U.S. patent application number 14/295748 was filed with the patent office on 2014-09-25 for surface acoustic wave device, electronic apparatus, and sensor apparatus.
This patent application is currently assigned to Seiko Epson Corporation. The applicant listed for this patent is Seiko Epson Corporation. Invention is credited to Naohisa OBATA.
Application Number | 20140285063 14/295748 |
Document ID | / |
Family ID | 45817116 |
Filed Date | 2014-09-25 |
United States Patent
Application |
20140285063 |
Kind Code |
A1 |
OBATA; Naohisa |
September 25, 2014 |
SURFACE ACOUSTIC WAVE DEVICE, ELECTRONIC APPARATUS, AND SENSOR
APPARATUS
Abstract
A SAW device includes an IDT which is provided on the principal
surface of a quartz crystal substrate having Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
|.psi.|90.degree..times.n (where n=0, 1, 2, 3)) and excites a
Rayleigh wave (wavelength: .lamda.) in a stopband upper end mode.
Inter-electrode-finger grooves are recessed between electrode
fingers of the IDT. An IDT line occupancy .eta. and an
inter-electrode-finger groove depth G satisfy a predetermined
relationship in terms of the wavelength .lamda., such that the SAW
device has a frequency-temperature characteristic of a cubic curve
having an inflection point between a maximum value and a minimum
value in an operation temperature range. The inflection point is
adjustable to a desired temperature or a desired temperature range
depending on the IDT line occupancy .eta. within an operation
temperature range.
Inventors: |
OBATA; Naohisa; (Suwa,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Seiko Epson Corporation |
Tokyo |
|
JP |
|
|
Assignee: |
Seiko Epson Corporation
Tokyo
JP
|
Family ID: |
45817116 |
Appl. No.: |
14/295748 |
Filed: |
June 4, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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13223405 |
Sep 1, 2011 |
|
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14295748 |
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Current U.S.
Class: |
310/313A |
Current CPC
Class: |
H01L 41/04 20130101;
H03H 9/0542 20130101; H03H 9/02551 20130101; H03H 9/14594
20130101 |
Class at
Publication: |
310/313.A |
International
Class: |
H01L 41/04 20060101
H01L041/04 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 9, 2010 |
JP |
2010-201751 |
Claims
1. A surface acoustic wave device comprising: a quartz crystal
substrate having Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
|.psi.|.noteq.90.degree..times.n (where n=0, 1, 2, 3)); an IDT
which has a plurality of electrode fingers in the principal surface
of the quartz crystal substrate and excites a Rayleigh wave in a
stopband upper endmode, each of the plurality of electrode fingers
being separated by a groove having a trapezoidal cross-sectional
shape; and a pair of reflectors on opposing sides of the IDT,
wherein a frequency-temperature characteristic is expressed by a
curve having a maximum value, a minimum value, and an inflection
point between the maximum value and the minimum value, and the
temperature of the inflection point is adjustable depending on an
IDT line occupancy so as to be within a desired operation
temperature range.
2. A surface acoustic wave device comprising: a quartz crystal
substrate having Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
|.psi.|.noteq.90.degree..times.n (where n=0, 1, 2, 3)); and an IDT
which has a plurality of electrode fingers on the principal surface
of the quartz crystal substrate and excites a Rayleigh wave in a
stopband upper end mode, wherein inter-electrode-finger grooves
having a trapezoidal cross section shape are recessed in the
surface of the quartz crystal substrate between adjacent electrode
fingers of the IDT, the wavelength .lamda. of the Rayleigh wave and
the depth G of the inter-electrode-finger grooves satisfy
0.01.lamda..ltoreq.G.ltoreq.0.07.lamda., an IDT line occupancy
.eta. and the depth G of the inter-electrode-finger grooves satisfy
the following relationships:
-2.0000.times.G/.lamda.+0.7200.ltoreq..eta..ltoreq.-2.5000.times.G/.lamda-
.+0.7775 where 0.0100.lamda..ltoreq.G.ltoreq.0.0500.lamda.;
-3.5898.times.G/.lamda.+0.7995.ltoreq..eta..ltoreq.-2.5000.times.G/.lamda-
.+0.7775 where 0.0500.lamda..ltoreq.G.ltoreq.0.0695.lamda.; and a
frequency-temperature characteristic is expressed by a curve having
a maximumvalue, a minimumvalue, and an inflection point between the
maximum value and the minimum value, and the temperature of the
inflection point is adjustable depending on the IDT line occupancy
so as to be within a range of .+-.30.degree. C. from the center
temperature Tc of a desired operation temperature range.
3. The surface acoustic wave device according to claim 2, wherein
the IDT line occupancy .eta. satisfies the following relationship:
a(Tc-30).sup.6+b(Tc-30).sup.5+c(Tc-30).sup.4+d(Tc-30).sup.3+e(Tc-30).sup.-
2+f(Tc-30)+0.606.ltoreq..eta..ltoreq.a(Tc+30).sup.6+b(Tc+30).sup.5+c(Tc+30-
).sup.4+d(Tc+30).sup.3+e(Tc+30).sup.2+f(Tc+30)+0.606, (where
a=-2.60.times.10.sup.-12, b=4.84.times.10.sup.-10,
c=-2.13.times.10.sup.-8, d=1.98.times.10.sup.-7,
e=1.42.times.10.sup.-5, f=1.48.times.10.sup.-4).
4. The surface acoustic wave device according to claim 2, wherein
the Euler angle .psi. of the quartz crystal substrate is within a
range of 42.79.degree..ltoreq.|.psi.|.ltoreq.149.57.degree..
5. The surface acoustic wave device according to claim 2, wherein
the IDT line occupancy .eta. satisfies the following relationship:
.eta.=-1963.05.times.(G/.lamda.).sup.3+196.28.times.(G/.lamda.).sup.2-6.5-
3.times.(G/.lamda.)-135.99.times.(H/.lamda.).sup.2+5.817.times.(H/.lamda.)-
+0.732-99.99.times.(G/.lamda.).times.(H/.lamda.), where H is a
thickness of the electrode fingers.
6. The surface acoustic wave device according to claim 4, wherein
the IDT line occupancy .eta. satisfies the following relationship:
.eta.=-1963.05.times.(G/.lamda.).sup.3+196.28.times.(G/.lamda.).sup.26.53-
.times.(G/.lamda.)-135.99.times.(H/.lamda.).sup.2+5.817.times.(H/.lamda.)+-
0.732-99.99.times.(G/.lamda.).times.(H/.lamda.), where H is a
thickness of the electrode fingers.
7. The surface acoustic wave device according to claim 2, wherein
the sum of the depth G of the inter-electrode-finger groove and a
thickness H of the electrode fingers satisfies
0.0407.lamda..ltoreq.G+H.
8. The surface acoustic wave device according to claim 4, wherein
the sum of the depth G of the inter-electrode-finger grooves and a
thickness H of the electrode fingers satisfies
0.0407.lamda..ltoreq.G+H.
9. The surface acoustic wave device according to claim 5, wherein
the sum of the depth G of the inter-electrode-finger grooves and a
thickness H of the electrode fingers satisfies
0.0407.lamda..ltoreq.G+H.
10. The surface acoustic wave device according to claim 2, further
comprising: a pair of reflectors which respectively have a
plurality of conductor strips on the principal surface of the
quartz crystal substrate and are arranged on both sides of the IDT
with the IDT sandwiched therebetween along an SAW propagation
direction, wherein inter-conductor-strip grooves are recessed in
the surface of the quartz crystal substrate between adjacent
conductor strips of the reflectors, an angle between a first
direction perpendicular to the electrode fingers and the conductor
strips and the electrical axis of the quartz crystal substrate is
the Euler angle .psi. of the quartz crystal substrate, at least
apart of the IDT and the reflectors is arranged in a second
direction intersecting the first direction at an angle .delta., and
the angle .delta. is set to be within a power flow angle
.+-.1.degree. of the quartz crystal substrate.
11. The surface acoustic wave device according to claim 4, further
comprising: a pair of reflectors which respectively have a
plurality of conductor strips on the principal surface of the
quartz crystal substrate and are arranged on both sides of the IDT
with the IDT sandwiched therebetween along an SAW propagation
direction, wherein inter-conductor-strip grooves are recessed in
the surface of the quartz crystal substrate between adjacent
conductor strips of the reflectors, an angle between a first
direction perpendicular to the electrode fingers and the conductor
strips and the electrical axis of the quartz crystal substrate is
the Euler angle .psi. of the quartz crystal substrate, at least
apart of the IDT and the reflectors is arranged in a second
direction intersecting the first direction at an angle .delta., and
the angle .delta. is set to be within a range of a power flow angle
.+-.1.degree. of the quartz crystal substrate.
12. The surface acoustic wave device according to claim 5, further
comprising: a pair of reflectors which respectively have a
plurality of conductor strips on the principal surface of the
quartz crystal substrate and are arranged on both sides of the IDT
with the IDT sandwiched therebetween along an SAW propagation
direction, wherein inter-conductor-strip grooves are recessed in
the surface of the quartz crystal substrate between adjacent
conductor strips of the reflectors, an angle between a first
direction perpendicular to the electrode fingers and the conductor
strips and the electrical axis of the quartz crystal substrate is
the Euler angle .psi. of the quartz crystal substrate, at least
apart of the IDT and the reflectors is arranged in a second
direction intersecting the first direction at an angle .delta., and
the angle .delta. is set to be within a power flow angle
.+-.1.degree. of the quartz crystal substrate.
13. The surface acoustic wave device according to claim 6, further
comprising: a pair of reflectors which respectively have a
plurality of conductor strips on the principal surface of the
quartz crystal substrate and are arranged on both sides of the IDT
with the IDT sandwiched therebetween along an SAW propagation
direction, wherein inter-conductor-strip grooves are recessed in
the surface of the quartz crystal substrate between adjacent
conductor strips of the reflectors, an angle between a first
direction perpendicular to the electrode fingers and the conductor
strips and the electrical axis of the quartz crystal substrate is
the Euler angle .psi. of the quartz crystal substrate, at least
apart of the IDT and the reflectors is arranged in a second
direction intersecting the first direction at an angle .delta., and
the angle .delta. is set to be within a power flow angle
.+-.1.degree. of the quartz crystal substrate.
14. The surface acoustic wave device according to claim 1, further
comprising: an IC which drives the IDT.
15. An electronic apparatus comprising: the surface acoustic wave
device according to claim 1.
16. A sensor apparatus comprising: the surface acoustic wave device
according to claim 1.
17. The surface acoustic wave device according to claim 3, wherein
the Euler angle .psi. of the quartz crystal substrate is within a
range of 42.79.degree..ltoreq.|.psi.|.ltoreq.49.57.degree..
