Piezoelectric thin film laminate

By integrating a conductive or insulating layer with negative thermal expansion between the piezoelectric thin film and substrate, the piezoelectric characteristics are improved, addressing composition and environmental issues, and reducing stress for enhanced performance in devices like ultrasonic sensors and microphones.

JP7761444B2Active Publication Date: 2025-10-28NITERRA CO LTD
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Patent Information

Application Number
JP2021167850
Authority / Receiving Office
JP · JP
Patent Type
Patents
Current Assignee / Owner
Filing Date
2021-10-13
Publication Date
2025-10-28
Estimated Expiration
2041-10-13

AI Technical Summary

Technical Problem

Existing piezoelectric thin film laminates face issues with changing piezoelectric characteristics due to Na composition changes, high production costs, and environmental impact from using PZT thin films, along with neglecting conductivity and thermal expansion coefficient considerations.

Method used

Incorporating a conductive or insulating layer with a negative thermal expansion coefficient between the piezoelectric thin film and the substrate to adjust internal stress and maintain electrical properties, while using alkali niobate piezoelectric materials to improve piezoelectric characteristics.

Benefits of technology

Enhances piezoelectric properties by reducing internal stress, preventing cracking, and minimizing environmental impact through cost-effective production without lead, suitable for applications like ultrasonic sensors and microphones.

✦ Generated by Eureka AI based on patent content.

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Abstract

To improve piezoelectric characteristics of a piezoelectric thin film laminated body comprising a piezoelectric thin film composed of an alkali niobate based piezoelectric material.SOLUTION: A piezoelectric thin film laminated body 10 includes: a substrate 11; a lower electrode 14 laminated above the substrate 11; and a piezoelectric thin film 16 composed of an alkali niobate based piezoelectric material laminated above the lower electrode 14. The piezoelectric thin film laminated body 10 is provided with a conductive layer 15 made of a material having a negative thermal expansion coefficient between the piezoelectric thin film 16 and the substrate 11.SELECTED DRAWING: Figure 1
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Description

[Technical Field]

[0001] The present invention relates to a piezoelectric thin film laminate. [Background technology]

[0002] Patent Document 1 states that (K 1-x Na x The paper discloses a substrate with a piezoelectric thin film that includes a piezoelectric thin film made of an alkali niobate piezoelectric material represented by NbO3 (0.4≦x≦0.7). It states that by changing the Na composition of this piezoelectric thin film, the ratio of change in internal stress relative to temperature change can be controlled, and the internal stress in the film plane direction at 20°C can be controlled.

[0003] Patent Document 2 discloses a piezoelectric film including an electrode layer stacked on a silicon substrate and a PZT-based ferroelectric layer stacked on the electrode layer. This piezoelectric film has a layer with a negative thermal expansion coefficient and an SiO2 layer interposed between the silicon substrate and the electrode layer. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2011-071150 [Patent Document 2] Japanese Patent Application Publication No. 2019-161145 Summary of the Invention [Problem to be solved by the invention]

[0005] In the configuration disclosed in Patent Document 1, there is a risk that the piezoelectric characteristics may change every time the Na composition of the piezoelectric thin film is changed. Furthermore, when the Na composition is changed without changing the film formation conditions of the piezoelectric thin film, it is necessary to prepare a target material, which is costly.

[0006] The configuration disclosed in Patent Document 2 uses a PZT thin film, so there is room for improvement in terms of environmental impact. Furthermore, Patent Document 2 does not consider the conductivity of the layer having a negative thermal expansion coefficient at all.

[0007] The present invention was completed in view of the above circumstances, and has an object to improve the piezoelectric characteristics of a piezoelectric thin film laminate including a piezoelectric thin film made of an alkali niobate piezoelectric material. [Means for solving the problem]

[0008] The piezoelectric thin film laminate according to the present invention is A substrate; a lower electrode laminated above the substrate; a piezoelectric thin film made of an alkali niobate piezoelectric material laminated above the lower electrode, Between the piezoelectric thin film and the substrate is provided a conductive layer made of a material having a negative coefficient of thermal expansion.

