Piezoelectric resonator and piezoelectric filter having a heat-radiating film

ABSTRACT

A piezoelectric resonator includes a substrate and a thin-film section. The thin-film section includes a first thin-film section supported by the substrate, and an acoustically-isolated second thin-film section which is separated from the substrate. In the second thin-film section, first and second electrodes are arranged on the respective main surfaces of a piezoelectric film, and a vibration section is provided at an area where the first and the second electrodes overlap each other on the second thin-film section when viewed through in the film-thickness direction. The thin-film section further includes a heat-radiating film which is in contact with peripheral edges of at least the first electrode among the first and second electrodes defining portions of a periphery of the vibration section, and which extends from the peripheral edges to the first thin-film section when viewed through in the film-thickness direction.
BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a piezoelectric resonator and a piezoelectric filter.
2. Description of the Related Art

In general, a piezoelectric resonator is configured such that a thin-film portion in which a piezoelectric film is sandwiched between an upper electrode and a lower electrode is arranged on a substrate, and a vibration section in which the upper and lower electrodes overlap with each other is acoustically isolated from the substrate. Heat is generated in the vibration section.
 For example, Japanese Unexamined Patent Application Publication No. 2004-120219, as shown in FIG. 17 which is a plan view and FIG. 18 which is a sectional view taken along a line A to A of FIG. 17, discloses a technique of improving a heat-radiating property and an electric-power resistance by forming a heat-radiating film 118 in a portion, except for a vibration portion 111 b, of a piezoelectric resonator having a substrate subjected to through-etching from a back surface thereof so that a space 110 a is formed. That is, a lower electrode 114 which has a substantially cross shape in a plan view and which includes a base portion 114 a, a tip portion 114 b, and wing portions 114 c, a piezoelectric thin-film 115, an upper electrode which has a projecting shape in a plan view and which includes a base portion 116 a and a tip portion 116 b which have different widths, and the heat-radiating film 118 are arranged on an SiO₂ film 111 which is formed on a first main surface of the substrate 110. The vibration portion 111 b corresponds to a portion in which the tip portion 114 b of the lower electrode 114 and the tip portion 116 b of the upper electrode 116 overlap each other (i.e., a hatched portion in FIG. 17). Note that a Si₂ film 112 arranged on a second main surface of the substrate 110 is removed in a step of manufacturing.
 However, since the upper electrode 116 is exposed in an opening 118 a provided in the heat-radiating film 118 with a gap between the heat-radiating film 118 and the exposed upper electrode 116, and the heat-radiating film 118 is arranged so as to be isolated from the vibration section 111 b which defines a heat-generation source, heat conduction is degraded due to the gap between the vibration section 111 b and the heat-radiating film 118, which results in a degraded heat-radiating property. Furthermore, deterioration of a Q factor occurs due to unnecessary vibration in the piezoelectric resonator, and the deterioration of the Q factor causes heat generation. Therefore, in order to improve electric-power resistance, the heat-radiating property is improved and the unnecessary vibration is prevented from occurring so that the heat generation due to the deterioration of the Q factor is prevented.
SUMMARY OF THE INVENTION

