PIEZOELECTRIC ELEMENT, PIEZOELECTRIC ACTUATOR, DROPLET DISCHARGE HEAD, LIQUID DROPLET EJECTION APPARATUS, AND FERROELECTRIC MEMORY

Abstract

A piezoelectric element comprising a first electrode, a second electrode, and a lead zirconate titanate film located between the first electrode and the second electrode. The piezoelectric element is formed on a Si substrate whose principal surface is (001) plane. The Si substrate has uniform crystalline orientation in an in-plane direction and an out-of-plane direction. (110) plane of the Si substrate and (100) plane of the lead zirconate titanate film are parallel. In a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate film obtained by X-rays incident from [100] direction of the Si substrate can be fitted with three component peaks.

Claims

1. A piezoelectric element comprising a first electrode, a second electrode, and a lead zirconate titanate film located between the first electrode and the second electrode, wherein the piezoelectric element is formed on a Si substrate whose principal surface is (001) plane, the Si substrate has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, (110) plane of the Si substrate and (100) plane of the lead zirconate titanate film are parallel, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate film obtained by X-rays incident from [100] direction of the Si substrate can be fitted with three component peaks.

2. A piezoelectric element comprising a first electrode, a second electrode, and a lead zirconate titanate film located between the first electrode and the second electrode, wherein at least one of the first electrode and the second electrode includes a Pt electrode whose principal surface is (001) plane, the Pt electrode has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, (110) plane of the Pt electrode and (100) plane of the lead zirconate titanate film are parallel, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate film obtained by X-rays incident from [100] direction of the Pt electrode can be fitted with three component peaks.

3. The piezoelectric element according to claim 1, wherein an angle of a plane angle formed by (001) plane of the Si substrate and (001) plane of the lead zirconate titanate film is in the range of 0.34 to 0.35.

4. The piezoelectric element according to claim 2, wherein an angle of a plane angle formed by (001) plane of the Pt electrode and (001) plane of the lead zirconate titanate film is in the range of 0.34 to 0.35.

5. The piezoelectric element according to claim 1, wherein an angle of a plane angle formed by (100) plane of the Si substrate and (100) plane of the lead zirconate titanate film is in the range of 40 to 50.

6. The piezoelectric element according to claim 2, wherein an angle of a plane angle formed by (100) plane of the Pt electrode and (100) plane of the lead zirconate titanate film is in the range of 40 to 50.

7. The piezoelectric element according to claim 1, wherein a diffraction peak of (004) plane of the lead zirconate titanate film obtained by out-of-plane 2- scanning of an X-ray diffraction method can be fitted with three component peaks.

8. The piezoelectric element according to claim 1, wherein the composition of lead zirconate titanate constituting the lead zirconate titanate film is Pb.sub.X(Zr.sub.Y, Ti.sub.1-Y)O.sub.3 [1.0X1.2, 0.4Y0.6].

9. The piezoelectric element according to claim 1, wherein a thickness of the lead zirconate titanate film is in the range of 0.1-5.0 m.

10. The piezoelectric element according to claim 1, wherein at the interface between the second electrode and the lead zirconate titanate film, a dielectric film composed of a dielectric having a dielectric constant lower than that of lead zirconate titanate constituting the lead zirconate titanate film is present, and the dielectric film and the lead zirconate titanate film have epitaxial relations such that (100) plane of the dielectric film and (100) plane of the lead zirconate titanate film are parallel.

11. The piezoelectric element according to claim 10, wherein the dielectric is lanthanum lead titanate.

12. The piezoelectric element according to claim 10, wherein a total thickness of the lead zirconate titanate film and the dielectric film is in the range of 0.1 to 5.0 m.

13. The piezoelectric element according to claim 10, wherein a RMS value of surface roughness of the dielectric film at the side of the second electrode is 5.0 nm or less.

14. The piezoelectric element according to claim 1, wherein when the piezoelectric constant measured by grounding the first electrode and applying a voltage of 30V to the second electrode is A and the piezoelectric constant measured by applying a voltage of 10V to the second electrode is B, B is 95% or more of A.

15. A piezoelectric actuator comprising a piezoelectric element, wherein the piezoelectric element is a piezoelectric element according to claim 1.

16. A droplet discharge head comprising a piezoelectric actuator, wherein the piezoelectric actuator is a piezoelectric actuator according to claim 15.

17. A liquid droplet ejection apparatus comprising a droplet discharge head, wherein the droplet discharge head is a droplet discharge head according to claim 16.

18. A ferroelectric memory comprising a piezoelectric element, wherein the piezoelectric element is a piezoelectric element according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] FIG. 1 Schematic cross-section view of a piezoelectric element

[0052] FIG. 2 Schematic view of a sample for measurement of the piezoelectric constant

[0053] FIG. 3 Schematic view of a measuring device for the piezoelectric constant

[0054] FIG. 4 Result of out-of-plane XRD measurement of a piezoelectric element No. 1

[0055] FIG. 5 Result (magnified) of out-of-plane XRD measurement of a piezoelectric element No. 1

[0056] FIG. 6 Fitting curve when fitting a peak derived from (004) plane of a PZT film of a piezoelectric element No. 1 with one component peak

[0057] FIG. 7 Fitting curve when fitting a peak derived from (004) plane of a PZT film of a piezoelectric element No. 1 with three component peaks

[0058] FIG. 8 Result of in-plane XRD measurement of a piezoelectric element No. 1

[0059] FIG. 9 Fitting curve when fitting symmetric surface reflection peak of RC measurement of a piezoelectric element No. 1 with one component peak

[0060] FIG. 10 Fitting curve when fitting symmetric surface reflection peak of RC measurement of a piezoelectric element No. 1 with two component peaks

[0061] FIG. 11 Fitting curve when fitting symmetric surface reflection peak of RC measurement of a piezoelectric element No. 1 with three component peaks

[0062] FIG. 12 Result of out-of-plane XRD measurement of a piezoelectric element No. 2

[0063] FIG. 13 Result (magnified) of out-of-plane XRD measurement of a piezoelectric element No. 2

[0064] FIG. 14 Fitting curve when fitting a peak derived from (004) plane of a PZT film of a piezoelectric element No. 2 with one component peak

[0065] FIG. 15 Result of in-plane XRD measurement of a piezoelectric element No. 2

[0066] FIG. 16 Fitting curve when fitting symmetric surface reflection peak of RC measurement of a piezoelectric element No. 2 with one component peak

[0067] FIG. 17 Atomic force microscope image of a PLT film of a piezoelectric element No. 1

[0068] FIG. 18 Atomic force microscope image of a PLT film of a piezoelectric element No. 2

MODE FOR CARRYING OUT THE INVENTION

[0069] A piezoelectric element of the present invention is characterized in that, as an embodiment, the piezoelectric element includes a first electrode, a second electrode, and a lead zirconate titanate film located between the first electrode and the second electrode, wherein the piezoelectric element is formed on a Si substrate whose principal surface is (001) plane, the Si substrate has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, (110) plane of the Si substrate and (100) plane of the lead zirconate titanate film are parallel, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate film obtained by X-rays incident from [100] direction of the Si substrate can be fitted with three component peaks.