[0009] The thermal expansion coefficient of alkali niobate piezoelectric thin films is larger than that of typical substrates. If a layer made of a material with a negative thermal expansion coefficient is not provided between the piezoelectric thin film and the substrate, tensile stress will act on the piezoelectric thin film when it is cooled from the temperature at which it was formed to room temperature. According to the above-described configuration, which is one of the present invention, a layer made of a material with a negative thermal expansion coefficient is provided between the piezoelectric thin film and the substrate, thereby adjusting internal stress that may arise due to the difference in thermal expansion coefficient between the piezoelectric thin film and the substrate. Furthermore, because this layer made of a material with a negative thermal expansion coefficient is a conductive layer, a layer made of a material with a negative thermal expansion coefficient can be disposed in a position where interlayer conductivity is required without impairing electrical properties. Thus, providing a conductive layer made of a material with a negative thermal expansion coefficient between the piezoelectric thin film and the substrate can improve the piezoelectric properties of the piezoelectric thin film laminate.

[0010] The piezoelectric thin film laminate according to the present invention is A substrate; a lower electrode laminated above the substrate; a piezoelectric thin film made of an alkali niobate piezoelectric material laminated above the lower electrode, An insulating layer made of a material having a negative coefficient of thermal expansion is provided between the lower electrode and the substrate.

[0011] According to the above-described configuration of one aspect of the present invention, a layer made of a material having a negative thermal expansion coefficient is provided between the lower electrode and the substrate, thereby adjusting internal stress that may occur due to the difference in thermal expansion coefficient between the piezoelectric thin film and the substrate. Furthermore, because this layer made of a material having a negative thermal expansion coefficient is an insulating layer, the layer made of a material having a negative thermal expansion coefficient can improve the insulation between the lower electrode and the substrate. Thus, by providing a conductive layer made of a material having a negative thermal expansion coefficient between the lower electrode and the substrate, the piezoelectric properties of the piezoelectric thin film laminate can be improved. [Effects of the Invention]

[0012] According to the present invention, it is possible to improve the piezoelectric characteristics of a piezoelectric thin film laminate including a piezoelectric thin film made of an alkali niobate piezoelectric material. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a cross-sectional view schematically showing a piezoelectric thin film laminate of a first embodiment. [Figure 2] FIG. 10 is a cross-sectional view schematically showing a piezoelectric thin film laminate of a comparative example. [Figure 3] FIG. 10 is a cross-sectional view schematically showing a piezoelectric thin film laminate according to a second embodiment. [Figure 4] FIG. 10 is a cross-sectional view schematically showing a piezoelectric thin film laminate according to a third embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, embodiments embodying the present invention will be described in detail. In this specification, when a numerical range is indicated using "to" it is assumed that the range includes both the lower limit and the upper limit unless otherwise specified. For example, the expression "10 to 20" includes both the lower limit "10" and the upper limit "20". In other words, "10 to 20" has the same meaning as "10 or more and 20 or less".

[0015] [First embodiment] 1 includes a substrate 11, a lower electrode 14 laminated on the substrate 11, and a piezoelectric thin film 16 made of an alkali niobate piezoelectric material laminated on the lower electrode 14. The piezoelectric thin film laminate 10 includes a conductive layer 15 made of a material having a negative thermal expansion coefficient between the piezoelectric thin film 16 and the substrate 11. Hereinafter, the conductive layer 15 made of a material having a negative thermal expansion coefficient will also be referred to as a conductive NTE layer 15.

[0016] The piezoelectric thin film laminate 10 includes a substrate 11, an SiO2 layer 12, an adhesive layer 13, a lower electrode 14, a conductive NTE layer 15, and a piezoelectric thin film 16 laminated in this order. The SiO2 layer 12 and the adhesive layer 13 are optional layers. The piezoelectric thin film laminate 10 may further include other optional layers laminated between the layers.

[0017] The substrate 11 is preferably a silicon substrate. The substrate 11 can be formed using, for example, single crystal silicon. The thermal expansion coefficient of single crystal silicon is 3×10 -6 / K~5×10 -6 / K. The thickness of the substrate 11 is preferably 200 μm to 1000 μm, for example, 525 μm. The SiO2 layer 12 is formed on the surface of the substrate 11. The thermal expansion coefficient of SiO2 is 0.52×10 -6 / K~0.56×10 -6 / K. The thickness of the SiO2 layer 12 is preferably 50 nm to 200 nm, for example, 100 nm.

