Temperature and Temperature-

Although most of the known aging mechanisms are thermally activated, the expected strong temperature dependence of aging rates has not been observed in many medium stability and high stability resonators. For example, in one study of eight AT-cut resonator types, from several manufacturers, the resonators were aged at room temperature, 85° C and 120° C. No systematic aging rate variations with temperature were found [85]. The resonators did not always exhibit a higher aging rate at elevated temperatures; some even aged at a lower rate at the elevated temperatures. The resonators ranged from 14.4-MHz fundamental mode to 70-MHz third overtone.

In another study, groups of resonators were aged at 50° C, 60° C and 70° C. It was found that, although the aging improved for many resonators when the temperature was lower, the low-aging rate resonators did not change their aging characteristics notably when the temperature was lowered [86].

When groups of low and medium stability resonators were aged at various temperatures ranging from 25° C to 100° C, the aging rates were found to increase with increasing temperatures [87]. The increases varied with crystal type. A conclusion the authors draw concerning aging prediction is "that such prognosis will be sufficiently reliable only when the crystal unit will operate under more or less identical conditions during all its service life. If the ambient temperature or drive level changes, even the sign of frequency aging may change." In some earlier studies on precision 2.5-MHz 5th overtone AT-cut resonators [88], and 550-kHz wire mounted DT-cut resonators [89], an increase in aging temperature increased the aging rates.

The aging of groups of six high precision SC-cut resonators and two high precision AT-cut resonators were measured successively at the lower turnover point (LTP) and upper turnover point (UTP) temperatures. The UTP to LTP differences ranged from 19° C to 40° C for the SC-cuts, and it was about 100° C for the AT-cuts. The higher aging temperatures at the UTP introduced a small positive aging contribution to the SC-cuts' aging, i.e., the aging of both positive and negative aging resonators became more positive at the UTP. The results for the AT-cuts indicated no drastic improvements in aging rates at the LTP [57].

If aging were due to a single thermally activated process, then one ought to be able to observe phenomenally low-aging rates by cooling the resonators to cryogenic temperatures. Although the definitive aging experiment at low temperatures is yet to be performed, the limited data at such temperatures indicates no drastic improvements in aging rates [90-92]. When the aging of high precision SC-cut resonators was measured at (the lower turnover) temperatures in the vicinity of -10° C and compared with the aging of similarly fabricated resonators aged at turnover temperatures that were 90° C to 120° C higher, no significant improvement in aging was observed at the lower temperatures [57,93].

When an aging interruption is accompanied by a significant temperature excursion, the effects can range from drastic to small. For an example of drastic change, when the aging of an oscillator containing a high precision 5-MHz 5th overtone glass enclosed AT-cut resonator was interrupted and the oscillator was cooled to -40° C for nine days, the aging rate increased drastically subsequent to the resumption of aging. Months elapsed before the aging rate returned to its value prior to the interruption. Fig. 4 shows this example. This oscillator was aging at an approximately constant rate of -1.1 X 10^-11 per day prior to interruption. After the aging resumed: 1) the aging rate became positive at first, 2) the rate reversed direction after about 150 days, and 3) the aging rate stabilized at -4.0 X 10^-12 per day after about one year and it stayed at that rate for the subsequent four years.

Low temperature storage can produce drastic aging rate changes in SC-cut oscillators too [57]. In another aging experiment, groups of high stability OCXOs and TCXOs were on-off cycled and temperature cycled during the experiment. For most of the oscillators, the interruptions did not worsen the total frequency changes during the aging period [93]. Similarly, when high stability microcomputer compensated crystal oscillators were aged with repeated interruptions for temperature cycling, the aging rates were not made worse by the cyclings [94].

It has been shown that stability under intermittent operation is dependent on the processes used in fabricating the resonator. For example, upon restarting an oscillator following an oven shutdown, those containing high temperature processed crystal units exhibit much smaller frequency offsets, and the aging rates return to their pre-shutdown values much faster, than do low temperature processed units [89,95].
Fig4

Since most of the known aging mechanisms are associated with the resonator's surfaces, it is not surprising that, in general, resonators of higher volume-to-surface ratio tend to exhibit a lower aging rate than resonators of lower volume-to-surface ratio. For a given fabrication process, the aging rate tends to scale with the volume-to-surface ratio of the resonator's active area, i.e., with the frequency of the plate. For example, the aging of 333-MHz fundamental mode SC-cut resonators [96] at 25° C (the test OCXOs were kept in a freezer to permit stabilization of the OCXO ovens at 25° C) was found to range from 1 to 3 x 10^-8 per day after one year of continuous aging [97]. The aging of comparably fabricated 5-MHz fundamental mode resonators under the same aging conditions would typically be on the order of 333/5 times lower, i.e., on the order of a few parts in 10¹⁰ per day. The scaling with frequency appears to apply to SAW devices too; e.g., the aging rates of "good" 500-MHz SAW resonators [98] are typically on the order of 100 times higher than the aging rates of "good" 5-MHz bulk acoustic wave resonators.

