Patent Publication Number: US-2004051763-A1

Title: Piezoelectric thin film element, actuator, ink-jet head and ink-jet recording apparatus therefor

Description:
BACKGROUND OF THE INVENTION  
       [0001] The present invention relates to a piezoelectric thin film element for use in a piezoelectric element, an infrared-ray detecting element of pyro-electricity type, an un-volatilizing memory, an electro-optics effect element, and so on. In particular, it relates to an actuator using a piezoelectric effect of dielectric material with a piezo-electric nature, an ink-jet head therefor, and an ink-jet apparatus with the head.  
       [0002] In electronics fields, there are many applied technologies using dielectric materials, for example piezoelectric elements, infrared sensors, optical modulation elements, memory elements, and so on.  
       [0003] According to developments of micromachine processing technology and demands for compactness and light weight of various apparatuses, various thin film devices have been in practical use.  
       [0004] I. Kanno et. al: Applied Physics Let. 70(1997) P1378-1380 provides an example of a piezoelectric thin film element to create these thin film elements. FIG. 12 shows a cross-sectional view of the piezoelectric thin film element  90 . The piezoelectric thin film element  90  includes a MgO substrate  91 , a Pt lower electrode  92  as a first electrode, a PZT piezoelectric thin film  93  and a Pt upper electrode  94  as a second electrode. The Pt lower electrode  92 , the PZT piezoelectric thin film  93  and the Pt upper electrode  94  are formed on the MgO substrate  41  in order.  
       [0005] In a forming process of the piezoelectric thin film  90 , the piezoelectric thin film  90  requires a crystallization treatment at 500 to 700 degrees. Because of this, in a process of cooling the piezoelectric thin film  90  down to room temperature, some compression or depression stresses in the PZT piezoelectric thin film  93  occur due to the difference between the heat expansion coefficients of the PZT piezoelectric thin film  93  and the substrate  91  supporting the PZT piezoelectric thin film  93 .  
       [0006] Because of this, the mechanical intensity of the PZT piezoelectric thin film  93  falls, and there is a problem of occurrence of some cracks and an insulated destruction in the PZT piezoelectric thin film  93 , successively, during operation of the PZT piezoelectric thin film  93 .  
       [0007] The present invention was devised under these circumstances. An object of the invention is to reduce an internal stress of the piezoelectric thin film.  
       SUMMARY OF THE INVENTION  
       [0008] In order to achieve the aforementioned object, according to the invention, the piezoelectric thin film element includes a substrate, a first electrode formed on the substrate, a dielectric thin film formed on the first electrode, and a second electrode formed on the dielectric thin film. The piezoelectric thin film includes a piezoelectric layer (i.e., a material layer that exhibits piezoelectric characteristics) and a stress reduction layer having smaller young&#39;s modulus than the piezoelectric layer. The stress reduction layer is isolated from the first and second electrodes.  
       [0009] Due to this structure, the internal stress of the dielectric thin film can be reduced, and the reduction in the mechanical intensity of the dielectric thin film can be prevented. Also, the occurrence of cracks and the dielectric breakdown of the dielectric thin film can be suppressed. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0010]FIG. 1 is a schematic perspective view of an ink-jet printer using a piezoelectric thin film of the first embodiment.  
     [0011]FIG. 2 is a sectional perspective view of an ink-jet head of the ink-jet printer in FIG. 1.  
     [0012]FIG. 3 is a sectional perspective view of primary portion of the ink-jet head in FIG. 2.  
     [0013]FIG. 4 is a sectional view of an actuator portion of the ink-jet head in FIG. 2.  
     [0014]FIG. 5 is a sectional view of a piezoelectric thin film of the first embodiment.  
     [0015]FIG. 6 is a sectional view of other piezoelectric thin film of the first embodiment.  
     [0016]FIG. 7 is a sectional view of a piezoelectric thin film of the second embodiment.  
     [0017]FIG. 8 is a graph showing a relationship between the composition of a Pb(Z ry +Ti 1−y )O 3  thin film and the lattice constant of Pb(Z ry +Ti 1−y )O 3  thin film under room temperature.  