18. The surface acoustic wave device according to claim 3, wherein
the IDT line occupancy .eta. satisfies the following relationship:
.eta.=-1963.05.times.(G/.lamda.).sup.3+196.28.times.(G/.lamda.).sup.2-6.5-
3.times.(G/.lamda.)-135.99.times.(H/.lamda.).sup.2+5.817.times.(H/.lamda.)-
+0.732-99.99.times.(G/.lamda.).times.(H/.lamda.), where H is a
thickness of the electrode fingers.
19. The surface acoustic wave device according to claim 3, wherein
the sum of the depth G of the inter-electrode-finger groove and a
thickness H of the electrode fingers satisfies
0.0407.lamda..ltoreq.G+H.
20. The surface acoustic wave device according to claim 3, further
comprising: a pair of reflectors which respectively have a
plurality of conductor strips on the principal surface of the
quartz crystal substrate and are arranged on both sides of the IDT
with the IDT sandwiched therebetween along an SAW propagation
direction, wherein inter-conductor-strip grooves are recessed in
the surface of the quartz crystal substrate between adjacent
conductor strips of the reflectors, an angle between a first
direction perpendicular to the electrode fingers and the conductor
strips and the electrical axis of the quartz crystal substrate is
the Euler angle .psi. of the quartz crystal substrate, at least
apart of the IDT and the reflectors is arranged in a second
direction intersecting the first direction at an angle .delta., and
the angle .delta. is set to be within a power flow angle
.+-.1.degree. of the quartz crystal substrate.
21. The surface acoustic wave device according to claim 2, further
comprising: an IC which drives the IDT.
22. The surface acoustic wave device according to claim 3, further
comprising: an IC which drives the IDT.
23. An electronic apparatus comprising: the surface acoustic wave
device according to claim 2.
24. An electronic apparatus comprising: the surface acoustic wave
device according to claim 3.
25. A sensor apparatus comprising: the surface acoustic wave device
according to claim 2.
26. A sensor apparatus comprising: the surface acoustic wave device
according to claim 3.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 13/223,405 filed on Sep. 1, 2011. This
application claims the benefit of Japanese Patent Application No.
2010-201751 filed Sep. 9, 2010. The disclosures of the above
applications are incorporated herein by reference.
TECHNICAL FIELD
[0002] The present invention relates to a surface acoustic wave
device, such as a resonator or an oscillator using a surface
acoustic wave (SAW), and an electronic apparatus and a sensor
apparatus including the same.
RELATED ART
[0003] SAW devices are widely used in electronic apparatuses, such
as a mobile phone, a hard disk, a personal computer, a receiver
tuner of BS and CS broadcasts, an apparatus which processes a
high-frequency signal or an optical signal propagating through a
coaxial cable or an optical cable, a server network apparatus which
requires a high-frequency and high-precision clock (low jitter and
low phase noise) in a wide temperature range, and a wireless
communication apparatus, or various sensor apparatuses, such as a
pressure sensor, an acceleration sensor, and a rotational speed
sensor. In these apparatuses and devices, in particular, with the
realization of a high-frequency reference clock due to recent
high-speed performance of information communication or the
reduction in the size of the apparatus casing, there is an
increasing influence of heat generation inside the apparatus. For
this reason, with regard to an electronic device which is mounted
in the apparatus, expansion or high-precision performance of an
operation temperature range is required. A stable operation is
required over a long period in an environment in which there is a
severe change in the temperature from a low temperature to a high
temperature, like a wireless base station outdoors.
[0004] In general, in a SAW device, such as a SAW resonator, a
change in the frequency-temperature characteristic is significantly
influenced by the SAW stopband, the cut angle of a quartz crystal
substrate to be used, the form of an IDT (interdigital transducer)
formed on the substrate, or the like. For example, a reflection
inverting-type SAW converter is suggested in which an IDT having a
unit segment repeatedly arranged on a piezoelectric substrate is
provided, the unit segment having three electrode fingers per SAW
wavelength, and the upper mode and lower mode of the SAW stopband
are excited (for example, see Japanese Patent No. 3266846). If a
SAW filter is constituted by the reflection inverting-type SAW
converter, it is possible to realize a high attenuation amount in a
blocked band on a high-frequency band side near a passband.
[0005] A reflection inverting-type SAW converter is known in which
a so-called ST cut quartz crystal substrate having Euler angles
(.phi., .theta., .psi.)=(0.degree., 123.degree., 0.degree.) is used
(for example, see JP-A-2002-100959). JP-A-2002-100959 describes
that the resonance of the upper end of the stopband can be excited,
and the frequency-temperature characteristic is improved compared
to a case where the resonance of the lower end of the stopband is
used. It is reported that the upper end of the SAW stopband has a
satisfactory frequency-temperature characteristic compared to the
lower end of the stopband (for example, see JP-A-2006-148622,
JP-A-2007-208871, JP-A-2007-267033, and JP-A-2007-300287).
[0006] In particular, JP-A-2006-148622 and JP-A-2007-208871
describe a technique which adjusts the cut angle of the quartz
crystal substrate and thickens the standardized thickness
(H/.lamda.) of an IDT electrode to about 0.1 so as to obtain a
satisfactory frequency-temperature characteristic in a SAW device
using a Rayleigh wave. A SAW resonator described in
JP-A-2006-148622 has a single-type IDT electrode in which a unit
segment having two electrode fingers per SAW wavelength is
repeatedly arranged on a quartz crystal substrate having Euler
angles (.phi., .theta., .psi.)=(.phi.=0.degree.,
0.degree..ltoreq..theta..ltoreq.180 .degree.,
0.degree.<|.psi.|<90.degree.). Thus, the Rayleigh wave is
excited in the stopband upper limit mode, thereby realizing
high-frequency performance and a satisfactory frequency-temperature
characteristic of a SAW resonator.
[0007] JP-A-2007-208871 describes a technique which, in a SAW
device which has the single-type IDT electrode, sets a quartz
crystal substrate at Euler angles (.phi., .theta.,
.psi.)=(.phi.=0.degree.,
110.degree..ltoreq..theta..ltoreq.140.degree.,
38.degree..ltoreq.|.psi.|.ltoreq.44.degree.), and sets the
relationship between the standardized electrode thickness
(H/.lamda.) and the standardized electrode width .eta. (=d/P)
defined by the thickness H of the IDT electrode, the width d of an
electrode finger in the IDT electrode, the pitch P between
electrode fingers in the IDT electrode, and the SAW wavelength
.lamda. as follows.
H/.lamda..gtoreq.0.1796.eta..sup.3-0.4303.eta..sup.2+0.2071.eta.+0.0682
[0008] Thus, it is possible to strongly excite the Rayleigh wave in
the stopband upper limit mode.
[0009] JP-A-2007-267033 describes a SAW element in which a
single-type IDT electrode is arranged on a quartz crystal substrate
having Euler angles (.phi., .theta., .psi.)=(0.degree., .theta.,
9.degree.<|.psi.|<46.degree.), preferably, (0.degree.,
95.degree.<.theta.<155.degree.,
33.degree.<|.psi.|<46.degree., and the standardized electrode
thickness (H/.lamda.) is 0.045.ltoreq.H/.lamda..ltoreq.0.085. Thus,
the Rayleigh wave is excited in the stopband upper limit mode,
thereby realizing a satisfactory frequency-temperature
characteristic.
[0010] JP-A-2007-300287 describes a SAW element in which the
single-type IDT electrode is arranged on an in-plane rotation ST
cut quartz crystal substrate having Euler angles (.phi., .theta.,
.psi.)=(0.degree., 123.degree., 43.2.degree.), and the standardized
electrode thickness (H/.lamda.) is H/.lamda.=0.06, so-called 6%
.lamda., thereby exciting the Rayleigh wave in the stopband upper
limit mode. The SAW element sets the standardized electrode width
.eta. (=Lt/Pt) defined by the electrode finger width Lt of the IDT
electrode and the electrode finger pitch Pt to
0.5.ltoreq..eta..ltoreq.0.7, thereby realizing a frequency
deviation of maximum 830 ppm at normal temperature (25.degree.
C.).
[0011] A SAW resonator is also known in which grooves are formed in
the surface of a quartz crystal substrate between electrode fingers
constituting an IDT and between conductor strips constituting a
reflector (for example, see JP-B-2-7207 (JP-A-57-5418) and
Manufacturing Conditions and Characteristics of Groove-type SAW
Resonator (IECE, Technical Research Report MW82-59 (1982))).
JP-B-2-7207 (JP-A-57-5418) describes a SAW resonator in which an
IDT and a reflector are formed of aluminum electrodes on an ST cut
X-propagation quartz crystal substrate, and grooves are formed in
the corresponding regions between electrode fingers constituting
the IDT and between conductor strips (electrode fingers)
constituting the reflector, thereby realizing a high Q value, a low
capacitance ratio, and low resonance resistance. JP-B-2-7207
(JP-A-57-5418) describes a structure in which the groove of the IDT
and the groove of the reflector have the same depth and a structure
in which the groove of the reflector is greater in depth than the
groove of the IDT.
[0012] Manufacturing Conditions and Characteristics of Groove-type
SAW Resonator (Manufacturing Conditions and Characteristics of
Groove-type SAW Resonator (IECE, Technical Research Report MW82-59
(1982))) describes the characteristic of a groove-type SAW
resonator using an ST cut quartz crystal substrate. It has been
reported that the frequency-temperature characteristic changes
depending on the depth of the grooves formed in a quartz crystal
surface uncovered with the electrodes of the SAW propagation
substrate, and as the depth of the grooves increases, the peak
temperature Tp of an upward convex quadratic curve decreases.
[0013] A method which forms grooves in a piezoelectric substrate,
such as quartz crystal, to adjust an effective thickness and to
adjust a frequency is well known to those skilled in the art (for
example, see JP-A-2-189011, JP-A-5-90865, JP-A-1-231412, and
JP-A-61-92011). In a SAW device described in JP-A-2-189011, the
surface of the piezoelectric substrate having an IDT formed thereon
is etched under the condition that the etching rate of the
piezoelectric substrate is greater than the etching rate of the
IDT, and fine adjustment is performed to lower the frequency. In
JP-A-5-90865, JP-A-1-231412, and JP-A-61-92011, similarly, the
surface of a piezoelectric substrate is dry-etched with the IDT
formed thereon as a mask, such that the frequency of the SAW device
is shifted to a low-frequency band.
[0014] In a transversal SAW filter, a technique is known in which
the surface of a piezoelectric substrate between electrode fingers
of an IDT electrode is etched to form grooves, thereby reducing an
apparent propagation speed (for example, see JP-A-10-270974). Thus,
it is possible to make the electrode finger pitch of the IDT
electrode small without changing the preliminary design of the SAW
filter, thereby realizing reduction in size of a chip.
