Transducer and acoustic transducer

Abstract

To suppress a bending mode of a vibration film 1 in a width direction (Y direction) in relative to bending modes M1, M2 and M3 in a length direction (X direction).SOLUTION: A transducer 100 comprises: a vibration film 1 which consists of single crystal silicon and of which at least one end portion 1a in the length direction (X direction) is a fixed end; a film support part 2 to which the fixed end 1a of the vibration film 1 is coupled; and a piezoelectric element 3 which is disposed on a principal surface 1A of the vibration film 1. The principal surface 1A and the length direction (X direction) are a {011} plane and a <100> direction of the single crystal silicon or a crystal plane obtained by rotating the {011} plane around any axis in the {011} plane within the range of -20° or more to 20°or less and a crystal azimuth corresponding to the <100> direction before the rotation.SELECTED DRAWING: Figure 1B

Description

Technical Field

[0001] The present disclosure relates to a transducer and an acoustic transducer.

Background Art

[0002] Patent Document 1 discloses a MEMS (Micro Electro Mechanical System) including a displaceable membrane portion, and a transducer that controls or detects the displacement of the membrane portion using a piezoelectric element.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

[0004] [Summary] All structures including a transducer have a resonance mode that increases the vibration of the structure at a specific frequency. During resonance, the vibrating membrane is greatly displaced and a large stress is applied to the vibrating membrane, so there is a risk that the transducer may be damaged. In particular, damage to the vibrating membrane due to displacement in the short side direction intersecting the longitudinal direction of the vibrating membrane in plan view often becomes a practical problem.

[0005] An object of the present disclosure is to provide a transducer and an acoustic transducer in which the displacement amount in the short side direction of the vibrating membrane is relatively suppressed with respect to the displacement amount in the longitudinal direction.

[0006] In order to solve the above-described problems, one aspect of the present disclosure is a transducer including a diaphragm made of single crystal silicon, having at least one end in the longitudinal direction being a fixed end, a diaphragm support portion to which the fixed end of the diaphragm is connected, and a piezoelectric element disposed on the main surface of the diaphragm. The main surface and the longitudinal direction of the diaphragm are the {011} plane and the <100> direction of single crystal silicon, or a crystal plane obtained by rotating the {011} plane within a range of -20° or more and 20° or less around an arbitrary axis within the {011} plane, and a crystal orientation corresponding to the <100> direction before rotation.

Brief Description of Drawings

[0007]

Figure 1A

Figure 1B

Figure 2A

Figure 2B

Figure 3

Figure 4

Figure 5

Figure 6A

Figure 6B

Figure 6C

Figure 7

Figure 8A

Figure 8B

Figure 8C

Figure 9

Figure 10

Figure 11

Figure 12

[0008] [Detailed Description] Hereinafter, the transducer and the acoustic transducer according to a plurality of embodiments will be described in detail with reference to the drawings. Note that the embodiments described below show comprehensive or specific examples. The numerical values, shapes, materials, components, installation positions of the components, and connection forms shown in the following embodiments are merely examples and are not intended to limit the present disclosure. In addition, among the components in the following embodiments, the components not described in the independent claims indicating the most general concept are described as optional components. Furthermore, the dimensional ratios in the drawings are exaggerated for convenience of explanation and may differ from the actual ratios. In addition, the following embodiments and their modifications may include similar components. The same reference numerals are assigned to the similar components, and duplicate explanations are omitted.

[0009] FIG. 1A is a plan view showing the configuration of a transducer 100 according to an embodiment. FIG. 1B is a cross-sectional view showing the configuration of the transducer 100 according to an embodiment. The cross-sectional view of FIG. 1B shows the cross-section of the transducer 100 along the cutting plane A-A' of FIG. 1A.

[0010] As shown in FIGS. 1A and 1B, the transducer 100 according to the embodiment includes a diaphragm 1, a diaphragm support portion 2, and a piezoelectric element 3. The diaphragm 1 is a flexible thin film made of single-crystalline silicon. The diaphragm 1 has a cantilever structure. That is, one end 1a in the longitudinal direction (X direction) of the diaphragm 1 is a fixed end, and the other end 1b is a free end. The planar shape of the diaphragm 1 is not particularly limited. For example, as shown in FIG. 1A, it has a rectangular shape. In this case, the fixed end 1a is located on one of the four sides, and the free end 1b is located on the side opposite to this one side.

[0011] The direction from the fixed end 1a to the free end 1b (X direction) is the longitudinal direction of the diaphragm 1. On the main surface 1A of the diaphragm 1, the direction perpendicular to the X direction (Y direction) is the short-side direction of the diaphragm 1. The length of the diaphragm 1 in the X direction and the width of the diaphragm 1 in the Y direction are not particularly limited. For example, in the transducer 100 shown in FIGS. 1A and 1B, the length of the diaphragm 1 is 3 mm, and the width of the diaphragm 1 is 2 mm.