     [0018]FIG. 9 is a graph showing a relationship in condition y&lt;0.6 between the temperature of a Pb(Z ry +Ti 1−y )O 3  thin film and the lattice constant of a Pb(Z ry +Ti 1−y )O 3  thin film under room temperature.  
     [0019]FIG. 10 is a graph showing a relationship between the composition of a Pb(Z ry +Ti 1−y )O 3  thin film and the heat expansion coefficient of a Pb(Z ry +Ti 1−y )O 3  thin film.  
     [0020]FIG. 11 is a sectional view of another piezoelectric thin film of the third and forth embodiments.  
     [0021]FIG. 12 is a sectional view of a piezoelectric thin film of the related art.  
     [0022]FIG. 13 is a sectional view of a step in manufacturing the piezo-electric thin film element of the first embodiment.  
     [0023]FIG. 14 is a sectional view of a step in manufacturing the piezo-electric thin film element of the first embodiment.  
     [0024]FIG. 15 is a sectional view of a step in manufacturing the piezo-electric thin film element of the first embodiment.  
     [0025]FIG. 16 is a sectional view of a step in manufacturing the piezo-electric thin film element of the first embodiment.  
     [0026]FIG. 17 is a sectional view of a step in manufacturing the piezo-electric thin film element of the first embodiment.  
     [0027]FIG. 18 is a sectional view of a step in manufacturing the piezo-electric thin film element of the first embodiment. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
     [0028] Now, preferred embodiments of the invention will be described using FIGS. 1 through 11. In addition, the same number is given to the same component, and any overlapping explanation is omitted.  
     [0029] (First Embodiment)  
     [0030]FIG. 1 shows an ink-jet printer using a piezoelectric thin film of the first embodiment.  
     [0031]FIG. 2 shows an ink-jet head of the ink-jet printer in FIG. 1. FIG. 3 shows a primary portion of the ink-jet head in FIG. 2. FIG. 4 shows an actuator portion of the ink-jet head in FIG. 2 FIG. 5 shows a piezoelectric thin film of the first embodiment. FIG. 6 shows another piezoelectric thin film of the first embodiment.  
     [0032] An ink-jet recording apparatus  40  shown in FIG. 1 carries an ink-jet head  41  to record utilizing a piezoelectric effect of a piezoelectric thin film element. The ink-jet printer  40  records on a recording medium  42  by ejecting some ink-droplets from the ink-jet head  41  toward the recording medium  42 .  
     [0033] The ink-jet head  41  is carried on a carriage  44 . The carriage  44  is located on a carriage axis  43  set along the main scanning direction X. The ink-jet head  41  reciprocates along the main-scanning direction X in accordance with the carriage  44  reciprocating along the carriage axis  43 .  
     [0034] The ink-jet recording apparatus  40  includes a plurality of rollers  45  to make a recording medium  42  move in the sub-scanning direction Y orthogonal to the width direction of the ink-jet head  41 (that is, the main-scanning direction X).  
     [0035]FIG. 2 shows a view of the whole structure of the ink-jet head  41 , and FIG. 3 shows a view of a primary portion of the ink-jet head  41 . In FIG. 2 and FIG. 3, the ink-jet head  41  comprises a pressure chamber part A, an actuator portion B, a ink passage portion C and a nozzle plate D.  
     [0036] The pressure chamber part A has a plurality of opening portions  1 . The opening portions  1  are covered with the actuator portion B and the ink passage portion C on both edge surfaces of the pressure chamber A. The spaces of the opening portions  1  closed by portions B and C function as pressure chambers  2 .  
     [0037] The actuator portion B includes a plurality of second electrodes  3  located on the pressure chambers  2 . The second electrodes  3  are separated from each other. As shown in FIG. 2, the sets of pressure chambers  2  and second electrodes  3  are arranged alternately.  
     [0038] The ink passage portion C includes a common ink passage  5  connected with the plurality of pressure chambers  2 , an inlet port  6  connected between chambers  2  and passage  5 , and an ink passage  7  allowing the ink to flow to nozzle plate D. The plurality of pressure chambers  2  are arranged along the ink flowing direction YY in the common ink passage  5 .  
     [0039] The nozzle plate D has a plurality of nozzles  8  communicating with the ink passage  7 . As shown in FIG. 2, IC chip E connects to the second electrodes  3  via bonding wires BW, and supplies the electricity for the second electrodes.  
