Title: Quartz resonating piece, quartz resonator, and quartz device
Abstract: The invention provides a stabilized frequency characteristic over a wide temperature range. A quartz resonating piece is provided such that an electrical axis of quartz corresponds to an X axis, a mechanical axis of the quartz corresponds to a Y axis, and an optical axis of the quartz corresponds to a Z axis. The quartz resonating piece includes a quartz plate having a side that is parallel to an X'axis set by clockwise rotation of the X axis around the Z axis by an angle equal to or greater than -5.0.degree. and less than -1.0.degree. or by an angle greater than +1.0.degree. and equal to or less than 15.9.degree., and another side that is parallel to a Z' axis set by clockwise rotation of the Z axis around the X' axis by an angle in a range from 34.6.degree. to 35.1.degree. inclusive; or a quartz plate having a side that is parallel to the X' axis set by clockwise rotation of the X axis around the Z axis by an angle in a range from -15.9.degree. to -5.0.degree. inclusive, and another side that is parallel to the Z' axis set by clockwise rotation of the Z axis around the X' axis by an angle in a range from 34.2.degree. to 35.3.degree. inclusive.
Patent Number: 6,849,991 Issued on 02/01/2005 to Zhang, et al.
| Inventors:
|
Zhang; Guoqing (Minowa-machi, JP);
Tanaka; Masako (Okaya, JP);
Karaki; Eiji (Ina, JP);
Unno; Yukihiro (Okaya, JP)
|
| Assignee:
|
Seiko Epson Corporation (Tokyo, JP)
|
| Appl. No.:
|
391745 |
| Filed:
|
March 20, 2003 |
Foreign Application Priority Data
| Mar 26, 2002[JP] | 2002-087121 |
| Feb 14, 2003[JP] | 2003-036605 |
| Current U.S. Class: |
310/361 |
| Intern'l Class: |
H01L 041/08 |
| Field of Search: |
310/361
|
References Cited [Referenced By]
U.S. Patent Documents
| 3072806 | Jan., 1963 | Sogn | 310/361.
|
| 4178566 | Dec., 1979 | Kawashima | 331/156.
|
| 4419600 | Dec., 1983 | Sinha | 310/361.
|
| Foreign Patent Documents |
| B2-3218537 | Aug., 2001 | JP.
| |
| A-2003-324332 | Nov., 2003 | JP.
| |
Other References
P.C.Y. Lee & Y.K. Yong, "Frequency-Temperature Behavior of Thickness
Vibrations of Doubly Rotated Quartz Plates Affected by Plate Dimensions
and Orientations", Journal of Applied Physics, vol. 60, No. 7, Oct. 1,
1986, p. 2340.
|
Primary Examiner: Budd; Mark
Attorney, Agent or Firm: Oliff & Berridge, PLC
Claims
What is claimed is:
1. A quartz resonating piece, comprising:
a quartz plate having:
a side that is parallel to an X' axis set by clockwise rotation of an X
axis around a Z axis by an angle equal to or greater than -5.0.degree. and
less than -1.0.degree. or by an angle greater than +1.0.degree. and equal
to or less than 15.9.degree., and
another side that is parallel to a Z' axis set by clockwise rotation of the
Z axis around the X' axis by an angle in a range from 34.6.degree. to
35.1.degree. inclusive;
an electrical axis of quartz corresponding to the X axis, a mechanical axis
of the quartz corresponding to a Y axis, and an optical axis of the quartz
corresponding to the Z axis.
2. The quartz resonating piece according to claim 1,
a length along the X'-axis direction of the quartz plate being equal to or
greater than 15 times and less than 22 times a thickness of the quartz
plate, and
the following condition being satisfied:
.phi..degree.=(-1.0222350.times.10.sup.2.times..theta..sup.3
+1.0670709.times.10.sup.4.times..theta..sup.2
-3.7128983.times.10.sup.5.times..theta.+4.3063628.times.10.sup.
6.+-.3).degree. [Formula 1]
where .phi. is an angle of rotation around the Z axis, .theta. is an angle
of rotation around the X' axis, and
34.6.ltoreq..theta..ltoreq.35.1.degree..
3. The quartz resonating piece according to claim 1,
a length along the X'-axis direction of the quartz plate being less than 15
times a thickness of the quartz plate, and:
the following condition being satisfied:
.phi..degree.=(-1.7916667.times.10.sup.2.times..theta..sup.3
+1.8731250.times.10.sup.4.times..theta..sup.2
-6.5277908.times.10.sup.5.times..theta.+7.5832595.times.10.sup.
