Abstract:
A MEMS or NEMS device with at least one component made of a non-naturally occurring isotope material. The refined isotopic material provides advantages to device operation such as reduced mechanical loss, increased breakdown voltage, improved tunability and other advantages.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application claims the benefit of the filing date of U.S. Provisional Patent Application No. 61/495,068 filed Jun. 9, 2011, the disclosure of which is hereby incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to MEMS devices manufactured with thin film processing techniques and, more particularly, to the nature of the materials used to make MEMS devices. 
       BACKGROUND OF THE INVENTION 
       [0003]    Many MEMS (Micro-Electro-Mechanical Systems), NEMS (Nano-Electro-Mechanical Systems) and nano devices implement their function by transferring, modulating or transducing mechanical energy. In the process of transfer, modulation and/or transduction of mechanical energy, some energy is dissipated. Such energy dissipation is a consequence of the First and Second Laws of Thermodynamics. 
         [0004]    For example, a MEMS cantilever is the simplest embodiment of a MEMS inertial device. The cantilever is set into motion by an external impulse, such as an external inertial force, or through electrostatic coupling. The energy dissipation is quantified by a metric called the attenuation coefficient. When the mechanical response of the cantilever in such devices is a mass-spring-damper system, the energy dissipation term corresponds to the damper in the system. 
         [0005]    Another example of a MEMS device that transfers mechanical energy is a MEMS bulk acoustic wave (BAW) resonator. Such resonators are realized in suspended (Film Bulk Acoustic Resonator—FBAR) and solidly mounted (Solidly Mounted Resonator—SMR) configurations. 
         [0006]    A metric of energy dissipation in resonating or vibrating devices is the quality factor Q, which is expressed as a ratio of the energy stored to the energy dissipated per cycle: 
         [0000]        Q=Energy stored/Energy dissipated per cycle    (1).
 
         [0007]    Both configurations consist of charge collecting electrodes coupled to a piezoelectric transducer. The transducer, usually a piezoelectric layer (but can also be an electrostatic transducer), converts an applied AC electrical stimulus to an AC mechanical strain. The mechanical strain propagates through the device, and is reflected at the boundaries of the device. The “boundary” is a mechanical impedance discontinuity, such as the electrode-air interface in the case of the FBAR, or the electrode-bragg interface in the case of the SMR. This sets up a standing wave within the resonator, which can be represented by a model known as the BVD model. The BVD model is analogous to the spring-mass-damper model used for the inertial cantilever, with an additional parallel capacitance representing the dielectric of the transducer. As before, the damper represents the energy dissipated in the device. 
         [0008]    Inertial MEMS structures and BAW resonators have been extensively studied and manufactured. Such structures are formed by patterning the structure in a substrate and releasing the structure therefrom using semiconductor processing techniques. 
         [0009]    Such devices have had widespread commercial use. For example, silicon, polysilicon and diamond-based resonators have made it into a multitude of inertial MEMS based sensors manufactured by companies like ST Microelectronics, Bosch, Analog Devices, Invensense, Virtus Advanced Sensors, SiTime, Discera, Sand9 and others. These sensors are found in a wide array of products such as acceleration sensors, gyros, shock sensors, oscillators, chemical and biological sensors, etc. 
         [0010]    BAW devices are described in Rosenbaum, T., “RF Bulk Acoustic Wave Filters for Communications” (Artech House, Publ. 1 st  Ed., May 31, 2009). Quartz-based BAW resonators have been manufactured for many years and more recently piezoelectric materials such as Aluminum Nitride (AlN) and Zinc Oxide (ZnO) have been extensively studied and commercialized in BAW devices. Tunable materials such as Strontium Titanate (STO), Barium Strontium Titanate (BST) and other incipient ferroelectrics (disclosed in commonly owned patent application U.S. Ser. No.  12 / 391 , 490 ), which is incorporated by reference herein, are being examined to complement the functionality of AlN or ZnO in a BAW resonator. AlN-based BAW resonators have been used in RF filter and power amplifier products. 
         [0011]    BAW resonators are also being investigated as a frequency reference for oscillators as described in Hashimoto, K. Y., “RF Bulk Acoustic Wave Filters for Communication,” (Artech House Publ. 1 st  Ed., May 31, 2009). The BAW resonator provides a large change in impedance (magnitude, phase, or both) over a frequency range. A wide range of oscillator architectures can be implemented around such a resonator. However, in all instances, the oscillator performance is enhanced by a high quality (Q) factor resonator. 