     [0040] Next, the structure of the actuator portion B is described in detail based on FIG. 4. FIG. 4 shows a sectional view orthogonal to the direction YY of an actuator portion of the ink-jet head  4  in FIG. 2. Referentially, FIG. 4 shows the pressure chamber part A having four pressure chambers  2 , and shows the actuator portion B corresponding to the pressure chamber part A. The actuator part B, includes a dielectric thin film  10  located under the second electrode  3 , and includes a vibration plate  11  for carrying a displacement and vibration due to the piezo-electric characteristics of the dielectric thin film. The vibration plate  11  also forms a first electrode.  
     [0041] The vibration plate  11  is formed from a conductive material. The vibration plate  11  is common to each pressure chamber  2 . Furthermore, the actuator portion B includes a plurality of longitudinal walls  13  located on a partition wall  2   a  disposed between two adjacent pressure chambers  2 . The pressure chamber part A and the actuator portion B are united with adhesive  14 . Because the longitudinal walls  13  are located between the partition wall  2   a  and the vibration plate  11 , each of the partition walls  2   a  is separated from the vibration plate  11 . The longitudinal walls  13  prevent the vibration plate  11  from attaching to adhesive  14  even if the adhesive  14  overflows from the partition wall  2   a  at the time of adhesion.  
     [0042] A piezo-electric thin film element is made up of the dielectric thin film  10 , the second electrode  3  and the vibration plate  11 .  
     [0043] Though in this embodiment the vibration plate  11  also serves as (forms) the first electrode, the vibration plate and the first electrode may be disposed separately. A case like this is shown in FIGS.  5  to  7 .  
     [0044] The second electrodes  3  are formed with a metal whose main ingredient is the Platinum Group precious metal, such as, for example, Pt, Ir, Ru, Os and Pd, an alloy of the metals, or the oxide of the metal or the alloy. The vibration plate  11  is formed with a metal, such as for example, Pt, Cr, Cu, Mo and Ta, an alloy containing at least one of the metals, or the oxide of the metal or the alloy.  
     [0045] In FIG. 5, a piezo-electric thin film element includes a substrate  21  of silicon, a first electrode  22  of Pt formed on the substrate  21 , a dielectric thin film element  10  formed on the first electrode  22 , and the second electrode  3  of Pt formed on the dielectric thin film element  10 . The dielectric thin film element  10  includes a piezo-electric layer  10   a  formed of a PZT thin film with a composition of Pb(Zr 0.52 Ti 0.48 ) 0   3 , and includes a stress reducing layer  10   b  formed of a material having a smaller young&#39;s modulus than that of the piezo-electric layer  10   a . The stress-reducing layer  10   b  includes two layers with a total thickness of 0.03 to 0.3 μm and is isolated from the first electrode  22  and the second electrode  3 .  
     [0046] An insulation material  15  covers the side wall of the dielectric thin film  10  to prevent any short-circuiting between the two stress-reducing layers. In addition, the substrate  21  can be made from stainless steel, glass or MgO single crystal.  
     [0047] Also, the piezo-electric layer  10   a  can be made from an oxide solid-solution having a perovskite structure expressed by chemical formula “ABO 3 ”, containing at least one element selected from Pb, Ba, Nb, La, Li, Sr, Bi, Na and K as “A”, and at least one element selected from Cd, Fe, Ti, Ta, Mg, Mo, Ni, Nb, Zr, Zn, W and Yb as “B”. Preferably, the piezo-electric layer  10   a  can be made from one of the oxide solid-solutions of perovskite structure containing “Pb” as “A”. Furthermore, Pb 1+x (Z ry +Ti 1−y )O 3  (x=0˜0.5) is the most proper material to be used as the piezo-electric layer  10   a.    
     [0048] In addition, Pb(Zr,Ti)O 3 , (Pb,La) (Zr,Ti)O 3 , Pb(Mg 1/3 , Nb 2/3 )O 3 , Pb(Mg 1/2 , W 1/2 )O 3 , Pb(Zn 1/3 , Nb 2/3 )O 3 , Pb(Cd 1/2 , W 1/2 )O 3 , Pb(Fe 2/3 , W 1/3 )O 3 , Pb(Yb 1/2 , Nb 1/2 )O 3 , PbTiO 3  and solid-solutions of these materials, or PbZrO3 and solid-solutions of these materials are known as the oxide solid solutions of perovskite structure containing “Pb” as “A”.  