[0070] Further, a piezoelectric element of the present invention is characterized in that, as an embodiment, the piezoelectric element includes a first electrode, a second electrode, and a lead zirconate titanate film located between the first electrode and the second electrode, wherein at least one of the first electrode and the second electrode includes a Pt electrode whose principal surface is (001) plane, the Pt electrode has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, (110) plane of the Pt electrode and (100) plane of the lead zirconate titanate film are parallel, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate film obtained by X-rays incident from [100] direction of the Pt electrode can be fitted with three component peaks.

[0071] These features are technical features common to or corresponding to embodiments below.

[0072] In an embodiment of a piezoelectric element of the present invention, the angle formed by (001) plane of the Si substrate or the Pt electrode and (001) plane of the lead zirconate titanate film is preferably in the range of 0.34 to 0.35, from the viewpoint of crystalline structure.

[0073] In an embodiment of a piezoelectric element of the present invention, the angle formed by (100) plane of the Si substrate or the Pt electrode and (100) plane of the lead zirconate titanate film is preferably in the range of 40 to 50, from the viewpoint of crystalline structure.

[0074] In an embodiment of a piezoelectric element of the present disclosure, it is preferable from the viewpoint of crystalline structure that a diffraction peak of (004) plane of the lead zirconate titanate film obtained by out-of-plane 2- scanning of an X-ray diffraction method can be fitted with three component peaks.

[0075] In an embodiment of a piezoelectric element of the present invention, from the viewpoint of the piezoelectric constant, it is preferable that the composition of lead zirconate titanate constituting the lead zirconate titanate film has a Pb.sub.X(Zr.sub.Y, Ti.sub.1-Y)O.sub.3 [1.0X1.2, 0.4Y0.6].

[0076] In an embodiment of a piezoelectric element of the present invention, the thickness of the lead zirconate titanate film is preferably in the range of 0.1 to 5.0 m. As a result, the displacement-generating force required for a piezoelectric element can be obtained.

[0077] In an embodiment of a piezoelectric element of the present invention, it is preferable that at the interface between the second electrode and the lead zirconate titanate film, a dielectric film composed of a dielectric having a dielectric constant lower than that of lead zirconate titanate constituting the lead zirconate titanate film is present, and the dielectric film and the lead zirconate titanate film have epitaxial relations such that (100) plane of the dielectric film and (100) plane of the lead zirconate titanate film are parallel. As a result, the dielectric constant can be lowered, and an electromechanical coupling coefficient can be further improved.

[0078] In an embodiment of a piezoelectric element of the present invention, from the viewpoint of dielectric constant, it is preferable that the dielectric is lanthanum lead titanate.

[0079] In an embodiment of a piezoelectric element of the present invention, the total thickness of the lead zirconate titanate film and the dielectric film is preferably in the range of 0.1 to 5.0 m. As a result, the displacement-generating force required for a piezoelectric element can be obtained.

[0080] In an embodiment of a piezoelectric element of the present invention, a RMS value of surface roughness of the dielectric film at the side of the second electrode is preferably 5.0 nm or less. This improves reliability in long-term driving, adhesion of film, and the like.

[0081] In an embodiment of a piezoelectric element of the present invention, from the viewpoint of linearity of the piezoelectric constant, it is preferable that when the piezoelectric constant measured by grounding the first electrode and applying a voltage of 30V to the second electrode is A and the piezoelectric constant measured by applying a voltage of 10V to the second electrode is B, B is 95% or more of A.

[0082] A piezoelectric actuator of the present invention is a piezoelectric actuator including a piezoelectric element, wherein the piezoelectric element is a piezoelectric element of the present invention.

[0083] A droplet discharge head of the present invention is a droplet discharge head including a piezoelectric actuator, wherein the piezoelectric actuator is a piezoelectric actuator of the present invention.

[0084] A liquid droplet ejection apparatus of the present invention is a liquid droplet ejection apparatus including a droplet discharge head, wherein the droplet discharge head is a droplet discharge head of the present invention.

[0085] A ferroelectric memory of the present invention is a ferroelectric memory including a piezoelectric element, wherein the piezoelectric element is a piezoelectric element of the present invention.

[0086] Hereinafter, the present invention, its constituent elements, and embodiments and aspects for carrying out the present invention will be described in detail. In the present application, to is used in the meaning that numerical values described before and after are included as a lower limit value and an upper limit value.

<1. Summary of a Piezoelectric Element of the Present Invention>

[0087] A piezoelectric element of the present invention is characterized in that, as an embodiment, the piezoelectric element includes a first electrode, a second electrode, and a PZT film located between the first electrode and the second electrode, wherein the piezoelectric element is formed on a Si substrate whose principal surface is (001) plane, the Si substrate has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, (110) plane of the Si substrate and (100) plane of the PZT film are parallel, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate (PZT) film obtained by X-rays incident from [100] direction of the Si substrate can be fitted with three component peaks.

[0088] Further, a piezoelectric element of the present invention is characterized in that, as an embodiment, the piezoelectric element includes a first electrode, a second electrode, and a PZT film located between the first electrode and the second electrode, wherein at least one of the first electrode and the second electrode includes a Pt electrode whose principal surface is (001) plane, the Pt electrode has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, (110) plane of the Pt electrode and (100) plane of the PZT film are parallel, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of the lead zirconate titanate (PZT) film obtained by X-rays incident from [100] direction of the Pt electrode can be fitted with three component peaks.

[0089] The PZT film or the like included in the piezoelectric element is composed of crystals. In the present invention, the crystal plane and the crystal orientation of the crystal are expressed using the Miller index (Miller index). A crystal is a collection of unit lattices, which are formed by a collection of planes made up of atoms. The plane made by these atoms is called a crystal plane. In addition, although the crystal planes are arranged at equal intervals in parallel with each other, a direction of arrangement of the crystal planes (a direction perpendicular to the crystal plane) is referred to as a crystal orientation. Crystal planes are denoted as (100) planes, (110) planes, etc. using the plane indexes of the Miller index. Further, the crystal orientation is expressed as [100] direction or the like by using the direction index (orientation index) of the Miller index.