To overcome the problems described above, preferred embodiments of the present invention provide a piezoelectric resonator and a piezoelectric filter with an improved heat-radiating property and which prevents heat generation caused by unnecessary vibration.
 A piezoelectric resonator according to a preferred embodiment of the present invention includes a substrate and a thin-film section. The thin-film section includes a first thin-film section that is supported by the substrate and a second thin-film section that is acoustically isolated from the substrate. The second thin-film section includes a piezoelectric thin film in which first and second electrodes are disposed on respective main surfaces thereof, so that a vibration section is provided in a portion in which the first and second electrodes overlap each other in the second thin-film section when viewed through in a film-thickness direction. The thin-film section further includes a heat-radiating film which is in contact with a peripheral edge of at least one of the first and second electrodes defining portions of a periphery of the vibration section, and which extends from the peripheral edge of the at least one of the first and second electrodes to the first thin-film section when viewed through in the film-thickness direction.
With the configuration described above, a portion of heat that is generated in the vibration section included in the second thin-film section is transmitted from one of the first and second electrodes, which are in contact with the heat-radiating film, through the heat-radiating film to the first thin-film section. Therefore, a heat-radiating path is enlarged, and the heat generated in the vibration section is effectively radiated to the substrate. Accordingly, a piezoelectric resonator having excellent electric-power resistance is obtained.
Furthermore, since the heat-radiating film is arranged so as to surround the vibration section, unnecessary vibration is prevented from being generated in a surrounding region of the heat-radiating film. Accordingly, spurious responses are effectively suppressed, and heat generation caused by a degraded Q factor is suppressed. Consequently, a piezoelectric resonator having excellent electric-power resistance is obtained.
 Moreover, since a thickness of the thin-film section can be increased by adding the heat-radiating film while a film configuration of the vibration section which achieves a desired resonant frequency is maintained, the mechanical strength of the membrane configuration in which the second thin-film section is isolated from the substrate is improved.
Note that when the electrode is in contact with the peripheral edge of only one of the first and second electrodes, when the electrode is in contact with the peripheral edge of the one of the first and second electrodes which defines the majority of the periphery of the vibration section, heat is more effectively radiated.
A piezoelectric resonator according to a preferred embodiment of the present invention includes a substrate and a thin-film section. The thin-film section includes a first thin-film section supported by the substrate and a second thin-film section acoustically isolated from the substrate. The second thin-film section includes a piezoelectric thin film in which first and second electrodes are disposed on respective main surfaces thereof so that a vibration section is defined in a portion in which the first and second electrodes overlap each other in the second thin-film section when viewed through in a film-thickness direction. The thin-film section further includes a heat-radiating film which overlaps with a peripheral edge of at least one of the first and second electrodes defining portions of a periphery of the vibration section, and which extends from a portion inside the vibration section relative to the periphery of the vibration section to the first thin-film section when viewed through in the film-thickness direction.
 With the configuration described above, a portion of heat that is generated in the vibration section included in the second thin-film section is transmitted from one of the first and second electrodes, with which the heat-radiating film overlaps, through the heat-radiating film to the first thin-film section. Therefore, a heat-radiating path is enlarged, and the heat that is generated in the vibration section is effectively radiated to the substrate. Accordingly, a piezoelectric resonator having excellent electric-power resistance is obtained.
Furthermore, since the heat-radiating film is arranged so as to surround the vibration section, unnecessary vibration is prevented from being generated in a surrounding region of the heat-radiating film. Accordingly, a spurious response is effectively suppressed, and heat generation caused by a degraded Q factor is suppressed. Consequently, a piezoelectric resonator having excellent electric-power resistance is obtained.
Moreover, since a thickness of the thin-film section can be increased by adding the heat-radiating film while a film configuration of the vibration section which achieves a desired resonant frequency is maintained, the mechanical strength of a membrane configuration in which the second thin-film section is isolated from the substrate is improved.
Note that when the electrode overlaps the peripheral edge of only one of the first and second electrodes, when the electrode overlaps the peripheral edge of the one of the first and second electrodes which defines the majority of the periphery of the vibration section, heat is more effectively radiated.
In the vicinity of a peripheral edge of the heat-radiating film arranged towards the inside relative to the periphery of the vibration section when viewed through in a film-thickness direction, thicknesses of portions of the heat-radiating film preferably increase as the portions are farther from the periphery edge.
 In this case, when a portion corresponding to the peripheral edge of the heat-radiating film is configured so as to have a tapered shape in cross section, a range of allowable displacement of the peripheral edge of the heat-radiating film which is located inside the periphery of the vibration section is increased, and accordingly, mass production of products having excellent manufacturing yields is achieved.
The piezoelectric thin-film section preferably includes a step-forming film having a step portion with an interval between the step portion and the periphery of the vibration section when viewed through in the film-thickness direction.
In this case, since the step portion is provided in the step-forming film with the interval between the step portion and the periphery of the vibration section, a spurious response lower than a resonant frequency is effectively suppressed. Accordingly, a piezoelectric resonator with reduced loss is obtained.
A film thickness of the first electrode included in the vibration section and a film thickness of the second electrode included in the vibration section are preferably different from each other.
In this case, piezoelectric resonators having different frequencies for a filter are obtained with increased precision, for example.
More preferably, the film thickness of the first electrode included in the vibration section is relatively small and the film thickness of the second electrode included in the vibration section is relatively large.
In this case, a spurious response is efficiently suppressed for all of the piezoelectric resonators having different frequencies included in the filter, for example.
 A piezoelectric filter according to a preferred embodiment of the present invention includes a plurality of piezoelectric resonators each corresponding to one of the piezoelectric resonators described above on a single substrate, which include respective vibration sections. The first and second electrodes which define the vibration sections are electrically connected to each other so as to define a filter circuit.
In this case, a ripple is effectively suppressed, and heat generation caused by an increase of loss is effectively suppressed. Accordingly, a piezoelectric filter having excellent electric-power resistance is obtained. Furthermore, a heat-radiating path is enlarged, and the heat generated in the vibration section is effectively radiated to the substrate.
Each of the vibration sections preferably has a substantially square shape or a substantially rectangular shape having a ratio of a long side to a short side of about 2 or less, for example, when viewed through in the film-thickness direction.
In this case, since vibration sections are arranged with high density, an unnecessary region is eliminated and can be omitted. Accordingly, an overall area of the filter is reduced.
Each of the plurality of vibration sections preferably has a substantially square shape or a substantially rectangular shape having approximately a golden ratio of a long side to a short side when viewed through in the film-thickness direction.
In this case, since vibration sections are arranged with high density, an unnecessary region is omitted. Accordingly, an overall area of the filter is reduced.
Use of the piezoelectric resonator and the piezoelectric filter according to preferred embodiments of the present invention improves the heat-radiating property and prevents heat from being generated due to unnecessary vibration.
 Other features, elements, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of preferred embodiments of the present invention with reference to the attached drawings.
BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view illustrating a piezoelectric resonator according to a first preferred embodiment of the present invention.
FIGS. 2A and 2B are sectional views illustrating the piezoelectric resonator according to the first preferred embodiment of the present invention.
FIGS. 3A to 3F are Smith charts of the piezoelectric resonator according to the first preferred embodiment of the present invention.
FIGS. 4A and 4B are Smith charts of the piezoelectric resonator according to the first preferred embodiment of the present invention.
FIG. 5 is a model chart illustrating heat transfer.
FIG. 6 is a sectional view illustrating a piezoelectric resonator according to a first modification of the first preferred embodiment of the present invention.
FIG. 7 is a plan view illustrating a piezoelectric resonator according to a second modification of the first preferred embodiment of the present invention.
FIGS. 8A to 8F are Smith charts of a piezoelectric resonator according to a second preferred embodiment of the present invention.
FIGS. 9A to 9C are sectional views illustrating a piezoelectric resonator according to a third preferred embodiment of the present invention.
FIG. 10 is a sectional view illustrating a piezoelectric filter according to a fourth preferred embodiment of the present invention.
FIG. 11 is a circuit diagram illustrating the piezoelectric filter according to the fourth preferred embodiment of the present invention.
FIG. 12 is a diagram of a layout of a piezoelectric filter according to a sixth preferred embodiment of the present invention.
 FIG. 13 is a circuit diagram illustrating the piezoelectric filter according to the sixth preferred embodiment of the present invention.
FIGS. 14A to 14C are sectional views illustrating a piezoelectric resonator according to a seventh preferred embodiment of the present invention.
FIG. 15 is a circuit diagram illustrating a piezoelectric resonator according to an eighth preferred embodiment of the present invention.
FIG. 16 is a circuit diagram illustrating a piezoelectric resonator according to a ninth preferred embodiment of the present invention.
FIG. 17 is a plan view illustrating a piezoelectric resonator according to the related art.
FIG. 18 is a sectional view illustrating the piezoelectric resonator according to the related art.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will be described with reference to FIGS. 1 to 16.
First Preferred Embodiment