     [0049] The stress reducing layer  10   b  can be made from a metal or an oxide thereof whose main ingredient is a precious metal of Pt system having a spread nature like Pt, Ir, Ru, Os, Pd etc.  
     [0050] Next, a process of manufacturing the piezo-electric thin film element  16  will be described using FIGS. 13 through 18.  
     [0051] First, as shown in FIG. 13, a first Pt film  10   ba  with a thickness of 0.2 μm is formed by sputtering on the surface of the substrate  21  heated to about 600 to 650 degrees, then, as shown in FIG. 14, a first PZT film  10   aa  with a thickness of 1 μm is formed by sputtering on the surface of the first Pt film  10   ba . After that, as shown in FIG. 15, a second Pt film  10   bb , a second PZT film  10   ab , a third Pt film  10   bc  and a third PZT film  10   ac  are formed, in order, by repeating the above procedure two times. At last, a fourth Pt film  10   bd  with a thickness of 0.2 μm is formed on the third PZT film  10   ac . The sputtering is accomplished by RF magnetron sputtering equipment. Pt films are formed in conditions such that the atmosphere is Ar gas of about 0.3 Pa and the temperature of the substrate  21  is around 650 degrees. PZT films are formed in condition that the atmosphere is Ar mixed gas with a partial pressure 10% of Oxygen of about 0.3 Pa, and the temperature of the substrate  21  is around 620 degrees.  
     [0052] The first Pt film  1   10   ba  formed on the substrate  21  forms the first electrode  22 . The first, second and third PZT films  10   aa ,  10   ab , and  10   ac  form the piezoelectric layer  10   a . The second and third Pt films  10   bb  and  10   bc  located between PZT films  10   aa ,  10   ab  and  10   ac  works form the stress-reducing layer  10   b.    
     [0053] Subsequently, as shown in FIG. 16, the fourth Pt film  10   bd  located on the top of the dielectric thin film element  10  is etched by photolithography. After that, the fourth Pt film  10   bd  is divided into a plurality of electrodes which are separated, respectively, and those electrodes form the second electrodes  3 .  
     [0054] Furthermore, as shown in FIGS. 6 and 17, the piezo-electric layers  10   a  and the stress-reducing layers  10   b  are separated by dry or wet etching, due to the separation, side walls  10   e  of the piezo-electric layers  10   a  and the stress-reducing layers  10   b  are formed. Insulation material  15  is formed on the side walls  10   e . The insulation material  15  prevents short-circuiting between the stress-reducing layers  10   b . As shown in FIG. 18, the insulation material  15  can be made from inorganic material such as SiO 2  and Si 3 N 4 , or organic resin such as resist and polyimide. The insulation material  15  can be formed by applying a coat of insulation material or using one of the well-known semiconductor manufacturing methods.  
     [0055] Additionally, as shown in FIG. 6, an electric short circuit may be prevented by changing the area of the stress-reducing layers  10   b  which sandwich the piezo-electric layers  10   a  as insulated layers. In this case, it is desirable so that the areas of the stress-reducing layers  10   b  may become smaller in order as these are away from the substrate  21 .  
     [0056] In the above-described embodiment, the piezo-electric thin film  16  can lessen the internal stresses due to the stress-reducing layer  10   b  if the internal stresses originate from the difference between heat expansion coefficient of the PZT piezoelectric thin film  16  and the substrate  21  during a process of cooling the substrate  21  down to room temperature, and a drop in the mechanical intensity of the dielectric thin film can be prevented. Also, the occurrence of cracks and the dielectric breakdown of the dielectric thin film can be suppressed.  