[0090] As a reference of the Miller index in the present invention, the out-of-plane direction, which is the normal direction of the principal surface of Si substrate, is defined as [001] direction, and the direction perpendicular to (100) plane or (010) plane among the in-plane direction, which is the direction parallel to the principal surface of a Si substrate, is defined as [100] direction or [010] direction, respectively. [100] orientation and [010] orientation are indistinguishable because Si is cubic phase and rotationally symmetric. In addition, when the relation with a Pt electrode is defined instead of Si substrate, similarly, the out-of-plane direction, which is the normal direction of the principal surface of a Pt electrode, is defined as [001] direction, and the direction perpendicular to (100) plane or (010) plane among the in-plane direction, which is the direction parallel to the principal surface of a Pt electrode, is defined as [100] direction or [010] direction, respectively. Since Pt is also rotationally symmetric in the plane, [100] direction and [010] direction are indistinguishable.

<2. Configuration of a Piezoelectric Element>

[0091] A piezoelectric element of the present invention includes a first electrode, a second electrode, and a PZT film located between the first electrode and the second electrode.

[0092] A piezoelectric element of the present invention is preferably formed on a Si substrate whose principal surface is (001) plane. However, after the PZT film or the like is made of film, the Si substrate can be removed and used, and therefore, a piezoelectric element of the present invention is not limited to those formed on the Si substrate.

[0093] Here, a principal surface in the present invention means a surface having the largest surface area.

[0094] Materials of the first electrode and the second electrode are not particularly limited, and Cr, Ni, Cu, Pt, Ir, Ti, IrTi alloy, LaNiO.sub.3, SRO (SrRuO.sub.3), STO(SrTiO.sub.3), or the like can be used. The first electrode may be formed by two or more electrodes. Similarly, the second electrode may be formed by two or more electrodes.

[0095] At least one of the first electrode and the second electrode preferably includes a Pt electrode, and the Pt electrode preferably has (001) plane as a principal surface and preferably has an uniform crystalline orientation in an in-plane direction and an out-of-plane direction. When one of the first electrode and the second electrode includes a Pt electrode, the other electrode is preferably a Cu electrode.

[0096] The first electrode or the second electrode including a Pt electrode is preferably a two-layer structure further including an electrode made of another material. The electrode made of another material may be an SRO electrode or an STO electrode, and is more preferably a SRO electrode. Like the Pt electrode, the electrodes made of other materials preferably have uniform crystalline orientation in an in-plane direction and an out-of-plane direction.

[0097] In a PZT film according to the present invention, the composition of PZT is preferably Pb.sub.X(Zr.sub.Y, Ti.sub.1-Y)O.sub.3 [1.0X1.2, 0.4Y0.6] in terms of the piezoelectric constant.

[0098] In a piezoelectric element of the present invention, it is preferable that a dielectric film formed of a dielectric material having a dielectric constant lower than that of a PZT constituting a PZT film is present at the interface between the second electrode and the PZT film. As a result, the dielectric constant can be lowered, and an electromechanical coupling coefficient can be further improved. The crystalline structure of the dielectric constituting the dielectric film is preferably a perovskite-type structure. Examples of the dielectric having a perovskite-type structure include lead titanate (PbTiO.sub.3), lanthanum lead titanate (PLT:(Pb,La) TiO.sub.3, and barium titanate (BaTiO.sub.3). Among these, those containing lead are preferred, and PLT is particularly preferred from the viewpoint of the dielectric constant.

[0099] A piezoelectric element of the present invention may have another layer, for example, a ZrO.sub.2 layer or a HfO.sub.2 layer between the Si substrate and the first electrode.

[0100] A preferred configuration of a piezoelectric element of the present invention will be described below. The configuration of a piezoelectric element of the present invention is not limited thereto. [0101] (1) Second electrode/dielectric film (PLT film)/PZT film/first electrode (SRO electrode+Pt electrode)/ZrO.sub.2 layer/Si substrate [0102] (2) Second electrode/dielectric film (PLT film)/PZT film/first electrode (SRO electrode+Pt electrode)/HfO.sub.2 layer/Si substrate [0103] (3) Second electrode/dielectric film (PLT film)/PZT film/first electrode (STO electrode+Pt electrode)/ZrO.sub.2 layer/Si substrate [0104] (4) Second electrode/dielectric film (PLT film)/PZT film/first electrode (STO electrode+Pt electrode)/HfO.sub.2 layer/Si substrate [0105] (5) Second electrode/dielectric film (PLT film)/PZT film/first electrode (SRO electrode+Pt electrode)/ZrO.sub.2 layer [0106] (6) Second electrode/PZT film/Second electrode (SRO electrode+Pt electrode)/ZrO.sub.2 layers/Si substrate [0107] (7) Second electrode/dielectric film (PLT film)/PZT film/first electrode (Pt electrode)/ZrO.sub.2 layer/Si substrate [0108] (8) Second electrode/dielectric film (PLT film)/PZT film/first electrode (SRO electrode+Pt electrode)/Si substrate

[0109] Among configuration examples mentioned above, the configuration (1) is particularly preferable. FIG. 1 is a schematic cross-sectional view of a a piezoelectric element having the configuration (1). A piezoelectric element 10 shown in FIG. 1 is formed by laminating a ZrO.sub.2 layer 12, a first electrode 13(Pt electrode 14, and a SRO electrode 15), a PZT film 16, a dielectric film 17, and a second electrode 18 on a Si substrate 11.

[0110] In a piezoelectric element of the present invention, the thickness of a PZT film is preferably in the range of 0.1 to 5.0 m. When a dielectric film is provided, the combined thickness of the PZT film and the dielectric film is preferably 0.1 to 5.0 m. As a result, the displacement-generating force required for a piezoelectric element is obtained.

<3. Crystalline Structure>

[0111] A piezoelectric element of the present invention is characterized in that (110) plane of a Si substrate or a Pt electrode is parallel to (100) plane of a PZT film. When (110) plane of a Si substrate or a Pt electrode and (100) plane of a PZT film are parallel to each other, epitaxial growth/epitaxy of a PZT film is performed, and an epitaxial strain received from the layers below the PZT film (for example, SRO layers) becomes a tensile strain from a compressive strain, so that a mixed crystal of a monoclinic phase and a rhombohedral phase is stabilized and a higher piezoelectric constant is obtained. In addition, since the PZT film becomes an epitaxial film, the dielectric constant of the epitaxial film becomes lower than that of an oriented film, and thus an electromechanical coupling coefficient can be increased.

[0112] In the present invention, (110) plane of a Si substrate and (100) plane of a PZT film are parallel means that when X-rays are incident from [110] direction of a Si substrate in the in-plane measuring of XRD (X-ray diffraction) method, a diffraction peak of (H00) plane of the PZT film is obtained. Similarly, (110) plane of a Pt electrode and (100) plane of a PZT film are parallel means that when X-rays are incident from [110] direction of a Pt electrode in the in-plane measurement of X-ray diffraction method, a diffraction peak of (H00) plane of the PZT film is obtained.