[0015] In a SAW resonator which excites a shear wave called an SSBW
(Surface Skimming Bulk Wave), it is known that an IDT electrode
having a standardized electrode thickness (H/.lamda.) of
2.01.ltoreq.H/.lamda..ltoreq.4.0% is formed of aluminum on a
rotation Y cut quartz crystal substrate in which a cut angle is
-43.degree. to -52.degree. and a shear wave propagation direction
is a Z'-axis direction (Euler angles (.phi., .theta.,
.psi.)=(0.degree., 38.ltoreq..theta..ltoreq.47, 90.degree.)),
thereby realizing a frequency-temperature characteristic of a cubic
curve (for example, see JP-B-1-34411). A shear wave (SH wave)
propagates directly below the surface of the piezoelectric
substrate in a state where vibration energy is confined directly
below the electrode. Thus, the reflection efficiency of the SAW by
the reflector is unsatisfactory compared to an ST cut quartz
crystal SAW device in which a SAW propagates along the substrate
surface, making it difficult to realize reduction in size and a
high Q value.
[0016] In order to solve this problem, a SAW device is suggested in
which an IDT and a grating reflector are formed in the surface of a
rotation Y cut quartz crystal substrate having Euler angles (.phi.,
.theta., .psi.)=(0.degree.,
-64.degree.<.theta.<-49.3.degree.,
85.degree..ltoreq..psi..ltoreq.95.degree.) to excite an SH wave
(for example, see International Publication No. WO2005/099089A1).
The SAW device sets the electrode thickness H/.lamda. standardized
with the SAW wavelength .lamda. to 0.04<H/.lamda.<0.12,
thereby realizing reduction in size, a high Q value, and excellent
frequency stability.
[0017] In such a SAW device, in order to solve a problem in that
the Q value or frequency stability is deteriorated due to stress
migration caused by a large electrode thickness, a technique is
suggested in which grooves are formed in the quartz crystal
substrate between the electrode fingers of the IDT (for example,
see JP-A-2006-203408). When the depth of the grooves is Hp and the
thickness of a metal film of the IDT is Hm, the electrode thickness
H/.lamda. standardized with the SAW wavelength .lamda. is set to
0.04<H/.lamda.<0.12 (where H=Hp+Hm), such that the apparent
thickness of the metal film can be made small. Thus, it is possible
to suppress a frequency fluctuation due to stress migration at the
time of electrical conduction, thereby realizing a SAW device
having a high Q value and excellent frequency stability.
[0018] During the mass production of SAW devices, when electrode
fingers of an IDT are formed in the surface of a quartz crystal
substrate by etching, if the thickness of the electrode fingers is
large, a variation is likely to occur in the line occupancy (line
space ratio) .eta. of the IDT due to side etching. As a result, if
a variation occurs in the frequency fluctuation with a change in
the temperature of the SAW device, product reliability and quality
are damaged. In order to solve this problem, a SAW device is known
in which an in-plane rotation ST cut quartz crystal substrate
having Euler angles (.phi., .theta., .omega.)=(0.degree.,
95.degree..ltoreq..theta..ltoreq.155.degree.,
33.degree..ltoreq.|.psi.|.ltoreq.46.degree.) is used, a SAW
stopband upper limit mode is excited, and inter-electrode-finger
grooves are formed in the surface of the quartz crystal substrate
between electrode fingers of an IDT (for example, see
JP-A-2009-225420).
[0019] When the frequency-temperature characteristic of the SAW
device is a quadratic curve in the operation temperature range, it
is difficult to realize minimization of a frequency fluctuation
range or an inflection point. Accordingly, a SAW device is
suggested in which, in order to obtain a frequency-temperature
characteristic of a cubic curve, an IDT electrode is formed on an
LST cut quartz crystal substrate through a void layer and a
dielectric film to excite a leaky SAW (for example, see Japanese
Patent No. 3851336). Japanese Patent No. 3851336 describes that, in
a SAW device using a Rayleigh wave, a quartz crystal substrate
having a cut angle such that a frequency-temperature characteristic
expressed by a cubit curve is realized could not be found.
[0020] In an ST cut quartz crystal SAW resonator or the like, in
order to increase the Q value without deteriorating an excellent
frequency-temperature characteristic, an inclined IDT is known in
which an IDT and a reflector are arranged on the surface of a
quartz crystal substrate to be inclined at a power flow angle
PFA.+-.3.degree. with respect to a SAW phase velocity direction
(for example, see Japanese Patent No. 3216137 and
JP-A-2005-204275). In the SAW device having the inclined IDT, the
IDT and the reflector are arranged so as to cover a SAW phase
direction and a vibration energy direction, such that the SAW can
be efficiently reflected by the reflector. Thus, it is possible to
efficiently perform energy confinement and to further increase the
Q value.
[0021] As described above, many elements are related to the
frequency-temperature characteristic of the SAW device, and various
studies are conducted for improvement. In particular, in a SAW
using a Rayleigh wave, it is considered that an increase in the
thickness of the electrode fingers constituting the IDT contributes
to the improvement of the frequency-temperature characteristic. If
the electrode thickness of the IDT simply increases, there is a
problem in that deterioration in frequency stability or the like
occurs due to stress migration at the time of electrical conduction
or side etching at the time of IDT formation. As a countermeasure,
grooves are formed between the electrode fingers of the IDT in the
surface of the quartz crystal substrate, and it is effective to
suppress a frequency fluctuation by increasing the effective
thickness while making the electrode thickness small.
[0022] However, in all the SAW devices, excluding the SAW device
described in JP-B-1-34411 which excites a leaky SAW, the
frequency-temperature characteristic in the operation temperature
range is expressed by a quadratic curve, it is not difficult to
sufficiently reduce a frequency fluctuation range or to realize an
inflection point. For this reason, it may be impossible to
sufficiently cope with recent requirements for a SAW device, such
as expansion or high-precision performance of an operation
temperature range, long-term operation stability in an environment
in which temperature undergoes severe changes, and the like.
[0023] The present invention is made by considering the
above-described problems, and the object thereof is to provide a
SAW device, such as a resonator or an oscillator, capable of
exhibiting an excellent frequency-temperature characteristic with a
very small frequency fluctuation in an operation temperature range,
having an excellent environment-resistant characteristic ensuring a
stable operation even in an environment in which a temperature
varies extremely, and realizing a high Q value.
SUMMARY
[0024] With regard to a SAW resonator in which an in-plane rotation
ST cut quartz crystal substrate is used, an IDT which excites a SAW
in a stopband upper end mode is formed on the surface of the quartz
crystal substrate, and the surface of the quartz crystal substrate
between electrode fingers constituting the IDT is recessed to form
grooves, the inventors have verified the relationship between
parameters, such as the wavelength .lamda. of the SAW, the depth G
of the grooves, the electrode thickness H of the IDT, and the line
occupancy .eta. of the electrode fingers, and the
frequency-temperature characteristic. As a result, the inventors
have devised a novel SAW resonator which can realize minimization
of a frequency fluctuation range and an inflection point in the
operation temperature range.
[0025] A SAW resonator according to a new embodiment (hereinafter,
referred to as a SAW resonator of this embodiment) includes an IDT
which is provided on a quartz crystal substrate having Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.ltoreq..theta..ltoreq.142.degree.,
42.79.degree..ltoreq.|.psi.|.ltoreq.49.57.degree.), and excites a
SAW in a stopband upper end mode. The quartz crystal substrate
between electrode fingers constituting the IDT is depressed to form
inter-electrode-finger grooves. When the wavelength of the SAW is
.lamda., and the depth of the inter-electrode-finger groove is G,
the relationship 0.01.lamda..ltoreq.G is satisfied. When the line
occupancy of the IDT is .eta., the depth G of the
inter-electrode-finger grooves and the line occupancy .eta. satisfy
the following relationships.
[Equation 1]
-2.0000.times.G/.lamda.+0.7200.ltoreq..eta..ltoreq.-2.5000.times.G/.lamd-
a.+0.7775 where 0.0100.lamda..ltoreq.G.ltoreq.0.0500.lamda. (1)
[Equation 2]
-3.5898.times.G/.lamda.+0.7995.ltoreq..eta..ltoreq.-2.5000.times.G/.lamd-
a.+0.7775 where 0.0500.lamda..ltoreq.G.ltoreq.0.0695.lamda. (2)
[0026] In the SAW resonator of this embodiment, the depth G of the
inter-electrode-finger grooves may satisfy the relationship
0.01.lamda..ltoreq.G.ltoreq.0.0695.lamda.. If the depth G of the
inter-electrode-finger grooves is set within this range, it is
possible to suppress a frequency fluctuation in an operation
temperature range (for example, -40.degree. C. to +85.degree. C.)
to be very small, and even when a manufacturing variation occurs in
the depth of the inter-electrode-finger grooves, it is possible to
suppress the shift amount of a resonance frequency between
individual SAW resonators within a correctable range.
[0027] In the SAW resonator of this embodiment, when the electrode
thickness of the IDT is H, the relationship
0<H.ltoreq.0.035.lamda. may be satisfied. Therefore, a
satisfactory frequency-temperature characteristic in an operation
temperature range is realized, and deterioration in an
environment-resistant characteristic which may occur when the
electrode thickness is large is prevented.
[0028] In the SAW resonator of this embodiment, the line occupancy
.eta. may satisfy the following relationship.
[Equation 3]
.eta.=-1963.05.times.(G/.lamda.).sup.3+196.28.times.(G/.lamda.).sup.2-6.-
53.times.(G/.lamda.)-135.99.times.(H/.lamda.).sup.2+5.817.times.(H/.lamda.-
)+0.732-99.99.times.(G/.lamda.).times.(H/.lamda.) (3)
[0029] Therefore, it is possible to suppress a secondary
temperature coefficient of the frequency-temperature characteristic
to be small.
[0030] In the SAW resonator of this embodiment, the sum of the
depth G of the inter-electrode-finger grooves and the electrode
thickness H may satisfy the relationship 0.0407.lamda..ltoreq.G+H.
Therefore, a high Q value is obtained compared to the related art
which uses resonance in a stopband lower end mode with no grooves
between electrode fingers.
[0031] FIG. 1(A) to (D) show an example of a SAW resonator of this
embodiment. As shown in FIG. 1(A), a SAW resonator 1 of this
embodiment has a rectangular quartz crystal substrate 2, and an IDT
3 and a pair of reflectors 4 and 4 which are formed on the
principal surface of the quartz crystal substrate.
[0032] For the quartz crystal substrate 2, an in-plane rotation ST
cut quartz crystal substrate which is expressed by Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
42.79.degree..ltoreq..theta.|.psi.|.ltoreq.149.57.degree.) is used.
