Patent Description:
Vibration-driven energy-harvesting devices produced by processing silicon substrates with micro electro-mechanical system (MEMS) process techniques have been known. A vibration-driven energy-harvesting device has a structure in which teeth provided in a movable electrode supported by elastic supporting portions are disposed to be insertable into and retractable from gaps between teeth provided in fixed electrodes. An external impact applied to the vibration-driven energy-harvesting device causes the elastically supported movable electrode to vibrate with respect to the fixed electrodes. The teeth of the movable electrode are accordingly inserted into and retracted from the gaps between the teeth of the fixed electrodes, resulting in electric power generation.

In each fixed electrode, which is a fixed portion, an elastic regulating member provided in the fixed electrode receives acceleration generated by external vibrations in the movable electrode, which is a movable portion, thereby regulating the vibration range of the movable electrode. The elastic regulating member in the fixed electrode therefore requires rigidity capable of tolerating acceleration forces of the movable electrode. Unfortunately, in conventional MEMS elements, increasing the spring constant of the elastic regulating member makes the elastic regulating member prone to damages from stress concentrated in basal regions of an elastic portion of the elastic regulating member. This prevents increasing the amount of power generatable.

An exemplary structure of the fixed electrode having the elastic regulating member includes a slit provided in an inner region of a side portion of the fixed electrode so that the side portion of the fixed electrode serves as the elastic regulating member (e.g., see <FIG> in Patent Literature <NUM> = <CIT>).

<CIT> discloses a MEMS device where the elastic regulating member is a clamped beam with a centrally located rectilinear stopping block which contacts the MEMS moving part to reduce its motion and prevent the moving part form crashing into the fixed walls of the MEMS component. <CIT> discloses a similar MEMS device where the elastic regulating member comprises a beam fixed at either end but with a curved protrusion which makes contact with the moving part while the beam bends to decelerate the moving part. The protrusion is placed asymmetrically on the beam. "<NPL>discloses a MEMS energy harvester with fixed and moving electrodes having an interdigitated comb structure.

<FIG> in Patent Literature <NUM> shows a structure of a fixed portion in which, along a side surface with which a movable electrode collides, a slit is provided in an inner region of the side surface. This structure, however, is limited by the inability to receive strong forces of vibrations of the movable portion.

The problem is solved by a MEMS element according to claim <NUM>. Further improvements are given in the dependent claims.

The present invention can provide a MEMS element and a vibration-driven energy-harvesting device that employ a structure for restricting the amount of movement of a movable portion, and that are resistant to damages from strong external forces.

Embodiments of the present invention will be described below with reference to the following figures with the exception of <FIG>.

<FIG> is a plan view illustrating a vibration-driven energy-harvesting device <NUM>, viewed through a upper cover <NUM> assumed to be transparent, in which a MEMS element <NUM> is enclosed in a vacuum package. <FIG> is a cross-sectional view taken along a line IB - IB in <FIG>.

A case <NUM> and the upper cover <NUM> form the vacuum package, which houses the MEMS element <NUM>. For clear illustration of the planar structure of the MEMS element <NUM>, the plan view in <FIG> does not show the upper cover <NUM> provided on the upper side (the positive z-axis direction side).

Note that the x-axis direction, y-axis direction, and z-axis direction in this embodiment are supposed to be the respective directions shown in each figure.

The MEMS element <NUM> includes four fixed electrode portions <NUM>, a movable electrode portion (movable portion) <NUM>, and elastic supporting portions <NUM> elastically supporting the movable electrode portion <NUM>. A base <NUM> of the MEMS element is fixed to the case <NUM> by die bonding. The case <NUM> is formed of, for example, an electric insulation material (e.g., ceramic). The upper cover <NUM> is seam welded to the upper end of the case <NUM> to vacuum seal the case <NUM>.

The MEMS element <NUM> includes the base <NUM> made of Si, a device layer <NUM> made of a Si active layer, and a bonding layer <NUM> made of an inorganic insulation material such as SiO<NUM> and bonding the base <NUM> and the device layer <NUM>. The MEMS element <NUM> is thus configured as a three-layer structure in which the base <NUM>, the bonding layer <NUM>, and the device layer <NUM> made of a Si active layer are stacked in the z-axis direction, as illustrated in <FIG>. The MEMS element <NUM> having such a configuration is typically produced from a silicon on insulator (SOI) substrate by a general MEMS process technique.

The device layer <NUM> includes the four fixed electrode portions <NUM>, the movable electrode portion <NUM>, and a fixed-electrode outer periphery portion <NUM>. The fixed electrode portions <NUM> each include multiple fixed teeth <NUM>, a fixed-tooth connecting portion <NUM> connecting the fixed teeth <NUM>, and a lead portion <NUM>. The fixed teeth <NUM> extend in the x-axis direction and are arranged in the y-axis direction at predetermined intervals. The fixed-tooth connecting portion <NUM> extends in the y-axis direction and connects the fixed teeth <NUM> arranged in the y-axis direction. The lead portion <NUM> extends in a direction perpendicular to the fixed-tooth connecting portion <NUM>, that is, in the x-axis direction. The lead portion <NUM> has a rectangular terminal portion formed in a tip portion of the lead portion <NUM>. On the upper surface of the terminal portion, a conductive metal such as aluminum is provided to form an electrode pad <NUM>.

Although not shown, a gap is provided between the fixed-electrode outer periphery portion <NUM> and the lead portion <NUM> and fixed-tooth connecting portion <NUM> of each fixed electrode portion <NUM>, thereby physically separating the fixed-electrode outer periphery portion <NUM> from the lead portion <NUM> and fixed-tooth connecting portion <NUM> of each fixed electrode portion <NUM>. This provides electric insulation between the fixed-electrode outer periphery portion <NUM> and each fixed electrode portion <NUM>. The lead portion <NUM> and fixed-tooth connecting portion <NUM> of each fixed electrode portion <NUM> are supported by the base <NUM> with the bonding layer <NUM> therebetween. The fixed teeth <NUM> of each fixed electrode portion <NUM> extend in a region corresponding to a rectangular opening 7a provided in the base <NUM> (see <FIG> and <FIG>).

