Patent Publication Number: US-7911299-B2

Title: Microactuator, optical apparatus, and optical switch

Description:
TECHNICAL FIELD 
     The present invention relates to a microactuator, and an optical apparatus and optical switch using the same. 
     BACKGROUND ART 
     With development of micromachining technologies, the importance of actuators has been increasing in various fields. An example of the field in which microactuators are used is, for example, an optical switch that is used in optical communication or the like to switch the optical path. Examples of such an optical switch include, for example, optical switches disclosed in Japanese Patent Application Laid-Open No. 2001-42233 and the pamphlet of International Publication WO03/060592. 
     A microactuator generally has a fixed portion and a movable portion that is adapted to be movable relative to the fixed portion, and the movable portion can be moved and retained at a predetermined position by a driving force applied thereto. 
     In a microactuator that utilizes as the driving force an electrostatic force, a fixed electrode and a movable electrode are provided in the fixed portion and the movable portion respectively. In such a microactuator, since an electrostatic force is generated between the electrodes by applying a voltage between the electrodes, advantages such as simplification of the structure can be achieved. For this reason, in many conventional microactuators, an electrostatic force is utilized as the driving force. 
     In a microactuator for moving a micro mirror used in an optical switch disclosed in Japanese Patent Application Laid-Open No. 2001-42233, an electrostatic force is used to move a movable portion to a predetermined position against a spring force acting on the movable portion and to retain it at that position. A microactuator used in an optical switch disclosed in the pamphlet of International Publication WO03/060592 is adapted to be capable of utilizing, as a driving force, a Lorentz force in addition to an electrostatic force. For example, a movable portion is moved to a predetermined position by a Lorentz force against a spring force acting on the movable portion, and the movable portion is retained at that position by an electrostatic force. 
     In conventional microactuators that utilize an electrostatic force including the microactuators disclosed in Japanese Patent Application Laid-Open No. 2001-42233 and the pamphlet of the International Publication WO03/060592, the fixed electrode and the movable electrode are arranged in such a way that they overlap each other for the most part as seen from the direction of movement of the movable portion. 
     In conventional microactuators utilizing an electrostatic force, since the fixed electrode and the movable electrode are arranged in such a way that they overlap each other for the most part as seen from the direction of movement of the movable portion, when an electrostatic force is generated, the state in which the movable portion is in contact with the fixed portion (which state will be referred to as “pull-in state” in this specification) occurs, and it has not been possible to retain the movable portion stably at a position before it comes in contact with the fixed portion in the state in which an electrostatic force is generated. 
     In conventional microactuators utilizing an electrostatic force, troubles have occurred, or their uses have been limited due to occurrence of the above mentioned pull-in state. 
     For example, since the movable portion is pressed against the fixed portion in the above mentioned pull-in state, the movable portion may stick to the fixed portion to become inoperable, or even if it does not become inoperable, operation delay may occur due to time taken in detaching the movable portion from the fixed portion. 
     Furthermore, for example, due to occurrence of the above mentioned pull-in state, it is not possible to control the position of the movable portion in such an analogue manner as to change the stop position of the movable portion to a desired position according to the magnitude of the voltage applied between the fixed electrode and the movable electrode, conventional microactuators that utilize an electrostatic force have had only limited applications such as optical switches which can be satisfactorily position-controlled in a digital manner. 
     DISCLOSURE OF THE INVENTION 
     The present invention has been made in view of the above described situations, and has as an object to provide a microactuator that can prevent the pull-in state from occurring while still utilizing an electrostatic force and to provide an optical switch and optical apparatus using the same. 
     To solve the above described problem, a micro actuator according to a first aspect of the present invention comprises a fixed portion and a movable portion that is provided in such a way as to be movable relative to said fixed portion between a first position at which it is in contact with a predetermined portion of said fixed portion and a second position away from said first position, wherein said fixed portion has a first electrode portion, said movable portion has a second electrode portion that can produce an electrostatic force between it and said first electrode portion by a voltage between it and said first electrode portion, and said first and second electrode portions are arranged in such a way that a first force that biases said movable portion in a direction toward said first position according to said electrostatic force created when said voltage is constant reaches a peak when said movable portion is at a third position between said first position and said second position. 
     According to a second aspect of the present invention, in the microactuator according to said first aspect, said first and second electrode portions are arranged in such a way that said first and second electrode portions substantially do not overlap each other when seen in the direction of movement of said movable portion between said first and second positions. 
     A microactuator according to a third aspect of the present invention comprises a fixed portion and a movable portion that is provided in such a way as to be movable relative to said fixed portion between a first position at which it is in contact with a predetermined portion of said fixed portion and a second position away from said first position, wherein said fixed portion has a first electrode portion, said movable portion has a second electrode portion that can produce an electrostatic force between it and said first electrode portion by a voltage between it and said first electrode portion, and said first and second electrode portions are arranged in such a way that said first and second electrode portions substantially do not overlap each other when seen in the direction of movement of said movable portion between said first and second positions. 