[0113] In a piezoelectric element of the present invention, an angle of a plane angle formed by (100) plane of the Si substrate and (100) plane of the PZT film is preferably in the range of 40 to 50, from the view point of crystalline structure.

[0114] An angle of a plane angle which (100) plane of a Si substrate and (100) plane of a PZT film form can be confirmed from a diffraction peak of (H00) plane of a PZT film when X-rays are incident from [110] direction of a Si substrate or a Pt electrode in an in-plane measurement of X-ray diffraction method.

[0115] In addition, in a piezoelectric element having a dielectric film, it is preferable that (100) plane of the dielectric film and (100) plane of the PZT film are in epitaxial relation.

[0116] The epitaxial relation in which (100) plane of the dielectric film and (100) plane of the PZT film are parallel can be confirmed from the fact that, in an in-plane measurement of X-ray diffraction method, when X-rays are incident from [110] direction of the Si substrate or the Pt electrode, a diffraction peak of (H00) plane of the PZT film and a diffraction peak of (H00) plane of the dielectric film are obtained.

[0117] A piezoelectric element of the present invention is characterized in that, in a rocking curve measurement of an X-ray diffraction method, symmetric surface reflection peak of a PZT film obtained by X-ray incident from [100] direction of a Si substrate or a Pt electrode can be fitted with three component peaks. A PZT film satisfying the above-mentioned conditions has a monoclinic phase and a rhombohedral phase, and therefore a higher piezoelectric constant is obtained. In addition, since the PZT film becomes an epitaxial film, the dielectric constant of the PZT film becomes lower than that of an oriented film, and thus an electromechanical coupling coefficient can be increased.

[0118] In the present invention, the phrase can be fitted with three component peaks means that when fitting is performed while increasing the number of component peaks under the fitting condition described below, there are three component peaks whose determination factor R.sup.2 does not become larger than that.

(Fitting Conditions)

[0119] A Symmetric Pseudo Voigt probability-density-distribution function, which is a mixture of a Lorentz function and a Gaussian function, is adopted for the fitting function. The function f is expressed by the following equation (2).

[00002]$\begin{array}{cc}\left[\mathrm{Mathematical}\mathrm{equation}2\right]& \\ & \mathrm{EQUATION}\left(2\right)\end{array}$$f_{\left(x\right)}=\text{?}*\left(\frac{1}{1+{\left(\frac{2\left(x-x_0\right)}{h_1}\right)}^2}+\left(1-\right)\sqrt{\ln 2}\exp \left(-{\left(\frac{2\left(x-x_0\right)}{h_g}\right)}^2\right)\right)$$\text{?}\text{indicates text missing or illegible when filed}$

[0120] In equation (2), I represents peak intensity, represents a ratio of a Lorentz function to a Gaussian function, h.sub.1, h.sub.g represents half-width, and x.sub.0 represents peak position. The combination of a plurality of peaks is given by the sum of respective distribution functions. Each peak on which the combination is based is referred to as a component peak in the present invention.

[0121] The determination factor R.sup.2 is defined by the following equation (3).

[00003]$\begin{array}{cc}\left[\mathrm{Mathematical}\mathrm{equation}3\right]& \\ R^2=1-\frac{\text{?}{\left(\text{?}-\text{?}\right)}^2}{\text{?}{\left(y_i-\stackrel{\_}{y}\right)}^2}& \mathrm{EQUATION}\left(3\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$

[0122] In equation (3), yi={y.sub.1, . . . y.sub.N}: observation point, y-bar: mean of observation point, fi={f.sub.1, . . . f.sub.N}: presumed value.

[0123] In a piezoelectric element of the present invention, an angle of a plane angle formed by (001) plane of a Si substrate or a Pt electrode and (001) plane of a PZT film is preferably in the range of 0.34 to 0.35. In a rocking curve measurement of an X-ray diffraction method, when symmetric surface reflection peak of a PZT film obtained by X-ray incident from [100] direction of a Si substrate or a Pt electrode is fitted with three component peaks, the angle can be obtained from the split-width of each component peak.

[0124] Specifically, the difference between .sub.1 and .sub.2 and the difference between .sub.2 and .sub.3 are calculated, assuming that the angle (three) at which the peak intensity is maximized at the respective component peaks is .sub.1, .sub.2, .sub.3 from the smaller one. The mean of these two differences (in other words, the value determined by (.sub.3.sub.1)/2) is an angle of a plane angle formed by (001) plane of the Si substrate or the Pt electrode and (001) plane of the PZT film.

<4. The Piezoelectric Constant>

[0125] In a piezoelectric element of the present invention, from the viewpoint of linearity of the piezoelectric constant, when the piezoelectric constant d.sub.31,f measured by grounding the first electrode and applying a voltage of 30V to the second electrode is A and the piezoelectric constant d.sub.31,f measured by applying a voltage of 10V to the second electrode is B, it is preferable that B is 95% or more of A. Further, from the viewpoint of the polarization-maintaining property, when the piezoelectric constant d.sub.31,f measured by applying a voltage of 20V to the second electrode is C, it is preferable that C is in the range of 40 to 50% of A. When C is in the range of 40 to 50% of A, the depolarization field is moderated and the polarization-maintaining property is improved, suggesting that the ferroelectric is imprinted.

[0126] In the present invention, the piezoelectric constant d.sub.31,f of a piezoelectric element is measured by preparing a sample for measurement and using the sample for measurement. The piezoelectric constant d.sub.31,f in the present invention refers to the piezoelectric constant obtained by an inverse piezoelectric effect.

[0127] The sample for measurement is prepared using a second electrode-free piezoelectric element formed on a Si substrate. The second electrode-free piezoelectric element is cut into strips of 2 mm15 mm. Next, 3 mm of the longitudinal end portion is masked, and a second electrode such as Cu, Al, Ag is formed to be a film by sputtering or by a vacuum-deposition device. The thickness of the second electrode shall be in the range of 0.05 to 0.2 m. After removing mask, a part (about 2 mm at the end portion) of the portion other than the first electrode where the second electrode is not formed is removed by etching. The first electrode exposed after the etching is coated with Ag paste as a first electrode contact for measurement. The sample for measurement of the piezoelectric constant is prepared by the above procedure.

[0128] FIG. 2 is a schematic view of a sample for measurement of the piezoelectric constant viewed from the upper side (a second electrode-side for measurement). The sample 20 for measurement shown in FIG. 2 includes an exposed first electrode 13, a first electrode contact 22 coated on the first electrode 13, an exposed inter-electrode layer 21, and a second electrode 18. Further, although not shown, a Si substrate is provided below the first electrode. Here, the inter-electrode layer 21 is a layer including a PZT film, a dielectric film, or the like between the first electrode 12 and the second electrode 18.