The movable electrode portion <NUM> includes multiple movable teeth <NUM>, a center band portion <NUM> (see <FIG>), and movable-tooth connecting portions <NUM> connecting the movable teeth <NUM>. The movable-tooth connecting portions <NUM> extend in the positive and negative y-axis directions, respectively, from the center in the x-axis direction of the center band portion <NUM>. The movable teeth <NUM> extend in the positive or negative x-axis directions from the movable-tooth connecting portions <NUM> extending in the positive and negative y-axis directions, and are arranged in the y-axis direction at predetermined intervals.

Weights 105a and 105b are fixed, by means such as bonding, to the upper and bottom surfaces of the center band portion <NUM> of the movable electrode portion <NUM>, which are surfaces on the positive and negative z-axis direction sides of the center band portion <NUM>, respectively. The positions of the gravity centers of the weights 105a and 105b are coaxial with a z-axis that passes through the center in the x-axis and y-axis directions of the center band portion <NUM>.

Two of the fixed electrode portions <NUM> on the positive y-axis direction side of the center band portion <NUM> are disposed in line symmetry with respect to the center line to the x-axis direction of the center band portion <NUM>. The other two of the fixed electrode portions <NUM> on the negative y-axis direction side of the center band portion <NUM> are disposed in line symmetry with respect to the center line to the x-axis direction of the center band portion <NUM>.

The fixed teeth <NUM> extending in the x-axis direction from the fixed-tooth connecting portions <NUM> and the movable teeth <NUM> extending in the x-axis direction from the movable-tooth connecting portions <NUM> are disposed such that the fixed teeth <NUM> and the movable teeth <NUM> mesh with each other, with gaps interposed therebetween in the y-axis direction.

The movable electrode portion <NUM> is mechanically and electrically connected, via the elastic supporting portions <NUM>, to fixed portions <NUM> fixed to the base <NUM> via the bonding layer <NUM>. The fixed portions <NUM> are provided respectively on the positive and negative x-axis direction sides of the center band portion <NUM>, that is, in a pair. The pair of fixed portions <NUM> are formed into the same shape and disposed in line symmetry with respect to the central axis to the x-axis direction of the center band portion <NUM>. The center line to the y-axis direction of each fixed portion <NUM> is coaxial with the center line to the y-axis direction of the center band portion <NUM>.

The movable electrode portion <NUM> supported by the elastic supporting portions <NUM> is vibrated in the x-axis direction by external vibration, and one side surface 121a (see <FIG>) of the center band portion <NUM> of the movable electrode portion <NUM> collides with one of the fixed portions <NUM>. At this point, if the position in the y-axis direction of the contact portion of the fixed portion <NUM> with which the movable portion collides deviates in the y-axis direction from the central axis passing through the gravity center of the center band portion <NUM> including the weights 105a and 105b, a moment occurs in the center band portion <NUM> of the movable electrode portion <NUM>. The moment occurring in the center band portion <NUM> of the movable electrode portion <NUM> deforms the elastic supporting portions <NUM>, preventing the center band portion <NUM> to vibrate normally. It is therefore necessary for the center line to the y-axis direction of the contact portion of the fixed portion <NUM> with which the center band portion <NUM> of the movable electrode portion <NUM> collides to be coaxial with the center line of the center band portion <NUM> of the movable electrode portion <NUM> extending in the x-axis direction.

An electrode pad <NUM> is connected to each fixed portion <NUM>. Each fixed portion <NUM> has a rectangular terminal portion formed integrally with the fixed portion <NUM>. On the upper surface of the terminal portion, a conductive metal such as aluminum is provided to form the electrode pad <NUM>.

The electrode pads <NUM> and <NUM> are connected, with wires <NUM>, to respective electrodes 21a and 21b provided on the case <NUM>.

The fixed electrode portions <NUM> and the movable electrode portion <NUM> have electrets formed therein. In a case where only either the fixed electrode portions <NUM> or the movable electrode portion <NUM> have/has electrets formed therein, an electric charge of the reversed polarity is produced in the other. Therefore, only either the fixed electrode portions <NUM> or the movable electrode portion <NUM> may have electrets formed therein.

In this embodiment, the movable electrode portion <NUM> is configured to vibrate in the x-axis direction. The vibration of the movable electrode portion <NUM> in the x-axis direction changes the degree of insertion of the movable teeth <NUM> of the movable electrode portion <NUM> into the gaps between the fixed teeth <NUM> of the fixed electrode portions <NUM>. This causes movement of an electric charge, by which electric power is generated.

<FIG> is a diagram illustrating the MEMS element <NUM> before the weights 105a and 105b are fixed thereto.

As described above, the MEMS element <NUM> is produced from a silicon on insulator (SOI) substrate by a general MEMS process technique. The SOI substrate is configured to have a three-layer structure in which the base <NUM>, the bonding layer <NUM>, and the device layer <NUM> made of a Si active layer are stacked in the z-axis direction. As illustrated in <FIG>, the device layer <NUM> is supported by the base <NUM> via the bonding layer <NUM>. The fixed electrode portions <NUM>, the movable electrode portion <NUM>, and the elastic supporting portions <NUM> are formed of the Si active layer.

In <FIG>, the fixed electrode portions <NUM>, the movable electrode portion <NUM>, the elastic supporting portions <NUM>, and the fixed portions <NUM> on the base <NUM> are illustrated by hatching them. The movable electrode portion <NUM> is elastically supported by the four elastic supporting portions <NUM>. The elastic supporting portions <NUM> each include three beams 13a to 13c that are elastically deformable. The movable electrode portion <NUM> is disposed in a region corresponding to the opening 7a provided in the base <NUM>. The movable electrode portion <NUM> is connected to the fixed portions <NUM> via the beams 13a to 13c of the elastic supporting portions <NUM>. The fixed portions <NUM> are fixed to the base <NUM> via the bonding layer <NUM>. The movable electrode portion <NUM> is thus supported by the base <NUM> via the four elastic supporting portions <NUM> and the fixed portions <NUM>.

