i.e., torsional) stresses. Resonator structure designs must account for the differences in thermal expansion coefficients between the various parts of the resonator assembly to minimize temperature dependent stresses applied to the resonator.
Since stresses are inevitable, the materials used in the mounting structure of low-aging resonators should anneal either very rapidly, or very slowly, i.e., be either perfectly soft or perfectly elastic. Materials which anneal very rapidly are usually not a viable option because such materials generally result in unacceptable behavior under shock and vibration. Mounting structures that are nearly stress-free have been developed [35,62].
The slow and progressive deformation of a material under constant stress is called creep. Creep is observed in metals, glasses, polymers, and even in single crystals. Metals usually exhibit creep at a temperature greater than 0.4 Tm, where Tm is the metal's melting point in degrees Kelvin [63,64]. The rate of creep, especially in amorphous materials, and organic materials such as the epoxies commonly used for bonding crystals, is highly sensitive to temperature. Numerous alloys have been developed for high resistance to stress relief, for electrical connector and other spring applications. Mounting clips made of such alloys can serve to minimize aging due to stress relief in the mounting structure, as can designs that use carefully oriented quartz for mounting , and for the enclosure .
The amount of aging produced by a given amount of stress relief is a function of the orientation of the mounting clips with respect to the crystallographic axes of the quartz plate, and the types of stresses . For in-plane diametric forces, the force-frequency coefficient Kf vs. azimuth angle y has been found to have zeroes for all the commonly used cuts, such as the AT- and SC-cuts . Therefore, one might conclude that aging due to stress relief in the mounting clips can be eliminated by mounting the crystals where Kf = 0. Unfortunately, it is difficult to completely eliminate aging due to stress relief in the mounting structure because: 1) the azimuthal angles where Kf = 0 are functions of temperature , so that the mounting point orientations would have to be different for resonators of different turnover temperatures, 2) the y where the effects of bonding stresses are zero is different from the y where the Kf = 0, at least for the AT-cut, the only cut for which bonding stress effects have been reported , and 3) the forces due to mounting clips are generally not purely in-plane diametric forces. This is especially true for three and four-point mounted resonators because, since the thermal expansion coefficient of quartz is highly anisotropic whereas that of the typical package base is isotropic, the forces due to thermal expansion coefficient mismatches will have tangential components. In two-point mounted resonators also, the base's thermal expansion applies torsional-type forces in addition to the in-plane diametric forces.
Even when the mounting stresses are made negligible, the bonding stresses alone can cause significant frequency shifts, which, upon annealing, can cause aging . The temperature coefficient of frequency will also change with large changes in stress. In these cases, measuring temperature coefficients along with the aging can be used to determine whether or not stress relief is a significant aging mechanism.
Although it is likely that diffusion processes cause aging in resonators, very few authors have reported analyses of aging in terms of diffusion [4,68]. Solid-solid diffusion processes can occur between the electrodes and the quartz, within the quartz itself, and in the mounting and electrical attachments; gas-solid diffusion processes can be rate determining steps for some processes occurring at the resonator surface. Another conceivable aging mechanism is the diffusion of impurities in the quartz to dislocations and surfaces.
The rate of a simple diffusion-controlled process in an isotropic medium is given by 
|Rate = -D *concentration gradient||(1)|
m is the mass of the diffusing material, h is the thickness of the slab in which the diffusion is occurring, A is the area participating in the diffusion, and d2 and d1 are the concentrations (mass per unit volume) of the diffusing material on the two sides of the slab [69,70].
Table I shows diffusion constants at room temperature for some metals commonly used as electrodes or attachments in resonators :
|Al into Cu||1.75 X 10-2|
|Au into Cu||4 to 16 X 10-2|
|Cu into Ag||5.95 X 10-5|
|Ni into Cu||6.5 X 10-5|
|Pd into Cu||1.6 X 10-4|
The movements of point defects in the quartz lattice have energies and activation energies of 0.03 eV to 0.154 eV . Although these activation energies are similar in magnitude to observed aging activation energies , the validity of a direct comparison has not yet been established.
Diffusion processes often have an approximately power dependence on time, with the power being about 0.5 . For some diffusion configurations, the diffusion rate equation also contains an exponential time factor .
Diffusion rates are usually thermally activated, with an Arrhenius dependence on temperature [10,73]. The activation energy for Cu into Al (33.9 kcal/mole) seems higher than most reported aging activation energies . However, the activation energy for grain boundary diffusion of Ag into Ag is 21.5 kcal/mole, which is not much higher than the reported aging activation energies [72,73].