[0129] The sample for measurement is sandwiched between the lower support and the upper support, and one side is restrained in a cantilever shape to be fixed. The position of the restraint point shall be the same as that of the upper support or the lower support, and the distance from the upper restraint point to the other end of the sample for measurement shall be measured to be the length 1 [m] of the sample for measurement. A lead wire is pulled out from the first electrode contact, the second electrode side for measurement is brought into contact with the tip of the thin wire-like electric wire or the like which does not interfere with the vibration to form a second electrode contact for measurement, and a sine wave formed from a waveform generator is applied between the first electrode and the second electrode for measurement. The frequency for measurement is 500 Hz, and the voltage is applied in the range of 30V to +30V. A laser is applied to the end of the sample for measurement which vibrates by applying a waveform, using a Doppler displacement meter, to obtain a signal. By performing Fourier transform or the like on the signal, the displacement amount [m] is calculated.

[0130] FIG. 3 is a schematic view of a measuring device viewed from the side. One side of the sample 20 for measurement is fixed by a lower support 31 and an upper support 32. A second electrode contact 23 is in contact with the second electrode 18 of the sample for measurement. A measuring device 30 includes a waveform generator 33 and a Doppler displacement meter 34.

[0131] The piezoelectric constant d.sub.31,f can be obtained using the calculated displacement amount and the following equation (4).

[00004]$\begin{array}{cc}\left[\mathrm{Mathematical}\mathrm{equation}4\right]& \\ & \mathrm{EQUATION}\left(4\right)\end{array}$$=\frac{3d_{31,f}{s}_1{s}_2{t}_1\left(t_1+t_2\right)\text{?}V}{s_1^2\text{?}+4s_1{s}_2{t}_1{t}_2^3+6s_1{s}_2{t}_1^2{t}_2^2+4s_1{s}_2\text{?}{t}_2+s_2^2\text{?}}$$\text{?}\text{indicates text missing or illegible when filed}$ [0132] : Displacement amount [m] [0133] d.sub.31,f: the piezoelectric constant [m/V] [0134] 1: Sample length for measurement [m] [0135] V: Applied voltage [V] [0136] s.sub.1: Elastic Compliance of PZT film [m.sup.2/N] [0137] s.sub.2: Elastic Compliance of Si substrate [m.sup.2/N] [0138] t.sub.1: Distance between electrodes [m] [0139] t.sub.2: Thickness of Si substrate [m]

[0140] For the elastic compliance s.sub.1 of PZT film, the elastic compliance s.sub.2 of Si substrate, values shown in the literature can be adopted.

<5. Surface Roughness of Dielectric Film>

[0141] As described above, a piezoelectric element of the present invention preferably has a dielectric film at the interface between the second electrode and the PZT film. Further, it is preferable that a RMS(root mean square) value of surface roughness of the dielectric film at the side of the second electrode is 5.0 nm or less. Further, it is more preferably 2.0 nm or less, and even more preferably 1.6 nm or less. This improves reliability in long-term driving, adhesion of film, and the like.

[0142] The RMS value of surface roughness can be measured, for example, using an atomic force microscope (Dimension Icon manufactured by Bruker Corporation).

<6. Use of a Piezoelectric Element>

[0143] A piezoelectric actuator, a droplet discharge head, a liquid droplet ejection apparatus, and a ferroelectric memory of the present invention are characterized by including a piezoelectric element of the present invention. As long as the piezoelectric actuator or the like includes a piezoelectric element of the present invention, other parts of the piezoelectric actuator or the like are not particularly limited, and they may be configured using a commonly used member.

[0144] A piezoelectric element of the present invention can be used in, for example, a piezoelectric microphone, a vibrating sensor, a displacement sensor, an ultrasonic detector, an oscillator, a resonator, a ceramic filter, a piezoelectric transformer, a piezoelectric buzzer, an ultrasonic motor, and the like.

EXAMPLES

[0145] Hereinafter, the present invention will be described in detail with reference to examples, but the present invention is not limited thereto. In examples, part or % is used, but unless otherwise specified, part by mass or % by mass is used.

[0146] A piezoelectric element No. 1 (the present invention) and a piezoelectric element No. 2 (comparative example) were prepared, and XRD, surface roughness of a PLT film, and electric properties were measured using these piezoelectric elements. These measurements were carried out under conditions of a temperature of 23 C.

<Preparation of a Piezoelectric Element No. 1>

[0147] For a substrate, an 8-inch substrate (manufactured by KRYSTAL Corporation) composed of each layer in SRO/Pt/ZrO.sub.2/Si order was used. In the substrate, a Si layer corresponds to a Si substrate of the present invention. In the substrate, a Pt layer and an SRO layer correspond to the first electrodes composed of two layers of a Pt electrode and an SRO electrode. Each layer of the substrate has uniform crystalline orientation in an in-plane direction and an out-of-plane direction, and the principal surface is (001) plane.

[0148] On an SRO layer of the substrate, a PZT film was formed by RF magnetron sputtering method. PZT ceramic target made of a lead-rich composition (Pb.sub.1.25(Zr.sub.0.52, Ti.sub.0.43)O.sub.3) having a Pb of 25% higher than the stoichiometric composition was used.

[0149] The thickness of the PZT film and sputtering conditions are as follows. [0150] Thickness . . . 3.38 m [0151] RF power supply . . . 3.0 kW [0152] Gas flow rate . . . Ar:O.sub.2=39.5:0.5 sccm [0153] Sputtering pressure . . . 0.2 Pa [0154] Substrate setting temp . . . . 550 C.

[0155] In the PZT film forming step described above, the PZT film was formed in two times, and the cleaning was performed between the first and second times.

[0156] Next, a dielectric film (PLT film) was formed on the PZT film by RF magnetron sputtering method. PLT ceramic target made of a lead-rich composition (Pb.sub.1.125, La.sub.0.1)TiO.sub.3) having a Pb of 25% higher than the stoichiometric composition of Pb:La=0.9:0.1, was used.

[0157] The thickness of the dielectric film (PLT film) and sputtering conditions are as follows. [0158] Thickness . . . 0.12 m [0159] RF power supply . . . 2.0 kW [0160] Gas flow rate . . . Ar:O.sub.2=39.5:0.5 sccm [0161] Sputtering pressure . . . 0.2 Pa [0162] Substrate setting temp . . . . 560 C.

[0163] A second electrode-free piezoelectric element No. 1 was prepared by the above-described procedure.

<Preparation of a Piezoelectric Element No. 2>

[0164] On an 8-inch Bare-Si wafer (a Si substrate) having (001) plane as the principal surface, a first electrode was formed by RF magnetron sputtering method using a IrTi alloy target.