A piezoelectric resonator 10 according to a first preferred embodiment of the present invention will be described with reference to FIGS. 1 to 5.
As schematically shown in FIG. 1 which is a plan view, FIG. 2A which is a sectional view taken along a line A to A of FIG. 1, and FIG. 2B which is a sectional view taken along a line B to B, a thin-film section is provided on a substrate 12 of the piezoelectric resonator 10. That is, a supporting film 14, a lower electrode 16, a piezoelectric film 17, an upper electrode 18, a heat-radiating film 20, and a step-forming film 22 are laminated on the substrate 12 in that order. In FIG. 1, the lower electrode 16 and the upper electrode 18 are indicated by hatching, and portions of the lower electrode 16 and the upper electrode 18 which are hidden by other films which overlap thereon are indicated by a dashed hatching.
 The thin-film section includes a first thin-film section (denoted by a reference character S in FIG. 2A) supported by the substrate 12 and a second thin-film section (denoted by reference characters R, L, and W in FIG. 2A) which is isolated from the substrate 12 with a gap 13 interposed therebetween. In the second thin-film section, a vibration section (denoted by the reference character W in FIG. 2A) which is arranged such that a piezoelectric film 17 is interposed between the lower electrode 16 and the upper electrode 18 is provided. The gap 13 is configured such that a sacrificial film 11 is arranged on the substrate 12 as indicated by a dashed line in FIG. 1, the lower electrode 16, for example, is further provided on the sacrificial film 11, and thereafter, the sacrificial film 11 is removed.
The vibration section 24 is provided at a portion in which the lower electrode 16 and the upper electrode 18 which are denoted by the hatching in FIG. 1 overlap each other when viewed through in a film-thickness direction (i.e., in a vertical direction relative to the paper of FIG. 1, and in a vertical direction of the drawing in FIGS. 2A and 2B).
As shown in FIG. 1, a width of the lower electrode 16 is preferably greater than that of the upper electrode 18 in and in the vicinity of the vibration section 24. As indicated by the reference character L in FIG. 2A, when viewed through in the film-thickness direction, an additional-film region corresponds to a portion of the lower electrode 16, which protrudes outward from the vibration section corresponding to the reference character W. The additional-film region traps vibration in the vibration section by a mass addition operation.
 The heat-radiating film 20 includes an opening 21 as shown in FIG. 1. The opening 21 of the heat-radiating film 20 is in contact with a periphery of the vibration section 24 when viewed from the film-thickness direction. As shown in FIGS. 2A and 2B, the heat-radiating film 20 extends from the periphery of the vibration section 24 to the first thin-film section. As shown in FIG. 1 and FIGS. 2A and 2B, the heat-radiating film 20 is preferably in contact with peripheral edges 18 a, 18 b, and 18 c of the upper electrode 18 which correspond to portions (three sides) of the periphery of the vibration section 24.
The heat-radiating film 20 should preferably be in contact with at least a portion of the vibration section 24 when viewed through in the film-thickness direction. A configuration in which the heat-radiating film 20 is in contact with three sides, two side, or only one side of the periphery of the vibration section 24 of a substantially rectangular shape may preferably be used, for example, instead of the configuration shown in FIG. 1 in which the heat-radiating film 20 is in contact with four sides of the periphery of the substantially rectangular vibration section 24 when viewed through in the film-thickness direction. Alternatively, the heat-radiating film 20 may preferably be in contact with only a portion of a certain side of the periphery of the vibration section 24, or may preferably be partially in contact with the periphery of the vibration section 24 (that is, the heat-radiating film 20 partially has portions which are not in contact with the vibration unit 24).
 The step-forming film 22 is arranged inside the opening 21 of the heat-radiating film 20. A resonant frequency of the vibration section 24 is controlled by changing a thickness of the step-forming film 22. The step-forming film 22 is preferably formed by, for example, etching performed on an entire wafer after a device is manufactured, etching performed on a portion of a wafer after partial masking is performed, or etching performed for individual devices, and is used for frequency control.
A thickness of a periphery-vicinity portion 23 of the step-forming film 22 is preferably less than other portions of the step-forming film 22. A step 19 is provided along the opening 21 of the heat-radiating film 20. The step 19 reduces a spurious response in a frequency region substantially equal to or less than the resonant frequency.
Note that the supporting film 14 and the step-forming film 22 may be omitted.
An example of a method for manufacturing the piezoelectric resonator 10 will now be described.
The sacrificial film 11 preferably made of ZnO, for example, is arranged on the substrate 12 so as to form a gap. The ZnO sacrificial film 11 is formed by an appropriate method, such as wet etching, for example.
 Then, the supporting film 14 which preferably has a thickness of about 100 nm, for example, and which is preferably made of a SiO₂ film, for example, is formed so as to cover the ZnO sacrificial film 11. Thereafter, a laminated metal film which preferably has a thickness of about 10 nm, for example, and which is preferably made of Ti, for example, a laminated metal film which preferably has a thickness of about 30 nm, for example, and which is preferably made of Pt, for example, a laminated metal film which preferably has a thickness of about 60 nm, for example, and which is preferably made of Au, for example, a laminated metal film which preferably has a thickness of about 10 nm, for example, and which is preferably made of Pt, for example, and a laminated metal film which preferably has a thickness of about 10 nm and which is preferably made of Ti, for example, are formed in this order on the supporting film 14 by sputtering. Then, a resultant object is patterned by a photolithography method so that the lower electrode 16 is formed.
Next, the piezoelectric film 17 preferably made of AlN, for example, is formed by sputtering so as to cover the lower electrode 16 and so as to preferably have a thickness of about 1580 nm, for example. Thereafter, patterning is performed so that a portion of the lower electrode 16 is exposed.
 Then, a laminated metal film which preferably has a thickness of about 10 nm, for example, and which is preferably made of Ti, for example, a laminated metal film which preferably has a thickness of about 10 nm, for example, and which is preferably made of Pt, for example, a laminated metal film which preferably has a thickness of about 60 nm, for example, and which is preferably made of Au, for example, a laminated metal film which preferably has a thickness of about 30 nm, for example, and which is preferably made of Pt, for example, and a laminated metal film which preferably has a thickness of about 10 nm, for example, and which is preferably made of Ti, for example, are formed in this order on the piezoelectric film 17 by sputtering, and a resultant object is patterned by the photolithography method so that the upper electrode 18 is formed.
Thereafter, the heat-radiating film 20 preferably made of AlN, for example, is formed from a periphery of the upper electrode 18 to the first thin-film portion so as to have a thickness of 680 nm, for example, and patterning is performed so that the opening 21 is formed and the upper electrode 18 is exposed.
Then, the step-forming film 22 preferably made of a SiO₂ film, for example, is arranged on an entire or substantially an entire upper surface of the upper electrode 18 which is exposed from the opening 21 of the heat-radiating film 20 so as to preferably have a thickness of about 100 nm, for example.
 Next, an upper surface of the step-forming film 22 is subjected to dry etching so that a portion along the periphery of the step-forming film 22 (that is, a portion along the opening 21 of the heat-radiating film 20) is removed. By this process, the step 19 is formed in the step-forming film 22 along the periphery of the step-forming film 22. Note that the dry etching is performed so that a thickness of the periphery-vicinity portion 23 of the step-forming film 22 is reduced by about 20 nm, for example.
After the piezoelectric film 17 of AlN is formed, a surface of the piezoelectric film 17 may preferably be subjected to etching by an ICP (Inductively Coupled Plasma) etching device using an Ar plasma and subjected to flattening processing. Alternatively, a thin piezoelectric film may preferably be formed, and the flattening processing may be performed on a surface of the thin piezoelectric film. Thereafter, a thick piezoelectric film may preferably be formed, and the flattening processing may be performed on a surface of the thick piezoelectric film. As described above, by flattening the piezoelectric film 17, the crystallinity of the piezoelectric film 17 is improved, and the piezoelectric resonator having excellent electric-power resistance is obtained. Note that a noble gas such as He, Ne, Kr, Xe, or Rn or gas cluster may preferably be used instead of Ar, for example.
A film thickness, a resonant frequency, and an area for a capacitance of about 1 pF in the example of the method for manufacturing of the piezoelectric resonator 10 are shown in Table 1 below.
 TABLE 1 Film Configuration of Resonator, Resonant Frequency, and Area for 1 pF Film Thickness (nm) Step Forming Film SiO₂ 100 nm Amount of Step Etching  20 nm Heat-Radiating Film AlN 680 Upper Electrode (Ti/Pt/Au/Pt/Ti) 10/10/60/30/10 Piezoelectric Film AlN 1580  Lower Electrode (Ti/Pt/Au/Pt/Ti) 10/30/60/10/10 Supporting Film SiO₂ 100 Resonant Frequency (MHz) 1880  Area for Capacitance of 1 pH (μm²) 18000 