[0018] The adhesion layer 13 is in contact with the upper surface of the SiO2 layer 12 when the SiO2 layer 12 is present, and is in contact with the upper surface of the substrate 11 when the SiO2 layer 12 is not present. The adhesion layer 13 is also in contact with the lower surface of the lower electrode 14. The adhesion layer 13 improves the adhesion of the lower electrode 14 to the substrate 11. The adhesion layer 13 is not particularly limited, but can be formed using a metal such as titanium (Ti) or a metal oxide. The thermal expansion coefficient of Ti is 8.4 × 10 at temperatures around 0°C to 100°C. -6 / K. The thickness of the adhesive layer 13 is preferably 10 nm to 50 nm, for example, 20 nm.

[0019] The lower electrode 14 is made of a conductive material. The lower electrode 14 can be formed using, for example, various metals such as platinum (Pt), gold (Au), ruthenium (Ru), iridium (Ir), alloys containing these as main components, metal oxides, etc. The lower electrode 14 may be a single layer or a multi-layer. The thermal expansion coefficient of Pt is 8.8×10 at temperatures in the range of 20°C to 227°C. -6 / K~9.6×10 -6 / K. The thickness of the lower electrode 14 is preferably 100 nm to 400 nm, for example, 200 nm.

[0020] The conductive NTE layer 15 is made of a material having a negative thermal expansion coefficient. The thermal expansion coefficient of the material having a negative thermal expansion coefficient is not particularly limited. The thermal expansion coefficient of the material having a negative thermal expansion coefficient is preferably −8.0×10 in at least a part of the temperature range from the temperature during manufacturing to the temperature during use. -6 / K~-40×10 -6 / K. If the thickness is within the above range, the internal stress of the piezoelectric thin film laminate 10 can be easily controlled, which is preferable.

[0021] The conductive NTE layer 15 is conductive. The conductive material having a negative thermal expansion coefficient is preferably one or more selected from the group consisting of LiAlSiO4 and Mn-Sn-Zn-N. For example, at 27°C to 927°C, the thermal expansion coefficient of LiAlSiO4 is -8.0 x 10 -6 / K, and the thermal expansion coefficient of Mn-Sn-Zn-N is -40×10 -6 / K. An example of Mn-Sn-Zn-N is Smartec (registered trademark) (manufactured by Kojundo Chemical Laboratory Co., Ltd.).

[0022] The thickness of the conductive NTE layer 15 can be appropriately designed depending on its own thermal expansion coefficient and the thermal expansion coefficients of the other layers in the piezoelectric thin film laminate 10. The thickness of the conductive NTE layer 15 is preferably 20 nm to 5 μm. If the thickness is equal to or greater than the lower limit of the above range, it is preferable from the viewpoint of alleviating the internal stress of the piezoelectric thin film laminate 10. If the thickness is equal to or less than the upper limit of the above range, it is preferable from the viewpoint of productivity and cost.

[0023] The conductive NTE layer 15 of this embodiment is disposed between the piezoelectric thin film 16 and the lower electrode 14. In this configuration, the conductive NTE layer 15 may function as a barrier layer that prevents metal components of the piezoelectric thin film 16 from diffusing into the lower electrode 14. The conductive NTE layer 15 may be in contact with the upper surface of the lower electrode 14. In this configuration, the conductive NTE layer 15 may constitute part of the electrode of the piezoelectric thin film stack 10 together with the lower electrode 14. The conductive NTE layer 15 may also be in contact with the lower surface of the piezoelectric thin film 16. When the conductive NTE layer 15 is in contact with the piezoelectric thin film 16, it is preferable that the conductive NTE layer 15 be preferentially oriented in a predetermined plane direction, from the viewpoint of the orientation of the piezoelectric thin film 16. In this configuration, the conductive NTE layer 15 can be used as an underlayer that improves the orientation of the piezoelectric thin film 16.

[0024] The piezoelectric thin film 16 is preferably made of an alkali niobate piezoelectric material that does not contain lead (Pb). The alkali niobate piezoelectric material contains at least a main phase made of an alkali niobate perovskite oxide that has piezoelectric properties, and may contain a subphase, which is a crystalline phase other than the main phase. The subphase stabilizes the structure of the main phase by being mixed with the main phase, and the piezoelectric constant d 33 and improves the electromechanical coupling coefficient kr.