         [0012]    In MEMS design, one objective is to reduce the dissipated energy as much as possible. This provides a commensurate reduction in operating power, and device lifetime is increased and the desired product performance metrics are more readily achieved. A reduction in dissipated energy can be achieved by improving materials and processes or by improving device geometry. However, although some reduction in dissipation of energy in MEMS devices has been achieved by improving materials and processes, further improvement continues to be pursued. 
       SUMMARY OF THE INVENTION 
       [0013]    Described herein are devices that deploy a non-naturally occurring isotopic material that has been refined to have an altered isotopic dominance. The non-naturally occurring isotopic material cooperates with other device components to provide a desired device response. In one embodiment the device is a micro-electro-mechanical system (MEMS) device or a nano-electro-mechanical system (NEMS) device. The device is provided on a supporting substrate. A transducer element is formed over the substrate. The device is further formed of a conductor and an insulator defining conductive regions of the device. The conductor and transducer element cooperate to provide a device response. The isotopic material provides reduced mechanical loss to the MEMS device as compared to a device that does not have the isotopic material. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1A  is a symbol view of an isotope 18 effect; 
           [0015]      FIG. 1B  is a plot view of a first-order Raman spectra of diamond; 
           [0016]      FIG. 2  is a schematic view of a prior art MEMS device; 
           [0017]      FIG. 3A  is a schematic view of a different prior art MEMS device; 
           [0018]      FIG. 3B  is a schematic view of a different prior art MEMS device; 
           [0019]      FIG. 4  is a front sectional view of a MEMS inertial cantilever device according to one embodiment of the present invention; 
           [0020]      FIG. 5  is a front sectional view of a MEMS bulk acoustic wave resonator device according to one embodiment of the present invention; 
           [0021]      FIG. 6  compares the performance of the BAW resonator of the preset invention with a prior art BAW resonator; and 
           [0022]      FIG. 7  is a scaled view of the comparison in  FIG. 6 . 
       
    
    
     DETAILED DESCRIPTION 
       [0023]    Most methods of manufacturing MEMS devices involve semiconductor process steps that deposit, mask and etch layer of materials, such methods generally, are well known to one skilled in the art and not discussed in detail herein. Further discussion of processes will assume general knowledge of these methods, with the understanding that they can be generalized to other, emerging MEMS and nanodevice manufacturing techniques such as self-assembly, growth of single- and multiwalled-walled nanotubes; etc. 
         [0024]    Improvement in materials and processes comes from new material deposition techniques that deposit the material on the substrate in a particular crystallographic orientation. Such orientation is achieved by the deposition, and can be in combination with specialized material layers underneath. Many such methods exist, and several are summarized in Maluf, N., et al., “An Introduction to Micro-electro-mechanical Systems Engineering” (Artech House Publ., 2 nd  Ed., June 2004) and Hashimoto, K. Y. et al., “RF Bulk Acoustic Wave Filters for Communications,” (Artech House, Publ., 1 st  Ed., May 31, 2009), which are hereby incorporated by reference. 
         [0025]    Improvements in device geometry that yield improved device performance include altering the shape and layout of each device layer as well as the thickness of each device layer. Many methods exist, and several are described in Hashimoto, K. Y., et al. above. 
         [0026]    In semiconductor materials, isotopic materials have been used to improve carrier mobility and power handling in transistors. For example, see U.S. Pat. Nos. 5,144,409 and 5,442,191, which issued on Sept. 1, 1992 and Aug. 15, 1995 respectively and are incorporated by reference herein. US Patent Application Publication No. 2004/0227202 filed on Nov. 21, 2003 describes the use of isotopically enriched quartz in the context of transistor devices. Several other applications of the isotope effect have been described, including neutron transmittive doping, optical fibers, and lasers. Some researchers have also suggested applications for the use of the isotope effect in information storage and quantum computers. 
         [0027]    Most naturally occurring materials used in the manufacture of MEMS, NEMS and nanomechanical devices are of mixed isotopic composition. The stable isotopes of the constituent atoms are present in a fixed proportion. For example, silicon occurs in the composition 28Si (92.2%), 29Si (4.6%) and 30Si (3.0%), with 0.2% being other negligible contributions. The material is deposited on the substrate via a variety of methods such as chemical vapor deposition (CVD) and its variants; RF sputtering from a target; and atomic layer deposition (ALD). 