[0012] The film support part 2 (2b) has a cylindrical shape surrounding the periphery of the diaphragm 1 in the plan view shown in Fig. 1A. A slit 5 (gap) is formed between the outer periphery (three sides) of the diaphragm 1 excluding the fixed end 1a (one side) of the diaphragm 1 and the inner periphery of the film support part 2. The diaphragm 1 with the fixed end 1a fixed to the film support part 2 can be freely elastically deformed with respect to the film support part 2 by the slit 5.

[0013] The fixed end 1a of the diaphragm 1 is connected to the film support part 2. As shown in Fig. 1B, the film support part 2 has a laminated structure including an upper layer part 2b arranged at the same position in the Z direction (film thickness direction) as the diaphragm 1 and a lower layer part 2a connected to the upper layer part. The Z direction is the normal direction of the main surface 1A of the diaphragm 1.

[0014] The diaphragm 1 and the film support part 2 can be formed simultaneously from a single silicon substrate. The silicon substrate between the periphery (three sides) of the diaphragm 1 excluding the fixed end 1a and the upper layer part 2b is etched. Thereby, the space between the periphery (three sides) of the diaphragm 1 and the upper layer part 2b is separated, and the slit 5 is formed. Then, by etching the silicon substrate from its lower surface side (lower layer part 2a side), a cavity surrounded by the lower layer part 2a and the diaphragm 1 is formed as shown in Fig. 1B.

[0015] When an SOI substrate is used as the silicon substrate, the Si active layer of the SOI substrate can be used as the diaphragm 1 and the upper layer part 2b, and the Si support substrate of the SOI substrate can be used as the lower layer part 2a.

[0016] The piezoelectric element 3 is arranged over the entire main surface 1A of the diaphragm 1. In practice, the outer shapes of the diaphragm 1 and the piezoelectric element 3 are patterned by different processes. Due to limitations in pattern processing accuracy such as mask alignment accuracy, the maximum outer shape of the piezoelectric element 3 formed on the main surface 1A of the diaphragm 1 is narrower with a certain margin with respect to the outer shape of the diaphragm 1. In Figs. 1A and 1B, a protective film covering the diaphragm 1 and the piezoelectric element 3 is omitted.

[0017] Although illustration is omitted, the transducer 100 may include a silicon (Si) sub-frame for reinforcing the strength of the film support portion 2. The Si sub-frame is connected to the upper end portion of the film support portion 2.

[0018] Although illustration is omitted, the piezoelectric element 3 has a laminated structure of a pair of electrodes and a piezoelectric film sandwiched between the pair of electrodes. Each of the pair of electrodes is formed of a thin film of a metal having conductivity such as aluminum (Al) or copper (Cu), for example. Alternatively, the lower electrode of the pair of electrodes may have a laminated structure in which titanium (Ti) and platinum (Pt) are laminated in this order. The upper electrode of the pair of electrodes may have a laminated structure in which iridium oxide (IrO2) and iridium (Ir) are laminated in this order. The piezoelectric film is composed of, for example, a lead zirconate titanate (PZT) film. In addition to lead zirconate titanate, the piezoelectric film may be made of aluminum nitride (AlN), zinc oxide (ZnO), lead titanate (PbTiO3), potassium sodium niobate (KNN), or the like.

[0019] When an alternating voltage is applied to the pair of electrodes, an electric field is generated between the pair of electrodes. Due to this electric field, the piezoelectric film expands and contracts or expands in a direction parallel to the XY plane, and the free end 1b side of the vibrating membrane 1 is displaced so as to bend in the Z direction or the opposite direction thereof. By repeatedly applying the voltage, the vibrating membrane 1 repeatedly alternates between displacement in the Z direction and displacement in the direction opposite to the Z direction. Due to the vibration of the vibrating membrane 1, the air around the vibrating membrane 1 vibrates, and the vibration of the air is output as an audible sound wave or ultrasonic wave in the audible range. In this way, the transducer 100 functions as a vibration generating device that generates vibration in the vibrating membrane 1 by inputting a voltage signal to the piezoelectric element 3 and deforming the piezoelectric element 3. Further, the transducer 100 functions as an acoustic transducer such as a piezoelectric speaker or a crystal earphone by converting the vibration of the vibrating membrane 1 into an audible sound wave or ultrasonic wave that is the vibration of the air around it. Note that the frequency of the audible sound wave or ultrasonic wave is controlled by the frequency of the alternating voltage.

[0020] Conversely, the piezoelectric film expands and contracts or expands in a direction parallel to the XY plane due to vibrations transmitted from the outside to the diaphragm 1, and the piezoelectric element 3 outputs a voltage signal. In this way, the transducer 100 functions as a vibration sensor that converts vibrations transmitted from the outside to the diaphragm 1 into voltage signals. Furthermore, the transducer 100 functions as an acoustic transducer such as a microphone by converting vibrations of air, which are sound waves or ultrasonic waves in the audible range, into voltage signals through the vibrations of the diaphragm 1.