[0165] The thickness of the first electrode and sputtering conditions are as follows. [0166] Thickness . . . 0.12 m [0167] RF power supply . . . 0.75 kW [0168] Gas flow rate . . . Ar:O.sub.2=38:2 sccm [0169] Sputtering pressure . . . 0.2 Pa [0170] Substrate setting temp . . . . 350 C.

[0171] Next, a dielectric film (PLT film) at the side of the first electrode was formed on the first electrode by RF magnetron sputtering method. PLT ceramic target made of a lead-rich composition (Pb.sub.1.125, La.sub.0.1)TiO.sub.3) having a Pb of 25% higher than the stoichiometric composition of Pb:La=0.9:0.1, was used.

[0172] The thickness of the dielectric film (PLT film) at the side of the first electrode and sputtering conditions are as follows. [0173] Thickness . . . 0.12 m [0174] RF power supply . . . 2.0 kW [0175] Gas flow rate . . . Ar:O.sub.2=39.5:0.5 sccm [0176] Sputtering pressure . . . 0.2 Pa [0177] Substrate setting temp . . . . 560 C.

[0178] Next, a PZT film was formed on the dielectric film at the side of the first electrode by RF magnetron sputtering method. PZT ceramic target made of a lead-rich composition (Pb.sub.1.25(Zr.sub.0.52, Ti.sub.0.48)O.sub.3) having a Pb of 25% higher than the stoichiometric composition was used.

[0179] The thickness of the PZT film and sputtering conditions are as follows. [0180] Thickness . . . 3.26 m [0181] RF power supply . . . 3.0 kW [0182] Gas flow rate . . . Ar:O.sub.2=39.5:0.5 sccm [0183] Sputtering pressure . . . 0.2 Pa [0184] Substrate setting temp . . . . 550 C.

[0185] Next, a dielectric film (PLT film) was formed on the PZT film by RF magnetron sputtering method. PLT ceramic target made of a lead-rich composition (Pb.sub.1.125, La.sub.0.1)TiO.sub.3) having a Pb of 25% higher than the stoichiometric composition of Pb:La=0.9:0.1, was used.

[0186] The thickness of the dielectric film (PLT film) and sputtering conditions are as follows. [0187] Thickness . . . 0.12 m [0188] RF power supply . . . 2.0 kW [0189] Gas flow rate . . . Ar:O.sub.2=39.5:0.5 sccm [0190] Sputtering pressure . . . 0.2 Pa [0191] Substrate setting temp . . . . 560 C.

[0192] A second electrode-free piezoelectric element No. 2 was prepared by the above-described procedure.

<XRD Measurement of a Piezoelectric Element No. 1>

[0193] A second electrode-free piezoelectric element No. 1 was subjected to an out-of-plane XRD measurement (out-of-plane 2- scanning) under the following conditions. The out-of-plane measurement was made in the range of 2=10-110. In addition, X-rays entered from [100] direction of a Si substrate.

(Measuring Conditions of Out-of-Plane XRD)

[0194] Measuring device: SmartLab manufactured by Rigaku Corporation [0195] X-ray generator: Anticathode Cu [0196] : Output 45 kV 200 mA [0197] Detector: Semiconductor detector [0198] Incident optical system: Ge(220) channel-cut monochromator [0199] Solar Slit: Incident side [0200] : Receiving side 5.0 [0201] Slit: Incident side IS=1 (mm) [0202] : Longitudinal limit 10 (mm) [0203] : Receiving side RS1=1 RS2=1.1 (mm) [0204] Scanning conditions: Scanning axis 2/ [0205] : Scanning mode continuous scanning [0206] : Scanning range 10 to 110 [0207] : Step width 0.024 [0208] : Scanning rate 2/min

[0209] Measuring result of the out-of-plane XRD of a piezoelectric element No. 1 is shown in FIG. 4. From FIG. 4, 00L preferred orientation of the PZT film and the PLT film was confirmed. Here, focusing on a diffraction peak of (004) plane seen at 2=90 to 110, and enlarging the horizontal axis to 20=90 to 110, FIG. 5 mentioned below is obtained.

[0210] From FIG. 5, it was confirmed that a diffraction peak of (004) plane of the PZT film around 2=980 is not a single peak but peaks in which a plurality of peaks are superimposed.

[0211] The peaks derived from (004) plane of the PZT film around 2=980 were fitted under the above-described conditions.

[0212] When fitting was performed with one component peak, it is shown in FIG. 6, and the determination factor was R.sup.2=0.997724. On the other hand, when fitting was performed with three component peaks, the determination factor was R.sup.2=0.999931 as shown in FIG. 7. In addition, fitting with four or more component peaks was divided into the same peaks or did not show an increase in the determination factor. From the above, it was confirmed that a diffraction peak of (004) plane of the PZT film can be fitted with three component peaks of 2=97.28, 97.94, and 98.47.

[0213] Subsequently, a second electrode-free piezoelectric element No. 1 was subjected to an in-plane XRD measurement under the following conditions. Here, the X-rays entered from [110] direction of the Si substrate. The measurement was made in the range of 2=10-110.

(Measuring Conditions of In-Plane XRD)

[0214] Measuring device: SmartLab manufactured by Rigaku Corporation [0215] X-ray generator: Anticathode Cu [0216] : Output 45 kV 200 mA [0217] Detector: Semiconductor detector [0218] Solar Slit: Incident side Vertical divergence angle 0.5 [0219] : Receiving side Vertical divergence angle 0.5 [0220] Slit: Incident side IS=0.1 (mm) [0221] : Longitudinal limit 10 (mm) [0222] : Receiving side RS1=20 RS2=20.1 (mm) [0223] Scanning conditions: Scanning axis 2.sub./ [0224] : Incident angle 0.60 [0225] : Scanning mode continuous scanning [0226] : Scanning range 10 to 110 [0227] : Step width 0.024 [0228] : Scanning rate 2/min

[0229] Measuring result of the in-plane XRD of a piezoelectric element No. 1 is shown in FIG. 8. It was confirmed that (110) plane of the Si substrate and (100) plane of the PZT film were parallel to each other, as shown in FIG. 8, when X-rays were incident so as to be parallel to (110) plane of the Si substrate and a diffraction peak of (H00) plane of the PZT film was obtained. Further, since (110) plane of the Si substrate and (110) plane of the Pt electrode are parallel, it can be seen that (110) plane of the Pt electrode and (100) plane of the PZT film are parallel.

[0230] In addition, since a diffraction peak of (H00) plane of the PZT film was seen in FIG. 8, it was confirmed that an angle of a plane angle formed by (100) plane of the Si substrate and (100) plane of the PZT film is 45. Further, since (100) plane of the Si substrate and (100) plane of the Pt electrode are parallel, it can be seen that an angle of a plane angle formed by (100) plane of the Pt electrode and (100) plane of the PZT film is 45.