In the example of the manufacturing method, when a width D (refer to FIG. 2A) of a step region which corresponds to the periphery-vicinity portion 23 of the step-forming film 22 is within a range from about 5 μm to about 25 μm, for example, a spurious response caused by a Lamb wave is suppressed. Furthermore, when an amount of etching for forming the step 19 is within a range of about 20 nm±5 nm (a center value±25%), for example, the spurious response caused by the Lamb wave can be suppressed. Moreover, when a width L (refer to FIG. 2A) corresponding to the additional-film region of the lower electrode 16 is substantially equal to or greater than about 10 μm, for example, the spurious response caused by the Lamb wave is suppressed.
 The spurious response changes in accordance with the film thickness of the heat-radiating film 20. A change of a spurious characteristic when the thickness of the heat-radiating film AlN is gradually increased from 0 nm (that is, the heat-radiating film 20 is not formed) will be shown in Smith charts of FIGS. 3A to 3F. As shown in FIGS. 3C, 3D and 3E, when the thickness of the heat-radiating film AlN is in a range from about 660 nm to about 700 nm, for example, the spurious response is suppressed. However, as shown in FIGS. 3A, 3B, and 3F, when the thickness of the heat-radiating film AlN is in a range other than the range from about 660 nm to about 700 nm, the spurious response is frequently generated. Unnecessary vibration is trapped in the vibration section and is scattered in peripheral portions of the electrodes, resulting in a deterioration of the Q factor. Meanwhile, energy of the unnecessary vibration is converted into heat energy resulting in heat generation.
Accordingly, when the thickness of the heat-radiating film 20 is within a range of about 680±20 nm (a enter value±3%), for example, the spurious response caused by the Lamb wave is suppressed.
Next, an example of the deterioration of electric-power resistance caused by the deterioration of the Q factor is shown in FIGS. 4A and 4B.
 A test of the electric-power resistance is performed on resonators having resonant characteristics as shown in Smith charts of FIGS. 4A and 4B. As a result of the test, breakdown powers of devices of the resonators are about 1.0 W and about 3.4 W, and temperatures of the devices of the resonators are both about 200° C. That is, it is apparent that, as shown in FIG. 4A, in the piezoelectric resonator in which the spurious response is frequently generated, the device has a high heat value even when a low electric power is supplied, and has a low electric-power resistance. On the other hand, it is apparent from the test that, in the piezoelectric resonator in which the spurious response is suppressed as shown in FIG. 4B, excellent electric-power resistance is obtained.
Note that the test of electric-power resistance described herein is a test (step-up test) in which electric power to be supplied to a piezoelectric resonator is gradually increased in accordance with a frequency shift caused by heat generation, that is, electric power to be supplied is stepped up.
By additionally arranging the heat-radiating film 20, the spurious response is suppressed, and heat generation due to a degraded Q factor is suppressed.
Furthermore, since the step 19 is formed along the periphery of the step-forming film 22, the spurious response in a frequency region substantially equal to or less than the resonant frequency is suppressed, and accordingly, heat generation due to a degraded Q factor is suppressed.
 Moreover, a portion of heat generated in the vibration section is transmitted from the upper electrode 18 through the step-forming film 22 which is in contact with the upper electrode 18 to the first thin-film section. Therefore, a heat-radiating path is enlarged, and heat generated in the vibration section is effectively radiated to a supporting section.
Next, the enlargement of the heat-radiating path and effective radiation of heat generated in the vibration section to the supporting unit will be described.
In general, a heat value Q transmitted from a surface A to a surface B shown in FIG. 5 is represented by the following Equation (1): Q=λ·W·t·(T _(A) −T _(B))/L  (1) wherein, λ denotes a heat conductivity, W denotes a width of a heat-transfer path in cross section, t denotes a thickness of the heat-transfer path in cross section, T_(A) denotes a temperature of the surface A, T_(B) denote a temperature of the surface B, and L denotes a length of the heat-transfer path.
An inverse number 1/R of thermal resistance R denotes an index representing a level of the heat-radiating property, and as the value 1/R is increased, the level the heat-radiating property is also increased. Using the values λ, W, t, and L of Equation (1), the value 1/R is represented by Equation (2) below: 1/R=λ·W·t/L  (2)