     [0057] (Second Embodiment)  
     [0058]FIG. 7 shows a sectional view of a piezoelectric thin film of the second embodiment. FIG. 8 shows a graph of a relationship between the composition of a Pb(Z ry +Ti 1−y )O 3  thin film and the lattice constant of a Pb(Z ry +Ti 1−y)O   3  thin film under room temperature. FIG. 9 shows a graph of a relationship in condition y&lt;0.6 between the temperature of a Pb(Z ry +Ti 1−y )O 3  thin film and the lattice constant of a Pb(Z ry +Ti 1−y )O 3  thin film under room temperature. FIG. 10 shows a graph showing a relationship between the composition of a Pb(Z ry +Ti 1−y )O 3  thin film and the heat expansion coefficient of a Pb(Z ry +Ti 1−y )O 3  thin film.  
     [0059] A piezo-electric thin film element  20  in FIG. 7 comprises a substrate  21 , a first electrode  22  formed on the substrate  21 , a dielectric thin film  10  formed on the first electrode  22  and a second electrode  3  formed on the dielectric thin film  10 . The first and second electrodes can be made from metal material such as Pt, Ir, Ru, Os and Pd, a alloy of the metals, or the oxide of the metal or the alloy.  
     [0060] The dielectric thin film element  10  includes a piezo-electric layer  10   c  formed with a PZT thin film whose composition is Pb(Zr 0.52 Ti 0.48 )O 3  and a stress-reducing layer  10   d  formed of a material having a different heat expansion coefficient from that of the piezo-electric layer  10   c . The stress-reducing layer  10   d  is formed between the piezo-electric layer  10   c  and the first electrode  22  with a total thickness 0.03 to 0.3 μm. In addition, the total thickness of the stress-reducing layer  10   d  may be beyond the aforesaid range more or less, and the stress-reducing layer  10   d  should just consist of at least one or more layers.  
     [0061] Also, the piezo-electric layer  10   c  and the stress-reducing layer  10   d  can be made from an oxide solid-solution of a perovskite structure expressed by chemical formula “ABO 3 ”, containing at least an element selected from Pb, Ba, Nb, La, Li, Sr, Bi, Na and K as “A”, and at least an element selected from Cd, Fe, Ti, Ta, Mg, Mo, Ni, Nb, Zr, Zn, W and Yb as “B”. Preferably, the piezo-electric layer  10   a  can be made from one of the oxide solid-solutions of perovskite structure containing “Pb” as “A”. Furthermore, Pb 1+x (Z ry +Ti 1−y )O 3  (x=0˜0.5) is the most proper material for the piezoelectric layer  10   a . In addition, Pb(Zr,Ti)O 3 , (Pb,La) (Zr,Ti)O 3 , Pb(Mg 1/3 , Nb 2/3 )O 3 , Pb (Mg 1/2 , W 1/2 )O 3 , Pb(Zn 1/3 , Nb 2/3 )O 3 , Pb(Cd 1/2 , W 1/2 )O 3 , Pb(Fe 2/3 , W 1/3 )O 3 , Pb(Yb 1/2 , Nb 1/2 )O 3 , PbTiO 3  and solid-solutions of these materials, or PbZrO 3  and solid-solutions of these materials are known as the oxide solid solutions of a perovskite structure containing “Pb” as “A”.  
     [0062] When the piezo-electric layer  10   c  and the stress-reducing layer  10   d  are formed by PZT films such as Pb 1+x (Z ry +Ti 1−y ) O 3  (x=0˜0.5), the lattice constant of the PZT films change with composition, as shown in FIG. 8, and with temperature, as shown in FIG. 9. Because of these features, the heat expansion coefficient of the PZT films with random orientation polarization changes continuously with the composition as shown in FIG. 10, and the polarity of the PZT film changes near y=0.25. Utilizing this feature, the heat expansion coefficient of the piezo-electric layer  10   c  can be changed with the heat expansion coefficient of the stress-reducing layer  10   d  by setting the “y” of the piezo-electric layer  10   c  from 0.5 to 0.6 and setting the “y” of the stress reducing layer  10   d  from 0.1 to 0.3.  
     [0063] Next, a manufacturing method of the piezo-electric thin film  20  will be described.  
     [0064] First, Pt film as the first electrode  22  is formed by sputtering on the surface of the substrate  21  heated to about 600 degrees. Then, a PZT film as the stress-reducing layer  10   d  is formed by sputtering on the surface of the first electrode  22 . After that, a PZT film as the piezo-electric layer  10   c  is formed by sputtering on the surface of layer  10   d . At last, Pt film as the second electrode  3  is formed on the piezo-electric layer  10   c.    