The fixed portions <NUM> also function as restricting portions that restrict the vibration range in the x-axis direction of the movable electrode portion <NUM>. As illustrated in <FIG>, the fixed portions <NUM> each include a fixed portion body <NUM>, an elastic portion <NUM>, and a slit <NUM> provided between the fixed portion body <NUM> and the elastic portion <NUM>.

Vibrations of the movable electrode portion <NUM> in the x-axis direction are regulated by collision of the movable electrode portion <NUM> with the fixed portions <NUM> and resultant deformation of the elastic portions <NUM>. That is, forces of the movable electrode portion <NUM> act on the fixed portions <NUM>. The fixed portions <NUM> need to have rigidity for receiving the forces of the movable electrode portion <NUM> without being damaged. Employing the fixed portions <NUM> in this embodiment provides a structure capable of preventing damages from strong acceleration acting on the MEMS element <NUM> in the x-axis direction, as well as capable of downsizing, compared with conventional structures. This will be described later.

<FIG> is a plan view illustrating a state in which the fixed electrode portions <NUM> and the movable electrode portion <NUM> are removed from the MEMS element <NUM> illustrated in <FIG>. Hatched zones 11C in <FIG> illustrate a pattern of bonding portions in which the fixed-tooth connecting portions <NUM> and the lead portions <NUM> of the fixed electrode portions <NUM> are bonded to the bonding layer <NUM>. Hatched zones 11A in <FIG> illustrate a pattern of bonding portions in which end portions of the beams 13a of the elastic supporting portions <NUM> are bonded to the bonding layer <NUM>. Hatched zones 11B in <FIG> illustrate a pattern of bonding portions in which the fixed portions <NUM> are bonded to the bonding layer <NUM>.

<FIG> is an enlarged view of a region IIIA in <FIG>, and <FIG> is an enlarged view of a region IIIB in <FIG>. Each fixed portion <NUM> includes the fixed portion body <NUM>, the elastic portion <NUM>, and the slit <NUM> provided between the fixed portion body <NUM> and the elastic portion <NUM>. The central axis to the y-axis direction of the fixed portion <NUM> is coaxial with the central axis to the y-axis direction of the center band portion <NUM> of the movable electrode portion <NUM>.

The elastic portion <NUM> extends along the one side surface 121a to the x-axis direction of the center band portion <NUM>. The elastic portion <NUM> includes four beam sections 152a to 152d, and two beam-section connecting portions <NUM>, respectively connecting the beam sections 152a and 152b and the beam sections 152c and 152d.

<FIG> is a principle diagram describing the surface shape of the elastic portion <NUM> and illustrates an elastic portion <NUM> formed of a parabolic beam <NUM>, which is a double-clamped beam having four beam sections 252a to 252d. The four beam sections 252a each have a parabolic shape and form a pseudo beam of uniform strength that provides substantially uniform stress distribution across the entire length of the double-clamped beam.

The vertex of the parabola of the beam section 252a is connected by a beam-section connecting portion <NUM> with the vertex of the parabola of the beam section 252b. The vertex of the parabola of the beam section 252c is connected by another beam-section connecting portion <NUM> with the vertex of the parabola of the beam section 252d.

The elastic portion <NUM> in <FIG> is a pseudo beam of uniform strength having the four beam sections 152a to 152d. This pseudo beam of uniform strength is a beam resulting from modifying the shape of the parabolic beam <NUM> in <FIG> by flattening the side surface on the right of the axis of the parabolas of the beam sections 252a to 252d.

The beam structure in <FIG> will be described in detail later.

Returning to <FIG>, description will be continued. The surface of the elastic portion <NUM> facing the center band portion <NUM> has a substantially parabolic contour similar to the contour of each of the beam sections 252a to 252d in <FIG>. The beam sections 152a and 152b and the beam sections 152c and 152d are connected by the beam-section connecting portions <NUM> on the vertex sides of the parabolas. The beam sections 152b and 152c are connected on the opposite sides of the vertices of the parabolas. Hereafter, the opposite side of the vertex of a parabola will be referred to as a basal side. The beam sections 152a and 152d are integrated into one end 151T and the other end 152T in the y-axis direction of the fixed portion body <NUM>, respectively, so that the elastic portion <NUM> functions as a double-clamped beam.

In the end portion of the fixed portion body <NUM> with which the center band portion <NUM> of the movable electrode portion <NUM> collides, the slit <NUM> extends in the y-axis direction in parallel with the one side surface 121a of the center band portion <NUM>. Forming the slit <NUM> creates the elastic portion <NUM> serving as a double-clamped beam.

The slit <NUM> includes a first slit portion 153a formed in a central portion in the y-axis direction, or in other words, in a region corresponding to the beam sections 152b and 152c. The slit <NUM> also includes second slit portions 153b formed in both end portions in the y-axis direction, that is, in regions corresponding to the beam-section connecting portions <NUM>. The two second slit portions 153b are substantially the same in shape and size. The width in the x-axis direction of the first slit portion 153a defines the maximum amount of movement in the x-axis direction of the elastic portion <NUM>. The first slit portion 153a is formed between a side surface of the beam sections 152b and 152c facing the slit <NUM> and an ultimate regulating tip surface <NUM> of a protruding portion 151a inside the slit <NUM>. The width, or in other words, the length in the x-axis direction, of the first slit portion 153a is smaller than the width in the x-axis direction of the second slit portions 153b.

The second slit portions 153b are formed in a semicircular shape in regions near corner portions <NUM> of the fixed portion body <NUM>.

The center in the y-axis direction of the connecting portion between the beam sections 152b and 152c is coaxial with the center in the y-axis direction of the center band portion <NUM>. A side surface <NUM> of the connecting portion between the beam sections 152b and 152c protrudes to be closest in the elastic portion <NUM> to the one side surface 121a of the center band portion <NUM>. Side surfaces <NUM> of the two beam-section connecting portions <NUM> are farthest in the elastic portion <NUM> from the one side surface 121a of the center band portion <NUM>. Thus, the thickness, or the length in the x-axis direction, of the beam-section connecting portions <NUM> is smaller than that of the connecting portion between the beam sections 152b and 152c.

