NITRIDE PIEZOELECTRIC BODY AND MEMS DEVICE USING SAME

Abstract

An object is to provide a piezoelectric body having a value indicating a higher performance index (d.sub.33, e.sub.33, C.sub.33, g.sub.33, and/or k.sup.2) than aluminum nitride not doped with any element. The piezoelectric body is represented by a chemical formula Al.sub.1-X-YMg.sub.XM.sub.YN where X+Y is less than 1, X is in a range of more than 0 and less than 1, and Y is in a range of more than 0 and less than 1.

Claims

1. A nitride material represented by a chemical formula Al.sub.1-X-YMg.sub.XM.sub.YN where X+Y is less than 1, X is in a range of more than 0 and less than 1, and Y is in a range of more than 0 and less than 1 (M represents any one of Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, Rh, Pd, Ag, W, Re, Os, Ir, Pt, and Au).

2. The nitride material according to claim 1, wherein X+Y is 0.65 or less, X is in a range of more than 0 and less than 0.65, and Y is in a range of more than 0 and less than 0.65.

3. The nitride material according to claim 1, wherein X+Y is 0.375 or less, X is in a range of more than 0 and 0.1875 or less, and Y is in a range of more than 0 and 0.1875 or less.

4. The nitride material according to claim 1, wherein X+Y is 0.125 or less, X is in a range of more than 0 and 0.0625 or less, and Y is in a range of more than 0 and 0.0625 or less.

5. The nitride material according to claim 1, wherein M is any one of Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, Rh, Pd, Ag, W, Os, Ir, Pt, and Au.

6. The nitride material according to claim 1, wherein M is Cr or Mn.

7. A piezoelectric body comprising the nitride material according to claim 1.

8. A MEMS device using the piezoelectric body according to claim 7.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0029] FIG. 1 is a graph showing values of the mixing enthalpy of Al.sub.0.875Mg.sub.0.0625Cr.sub.0.0625N, Al.sub.0.875Sc.sub.0.125N, and Al.sub.0.875Cr.sub.0.125N.

[0030] FIG. 2 is a diagram illustrating an example of a calculation model of doped AlN used for a simulation according to a first embodiment.

[0031] FIG. 3 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the lattice constant ratio c/a.

[0032] FIG. 4 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the piezoelectric stress constant e.sub.33.

[0033] FIG. 5 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the elastic constant C.sub.33.

[0034] FIG. 6 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the mixing enthalpy.

[0035] FIG. 7 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the electromechanical coupling constant k.sup.2.

[0036] FIG. 8 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the piezoelectric charge constant d.sub.33.

[0037] FIG. 9 is a graph showing the relation between non-doped AlN, AlN doped with only Sc, and each kind of doped AlN, and the piezoelectric voltage constant g.sub.33.

[0038] FIG. 10 is a graph showing the relation between concentrations X(Sc) and X+Y (Mg+Cr), and the mixing enthalpy of the piezoelectric bodies.

[0039] FIG. 11 is a graph showing the relation between concentrations X(Sc) and X+Y (Mg+Cr), and the lattice constant ratio c/a of the piezoelectric bodies.

[0040] FIG. 12 is a graph showing the relation between a concentration X+Y (Mg+Cr) and the piezoelectric stress constant e.sub.33 of the piezoelectric bodies.

DESCRIPTION OF EMBODIMENTS

[0041] Hereinafter, embodiments of piezoelectric bodies according to the present invention will be described with reference to the accompanying drawings. Note that the present invention is not limited to the following embodiments.

First Embodiment

[0042] First, a description will be given of a simulation performed by the inventor using aluminum nitride constituted by only aluminum (Al) and nitrogen (N) (non-doped AlN). The simulation was performed by using a software known as VASP (Vienna Ab initio Simulation Package) in which a calculation method referred to as “first principle calculation” was employed. The first principle calculation described herein is a general term for an electronic state calculating method without using a fitting parameter or the like and a method capable of calculating an electronic state by using only the atomic number and a coordinate of each atom constituting a unit lattice, a molecule, or the like.