         [0028]    The isotope effect is a physical phenomenon where replacement of atoms in the crystal lattice by their isotopes results in a change in the physical properties of the lattice. In particular, the mass, lattice constants and dissipation constants are altered by the change in isotopic composition. An important example is the strong isotope effect on the superconducting transition temperature that has indicated that phonons are important in BCS superconductivity. 
         [0029]    As described herein, the isotope effect is used to reduce the attenuation constants of materials used in the manufacture of MEMS devices, nanoelectrical mechanical systems (NEMS) and nanomechanical devices. More specifically, the isotopic effect is used to alter certain properties of materials to improve the performance of devices in which those materials are incorporated. 
         [0030]    Phonon frequency in isotopes is affected by changes in the mass of the crystal. The processes that cause these changes can be broadly classified into two classes according to Lockwood et al. “Light Scattering in Semiconductor Structures and Super Lattices,” pp. 132 (NATO Science Series B: Physics; Springer, 1 st  Ed., Jan. 31, 1992); and Plekhanov, v., “Applications of the Isotopic Effect in Solids” (Springer Series in Materials Science; 1 st  Ed., Aug. 26, 2004), which is incorporated by reference herein. These classes are anharmonic interactions and elastic scattering. The former are due to higher order terms in the expansion of the lattice potential. The latter are due to wave-vector conservation in isotopically mixed and/or disordered samples. In isotopically pure samples, the elastic scattering processes are largely absent, so one would expect the corresponding samples to have lower phonon dissipation. 
         [0031]    Anharmonic interaction processes are determined largely by the isotope mass. As described in Cordona, M., “Isotopic Effects in the Phonon and Electron Dispersion Relations of Crystals,” Phys. Stat. 501., Vol. 220, No. 5 (2000), which is hereby incorporated by reference, in an isotopically pure crystal, the frequency w of a phonon corresponding to wavevector k and branch j is: 
         [0000]        w =√{square root over (( f ( k, j )/ M ))}   (2)
 
         [0032]    where f(k,j) is a restoring force constant and M is the isotopic mass. According to equation (2) crystals of isotopes of lower mass possess higher frequency phonons. According to Cordona, the higher the phonon frequency, in general the lower the dissipation. One skilled in the art is aware that exceptions to this relationship exist. 
         [0033]    Scattering spectra are very useful tools to characterize the properties of materials. Such techniques are described in Lockwood et al., and Pelletier, M. J., Analytical Applications of Raman Spectroscopy, (Blackwell Publ., May 11, 1999). Pelletier is also hereby incorporated by reference. For example, for an isotopically mixed sample of silicon, peaks in the intensity occur for each phonon interaction. These intensity peaks correspond to particular isotope atoms in the crystal. The energy shifts between peaks is related to the isotopic mass of each peak. For example, with reference to Manzowa, H., et al., “Disorder Effects of Nitrogen Impurities, Irradiation Induced Defects, and 13C Isotope Composition on the Raman Spectrum in Synthetic Ib Diamond,” Phys. Review B, Vol. 54, No. 6 (Aug. 1, 1996) which is hereby incorporated by reference, six isotopically mixed compositions of diamond were examined. These compositions were formed by growing diamond crystals using both 12C and 13C isotopes of carbon. Referring to  FIG. 1B  of Manzowa et al. (reproduced as  FIG. 1B  herein), there are six peaks corresponding to each of the six compositions A through F. The spacing between peaks is described as related to the different reduced mass of each peak according to Manzowa et al. 
         [0034]    The line width is a property of the Raman spectra of a crystal. Raman spectroscopy is described in Pelletier described above. The line width characterizes the width of a spectral line. The width is reported as the Full Width Height Maximum (FWHM) of the line and has dimensions of L −1 . Narrower or smaller line widths indicate lower phonon scattering. 