That is, the elastic portion <NUM> has a structure including the central portion, the one end, and the other end that are thicker, and thin portions thinner than the central portion, respectively between the central portion and the one end and between the central portion and the other end.

Now, operations of restricting the vibration range of the movable electrode portion <NUM> by the fixed portion <NUM> will be described.

When the movable electrode portion <NUM> vibrates to move the center band portion <NUM> in the x-axis direction, the one side surface 121a of the center band portion <NUM> collides with the side surface <NUM> of the connecting portion in the elastic portion <NUM> of the fixed portion <NUM>. The elastic portion <NUM> of the fixed portion <NUM> is pressed and deformed by the one side surface 121a of the center band portion <NUM>. An inner side surface <NUM> of the elastic portion <NUM> facing the first slit portion 153a then contacts the ultimate regulating tip surface <NUM> of the protruding portion 151a of the fixed portion body <NUM> facing the first slit portion 153a. At this position, the center band portion <NUM> stops its movement in the x-axis direction. The ultimate regulating tip surface <NUM> of the fixed portion body <NUM> thus serves as a restricting portion that restricts the vibration range of the center band portion <NUM>, that is, the movable electrode portion <NUM>.

Upon collision of the elastic portion <NUM> with the ultimate regulating tip surface <NUM>, the movable electrode portion <NUM> stops. In a conventional structure, the slit may have a width that corresponds to the maximum amount of movement of the movable electrode portion <NUM> and that is set to be constant across the entire length in the y-axis direction of the elastic portion, and the elastic portion may have a uniform rectangular cross section across the entire length in the y-axis direction. In such a conventional structure, stress would concentrate around the corner portions <NUM> of the elastic portion <NUM> near both ends in the y-axis direction of the slit <NUM>. This would increase the likelihood of a damage to the corner portions <NUM> in both end portions in the y-axis direction of the elastic portion <NUM>.

As a comparative example, consider the structure of an elastic portion in which the slit <NUM> formed in the fixed portion <NUM> has only the first slit portion 153a, which extends to both end portions in the y-axis direction of the fixed portion body <NUM>, and the elastic portion has a uniform rectangular cross section across the entire length of the beam. In this structure in the comparative example, the radius of curvature of semicircles formed at both ends in the y-axis direction of the first slit portion 153a near the corner portions <NUM> of the fixed portion body <NUM> is a radius Ra of a circle inscribed in the first slit portion 153a, as illustrated in <FIG>.

By contrast, the elastic portion <NUM> in this embodiment is a pseudo beam of uniform strength that has a greater flexural rigidity, or in other words, a greater spring constant, than the beam in the comparative example, and that allows stress to be substantially uniform across the entire length of the beam. Therefore, the magnitude of elastic energy (energy of absorbing an impact) of the elastic portion <NUM> of the beam in this embodiment is greater than that of the beam in the comparative example. This embodiment also has the second slit portions 153b wider than the first slit portion 153a on both sides in the y-axis direction of the first slit portion 153a. The second slit portions 153b formed near the corner portions at both ends in the y-axis direction of the fixed portion body <NUM> can have the radius of curvature Rb greater than the radius of curvature Ra of the first slit portion 153a. This can reduce stress concentrating on the corner portions at both ends in the y-axis direction of the fixed portion body <NUM>.

The first slit portion 153a may have a width of approximately <NUM> to <NUM>, for example. The second slit portions 153b may have a width equal to or greater than <NUM>, for example. These widths are mere examples for reference purposes, and any optimal width may be employed as appropriate.

The side surface of the elastic portion <NUM> illustrated in <FIG> is formed to be gently curved from the side surface <NUM> of the central portion in the y-axis direction toward the side surfaces <NUM> of the beam-section connecting portions <NUM>. This allows substantially uniform stress distribution between the side surface <NUM> of the basal-side connecting portion and each of the side surfaces <NUM> of the beam-section connecting portions <NUM>.

Further, because the fixed portion <NUM> illustrated in <FIG> has the second slit portions 153b provided on both sides in the y-axis direction of the first slit portion 153a, the length in the y-axis direction of the first slit portion 153a, or in other words, the length of the ultimate regulating tip surface <NUM>, is reduced. This can improve the discharge performance of reactive gas, as will be described below.

The slit <NUM> is typically formed by deep reactive ion etching (DRIE).

What is important in DRIE etching for improving the rate of reaction with Si, which is a material to be etched, is good discharge performance of reactive gas flowing from the slit after reaction. If the slit processed by etching is narrow and elongated, the discharge performance of the reactive gas flowing from the slit is degraded to increase the process time. In this embodiment, the first slit portion 153a is short in the y-axis direction, or in other words, in the direction perpendicular to the slit width direction. This can improve the discharge performance of the reactive gas from the slit after reaction, leading to more efficient processing of the slit <NUM> in a shorter time.

<FIG> is a diagram illustrating relationships between the amount of amplitude of the movable portion and acceleration applied to the vibration-driven energy-harvesting device <NUM> in the comparative example and this embodiment.

In <FIG>, the ordinate indicates the amount of amplitude of the movable portion, and the abscissa indicates acceleration applied to the vibration-driven energy-harvesting device <NUM>. A point T1 on the ordinate indicates the position where the one side surface 121a of the center band portion <NUM> contacts the side surface <NUM> of the elastic portion <NUM> of the fixed portion <NUM>. A point T2 on the ordinate indicates the position where the inner side surface <NUM> of the elastic portion <NUM> hits the ultimate regulating tip surface <NUM> of the fixed portion body <NUM>. While the elastic portion <NUM> moves from the position T1 to the position T2 and deforms, the elastic portion <NUM> absorbs impact energy acting on the MEMS element <NUM>.

Once the movable electrode portion <NUM> starts vibrating, the one side surface 121a of the center band portion <NUM> reaches the point T1. Up to this point, the same relationship is observed between the amount of amplitude of the movable portion and the acceleration applied to the vibration-driven energy-harvesting device <NUM> as indicated by a straight line Lc, irrespective of whether the elastic portion <NUM> has a small spring constant or a great spring constant.