[0043] In the simulation of the present embodiment, a supercell of the non-doped AlN having a wurtzite crystal structure was used for the simulation. The supercell containing sixteen aluminum atoms and sixteen nitrogen atoms was obtained by doubling a unit lattice containing two aluminum atoms and two nitrogen atoms in the a-axis, b-axis, and c-axis directions. Then, the first principle calculation was performed to this AlN having the wurtzite crystal structure by simultaneously changing the atomic coordinate, the cell volume, and the cell shape, thereby calculating the electronic state of the non-doped AlN in a stable structure.

[0044] Table 1 shows values (calculated values) of the lattice constant in the a-axis direction, the lattice constant in the c-axis direction, and a ratio (c/a) of the lattice constant in the c-axis direction with respect to the lattice constant in the a-axis direction, calculated from the electronic state of the AlN in the stable structure obtained by the first principle calculation. Further, Table 1 also shows experimental values measured by actually forming a non-doped AlN film using a sputtering method and subjecting this AlN film to an X-ray diffraction method.

TABLE-US-00001 TABLE 1 Lattice Constant in Lattice Constant in a-Axis Direction c-Axis Direction (Å) (Å) c/a Calculated 3.13 5.02 1.60 Value Experimental 3.11 4.98 1.60 Value

[0045] As shown in this Table, each calculated value has almost the same numerical value as the experimental value with the relative error of 1% or less. This result demonstrated that the simulation of the present embodiment was sufficiently reliable.

[0046] The following shows that, when aluminum nitride (AlN) is doped with magnesium (Mg) and the substituent element M (M represents any one of Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, Rh, Pd, Ag, W, Re, Os, Ir, Pt, and Au) together, the AlN can be doped with the more amount of the elements (Mg and the substituent element M) than if the AlN is doped with only the substituent element M.

[0047] As an example of this, FIG. 1 shows the mixing enthalpy of each of aluminum nitride (Al.sub.0.875Mg.sub.0.0625Cr.sub.0.0625N) doped with Mg as well as Cr as the substituent element M, aluminum nitride (Al.sub.0.875Sc.sub.0.125N) doped with only Sc at the same concentration, and aluminum nitride (Al.sub.0.875Cr.sub.0.125N) doped with only Cr at the same concentration. Note that the mixing enthalpy (ΔH.sub.mixing) of each kind of aluminum nitride can be obtained by substituting each numerical value calculated by VASP in the following mathematical formula 1.

[00001]$\begin{array}{cc}\Delta H_{\mathrm{mixing}}=E_{\mathrm{total}}^{{\mathrm{Mg}}_{0.0625}{\mathrm{Cr}}_{0.0625}{\mathrm{Al}}_{0.875}N}-\frac{1}{16}{E}_{\mathrm{total}}^{\mathrm{MgN}}-\frac{1}{16}{E}_{\mathrm{total}}^{\mathrm{CrN}}\frac{14}{16}{E}_{\mathrm{total}}^{\mathrm{AlN}}{E}_{\mathrm{total}}^{\mathrm{MgN}}\text{:}\mathrm{Total}\mathrm{Energy}\mathrm{of}\mathrm{MgN}\mathrm{with}\mathrm{Wurtzite}\mathrm{structure}{E}_{\mathrm{total}}^{\mathrm{CrN}}\text{:}\mathrm{Total}\mathrm{Energy}\mathrm{of}\mathrm{CrN}\mathrm{with}\mathrm{Wurtzite}\mathrm{structure}\text{.Math.}{E}_{\mathrm{total}}^{\mathrm{AlN}}\text{:}\mathrm{Total}\mathrm{Energy}\mathrm{of}\mathrm{AlN}\mathrm{with}\mathrm{Wurtzite}\mathrm{structure}& \left[\mathrm{Mathematical}\mathrm{formula}1\right]\end{array}$

[0048] As is evident from this diagram, it is found that the mixing enthalpy of the AlN doped with Mg and Cr together is lower than the mixing enthalpy of the AlN doped with only Sc or Cr at the same concentration. That is, it is shown that dissolving the elements (Mg+Cr) in the AlN as a solid is more thermodynamically advantageous than dissolving Cr in the AlN as a solid, at the same concentration. This demonstrated that the AlN could be doped with the more amount (at higher concentrations) of the elements (Mg and Cr) than scandium.