         [0035]    The line width is related to the attenuation in the crystal according to Lockwood et al. This has been shown in the literature for diamond according to N V Surovtsev, N. V., et al., “Effect of nitrogen impurities on the Raman line width in diamonds”, J. Phys.: Condens. Matter Vol. 11, pp. 4767-4774 (1999); Inyushkina, A. V., et al., “Considerable Increase in Thermal Conductivity of a Polycrystalline CVD Diamond upon Isotope Enrichment”, Bul. Lebedev Phys. Inst., Vol. 34, No. 11, pp. 329-333, (2007); and which are hereby incorporated by reference, and for Ge and Si as described in Kuleev, I. G., et al., “Anisotropic Attenuation of Transverse Ultrasound in Cubic Crystals of Ge, Si, and Diamond with Various Isotopic Compositions”, Phys. Solid State, Vol. 49, No. 9, pp. 1643-1651 (2007), which is hereby incorporated by reference, and for silica porous systems as described in Caponi, S. et al., “Acoustic attenuation in silica porous systems”, J. Non-Crystalline Solids, Vol. 322, pp. 29-34 (2003). Similar results have been obtained for other systems. 
         [0036]    The line width Aw can be related to the attenuation as: 
         [0000]      Δ w =2 αv    (3)
 
         [0037]    where α is the attenuation coefficient and v is the acoustic velocity. This relationship is described in Lockwood et al. Non-linear relationships between α and Δw have also been reported. In all cases, however, an increase in α is accompanied by an increase in the line width Δw. 
         [0038]    Naturally occurring isotopic mixtures have point defects in the crystal structure, because the lattice contains atoms of all the naturally occurring isotopic variations. This results in an increase in the line width of the Raman spectra for the crystal, due to increased elastic scattering. For example, it has been reported that diamond has a line width that has a non-monotonic relationship with isotopic composition. The isotopically purest samples exhibited the lowest line widths, with a maximum in the line width occurring for an isotopically mixed sample.  FIG. 1B  shows the results obtained by Hanzawa et al. (Hanzawa, H., et al., “Disorder effects of nitrogen impurities, irradiation-induced defects, and 13C isotope composition on the Raman spectrum in synthetic Ib diamond”, Physical Review B (Condensed Matter), Vol. 54(6) pp.3793-3799 (Aug. 1, 1996), which is hereby incorporated by reference). For six different isotopic compositions of diamond varying from nearly pure 12C to nearly pure 13C, labeled A through F, the FWHM of the line width of the spectra varies from around 2.0 cm −1  for the purest compositions, to 8.0 cm −1  for the mixed samples. 
         [0039]    Another important feature is the effect of anharmonic interactions. Hanzawa et al. also report that the line width of the isotopically pure composition consisting of the lightest isotope (12C) was slightly smaller than the corresponding line width of the isotopically pure composition of 13C (the heaviest isotope). This small difference arises from the previously described class of anharmonic interactions. These dissipative processes are due to higher order terms in the expansion of the lattice potential. 
         [0040]    Therefore, according to the embodiments described herein, non-naturally occurring isotopically enriched materials are used in the manufacture of MEMS, NEMS and nanomechanical devices. The benefits are two-fold. First, an isotopically “refined” material will have far fewer point defects in the crystal structure. Second, if the crystal lattice consists of the lighter isotopes of the element, the line width is smaller (as there are fewer point defects) than if the lattice were constructed out of the heavier isotopes of the element as illustrated in  FIG. 1B . Both mechanisms are exploited to achieve the highest possible Q factor for the device made using such materials. 
         [0041]    In one embodiment, the MEMS device or NEMS device is an inertial structure. One example of the model of a mass-spring-damper structure is illustrated in  FIG. 2 . Such structures are embodied by a cantilever. The model  200  illustrated in  FIG. 2  is representative of structures such as  201 . The device  201  is manufactured using standard techniques to pattern the structure in the substrate and release the structure therefrom for operation (e.g., etching and deposition techniques such as RF sputtering, CVD, ALD, etc.). As noted above, the model  200  in  FIG. 2  represents the structure  201  as an electrical network. In the electrical network representation, the resistor corresponds to the damper  211 . A reduction in the attenuation constants of the materials in the inertial device  201  corresponds to a reduction of the value of this resistor  210 . This in turn results in an increase of the Q factor of the device  201 . 