The aging rates of 2.5-MHz and 5-MHz 5th overtone AT-cut resonators made according to designs and processes developed by Warner and coworkers in the late-1950's and 1960's [88,89,95,99-103] are still difficult to surpass. This is probably due, in part, to the large volume-to-surface ratio of these resonators. No larger volume-to-surface ratio resonators have been developed since. (In fact, 2.5-MHz 5th overtone resonators are no longer made regularly.)

In general, overtone resonator aging rates are lower than aging rates of comparably fabricated fundamental resonators of the same frequency. The reasons are, not only that overtone resonators have a larger volume-to-surface ratio, but also, that overtone resonators, having a smaller C₁, exhibit a lower aging rate due to oscillator circuit component aging and a lower sensitivity to changes at the resonators' edges.

The experimental evidence concerning the effect of drive level is mixed. In one report on the aging of (low stability) 32.8-kHz flexural mode resonators [87], an increase to "inadmissibly high values of crystal unit drive level," from 10 m W to 100 m W, produced a significant increase in aging rates. (An increase in aging temperature was also found to increase the aging rates of these resonators.) The report, however, references an earlier study which showed "the absence of any amount of significant influence of drive conditions on the crystal unit aging...," at reasonable drive levels.

The aging rate of AT-cut resonators has been reported to be degraded by high drive levels [104]. Increasing the current through 2.5- and 5-MHz 5th overtone resonators ten fold from 75 m a resulted in an increase in monthly aging rate from 1 X 10^-10 to 1.5 X 10^-9. The aging of BVA resonators has also been reported to be sensitive to drive level [105,106]. The drive level sensitivity has been used to produce oscillators that exhibit "zero aging" at a particular time. (It is highly unlikely, however, that such a balancing of aging mechanisms can last for long periods.)

Changing the resonator drive levels in discrete steps did not affect the aging rates of precision, high temperature processed SC-cut resonators, up to a 2.5-ma drive current (594 m W), the maximum that was tried in the study [94].

Since resonator frequency is a function of drive level [81], if the oscillator circuitry ages so as to gradually change the drive level, oscillator aging can result. At very high drive levels, the power dissipation in the resonator will raise the temperature of the resonator's active area. Therefore, resonators which are adversely affected by increased aging temperatures would also be expected to be adversely affected by increased drive levels. From the limited data available, it appears that, at a constant drive level, the aging of low stability and AT-cut resonators is adversely affected by high drive levels, whereas that of precision SC-cuts is not affected. (It may be worthwhile to repeat the measurement of the drive level dependence of precision AT-cuts, in carefully designed oscillators, to eliminate the possibility that the drive level dependence of aging was circuit induced, e.g., via higher DC bias on the resonator at higher drive levels.)

Increasing the drive level increases the displacements, velocities and accelerations of particles at resonator surfaces. At high frequencies, especially, particle accelerations can be on the order of a million g's. High drive levels' ability to remove particulate contamination from surfaces is well known. Whether or not high drive levels can affect the desorption of adsorbed contaminants has been considered [107]. Since the increased kinetic energy of an adsorbed molecule due to a high drive level is very much less than 20 kcal/mol (which is the typical adsorption energy of concern), and is also much less than the thermal energies at normal operating temperatures, high drive levels probably do not directly affect adsorption-desorption phenomena.

If during an interruption in aging the resonator or oscillator experiences a change in its environment, then upon resuming the aging, the aging rate can be significantly different from what it was prior to the interruption. The effects of thermal interruptions, drive level changes, and DC fields were discussed earlier. Other interruptions that can result in increased aging include mechanical and thermal shock, vibration, magnetic and electric fields, AC signals, and radiation [108,109]. Few studies have been reported on the effects of interruptions other than thermal. In general, the effects will depend on the nature of the interruption, and on the aging mechanisms that are disturbed by the interruption. For example, if during a shock some elastic limit in the resonator's mounting structure is exceeded, then the shock may change the stress-relief component of aging. Similarly, if a radiation pulse displaces impurities to higher energy sites in the lattice, then the subsequent aging may be affected by the migration of impurities to low energy sites.