[0049] Note that, in the present embodiment, the mixing enthalpy of the aluminum nitride (Al.sub.0.875Mg.sub.0.0625Cr.sub.0.0625N) doped with Mg and Cr together has been described as an example. However, the mixing enthalpy of the aluminum nitride doped with Mg and the substituent element M other than Cr (excluding Re) together is also similarly lowered. Thus, the AlN can be doped with the more amount (at the higher concentrations) of the elements (Mg+the substituent element M (excluding Re)) than scandium.

[0050] Next, a description will be given of a simulation using doped AlN in which aluminum nitride (AlN) is doped with magnesium (Mg) and the substituent element M together. FIG. 2 is a diagram illustrating an example of a crystal structure of the doped AlN in which the AlN is doped with magnesium and the substituent element M, used in the simulation according to the present embodiment.

[0051] As shown in this diagram, the crystal structure of this doped AlN forms a wurtzite crystal structure in which one Al atom is substituted with a Mg atom and one Al atom is substituted with an atom of the substituent element M in a unit lattice containing sixteen Al atoms and sixteen nitrogen atoms. Here, when the total of the number of Al atoms, the number of Mg atoms, and the number of atoms of the substituent element M is set to 1, the number of Mg atoms is defined as X and the number of atoms of the substituent element M is defined as Y. In such a case, in the doped AlN used in this simulation, both the concentration X of Mg atoms and the concentration Y of the substituent element M are given as 0.0625. Note that these kinds of doped AlN can be actually produced by the production method described in the aforementioned Non-Patent Literature 1.

[0052] In the present embodiment, chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), molybdenum (Mo), technetium (Tc), ruthenium (Ru), rhodium (Rh), palladium (pd), silver (Ag), tungsten (W), rhenium (Re), osmium (Os), iridium (Ir), platinum (Pt), and gold (Au) were used as the substituent element M.

[0053] As is the case with the non-doped AlN, the electronic state of these kinds of doped AlN and the AlN doped with only Sc in the stable structure can be calculated by the first principle calculation. Then, values of the lattice constant in the a-axis direction, the lattice constant in the c-axis direction, and the lattice constant ratio c/a can be calculated from the electronic state.

[0054] Then, a small strain is forcibly applied to each crystal lattice of the non-doped AlN, the AlN doped with only Sc, and the doped AlN in the stable structure. As a result, a small change in the total energy caused by this operation makes it possible to calculate each of the piezoelectric stress constant e.sub.33, the elastic constant C.sub.33, and the dielectric constant ε.sub.33 of the non-doped AlN, the AlN doped with only Sc, and the doped AlN. That is, each of the piezoelectric stress constant e.sub.33, the elastic constant C.sub.33, and the dielectric constant ε.sub.33 of the non-doped AlN, the AlN doped with only Sc, and the doped AlN can be calculated by using the first principle calculation.

[0055] Table 2 shows the lattice constant c, the lattice constant a, the lattice constant ratio c/a, the piezoelectric stress constant e.sub.33, the elastic constant C.sub.33, and the dielectric constant ε.sub.33 of the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN thus obtained. Note that the higher numerical value of the piezoelectric stress constant e.sub.33 indicates the higher performance index. On the other hand, the lower numerical value of the elastic constant C.sub.33 indicates the higher performance index.