     [0065] The sputtering is conducted by RF magnetron sputtering equipment. Pt films are formed in a condition such that the atmosphere is Ar gas of about 0.3 Pa and the temperature of the substrate  21  is around 650 degrees. PZT films are formed in conditions such that the atmosphere is Ar mixed gas with partial pressure 10% of Oxygen of about 0.3 Pa and the temperature of the substrate  21  is around 620 degrees.  
     [0066] In the above-described embodiment, the piezo-electric thin film  20  can lessen the internal stresses in view of the stress-reducing layer  10   d  if the internal stresses in the dielectric thin film  10  originate from the difference between the heat expansion coefficient of the dielectric thin film  10  and the substrate  21  in a process of cooling the substrate  21  down to room temperature, and a reduction in the mechanical intensity of the dielectric thin film  10  can be prevented. Also, the occurrence of cracks and the dielectric breakdown of the dielectric thin film  10  can be suppressed.  
     [0067] (Third Embodiment)  
     [0068]FIG. 11 shows a sectional view of a piezoelectric thin film of a third and embodiment. A piezo-electric thin film element  30  in FIG. 11 comprises a silicon substrate  21 , Pt ilm as a first electrode  22  formed on the substrate  21 , a dielectric thin film  10  formed on the first lectrode  22 , and a Pt film as a second electrode  3  formed on the dielectric thin film  10 .  
     [0069] The dielectric thin film  10  is formed of a composition such as Pb 1+x (Z ry +Ti 1−y )O 3  (X=0˜0.5). When the heat expansion coefficient of the substrate  21  is from 20×10 −7  (K−1) to 40×10 −7  (K −1 ), the “y” of The dielectric thin film  10  is controlled from 0.4 to 0.5. When the heat expansion coefficient of the substrate  21  is from 60×10 −7  (K− 1 ) to 150×10 −7 (K −1 ), the “y” of the dielectric thin film  10  is controlled from 0.5 to 0.7.  
     [0070] That is, when the heat expansion coefficient of the substrate  21  is from 20×10 −7  (K −1 ) to 40×10 −7  (K −1 ), a tensile stress is applied to the dielectric thin film  10 . Then if the “y” of the dielectric thin film  10  is controlled from 0.4 to 0.5, the anisotropy of the dielectric thin film  10  (c/a in figs.) becomes larger in the crystal structure as the temperature of the substrate  21  lowers from high temperature to room temperature. Therefore, the tensile stress applied to the dielectric thin film  10  is relaxed as the anisotropy of the dielectric thin film  10  changes in the direction to relax the tensile stress when the tensile stress is applied from the substrate  21 .  
     [0071] On the other hand, a compressive stress is applied to the dielectric thin film  10  when the heat expansion coefficient of the substrate  21  is from 60×10 −7  (K −7 ) to 150×10 −7  (K −1 ). In this case, the “y” of the dielectric thin film  10  can be controlled from 0.5 to 0.7, at which the piezo-electric characteristics of the dielectric thin film  10  can have some higher values because the dielectric thin film  10  does not have to be coordinated with its internal stress.  
     [0072] Next, a manufacturing method of the piezo-electric thin film  30  will be described. First, a Pt film as the first electrode  22  is formed by sputtering on the surface of the substrate  21  heated about 600 degrees. Then, a PZT film made of Pb 1+x (Zry+Ti 1−y )O 3  (X=0˜0.5) for the dielectric thin film  10  is formed by sputtering on the surface of the first electrode  22  while controlling the composition of “y” of the dielectric thin film  10  in accordance with the heat expansion coefficient of the substrate  21 . At last, a Pt film as the second electrode  3  is formed on the dielectric thin film  10 .  
     [0073] The sputtering is conducted by the RF magnetron sputtering equipment. Pt films are formed in conditions such that the atmosphere is Ar gas of about 0.3 Pa and the temperature of the substrate  21  is around 650 degrees. PZT films are formed in conditions such that the atmosphere is Ar mixed gas with partial pressure 10% of Oxygen of about 0.3 Pa and the temperature of the substrate  21  is around 620 degrees. The way to control the composition of “y” of the dielectric thin film  10  is to change the composition of Zr or Ti in the sputtering target in accordance with the heat expansion coefficient of the substrate  21 .  