Since there are very few reports on common applications that use different materials or modes, the effects of material and mode type on aging are not easily separable. No reports on the effects of changing material for the same mode type were found in the literature. No reports on aging for bulk wave devices made from lithium niobate, berlinite, or other new piezoelectric materials were found. In this section, aging data on extensional mode lead zirconate titanate and lithium tantalate resonators, other modes using lead zirconate titanate, hydrophones made from poly (vinylidene fluoride), quartz flexural tuning forks, and quartz surface wave resonators are presented. Where possible, the material effects are separated from the device type effects.

Extensional resonators made from lead zirconate titanate and similar materials age from 700 to 10000 ppm per decade in time [110]. Improved lead zirconate titanate type materials operating in all modes age about 1000 ppm to end-of-life of 10 years [111].

For piezoelectric ceramic materials the aging usually proceeds as log-time [112] and is therefore reported as a frequency change per decade of time. No recent reports with a detailed description of the time and temperature dependence of aging in materials like lead zirconate titanate could be found.

Extensional mode lithium tantalate resonators, with frequencies from 455-kHz to 2-MHz, were aged at room temperature for more than 900 days. Aging did not depend significantly on frequency. The frequency decreased about 100 ppm during the first year; after two years, the aging rate was 3 X 10^-7 per month [113].

Hydrophones made from a plastic piezoelectric polymer, poly (vinylidene fluoride) age a few 10000 ppm per decade in time, with an upper temperature limitation of 80° C [114]. For the hydrophone aging, the mode of vibration used was not stated, but it was implied that this aging value was determined for the 31 and 33 modes.

Most reported aging studies have been for quartz and lead zirconate titanate devices.

Some reports on aging of low frequency and high frequency quartz bulk wave devices, as well as the aging of surface acoustic wave (SAW) resonators and delay lines, are summarized by Gerber [4].

The aging of low frequency wire mounted quartz crystal resonators operating in different contour (length-width) modes was reported by Armstrong, et al. [89], and by Gerber and Sykes [115]. For these devices the aging proceeded as log-time.

Kanbayashi [116], Engdahl and Matthey [117], Yoda [118], and Forrer [119] have reported aging results for quartz flexural mode tuning forks at frequencies of about 32.768-kHz. Yoda reported aging results for 32.768-kHz flexural (XY, NT, tuning fork) mode resonators to be 5 ppm per year. Some examples of -0.2 to +0.3 ppm per year were shown [120]. Table II summarizes the aging of several types of low frequency quartz resonators.

The data in Table II suggest that flexural and width-shear resonators age less than extensional or face shear resonators. The data in Table II also suggest that lower frequency resonators age less than higher frequency resonators of the same type. From the data in Table II, it is not possible to assign the cause of the low-aging flexures and width-shears to mode type or frequency alone.

Table II
Aging ofLow Frequency Quartz Resonator
(Probably at room temperature)

Mode Type (frequency)	Aging (ppm)	Time of Aging
Extensional (200-kHz)	8.0	100 days
Face Shear (200-kHz)	4.0	100 days
Extensional (100-kHz)	3.0	100 days
Width-Shear (990-kHz)	3.0	100 days
Flexure(8-kHz)	1.2	100 days
Flexure (445-kHz)	-0.2 to +0.3	365 days
Width-Shear (550-kHz)	1.0	100 days
Width-Shear (230-kHz)	0.5	100 days
Flexural Tuning Fork (32.768-kHz)	-0.5 to +2.0	365 days

Gerber [4] also summarized some reports on the aging of quartz surface acoustic wave resonators and delay lines. For some 184- and 194-MHz SAW resonators there was little or no difference in aging at 50° C to 150° C, but increased aging was observed at 200° C to 250° C [121,122]. For some 160-MHz SAW resonators powered in an oscillator at 60° C the log-time aging rates approached 1 X 10^-9 per day; -5 to +5 X 10^-9 per day after 162 days. According to the general rule that the aging is proportional to the frequency, these SAW resonators had an aging equivalent to a bulk wave resonator of about 6 X 10^-10 per day at 10-MHz. For these devices the best long term aging was -0.64 to -0.31 ppm per year [123-125]. For 160-MHz SAW resonators, aging data were best fitted with two simultaneous log-time aging mechanisms [124,125].

Some 300-MHz SAW resonators had aging rates of 1 to 2 ppm per 30 days at room temperature [126]. Some 1.4-GHz SAW delay lines aged several ppm in 52 weeks, also probably at room temperature [127]; 200- to 400-MHz SAW delay lines in powered oscillators at about 30° C aged between -10 to +17 ppm in about 60 to 120 weeks [128]; 400-MHz SAW devices aged less than 1 ppm per year (-2 to +4 ppm per year) on a production basis [129,130]; 187-MHz to 425-MHz SAW resonator oscillators operating at room temperature aged between 0.1 and 0.5 ppm per year with aging times from 27 weeks to 80 weeks [65]; 425-MHz SAW resonators oscillators aged less than 0.1 ppm in 100 weeks at 60° C [98].