[0025] The alkali component of the alkali niobate perovskite oxide contains at least an alkali metal (such as potassium (K), sodium (Na), lithium (Li), rubidium (Rb), cesium (Cs), etc.), and may also contain an alkaline earth metal (such as calcium (Ca), strontium (Sr), barium (Ba), etc.). From the viewpoint of piezoelectric properties, the alkali niobate perovskite oxide is preferably represented by the general formula (K 1-x Na x )NbO3 (0 < x < 1, preferably 0.3 ≤ x ≤ 0.7). The thermal expansion coefficient of the piezoelectric thin film 16 is not particularly limited, but is usually larger than that of the conductive NTE layer 15. For example, the thermal expansion coefficient of the piezoelectric thin film 16 may be larger than that of the substrate 11.

[0026] The use of the piezoelectric thin film element using the piezoelectric thin film laminate 10 of the present embodiment is not limited. The piezoelectric thin film element is suitable for various applications such as an ultrasonic distance sensor, an ultrasonic oscillation device (haptic device), a microphone, a micromirror, a microphone, an ultrasonic diagnostic apparatus, a fingerprint authentication sensor, a blood vessel authentication sensor, a vibration power generation element, a micropump, and autofocus.

[0027] An example of the manufacturing method of the piezoelectric thin film laminate 10 will be described. A silicon substrate is prepared as the substrate 11. When the SiO2 layer 12 is present, for example, the SiO2 layer 12 is formed by thermal oxidation treatment or chemical vapor deposition (CVD) method. [[ID=第十六]]

[0028] [[ID=第十七]] Next, the adhesion layer 13 and the lower electrode 14 are sequentially formed on the substrate 11 or the SiO2 layer 12 by a physical vapor deposition method (for example, sputtering method, thermal evaporation method, electron beam evaporation method, etc.).

[0029] Next, a conductive NTE layer 15 is formed on the lower electrode 14 by a sol-gel method, a sputtering method, an aerosol deposition method, a pulsed laser deposition method, or the like. By appropriately adjusting the composition of the raw material, the firing atmosphere (such as oxygen partial pressure), and the firing temperature, a conductive NTE layer 15 with a desired composition can be obtained. Further, by appropriately adjusting the viscosity of the raw material liquid, the coating method, and the coating number, the thickness of the conductive NTE layer 15 can be controlled.

[0030] Next, a piezoelectric thin film 16 is formed on the conductive NTE layer 15. The method for forming the piezoelectric thin film 16 is not particularly limited. For example, a method of sputtering at a high temperature (high-temperature sputtering method), a method of crystallizing at a high temperature after sputtering at room temperature (room-temperature sputtering method), a method of crystallizing at a high temperature after applying a raw material liquid (Metal Organic Decomposition, MOD method or sol-gel method), a method of heat-treating at a high temperature after forming an aerosol deposition film by high-speed collision of raw material fine particles (aerosol deposition method), a pulsed laser deposition method, a chemical vapor deposition method (for example, Metal Organic Chemical Vapor Deposition, MOCVD method), or the like can be employed.

[0031] The operation and effects of this embodiment will be described. When a layer made of a material having a negative thermal expansion coefficient is not provided between the piezoelectric thin film 16 and the substrate 11 as in the piezoelectric thin film laminate 1 of the comparative example shown in FIG. 2, when cooled from the temperature during film formation of the piezoelectric thin film 16 to room temperature, tensile stress acts on the piezoelectric thin film 16. On the other hand, according to this embodiment, since the conductive NTE layer 15 is provided between the piezoelectric thin film 16 and the substrate 11, the magnitude relationship of the thermal expansion coefficients is, for example, conductive NTE layer 15 < SiO2 layer 12 < substrate 11 < piezoelectric thin film 16 < adhesion layer 13 < lower electrode 14, and the internal stress that may occur due to the difference in the thermal expansion coefficients between the piezoelectric thin film 16 and the substrate 11 can be adjusted. Further, in this embodiment, since the layer made of a material having a negative thermal expansion coefficient is the conductive NTE layer 15, the conductive NTE layer 15 can be disposed at a position where the conductivity between layers should be ensured without impairing the electrical characteristics.