If the elastic portion <NUM> provided in the fixed portion <NUM> has a small spring constant, the one side surface 121a of the center band portion <NUM> reaches the point T2 with a small gradient of amplitude increase of the movable electrode portion <NUM> during the movement of the movable electrode portion <NUM>, as indicated by a straight line Lw. That is, if the elastic portion <NUM> has a small spring constant, a small acceleration αw is applied to the vibration-driven energy-harvesting device <NUM> when the one side surface 121a of the center band portion <NUM> reaches the point T2. By contrast, if the elastic portion <NUM> provided in the fixed portion <NUM> has a great spring constant, the force of the movable electrode portion <NUM> is continuously received after the acceleration applied to the vibration-driven energy-harvesting device <NUM> exceeds the acceleration αw during the movement of the movable electrode portion <NUM>, as indicated by a straight lines. When the acceleration reaches a certain magnitude αs, the point T2 is reached. That is, if the elastic portion <NUM> has a great spring constant, the acceleration αs greater than the acceleration αw is applied to the vibration-driven energy-harvesting device <NUM> when the one side surface 121a of the center band portion <NUM> reaches the point T2.

Thus, increasing the spring constant of the elastic portion <NUM> of the fixed portion <NUM> allows an increase in the energy absorbed during the period in which the elastic portion <NUM> deforms by the distance T2 - T1 after collision of the movable electrode portion <NUM> with the fixed portion <NUM>. This can prevent damages to the MEMS element <NUM> due to greater acceleration acting on the MEMS element <NUM> than in the comparative example. The absorbed energy will be described later.

In this embodiment, the slit <NUM> formed in the fixed portion <NUM> is configured with the first slit portion 153a with a smaller slit width for regulating the movement of the movable electrode portion <NUM>, and the second slit portions 153b with a greater slit width connected to the first slit portion 153a and extending to positions near the corner portions <NUM> of the fixed portion <NUM>. The regions of the second slit portions 153b closer to the corner portions <NUM> are formed in an arc shape with a greater radius of curvature. The side surface of the elastic portion <NUM> facing the center band portion <NUM> is gently curved from the side surface <NUM> of the central portion in the y-axis direction toward the side surfaces <NUM> of the beam-section connecting portions <NUM>.

If increased external acceleration acts on the MEMS element <NUM>, the above configuration still allows uniform stress to occur across the corner portions <NUM> in which the elastic portion <NUM> is fixed to the fixed portion body <NUM>, and the region from the side surface <NUM> to the side surfaces <NUM> of the beam-section connecting portions <NUM> of the elastic portion <NUM>. This can provide the elastic portion having a great spring constant while reducing the size of the elastic portion <NUM>.

The elastic portion <NUM> of the fixed portion <NUM> has a beam structure allowing stress to be substantially uniform across the entire length of the beam, unlike the rectangular beam structure with a uniform cross section as in the comparative example. The elastic portion <NUM> also has a great spring constant compared with the beam in the comparative example. That is, the elastic portion <NUM> has a spring constant greater than that of the beam in the comparative example. Thus, as described with reference to <FIG>, if the slit width of the first slit portion 153a is the same as that in the comparative example, or in other words, if the movable range of the movable electrode portion is the same as that in the comparative example, damages to the elastic portion <NUM> can still be prevented when the MEMS element <NUM> is dropped off or when some other member collides with the MEMS element <NUM> during installation of the MEMS element <NUM>.

Stress distribution in the comparative example and the embodiment will be described with reference to <FIG>.

<FIG> is a perspective view illustrating simulated stress distribution occurring in an elastic portion <NUM>, which is a double-clamped beam with a uniform rectangular cross section across the entire length, when a concentrated load f is applied to the center in the y-axis direction of the elastic portion <NUM>. The elastic portion <NUM> is formed of Si. Note that the elastic portion <NUM> is a beam equivalent to the elastic portion in the above-described comparative example.

<FIG> is a perspective view of a beam equivalent to the beam according to the principle diagram in <FIG> describing the parabolic beam <NUM> having the four beam sections 252a to 252d in the embodiment.

In <FIG>, hatching A represents great stress, hatching C represents small stress, and hatching B represents middle stress.

As illustrated in <FIG>, great stress occurs on the surfaces of the side surfaces to the positive and negative x-axis directions in a middle portion <NUM> in the y-axis direction of the elastic portion <NUM>. Great stress also occurs on the surfaces of the side surfaces to the positive and negative x-axis directions at one end 301ta and the other end 301tb in the y-axis direction of the elastic portion <NUM>.

On the other hand, small stress occurs on the surfaces between the middle portion <NUM> in the y-axis direction and the one end 301ta in the y-axis direction of the elastic portion <NUM>, and on the surfaces between the middle portion <NUM> in the y-axis direction and the other end 301tb in the y-axis direction of the elastic portion <NUM>.

From the above, it can be seen that the rectangular beam still has room for reducing the rigidity in the small-stress regions between the middle portion <NUM> in the y-axis direction and the one end 301ta and the other end 301tb in the y-axis direction.

Here, the pseudo beam of uniform strength in <FIG> will be described in detail.

<FIG> is a side view illustrating the shape of the elastic portion allowing stress to be substantially uniform across the entire length of the surfaces of side surfaces. <FIG> is an enlarged view of a region IVB in <FIG>.

The parabolic beam <NUM> includes the first to fourth beam sections 252a to 252d, and the two beam-section connecting portions <NUM> respectively connecting the first and second beam sections 252a and 252b and the third and fourth beam sections 252c and 252d. The four beam sections, that is, the first to fourth beam sections 252a to 252d, each have a substantially parabolic contour.

As illustrated in <FIG>, the first and second beam sections 252a and 252b and the third and fourth beam sections 252c and 252d are connected by the beam-section connecting portions <NUM> on the vertex sides of the parabolas. The vertices and regions around the vertices of the first and the second beam sections 252a and 252b are integrated together to form one of the beam-section connecting portions <NUM> in which the vertices contact each other. Similarly, the vertices and regions around the vertices of the third and fourth beam sections 252c and 252d are integrated together to form the other beam-section connecting portion <NUM> in which the vertices contact each other.

The second and third beam sections 252b and 252c are integrated together on the basal sides of the parabolas. The basal sides of the first and fourth beam sections 252a and 252d are fixed.