Here, the Euler angles will be described. A substrate which is
expressed by Euler angles (0.degree., 0.degree., 0.degree.) becomes
a Z cut substrate which has a principal surface perpendicular to
the Z axis. Of the Euler angles (.phi., .theta., .psi.), .phi.
relates to the first rotation of the Z cut substrate, and is a
first rotation angle with the Z axis as a rotation axis. The
rotation direction from the +X axis to the +Y axis is defined as a
positive rotation angle. Of the Euler angles, .theta. relates to
the second rotation after the first rotation of the Z cut
substrate, and is a second rotation angle with the X axis after the
first rotation as a rotation axis. The rotation direction from the
+Y axis after the first rotation to the +Z axis is defined as a
positive rotation angle. The cut plane of the piezoelectric
substrate is determined by the first rotation angle .phi. and the
second rotation angle .theta.. Of the Euler angles, .psi. relates
to the third rotation after the second rotation of the Z cut
substrate, and is a third rotation angle with the Z axis after the
second rotation as a rotation axis. The rotation direction from the
+X axis after the second rotation to the +Y axis after the second
rotation is defined as a positive rotation angle. The SAW
propagation direction is expressed by the third rotation angle
.psi. with respect to the X axis after the second rotation.
[0033] As shown in FIG. 2, when three crystal axes perpendicular to
quartz crystal, that is, an electrical axis, a mechanical axis, and
an optical axis are respectively expressed by the X axis, the Y
axis, and the Z axis, the in-plane rotation ST cut quartz crystal
substrate is cut from a wafer 5 which has an XZ' plane
perpendicular to the Y' axis of the coordinate axes (X, Y', Z')
obtained by rotating an XZ plane 5a perpendicular to the Y axis at
an angle .theta.' (.degree.) from the +Z axis to the -Y axis with
the X axis as a rotation axis. The quartz crystal substrate 2 is
cut and individualized from the wafer 5 along new coordinate axes
(X', Y', Z'') at an angle +.psi. (or -.psi.) (.degree.) from the +X
axis to the +Z' axis with the Y' axis as a rotation axis. The
direction from the +X axis to the +Z' axis is defined as positive.
At this time, the long side (or short side) of the quartz crystal
substrate 2 may be arranged along either the X'-axis direction or
the Z''-axis direction. The angle .theta.' and .theta. of the Euler
angles satisfy the relationship .theta.'=.theta.-90.degree..
[0034] An IDT 3 has a pair of interdigital transducers 3a and 3b
which respectively have a plurality of electrode fingers 6a and 6b,
and bus bars 7a and 7b connecting the base portions of the
electrode fingers together. The electrode fingers 6a and 6b are
arranged such that the extension direction thereof is perpendicular
to the propagation direction X' of the SAW which is excited by the
IDT. The electrode fingers 6a of the interdigital transducer 3a and
the electrode fingers 6b of the interdigital transducer 3b are
arranged with a given pitch alternately and at a predetermined
interval. As shown in FIG. 1(B), inter-electrode-finger grooves 8
having a given depth are recessed in the surface of the quartz
crystal substrate 2 which is exposed between the electrode fingers
6a and 6b by removing the surface through etching or the like.
[0035] A pair of reflectors 4 and 4 are arranged outside the IDT 3
with the IDT sandwiched therebetween along the SAW propagation
direction X'. The reflectors 4 respectively have a plurality of
conductor strips 4a and 4a arranged with a given pitch in the SAW
propagation direction X'. Similarly to the electrode fingers of the
IDT 3, the conductor strips are arranged such that the extension
direction thereof is perpendicular to the SAW propagation direction
X'. As shown in FIG. 1(B), inter-conductor-strip grooves 9 having a
given depth are recessed in the surface of the quartz crystal
substrate 2 which is exposed between the conductor strips 4a and 4a
by removing the surface through etching or the like.
[0036] In this embodiment, the electrode fingers 6a and 6b and the
conductor strips 4a and 4a are formed of a metal film using, for
example, Al or an alloy mainly containing Al to have the same
thickness H, and may be collectively referred to as electrode
fingers. The inter-electrode-finger grooves 8 and the
inter-conductor-strip grooves 9 are formed to have the same depth
G. Grooves are recessed between the outermost electrode fingers 6a
(or 6b) of the IDT 3 and the conductor strips 4a and 4a of the
reflectors 4 and 4 adjacent to the electrode fingers by removing
the surface of the quartz crystal substrate to have the same depth
as the inter-conductor-strip grooves.
[0037] The SAW resonator 1 configured as above excites a
Rayleigh-type SAW which has vibration displacement components in
both the X'-axis direction and the Y'-axis direction of the quartz
crystal substrate 2. In the quartz crystal substrate 2 having the
above-described Euler angles, the SAW propagation direction is
shifted from the X axis serving as the crystal axis of quartz
crystal, making it possible to excite the SAW in the stopband upper
end mode.
[0038] The Euler angles (.phi., .theta., .psi.) of the quartz
crystal substrate 2 were selected as follow. In general, the
frequency-temperature characteristic of the SAW resonator is
expressed by the following expression.
.DELTA.f=.alpha..times.(T-T0)+.beta..times.(T-T0).sup.2
[0039] Here, .DELTA.f is a frequency change amount (ppm) between a
temperature T and a peak temperature T0, .alpha. is a primary
temperature coefficient (ppm/.degree. C.), .beta. is a secondary
temperature coefficient (ppm/.degree. C..sup.2), T is a
temperature, and T0 is a temperature (peak temperature) at which a
frequency is maximum. The absolute value of the secondary
temperature coefficient .beta. is set to be minimum, preferably,
equal to or smaller than 0.01 (ppm/.degree. C..sup.2), and more
preferably, substantially zero, such that a frequency-temperature
characteristic shows a cubic curve, a frequency fluctuation becomes
small even in a wide operation temperature range, thereby obtaining
high frequency stability.
[0040] First, the Euler angles of the quartz crystal substrate 2
were set to (0.degree., 123.degree., .psi.), and the relationship
between the Euler angle .psi. and the depth G of the
inter-electrode-finger grooves when the line occupancy .eta.
resulting in .beta.=.+-.0.01 (ppm/.degree. C..sup.2) has been
obtained was simulated. The Euler angle .psi. was appropriately
selected such that the absolute value of the secondary temperature
coefficient .beta. became 0.01 (ppm/.degree. C..sup.2). As a
result, the range of the Euler angle .psi. for obtaining the
secondary temperature coefficient .beta. of
-0.01.ltoreq..beta..ltoreq.+0.01 under the above-described
condition could be determined to
43.degree.<.psi.<45.degree..
[0041] As shown in FIG. 1(C), the line occupancy .eta. of the IDT 3
is a value obtained by dividing an electrode finger width L by an
electrode finger pitch .lamda./2(=L+S). FIG. 1(D) illustrates a
method of specifying the line occupancy .eta. of the IDT 3 in a
trapezoidal cross-section which will be formed when the electrode
fingers 6a and 6b of the IDT 3 and the inter-electrode-finger
grooves 8 are manufactured by a photolithography technique and an
etching technique. In this case, the line occupancy .eta. is
calculated on the basis of the electrode finger width L and an
inter-electrode-finger groove width S measured at a height half the
sum (G+H) of the depth G of the inter-electrode-finger grooves from
the bottom of the inter-electrode-finger grooves 8 and the
electrode thickness H.
[0042] Next, when the cut angle and the quartz crystal substrate 2
and the SAW propagation direction were (0,.theta.,.psi.) in the
Euler angle expression, the depth G of the inter-electrode-finger
grooves was 0.04.lamda., the thickness H of the electrode fingers
was 0.02.lamda., and the line occupancy .eta. was 0.6383 by
Expression (3), changes in the secondary temperature coefficient
.beta. depending on the Euler angle .theta. were simulated. The
Euler angle .psi. was appropriately selected in the above-described
range 43.degree.<.psi.<45.degree. such that the absolute
value of the secondary temperature coefficient .beta. was minimum
on the basis of the set angle of the angle .theta.. As a result, if
the Euler angle .theta. was within the range of
117.degree..ltoreq..theta..ltoreq.142.degree., it was confirmed
that, even when the thickness H of the electrode fingers, the depth
G of the inter-electrode-finger grooves, and the line occupancy
.eta. were changed, the absolute value of the secondary temperature
coefficient .beta. was within the range of 0.01 (ppm/.degree.
C..sup.2).
[0043] Next, the quartz crystal substrate 2 was (.phi.,
123.degree., 43.77.degree.) in the Euler angle expression, the
depth G of the inter-electrode-finger grooves was 0.04.lamda., the
thickness H of the electrode fingers was 0.02.lamda., and the line
occupancy .eta. was 0.65, changes of the secondary temperature
coefficient .beta. depending on the Euler angle .phi. were
simulated. As a result, if the Euler angle .phi. was within the
range of -1.5.degree..ltoreq..phi..ltoreq.+1.5.degree., it was
confirmed that the absolute value of the secondary temperature
coefficient .beta. was within the range of 0.01 (ppm/.degree.
C..sup.2).
[0044] A highly desirable relationship between the Euler angles
.beta. and .psi. such that a frequency fluctuation was minimum in
an operation temperature range (-40.degree. C. to +85.degree. C.)
was obtained by a simulation. In this case, the depth G of the
inter-electrode-finger grooves and the thickness H of the electrode
fingers were respectively G=0.04.lamda. and H=0.02.lamda.. As a
result, the Euler angle .psi. increased within the above-described
range of the Euler angle .theta. such that a cubic curve was drawn
with an increase in the Euler angle .psi.. This relationship can be
approximated by the following expression.
.psi.=1.19024.times.10.sup.-3.times..theta..sup.3-4.48775.times.10.sup.--
1.times..theta..sup.2+5.64362.times.10.sup.1.times..theta.-2.32327.times.1-
0.sup.3.+-.1.0 [Equation 4]
[0045] Thus, the Euler angle .psi. becomes .psi.=42.79.degree. with
respect to the lower limit value .theta.=117.degree. of the Euler
angle .theta., and .psi.=49.57.degree. with respect to the upper
limit value .theta.=142.degree. of the Euler angle .theta..
Therefore, the Euler angle .psi. can be set to 42.79
.degree..ltoreq..psi..ltoreq.49.57.degree. within the range of
117.degree..ltoreq..theta..ltoreq.142.degree..
[0046] If the Euler angles of the quartz crystal substrate 2 are
set in the above-described manner, the SAW resonator 1 of this
embodiment can realize an excellent frequency-temperature
characteristic in which the absolute value of the secondary
temperature coefficient .beta. is equal to or smaller than 0.01
(ppm/.degree. C..sup.2).
[0047] With regard to the SAW resonator 1 of this embodiment, a
frequency-temperature characteristic was simulated under the
following conditions.