[0032] Reducing the internal stress of the piezoelectric thin film laminate 10 allows for greater amplitude of the vibration part of the piezoelectric thin film element including the piezoelectric thin film laminate 10. Furthermore, reducing the internal stress of the piezoelectric thin film laminate 10 can suppress cracking of the piezoelectric thin film 16 itself and deflection or damage to the vibration part such as the diaphragm. In this way, providing the conductive NTE layer 15 between the piezoelectric thin film 16 and the substrate 11 can improve the piezoelectric characteristics of the piezoelectric thin film laminate 10.

[0033] Furthermore, in the piezoelectric thin film laminate 10 of this embodiment, the internal stress can be adjusted by the conductive NTE layer 15 without changing the sputtering conditions for the piezoelectric thin film 16 itself. This is therefore preferable from the viewpoints of productivity and cost of the piezoelectric thin film laminate 10. Furthermore, the piezoelectric thin film laminate 10 of this embodiment does not contain lead, and therefore has a low environmental impact. Such a piezoelectric thin film laminate 10 is particularly effective in, for example, disposable applications.

[0034] Furthermore, in this embodiment, the conductive NTE layer 15 is provided between the piezoelectric thin film 16 and the lower electrode 14, and therefore, unlike a configuration in which the conductive NTE layer 15 is provided between the lower electrode 14 and the substrate 11, the internal stress of the piezoelectric thin film 16 can be directly adjusted.

[0035] Second Embodiment 3 differs from the first embodiment in the position of the conductive NTE layer 115. In this embodiment, the same configuration as in the above-described embodiment will not be described.

[0036] The piezoelectric thin film laminate 110 is formed by laminating a substrate 11, an SiO2 layer 12, an adhesive layer 13, a conductive NTE layer 115, a bottom electrode 14, and a piezoelectric thin film 16 in this order. The SiO2 layer 12 and the adhesive layer 13 are optional layers. The piezoelectric thin film laminate 110 may further include other optional layers laminated between the layers.

[0037] In this embodiment, the conductive NTE layer 115 is disposed between the lower electrode 14 and the substrate 11. The conductive NTE layer 115 may be in contact with the lower surface of the lower electrode 14. In this configuration, the conductive NTE layer 115 may form part of the electrode of the piezoelectric thin film stack 110 together with the lower electrode 14.

[0038] In this embodiment, the conductive NTE layer 115 is provided between the lower electrode 14 and the substrate 11, and therefore, unlike a configuration in which the conductive NTE layer 115 is provided between the piezoelectric thin film 16 and the lower electrode 14, it is possible to adjust the internal stress while maintaining the orientation of the piezoelectric thin film 16.

[0039] Third Embodiment 4 includes a substrate 11, a lower electrode 14 laminated on the substrate 11, and a piezoelectric thin film 16 made of an alkali niobate piezoelectric material laminated on the lower electrode 14. The piezoelectric thin film laminate 210 has an insulating layer 215 made of a material having a negative thermal expansion coefficient between the lower electrode 14 and the substrate 11. Hereinafter, the insulating layer 215 made of a material having a negative thermal expansion coefficient will also be referred to as an insulating NTE layer 215. In this embodiment, descriptions of configurations similar to those of the above-described embodiments will be omitted.

[0040] The piezoelectric thin film laminate 210 is formed by laminating a substrate 11, an insulating NTE layer 215, an adhesion layer 13, a lower electrode 14, an underlayer 17, and a piezoelectric thin film 16 in this order. The adhesion layer 13 and the underlayer 17 are optional layers. The piezoelectric thin film laminate 210 may further include other optional layers laminated between the layers.

[0041] The underlayer 17 is disposed in contact with the piezoelectric thin film 16 and the lower electrode 14. The underlayer 17 has conductivity and constitutes part of the electrode of the piezoelectric thin film laminate 210 together with the lower electrode 14. The underlayer 17 preferably contains a perovskite-type inorganic oxide. By disposing such an underlayer 17 in contact with the piezoelectric thin film 16, the orientation of the piezoelectric thin film 16 can be improved. The underlayer 17 preferably contains at least one perovskite-type inorganic oxide selected from the group consisting of SrRuO3, CaRuO3, BaRuO3, and LaNiO3.