[0021] Note that the embodiment (FIGS. 1A and 1B) shows the transducer 100 having a cantilever structure or a single-ended beam structure with a fixed end 1a and a free end 1b, but the present disclosure is not limited to the transducer 100 having a cantilever structure or a single-ended beam structure. For example, as shown in FIGS. 2A and 2B, the present disclosure can also be applied to the transducer 101 having a double-ended beam structure in which both longitudinal ends (1a, 1b') are fixed ends. Hereinafter, the description will continue with the transducer 100 as an example.

[0022] The transducer 100 has a plurality of resonance modes in which the maximum displacement amount is maximized at a specific vibration frequency. This plurality of resonance modes includes a plurality of bending modes in which the diaphragm 1 bends in the longitudinal direction (X direction). FIG. 3 is a graph showing the displacement shape of the diaphragm 1 when the transducer 100 resonates in a plurality of bending modes. The horizontal axis represents the coordinate (X coordinate) in the length direction (X direction) of the diaphragm 1, and the vertical axis represents the Z-direction component of the displacement of the diaphragm 1. Hereinafter, the "Z-direction component of the displacement" will be simply referred to as the "displacement amount". In any of the bending modes, the X coordinate of the fixed end 1a of the diaphragm 1 is normalized to 0, and the X coordinate of the free end 1b is normalized to 1. Furthermore, the displacement amount of the free end 1b of the diaphragm 1 is also normalized to 1 or -1.

[0023] FIG. 3 shows, as examples of a plurality of bending modes, a bending first mode M1, a bending second mode M2, and a bending third mode M3. These bending modes are resonance modes characterized by the shape of the displacement in the longitudinal direction (X direction) of the diaphragm 1.

[0024] In the first bending mode M1, no part where the Z-direction component of displacement reaches an extreme value (hereinafter referred to as the "vibration antinode") is formed between the fixed end 1a and the free end 1b. In the second bending mode M2, one vibration antinode M2-1 is formed between the fixed end 1a and the free end 1b. In the third bending mode M3, two vibration antinodes M3-1 and M3-2 are formed between the fixed end 1a and the free end 1b.

[0025] FIG. 4 is a contour diagram showing the displacement shape of the diaphragm 1 when it resonates in the butterfly mode BF as another example of the resonance mode of the transducer 100. The "butterfly mode" is a resonance mode characterized by the shape of the displacement in the short side direction (Y direction) of the diaphragm 1. As shown in FIG. 4, in the butterfly mode BF, for example, at the free end 1b, the diaphragm 1 is bent in the short side direction (Y direction). The central portion 1b-1 of one side of the diaphragm 1 forming the free end 1b is displaced in the +Y direction from the frame 6, and both end portions 1b-2 and 1b-3 of one side of the diaphragm 1 forming the free end 1b are displaced in the -Y direction from the frame 6. Note that the frame 6 indicates the position where the Y coordinate is 0, that is, the XY plane. By the central portion 1b-1 and both end portions 1b-2 and 1b-3 being displaced alternately in the Z direction, the diaphragm 1 resonates in the butterfly mode BF.

[0026] Here, in order to explain the butterfly mode BF, a contour diagram in which the diaphragm 1 is bent only in the short side direction (Y direction) is shown. However, the butterfly mode may occur in combination with the bending modes M1, M2, M3, etc. in the longitudinal direction (X direction) shown in FIG. 3. Also, the position in the short side direction of the diaphragm 1 where the butterfly mode occurs is not limited to the free end 1b. The butterfly mode also occurs at positions in the longitudinal direction (X direction) of the diaphragm 1 other than the free end 1b.

[0027] When the transducer 100 resonates, the diaphragm 1 is greatly displaced and a large stress is applied to the diaphragm 1, so there is a risk that the transducer 100 may be damaged. In particular, when viewed from the normal direction (Z direction) of the XY plane, damage to the diaphragm 1 caused by displacement in the short side direction (Y direction) intersecting the longitudinal direction (X direction) of the diaphragm 1 often becomes a practical problem. Therefore, it is desirable to relatively suppress the displacement amount in the short side direction (Y direction) of the diaphragm 1 with respect to the displacement amount in the longitudinal direction (X direction).

[0028] By the way, single-crystalline silicon used as the material of the diaphragm 1 is known to exhibit different physical properties (for example, elastic constants such as Young's modulus and Poisson's ratio) depending on the plane orientation due to its crystal anisotropy. When obtaining the elastic constant indicating the bending difficulty of the diaphragm 1 having an extent in the two-dimensional direction (XY direction), not only the bending direction (longitudinal direction) but also the elastic constant in the direction perpendicular to the bending direction (short side direction) must be considered.