Basic data of SAW resonator 1 of this embodiment
H: 0.02.lamda.
[0048] G: change IDT line occupancy .eta.: 0.6 Reflector line
occupancy .eta.r: 0.8 Euler angles: (0.degree., 123.degree.,
43.5.degree.) Number of pairs of IDT: 120 Electrode finger cross
width: 40.lamda. (.lamda.=10 .mu.m) Number of reflectors (per
side): 60 Inclination angle of electrode fingers: none
[0049] The simulation result is shown in FIG. 3. As will be
understood from FIG. 3, the frequency-temperature characteristic
substantially shows a cubic curve in the operation temperature
range (-40 to +85.degree. C.), and the frequency fluctuation range
can be suppressed with a very small fluctuation within 20 ppm.
[0050] With regard to the SAW resonator 1 showing the
frequency-temperature characteristic of FIG. 3, if the frequency,
the equivalent circuit constant, and the static characteristic are
put together, Table 1 is obtained.
TABLE-US-00001 TABLE 1 F (MHz) Q .gamma. CI (.OMEGA.) M AVG 318.25
13285 2476 21.8 5.4
[0051] Here, F is a frequency, Q is a Q value, .gamma. is a
capacitance ratio, CI is a CI (Crystal Impedance) value, and M is a
figure of merit.
[0052] The SAW resonator 1 is preferably set such that the
frequency ft2 of the stopband upper end of the IDT 3, the frequency
fr1 of the stopband lower end of the reflector 4, and the frequency
fr2 of the stopband upper end of the reflector 4 satisfy the
relationship fr1<ft2<fr2. FIG. 4 shows the SAW reflection
characteristics of the IDT 3 and the reflector 4 depending on the
frequency. As shown in FIG. 4, if the frequency ft2 is set between
the frequency fr1 and the frequency fr2, the reflection coefficient
of the reflector 4 becomes larger than the reflection coefficient
of the IDT 3 at the frequency ft2. As a result, the SAW in the
stopband upper end mode excited from the IDT 3 is reflected from
the reflector 4 to the IDT with a higher reflection coefficient.
Therefore, the vibration energy of the SAW can be efficiently
confined, thereby realizing a low-loss SAW resonator 1.
[0053] The relationship between the Q value of the SAW resonator 1
and the magnitude (G+H) of a step formed by the height, that is,
thickness H of the electrode fingers 6a and 6b and the depth G of
the inter-electrode-finger grooves 8 was verified by a simulation.
For comparison, with regard to a SAW resonator of the related art
in which no grooves are formed between the electrode fingers and
resonance in the stopband upper end mode is used, the relationship
between the Q value and the height, that is, thickness of the
electrode fingers was simulated under the following conditions.
[0054] Basic data of SAW resonator of the related art
H: change G: zero (none) IDT line occupancy .eta.: 0.4 Reflector
line occupancy .eta.r: 0.3 Euler angles (0.degree., 123.degree.,
43.5.degree.) Number of pairs of IDT: 120 Electrode finger cross
width: 40.lamda. (.lamda.=10 .mu.m) Number of reflectors (per
side): 60 Inclination angle of electrode fingers: none
[0055] The simulation result is shown in FIG. 5. In FIG. 5, a bold
line indicates the SAW resonator 1 of this embodiment, and a thin
line indicates the SAW resonator of the related art. As will be
understood from FIG. 5, in the SAW resonator 1 of this embodiment,
a high Q value can be obtained in a region where the step (G+H) is
equal to or greater than 0.0407.lamda. (4.07%.lamda.), compared to
the SAW resonator of the related art.
[0056] On the other hand, in the SAW resonator of this embodiment,
it was ascertained that a variation in the frequency-temperature
characteristic occurred between individuals. As described above, in
this embodiment, an excellent frequency-temperature characteristic
of a cubic curve is realized with the SAW wavelength .lamda., the
depth G of the inter-electrode-finger grooves, and the IDT line
occupancy .eta., and the electrode finger thickness H as
parameters. Thus, the inventors have considered that manufacturing
errors in the parameters have no influence on a variation in the
frequency-temperature characteristic, and have verified the
relationship.
[0057] At the time of the mass production of SAW devices, in
general, the electrode fingers of the IDT are formed by
photoetching an electrode film, but it is postulated that the line
width L has normally a manufacturing error of about 0.5%. In this
case, it is considered that the IDT line occupancy .eta. has a
manufacturing variation at the same level. On the basis of the
postulation, in the SAW resonator 1 of FIG. 1, when the electrode
finger thickness is H=2%.lamda., the groove depth is G=3.5%.lamda.,
the IDT line occupancy is .eta.=0.63 (=63%), and when the
parameters are shifted by .+-.0.005 (=.+-.0.5%), the
frequency-temperature characteristics were calculated by
simulations. FIG. 6 shows the results.
[0058] In both cases, the frequency-temperature characteristic is
expressed by a cubic curve having a maximum value, a minimum value,
and an inflection point between the maximum value and the minimum
value in a use temperature range. When .eta.=0.63 (solid line), an
exceptional frequency-temperature characteristic was shown in which
the frequency fluctuation in the use temperature range (-40.degree.
C. to +85.degree. C.) was within .+-.5 ppm, and the position of the
inflection point, that is, the inflection-point temperature was
substantially the center of the use temperature range and
substantially rotationally symmetric. Meanwhile, when .eta.=0.625
(fine broken line) and 0.635 (large broken line), it is understood
that the frequency-temperature characteristic is deteriorated in
which a frequency fluctuation increases to be equal to or greater
than .+-.5 ppm in the use temperature range, and the
inflection-point temperature is significantly shifted to the
low-temperature side or the high-temperature side and rotationally
asymmetric.
[0059] Next, the inventors have verified an influence of a change
in an inflection-point temperature on a frequency fluctuation in a
frequency-temperature characteristic. FIG. 7 shows the relationship
between a change amount in the inflection-point temperature and a
deviation in the frequency fluctuation when .eta.=0.63 of FIG. 6.
From FIG. 7, it is understood that, if the inflection-point
temperature changes, a deviation in the frequency fluctuation
increases, affecting the frequency-temperature characteristic.
[0060] The inventors have verified an influence of a change in the
depth G of the inter-electrode-finger grooves relating to the
electrode finger thickness H on a change amount in the
inflection-point temperature due to a variation (.+-.0.005) in the
IDT line occupancy .eta., that is, the frequency-temperature
characteristic. In this specification, it is assumed that a change
amount in the inflection-point temperature due to a variation in
the IDT line occupancy .eta. is called inflection-point sensitivity
as an index representing the influence on the frequency-temperature
characteristic.
[0061] First, in the SAW resonator 1 of FIG. 1, when the Euler
angles of the quartz crystal substrate 2 are set to (0.degree.,
123.degree., .psi.), the electrode finger thickness H is fixed to
1% .lamda., and the inter-electrode-finger groove depth G changes
by 1% .lamda. in a range of 2% .lamda. to 7% .lamda., the
relationship between the IDT line occupancy .eta. such that the
secondary temperature coefficient .beta. of the
frequency-temperature characteristic is equal to or smaller than
0.01 and the inflection-point sensitivity due to a variation of
.+-.0.005 in the .eta. value was calculated by a simulation. The
result is shown in FIG. 8. As will be understood from FIG. 8, in
both cases, as .eta. increases, the inflection-point sensitivity
decreases, such that the influence on the frequency-temperature
characteristic is reduced.
[0062] Next, when the electrode finger thickness H is fixed to 1.5%
.lamda., and the groove depth G changes by 1% .lamda. in a range of
2% .lamda. to 7% .lamda., the relationship between the IDT line
occupancy .eta. such that the secondary temperature coefficient
.beta. of the frequency-temperature characteristic is equal to or
smaller than 0.01 and the inflection-point sensitivity due to a
variation of .+-.0.005 in the .eta. value was calculated by a
simulation under the same conditions as in FIG. 8. The result is
shown in FIG. 9. From FIG. 9, it is understood that, in both cases,
as .eta. increases, the inflection-point sensitivity decreases,
such that the influence on the frequency-temperature characteristic
is reduced.
[0063] FIG. 10 is a plot diagram of a change in the
inflection-point temperature relating to the IDT line occupancy
.eta. in the simulation result of FIG. 8. FIG. 10 shows that, as
.eta. increases, the change rate of the inflection-point
temperature increases.
[0064] In general, in an AT cut quartz crystal vibrator of a
thickness-shear vibration mode, it is known that the inflection
point of the frequency-temperature characteristic is preferably
determined only by the cut angle of the quartz crystal substrate
and does not change depending on other parameters. Meanwhile, in a
SAW device, it is not obvious how much the parameters other than
the cut angle of the quartz crystal substrate affect the
frequency-temperature characteristic and the inflection-point
temperature.
[0065] Accordingly, the inventors have verified the influence of
the relationship between the IDT line occupancy .eta., the
electrode thickness H of the IDT 3 and the inter-electrode-finger
groove depth G, and the relationship therebetween on the
frequency-temperature characteristic and the inflection-point
sensitivity in the SAW resonator 1 of this embodiment. As a result,
the inventors have found that the inflection-point temperature of
the frequency-temperature characteristic may be optimally
adjustable in the operation temperature range depending on the IDT
line occupancy while maintaining a satisfactory
frequency-temperature characteristic. The inventors have devised
the invention on the basis of the findings.
[0066] A SAW device according to an aspect of the invention
includes a quartz crystal substrate having Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
|.psi.|.noteq.90.degree..times.n (where n=0, 1, 2, 3)), and
[0067] an IDT which has a plurality of electrode fingers in the
principal surface of the quartz crystal substrate and excites a
Rayleigh wave in a stopband upper end mode.
[0068] A frequency-temperature characteristic is expressed by a
curve having a maximum value, a minimum value, and an inflection
point between the maximum value and the minimum value, and the
temperature of the inflection point is adjustable depending on an
IDT line occupancy so as to be within a desired operation
temperature range.
[0069] With this configuration, the frequency-temperature
characteristic controls the inflection point to a desired
temperature or a desired temperature region within the operation
temperature range depending on the IDT line occupancy .eta.,
thereby improving a frequency fluctuation to be smaller. Therefore,
it is possible to constantly obtain an optimum
frequency-temperature characteristic in the required operation
temperature range of the SAW device.
[0070] A SAW device according to another aspect of the invention
includes a quartz crystal substrate having Euler angles
(-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
|.psi.|.noteq.90.degree..times.n (where n=0, 1, 2, 3)), and
[0071] an IDT which has a plurality of electrode fingers in the
principal surface of the quartz crystal substrate and excites a
Rayleigh wave in a stopband upper end mode.
[0072] Inter-electrode-finger grooves are recessed in the surface
of the piezoelectric substrate between adjacent electrode fingers
of the IDT.