6.+-.3).degree. [Formula 2]
where .phi. is an angle of rotation around the Z axis, .theta. is an angle
of rotation around the X' axis, and
34.6.degree..ltoreq..theta..ltoreq.35.10.
4. A quartz resonating piece, comprising:
a quartz plate having:
a side that is parallel to an X' axis set by clockwise rotation of an X
axis around a Z axis by an angle in a range from -15.9.degree. to
-5.0.degree. inclusive, and
another side that is parallel to a Z' axis set by clockwise rotation of the
Z axis around the X' axis by an angle in a range from 34.2.degree. to
35.3.degree. inclusive;
an electrical axis of quartz corresponding to the X axis, a mechanical axis
of the quartz corresponding to a Y axis, and an optical axis of the quartz
corresponding to the Z axis.
5. The quartz resonating piece according to claim 4,
a length along the X'-axis direction of the quartz plate being less than 80
times a thickness of the quartz plate, and
the following condition being satisfied:
.theta..degree.=(-2.91652.times.10.sup.-3.times..phi..sup.2
+1.39515.times.10.sup.-4.phi.+35.1541.+-.0.2).degree. [Formula 3]
where .phi. is an angle of rotation around the Z axis, .theta. is an angle
of rotation around the X' axis, and
-15.9.degree..ltoreq..phi..ltoreq.-5.degree..
6. A quartz resonator, comprising:
the quartz resonating piece according to claim 1.
7. A quartz device, comprising:
the quartz resonator according to claim 6.
Description
BACKGROUND OF THE INVENTION
1. Field of Invention
The present invention relates to a resonating piece that utilizes a
piezoelectric effect. More particularly, the invention relates to a quartz
resonating piece that utilizes a new cut quartz plate, a quartz resonator,
and a quartz device.
2. Description of Related Art
Computerization of various devices and development of communication systems
have enabled the usage of quartz devices including piezoelectric
oscillators in the related art. In particular, quartz crystals can be used
as piezoelectric materials in quartz devices because they provide high
frequencies and have stable frequency characteristics. Since an AT cut
quartz plate (hereinafter "AT cut plate") can be used to provide a quartz
resonator having stable frequency characteristics over a wide temperature
range, the related art has used it in quartz devices. This AT cut plate
has one side that is parallel to an X axis and is obtained by a cutting
operation at a cut angle .theta. set by clockwise rotation of an XZ plane
by 35.25 degrees around the X axis (as viewed from the -X direction to the
+X direction of the X axis).
Frequency-temperature characteristics of a quartz resonator formed of the
AT cut plate is shown in FIG. 11. In FIG. 11, the horizontal axis
indicates the temperature (in .degree. C.), and the vertical axis
indicates the frequency shift (in ppm) from the standard frequency at
25.degree. C.
The related art includes the apparatus disclosed in Japanese Patent No.
3,218,537 and P. C. Y. Lee & Y. K. Yong, "Frequency-Temperature Behavior
of Thickness Vibrations of Doubly Rotated Quartz Plates Affected by Plate
Dimensions and Orientations", Vol. 60, No. 7, United States, Journal of
Applied Physics, Oct. 1, 1986, p. 2340.
SUMMARY OF THE INVENTION
As shown in FIG. 11, in an AT cut plate that is used in the related art,
the frequency shift from the frequency at a temperature of 25.degree. C.
in a frequency-temperature characteristic becomes abruptly large at a
temperature near 100 degrees. Therefore, for example, in a temperature
range from -25.degree. C. to +120.degree. C., there is no cut angle at
which a variation width of the frequency shift stay within 30 ppm. For
this reason, when a quartz resonator formed of an AT cut plate is
installed in a device that is used in a wide temperature range, such as an
automobile part, it becomes difficult to perform a controlling operation
with high precision. Therefore, there is a demand for a quartz resonator
that oscillates at a stable frequency so that the frequency shift is
within .+-.15 ppm in a wide temperature range, particularly, in the range
from -25.degree. C. to +120.degree. C.
In addition, as mentioned above, since, in the related art, the variation
width of the frequency shift in the temperature range from -25.degree. C.
to +120.degree. C. is greater than 30 ppm, when an oscillator is used in,
for example, an automobile part, a temperature-compensating circuit is
used to get a more stable frequency oscillator. However, when a
temperature-compensating circuit is used, the number of parts and the
number of man-hours are increased, thereby increasing costs.
The present invention addresses or overcomes the aforementioned and/or
other problems of the related art. The present invention can provide a
stable frequency characteristic in a wide temperature range.