[0029] Therefore, in order to consider the influence of the direction perpendicular to the bending direction (longitudinal direction), the inventor of the present application uses the "effective Young's modulus" indicating the bending difficulty of the diaphragm 1 considering Poisson's ratio, and sets the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction (X direction) of the diaphragm 1 within an appropriate range, thereby devising to relatively suppress the displacement amount in the short side direction (Y direction) of the diaphragm 1 with respect to the displacement amount in the longitudinal direction (X direction).

[0030] Before explaining the embodiment, a comparative example will be explained. In the comparative example, the (001) plane is used as the crystal plane exposed on the main surface 1A of the diaphragm 1. FIG. 5 shows the unit cell of single-crystalline silicon defined by the a-axis, b-axis, and c-axis that are orthogonal to each other. The unit cell of single-crystalline silicon is a cube, and among the surfaces of the cube, the (001) plane is a plane parallel to the a-axis and the b-axis. The a-axis direction is the

[0100] direction, the b-axis direction is the

[0010] direction, and the c-axis direction is the

[0001] direction.

[0031] FIG. 6A is a graph showing the Young's moduli (Ex, Ey, Ez) in the longitudinal direction (X direction), the short-side direction (Y direction), and the film thickness direction (Z direction) of the diaphragm 1 in the comparative example. The horizontal axis (Angle) indicates the angle in the longitudinal direction (X direction) of the diaphragm 1. Specifically, the horizontal axis sets the <100> direction in FIG. 5 as 0°, and indicates the angle of rotating the longitudinal direction (X direction) of the diaphragm 1 within the (001) plane with the c-axis as the rotation axis. Therefore, when the horizontal axis is 0°, the longitudinal direction (X direction) of the diaphragm 1 is the <100> direction; when the horizontal axis is 45°, the longitudinal direction (X direction) of the diaphragm 1 is the <110> direction; and when the horizontal axis is 90°, the longitudinal direction (X direction) of the diaphragm 1 is the <010> direction.

[0032] In FIG. 6A, the Young's modulus (Ex) in the longitudinal direction (X direction) and the Young's modulus (Ey) in the short-side direction (Y direction) of the diaphragm 1 are consistent within the angular range (0° to 90°) of the longitudinal direction (X direction) of the diaphragm 1. When the horizontal axis is 0° and 90°, that is, the Young's moduli (Ex, Ey) in the <100> direction and the <010> direction are approximately 130 GPa. When the horizontal axis is 45°, the Young's moduli (Ex, Ey) are approximately 169 GPa (maximum value). On the other hand, since the film thickness direction (Z direction) does not change even when rotating around the c-axis, the Young's modulus (Ez) is approximately 130 GPa (constant value).

[0033] FIG. 6B is a graph showing the Poisson's ratios (vyz, vzx, vxy) of the diaphragm 1 in the comparative example. The horizontal axis (Angle) indicates the angle in the longitudinal direction (X direction) of the diaphragm 1. For example, the Poisson's ratio (vxy) indicates the ratio of the lateral strain in the Y direction to the longitudinal strain in the X direction when a load is applied in the longitudinal direction (X direction) of the diaphragm 1. The Poisson's ratio (vxy) is 0.26 in the <100> direction, 0.06 (minimum value) in the <110> direction, and 0.26 in the <010> direction.

[0034] Define equations (1) and (2) as the "effective Young's modulus (E')" indicating the bending resistance of the diaphragm 1 considering the Poisson's ratio (vxy). Specifically, define the "longitudinal effective Young's modulus (Ex')" indicating the bending resistance of the diaphragm 1 in the longitudinal direction (X direction) and the "transverse effective Young's modulus (Ey')" indicating the bending resistance of the diaphragm 1 in the transverse direction (Y direction) by equations (1) and (2), respectively.

[0035]

Number

[0036]

Number

[0037] Figure 6C is a graph showing the ratio (Ey' / Ex') of the transverse effective Young's modulus (Ey') to the longitudinal effective Young's modulus (Ex') according to the comparative example. The horizontal axis (Angle) indicates the angle in the longitudinal direction (X direction) of the diaphragm 1. The effective Young's modulus is a value indicating the bending resistance of the diaphragm 1. Therefore, the larger this ratio (Ey' / Ex'), the more difficult it is for the transverse direction (Y direction) of the diaphragm 1 to bend relative to the longitudinal direction (X direction). That is, the larger this ratio (Ey' / Ex'), the more the displacement in the transverse direction (Y direction) of the diaphragm can be relatively suppressed with respect to the displacement in the longitudinal direction (X direction).