         [0042]    One embodiment of an acoustic wave structure is represented by a Butterworth Van-Dyke (BVD) model as illustrated in  FIG. 3A . This model  300  captures the electrical behavior of an acoustic wave (e.g. BAW) resonator. For simplicity this model excludes dielectric loss elements such as the one illustrated in  FIG. 5 . Thus the only loss term in this model  300  is the motion resistance in the motional arm  520  of the BAW resonator device illustrated in  FIG. 5 . A reduction in the attenuation coefficients of the materials in the BAW device reduces the value of the resistor  310  in this model. This in turn results in an increase in the Q factor for the device. 
         [0043]    The one dimensional mechanical behavior of the acoustic wave structure can also be represented by a 1-D lossy transmission line model as illustrated in  FIG. 3B . Several transmission elements from  FIG. 3B  (i.e., elements  360 ,  370 ,  380  and  390 ), representing each of the material layers in the BAW device (e.g., lower electrode, piezoelectric layer and upper electrode) are formed and connected through their ports as illustrated by  FIG. 3B . The mechanical behavioral model is completed by applying appropriate termination impedances to represent the air- or vacuum-break at the electrodes. The loss terms in this transmission line are represented by the series resistance and shunt conductance. As described in van Deventer, J., et al., “PSpice Simulation of Ultrasonic Systems”, IEEE Trans. Ultrasonics, Ferroelectrics, and Freq. Cont.“, Vol. 47, No. 4, pp. 1014-1024 (July 2000), the disclosure of which are incorporated by reference, the loss terms can be related to the acoustic attenuation coefficient by: 
         [0000]        R =2 *ρ*v*A* α   
         [0000]        G =2α/(ρ* v*A )   (4)
 
         [0044]    where ρ is the density of each material layer, v is the acoustic velocity in each layer, A is the cross-sectional area, and α is the acoustic attenuation coefficient. 
         [0045]    A reduction in the attenuation in the material system results in a reduction in the values of all the resistors in the above models. This reduction is achieved by constructing the devices out of non naturally occurring isotopic materials, preferably using isotopes that are lighter than their naturally occurring counterparts. 
         [0046]    Before specific embodiments of the invention are discussed, it is useful to keep in mind the following information about the isotope effect generally.  FIG. 1A  is a symbol view of an isotope  18  effect. An atom  10  of a particular element consists of a fixed number of protons  14 , neutrons  16  and electrons  12 . An isotope  18  of an element has a different number of neutrons  16  while keeping the number of protons  14  and electrons  12  unchanged. For example,  12   c  and  13   c  are both isotopes of carbon, with  13   c  having one extra neutron  20  than  12   c.  In the crystal lattice  22 , the elemental atoms are present in a natural isotopic composition. The presence of multiple isotopes of an element in the same lattice alters the properties of the lattice. 
         [0047]    Referring to  FIG. 1B  there is provided a plot view of a first-order Raman spectra of diamond of varied isotopic compositions. Six different compositions, designated (a) through (f), are presented. Compositions (a) and (f) are the isotopically pure compositions, with (a) corresponding to nearly pure  12   c  and (f) corresponding to nearly pure  13   c . Compositions (b) through (e) are isotopically mixed compositions. The left-hand plot of the Raman spectra illustrates that the isotopically pure compositions have smaller line widths. Furthermore, as is illustrated in the right-hand plot of the line width f whm , the composition a (nearly pure  12   c ) has a slightly smaller line width than composition (f) (nearly pure  13   c ). This difference in line width is because crystals constructed from lighter isotopes (a) have slightly less anharmonic interactions than those constructed from heavier isotopes (f). As a result compositions (a) and (f) have lower attenuation compared to the other compositions. 
         [0048]      FIG. 2  is a schematic view of a mass  213 -spring  215 -damper  211  MEMS device which is known in the art. This is one example of what is known as MEMS inertial devices (e.g. a cantilever). A mass  213  is connected to a reference ground  217  through a spring  215  and damped by a damper  211 . A displacement force  219  (induced by a transducer, not shown) causes the system to move away from its equilibrium. This results in a restoring force acting on the inertial structure  201 . If the structure  201  is allowed to return to its equilibrium position (for example, by applying a force that is no longer stronger than the restoring force), the structure oscillates about its equilibrium position. Analogizing to electrical networks, the spring  215  can be viewed as equivalent to a capacitor  216 , the mass  213  equivalent to an inductor  214 , and the damper  211  equivalent to a resistor  210 . The damper  211  (resistor  210  in the electrical network) represents the mechanical loss in the inertial device. For particular structures, it is possible to relate these operational parameters to the geometric parameters of the inertial device. 