According to Expression (2), as the values λ, W, and t increase, and the value L is reduced, the level of the heat-radiating property is increased.
 That is, in the related art disclosed in Japanese Unexamined Patent Application Publication No. 2004-120219, the heat generated in the vibration section is transmitted to a wiring unit which is defined by a metal film having a thickness of about 100 nm to about 200 nm and which has a relatively low heat conductivity and a portion of the piezoelectric film disposed outside the vibration section, and thereafter, transmitted through a region in which the heat-radiating film is provided to the supporting unit. Then, the heat is radiated through an Si substrate which is a good heat conductor, for example.
On the other hand, in the configuration of the first preferred embodiment according to the present invention, since the heat-radiating film is in contact with the vibration section, the heat generated in the vibration section is directly transmitted to the region corresponding to the heat-radiating film. Thereafter, the heat reaches the supporting unit, and is radiated through the Si substrate which is the good heat conductor. Accordingly, the heat-radiating efficiency is dramatically improved when compared to that in the related art.
When material included in the configuration of the piezoelectric resonator 10 is used for the heat-radiating film 20, it is not necessary to prepare another material. Therefore, the cost of a device is reduced. Heat conductivities of various material members used in the piezoelectric resonator are shown in Table 2.
 TABLE 2 Various Material Members and Heat Conductivities Heat Conductivity Material Form (W/mK) AlN C-axis alignment 50 thin film AlN non-alignment thin 25 film ZnO C-axis alignment 5 thin film SiO₂ amorphous thin film 1 Diamond polycrystal/single- 900-2000 crystal thin film DLC (Diamond-Like- polycrystal thin 40 Carbon) film Pt polycrystal 70 Au polycrystal 320 Cu polycrystal 390 Si single-crystal bulk 150