[0038] However, as shown in FIG. 6A, the Young's modulus (Ex) in the longitudinal direction (X direction) and the Young's modulus (Ey) in the short transverse direction (Y direction) of the diaphragm 1 are the same within the angular range (0° to 90°) in the longitudinal direction (X direction) of the diaphragm 1. Therefore, the effective Young's modulus (Ex') in the longitudinal direction and the effective Young's modulus (Ey') in the short transverse direction obtained from equations (1) and (2) are also the same within the angular range (0° to 90°) in the longitudinal direction (X direction) of the diaphragm 1. For this reason, as shown in FIG. 6C, the ratio (Ey' / Ex') is 1 (a constant value) within the angular range (0° to 90°). Therefore, in the comparative example using the (001) plane as the crystal plane exposed on the main surface 1A of the diaphragm 1, even if the plane orientation in the longitudinal direction of the diaphragm 1 is changed, the displacement amount in the short transverse direction (Y direction) of the diaphragm 1 cannot be relatively suppressed with respect to the displacement amount in the longitudinal direction (X direction).

[0039] In the embodiment, as shown in FIG. 7, the (011) plane is used as the crystal plane exposed on the main surface 1A of the diaphragm 1. Similar to FIG. 5, FIG. 7 shows the unit cell of single-crystalline silicon defined by the a-axis, b-axis, and c-axis that are perpendicular to each other. The (011) plane is a crystal plane obtained by cutting the unit cell with a cross-section including two sides that are parallel to the a-axis and intersect the b-axis or c-axis among the 12 sides forming the unit cell. Crystal orientations such as the <100> direction, <11-1> direction, and <01-1> direction exist within the (011) plane.

[0040] FIG. 8A is a graph showing the Young's moduli (Ex, Ey, Ez) in the longitudinal direction (X direction), short transverse direction (Y direction), and film thickness direction (Z direction) of the diaphragm 1 in the embodiment, respectively. The horizontal axis (Angle) represents the angle in the longitudinal direction (X direction) of the diaphragm 1. Specifically, the horizontal axis designates the <100> direction in FIG. 7 as 0°, and represents the angle of rotating the longitudinal direction (X direction) of the diaphragm 1 within the (011) plane. Therefore, when the horizontal axis is 0°, the longitudinal direction (X direction) of the diaphragm 1 is the <100> direction; when the horizontal axis is approximately 53°, the longitudinal direction (X direction) of the diaphragm 1 is the <11-1> direction; and when the horizontal axis is 90°, the longitudinal direction (X direction) of the diaphragm 1 is the <01-1> direction.

[0041] In FIG. 8A, the Young's modulus (Ex) in the longitudinal direction (X direction) and the Young's modulus (Ey) in the transverse direction (Y direction) of the diaphragm 1 do not match within the angular range (0° to 90°) in the longitudinal direction (X direction) of the diaphragm 1.

[0042] When the horizontal axis is 0°, that is, when the longitudinal direction (X direction) of the diaphragm 1 is in the <100> direction, the Young's modulus (Ex) is approximately 130 GPa, and the Young's modulus (Ey) is approximately 169 GPa. When the horizontal axis is approximately 35.3°, that is, when the transverse direction (Y direction) of the diaphragm 1 is in the <21-1> direction, the Young's modulus (Ey) is approximately 183 GPa (maximum value). When the horizontal axis is approximately 54.7°, that is, when the longitudinal direction (X direction) of the diaphragm 1 is in the <11-1> direction, the Young's modulus (Ex) is approximately 183 GPa (maximum value). When the horizontal axis is 90°, that is, when the longitudinal direction (X direction) of the diaphragm 1 is in the <01-1> direction, the Young's modulus (Ex) is approximately 169 GPa, and the Young's modulus (Ey) is approximately 130 GPa.

[0043] Thus, within the range where the horizontal axis is 0° or more and less than 45°, the Young's modulus (Ey) in the transverse direction is greater than the Young's modulus (Ex) in the longitudinal direction. Within the range where the horizontal axis is greater than 45° and 90° or less, the Young's modulus (Ex) in the longitudinal direction is greater than the Young's modulus (Ey) in the transverse direction. It should be noted that when the horizontal axis is 45°, the Young's modulus (Ey) in the transverse direction and the Young's modulus (Ex) in the longitudinal direction match. On the other hand, the Young's modulus (Ez) in the film thickness direction (Z direction) becomes a constant value, approximately 169 GPa, independent of the angle.

[0044] FIG. 8B is a graph showing the Poisson's ratio (vyz, vzx, vxy) of the diaphragm 1 in the embodiment. The horizontal axis (Angle) indicates the angle in the longitudinal direction (X direction) of the diaphragm 1. For example, the Poisson's ratio (vxy) indicates the ratio of the transverse strain in the Y direction to the longitudinal strain in the X direction when a load is applied in the longitudinal direction (X direction) of the diaphragm 1. Compared with the comparative example in FIG. 6B, each Poisson's ratio (vyz, vzx, vxy) in the embodiment of FIG. 8B is different.