[0073] The wavelength .lamda. of the Rayleigh wave and the depth G
of the inter-electrode-finger grooves satisfy the relationship
0.01.lamda..ltoreq.G.ltoreq.0.07.lamda.. The line occupancy .eta.
of the IDT and the depth G of the inter-electrode-finger grooves
satisfy the following relationships.
-2.0000.times.G/.lamda.+0.7200.ltoreq..eta..ltoreq.-2.5000.times.G/.lamd-
a.+0.7775 where 0.0100.lamda..ltoreq.G.ltoreq.0.0500.lamda.
[Equation 5]
-3.5898.times.G/.lamda.+0.7995.ltoreq..eta..ltoreq.-2.5000.times.G/.lamd-
a.+0.7775 where 0.0500.lamda..ltoreq.G.ltoreq.0.0695.lamda.
[Equation 6]
[0074] A frequency-temperature characteristic is expressed by a
curve having a maximum value, a minimum value, and an inflection
point between the maximum value and the minimum value, and the
temperature of the inflection point is adjustable depending on the
IDT line occupancy so as to be within a range of .+-.30.degree. C.
from the center temperature Tc of a desired operation temperature
range.
[0075] In a satisfactory frequency-temperature characteristic which
is obtained by defining the relationship between the
inter-electrode-finger groove depth G, the electrode finger
thickness H, and the IDT line occupancy .eta. in the
above-described manner, the inflection point temperature changes
depending on the IDT line occupancy .eta. and is adjusted so as to
fall within a range of the center temperature Tc.+-.30.degree. C.
of a desired operation temperature range, thereby suppressing a
frequency fluctuation to be small. While the frequency-temperature
characteristic of the SAW device is basically determined by the cut
angle of the quartz crystal substrate to be used, the
frequency-temperature characteristic can be optimally improved by
changing the inflection-point temperature.
[0076] In the SAW device having the inter-electrode-finger grooves,
the IDT line occupancy .eta. may satisfy the following
relationship.
a(Tc-30).sup.6+b(Tc-30).sup.5+c(Tc-30).sup.4+d(Tc-30).sup.3+e(Tc-30).sup-
.2+f(Tc-30)+0.606.ltoreq..eta..ltoreq.a(Tc+30).sup.6+b(Tc+30).sup.5+c(Tc+3-
0).sup.4+d(Tc+30).sup.3+e(Tc+30).sup.2+f(Tc+30)+0.606
(where a=-2.60.times.10.sup.-12, b=4.84.times.10.sup.-10,
c=-2.13.times.10.sup.-8, d=1.98.times.10.sup.-7,
e=1.42.times.10.sup.-5, f=1.48.times.10.sup.-4)
[0077] Therefore, it is possible to control the
frequency-temperature characteristic such that the inflection-point
temperature reliably falls within a range of the center temperature
Tc.+-.30.degree. C. of the operation temperature range.
[0078] The Euler angle .psi. of the quartz crystal substrate may be
within a range of
42.79.degree..ltoreq.|.psi.|.ltoreq.49.57.degree.. Therefore, an
excellent frequency-temperature characteristic having a very small
frequency fluctuation in a wide operation temperature range is
obtained.
[0079] The IDT line occupancy .eta. may satisfy the following
relationship.
.eta.=-1963.05.times.(G/.lamda.).sup.3+196.28.times.(G/.lamda.).sup.2-6.-
53.times.(G/.lamda.)-135.99.times.(H/.lamda.).sup.2+5.817.times.(H/.lamda.-
)+0.732-99.99.times.(G/.lamda.).times.(H/.lamda.) [Equation 7]
[0080] Therefore, it is possible to suppress the secondary
temperature coefficient of the frequency-temperature characteristic
to be smaller, thereby obtaining a more excellent
frequency-temperature characteristic of a cubic curve having a
smaller frequency fluctuation.
[0081] The sum of the depth G of the inter-electrode-finger grooves
and the thickness H of the electrode fingers may satisfy
0.0407.lamda..ltoreq.G+H. Therefore, in the aspect of the invention
which uses resonance in the stopband upper end mode, a high Q value
is obtained compared to a SAW resonator of the related art which
uses resonance in the stopband lower end mode with no grooves
between the electrode fingers of the IDT.
[0082] The SAW device may further include a pair of reflectors
which respectively have a plurality of conductor strips on the
principal surface of the quartz crystal substrate and are arranged
on both sides of the IDT with the IDT sandwiched therebetween along
a SAW propagation direction. Inter-conductor-strip grooves are
recessed in the surface of the quartz crystal substrate between
adjacent conductor strips of the reflectors. An angle between a
first direction perpendicular to the electrode fingers and the
conductor strips and the electrical axis of the quartz crystal
substrate may be the Euler angle .psi. of the quartz crystal
substrate. At least a part of the IDT and the reflectors may be
arranged in a second direction intersecting the first direction at
an angle .delta.. The angle .delta. is set to be within a range of
a power flow angle .+-.1.degree. of the quartz crystal substrate.
Therefore, it is possible to further improve the Q value.
[0083] The SAW device may further include an oscillation circuit
which drives the IDT. Therefore, it is possible to obtain a SAW
oscillator having a very small frequency fluctuation in a wide
operation temperature range, a low CI value, and excellent
oscillation stability.
[0084] According to still another aspect of the invention, an
electronic apparatus and a sensor apparatus include the
above-described SAW device. Therefore, an electronic apparatus and
a sensor apparatus which stably exhibit satisfactory performance in
a wide operation temperature range with high reliability are
provided.
BRIEF DESCRIPTION OF THE DRAWINGS
[0085] FIG. 1(A) is a plan view showing the configuration of a SAW
resonator of this embodiment, FIG. 1(B) is a partial enlarged
longitudinal sectional view, FIG. 1(C) is a partial enlarged view,
and FIG. 1(D) is a partial enlarged sectional view showing the
shape of inter-electrode-finger grooves which are formed by
photolithography and etching techniques, and corresponding to FIG.
1(C).
[0086] FIG. 2 is an explanatory view schematically showing a quartz
crystal substrate of this embodiment.
[0087] FIG. 3 is a diagram showing a frequency-temperature
characteristic of this embodiment.
[0088] FIG. 4 is a diagram showing SAW reflection characteristics
of an IDT and a reflector.
[0089] FIG. 5 is a diagram showing the relationship between a step
between electrode fingers of this embodiment and a Q value.
[0090] FIG. 6 is a diagram showing a variation in a
frequency-temperature characteristic due to a variation in an IDT
line occupancy .eta. of this embodiment.
[0091] FIG. 7 is a diagram showing the relationship between a
change amount in an inflection-point temperature and a deviation in
a frequency fluctuation in a frequency-temperature characteristic
of this embodiment.
[0092] FIG. 8 is a diagram showing the relationship between an IDT
line occupancy .eta. and an inflection-point sensitivity such that
a secondary temperature coefficient is .beta..ltoreq.0.01 when an
electrode finger thickness is H=1% .lamda. and an
inter-electrode-finger groove depth is G=2% .lamda. to 7% .lamda.
in this embodiment.
[0093] FIG. 9 is a diagram showing the relationship between an IDT
line occupancy .eta. and an inflection-point sensitivity such that
a secondary temperature coefficient is .beta..ltoreq.0.01 when an
electrode finger thickness is H=1.5% .lamda. and an
inter-electrode-finger groove depth is G=2% .lamda. to 7% .lamda.
in this embodiment.
[0094] FIG. 10 is a diagram showing the relationship between an IDT
line occupancy .eta. and an inflection-point temperature in the
case of FIG. 8.
[0095] FIG. 11 is a diagram showing the relationship between an IDT
line occupancy .eta. and an inflection-point temperature in an
example of a SAW resonator according to the invention.
[0096] FIG. 12 is a diagram showing the relationship between an IDT
line occupancy .eta. and an inflection-point temperature in a SAW
resonator with no inter-electrode-finger grooves.
[0097] FIG. 13 is a diagram showing a change in an IDT line
occupancy .eta. depending on an inflection-point temperature by an
approximate curve in this example.
[0098] FIG. 14 is a diagram showing the relationship between an
inflection-point temperature and a frequency fluctuation deviation
in this example.
[0099] FIGS. 15(A) to 15(C) are diagrams showing changes in a
frequency-temperature characteristic corresponding to the range of
three different inflection-point temperatures of Table 2.
[0100] FIGS. 16(A) and 16(B) are plan views showing SAW resonators
having inclined IDTs of different structures according to a second
example of the invention.
[0101] FIG. 17(A) is a plan view showing a SAW oscillator according
to an embodiment of the invention, and FIG. 17(B) is a longitudinal
sectional view taken along the line B-B.
DETAILED DESCRIPTION
[0102] Hereinafter, preferred examples of the invention will be
described in detail with reference to the accompanying drawings. In
the accompanying drawings, the same or similar constituent elements
are represented by the same or similar reference numerals.
[0103] A SAW resonator which is a first example of a SAW device
according to the invention has the same basic configuration as the
SAW resonator 1 shown in FIG. 1, and description thereof will be
provided with reference to FIG. 1. That is, the SAW resonator 1 of
this example has a rectangular quartz crystal substrate 2, and an
IDT 3 and a pair of reflectors 4 and 4 which are formed on the
principal surface of the quartz crystal substrate. The quartz
crystal substrate 2 uses a quartz crystal substrate having Euler
angles (-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree., .psi.). The Euler
angle .psi. is set such that |.psi.|.noteq.90.degree..times.n
(where n=0, 1, 2, 3) is satisfied.
[0104] The IDT 3 has a pair of interdigital transducers 3a and 3b
which respectively have a plurality of electrode fingers 6a and 6b,
and bus bars 7a and 7b connecting the base portions of the
electrode fingers 6a and 6b. The electrode fingers 6a and 6b are
arranged such that the extension direction thereof is perpendicular
to the propagation direction of a SAW which is excited by the IDT.
The electrode fingers 6a of the interdigital transducer 3a and the
electrode fingers 6b of the interdigital transducer 3b are arranged
with a given pitch alternately and at a predetermined interval.
Inter-electrode-finger grooves 8 having a given depth are recessed
in the surface of the quartz crystal substrate 2 exposed between
the electrode fingers 6a and 6b by removing the surface through
etching or the like.
[0105] A pair of reflectors 4 and 4 are arranged outside the IDT 3
with the IDT sandwiched therebetween along the SAW propagation
direction. The reflectors 4 respectively have a plurality of
conductor strips (electrode fingers) 4a and 4a arranged with a
given pitch in the SAW propagation direction. The conductor strips
are arranged such that the extension direction thereof is
perpendicular to the SAW propagation direction.