     [0074] In the above-described piezo-electric thin film  30 , the internal stress of the dielectric thin film  10 , which originates during a process of cooling the substrate  21  down to room temperature, can be relaxed by selecting the composition of the dielectric thin film  10  in accordance with the heat expansion coefficient of the substrate  21 . Because of this, a reduction in the mechanical intensity of the dielectric thin film  10  can be prevented. Also, the occurrence of cracks and the dielectric breakdown of the dielectric thin film  10  can be suppressed.  
     [0075] (Fourth Embodiment)  
     [0076] Explanations about the piezo-electric thin film element  30  are omitted in this embodiment because the piezo-electric thin film element  30  is the same as that of the third embodiment.  
     [0077] The dielectric thin film  10  is a poly crystal PZT film(randomly oriented) made from the oxide solid solutions of perovskite structure containing a tetragonal structure, such as Pb 1+x (Z ry +Ti 1−y )O 3  (x=0˜0.5).  
     [0078] The heat expansion coefficient of the substrate  21  is defined as “αs”. The heat expansion coefficient of the dielectric thin film  10  is defined as “αf”, and the ratio αs/αf is set to “α”. When this ratio is 0.3&lt;α&lt;0.7, the c-axis oriented rate of the dielectric thin film  10  is around 10% to 40%, and when it is 1&lt;α&lt;2.5, the c-axis oriented rate of the dielectric thin film  10  is around 60% to 100%.  
     [0079] The “αf” changes greatly with a material composition around 30 to 110×10 −7  (K −1 ). For example, when the dielectric thin film  10  is made from Pb(Zr 0.52 , Ti 0.48 )O3, the “αf” is about 80×10 −7  (K −1 ). When the dielectric thin film  10  is made from Pb(Mg 1/3 , Nb 2/3 )O 3 , the “αf” is about 40×10 −7  (K −1 ). When the dielectric thin film  10  is made from Pb(Zr 1/3 , Nb 2/3 )O 3 , the “αf” is about 50×10 −7  (K −1 ).  
     [0080] The dielectric thin film  10  has the particular feature that the heat expansion coefficient changes with the direction of the axis. That is, the heat expansion coefficient in c-axis is a negative value, and the heat expansion coefficient in a-axis is a positive value. Utilizing this feature, the heat expansion coefficient of the oriented dielectric thin film can be controlled.  
     [0081] When the “αf” is larger than the “αs”, that is, 0.3&lt;α&lt;0.7, the c-axis oriented rate of the dielectric thin film  10  is controlled around 10% to 40% or the c-axis oriented rate of the dielectric thin film  10  is made larger than the a-axis oriented rate. Because of this, the “αf” is made small; and the internal stress of the dielectric thin film  10  can be relaxed.  
     [0082] On the other hand, when the “αf” is smaller than the “αs”, that is, 1&lt;α&lt;2.5, the c-axis oriented rate of the dielectric thin film  10  is controlled around 60% to 100% or the c-axis oriented rate of the dielectric thin film  10  is made smaller than the a-axis oriented rate. Because of this, the “αf” is made large; and the internal stress of the dielectric thin film  10  can be relaxed.  
     [0083] Specifically, when the “αs”l is around 20˜40×10 −7  (K −1 ), considering the aforementioned “αf”, the “αs” is smaller than the “αf”. Therefore, the c-axis oriented rate of the dielectric thin film  10  is controlled around 10% to 40%, then the “αf” is made small, and then the internal stress of the dielectric thin film  10  can be relaxed.  
     [0084] Further, when the “αs” is around 60-100×10 −7  (K −1 ), considering the aforementioned “αf”, the “αs” is larger than the “αf”. Therefore, the c-axis oriented rate of the dielectric thin film  10  is controlled around 60% to 100%, then the “αf” is made large, and then the internal stress of the dielectric thin film  10  can be relaxed.  