The inventors have conducted research and experiments concerning cut angles
of quartz, and have found the cut angles at which a relatively stable
frequency characteristic is provided in a wide temperature range. The
present invention has been achieved based on this and/or other knowledge.
According to one aspect of the present invention, there is provided a
quartz resonating piece including: a quartz plate having a side that is
parallel to an X' axis set by clockwise rotation of an X axis around a Z
axis by an angle equal to or greater than -5.0.degree. and less than
-1.0.degree. or by an angle greater than +1.0.degree. and equal to or less
than 15.9.degree., and another side that is parallel to a Z' axis set by
clockwise rotation of the Z axis around the X' axis by an angle in a range
from 34.6.degree.to 35.1.degree.inclusive. An electrical axis of quartz
corresponds to the X axis, a mechanical axis of the quartz corresponds to
a Y axis, and an optical axis of the quartz corresponds to the Z axis.
The present invention having this structural feature makes it possible to
cause the variation width of the frequency shift in a
frequency-temperature characteristic to be within 30 ppm in a temperature
range of from -25.degree. C. to +120.degree. C., so that a stable
frequency characteristic can be provided in a wide temperature range.
In the invention, "clockwise rotation around an axis" refers to clockwise
rotation as viewed from the minus side to the plus side of the axis.
Therefore, for example, "clockwise rotation around the Z axis" refers to
clockwise rotation as seen from the -Z direction to the +Z direction.
The frequency-temperature characteristic of the quartz resonating piece
changes due to the size of a blank, such as an X-side ratio of the blank
(divided value of the length along the X'-axis by the thickness of the
blank). Accordingly, the inventors investigated the relationship between
the cut angles and the X-side ratio of the blank, which provides a stable
frequency characteristic in a wide temperature range. In one form of the
quartz resonating piece, a length along the X'-axis direction of the
quartz plate is equal to or greater than 15 times and less than 22 times
the thickness of the quartz plate, and the following Formula 1 is
satisfied:
.phi..degree.=(-1.0222350.times.10.sup.2.times..theta..sup.3
+1.0670709.times.10.sup.4.times..theta..sup.2
-3.7128983.times.10.sup.5.times..theta.+4.3063628.times.10.sup.
6.+-.3).degree. [Formula 1]
where .phi. is an angle of rotation around the Z axis, .theta. is an angle
of rotation around the X' axis, and
34.6.degree..ltoreq..theta..ltoreq.35.1.degree.. By this, the frequency
characteristic of the quartz resonating piece having an X-side ratio that
is equal to or greater than 15 and less than 22 can be stabilized in the
wide temperature range from -25.degree. C. to +120.degree. C.
In another form of this aspect, a length in the X' axis direction of the
quartz plate is less than 15 times the thickness of the quartz plate, and
the following Formula 2 is satisfied:
.phi..degree.=(-1.7916667.times.10.sup.2.times..theta..sup.3
+1.8731250.times.10.sup.4.times..theta..sup.2
-6.5277908.times.10.sup.5.times..theta.+7.5832595.times.10.sup.
6.+-.3).degree. [Formula 2]
where .phi. is an angle of rotation around the Z axis, .theta. is an angle
of rotation around the X' axis, and
34.6.ltoreq..theta..ltoreq.35.1.degree.. By this, the frequency
characteristic of the small quartz resonating piece having an X-side ratio
that is less than 15 can be stabilized in the wide temperature range from
-25.degree. C. to +120.degree. C.
According to another aspect of the present invention, there is provided a
quartz resonating piece including: a quartz plate having a side that is
parallel to an X' axis set by clockwise rotation of an X axis around a Z
axis by an angle in a range from -15.9.degree. to -5.0.degree. inclusive,
and another side that is parallel to a Z' axis set by clockwise rotation
of the Z axis around the X' axis by an angle in a range from 34.2.degree.
to 35.3.degree. inclusive, where an electrical axis of quartz corresponds
to the X axis, a mechanical axis of the quartz corresponds to a Y axis,
and an optical axis of the quartz corresponds to the Z axis.
The present invention having this structural feature makes it possible to
cause the variation width of the frequency shift in a
frequency-temperature characteristic to be within 30 ppm in the
temperature range from -25.degree. C. to +120.degree. C., so that a stable
frequency characteristic can be provided in a wide temperature range.