[0042] The insulating NTE layer 215 is made of a material having a negative thermal expansion coefficient. The thermal expansion coefficient of the material having a negative thermal expansion coefficient is not particularly limited. The thermal expansion coefficient of the material having a negative thermal expansion coefficient is preferably -9.0×10 -6 / K to -187×10 -6 / K in at least a part of the temperature range from the manufacturing temperature to the use temperature. If it is within the above range, it is preferable because it is easy to control the internal stress of the piezoelectric thin film laminate 210.

[0043] The insulating NTE layer 215 has insulation. The material having insulation and a negative thermal expansion coefficient is, for example, BNi 1-x Fe x O3 (0.05 <x), ZrW2O8, and CaRuO4 and is preferably one or more selected from the group consisting of. The thermal expansion coefficient of BNi 1-x Fe x O3 (0.05 <x) is, for example, -187×10 at 10°C to 45°C -6 / K. The thermal expansion coefficient of ZrW2O8 is, for example, -9×10 at 45°C to 155°C -6 / K. The thermal expansion coefficient of CaRuO4 is -115×10 -6 / K.

[0044] The thickness of insulating NTE layer 215 can be appropriately designed depending on its own thermal expansion coefficient and the thermal expansion coefficients of the other layers in piezoelectric thin film laminate 210. The thickness of insulating NTE layer 215 is preferably 20 nm to 5 μm. If the thickness is equal to or greater than the lower limit of the above range, it is preferable from the viewpoint of alleviating the internal stress of piezoelectric thin film laminate 210. If the thickness is equal to or less than the upper limit of the above range, it is preferable from the viewpoint of productivity and cost. The thermal expansion coefficient of the piezoelectric thin film 16 is not particularly limited, but is usually larger than that of the insulating NTE layer 215. For example, the thermal expansion coefficient of the piezoelectric thin film 16 may be larger than that of the substrate 11.

[0045] In this embodiment, the insulating NTE layer 215 is disposed between the lower electrode 14 and the substrate 11. The piezoelectric thin film laminate 210 may not include the SiO2 layer 12, but may include only the insulating NTE layer 215 as an insulating layer between the lower electrode 14 and the substrate 11. With this configuration, the step of forming the SiO2 layer 12 can be omitted. Note that an adhesion layer 13 is provided between the lower electrode 14 and the insulating NTE layer 215 to prevent the lower electrode 14 and the insulating NTE layer 215 from peeling off.

[0046] The operation and effect of this embodiment will be described below. According to this embodiment, since the insulating NTE layer 215 is provided between the lower electrode 14 and the substrate 11, the magnitude relationship of the thermal expansion coefficient is, for example, insulating NTE layer 215<substrate 11<piezoelectric thin film 16<adhesion layer 13<lower electrode 14<underlayer 17, and internal stress that may occur due to the difference in the thermal expansion coefficient between the piezoelectric thin film 16 and the substrate 11 can be adjusted.

[0047] The invention is not limited to the embodiments described above and illustrated in the drawings, and the various features of the above-described embodiments may be combined in any compatible combination.

[0048] It should be noted that the embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present invention is not limited to the embodiments disclosed herein, but is intended to include all modifications within the scope indicated by the claims or the scope equivalent to the claims. [Explanation of symbols]

[0049] 10,110...Piezoelectric thin film laminate 11... Circuit board 12...SiO2 layer 13...Adhesion layer 14...Lower electrode 15,115...Conductive NTE layer (conductive layer made of a material with a negative thermal expansion coefficient) 16...Piezoelectric thin film 17…base layer 210... Piezoelectric thin film laminate 215...Insulating NTE layer (insulating layer made of a material with a negative thermal expansion coefficient)

Claims

1. A substrate; a lower electrode laminated above the substrate; a piezoelectric thin film made of an alkali niobate piezoelectric material laminated above the lower electrode, A conductive layer made of a material having a negative thermal expansion coefficient is provided between the piezoelectric thin film and the substrate. Piezoelectric thin film stack.

2. A substrate; a lower electrode laminated above the substrate; a piezoelectric thin film made of an alkali niobate piezoelectric material laminated above the lower electrode, an insulating layer made of a material having a negative thermal expansion coefficient is provided on the substrate in contact with the lower electrode and the substrate; Piezoelectric thin film stack.

Citation Information

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