[0045] FIG. 8C is a graph showing the ratio (Ey’ / Ex’) of the effective Young's modulus (Ey’) in the short direction to the effective Young's modulus (Ex’) in the longitudinal direction according to the embodiment. The horizontal axis (Angle) represents the angle in the longitudinal direction (X direction) of the diaphragm 1. As described above, the larger this ratio (Ey’ / Ex’), the more difficult it is for the short direction (Y direction) of the diaphragm 1 to bend compared to the longitudinal direction (X direction). That is, the larger this ratio (Ey’ / Ex’), the more the displacement in the short direction (Y direction) of the diaphragm can be relatively suppressed with respect to the displacement in the longitudinal direction (X direction).

[0046] As shown in FIG. 8A, in the embodiment, in the range where the horizontal axis is 0° or more and less than 45°, the Young's modulus (Ey) in the short direction is larger than the Young's modulus (Ex) in the longitudinal direction. In the range where the horizontal axis is 45° or more and 90° or less, the Young's modulus (Ex) in the longitudinal direction is larger than the Young's modulus (Ey) in the short direction. Therefore, as shown in FIG. 8C, the ratio (Ey’ / Ex’) is larger than 1 in the range where the horizontal axis is 0° or more and less than 45°, and smaller than 1 in the range where the horizontal axis is larger than 45° and 90° or less. When the horizontal axis is 45°, the ratio (Ey’ / Ex’) is 1. Also, the ratio (Ey’ / Ex’) monotonically decreases as the horizontal axis increases. The ratio (Ey’ / Ex’) is the largest when the horizontal axis is 0° and the smallest when the horizontal axis is 90°.

[0047] The larger the ratio (Ey’ / Ex’), the more difficult it is for the diaphragm 1 to bend in the short direction (Y direction) with respect to the longitudinal direction (X direction) of the diaphragm 1. In other words, as the diaphragm 1 becomes more difficult to bend in the short direction (Y direction), it becomes easier to bend in the longitudinal direction (X direction). Therefore, the butterfly mode BF shown in FIG. 4 can be suppressed, and the first-order or second-order or higher bending modes M1, M2, M3,... shown in FIG. 3 can be made dominant.

[0048] The inventors of the present application changed the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction (X direction), and calculated the displacement amounts of the diaphragm 1 in the bending first-order mode M1, bending second-order mode M2, bending third-order mode M3, and butterfly mode BF. The calculation results are shown in FIGS. 9 to 12.

[0049] The vertical axes in FIGS. 9 to 12 indicate values obtained by normalizing the maximum displacement amount of the diaphragm 1 when an AC voltage having a frequency at which each resonance mode (M1, M2, M3, BF) occurs in the piezoelectric element 3 is applied, by the maximum displacement amount of the diaphragm 1 when a DC voltage is applied. The vertical axis in FIG. 9 indicates the normalized maximum displacement amount (1st bending / Static) of the first bending mode M1. The vertical axis in FIG. 10 indicates the normalized maximum displacement amount (2nd bending / Static) of the second bending mode M2. The vertical axis in FIG. 11 indicates the normalized maximum displacement amount (3rd bending / Static) of the third bending mode M3. The vertical axis in FIG. 12 indicates the normalized maximum displacement amount (Butterfly / Static) of the butterfly mode BF. On the other hand, the horizontal axes in FIGS. 9 to 12 indicate the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation (Longitudinal direction) in the longitudinal direction (X direction).

[0050] As shown in FIG. 12, on the horizontal axis in the <100> direction of the (011) plane, the maximum displacement amount after normalization of the butterfly mode BF is smaller than that of other crystal orientations and other crystal planes. Not limited to the <100> direction of the (011) plane, there are combinations in which the maximum displacement amount after normalization of the butterfly mode BF becomes smaller for other crystal planes and crystal orientations. Specifically, the crystal plane of the main surface 1A of the diaphragm 1 is a crystal plane obtained by rotating the (011) plane around an arbitrary axis within the (011) plane in the range of -20° or more and 20° or less. And the crystal orientation in the longitudinal direction (X direction) of the diaphragm 1 is the crystal orientation corresponding to the <100> direction before rotation. In this range of crystal plane and crystal orientation, the maximum displacement amount after normalization of the butterfly mode BF could be reduced. As shown in FIG. 12, these combinations of crystal plane and crystal orientation include, for example, the <100> direction of the (012) plane, the <-1 -1 4> direction of the (221) plane, and the <-1 -1 6> direction of the (331) plane. The (012) plane is a plane obtained by rotating the (011) plane by 18.4° around the <100> direction. Also, the (122) plane is a plane obtained by rotating the (011) plane by 19.4° around the <01 -1> direction, and similarly, the (133) plane is a plane obtained by rotating the (011) plane by 13.2° around the <01 -1> direction. In view of the relationship with the (011) plane, here the (221) plane is denoted as the (122) plane and the (331) plane is denoted as the (133) plane. Thus, in suppressing the butterfly mode, the effect is maximized in the (011) plane, and the effect becomes smaller as the amount of rotation from the (011) plane increases.