In one form of this aspect, a length along the X'-axis direction of the
quartz plate is less than 80 times the thickness of the quartz plate, and
the following Formula 3 is satisfied:
.theta..degree.=(-2.91652.times.10.sup.-3
+1.39515.times.10.sup.-4.times..phi.+35.1541.+-.0.2).degree. [Formula 3]
where .phi. is an angle of rotation around the Z axis, .theta. is an angle
of rotation around the X' axis, and
-15.9.degree..ltoreq..phi..ltoreq.-5.degree.. By this, the frequency
characteristic of the quartz resonating piece having an X-side ratio equal
to or greater than 10 can be stabilized in the wide temperature range from
-25.degree. C. to +120.degree. C.
According to still another aspect of the present invention, there is
provided a quartz resonator including: any one of the above-described
quartz resonating pieces. By this, it is possible to provide a quartz
resonator having a stable frequency characteristic in the wide temperature
range from -25.degree. C. to +120.degree. C.
According to still another aspect of the present invention, there is
provided a quartz device including: the above-described quartz resonator.
By this, even for, for example, an automobile part that is used in a wide
temperature range, the frequency characteristic can be stabilized without
a temperature-compensating circuit, so that the number of parts and the
number of man-hours can be reduced, thereby reducing costs.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic that illustrates cut angles in an exemplary
embodiment of the present invention;
FIG. 2 is a graph showing dependence of a frequency-temperature
characteristic of a quartz resonator having an X-side ratio of 10 on a cut
angle .phi.;
FIG. 3 is a graph showing differences in optimum cut angles due to
differences in X-side ratios;
FIG. 4 is a graph showing differences in frequency-temperature
characteristics due to differences in electrode film thicknesses (plate
back amounts);
FIG. 5 is a graph showing a range of cut angles that provide a good
frequency-temperature characteristic in a quartz resonator having an
X-side ratio equal to or greater than 15 and less than 22;
FIG. 6 is a graph showing a range of cut angles that provide a good
frequency-temperature characteristic in a quartz resonator having an
X-side ratio less than 15;
FIG. 7 is a graph showing dependence of a frequency-temperature
characteristic on .phi. when .theta.for a quartz resonator having an
X-side ratio of 10 is 34.5.degree.;
FIG. 8 is a graph showing dependence of a frequency-temperature
characteristic on .theta. when .phi. for a quartz resonator having an
X-side ratio of 25.0 is -10;
FIG. 9 is a graph showing a range of cut angles that provide a good
frequency-temperature characteristic in a quartz resonator having an
X-side ratio in a range from 10 to less than 80;
FIGS. 10(1) and 10(2) are schematics that show a quartz resonator of an
embodiment of the present invention, where FIG. 10(1) is a sectional view
taken along plane B--B of FIG. 10(2), and FIG. 10(2) is a sectional view
taken along plane A--A of FIG. 10(1);
FIG. 11 is a graph showing a frequency-temperature characteristic of a
quartz resonator comprising an AT-cut quartz plate.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
A description of exemplary embodiments of a quartz resonating piece, a
quartz resonator, and a quartz device of the present invention is provided
in detail with reference to the attached drawings.
It is theoretically proven that, when a quartz plate (base plate) that is
obtained by a cutting operation at cut angles set by rotation of axes
around two of the three crystal axes (electrical axis, mechanical axis,
and optical axis), an inflection point of a frequency shift is shifted
towards high temperatures (see, for example, U.S. Pat. No. 3,218,537. A
cut angle at which a frequency characteristic is stabilized exists in a
temperature range from -25.degree. C. to +120.degree. C.
However, a frequency-temperature characteristic curve changes easily due to
the size of a blank. Therefore, the cut-angle area at which the frequency
characteristic is stabilized cannot be determined simply by determining
the cut angle. For example, in the AT cut quartz resonator having the
frequency-temperature characteristic shown in FIG. 11, even if the cut
angle is the same, as an X-side ratio of the blank (value resulting from
dividing the length in the X' direction of the blank by the thickness of
the blank) becomes larger, the frequency-temperature characteristic curve
represented as a 3rd function of temperature changes in the direction in
which a linear coefficient of the temperature increases, as shown by
arrows A and B in FIG. 11. The related art indicates that a quartz plate
having coordinate axes in which axes are rotated around two axes shows the
same tendency (for example, see the P. C. Y. Lee & Y. K. Yong Article).
Therefore, it is necessary to set the cut angle taking into consideration
the X-side ratio of the blank.
The temperature characteristic is also affected by the thickness of an
electrode formed on the blank. Accordingly, increasing the thickness of
the electrode reduces the linear coefficient as it is reduced when the
X-side ratio of the blank is reduced. It is also necessary to take into
consideration the thickness of the electrode just as it is necessary to
take into consideration the cut angle.
