Doubly Rotated Quartz Crystal Resonators With Reduced Sensitivity to Acceleration

Abstract

A doubts rotated quart/crystal resonator comprises a cantilever-mounted doubts rotated resonating element having a line of geometrical symmetry running from a supported end to a free end which is not perpendicular to the resonating element's crystallographic/axis. A method of manufacturing the crystal resonator comprises cutting a doubly rotated quartz crystal plate with x.sup.I and z.sup.I axes defining the plate's plane into one or more resonating elements at a non-zero degrees in-plane rotation angle in relation to the plate's x.sup.I axis. The resonator has reduced sensitivity to mechanical acceleration.

Claims

1.-12. (canceled)

13. A method of manufacturing of a doubly rotated quartz crystal resonator with reduced sensitivity to mechanical acceleration comprising a cantilever-mounted doubly rotated resonating element, which method comprises the step of cutting a doubly rotated quartz crystal plate with x.sup.I and z.sup.I axes defining the plate's x.sup.Iz.sup.I plane into one or more resonating elements at an in-plane rotation angle in relation to the plate's x.sup.I axis in the range from about 36° to about 56°.

14. A method according to claim 13, wherein the doubly rotated quartz crystal resonator is a stress-compensated (SC) cut quartz crystal resonator, the cantilever-mounted doubly rotated resonating element is a cantilever-mounted SC cut resonating element, and the doubly rotated quartz crystal plate is an SC cut quartz crystal plate.

15. A doubly rotated quartz crystal resonator with reduced sensitivity to mechanical acceleration comprising a cantilever-mounted doubly rotated resonating element having a line of geometrical symmetry running from a supported end to a free end of the cantilever-mounted resonating element wherein an angle between the line of the resonating element's geometrical symmetry and the crystallographic z axis is in the range from about 46° to about 61°.

16. A quartz crystal resonator with reduced sensitivity to mechanical acceleration according to claim 15, wherein the cantilever-mounted doubly rotated resonating element is a two-point cantilever-mounted doubly rotated resonating element.

17. A quartz crystal resonator with reduced sensitivity to mechanical acceleration according to claim 15, wherein the cantilever-mounted doubly rotated resonating element is a single-point cantilever-mounted doubly rotated resonating element.

18. A quartz crystal resonator with reduced sensitivity to mechanical acceleration according to claim 15 that exhibits total acceleration sensitivity of an absolute value below 2 ppb/g.

19. A quartz crystal resonator with reduced sensitivity to mechanical acceleration according to claim 15 that exhibits total acceleration sensitivity of an absolute value below 1 ppb/g .

20. A doubly rotated quartz crystal resonator according to claim 15, wherein the said resonator is a stress-compensated (SC) cut quartz crystal resonator and the cantilever-mounted doubly rotated resonating element is a cantilever-mounted doubly rotated SC cut resonating element.

21. A quartz crystal oscillator comprising a resonator according to claim 15.

22. An electronic device comprising a quartz crystal oscillator according to claim 21.

23. A method of manufacturing of a doubly rotated resonating element suitable to construct a doubly rotated quartz crystal resonator with reduced sensitivity to mechanical acceleration, which method comprises the step of cutting a doubly rotated quartz crystal plate with x.sup.I and z.sup.I axes defining the plate's x.sup.Iz.sup.I plane into one or more resonating elements at an in-plane rotation angle in relation to the plate's x.sup.I axis in the range from about 36° to about 56°.

24. A method according to claim 23, wherein the doubly rotated quartz crystal resonator is a stress-compensated (SC) cut quartz crystal resonator, the doubly rotated resonating element is an SC cut resonating element, and the doubly rotated quartz crystal plate is an SC cut quartz crystal plate.

25. A doubly rotated resonating element suitable to construct a doubly rotated quartz crystal resonator with reduced sensitivity to mechanical acceleration wherein an angle between a line of the resonating element's geometrical symmetry and the crystallographic z axis is in the range from about 46° to about 61°.

26. A doubly rotated resonating element according to claim 25, wherein the said doubly rotated quartz crystal resonator is a stress-compensated (SC) cut quartz crystal resonator and the doubly rotated resonating element is an SC cut resonating element.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The invention is further described with reference to the accompanying figures in which,

[0021] FIG. 1 shows the orientation of singly rotated and doubly rotated cuts (prior art).

[0022] FIG. 2 is a schematic cross-section view of the structure of a cantilever-mounted strip crystal resonator (prior art).

[0023] FIG. 3 is a schematic cross-section view of a two-point cantilever-mounted resonating element (prior art).

[0024] FIG. 4 is a schematic cross-section view of a single point cantilever-mounted resonating element (prior art).

[0025] FIG. 5 illustrates quartz wafer dicing as per prior art.

[0026] FIG. 6 illustrates wafer dicing as per the present invention.

[0027] FIG. 7 illustrates wafer dicing into multiple resonating elements with in-plane rotation as per the present invention.