A survey of aging for SAW devices showed best aging rates of less than 0.1 ppm per year [130]. SAW aging continues to be reduced as the SAW fabrication technology adopts bulk wave processes of cleanliness, high temperature processing, and careful attention to the selection of materials, mountings, and packages.

The lowest aging rate reported to date is a few parts in 10¹³ per day [104]. The date of this report is 1967. Unfortunately, the authors cite unpublished results obtained elsewhere. Several authors have reported few parts in 10¹² per day aging rates [36,88,93,95,99,131,132]. Such aging has been observed only in a few resonators, usually after extended stabilization periods. No manufacturer will guarantee such aging today even though the first report of parts in 10¹² aging (1 X 10^-10 per month) appeared in 1958 [99].

The slow progress in the best long term aging performance is puzzling because during the past 30 years, numerous advancements have taken place which ought to have yielded improvements. Among the advancements are: the SC-cut, better ultrahigh vacuum systems, better cleaning techniques, better understanding of stress effects, and better oscillator circuitry. These advancements seem to have resulted in significant improvements in initial aging, but not in the long term aging. As manufacturers adopted these advancements, the advancements have also resulted in improvements in the aging of resonators in high volume production.

In 1983-84, an informal survey of worldwide capabilities in making low-aging resonators was performed [57]. Ten organizations were identified which could make resonators with parts in 10¹¹ per day aging after 30 days of continuous operation. Although the processes used to make these resonators varied widely, the end results with respect to long term aging did not (the stabilization periods, however, were much shorter for some than for others).

Parts in 10¹¹ aging has been achieved with AT-, BT- and SC-cut resonators; with glass enclosed, metal enclosed, and ceramic flatpack enclosed resonators; with natural, cultured and swept cultured quartz; with lightly etched and deeply etched resonator plates; with mechanically polished and chemically polished plates; etc. A high temperature vacuum bake prior to sealing the resonators appeared to be the key step that was common to all the processes that produced low-aging. Although the bake temperatures, times and vacuum conditions varied widely, it is clear from the survey and other evidence, that vacuum baking before sealing is a necessary step in the production of low-aging resonators.

Aside from high temperature processing, the only parameter that was, in some respects, common to all the processes was the quartz material. No significant improvements in reducing quartz defects, such as dislocations and hydrogen content, have taken place during the past 30 years. In fact, the dislocation densities in cultured quartz have probably increased over the years. Since the quality of commercially available cultured quartz is adequate for nearly all high-volume applications, and since it is expensive for growers to "refresh" the seeds periodically by using natural quartz, the growers have had little incentive for refreshing seeds. If the seeds are not refreshed, cultured quartz grown on successive generations of cultured quartz seeds will contain increasing densities of dislocations. Although no data could be found on the defect densities in low-aging resonators from 30 years ago vs. today, it is conceivable that the aging of the lowest aging resonators is somehow related to quartz defects. The outgassing of quartz may also limit the lowest attainable aging.

Another parameter that is common to all resonators is background ionizing radiation due to cosmic rays and radioactive trace elements in the soil and building materials. The amount of background radiation depends on location. The average annual radiation dose from natural sources in the U.S.A. has been reported to be on the order of 0.1 rad [133].

The radiation sensitivities of resonators are a highly nonlinear function of dose at low doses. The low dose radiation effects are not well understood. The frequency changes per rad at low doses can be several orders of magnitude higher than at high doses [134]; sensitivity as high as 1 X 10^-9 per rad has been reported upon initial irradiations [109]. A resonator with such sensitivity would exhibit apparent aging (i.e., drift, according to the new definitions [2]) of 1 X 10^-10 per year or 3 X 10^-13 per day due to the background radiation. Although other resonators have been found to have smaller sensitivities [108], and the radiation was deposited much faster in the experiments than the rate of deposition of background radiation, since the low dose effects are not well understood, and the rate dependencies at very low rates are unknown, it is conceivable that the effects of background radiation are not negligible in the lowest aging resonators. A better understanding of low dose effects (and the means to minimize these effects) may be a prerequisite to making substantial improvements in the technology of ultra low-aging resonators.

To achieve the lowest aging rates, the oscillator circuitry must also be carefully designed. Achieving lower than parts in 10¹² per day oscillator stabilities is no easy task, however; the best circuits do not yet seem to limit the achievable long term aging of small C₁ resonators, such as 5-MHz 5th overtone SC-cuts.

In spite of the lack of significant progress in improving the aging of the lowest aging oscillators, no evidence exists to indicate that the barriers to further improvements are insurmountable. The definitive experiments, in which all known aging mechanisms are minimized, are yet to be done.