The both-ends-fixed beam connecting the four substantially parabolic beams illustrated in <FIG> will hereafter be referred to as a parabolic beam. The elastic portion <NUM> in <FIG>, having a beam structure resulting from flattening the side surface on the right of the axis of the parabolas in <FIG>, will also be referred to as a parabolic beam.

Forming the elastic portion <NUM> as a parabolic beam can make the spring constant greater than that of the rectangular beam in the comparative example and <FIG> having a uniform rectangular cross section across the entire length. This allows increasing the elastic energy that can be held by the elastic portion <NUM>.

<FIG> is a perspective view illustrating simulated stress distribution occurring in the elastic portions, in which <FIG> is for the structure in the comparative example and <FIG> is for the structure in this embodiment.

<FIG> illustrates, as the comparative example, stress distribution in the rectangular elastic portion <NUM> having a uniform cross section.

As described above, in the comparative example, great stress occurs on the surfaces of the side surfaces to the positive and negative x-axis directions in the middle portion <NUM>, the one end 301ta, and the other end 301tb in the y-axis direction of the elastic portion <NUM>. Small stress occurs on the surfaces of the side surfaces between the middle portion <NUM> in the y-axis direction and the one end 301ta in the y-axis direction of the elastic portion <NUM>, and on the surfaces of the side surfaces between the middle portion <NUM> in the y-axis direction and the other end 301tb in the y-axis direction of the elastic portion <NUM>. Thus, the magnitude of the stress occurring in the elastic portion <NUM> is not uniform but varies across the entire length.

<FIG> illustrates stress distribution of the elastic portion <NUM> formed of a parabolic beam bended so that the maximum stress occurring in the elastic portion <NUM> equals the maximum stress in the comparative example in <FIG>.

For the elastic portion <NUM> formed of the parabolic beam <NUM> illustrated in <FIG>, it was found that relatively great stress occurs on the surfaces of the side surfaces to the positive and negative x-axis directions of the first to fourth beam sections 252a to 252d except the beam-section connecting portions <NUM>, and that the stress is substantially uniform across the surfaces of the side surfaces of the first to fourth beam sections 252a to 252d.

The maximum amount of deflection was approximately <NUM> in the elastic portion <NUM> in the comparative example, and approximately <NUM> in the elastic portion <NUM> formed of the parabolic beam <NUM>.

The above structure allowing substantially uniform stress to occur across the first to fourth beam sections 252a to 252d enables increasing the spring constant, thereby increasing the elastic energy that can be held by the elastic portion <NUM>. The reason for this will be described below.

First, for comparison with the effects of this embodiment, a rectangular beam with a uniform cross section will be described.

<FIG> is a schematic diagram of a both-ends-fixed rectangular beam (hereafter simply referred to as a rectangular beam). <FIG> illustrates the shape of a cross section for <FIG> is a bending-stress distribution diagram for <FIG> is a bending moment diagram for <FIG> illustrates bending stress on the surface of the bottom surface to the x-axis direction of the beam illustrated in <FIG>.

In the following, the thickness is the length in the x-axis direction, or in other words, the length in the bending direction, of the beam; the beam length is the length in the direction in which the beam extends; and the width is the length in the z-axis direction of the beam perpendicular to the x-axis and y-axis directions.

The rectangular beam has a uniform rectangular cross section of the thickness w<NUM> and the width b<NUM> across the entire beam length. That is, the thickness w<NUM> and the width b<NUM> of the beam are constant at any position in the beam length direction. Both ends of the beam are fixed, and the center of the beam length receives a concentrated load P1. The position where the concentrated load P1 is received is the origin <NUM>, and y is the length from the origin. Li is the beam length. Therefore, the positions y of the one end and the other end of the beam are ±L<NUM>/<NUM>, respectively.

The bending moment M1(y), and the bending stress σmax1(y) on the surface of the bottom surface to the x-axis direction, at the position y, are expressed as equations (<NUM>) and (<NUM>), respectively. <MAT> <MAT>.

Z<NUM> is a section modulus and expressed as an equation (<NUM>).

Because the rectangular beam has a constant section modulus Z<NUM> irrespective of y, σmax1(y) is proportional to Mi(y). Therefore, at the positions where |M<NUM>(y)| is maximum (y = <NUM> and y = ±L<NUM>/<NUM>) illustrated in <FIG>, |σmax1(y)| takes the maximum σ<NUM> (see <FIG>).

That is, an equation (<NUM>) holds.

Thus, stress concentrates at y = <NUM> and y = ±L<NUM>/<NUM>, and increasing the concentrated load P1 will cause the stress in regions corresponding to these positions to exceed an allowable stress, leading to a collapse of the beam. At this point, regions other than these regions can still tolerate the stress. Improving the nonuniform stress in the rectangular beam to make the stress uniform enables effective use of the entire beam. This has been described with reference to the comparative beam illustrated in <FIG>.

The flexure δ<NUM> is expressed as an equation (<NUM>) using the bending moment and a second moment of area, <MAT> where E is the Young's modulus.

Next, a parabolic beam will be described.

<FIG> is a schematic diagram of a both-ends-fixed parabolic beam. <FIG> illustrates the shape of a cross section for <FIG> is a bending moment diagram for <FIG> illustrates bending stress on the surface of the bottom surface to the x-axis direction of the beam illustrated in <FIG>.

In the parabolic beam, the width b of the cross section is constant at any position in the beam length direction, but the thickness w is a function of y. w(y) is the thickness at a position y in the beam length direction. Both ends of the beam are fixed, and the center of the beam length receives a concentrated load P. The position where the concentrated load P is received is the origin <NUM>, and y is the length from the origin. L is the beam length. w<NUM> is the thickness of the beam at the one end and the other end, at which the parabolic beam is fixed (see <FIG>).

The function w(y) has the following symmetries:.

According to these symmetries, the bending moment M(y) and the bending stress σmax(y) on the surface of the bottom surface to the x-axis direction are expressed as equations (<NUM>) and (<NUM>), respectively. <MAT> <MAT>.

Z(y) is a section modulus and expressed as an equation (<NUM>).