FIG. 1 illustrates cut angles of quartz to provide a quartz vibrating
piece, which is a quartz resonating piece of the present invention. FIG. 1
shows three axes that are perpendicular to each other of a quartz crystal
10, in which an electrical axis corresponds to an X axis, a mechanical
axis corresponds to a Y axis perpendicular to the X axis, and an optical
axis corresponds to a Z axis perpendicular to the X and Y axes. A cut
angle of a quartz plate (quartz base plate) 12 to provide the quartz
vibrating piece of the present invention is formed setting an X' axis by
clockwise rotation of the X axis by an angle .phi. around the Z axis, so
that the quartz plate has a side parallel to the X' axis. The other cut
angle is formed by setting a Z' axis by clockwise rotation of the Z axis
by an angle .theta. around the X' axis, so that the quartz plate 12 has a
side parallel to the Z' axis.
The inventors conducted various investigations concerning double-rotation
cut angles formed by rotation of axes around the X axis and the Z axis of
the crystal quartz 10, and found cut angles at which a relatively stable
frequency characteristic was obtained in the temperature range from
-25.degree. C. to +120.degree. C.
FIG. 2 shows measured frequency-temperature characteristic curves for cut
angles for a quartz resonator having a principal vibration frequency of 10
MHz and having a rectangular flat shape with an X-side ratio (value
resulting from dividing the length in the X' direction of the blank
obtained from the quartz plate 12 shown in FIG. 1 by its thickness; this
also applies to the X-side ratio in the description below) of 10.0 and a
Z-side ratio (value resulting from dividing the length in the Z' direction
of the blank obtained from the quartz plate 12 shown in FIG. 1 by its
thickness; this also applies to the Z-side ratio in the description below)
of 6.2. Here, dependence of f set by clockwise rotation of the Z axis by
34.7 degrees (.theta.34.7 degrees) around the X' axis was investigated.
The plate back amount of the electrode was 2.5%.
In FIG. 2, the horizontal axis indicates the temperature (in .degree. C.),
and the vertical axis indicates the frequency shift (in ppm) from the
standard frequency at 25.degree. C. As shown in FIG. 2, when .phi.=8.3
degrees, a resonator having a variation width of the frequency shift (with
the frequency at a temperature of 25.degree. C. set as a standard) within
30 ppm in the temperature range from -25.degree. C. to +120.degree. C. can
be provided. Therefore, a quartz device which can be used for a device
that is used in a wide temperature range, such as an automobile part, can
be provided without a temperature-compensating circuit.
However, when .phi. is equal to or greater than 16 degrees, the central
temperature (corresponding to a point C in FIG. 11, that is, a point
intermediate between a low-temperature inflection point and a
high-temperature inflection point in each frequency-temperature
characteristic curve) becomes equal to or greater than 60 degrees, so that
the frequency in a low-temperature area becomes considerably low, thereby
making it impossible to set the variation width of the frequency shift
within 30 ppm. Similarly, when .phi. is from -1.degree. to +1.degree.
inclusive, since the central temperature is 25.degree. C. as in the AT cut
plate, the frequency increases considerably in a high-temperature area
Therefore, it is desirable than the range of +be equal to or greater than
-5.0.degree. and less than -1.degree., or greater than +1.degree.and equal
to or less than +15.9'. Therefore, it is desirable that the cut angle
.phi. be:
-5.degree..ltoreq..phi.<-1.degree. [Formula 4]
or
1.degree.<.phi..ltoreq.15.9.degree. [Formula 5]
Research conducted by the inventors showed that, by setting .phi. at a
value not deviating from 8.3 degrees by an angle considerably greater than
3 degrees, a resonator having a variation width of the frequency shift
within 30 ppm in the temperature range from -25.degree. C. to +120.degree.
C. can be reliably provided.
As mentioned above, the frequency-temperature characteristic of a quartz
resonator varies depending upon the shape of a blank, in particular, its
X-side ratio. Accordingly, the inventors compared optimum cut angles for
the frequency-temperature characteristics in the temperature range from
-25.degree. C. to +120.degree. C. for a quartz resonator having the
aforementioned X-side ratio of 10.0 and Z-side ratio of 6.2 and having a
principal vibration frequency of 10 MHz and for a quartz resonator having
an X-side ratio of 20 and Z-side ratio of 13 and having a principal
vibration frequency of 16 MHz. The results are provided in FIG. 3.