According to Table 2, it is apparent that AlN having a large heat conductivity is preferable for the insulating material used for the heat-radiating film. Furthermore, diamond or DLC may be used for the heat-radiating film, and ALN, diamond, or DLC may be used for the supporting film, for example.
A diamond thin film is preferably formed by a micro-wave plasma method, a thermal filament method, a high-frequency plasma method, or a combustion flame method, for example. A DLC thin film is preferably formed by a CVD (chemical vapor deposition) method, such as a plasma CVD method in particular, a PVC (physical vapor deposition) method, a sputtering method, or an ion plating method, for example.
Note that conductive material may be used for the heat-radiating film. However, when the conductive material is arranged so as to cover the entire or substantially the entire periphery of the vibration section, the configuration is complicated in order to prevent the conductive material from being short circuited with conductive lines. Therefore, the conductive material may be used around only a portion of the periphery of the vibration section, and in addition, unnecessary parasitic capacitance may be generated or electromagnetic interference, for example, may occur. Accordingly, an insulating film is preferably used for the heat-radiating film 20.
 In the piezoelectric resonator 10 of the first preferred embodiment, thicknesses of portions other than the vibration section in the second thin-film section are increased by adding the heat-radiating film 20 having the opening 21 for the vibration section, while a desired resonant frequency is obtained. By this, the strength of a membrane configuration in which the second thin-film section is isolated from the substrate is improved.
First Modification

As shown in FIG. 6 which is a sectional view of a piezoelectric resonator 10 a, a portion 21 a of the heat-radiating film 20 may preferably overlap at least a portion of the vibration section. In this case, the heat-radiating film 20 covers at least a portion of the vibration section.
Second Modification

As shown in FIG. 7 which is a plan view of a piezoelectric resonator 10 b, the heat-radiating film 20 may preferably extend only in a direction (in a lateral direction of the drawing) in which portions except for extending-line portions of the lower electrode 16 and the upper electrode 18 extend but not extend in a direction in which the extending-line portions extend (in a vertical direction of the drawing).
Second Preferred Embodiment

A configuration of a second preferred embodiment of the present invention is substantially the same as that of the first preferred embodiment. Hereinafter, components that are the same as or similar to those of the first preferred embodiment are denoted by the same reference numerals as those used in the first preferred embodiment, and a difference from the first preferred embodiment will primarily be described.
As shown in Table 3 which is different from Table 1 of the first preferred embodiment, a piezoelectric resonator of the second preferred embodiment is different from that of the first preferred embodiment in a film configuration.
 TABLE 3 Film Configuration of Resonator, Resonant Frequency, and Area for 1 pF Film Thickness (nm) Step Forming Film SiO₂ 100 nm Amount of Step Etching  20 nm Heat-Radiating Film AlN 900 Upper Electrode (Ti/Pt/Au/Pt/Ti) 10/10/80/70/10 Piezoelectric Film AlN 1135  Lower Electrode (Ti/Pt/Au/Pt/Ti) 10/70/80/10/10 Supporting Film SiO₂ 100 Resonant Frequency 1880  Area for Capacitance of 1 pH (μm²) 13000 