TABLE-US-00002 TABLE 2 Piezoelectric Lattice Lattice Stress Elastic Dielectric Constant c Constant a Constant Constant Constant Chemical Formula (Å) (Å) c/a e.sub.33 (C/m.sup.2) C.sub.33 (GPa) ∈.sub.33 (×10.sup.−11 F/m) AlN 5.02 3.13 1.60 1.46 357.71 8.65 Sc.sub.0.125Al.sub.0.875N 5.05 3.18 1.59 1.67 291.87 9.51 Mg.sub.0.0625Cr.sub.0.0625Al.sub.0.875N 5.02 3.15 1.59 1.65 308.52 10.13 Mg.sub.0.0625Mn.sub.0.0625Al.sub.0.875N 5.01 3.15 1.59 1.73 304.12 10.53 Mg.sub.0.0625Fe.sub.0.0625Al.sub.0.875N 5.01 3.16 1.59 1.82 253.29 34.10 Mg.sub.0.0625Co.sub.0.0625Al.sub.0.875N 5.01 3.15 1.59 1.68 306.31 11.77 Mg.sub.0.0625Ni.sub.0.0625Al.sub.0.875N 5.01 3.16 1.59 1.82 287.56 24.30 Mg.sub.0.0625Cu.sub.0.0625Al.sub.0.875N 5.03 3.16 1.59 1.25 163.12 61.95 Mg.sub.0.0625Mo.sub.0.0625Al.sub.0.875N 5.03 3.17 1.59 1.82 287.61 10.81 Mg.sub.0.0625Tc.sub.0.0625Al.sub.0.875N 5.03 3.16 1.59 1.94 284.36 10.86 Mg.sub.0.0625Ru.sub.0.0625Al.sub.0.875N 5.03 3.16 1.59 1.97 289.28 10.80 Mg.sub.0.0625Rh.sub.0.0625Al.sub.0.875N 5.02 3.17 1.59 2.02 284.73 11.11 Mg.sub.0.0625Pd.sub.0.0625Al.sub.0.875N 5.02 3.17 1.58 2.07 269.73 13.44 Mg.sub.0.0625Ag.sub.0.0625Al.sub.0.875N 5.06 3.17 1.60 1.86 259.65 41.18 Mg.sub.0.0625W.sub.0.0625Al.sub.0.875N 5.02 3.17 1.58 1.74 289.11 10.77 Mg.sub.0.0625Re.sub.0.0625Al.sub.0.875N 5.02 3.17 1.58 1.87 282.77 10.75 Mg.sub.0.0625Os.sub.0.0625Al.sub.0.875N 5.02 3.17 1.58 1.95 283.77 10.67 Mg.sub.0.0625Al.sub.0.0625Al.sub.0.875N 5.01 3.17 1.58 2.14 276.10 10.96 Mg.sub.0.0625Pt.sub.0.0625Al.sub.0.875N 5.01 3.18 1.58 2.27 262.96 12.23 Mg.sub.0.0625Au.sub.0.0625Al.sub.0.875N 5.06 3.18 1.59 2.54 251.22 24.82

[0056] Further, FIG. 3 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the lattice constant ratio c/a. FIG. 4 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the piezoelectric stress constant e.sub.33. FIG. 5 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the elastic constant C.sub.33.

[0057] On the other hand, the following relational expression of mathematical formula 2 holds between the piezoelectric stress constant e.sub.33, the elastic constant C.sub.33, and the dielectric constant ε.sub.33 in the c-axis direction, and the electromechanical coupling constant k.sup.2. Further, each of the following relational expressions of mathematical formula 3 holds between the piezoelectric charge constant d.sub.33, the piezoelectric stress constant e.sub.33, and the elastic constant C.sub.33. Thus, when the piezoelectric charge constant e.sub.33, the elastic constant C.sub.33, the dielectric constant ε.sub.33, and the like of the non-doped AlN, the AlN doped with only Sc, and the doped AlN calculated as above are each substituted in these relational expressions, it becomes possible to calculate each of the electromechanical coupling constant k.sup.2, the piezoelectric charge constant d.sub.33, and the piezoelectric voltage constant g.sub.33 of the non-doped AlN, the AlN doped with only Sc, and the doped AlN. Note that the elastic constants C.sub.11, C.sub.12, and C.sub.13, and the piezoelectric stress constant e.sub.31 can be calculated in the same manner as the piezoelectric stress constant e.sub.33 and the elastic constant C.sub.33.