In FIG. 3, the horizontal axis indicates the temperature (in .degree. C.),
and the vertical axis indicates the frequency shift (in ppm) with the
frequency at 25.degree. C. serving as a standard. As indicated by the
solid line in FIG. 3, for the small resonator having an X-side ratio of
10.0, the cut angles for the optimum frequency-temperature characteristic
are .phi.=8.3.degree. and .theta.=34.7.degree.. In contrast, for the large
resonator having an X-side ratio of 20 indicated by a dotted line in FIG.
3, the optimum frequency-temperature characteristic is obtained when the
cut angles are .phi.6.1.degree. and .theta.=34.7.degree..
Accordingly, it is clear that, by a difference between the X-side ratios,
the cut angles that provide an optimum or enhanced frequency-temperature
characteristic are different. In the temperature range from -25.degree. C.
to +120.degree. C., the range of cut angles at which the variation width
of the frequency shift stays within 30 ppm may greatly differ depending
upon the X-side ratio.
FIG. 4 shows a comparison between frequency-temperature characteristics
when the film thickness of an electrode (plate back amount) is varied from
1% to 4% for a blank having the same shape with the same cut angles
(.theta.=35.degree. and .phi.=4.5.degree.). In FIG. 4, the horizontal axis
indicates the temperature (in .degree. C.), and the vertical axis
indicates the frequency shift (in ppm) from the standard frequency at
25.degree. C. The solid curve indicates a plate back amount of 1%, and the
dotted curve indicates a plate back amount of 4%. As is clear from FIG. 4,
it was found that, when the electrode film thickness was changed, the
optimal area was also shifted.
The range of cut angles that provide good frequency-temperature
characteristics in which the variation width of the frequency shift was
within 30 ppm were investigated for the two quartz resonators.
FIG. 5 illustrates cut angles, indicated by black dots, which provide good
frequency-temperature characteristics, for a resonator having an X-side
ratio of 20, a Z-side ratio of 13, a plate back amount of 2.5%, and a
principal vibration frequency of 16 MHz. These pieces of experimental data
were found to exist on a functional curve indicated by a solid line. The
horizontal axis indicates an angle .theta. (in degrees) set by clockwise
rotation around the X' axis, and the vertical axis indicates an angle
.phi. (in degrees) set by clockwise rotation around the Z axis. However,
if the X-side ratio or the electrode film thickness changes, the optimal
area changes as mentioned above. Therefore, the optimal area was
extensively searched by changing the X-side ratio from 15 to 22, and by
changing the plate back amount from 1% to 6%. The results showed that, by
changing the conditions, optimal values existed at locations marked by
triangles on the graph. In other words, the optimal values existed within
an area bounded by dotted lines on both sides of the solid line.
Therefore, when the X-side ratio is equal to or greater than 15 and less
than 22, the angle .phi. in terms of the angle .theta. that provides a
good frequency-temperature characteristic is determined by:
.phi..degree.=(-1.0222350.times.10.sup.2.times..theta..sup.3
+1.0670709.times.10.sup.4.times..theta..sup.2
-3.7128983.times.10.sup.5.times..theta.+4.3063628.times.10.sup.
6.+-.3).degree. [Formula 1]
At this area, when the wideness of an area in which a good
frequency-temperature characteristic is obtained for variations in angles
is seen, even in the case where there are slight variations in the angle
.theta., in particular, in an area where .theta. is equal to or less than
35.1 degrees, if the angle .phi. is constant, a quartz resonator having a
good frequency temperature characteristic can be obtained. Therefore, when
mass productivity is considered, it is desirable that
.theta..ltoreq.35.1.degree.. However, the temperature characteristic
exhibited by such a resonator described above is greatly affected by the
X-side ratio and the electrode film thickness. When the X-side ratio and
the electrode film thickness are values outside the ranges of values in
this embodiment, that is, when the X-side ratio is a value equal to or
greater than 22 and/or when the electrode film is thin, that is, when the
plate back amount is equal to or less than 1%, there are angles that fall
outside the range shown in FIG. 5 or FIG. 6 (described below). Therefore,
in order to obtain a stable frequency-temperature characteristic in terms
of a wide range of manufacturing conditions, it is necessary for .phi. to
be equal to or greater than -5.0.degree. and less than -1.0.degree., or
greater than +1.degree. and equal to or less than 15.9.degree.; and for
.theta. to be from 34.6.degree. to 35.1.degree. inclusive. The condition
in which .phi. is .+-.1.degree. is excluded because, under this condition,
substantially the same frequency-temperature characteristics as those of
the AT cut resonator are only exhibited.