[0231] In addition, in FIG. 8, it was also confirmed that (100) plane of the PLT film and (100) plane of the PZT film were parallel and in epitaxial relation because a diffraction peak of (H00) plane of the PZT film and a diffraction peak of (H00) plane of the PLT film were respectively confirmed.

[0232] A rocking curve (RC) measurement was performed at 002 grid point reflections (2=44.3) of the PZT film under the following conditions.

(Conditions of a Rocking Curve Measurement)

[0233] Measuring device: SmartLab manufactured by Rigaku Corporation [0234] X-ray generator: Anticathode Cu [0235] : Output 45 kV 200 mA [0236] Detector: Semiconductor detector [0237] Injection optical system: Ge(220) channel-cut monochromator [0238] Solar Slit: Incident side [0239] : Receiving side 5.0 [0240] Slit: Incident side IS=1 (mm) [0241] : Longitudinal limit 10 (mm) [0242] : Receiving side RS1=1 RS2=1.1 (mm) [0243] Scanning conditions: Evaluated diffraction surface PZT(002) [0244] : Scanning axis [0245] : Scanning mode continuous scanning [0246] : Scanning range 10 to 30 [0247] : Step width 0.024 [0248] : Scanning rate 2/min

[0249] Peaks obtained by a rocking curve measurement were fitted under the above-described conditions.

[0250] When fitting is performed with one component peak, it was a graph shown in FIG. 9, and the determination factor was R.sup.2=0.992506. When fitting was performed with two component peaks, a graph shown in FIG. 10 was obtained, and the determination factor was R.sup.2=0.997887. When fitting was performed with three component peaks, a graph shown in FIG. 11 was obtained, and the determination factor was R.sup.2=0.999929. Fitting with four or more component peaks was either split into the same peaks as fitting with three component peaks or did not show an increase in the determination factor.

[0251] From the above result, in a rocking curve measurement of an X-ray diffraction method, it was confirmed that symmetric surface reflection peaks of the PZT film obtained by X-rays incident from [100] directions of the Si substrate and the Pt electrode could be fitted with three component peaks.

[0252] Further, from the split width of each component peak when fitting was performed with the three component peaks, it was confirmed that an angle of a plane angle formed by (001) plane of the Si substrate and (001) plane of the lead zirconate titanate film was 0.35.

[0253] From the result of the above XRD measurement, it was confirmed that a crystalline structure of the PZT film of a piezoelectric element No. 1 was mixed crystals of a monoclinic phase and a rhombohedral phase.

<XRD Measurement of a Piezoelectric Element No. 2>

[0254] A second electrode-free piezoelectric element No. 2 was subjected to an out-of-plane XRD measurement (out-of-plane 2- scanning) under the same conditions as described above. The out-of-plane measurement was made in the range of 2=10-110. In addition, X-rays entered from [100] direction of the Si substrate.

[0255] Measurement result of the out-of-plane XRD of a piezoelectric element No. 2 is shown in FIG. 12. From FIG. 12, 00L preferred orientation of the PZT film was confirmed. Here, focusing on a diffraction peak of (004) plane seen at 2=90 to 110, and enlarging the horizontal axis to 2=90 to 110, FIG. 13 mentioned below is obtained.

[0256] In addition, fitting was performed under the same conditions as described above with respect to the peaks derived from (004) plane of the PZT film at around 2=98.

[0257] When fitting was performed with one component peak, it is a graph shown in FIG. 14, and the determination factor was R.sup.2=0.99559. Further, no increase in the determination factor was observed even if the number of component peaks was increased further. From the above, it was confirmed that a diffraction peak of (004) plane is a single-peak.

[0258] Subsequently, the second electrode-free piezoelectric element No. 2 was subjected to an in-plane XRD measurement under the same conditions as described above.

[0259] Measurement result of the in-plane XRD of a piezoelectric element No. 2 is shown in FIG. 15. From the result shown in FIG. 15, it was confirmed that peaks derived from polycrystals were obtained and the crystals were random in the in-plane direction. From the above, it was confirmed that the PZT film of a piezoelectric element No. 2 is an oriented film in which the crystals are aligned in the out-of-plane direction but are randomly arranged in the in-plane direction.

[0260] A rocking curve measurement was performed at a 001 grid point reflections (2=21.74) of the PZT film under the same conditions as described above. The incidence was performed from [100] orientation of the Si substrate.

[0261] Peaks obtained by the rocking curve measurement were fitted under the same conditions as described above. As a result, when fitting with one component peak, the determination factor was the largest, and R.sup.2=0.92402 was obtained. FIG. 16 shows a graph when fitting was performed with one component peak.

[0262] From the result of the above XRD measurement, it was confirmed that a crystalline structure of the PZT film of a piezoelectric element No. 2 was a tetragonal phase.

<Measurement of Surface Roughness of PLT Film>

[0263] Surface roughness of a PLT film of each second electrode-free piezoelectric element was measured using an atomic force microscope (Dimension Icon manufactured by Bruker Corporation).

[0264] FIG. 17 shows an atomic force microscopic image of a PLT film of a piezoelectric element No. 1. The RMS value of surface roughness for the PLT film was 1.49 nm. FIG. 18 shows an atomic force microscopic image of a PLT film of a piezoelectric element No. 2. The RMS value of surface roughness for the PLT film was 4.97 nm.

<Measurement of Dielectric Constant s and Relative Dielectric Constant .sub.r>

[0265] A second electrode was formed on each second electrode-free piezoelectric element by a RF magnetron sputtering method using a Cu target.

[0266] The thickness of the second electrode and sputtering conditions are as follows. [0267] Thickness . . . 0.1 m [0268] RF power supply . . . 1 kW [0269] Gas flow rate . . . Ar=50 sccm [0270] Sputtering pressure . . . 0.15 Pa [0271] Substrate setting temp . . . room temperature

[0272] The second electrode (Cu electrode) formed above was patterned into a circular shape having an area 0.0314 mm.sup.2 using a metal mask. The capacitance of the piezoelectric element was measured using an LCR meter (IM3523 manufactured by Hioki Electric Co., Ltd.) under the following conditions. [0273] Excitation voltage: 1V [0274] Excitation frequency: 1 kHz [0275] Circuit model: Parallel capacitance model [0276] Measurement items: Cp-D

[0277] The dielectric constant s and the relative dielectric constant .sub.r were obtained from the measured capacitance and the respective values using the following equation (5). The measurement results are shown in Table 1.