Smith charts of FIGS. 8A to 8F represent resonant characteristics when only a thickness of a heat-radiating film AlN is changed. As shown in FIGS. 8C and 8D, the heat-radiating film AlN prevents generation of a spurious response due to a Lamb wave when the thickness of the heat-radiating film AlN is within a range of about 900 nm±20 nm (a center value±2.3%), for example.
When Table 3 is compared to Table 1, a required area for arranging a resonator having a capacitance of about 1 pF in a configuration of the second preferred embodiment is reduced by about 27% from the area of the configuration of the first preferred embodiment. Therefore, the second preferred embodiment achieves miniaturization of the device. Furthermore, since only a small area is required for a vibration section, a distance through which heat generated in the approximate center of the vibration section is transmitted to a heat-radiating film unit is reduced. Accordingly, an excellent heat-radiating property and an excellent electric-power resistance are obtained.
Third Preferred Embodiment

A piezoelectric resonator according to a third preferred embodiment of the present invention will be described with reference to FIGS. 9A to 9C which are sectional views.
 A configuration of the piezoelectric resonator of the third preferred embodiment is the substantially same as that of the first preferred embodiment except that a taper is provided in the vicinity of an end portion of a heat-radiating film which is in contact with the vibration section or an end portion of the heat-radiating film which overlaps the vibration portion. A step-forming film and a supporting film are not shown in FIG. 9. However, the step-forming film and the supporting film may preferably be provided.
In a piezoelectric resonator 10 p shown in FIG. 9A, an end portion 21 p having a tapered shape in cross section which is included in a heat-radiating film 20 overlaps an upper electrode 18 so that the heat-radiating film 20 overlaps a portion inside a periphery of the vibration section when transparently viewed from a film-thickness direction.
In a piezoelectric resonator 10 q shown in FIG. 9B, an end portion 21 q having a tapered shape in cross section which is included in a heat-radiating film 20 is in contact with an upper electrode 18 so that the heat-radiating film 20 is in contact with a vibration section when transparently viewed from a film-thickness direction.
In a piezoelectric resonator 10 r shown in FIG. 9C, an upper electrode 18 overlaps an end portion 21 r having a tapered shape in cross section which is included in a heat-radiating film 20 so that the heat-radiating film 20 is overlapped by a portion inside a periphery of a vibration section when transparently viewed from a film-thickness direction.
 Since an acoustic characteristic is gradually changed in the end portion of the vibration section due to the taper provided in each of the edge portions 21 p, 21 q, and 21 r of the respective heat-radiating films 20, a range of allowable displacement of the heat-radiating films 20 which suppress spurious responses is increased, and accordingly, manufacturing tolerances can be increased. For example, in a taper angle of about 90 degrees (i.e., substantially vertical), when a width X of an overlapping region (refer to FIG. 9A) satisfies X≦0.5 μm, the spurious response is sufficiently suppressed. In a taper angle of about 45 degrees, when the width X satisfies X<1.0 μm, the spurious response is sufficiently suppressed. That is, as the taper angle is decreased, the range of allowable displacement is increased.
Fourth Preferred Embodiment

A piezoelectric filter according to a fourth preferred embodiment of the present invention will be described with reference to FIGS. 10 and 11.
 As shown in FIG. 10, a piezoelectric filter 10 k is configured such that a plurality of piezoelectric resonators S1 and P1 are arranged on a single substrate 12. That is, a plurality of vibration sections 24 s and 24 t are provided on a second thin-film portion which is isolated from the substrate 12 with a gap 13 interposed therebetween. The vibration section 24 s is configured such that a piezoelectric film 17 k is sandwiched between electrodes 16 s and 18 s, and the vibration section 24 t is configured such that the piezoelectric film 17 k is sandwiched between electrodes 16 t and 18 t. The piezoelectric filter 10 k, as shown as a circuit diagram in FIG. 11, has a basic L-shape and a one-step configuration including a piezoelectric resonator S1 connected in series and a piezoelectric resonator P1 connected in parallel, and such basic configurations are connected to one another in several steps in a cascade manner.
A film configuration of an example of a method of manufacturing the piezoelectric filter 10 k is shown in Table 4 below.
 TABLE 4 Film Configuration of Resonator, Resonant Frequency, and Area for 1 pF Series Resonator Parallel Resonator Film Thickness (nm) (S1) (P1) Step Forming Film SiO₂ 100 nm 100 nm Amount of Step Etching  20 nm  20 nm Heat-Radiating Film AlN 680 680 Upper Electrode 10/10/60/30/10 10/10/60/30/10 (Ti/Pt/Au/Pt/Ti) Piezoelectric Film AlN 1580  1580  Lower Electrode 10/30/60/10/10 10/50/60/10/10 (Ti/Pt/Au/Pt/Ti) Supporting Film SiO₂ 100 100 Resonant Frequency 1880  1822  Area for Capacitance of 18000  18000  1 pH (μm²)