[00002]$\begin{array}{cc}{k}^2=\frac{e_{33}^2}{{\mathrm{.Math.}}_{33}\times c_{33}}& \left[\mathrm{Mathematical}\mathrm{formula}2\right]\\ d_{33}=\frac{e_{33}\left(C_{11}+C_{12}\right)-2e_{31}{C}_{13}}{\left(C_{11}+C_{12}\right)C_{33}-2C_{13}^2}{g}_{33}=\frac{d_{33}}{{\mathrm{.Math.}}_{33}}& \left[\mathrm{Mathematical}\mathrm{formula}3\right]\end{array}$

[0058] Next, Table 3 shows the mixing enthalpy, the electromechanical coupling constant k.sup.2, the piezoelectric charge constant d.sub.33, and the piezoelectric voltage constant g.sub.33 of the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN thus obtained. Note that the higher numerical values of the electromechanical coupling value k.sup.2, the piezoelectric charge constant d.sub.33, and the piezoelectric voltage constant g.sub.33 indicate the higher performance indexes.

TABLE-US-00003 TABLE 3 Electro- Piezo- mech- Piezo- electric Mixing anical electric Voltage Enthal- Coupling Charge Constant py (eV/ Constant Constant g.sub.33 Chemical Formula atom) k.sup.2 (%) d.sub.33 (pC/N) (m.sup.2/C) AlN 6.90 5.28 0.061 Sc.sub.0.125Al.sub.0.875N 0.0595 10.08 8.32 0.087 Mg.sub.0.0625Cr.sub.0.0625Al.sub.0.875N −0.0034 8.71 7.18 0.071 Mg.sub.0.0625Mn.sub.0.0625Al.sub.0.875N 0.0110 9.33 7.69 0.073 Mg.sub.0.0625Fe.sub.0.0525Al.sub.0.875N 0.0323 3.83 9.78 0.029 Mg.sub.0.0625Co.sub.0.0625Al.sub.0.875N 0.0503 7.78 7.30 0.062 Mg.sub.0.0625Ni.sub.0.0625Al.sub.0.875N 0.0507 4.76 8.75 0.036 Mg.sub.0.0625Cu.sub.0.0625Al.sub.0.875N 0.0437 1.55 7.63 0.012 Mg.sub.0.0625Mo.sub.0.0625Al.sub.0.875N 0.0352 10.62 8.59 0.079 Mg.sub.0.0625Tc.sub.0.0625Al.sub.0.875N 0.0387 12.23 9.23 0.085 Mg.sub.0.0625Ru.sub.0.0625Al.sub.0.875N 0.0457 12.42 9.19 0.085 Mg.sub.0.0625Rh.sub.0.0625Al.sub.0.875N 0.0519 12.90 9.65 0.087 Mg.sub.0.0625Pd.sub.0.0625Al.sub.0.875N 0.0498 11.81 10.95 0.082 Mg.sub.0.0625Ag.sub.0.0625Al.sub.0.875N 0.0471 3.24 11.23 0.027 Mg.sub.0.0625W.sub.0.0625Al.sub.0.875N 0.0451 9.70 8.51 0.079 Mg.sub.0.0625Re.sub.0.0625Al.sub.0.875N 0.0652 11.54 9.12 0.085 Mg.sub.0.0625Os.sub.0.0625Al.sub.0.875N 0.0451 12.59 8.98 0.084 Mg.sub.0.0625Al.sub.0.0625Al.sub.0.875N 0.0504 15.15 10.42 0.095 Mg.sub.0.0625Pt.sub.0.0625Al.sub.0.875N 0.0489 16.08 12.63 0.103 Mg.sub.0.0625Au.sub.0.0625Al.sub.0.875N 0.0485 10.39 17.11 0.069

[0059] Further, FIG. 6 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the mixing enthalpy. FIG. 7 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the electromechanical coupling value k.sup.2. FIG. 8 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the piezoelectric charge constant d.sub.33. FIG. 9 is a graph showing the relation between the non-doped AlN, the AlN doped with only Sc, and each kind of doped AlN, and the piezoelectric voltage constant g.sub.33.