     [0085] Next, a procedure for manufacturing the piezo-electric thin film element  30  will be described using FIG. 11. In FIG. 11, a Pt film (the first electrode  22 ) with a thickness of 0.2 μm and a PZT film (the dielectric thin film  10 ) with a thickness of 1 μm are formed in order on the surface of (001)MgO single crystal substrate(the substrate  21 ). Finally, a Pt film (the second electrode  3 ) with a thickness of 0.2 μm is formed on the PZT film. All kinds of films are formed by sputtering, which is conducted by the RF magnetron sputtering equipment. In addition, the first electrode  22  and the second electrode  3  can be made from metal material such as, Ir, Ru, Os and Pd, or an alloy of the metals.  
     [0086] The structures of crystal of the Pt film or the PZT film change with sputtering conditions. Pt film is formed in conditions such that the atmosphere is Ar gas of about 0.3 Pa, and the temperature of the substrate is around 650 degrees, and PZT film is formed in condition such that the atmosphere is Ar mixed gas with partial pressure 10% of Oxygen of about 0.3 Pa and the temperature of the substrate  21  is around 620 degrees. Consequently, the Pt film and the PZT film carry out epitaxial growth in the (001) direction on a single crystal substrate of (001) MgO.  
     [0087] When PZT film includes a tetragonal structure in its crystal structure, the (001) direction in PZT film is divided into a c-axis and a-axis, and c-domains and a-domains are produced in PZT film. When this PZT film is analyzed by the powder X-ray diffraction method, the diffraction intensity Ic from c-domains and the diffraction intensity  1   a  from a-domain will be obtained. The c-axis oriented rate is defined as Ic/(Ic+1a)×100(%).  
     [0088] On the other hand, The c-axis oriented nature of PZT film is controllable by adjusting the cooling speed of the substrate temperature after its deposition. That is, in the cooling process of substrate  21  after deposition of PZT film, if the substrate  21  is cooled slowly from 620° C. to 400° C., for example, at the cooling speed of 1° C. or less a minute, then the c-axis oriented rate of the PZT film will become 10-40%. On the other hand, if the substrate  21  is cooled rapidly from 620° to 400° C., for example, at the cooling speed of 20° C. or more a minute, then the c-axis oriented rate of the PZT film will become 60-100%.  
     [0089] Then, the cooling speed of the substrate after the deposition of the PZT film is controlled in order to make it a desired c-axis oriented rate of the PZT film according to the relation between the heat expansion coefficient of a substrate  21  and the heat expansion coefficient of the dielectric thin film  10 .  
     [0090] The reason why the c-axis oriented rate is controllable by adjusting the cooling speed of the substrate  21  is not clear. However, the following can be considered. PZT film having the tetragonal structure in the crystal growth starts the phase transition to the cubic structure at the Curie point. Then, cooling the substrate  21  slowly, the c axis of each crystal grain is turned at random to the thickness direction and the in-plane direction so that internal stress of the PZT film is relaxed. Consequently, the c-axis oriented nature of PZT film is reduced.  
     [0091] In the above-described piezo-electric thin film  30 , the heat expansion coefficient of the dielectric thin film  10  can be controlled by adjusting the c-axis oriented rate of the dielectric thin film  10  corresponding to the heat expansion coefficient of the substrate  21 . Therefore, when the substrate  21  heated in a thin film forming process is cooled to room temperature, the internal stress of the dielectric thin film  10  can be relaxed. Because of this, the occurrence of cracks and the dielectric breakdown of the dielectric thin film  10  can be suppressed.  
     [0092] In the above-described embodiments 1-4, although it is explained that the dielectric thin film elements are applied to an ink ejecting actuator for an ink-jet recording apparatus as examples, the dielectric thin film elements can be applied to various other devices, for example, such as a temperature sensor using the pyro-electricity nature, a light modulation device using the electro-optics effect, an optical actuator using the optical elastic effect, and a SAW device.  
     [0093] In addition, by using the aforementioned piezo-electric thin film elements for an actuator, it is possible for the actuator to perform a stable displacement operation. Also, by using the aforementioned actuator for an ink-jet head, it is possible for the ink-jet head to perform a stable ink-ejecting operation. Furthermore, by using the aforementioned ink-jet head for an ink-jet recording apparatus, it is possible for the ink-jet head to perform high-quality printing by the stable ink-ejecting operation of the ink-jet head. Additionally, the structures and the forming methods recited in embodiments 1-4 can be combinable with each other suitably.