[00005]$\begin{array}{cc}\left[\mathrm{Mathematical}\mathrm{equation}5\right]& \\ \text{?}=\frac{}{{}_0}=\frac{\mathrm{Cd}}{\text{?}}& \mathrm{EQUATION}\left(5\right)\end{array}$$\text{?}\text{indicates text missing or illegible when filed}$ [0278] : Dielectric constant [F/m] [0279] .sub.0: Vacuum dielectric constant [F/m](8.8510.sup.12 F/m) [0280] .sub.r: Relative dielectric constant [0281] C: Capacitance [F] [0282] d: Distance between electrodes [m] [0283] S: Area of electrode [m.sup.2]
<Measurement of the Piezoelectric Constant d.sub.31,f>

[0284] Each second electrode-free piezoelectric element was cut into strips of 2 mm15 mm. Next, about 3 mm of the longitudinal one-side end portion was masked and formed by a RF magnetron sputtering method using a Cu target.

[0285] The thickness of the second electrode and sputtering conditions are as follows. [0286] Thickness . . . 0.1 m [0287] RF power supply . . . 1 kW [0288] Gas flow rate . . . Ar=50 sccm [0289] Sputtering pressure . . . 0.15 Pa [0290] Substrate setting temp . . . room temperature

[0291] After removing mask, a part (about 2 mm at the end portion) of the portion other than the first electrode where the second electrode for measurement is not formed is removed by etching. Then, the first electrode exposed after the etching was coated with Ag paste as a first electrode contact for measurement.

[0292] A sample for measurement was prepared by the above-described operation.

[0293] Using the prepared sample for measurement, the displacement was calculated by the above-described measurement method, and further, the piezoelectric constant d.sub.31,f at the respective applied voltages (20V, 10V, 20V, 30V) was obtained by using the following equation (4). The sample length 1 for measurement was 19.5 mm. The elastic compliance s.sub.1 of the PZT film and the elastic compliance s.sub.2 of the Si substrate were adopted as values described in the literature (I. Kanno et al., Piezoelectric properties of c-axis oriented Pb(Zr,Ti) O.sub.3 thin films, APL 70, 1378 (1997). The calculated results are shown in Table 1.

[00006]$\begin{array}{cc}\left[\mathrm{Mathematical}\mathrm{equation}6\right]& \\ & E\mathrm{QUATION}\left(4\right)\end{array}$$=\frac{3\text{?}{s}_1{s}_2{t}_1\left(t_1+t_2\right)\text{?}V}{s_1^2\text{?}+4s_1{s}_2{t}_1{t}_2^3+6s_1{s}_2{t}_1^2{t}_2^2+4\text{?}{s}_2\text{?}{t}_2+s_2^2\text{?}}$$\text{?}\text{indicates text missing or illegible when filed}$ [0294] : Displacement amount [m] [0295] d.sub.31,f: the piezoelectric constant [m/V] [0296] 1: Sample length for measurement [m] [0297] V: Applied voltage [V] [0298] s.sub.1: Elastic Compliance of PZT film [m.sup.2/N] [0299] s.sub.2: Elastic Compliance of Si substrate [m.sup.2/N] [0300] t.sub.1: Distance between electrodes [m] [0301] t.sub.2: Thickness of Si substrate [m]
<Calculation of an Electromechanical Coupling Coefficient k.sub.31,f.sup.2>

[0302] From the measured dielectric constant s and the piezoelectric constant d.sub.31,f at the time of applying 30V, an electromechanical coupling coefficient k.sub.31,f.sup.2 was calculated using the following equation (1). The calculation results are shown in Table 1.

[00007]$\begin{array}{cc}\left[\mathrm{Mathematical}\mathrm{equation}7\right]& \\ k_{31,f}^2=\frac{d_{31,f}^2}{s}100& \mathrm{EQUATION}\left(1\right)\end{array}$ [0303] k.sub.31,f.sup.2: Electromechanical coupling coefficient [%] [0304] d.sub.31,f: Piezoelectric constant [m/V] [0305] : Dielectric constant [F/m] [0306] s: Elastic compliance[m.sup.2/N]

TABLE-US-00001 TABLE 1 TABLE I NO. 1 NO. 2 PIEZOELECTRIC (PRESENT (COMPARATIVE ELEMENT NO. INVENTION) EXAMPLE) NUMBER OF THREE ONE COMPONENT PEAKS OF DIFFRACTION PEAK OF (004) PLANE NUMBER OF THREE ONE COMPONENT PEAKS OF SYMMETRIC SURFACE REFLECTION PEAK OF R MEASUREMENT EPITAXIAL FILM OR EPITAXIAL FILM ORIENTED FILM ORIENTED FILM CRYSTALLINE PHASE MIXED CRYSTAL OF TETRAGONAL OF PZT FILM MONOCLINIC PHASE/ PHASE RHOMBOHEDRAL PHASE RMS VALUE OF SURFACE 1.4 nm 4. 7 nm ROUGHNESS OF PLT FILM DIELECTRIC CONSTANT 5.50 10 F/m 8.82 10 F/m RELATIVE DIELECTRIC 621.3 996.3 CONSTANT PIEZOELECTRIC 30 V APPLICATION (A) 164.7 pm/V 188.7 pm/V CONSTANT 20 V APPLICATION 164.6 pm/V 185.7 pm/V d 10 V APPLICATION (B) 161.1 pm/V 175.3 pm/V 20 V APPLICATION (C) 79.9 pm/V 175.7 pm/V RATIO OF (B/A) 97. % 92.9% PIEZOELECTRIC (C/A) 48.5% 93.1% CONSTANT d ELECTROMECHANICAL 45.69% 37.38% COUPLING COEFFICIENT k indicates data missing or illegible when filed

[0307] From the evaluation results shown in Table 1, it can be confirmed that a piezoelectric element of the present invention has higher electromechanical coupling coefficient than that of the comparative example. This is because the dielectric constant is significantly lower than that of the comparative example, and the piezoelectric constant can be maintained while the dielectric constant is lower.

INDUSTRIAL APPLICABILITY

[0308] The present invention can be applied to a piezoelectric element having a higher electromechanical coupling coefficient, and a piezoelectric actuator, a droplet discharge head, a liquid droplet ejection apparatus, and a ferroelectric memory, these having the piezoelectric element.

EXPLANATION OF REFERENCE NUMERALS

[0309] 10 Piezoelectric element [0310] 11 Si substrate [0311] 12 ZrO.sub.2 layers [0312] 13 First electrode [0313] 14 Pt electrode [0314] 15 SRO electrode [0315] 16 PZT film [0316] 17 Dielectric film [0317] 18 Second electrode [0318] 20 Sample for measurement [0319] 21 Inter-electrode layer [0320] 22 First electrode contact [0321] 23 Second electrode contact [0322] 30 Measuring device [0323] 31 Lower support [0324] 32 Upper support [0325] 33 Waveform generator [0326] 34 Doppler displacement meter