[0051] As described above, the diaphragm 1 becomes more likely to bend in the longitudinal direction (X direction) by the amount that it becomes less likely to bend in the short direction (Y direction). As a result, as shown in FIG. 11, it was found that the maximum displacement amount after normalization of the bending third mode M3 increases. As shown in FIG. 11, in the <100> direction of the (012) plane, the <1 - 14> direction of the (221) plane, and the <1 - 16> direction of the (331) plane where the maximum displacement amount becomes smaller in FIG. 12, compared with other crystal planes and crystal orientations, the maximum displacement amount after normalization becomes larger. Thus, by setting the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction within a predetermined range, it is possible to reduce the maximum displacement amount after normalization of the butterfly mode BF while increasing the maximum displacement amount after normalization of the bending third mode.

[0052] On the other hand, as shown in FIGS. 9 and 10, the maximum displacement amounts after normalization of the bending first mode M1 and the bending second mode M2 did not show a significant change even when the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction (X direction) changed.

[0053] As shown in FIG. 8C, the ratio (Ey’ / Ex’) of the effective Young's modulus in the short direction (Ey’) to the effective Young's modulus in the longitudinal direction (Ex’) takes the maximum value in the <100> direction of the (011) plane. However, even in the surrounding crystal planes and crystal orientations, the bending mode in the short direction of the diaphragm 1 can be relatively suppressed with respect to the longitudinal direction. Specifically, the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction (X direction) may be a crystal plane obtained by rotating the (011) plane within a range of -20° or more and 20° or less around an arbitrary axis within the (011) plane, and a crystal orientation corresponding to the <100> direction before rotation.

[0054] By narrowing the range of the rotation angle of the crystal plane centered on the (011) plane, the suppression effect of the bending mode in the short side direction of the diaphragm 1 is further enhanced. For example, the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction (X direction) may be the crystal plane obtained by rotating the (011) plane around an arbitrary axis within the (011) plane in the range of -10° or more and 10° or less, and the crystal orientation corresponding to the <100> direction before rotation. Further, in order to enhance the suppression effect, the crystal plane of the main surface 1A of the diaphragm 1 and the crystal orientation in the longitudinal direction (X direction) may be set to the crystal plane obtained by rotating the (011) plane around an arbitrary axis within the (011) plane in the range of -5° or more and 5° or less, and the crystal orientation corresponding to the <100> direction before rotation.

[0055] Furthermore, not only the rotation angle of the crystal plane centered on the (011) plane, but also an angular range centered on the <100> direction may be provided for the longitudinal direction (X direction) of the diaphragm 1. For example, the angular range in the longitudinal direction of the diaphragm 1 may be set so that the ratio (Ey’ / Ex’) shown in FIG. 8C is greater than 1.

[0056] Although the present disclosure has been described by taking the (011) plane of single crystal silicon as an example, it is applicable to the {011} plane of single crystal silicon including other crystal planes equivalent to the (011) plane.

[0057] As described above in detail about the present disclosure, it is obvious to those skilled in the art that the present disclosure is not limited to the embodiments described in the present disclosure. One or more elements of one embodiment can be combined with one or more elements of another embodiment. The present disclosure can be implemented as modified and changed modes without departing from the spirit and scope of the present disclosure defined by the description of the claims. Therefore, the description of the present disclosure is for the purpose of exemplification and has no restrictive meaning for the present disclosure.

[0058] <Appendix 1> The transducers 100 and 101 according to Supplementary Note 1 are made of single-crystalline silicon, and include a diaphragm 1 made of single-crystalline silicon with at least one end 1a, 1b' in the longitudinal direction (X direction) being a fixed end, a film support portion 2 to which the fixed ends 1a, 1b' of the diaphragm 1 are connected, and a piezoelectric element 3 disposed on the main surface 1A of the diaphragm 1. The main surface 1A and the longitudinal direction (X direction) are the {011} plane and the <100> direction of single-crystalline silicon, or a crystal plane obtained by rotating the {011} plane within a range of -20° or more and 20° or less around an arbitrary axis in the {011} plane, and a crystal orientation corresponding to the <100> direction before rotation. Thereby, the effective Young's modulus (Ey') in the short-side direction (Y direction) intersecting the longitudinal direction of the diaphragm 1 can be made larger than the effective Young's modulus (Ex') in the longitudinal direction. Therefore, the bending mode BF in the short-side direction (Y direction) of the diaphragm 1 can be relatively suppressed with respect to the bending modes M1, M2, M3,... in the longitudinal direction (X direction).

[0059] <Supplementary Note 2> In the transducers 100 and 101 described in Supplementary Note 1, the main surface 1A and the longitudinal direction of the diaphragm 1 may be the {011} plane and the <100> direction of single-crystalline silicon, or a crystal plane obtained by rotating the {011} plane within a range of -10° or more and 10° or less around an arbitrary axis in the {011} plane, and a crystal orientation corresponding to the <100> direction before rotation. The bending mode BF in the short-side direction (Y direction) can be relatively further suppressed.