Appropriately selecting the function w(y) allows |σmax(y)| to be a constant value σ irrespective of y.

Substituting the equations (<NUM>), (<NUM>), and (<NUM>) into the equation (<NUM>) and refining yields an equation (<NUM>).

From the beam thickness w(-L/<NUM>) = w<NUM> at the one end and the other end of the parabolic beam, the relationship between σ and w0 is obtained as an equation (<NUM>).

According to the equation (<NUM>), the equation (<NUM>) is turned into an equation (10a).

The absolute of the bending stress on the surface of the bottom surface to the x-axis direction is σ irrespective of the position y, resulting in uniform distribution.

The flexure δ, calculated from the bending moment and the second moment of area, is expressed as an equation (<NUM>).

The shape of the parabolic beam according to the equation (10a) is illustrated as in <FIG>.

The beam length L, the position y, and the beam thickness w<NUM> at the one end and the other end illustrated in <FIG> correspond to L, y, and w<NUM> in the equation (10a), respectively.

At the length y = ±L/<NUM> from the center in the y-axis direction, the beam thickness is w(y) = <NUM>. However, such a beam cannot receive the concentrated load P. Regions including these positions are therefore connected by the connecting portions.

Now, effects provided by replacing the rectangular beam of the elastic portion <NUM> with the parabolic beam will be described. As a condition for replacement, dimensions other than the beam thickness w are assumed to be the same.

That is, the beam width b<NUM> = b, and the beam length Li = L.

δ<NUM> is the flexure at the point when the maximum of the stress on the beam reaches the allowable stress σ<NUM> for the material, and both beams have the same conditions. That is, the flexure δ<NUM> = δ = δ<NUM>, and the bending stress σ<NUM> = σ = σ<NUM>.

Thus, in the case to be considered here, the rectangular beam and the parabolic beam are both bent on the verge of corruption with the same amount of deflection. Here, an equation (<NUM>) holds according to the equations (<NUM>), (<NUM>), (<NUM>), and (<NUM>).

The equation (<NUM>) indicates that forming the elastic portion <NUM> as a parabolic beam allows the one end and the other end at which the elastic portion <NUM> is fixed to the fixed portion <NUM> to be twice as thick as those of the rectangular beam. This suggests the ability to increase the elastic energy that can be held by the elastic portion <NUM>.

Here, the elastic energy that can be held by each of the rectangular beam and the parabolic beam will be determined as below.

The elastic energy Ui and U held by the rectangular beam and the parabolic beam, respectively, when the beams are bent to their limit, are expressed as equations (<NUM>) and (<NUM>), respectively. <MAT> <MAT>.

From the equations (<NUM>), (<NUM>), and (<NUM>), it can be seen that the relationship expressed as an equation (<NUM>) holds for the above magnitudes.

From the equation (<NUM>), it can be seen that replacing the rectangular beam with the parabolic beam of the same length can quadruple the elastic energy that can be held without collapse.

Thus, the elastic portion <NUM> employing the parabolic beam structure can effectively maintain its vibrating state against strong external vibrations.

<FIG>, corresponding to <FIG> presented as a principle diagram, is a principle diagram of the pseudo beam of uniform strength in the embodiment illustrated in <FIG>.

The parabolic beam <NUM> illustrated in <FIG> has a structure in which the four beam sections have contours in line symmetry with respect to the axis passing through the vertices in parallel with the y-axis direction.

An elastic portion <NUM> illustrated in <FIG> has a substantially parabolic beam structure in which one side surface extends straight and only the side surface opposite to the one side surface is curved.

In the elastic portion <NUM>, a side surface <NUM> opposite to the side surface facing the center band portion <NUM> of the movable electrode portion <NUM> extends straight in the y-axis direction.

The elastic portion <NUM> includes four beam sections 262a to 262d connected in the manner as in the parabolic beam <NUM> in <FIG>.

Specifically, the basal portions of the beam sections 262a and 262d are fixed. The basal portions of the beam sections 262b and 262c are integrated together at the center in the y-axis direction of the elastic portion <NUM>.

The beam sections 262a and 262b are connected by a beam-section connecting portion <NUM> on their vertex sides. The beam sections 262c and 262d are connected by another beam-section connecting portion <NUM> on their vertex sides.

The thickness in the x-axis direction, or in other words, the length from the side surface <NUM> to the curved surface, of the beam sections 262a to 262d at the position of a length y from the center in the y-axis direction of the elastic portion <NUM> is the same as the thickness w(y) at the corresponding position of the length y in the parabolic beam <NUM> illustrated in <FIG>. In other words, because the elastic portion <NUM> has a structure in which only one side surface is curved, the thickness of the beam sections of the elastic portion <NUM> is twice the thickness from the axis of the parabolic beam <NUM> illustrated in <FIG> passing through the vertices in parallel with the y-axis.

Note that the term "substantially parabolic" used herein includes a parabola as well as shapes similar to a parabola.

Because the thickness of the beam sections at a position y in the elastic portion <NUM> is the same as the thickness at the corresponding position y in the parabolic beam <NUM> illustrated in <FIG>, the elastic portion <NUM> provides the same effects as the elastic portion <NUM> formed of the parabolic beam <NUM> illustrated in <FIG>.

The elastic portions <NUM> and <NUM> have been illustrated above as members having a parabolic or substantially parabolic contour. However, the contour of the elastic portions <NUM> and <NUM> does not exactly need to be parabolic or substantially parabolic. As described with reference to <FIG>, the rectangular beam has small-stress regions between the central portion and each of the one end and the other end at which the beam is fixed. Providing thin portions in these small-stress regions to reduce the rigidity of these regions can make the stress on the entire surface of the elastic portions <NUM> and <NUM> more uniform, thereby achieving equivalent effects.

The above embodiment has illustrated the structure in which a side surface of the elastic portion <NUM> of the fixed portion <NUM> is curved, and the slit <NUM> provided between the elastic portion <NUM> and the fixed portion body includes the first slit portion 153a of a smaller slit width and the second slit portions 153b of a greater slit width.

However, the effects provided by the parabolic or substantially parabolic contour of the elastic portion <NUM> can be acquired irrespective of whether or not the slit <NUM> includes multiple slits of different slit widths.