Inter-conductor-strip grooves 9 are recessed in the surface of the
quartz crystal substrate 2 exposed between the conductor strips 4a
and 4a by removing the surface through etching or the like.
[0106] The electrode fingers and the conductor strips are formed of
a metal film using, for example, Al or an alloy mainly containing
Al to have the same thickness H. The inter-electrode-finger grooves
and the inter-conductor-strip grooves are formed to have the same
depth G. Similarly, grooves having the same depth as the
inter-electrode-finger grooves are formed between the innermost
conductor strips of the reflectors 4 and 4 and the outermost
electrode fingers 6a (or 6b) of the IDT 3 at a predetermined
interval by removing the surface of the quartz crystal
substrate.
[0107] With this configuration, the SAW resonator 1 excites a
Rayleigh-type SAW which has vibration displacement components in
both the X'-axis direction and the Y'-axis direction of the quartz
crystal substrate 2. With the use of the quartz crystal substrate 2
having the above-described Euler angles, the SAW propagation
direction is shifted from the X axis which is the crystal axis of
quartz crystal, thereby exciting the SAW in the stopband upper end
mode.
[0108] The SAW resonator 1 has a frequency-temperature
characteristic which is expressed by a curve (for example, a cubic
curve) having a maximum value, a minimum value, and an inflection
point between the maximum value and the minimum value in an
operation temperature range. In this example, it is assumed that
the center temperature Tc of the operation temperature range is a
target temperature, and a given allowable temperature region from
the center temperature Tc, for example, a range of .+-.30.degree.
C. is a target temperature range. For example, when the operation
temperature range is -40.degree. C. to +85.degree. C., the center
temperature is Tc=(-40+85)/2=22.5.degree. C. Thus, the target
temperature range is defined by an upper limit temperature
TH=22.5.degree. C.+30.degree. C.=52.5.degree. C. and a lower limit
temperature TL=22.5.degree. C.-30.degree. C.=-7.5.degree. C.
[0109] In this example, the line occupancy .eta. of the IDT 3 is
set such that the temperature of the inflection point of the
frequency-temperature characteristic falls within at least the
target temperature range. In the SAW resonator 1, when the Euler
angles of the quartz crystal substrate 2 are set to (0.degree.,
123.degree., .psi.), the thickness H of the electrode fingers of
the IDT 3 is 0.02.lamda. (2% .lamda.), and the depth G of the
inter-electrode-finger grooves is 0.05.lamda. (5% .lamda.), the
relationship between the IDT line occupancy .eta. and the
inflection-point temperature of the frequency-temperature
characteristic was calculated by a simulation in a range of
.eta.=0.6 to 0.8. The result is shown in FIG. 11.
[0110] As will be understood from FIG. 11, in this example, the
inflection-point temperature changes within the operation
temperature range depending on the IDT line occupancy .eta.. In a
region where the inflection-point temperature exceeds the
above-described upper limit temperature TH=52.5.degree. C., a
change in the inflection-point temperature with respect to the IDT
line occupancy .eta. is gradual. In a region where the
inflection-point temperature does not exceed the lower limit
temperature TL=-7.5.degree. C., a change in the inflection-point
temperature with respect to the IDT line occupancy .eta. is steep.
Meanwhile, in the target temperature range of the lower limit
temperature TL=-7.5.degree. C. to the upper limit temperature
TH=52.5.degree. C., a change in the inflection-point temperature
has a slope which is controllable depending on the IDT line
occupancy .eta. with comparatively satisfactory precision.
[0111] For comparison, in a quartz crystal resonator having the
configuration as that in FIG. 11, except that the thickness of the
electrode fingers of the IDT is set to 0.08.lamda. (8% .lamda.)
comparable to the effective thickness 0.07.lamda. (7% .lamda.) of
FIG. 11, and no inter-electrode-finger grooves are provided, the
relationship between the IDT line occupancy .eta. and the
inflection-point temperature of the frequency-temperature
characteristic was calculated by a simulation in a range of
.eta.=0.6 to 0.8. The result is shown in FIG. 12. From FIG. 12, it
is understood that, in the comparative example, the
inflection-point temperature is substantially constant and
undergoes little change with respect to the IDT line occupancy
.eta..
[0112] From the simulation result of FIG. 11, the value of the IDT
line occupancy .eta. with respect to the inflection-point
temperature can be approximately numerically expressed. When the
inflection-point temperature is x, and the IDT line occupancy .eta.
is y, the approximate expression is expressed as follows.
y=ax.sup.6+bx.sup.5+cx.sup.4+dx.sup.3+ex.sup.2+fx+0.606 (4)
(where a=-2.60.times.10.sup.-12, b=4.84.times.10.sup.-10,
c=-2.13.times.10.sup.-8, d=1.98.times.10.sup.-7,
e=1.42.times.10.sup.-5, f=1.48.times.10.sup.-4)
[0113] Expression (4) is expressed by an approximate curve of FIG.
13 in which the horizontal axis x is the inflection-point
temperature, and the vertical axis y is the IDT line occupancy
.eta..
[0114] In Expression (4), if the center temperature Tc of the
operation temperature range is substituted into x, the IDT line
occupancy .eta. corresponding to the center temperature Tc serving
as the inflection-point temperature. When the allowable temperature
region relating to the center temperature Tc is .+-.t (.degree.),
if (Tc+t) is substituted into x of Expression (4), the IDT line
occupancy .eta. corresponding to the upper limit temperature TH of
the target temperature range is obtained. If (Tc-t) is substituted
into x of Expression (4), the IDT line occupancy .eta.
corresponding to the lower limit temperature TL of the target
temperature range is obtained. Although in this example, the same
allowable temperature region is set on the upper limit side and the
lower limit side, different values may be set on the upper limit
side and the lower limit side.
[0115] As shown in FIG. 11, when the allowable temperature region
is t=30.degree., the upper limit temperature of the target
temperature range is TH=Tc+30 (.degree.), and the lower limit
temperature is TL=Tc-30 (.degree.). In this case, the range of the
IDT line occupancy .eta. corresponding to the target temperature
range is determined by Expression (4) and Relational Expression
(5).
a(Tc-30).sup.6+b(Tc-30).sup.5+c(Tc-30).sup.4+d(Tc-30).sup.3+e(Tc-30).sup-
.2+f(Tc-30)+0.606.ltoreq..eta..ltoreq.a(Tc+30).sup.6+b(Tc+30).sup.5+c(Tc+3-
0).sup.4+d(Tc+30).sup.3+e(Tc+30).sup.2+f(Tc+30)+0.606 (5)
[0116] The coefficients a to f are the same as those in Expression
(4).
[0117] When the SAW resonator 1 of this example has a
frequency-temperature characteristic which is expressed by a cubic
curve having an inflection point between a maximum value and a
minimum value, the influence of a change in the inflection-point
temperature on the frequency-temperature characteristic was
verified. When the Euler angles of the quartz crystal substrate 2
are set to (0.degree., 123.degree., .psi.), and the thickness H of
the electrode fingers of the IDT 3 is 0.02.lamda. (2% .lamda.), the
depth G of the inter-electrode-finger grooves is 0.02.lamda. (2%
.lamda.), and the IDT line occupancy .eta. is 0.69, the
inflection-point temperature changed in a range of -71.degree. C.
to +119.degree. C. at 10.degree. C. intervals, and a
frequency-temperature characteristic was calculated by a
simulation.
[0118] From the resultant simulation result, for each
frequency-temperature characteristic, an inflection-point
temperature Fp and a frequency fluctuation deviation .DELTA.f (ppm)
were computed. The computation result is as shown in Table 2.
TABLE-US-00002 TABLE 2 Temp. Inflection-Point Temperature Fp
(.degree. C.) (.degree. C.) -71 -61 -51 -41 -31 -26 -11 -1 9 19 29
-40 -14 -12 -10 -7 -5 -4 -1 1 1 1 -1 -30 -15 -14 -12 -10 -7 -6 -3
-1 1 1 1 -20 -16 -15 -14 -12 -10 -9 -5 -3 -1 1 1 -10 -15 -16 -15
-14 -12 -11 -7 -5 -3 -1 1 5 -12 -14 -15 -15 -15 -14 -11 -9 -6 -4 -2
20 -5 -10 -13 -15 -16 -15 -14 -12 -10 -7 -5 35 6 -2 -8 -12 -14 -15
-15 -15 -13 -11 -9 50 21 10 2 -5 -10 -12 -15 -16 -15 -14 -12 65 42
28 16 6 -2 -5 -12 -14 -15 -15 -15 85 79 59 42 28 16 10 -2 -8 -12
-14 -15 .DELTA.f (ppm) 95 75 57 43 31 26 15 16 17 17 17 Temp.
Inflection-Point Temperature Fp (.degree. C.) (.degree. C.) 39 49
54 69 79 89 99 109 119 -40 -4 -8 -11 -23 -33 -46 -61 -79 -100 -30
-1 -4 -6 -14 -23 -33 -46 -61 -79 -20 1 -1 -2 -8 -14 -23 -33 -46 -61
-10 1 1 0 -4 -8 -14 -23 -33 -46 5 0 1 1 0 -2 -6 -11 -18 -28 20 -3
-1 0 1 1 -1 -4 -8 -14 35 -6 -4 -3 0 1 1 0 -2 -6 50 -10 -7 -6 -3 -1
1 1 1 -1 65 -13 -11 -10 -6 -4 -2 0 1 1 85 -15 -15 -14 -11 -9 -6 -4
-2 0 .DELTA.f (ppm) 17 16 15 24 34 47 62 80 101
[0119] FIG. 14 shows the relationship between an inflection-point
temperature and a frequency fluctuation deviation shown in Table 2.
In FIG. 14, the frequency fluctuation deviation is stabilized
within the target temperature range (-7.5.degree. C. to
52.5.degree. C.) and has a low value of about 15 to 17 ppm.
Meanwhile, if the inflection-point temperature somewhat exceeds the
upper limit temperature and lower limit temperature of the target
temperature range, the frequency fluctuation deviation changes to
increase steeply.
[0120] FIG. 15(A) to (C) show changes in a frequency-temperature
characteristic corresponding to inflection-point temperatures of
FIG. 14. FIG. 15(A) shows a frequency-temperature characteristic at
an inflection-point temperature in a range of -71.degree. C. to
-26.degree. C. in Table 2. Similarly, FIG. 15(B) shows a
frequency-temperature characteristic at an inflection-point
temperature in a range of -11.degree. C. to +54.degree. C. in Table
2, and FIG. 15(C) shows a frequency-temperature characteristic at
an inflection-point temperature in a range of +69.degree. C. to
+119.degree. C. As shown in FIGS. 15(A) and (C), if the
inflection-point temperature is outside the target temperature
range, the frequency-temperature characteristic is significantly
deteriorated.