In FIG. 6, cut angles at which the variation width of the frequency shift
was within 30 ppm in the temperature range from -25.degree. C. to
+120.degree. C. were determined for a quartz resonator having an X-side
width of 10.0, a Z-side width of 6.2, a plate back amount of 2.5%, and a
principal vibration frequency of 10 MHz. The cut angles are indicated by
black dots. These pieces of experimental data were found to exist on a
functional curve indicated by a solid line. Similarly, as previously
mentioned, optimal values were extensively searched by changing the X-side
ratio from 5 to 15 and by changing the plate back amount from 0.5% to 4%.
From the results, it was found that the optimal values existed at
locations marked by triangles in FIG. 6. In other words, the optimal
values existed within an area bounded by dotted lines on both sides of the
solid line.
Therefore, when the X-side ratio is less than 15, the relationship between
angle .theta. and angle .phi. that provides a good frequency-temperature
characteristic is determined by:
.phi..degree.=(-1.7916667.times.10.sup.2.times..theta..sup.3
+1.8731250.times.10.sup.4.times..theta..sup.2
-6.5277908.times.10.sup.5.times..theta.+7.5832595.times.10.sup.
6.+-.3).degree. [Formula 2]
However, it is desirable for the angle .theta. to be equal to or less than
35.1 degrees as mentioned above. The desirable range of cut angles can be
applied to a small quartz resonator having an X-side ratio of less than
15.
FIG. 7 shows a frequency-temperature characteristic at .theta.=34.5.degree.
for a quartz resonator having an X-side ratio of 10. The horizontal axis
indicates the temperature (in .degree. C.), and the vertical axis
indicates the frequency shift (in ppm) with the frequency at 25.degree. C.
serving as a standard. In FIG. 7, the solid curve indicates the
frequency-temperature characteristic when .phi.=12.degree., and the dotted
line indicates the temperature-frequency characteristic when .phi.=13.
As shown in FIG. 7, it was found that, when .theta.=34.5.degree. under the
condition that the X-side ratio is 10, good frequency-temperature
characteristics could not be obtained over the temperature range from
-25.degree. C. to +120.degree. C. for any value of .phi.. This is because
the inflection points are too high. Therefore, the .theta. area has 34.5
degrees as its lower limit. However, the condition .theta.=34.5 degrees is
not included. In other words, it is desirable that the range of 0 be:
34.6.degree..ltoreq..theta..ltoreq.35.1.degree. [Formula 6]
As described above, in the area where .phi.=-5.degree. to 15.9.degree., a
quartz resonating piece having a good temperature characteristic can be
provided. Similarly, the inventors conducted experiments for an area in
which .phi. is equal to or less than -5 degrees on the assumption that a
good temperature characteristic existed for this area. In FIG. 8,
frequency temperature characteristics in terms of cut angles for a quartz
resonator having an X-side ratio of 25.0, a Z-side ratio of 16.5, and a
principal vibration frequency of 21 MHz were measured. The dependence of
temperature characteristic on 0 was investigated when a rectangular blank
formed by rotation in the minus direction (counterclockwise when viewed
from the -Z direction to the +Z direction) by 10 degrees with the Z axis
as the center was rotated clockwise around the X' axis up to 34.0 degrees
to 35.5 degrees (.theta.=34.0.degree. to 35.5.degree.). The plate back
amount of the electrode was 2.0%.
In FIG. 8, the horizontal axis indicates the temperature (in .degree. C.),
and the vertical axis indicates the frequency shift (in ppm) with the
frequency at 25.degree. C. serving as a standard. As shown in FIG. 8, when
.phi.=-10' and .theta.=34.9.degree., a resonator having a variation width
of a frequency shift (with the frequency at a temperature of 25.degree. C.
serving as a standard) within 30 ppm in the temperature range from
-25.degree. C. to +120.degree. C. can be provided. Therefore, a quartz
device which can be used for a device that is used in a high temperature
range, such as an automobile part, can be provided without using a
temperature-compensating circuit. The inventors conducted research and
discovered that, in the frequency-temperature characteristic of the quartz
resonator shown in FIG. 8, when .theta. was deviated from 34.9 degrees by
an angle equal to or greater than 0.3 degrees, the temperature linear
coefficient became too large as indicated by an alternate long and short
dash line where .phi.=10.degree. and .theta.=34.6.degree., or a
characteristic close to that of a quadratic curve as indicated by a dotted
line where .phi.=-10.degree. and .theta.=35.2.degree. was obtained, so
that a satisfactory characteristic could not be obtained.