Further, the effects provided by the slit <NUM> including multiple slits of different slit widths can be acquired irrespective of whether or not the contour of the elastic portion <NUM> is parabolic or substantially parabolic.

The MEMS element <NUM> may therefore be produced either by forming a side surface of the elastic portion <NUM> to be curved or by forming the slit <NUM> to include multiple slits of different slit widths, rather than by both.

<FIG> is a plan view illustrating a variation of the movable portion and the fixed portion which is not covered by the claims.

In the fixed portion <NUM> illustrated in <FIG>, a side surface <NUM> facing the center band portion <NUM> of the movable electrode portion <NUM> extends straight in the y-axis direction and has no protruding surface. On the other hand, the one side surface 121a of the center band portion <NUM> of the movable electrode portion <NUM> facing the fixed portion <NUM> has a protruding portion <NUM> protruding toward the movable electrode portion <NUM>. The protruding portion <NUM> has a tip portion 128a provided at a position corresponding to the center in the y-axis direction of the fixed portion <NUM>.

A slit <NUM> provided in the fixed portion <NUM> includes a first slit portion 155a provided in the central portion, and substantially circular second slit portions 155b provided on both sides in the y-axis direction of the first slit portion 155a.

In this manner, the protruding portion <NUM> may be provided in the movable electrode portion <NUM>. The second slit portions 155b may be circular or elliptic.

Although the above embodiment has illustrated the structure in which the elastic portion <NUM> is provided in the fixed portion <NUM>, the elastic portion <NUM> may be provided in the movable electrode portion <NUM>.

According to the above embodiment, the following effects are achieved.

For the elastic portion <NUM> formed of the parabolic beam as above, the thickness w(y) of the elastic portion <NUM> is preferably set to substantially satisfy the equation <MAT> where w(y) is the thickness of the parabolic beam at a position y that is a length y away from the center of the beam length of the elastic portion <NUM>, w<NUM> is the thickness at the one end of the elastic portion <NUM>, |y| is the absolute of the length from the center of the beam length of the elastic portion <NUM> to the position y, and L is the entire length of the beam length of the elastic portion <NUM>.

(<NUM>) The MEMS element <NUM> includes the base <NUM>, the movable electrode portion <NUM>, the and the fixed portions <NUM> each including the elastic portion <NUM> and the fixed portion body <NUM>. Each fixed portion <NUM> includes the slit <NUM> extending along the elastic portion <NUM> and provided to penetrate the fixed portion body <NUM>. The elastic portion <NUM> includes a central portion extending in a direction intersecting the moving direction of the center band portion <NUM> of the movable electrode portion <NUM> and receiving the force of the center band portion <NUM>, and one end and the other end fixed to the fixed portion body <NUM>. The slit <NUM> includes the first slit portion 153a provided to correspond to the central portion of the elastic portion <NUM>, and the second slit portions 153b connected to the first slit portion 153a and provided on the inner side of the elastic portion <NUM> near the one end and the other end. The second slit portions 153b are formed to have a width in the moving direction of the center band portion <NUM> greater than the width of the first slit portion 153a in the moving direction of the center band portion <NUM>. Arc-shaped curved portions are provided respectively in the second slit portions 153b near the corner portions <NUM> at the one end and the other end of the elastic portion <NUM>. The radius of curvature Rb of the arc-shaped curved portions is greater than the radius of curvature Ra of a circle inscribed in the first slit portion 153a. This can prevent stress from being concentrated on the corner portions <NUM> at the one end and the other end of the elastic portion <NUM>, thereby preventing the elastic portion <NUM> from being damaged by strong vibrations.

Although the above embodiment has illustrated the MEMS element <NUM> produced from an SOI substrate, the MEMS element <NUM> may be produced from a silicon substrate. Alternatively, materials such as glass, metal, and alumina may be used instead of a silicon substrate.

The above embodiment has illustrated the MEMS element <NUM> used for a vibration-driven energy-harvesting element. However, the MEMS element <NUM> may be used for a vibration actuator that vibrates the movable electrode portion by receiving a drive voltage from outside. A vibration actuator allows producing various devices that utilize vibrations of the movable electrode portion. Further, the MEMS element <NUM> according to this embodiment can be used for various types of sensors.

Claim 1:
A MEMS element (<NUM>) comprising:
a base (<NUM>);
a movable portion (<NUM>) fixed to the base (<NUM>) in at least a portion of the movable portion (<NUM>) and movable in a predetermined direction; and
a fixed portion (<NUM>) fixed to the base (<NUM>) in at least a portion of the fixed portion (<NUM>), the fixed portion (<NUM>) including an elastic portion (<NUM>, <NUM>, <NUM>) provided to be opposed to the movable portion (<NUM>); and a fixed portion body (<NUM>) to which the elastic portion (<NUM>, <NUM>, <NUM>) is fixed, wherein
the elastic portion (<NUM>, <NUM>, <NUM>) extends in a direction (Y) intersecting a moving direction (X) of the movable portion (<NUM>), includes a central portion (152b, 152c;
252b, 252c; 262b, 262c) receiving a force of the movable portion (<NUM>), and one end (152a; 252a; 262a) and another end (152d; 252d; 262d) fixed to the fixed portion body (<NUM>),
characterized in that
the elastic portion includes a thin portion (<NUM>; <NUM>; <NUM>) between the central portion (152b, 152c; 252b, 252c; 262b, 262c) and the one end (152a; 252a; 262a) and a thin portion (<NUM>; <NUM>; <NUM>) between the central portion (152b, 152c; 252b, 252c; 262b, 262c) and the other end (152d; 252d; 262d), the thin portions (<NUM>; <NUM>; <NUM>) being thinner than the central portion (152b, 152c; 252b, 252c; 262b, 262c), the one end (152a; 252a; 262a), and the other end (152d; 252d; 262d), and
the elastic portion (<NUM>, <NUM>, <NUM>) is formed to have a gently curved surface between the central portion (152b, 152c; 252b, 252c; 262b, 262c) and each thin portion (<NUM>; <NUM>; <NUM>).