[0121] In FIG. 15(B), in all cases, the frequency fluctuation is
within 20 ppm, and a satisfactory frequency-temperature
characteristic is shown. The range of the inflection-point
temperature of FIG. 15(B) is somewhat wider than the upper limit
TH=52.5.degree. C. and the lower limit TL=-7.5.degree. C. of the
target temperature range. From this, it is understood that, even
when the target temperature range is expanded in a wider range than
the allowable temperature region (.+-.30.degree. C.) set with
respect to the target temperature, that is, the center temperature
of the operation temperature range, the frequency fluctuation can
be suppressed to be small.
[0122] From the results, it is preferable to optimally determine
the target temperature range, that is, the target temperature, the
upper limit temperature, and the lower limit temperature from a
change amount in the frequency fluctuation deviation relating to
the inflection-point temperature. In particular, the
inflection-point temperature is set as the center temperature of
the operation temperature range, the frequency-temperature
characteristic is rotationally symmetric, and the frequency
fluctuation can be minimized, thereby obtaining the best
frequency-temperature characteristic.
[0123] According to this example, a SAW resonator is obtained which
has a frequency-temperature characteristic expressed by a cubic
curve having a maximum value, a minimum value, and an inflection
point between the maximum value and the minimumvalue, and in which
the inflection-point temperature is adjustable depending on the IDT
line occupancy .eta. so as to be within the target temperature
range. At this time, the target temperature range is optimally
selected from the relationship between the inflection-point
temperature and the frequency fluctuation deviation. Thus, even
when the inflection-point temperature changes, there is no case
where the frequency-temperature characteristic deteriorates.
Therefore, it is possible to optimally control the
frequency-temperature characteristic, which is basically determined
by the cut angle of the quartz crystal substrate to be used,
depending on the IDT line occupancy .eta. in correspondence with a
required operation temperature characteristic, a manufacturing
variation, or the like.
[0124] With regard to the SAW resonator of this example, similarly
to the SAW resonator of this embodiment, it is preferable that the
line occupancy .eta. of the IDT 3 is set to satisfy the following
relationship.
.eta.=-1963.05.times.(G/.lamda.).sup.3+196.28.times.(G/.lamda.).sup.2-6.-
53.times.(G/.lamda.)-135.99.times.(H/.lamda.).sup.2+5.817.times.(H/.lamda.-
)+0.732-99.99.times.(G/.lamda.).times.(H/.lamda.) [Equation 8]
[0125] Thus, it is possible to suppress the secondary temperature
coefficient of the frequency-temperature characteristic to be
smaller, and thus to further reduce a frequency fluctuation,
thereby obtaining a more excellent frequency-temperature
characteristic of a cubic curve.
[0126] In the SAW resonator of this example, similarly to the SAW
resonator of this embodiment, it is preferable that the sum of the
depth G of the inter-electrode-finger grooves 8 and the thickness H
of the electrode fingers 6a and 6b is set to satisfy
0.0407.lamda..ltoreq.G+H. Thus, in this example which uses
resonance in the stopband upper end mode, a high Q value is
obtained compared to the SAW resonator of the related art which
uses resonance in the stopband lower end mode with no grooves
between the electrode fingers of the IDT.
[0127] FIGS. 16(A) and (B) show a second example of SAW resonators
having inclined IDTs according to the invention. As in the first
example, a SAW resonator 21.sub.1 of FIG. 16(A) has an inclined IDT
23.sub.1 and a pair of reflectors 24.sub.1 and 24.sub.1 on the
principal surface of a quartz crystal substrate 22.sub.1 having
Euler angles (-1.5.degree..ltoreq..phi..ltoreq.1.5.degree.,
117.degree..ltoreq..theta..ltoreq.142.degree.,
42.79.degree..ltoreq.|.psi.|.ltoreq.49.57.degree.. The quartz
crystal substrate 22.sub.1 is such that the longitudinal direction
thereof is aligned in a direction inclined by a power flow angle
(PFA) .delta..degree. in the propagation direction of energy with
respect to the X' axis which is the propagation direction of the
phase velocity of the SAW excited by the IDT 23.sub.1.
[0128] The IDT 23.sub.1 has a pair of interdigital transducers
23a.sub.1 and 23b.sub.1 which respectively have a plurality of
electrode fingers 25a.sub.1 and 25b.sub.1, and bus bars 26a.sub.1
and 26b.sub.1 connecting the base portions of the electrode
fingers. A pair of reflectors 24.sub.1 and 24.sub.1 are arranged on
both sides of the IDT 23.sub.1 with the IDT sandwiched therebetween
along the SAW propagation direction, and respectively have a
plurality of conductor strips 24a.sub.1 and 24a.sub.1 arranged in
the SAW propagation direction. The electrode fingers 25a.sub.1 and
25b.sub.1 and the conductor strips 24a.sub.1 are arranged such that
the extension direction thereof is perpendicular to the X' axis
inclined at the power flow angle (PFA) .delta..degree..
[0129] As in the first example, inter-electrode-finger grooves are
recessed in the surface of the quartz crystal substrate 22.sub.2
exposed between the electrode fingers 25a.sub.1 and 25b.sub.1.
Similarly, inter-conductor-strip grooves are recessed in the
surface of the quartz crystal substrate 22.sub.2 between the
conductor strips 24a.sub.1 and 24a.sub.1.
[0130] If at least a part of the IDT and the reflectors is arranged
in a direction intersecting the X'-axis direction at the power flow
angle .delta., the SAW device 21.sub.1 exhibits the same functional
effects as in the first example, thereby further increasing the Q
value. Thus, a lower-loss SAW resonator is realized.
[0131] A SAW resonator 21.sub.2 of FIG. 16(B) has an inclined IDT
23.sub.2 and a pair of reflectors 24.sub.2 and 24.sub.2 having a
different configuration from FIG. 16(A) on the principal surface of
the quartz crystal substrate 22.sub.2. The quartz crystal substrate
22.sub.2 is such that the longitudinal direction thereof is aligned
along the X' axis which is the propagation direction of the phase
velocity of the SAW excited by the IDT 23.sub.2.
[0132] The IDT 23.sub.2 has a pair of interdigital transducers
23a.sub.2 and 23b.sub.2 which respectively have a plurality of
electrode fingers 25a.sub.2 and 25b.sub.2, and bus bars 26a.sub.2
and 26b.sub.2 connecting the base portions of the electrode
fingers. A pair of reflectors 24.sub.2 and 24.sub.2 are arranged on
both sides of the IDT 23.sub.2 with the IDT sandwiched therebetween
along the SAW propagation direction, and respectively have a
plurality of conductor strips 24a.sub.2 and 24a.sub.2 arranged in
the SAW propagation direction. The electrode fingers 25a.sub.2 and
25b.sub.2 and the conductor strip 24a.sub.2 are arranged such that
the extension direction thereof is perpendicular to the X' axis,
and the bus bars 26a.sub.2 and 26b.sub.2 are aligned in a direction
inclined at the power flow angle (PFA) .delta..degree. from the X'
axis.
[0133] As in the first example, inter-electrode-finger grooves are
recessed in the surface of the quartz crystal substrate 22.sub.2
exposed between the electrode fingers 25a.sub.2 and 25b.sub.2.
Similarly, inter-conductor-strip grooves are recessed in the
surface of the quartz crystal substrate 22.sub.2 between the
conductor strips 24a.sub.2 and 24a.sub.2.
[0134] In the SAW resonator 21.sub.2 of this example, if at least a
part of the IDT and the reflectors is arranged in a direction
intersecting the X'-axis direction at the power flow angle .delta.
in the above-described manner, a functional effect of realizing a
satisfactory frequency-temperature characteristic and a high Q
value is exhibited, thereby further increasing the Q value. Thus, a
lower-loss SAW resonator is realized.
[0135] The invention may be applied to an oscillator in which the
SAW resonator of this embodiment and an oscillation circuit are
incorporated. FIGS. 17(A) and 17(B) show the configuration of an
example of a SAW oscillator which is a second example of a SAW
device according to the invention. A SAW oscillator 31 of this
example includes a SAW resonator 32 of this embodiment, an IC
(integrated circuit) 33 which serves as an oscillation circuit to
drive and control the SAW resonator, and a package 34 which
accommodates the SAW resonator 32 and the IC 33. The SAW resonator
32 and the IC 33 are surface-mounted on a bottom plate 34a of the
package 34.
[0136] The SAW resonator 32 has the same configuration of the SAW
resonator 11 of the first example. The SAW resonator 32 has a
quartz crystal substrate 35 which is expressed by the same Euler
angles as in the first example, and an IDT having a pair of
interdigital transducers 36a and 36b and a pair of reflectors 37
and 37 formed on the surface of the quartz crystal substrate 35.
Electrode pads 38a to 38f are provided in the upper surface of the
IC 33. Electrode patterns 39a to 39g are formed on the bottom plate
34a of the package 34. The interdigital transducers 36a and 36b of
the SAW resonator 32 and the electrode pads 38a to 38f of the IC 33
are electrically connected to the corresponding electrode patterns
39a to 39g by bonding wires 40 and 41. The package 34 in which the
SAW resonator 32 and the IC 33 is sealed airtight by a lid 42
bonded to the upper part of the package 34.
[0137] The SAW oscillator 31 of this example includes the SAW
resonator of this embodiment, and has an excellent
frequency-temperature characteristic with a very small frequency
fluctuation in a wide operation temperature range and a high Q
value. Therefore, it is possible to perform a stable oscillation
operation and to realize reduction in power consumption because of
low impedance. As a result, a SAW oscillator is obtained which
copes with high-frequency and high-precision performance based on
recent high-speed information communication, and includes an
environment-resistant characteristic such that, even when a
temperature varies extremely, a stable operation is ensured for a
long period.
[0138] The invention is not limited to the foregoing examples, and
various modifications or changes may be made within the technical
scope. For example, although the SAW resonator of the first example
has the reflectors on both sides of the IDT, the invention can also
be applied to a SAW resonator with no reflectors. With regard to
the electrode structure of the IDT, in addition to the foregoing
examples, various known configurations may be used.
[0139] The invention may also be applied to a SAW device other than
the above-described SAW resonator and SAW oscillator. The SAW
device of this embodiment may also be widely applied to various
electronic apparatuses, such as a mobile phone, a hard disk, a
personal computer, a receiver tuner of BS and CS broadcasts,
various processing apparatuses for a high-frequency signal or an
optical signal which propagates through a coaxial cable or an
optical cable, a server network apparatus which requires
high-frequency and high-precision clock (low jitter and low phase
noise) in a wide temperature range, various electronic apparatuses
such as a wireless communication apparatus, and various sensor
apparatuses, such as a pressure sensor, an acceleration sensor, and
a rotation speed sensor.
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