[0060] Further, the piezoelectric charge constant d.sub.33, the piezoelectric stress constant e.sub.33, and the elastic constant C.sub.33 of the doped AlN different from those described in Table 3 were calculated using the same method as described above. The results are shown in Table 4.

TABLE-US-00004 TABLE 4 Piezoelectric Piezoelectric Charge Stress Elastic Constant Constant Constant Chemical Formula (pC/N) e.sub.33 (C/m.sup.2) C.sub.33 (GPa) Mg.sub.0.1875Cr.sub.0.1875Al.sub.0.625N 12.16 2.11 257.71 Mg.sub.0.25Cr.sub.0.25Al.sub.0.5N 7.81 2.17 303.66 Mg.sub.0.1875Mn.sub.0.1875Al.sub.0.625N 65.06 4.30 222.13 Mg.sub.0.25Mn.sub.0.25Al.sub.0.5N 6.67 1.09 304.58 Mg.sub.0.1875Fe.sub.0.1875Al.sub.0.625N 8.61 1.63 165.46 Mg.sub.0.25Fe.sub.0.25Al.sub.0.5N 11.34 0.64 135.08 Mg.sub.0.1875Mo.sub.0.1875Al.sub.0.625N 23.07 2.85 218.61 Mg.sub.0.25Mo.sub.0.25Al.sub.0.5N 28.92 2.51 189.92 Mg.sub.0.325Mo.sub.0.325Al.sub.0.35N 8.13 0.95 272.49 Mg.sub.0.25Tc.sub.0.25Al.sub.0.5N 63.01 4.65 186.41 Mg.sub.0.325Tc.sub.0.325Al.sub.0.35N 39.66 2.75 153.82 Mg.sub.0.1875Ru.sub.0.1875Al.sub.0.625N 21.55 4.30 244.65 Mg.sub.0.25Ru.sub.0.25Al.sub.0.5N 13.09 0.93 228.20 Mg.sub.0.325Ru.sub.0.325Al.sub.0.35N 6.79 1.00 192.05 Mg.sub.0.1875Rh.sub.0.1875Al.sub.0.625N 11.18 1.32 226.19 Mg.sub.0.25Rh.sub.0.25Al.sub.0.5N 42.19 2.86 152.70 Mg.sub.0.325Rh.sub.0.325Al.sub.0.35N 41.75 2.91 152.62 Mg.sub.0.1875Pd.sub.0.1875Al.sub.0.625N 31.92 3.37 198.10 Mg.sub.0.25Pd.sub.0.25Al.sub.0.5N 57.69 5.28 161.45 Mg.sub.0.325Pd.sub.0.325Al.sub.0.35N 47.32 4.13 157.13 Mg.sub.0.1875Ag.sub.0.1875Al.sub.0.625N 52.73 3.26 173.04 Mg.sub.0.25Ag.sub.0.25Al.sub.0.5N 40.89 2.08 163.33 Mg.sub.0.1875W.sub.0.1875Al.sub.0.625N 25.38 3.00 210.48 Mg.sub.0.25W.sub.0.25Al.sub.0.5N 53.29 3.71 159.79 Mg.sub.0.325W.sub.0.325Al.sub.0.35N 9.75 1.55 299.10 Mg.sub.0.1875Re.sub.0.1875Al.sub.0.625N 11.89 1.80 244.66 Mg.sub.0.25Re.sub.0.25Al.sub.0.5N 13.49 1.20 190.94 Mg.sub.0.325Re.sub.0.325Al.sub.0.35N 13.54 0.49 175.59 Mg.sub.0.1875Os.sub.0.1875Al.sub.0.625N 13.20 2.01 244.86 Mg.sub.0.25Os.sub.0.25Al.sub.0.5N 14.14 1.86 245.42 Mg.sub.0.325Os.sub.0.325Al.sub.0.35N 9.82 0.42 212.68 Mg.sub.0.1875Ir.sub.0.1875Al.sub.0.625N 12.34 1.99 255.46 Mg.sub.0.325Ir.sub.0.325Al.sub.0.35N 41.44 3.09 166.23 Mg.sub.0.1875Pt.sub.0.1875Al.sub.0.525N 5.67 1.37 255.46 Mg.sub.0.25Pt.sub.0.25Al.sub.0.5N 14.78 2.09 227.20 Mg.sub.0.325Pt.sub.0.325Al.sub.0.35N 31.34 2.65 186.51 Mg.sub.0.1875Au.sub.0.1875Al.sub.0.825N 23.14 2.16 183.97 Mg.sub.0.25Au.sub.0.25Al.sub.0.5N 24.64 2.64 195.68 Mg.sub.0.325Au.sub.0.325Al.sub.0.35N 47.80 2.43 140.67