[0060] <Supplementary Note 3> In the transducers 100 and 101 described in Supplementary Note 1, the main surface 1A and the longitudinal direction of the diaphragm 1 may be the {011} plane and the <100> direction of single-crystalline silicon, or a crystal plane obtained by rotating the {011} plane within a range of -5° or more and 5° or less around an arbitrary axis in the {011} plane, and a crystal orientation corresponding to the <100> direction before rotation. The bending mode BF in the short-side direction (Y direction) can be relatively further suppressed.

[0061] <Supplementary Note 4> In the transducer 100 according to any one of Supplementary Notes 1 to 3, the other end 1b in the longitudinal direction (X direction) may be a free end. In the transducer 100 having a cantilever beam structure, the bending mode BF in the short-side direction (Y direction) can be relatively suppressed.

[0062] <Supplementary Note 5> In the transducer 101 according to any one of Supplementary Notes 1 to 3, both ends 1a and 1b' in the longitudinal direction (X direction) may be fixed ends. In the transducer 101 having a simply supported beam structure, the bending mode BF in the short-side direction (Y direction) can be relatively suppressed.

[0063] <Supplementary Note 6> The transducers 100 and 101 according to any one of Supplementary Notes 1 to 5 may be configured by a microelectromechanical system (MEMS).

[0064] <Supplementary Note 7> The transducers 100 and 101 according to any one of Supplementary Notes 1 to 6 may convert the pressure applied to the piezoelectric element 3 by the vibration transmitted to the diaphragm 1 into a voltage signal. It can function as a vibration sensor using the piezoelectric effect.

[0065] <Supplementary Note 8> The transducers 100 and 101 according to any one of Supplementary Notes 1 to 6 may generate vibration in the diaphragm 1 by inputting a voltage signal to the piezoelectric element 3 and deforming the piezoelectric element 3. It can function as a piezoelectric speaker or a crystal earphone using the inverse piezoelectric effect.

[0066] <Supplementary Note 9> The transducers 100 and 101 according to Supplementary Note 7 may convert audible sound waves or ultrasonic waves into vibrations of the diaphragm 1. It can function as an acoustic transducer such as a microphone.

[0067] <Supplementary Note 10> The transducers 100 and 101 described in Supplementary Note 8 may convert the vibration of the diaphragm 1 into audible sound waves or ultrasonic waves. It can function as an acoustic transducer such as a piezoelectric speaker or a crystal earphone.

Explanation of Signs

[0068] 1 Diaphragm 1A Main surface 1a, 1b’ Fixed ends 1b Free end 2 Diaphragm support part 2a Lower layer part 2b Upper layer part 3 Piezoelectric element 5 Slit 100, 101 Transducers Ex, Ey Young's modulus Ex’, Ey’ Effective Young's modulus

Claims

1. A vibration membrane made of single crystal silicon, at least one end in a longitudinal direction of which is a fixed end; a membrane support part to which the fixed end of the vibration membrane is connected; A piezoelectric element is disposed on a main surface of the vibration membrane, a transducer, wherein the main surface and the longitudinal direction are a {011} plane and a <100> direction of the single crystal silicon, or a crystal plane obtained by rotating the {011} plane around an arbitrary axis within the {011} plane within a range of -20° to 20°, and a crystal orientation corresponding to the <100> direction before rotation.

2. 2. The transducer of claim 1, wherein the main surface and the longitudinal direction are a {011} plane and a <100> direction of the single crystal silicon, or a crystal plane obtained by rotating the {011} plane around an arbitrary axis in the {011} plane within a range of -10° to 10°, and a crystal orientation corresponding to the <100> direction before rotation.

3. 2. The transducer of claim 1, wherein the main surface and the longitudinal direction are a {011} plane and a <100> direction of the single crystal silicon, or a crystal plane obtained by rotating the {011} plane around an arbitrary axis in the {011} plane within a range of -5° to 5°, and a crystal orientation corresponding to the <100> direction before rotation.

4. 2. The transducer of claim 1, wherein the other end in the longitudinal direction is a free end.

5. The transducer of claim 1 , wherein both ends in the longitudinal direction are fixed ends.

6. The transducer of claim 1 , wherein the transducer is constructed from a microelectromechanical system.

7. 2. The transducer according to claim 1, wherein a pressure applied to said piezoelectric element by vibration transmitted to said vibration membrane is converted into a voltage signal.

8. 2. The transducer according to claim 1, wherein a voltage signal is input to said piezoelectric element to deform said piezoelectric element, thereby generating vibration in said vibration membrane.

9. 8. An acoustic transducer according to claim 7, which converts audible sound waves or ultrasonic waves into vibrations of the vibrating membrane.

10. 9. An acoustic transducer according to claim 8, which converts vibration of the vibrating membrane into sound waves or ultrasonic waves in the audible range.

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