Changes in the Quartz.
Changes in the quartz due to stresses or other causes could lead to aging, although no reports of such changes (at normal temperatures and pressures) could be found in the literature. Perfect quartz would not be expected to change with time (by definition). The imperfections that are subject to change include surface and point defects, dislocations, impurities, inclusions, and twins. Surface defects, such as the microcracks produced by lapping, can change with time, however, by properly etching the surfaces subsequent to mechanical treatment , the possibility of changes can be greatly reduced.
It is unlikely that dislocation motion due to stresses is a factor in aging at typical operating temperatures, although dislocation motion can occur at high temperatures and pressures . Even in sweeping experiments  which are usually conducted far above the normal operating temperatures of oscillators, no evidence of dislocation motion has been reported. The energy needed to anneal quartz damage due to neutron irradiation may be a clue to the energies needed to move dislocations. When quartz is irradiated with fast neutrons, displacement damage occurs. At high doses, the quartz gradually becomes disordered into an amorphous form. Annealing studies on neutron-damaged quartz indicate that the annealing temperature of quartz is above the inversion temperature [77,78]. The activation energy for structure annealing is 0.75 eV.
The outgassing of quartz is another possible aging mechanism, the magnitude of which is unknown. Although a large amount of information is available on the outgassing characteristics of vitreous SiO2[9,10], no reports on the outgassing characteristics of a -quartz were found. Presumably, since all materials outgas to some extent, a -quartz does too. Another unknown is the extent to which impurities in the quartz diffuse to dislocations and surfaces at normal operating temperatures. Quartz is known to contain impurities that are subject to diffusion . The impurity that is present in highest concentrations is hydrogen. Natural and cultured quartz both contain hydrogen, in amounts ranging from 200 ppm to 2500 ppm relative to Si (3 ppm to 42 ppm by weight).
Circuit Aging and Other Electrical Aging.
The oscillator circuit includes electrical elements that are subject to change. These elements determine some important operating factors, such as resonator load reactance, dc bias, and drive level. Changes in these electrical elements and factors cause oscillator aging.
Stray reactance changes due to movements of the electrical leads and the gradual deformation of circuit boards and enclosure walls also produce frequency changes. For example, in a 22-MHz fundamental mode AT-cut resonator, a lead length change of 0.005 mm results in a frequency change of 1 X 10-9 , and a load capacitance aging of 1 ppm per day causes oscillator aging of parts in 1010 per day. Capacitors can age due to the effects of humidity and temperature; e.g., humidity can change the dielectric constants and loss factors of capacitors and circuit boards. Inductors are notorious for their instabilities; e.g., the windings of inductors can stretch and move, especially during temperature changes. In one study , capacitors of various types aged 3 ppm/day to 70 ppm/day, and a 2 µH coil custom wound on a phenolic form (for high stability) aged 2 ppm/day. Amplifiers and varactors can also change with time. Drive level changes can result in frequency changes on the order of 10-7 per ma2. Significant improvements in medium and long term stability can often be obtained by hermetically sealing the oscillator to minimize the frequency instabilities due to changes in humidity and atmospheric pressure [82,83].
As was previously noted in the "Electrode Effects" section, a DC voltage between the electrodes of a resonator can dramatically increase the initial aging of a resonator, presumably because of electric field driven diffusion of impurities and electrodes. Oscillator designers often design circuits which (sometimes inadvertently) place a small DC voltage across the electrodes. When high stability TCXOs from several manufacturers were examined, DC voltages ranging from a fraction of a volt to about 4 volts were found. The DC voltage effect can be easily minimized, without a significant lowering of the resonator's effective Q, by placing a capacitor in series and a few megohm resistor in parallel with the resonator .
DC voltages can also result from static charges generated during fabrication. Static charges can result in high (> 1 kV) voltages. Since the surface resistivity of clean quartz is high, the "static" charges can take a long time to decay. This can lead to (initial) aging, especially in doubly rotated crystals, such as SC-cuts, which can have sensitivities of parts in 10-9 per volt. Well-known static ("ESD") control measures can be used to minimize this problem.
In OCXOs, aging of the temperature control circuitry can change the set point of the oven, resulting in aging. The amount of aging for a given set point change depends on the frequency vs. temperature characteristic of the resonator, and will, in general, be much smaller for a typical SC-cut OCXO than for an AT-cut one .