In the piezoelectric filter 10 k of the fourth preferred embodiment, a ripple is suppressed and heat generation caused by an increased loss is suppressed, and accordingly, excellent electric-power resistance is obtained. Furthermore, a heat-radiating path is enlarged, and heat generated in the vibration sections is effectively radiated to a supporting portion, and accordingly, excellent electric-power resistance is obtained.
When the piezoelectric film AlN of Table 4 is to be formed, as with the piezoelectric resonator of the first preferred embodiment, the piezoelectric film 17 k is formed and a surface of the piezoelectric film 17 k is subjected to flattening processing. Thereafter, a piezoelectric film of the parallel resonator P1 having a low resonant frequency is covered by a resist, and then, a surface of a piezoelectric film of the series resonator S1 having a high resonant frequency is subjected to flattening processing.
Fifth Preferred Embodiment

A configuration of a piezoelectric filter according to a fifth preferred embodiment of the present invention is substantially the same as that of the piezoelectric filter of the fourth preferred embodiment except for a film configuration. The film configuration of the fifth preferred embodiment is shown in Table 5 below.
 TABLE 5 Film Configuration of Resonator, Resonant Frequency, and Area for 1 pF Series Resonator Parallel Resonator Film Thickness (nm) (S1) (P1) Step Forming Film SiO₂ 100 nm 100 nm Amount of Step Etching  20 nm  20 nm Heat-Radiating Film AlN 900 900 Upper Electrode 10/10/80/70/10 10/10/80/70/10 (Ti/Pt/Au/Pt/Ti) Piezoelectric Film AlN 1135  1135  Lower Electrode 10/70/80/10/10 10/95/80/10/10 (Ti/Pt/Au/Pt/Ti) Supporting Film SiO₂ 100 100 Resonant Frequency 1880  1822  Area for Capacitance of 13000  13000  1 pH (μm²)

In the piezoelectric filter of the fifth preferred embodiment, areas required to arrange the resonators having capacitances of about 1 pF are reduced by about 27% as compared to the configuration of the fourth preferred embodiment. Therefore, the fifth preferred embodiment achieves miniaturization of a device. Furthermore, since only small areas are required for respective vibration sections, a distance through which heat generated in the approximate center of each of the vibration sections is transmitted to a heat-radiating film unit is reduced. Accordingly, an excellent heat-radiating property and an excellent electric-power resistance are obtained.
Sixth Preferred Embodiment

A piezoelectric filter according to a sixth preferred embodiment of the present invention will be described with reference to FIGS. 12 and 13.
As shown in FIG. 12, the piezoelectric filter of the sixth preferred embodiment is configured such that piezoelectric resonators P1 to P3 are connected in parallel to piezoelectric resonators S1 to S4 which are connected to one another in series. In the piezoelectric filter, the piezoelectric resonators S1 to S4 and P1 to P3 are preferably arranged as shown in FIG. 13 which is a top plan view.
Film configurations of the resonators S1 to S4 and P1 to P3 in an example of a method for manufacturing the piezoelectric filter of the sixth preferred embodiment are shown in Table 6 below.
 TABLE 6 Film Configuration of Resonator, Resonant Frequency, and Area for 1 pF Series Resonators Parallel Resonators Film Thickness (nm) (S1, S2, S3, S4) (P1, P2, P3) Step Forming Film SiO₂ 100 nm 100 nm Amount of Step Etching  20 nm  20 nm Heat-Radiating Film AlN 680 680 Upper Electrode 10/10/60/30/10 10/10/60/30/10 (Ti/Pt/Au/Pt/Ti) Piezoelectric Film AlN 1580  1580  Lower Electrode 10/30/60/10/10 10/50/60/10/10 (Ti/Pt/Au/Pt/Ti) Supporting Film SiO₂ 100 100 Resonant Frequency 1880  1822  Area for Capacitance of 18000  18000  1 pH (μm²)

Characteristic values of the resonators S1 to S4 and P1 to P3 are shown in Table 7 below.
TABLE 7 Characteristic Values of Resonators of Filter S1 S2 S3 S4 P1 P2 P3 capacitance (pF) 1.7 1.1 1.1 1.7 2.2 1.7 2.2 Δf (MHz) 57 56 56 57 55 55 55 area (μm²) 30300 19600 19600 30300 39300 30300 39300

Tables 6 and 7 show an example of a method for manufacturing a Tx filter for a US-PCS band (pass band: 1850 MHz to 1910 MHz).
Any of the first to fifth preferred embodiments may be used for cross-sectional configurations of the piezoelectric resonators and the piezoelectric filter. Furthermore, the film configurations of the piezoelectric resonators as shown in the fifth preferred embodiment (Table 5) may preferably be used.