         [0049]      FIG. 3B  is a schematic view of a transmission line element from the prior art. The transmission line is expressed as a delay that is implemented by two network elements: the inductance per unit length  370  and the shunt capacitance per unit length  380 . Loss in the line is represented by the resistance per unit length  360  and shunt conductance per unit length  390 . In transmission line-based representations of acoustic devices, it is possible to relate geometric and material parameters of the acoustic device to the transmission line parameters. 
         [0050]      FIG. 4  is a front sectional view of a MEMS inertial cantilever device. The device  400  is illustrated schematically as having a substrate  410 , an anchor  420  and cantilever  430 . Electrodes  440  are disposed on the substrate  410  and on the cantilever  430 . Any of the anchor  420 , cantilever  430  or electrodes  440  can be a non-naturally occurring (i.e. refined) istopic material to improve device performance. The released device is supported by the anchor  420  that tethers the device to the substrate  400 . The inertial structure  400  is released from the substrate (using the standard process for fabricating MEMS devices (e.g. the MUMPS process well known to those skilled in the art and not described in detail herein). A transducer (not shown) actuates the cantilever from its rest position. 
         [0051]      FIG. 5  is a front sectional view of a MEMS bulk acoustic wave resonator device. The device shown is in the film bulk acoustic wave resonator (FBAR) configuration, but a similar description applies to other acoustic wave devices such as SMRS and SAWS. The device  500  is supported over the substrate  510  by an anchor  520 . The FBAR in its simplest configurations has a lower electrode  530 , a piezoelectric layer  540 , and an upper electrode  550 . Any one or more of the lower electrodes  530 , the piezoelectric layer  540  and the upper electrode  550  can be made of a non-naturally occurring isotopic material to improve the quality factor of the device. 
         [0052]    A performance comparison of a BAW resonator in its simplest embodiment ( FIG. 5 ) is presented in  FIGS. 6 and 7 . The resonator system is an FBAR configuration, with AlN as the piezoelectric material and thin, 0.1 um sputtered iridium top and bottom electrodes. The suspension and substrate are not modeled. The 1-D transmission model ( FIG. 3B ) is used to represent the physical behavior of the materials. 1.9 um of AlN is used to obtain a series resonance frequency of about 1.72 GHz. 
         [0053]    Two examples are described, one with and one without isotopically enriched AlN. No change is made to the electrode material. The isotopic enrichment is represented by a 10× reduction in the line width of equation (3) (compare to about 4× reduction in the Hanzawa et al. result for diamond). For illustrative purposes, no change is assumed in the acoustic velocity ‘v’ or the k2 of the resonator. However, one skilled in the art will understand that both these properties will also improve as a result of this invention. 
         [0054]    The reduction of the linewidth of equation (3) is reflected in a 10× reduction of the attenuation coefficient. This causes a reduction in the transmission line resistors as predicted by equation (4). 
         [0055]      FIGS. 6 and 7  illustrate the result of this improvement. As illustrated by these FIGS., there is an approximately  4 × improvement in the series quality factor, from about 2000, to about 8000. A smaller improvement is seen in the parallel quality factor. There is no change in k2, as assumed. However, an improvement in k2 is also expected as a beneficial by-product of the use of non-naturally occurring isotopic materials in the device described herein. 
         [0056]      FIG. 6  is a simulation result of two BAW resonators in an FBAR configuration. A similar result applies to other acoustic wave devices such as SMRS and SAWS, as well as other MEMS, NEMS and nano devices. In this test, only the piezoelectric material is isotopically enhanced, while the thin electrode is not. The amplitude  620  and phase  640  of the impedance response are shown. 
         [0057]      FIG. 7  is an enlarged view of a portion of  FIG. 6 , with focus on the series resonance frequency. The amplitude  720  and phase  740  of the impedance response are shown. The response of the resonator constructed from naturally occurring materials is  760 , while the isotopically enriched resonator response is  780 . It is observed that the series quality factor has improved from about 2000 to about 8000, a 4× increase. 
         [0058]    Since other modifications and changes varied to fit particular operating requirements and environments will be apparent to those skilled in the art, the invention is not considered limited to the example chosen for purposes of disclosure, and covers all changes and modifications which do not constitute departures from the true spirit and scope of this invention.