FIG. 9 shows cut angles (indicated by black dots) at which a variation
width of a frequency shift is within 30 ppm in the temperature range from
-25.degree. C. to +120.degree. C. for a quartz resonator having an X-side
ratio of 25.0, a Z-side ratio of 16.5, a plate back amount of 2.0%, and a
principal vibration frequency of 20 MHz. These pieces of experimental data
were found to exist on a functional curve indicated by a solid line.
Similarly, as previously mentioned, optimal values were extensively
searched by changing the X-side ratio from 10 to 80. From the results, it
was found that the optimal values existed at locations marked by triangles
in FIG. 9. In other words, the optimal values existed within an area
bounded by dotted lines on both sides of the solid line.
Therefore, for the quartz resonator having an X-side ratio of from 10 to
80, the relationship between .theta. .phi. that provides a good
frequency-temperature characteristic is determined by:
.theta..degree.=(-2.91652.times.10.sup.-3.times..phi..sup.2
+1.39515.times.10.sup.-4.phi.+35.1541.+-.0.2).degree. [Formula 3]
At this area, when the wideness of an area in which a good
frequency-temperature characteristic is obtained for variations in angles
is seen, since the central temperature is equal to or greater than
60.degree. C. when .phi. is equal to or less than -16.degree., the
frequency is considerably reduced in a low-temperature area. Therefore, it
is desirable that the lower limit of .phi. be -16.degree.. However, the
condition .phi.=16.degree. is not included. In other words, it is
desirable that the range of .phi. be:
-15.9.ltoreq..phi..ltoreq.-5.degree. [Formula 7]
Within the 0 area, satisfactory temperature characteristics could not be
obtained for any value of .phi. where .theta.=35.4.degree.. This is
because the 2nd order function curves characteristics are exhibited in the
temperature area under consideration. When .theta.=34.10.degree., good
frequency-temperature characteristics could not be obtained for any value
of .phi. over the temperature range from -25.degree. C. to +120.degree. C.
This is because the 1st order coefficient becomes too large. Therefore, it
is desirable that the .theta. area be:
34.2.degree..ltoreq..theta..ltoreq.35.3.degree. [Formula 8]
A quartz resonating piece (quartz vibrating piece) formed of the quartz
plate 12 provided by a cutting operation at cut angles set by what is
called double rotation as described above can be used as a quartz
resonator by sealing it in a package. FIGS. 10(1) and 10(2) show a quartz
resonator. FIG. 10(1) is a plan sectional view taken along plane B--B of
FIG. 10(2), and FIG. 10(2) is a side sectional view taken along plane A--A
of FIG. 10-1.
In FIGS. 10(1) and 10(2), in a quartz resonator 20, a package 22 is formed
of, for example, a ceramic material. The package 22 has a cavity 26 to
accommodate a quartz resonating piece 24. In the package 22, an electrode
30 and a terminal pad (not shown) are disposed on the bottom surface
defining the cavity 26, so that they can be brought into electrical
conduction with an external terminal (not shown) disposed on the back
surface of the package 22. The quartz resonating piece 24 is mounted in a
cantilever manner inside the cavity 26. More specifically, electrically
conductive adhesive 32 is applied to the electrode 30 and a connecting
electrode 34 of the quartz resonating piece 24 is disposed on top of the
adhesive 32 and secured to the electrode 30. By this, electrical
conduction to an excitation electrode 36 on the quartz resonating piece 24
can be achieved from the external terminal at the bottom surface of the
package 22. A cover 38 is sealed to the top portion of the package 22 in
order to maintain the atmosphere, such as a nitrogen atmosphere, inside
the package 22.
The quartz resonating piece of the exemplary embodiment can be used as a
piezoelectric oscillator by combining it with an integrated circuit
element and forming an oscillating circuit. For example, by mounting the
quartz resonator 20 shown in FIGS. 10(1) and 10(2) and an integrated
circuit element (not shown) onto a module substrate having a terminal pad,
a piezoelectric oscillator module can be formed. By sealing in the quartz
resonating piece 24 and the integrated circuit element inside the package
22 shown in FIGS. 10(1) and 10(2), a piezoelectric oscillator package can
be formed.
The quartz resonating piece of the present invention may have a flat shape
or a convex shape, or an inverted mesa structure in which the central
portion is recessed.
As described above, it is possible to stabilize the frequency
characteristic in a wide temperature range by using what is called
double-rotation cut angles.
*