[0028] FIG. 8 shows plots of directional and total acceleration sensitivity versus in-plane rotation angle for two-point cantilever-mounted SC cut resonator.

[0029] FIG. 9 shows plots of directional and total acceleration sensitivity versus in-plane rotation angle for single-point cantilever-mounted SC cut resonator.

[0030] FIGS. 10A, 10B, 10C, and 10D are plots of X, Y, Z, and total sensitivity to acceleration for a number of single point cantilever-mounted SC-cut strip resonators, further referred to in the subsequent experimental Example.

DETAILED DESCRIPTION OF THE INVENTION

[0031] As stated, in accordance with the invention doubly rotated quartz crystal resonator elements are produced with a wafer dicing in-plane rotation.

[0032] FIGS. 5 and 6 illustrate the concept of the invention. In FIG. 5 (prior art) a doubly rotated quartz wafer 2, cut at angles of φ and θ relative to the crystallographic axes x and z respectively, is cut to produce individual doubly rotated resonating elements. For illustration purposes, a single resonating element 6 is shown in FIG. 5; in practice, a number of resonating elements are produced from a quartz wafer. In prior art, the individual resonating elements are produced by dicing up the wafer in directions parallel and perpendicular to the x.sup.I axis. The line of geometrical symmetry 7 of thus produced resonating elements is in parallel with the x.sup.I axis of the wafer and therefore at 90° (shown as angle α) to the crystallographic z axis. In FIG. 6 a doubly rotated quartz wafer 2, cut at angles of φ and θ relative to the crystallographic axes x and z respectively, is used for making individual doubly rotated resonating elements as per the invention. Instead of producing the resonating elements by dicing up the wafer in directions parallel and perpendicular to the x.sup.I axis of the wafer as is done in prior art (FIG. 5), the resonating elements of the present invention are produced (FIG. 6) by dicing up the wafer at a certain non-zero degrees angle Ψ (azimuth angle) of in-plane rotation in relation to the x.sup.I axis. A resonating element 6 produced by methods of the prior art and its line of geometrical symmetry 7 are also shown in FIG. 6 to illustrate the in-plane rotation. The line of geometrical symmetry 7a of resonating element 6a produced as per the invention is not parallel to the x.sup.I axis of the wafer and is not perpendicular to the crystallographic z axis, i.e. angle α≠90°. It can be shown that the exact value of the angle α between the line of geometrical symmetry 7a of resonating element 6a produced as per the invention and the crystallographic z axis is determined by the expression a α=90°−arcsin(cos θx sirΨ).

[0033] As stated, several resonating elements are usually produced from a single quartz wafer, as illustrated in FIG. 7 in which a quartz wafer and its x.sup.I, y.sup.I, and z.sup.I axes are shown, along with the (dashed) lines of dicing that are in-plane rotated by a non-zero degrees angle Ψ in relation to the x.sup.I axis as per the present invention.

[0034] Sensitivity to mechanical acceleration of a doubly rotated resonating element produced as per the present invention varies with, and depends on, the value of the in-plane rotation (azimuth) angle Ψ, and by selecting specific values of the azimuth angle the sensitivity to mechanical acceleration can be minimized or at least reduced. As explained further herein, the choice of a specific in-plane rotation angle Ψ value depends on factors such as the structure of cantilever mounting of the resonating element and the extent of acceleration sensitivity reduction to be achieved.

[0035] As with resonating elements of prior art (FIGS. 3 and 4), doubly rotated resonating elements of the present invention can also be cantilever-mounted, either on two mounting points or on one mounting point located at one end of the resonating element, with the other end of the resonating element being free.

[0036] Sensitivity to mechanical acceleration exhibited by doubly rotated, two-point cantilever-mounted SC cut resonating elements of the invention varies with in-plane rotation angle as shown in FIG. 8, in which acceleration sensitivity in each of three mutually perpendicular directions X, Y, and Z (gammaX, gammaY, and gammaZ) as well as the total acceleration sensitivity (gammaRMS) are plotted as functions of the in-plane rotation angle Ψ. Acceleration sensitivity values are measured in parts-per-billion of frequency change per acceleration unit (ppb/g), whereas the angle Ψ values are measured in angular degrees.

[0037] As shown in FIG. 8, the total acceleration sensitivity “gammaRMS” (a root mean square value of directional acceleration sensitivity values “gammaX”, “gammaY”, and “gammaZ” in three mutually perpendicular directions) is around its minimal value when an in-plane rotation of 36°≤Ψ≤56° is applied to produce the resonating elements from a doubly rotated SC cut quartz wafer. Compared to two-point cantilever mounted SC cut resonators produced without the in-plane rotation (i.e., zero rotation angle in FIG. 8) that exhibit a total acceleration sensitivity of about 3 ppb/g, similarly mounted SC cut resonators produced with the in-plane rotation of 36°≤Ψ≤56° exhibit a total acceleration sensitivity below 1 ppb/g.