[0061] These results demonstrated that the AlN doped with Mg and any one of Cr, Mn, Fe, Co, Ni, Mo, Tc, Ru, Rh, Pd, Ag, W, Re, Os, Ir, Pt, and Au together showed a value indicating the higher performance index (at least any one of d.sub.33, e.sub.33, C.sub.33, g.sub.33, and k.sup.2) than the AlN not doped with any atom.

[0062] Furthermore, these piezoelectric bodies exhibiting the high performance index have low losses and can be operated in a wide band. Thus, using these piezoelectric bodies makes it possible to provide a MEMS device which can further contribute to the operation at high frequencies and the reduction in size and power consumption of portable devices.

[0063] Note that the present embodiment has been described using an example in which the piezoelectric body represented by the chemical formula Al.sub.1-X-YMg.sub.XM.sub.YN has a value of X as 0.0625 and Y as 0.0625. However, the present invention is not limited thereto, and it only requires that X+Y is less than 1, X is in a range of more than 0 and less than 1, and Y is in a range of more than 0 and less than 1.

[0064] Further, it is preferable that, regarding these variables X and Y, X+Y is 0.65 or less, X is in a range of more than 0 and less than 0.65, and Y is in a range of more than 0 and less than 0.65. Having the variables within these ranges allows the piezoelectric body to be reliably produced. For example, as shown in FIG. 10, in the piezoelectric body doped with Cr as the substituent element M (Mg and Cr are doped at the same concentration (mol %)), the higher concentration X+Y causes a further reduction in the mixing enthalpy. On the other hand, in the piezoelectric body doped with Sc, the higher concentration X causes a further increase in the mixing enthalpy. This shows that the piezoelectric body doped with Mg and Cr together can be more easily produced than the piezoelectric body doped with Sc at the same concentration.

[0065] Next, FIG. 11 shows the relation between the concentration X+Y (Mg and Cr are doped at the same concentration (mol %)) and the lattice constant ratio c/a of the piezoelectric body. As is evident from this drawing, it is shown that, in the piezoelectric body doped with Mg and Cr together, as is the case with the piezoelectric body doped with Sc, the higher value of X+Y (X in the case of Sc) causes a further reduction in the lattice constant ratio c/a.

[0066] Further, FIG. 12 shows the relation between the concentration X+Y (Mg and Cr are doped at the same concentration (mol %)) and the piezoelectric stress constant e.sub.33 of the piezoelectric body. As is evident from this drawing, it is shown that, in the piezoelectric body doped with Mg and Cr together, the higher value of X+Y causes a further increase in the piezoelectric stress constant e.sub.33.

[0067] Further, it is more preferable that, regarding these variables X and Y, X+Y is 0.375 or less, X is in a range of more than 0 and 0.1875 or less, and Y is in a range of more than 0 and 0.1875 or less.

[0068] Further, it is particularly preferable that, regarding these variables X and Y, X+Y is 0.125 or less, X is in a range of more than 0 and 0.0625 or less, and Y is in a range of more than 0 and 0.0625 or less.