[0038] Sensitivity to mechanical acceleration exhibited by doubly rotated, single-point cantilever-mounted SC cut resonating elements of the invention varies with in-plane rotation angle as shown in FIG. 9, in which acceleration sensitivity in each of three mutually perpendicular directions X, Y, and Z (gammaX, gammaY, and gammaZ) as well as the total acceleration sensitivity (gammaRMS) are plotted as functions of the in-plane rotation angle Ψ. Acceleration sensitivity values are measured in parts-per-billion of frequency change per acceleration unit (ppb/g), whereas the angle Ψ values are measured in angular degrees.

[0039] As shown in FIG. 9, the total acceleration sensitivity “gammaRMS” (a root mean square value of directional acceleration sensitivity values “gammaX”, “gammaY”, and “gammaZ” in three mutually perpendicular directions) is around its minimal value when an in-plane rotation of 36≤Ψ≤56° is applied to produce the resonating elements from a doubly rotated SC cut quartz wafer. Compared to single-point cantilever mounted SC cut resonators produced without the in-plane rotation (i.e., zero rotation angle in FIG. 9) that exhibit a total acceleration sensitivity of about 4.5 ppb/g, similarly mounted SC cut resonators produced with the in-plane rotation of 36≤Ψ23 56° exhibit a total acceleration sensitivity below 2 ppb/g.

[0040] As has already been stated, in doubly rotated resonating elements of the present invention the line of geometrical symmetry is not perpendicular to the crystallographic z axis (angle α≠90°) and that the exact value of the angle α between the line of geometrical symmetry of resonating elements produced as per the invention and the crystallographic z axis is determined by the aforementioned expression. It follows from that expression that for doubly rotated resonating elements with θ=34°±20′ (such as, for example, the SC cut and IT cut resonating elements) and the in-plane rotation angle of 36°≤Ψ≤56°, the angle α will be within the range from 46° to 61°.

[0041] It should be noted that the sign of the azimuth angle (for example, positive +46° or negative −46°) depends in practice on the convention adopted within the manufacturing process implemented at a specific manufacturer: i.e., some manufacturers will consider a clockwise in-plane rotation to be “positive”, others may call an anticlockwise in-plane rotation “positive”. As follows from FIGS. 8 and 9, in-plane rotation in only one of directions will result in reduced sensitivity to acceleration. The important point for any embodiment of the present invention is the selection of the suitable absolute value of the azimuth angle.

EXAMPLE

[0042] A number of single-point cantilever-mounted SC-cut (θ=33°45′, φ=21°56′) strip resonators of size 5.0 mm×3.2 mm and nominal resonant frequency of 19.2 MHz were produced with in-plane rotation (azimuth) angle Ψ of 36°, 46°, and 56°, and their sensitivity to acceleration was measured in three mutually perpendicular directions X, Y, and Z, with the total sensitivity determined based on the measurement results. The results are plotted in FIGS. 10A-10D, in which FIG. 10A plots X axis acceleration sensitivity magnitude values, FIG. 10B plots Y axis acceleration sensitivity magnitude values, FIG. 10C plots Z axis acceleration sensitivity magnitude values, and FIG. 10D plots the total acceleration sensitivity magnitude values for each of the three in-plane rotation angles (36°, 46°, and 56°). In these figures each data point represents a result for one resonator at that in-plane rotation angle value, and the dotted lines plot an estimated relationship through an average of the data points at each angle. It follows from the experimental data presented in FIG. 10A-10D that in-plane rotation of 36° to 56° applied when producing single point cantilever mounted SC cut resonators allows to achieve a reduction in the resonators' total acceleration sensitivity to levels below 1 ppb/g.

[0043] Thus, by applying a specific in-plane rotation during the wafer dicing in manufacture of doubly rotated quartz crystal resonating elements, sensitivity to mechanical acceleration of cantilever-mounted strip resonators can be substantially reduced.

[0044] The choice of a specific value of the in-plane rotation angle for doubly rotated quartz crystal resonator manufacture depends on the resonator design goals. For example, if an SC cut single-point cantilever-mounted resonator design is aimed at achieving the minimal total sensitivity to acceleration, then, as shown in FIG. 10D, an in-plane rotation angle value in close vicinity of 46° should be selected for the manufacture of the resonating elements of the present invention. If, on the other hand, the resonator is intended for an application where reduced sensitivity to acceleration in direction Z is particularly important, then a lower in-plane rotation angle, perhaps within the range from 36° to 46° (refer to FIG. 10C), will be selected for manufacture, which would result in even lower acceleration sensitivity in Z direction, although at the expense of a slight increase in the total acceleration sensitivity value.

[0045] Cantilever-mounted doubly rotated quartz crystal resonators of the present invention can be used in a variety of frequency control products, including, but not limited to, crystal oscillators (XO), temperature-compensated crystal oscillators (TCXO), and oven-controlled crystal oscillators (OCXO). These devices, in turn, will benefit the performance of various electronic devices and systems, including, but not limited to, radio communication devices, where reduced sensitivity of the reference frequency to mechanical acceleration is important.