     According to a fourth aspect of the present invention, in the microactuator according to any one of said first to third aspects, each of said first and second electrode portions has a substantially plane symmetric shape with respect to at least one same plane containing the direction of movement of said movable portion between said first and second positions. 
     According to a fifth aspect of the present invention, in the microactuator according to any one of said first to fourth aspects, the microactuator is designed in such a way that a second force that biases said movable portion in a direction from said first position toward said second position can be generated. 
     According to a sixth aspect of the present invention, in the microactuator according to said fifth aspect, said movable portion is provided in such a way that a spring force that tends to return to said second position is regenerated as said second force. 
     According to a seventh aspect of the present invention, in the microactuator according to said fifth or sixth aspect, the microactuator is provided with generation means that generates a third force different from said first and second forces in said movable portion. 
     According to an eighth aspect of the present invention, in the microactuator according to said seventh aspect, said generation means comprises a current path that is provided in said movable portion and disposed in a magnetic field and generates a Lorentz force when supplied with a current. 
     An optical apparatus according to a ninth aspect of the present invention comprises the microactuator according to any one of said first to eighth aspects and a driven member mounted on said movable portion, wherein said driven member comprises an optical element. 
     An optical switch according to a tenth aspect of the present invention comprises the microactuator according to any one of said first to eighth aspects and a driven member mounted on said movable portion, wherein said driven member comprises an optical element. 
     In the first to tenth aspects, said movable portion may be composed of a thin film. 
     According to the present invention, there can be provided a microactuator in which occurrence of the pull-in state can be prevented even still using an electrostatic force, and an optical switch and an optical apparatus using the same. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a general diagram schematically showing an example of an optical system provided with an optical switch array according to a first embodiment of the present invention. 
         FIG. 2  is a schematic plan view schematically showing one optical switch as a unit element of the optical switch array shown in  FIG. 1 . 
         FIG. 3  is a schematic cross sectional view taken along line Y 3 -Y 4  in  FIG. 2 ,  FIG. 3  showing a state in which a mirror is retained at an upper position. 
         FIG. 4  is a schematic cross sectional view taken along line X 1 -X 2  in  FIG. 2 . 
         FIG. 5  is a schematic cross sectional view taken along line Y 3 -Y 4  in  FIG. 2 ,  FIG. 5  showing a state in which the mirror is retained at a lower position. 
         FIG. 6  is a schematic plan view showing an optical switch according to a comparative example. 
         FIG. 7  is a schematic cross sectional view taken along line Y 5 -Y 6  in  FIG. 6 ,  FIG. 7  showing a state in which a mirror is retained at an upper position. 
         FIG. 8  is a schematic cross sectional view taken along line Y 5 -Y 6  in  FIG. 6 ,  FIG. 8  showing a state in which a mirror is retained at a lower position. 
         FIG. 9  is a diagram illustrating a model of the actuator used in the first embodiment of the present invention. 
         FIG. 10  is a graph showing the relationship between the position of a movable plate and a force Fe by electromagnetic force and a spring force Fk drawn for the model shown in  FIG. 9 . 
         FIG. 11  is a diagram illustrating a model of an actuator according to the comparative example shown in  FIGS. 6 to 8 . 
         FIG. 12  is a graph showing the relationship between the position of a movable plate and a force Fe′ by electromagnetic force and a spring force Fk drawn for the model shown in  FIG. 11 . 
         FIG. 13  is a schematic plan view showing a modification of the first embodiment. 
         FIG. 14  is a schematic plan view showing another modification of the first embodiment. 
         FIG. 15  is a schematic plan view showing still another modification of the first embodiment. 
         FIG. 16  is a schematic plan view showing still another modification of the first embodiment. 
         FIG. 17  is a general diagram schematically showing an example of an optical system provided with an optical switch array according to a second embodiment of the present invention. 
         FIG. 18  is a schematic plan view schematically showing an optical switch array in  FIG. 17 . 
         FIG. 19  is a schematic plan view schematically showing one optical switch as a unit element of the optical switch array shown in  FIG. 17 . 
         FIG. 20  is a schematic cross sectional view taken along line M-M′ in  FIG. 19 . 
         FIG. 21  is a diagram showing a patterned shape of an Al film where the movable plate in  FIG. 19  is seen from above. 
         FIG. 22  is a schematic cross sectional view showing a cross section along line N-N′ in  FIGS. 19 and 21  as seen from the +Y direction in the −Y direction,  FIG. 22  showing a state in which a mirror is retained at an upper position. 
         FIG. 23  is a schematic cross sectional view showing a cross section along line K-K′ in  FIG. 21 ,  FIG. 23  showing a state in which the mirror is retained at the upper position. 
         FIG. 24  is a schematic cross sectional view showing a cross section along line N-N′ in  FIGS. 19 and 21  as seen from the +Y direction in the −Y direction,  FIG. 24  showing a state in which the mirror is retained at a lower position. 
         FIG. 25  is a schematic cross sectional view showing a cross section along line K-K′ in  FIG. 21 ,  FIG. 25  showing a state in which the mirror is retained at the lower position. 
     
    
    
     THE MOST PREFERRED EMBODIMENTS FOR CARRYING OUT THE INVENTION 
     In the following, the microactuator, the optical apparatus and the optical switch according to the present invention will be described with reference to the drawings. 
     First Embodiment 
       FIG. 1  is a general diagram schematically showing an example of an optical system (that is, in this embodiment, an optical switch system) provided with an optical switch array  1  that constitutes an optical switch apparatus as an optical apparatus according to the first embodiment of the present invention. As shown in  FIG. 1 , the X axis, Y axis and Z axis that are perpendicular to each other are defined for the convenience of explanation. (This also applies to drawings that will be referred to later.) The surface of a substrate  11  of the optical switch array  1  is parallel to the X−Y plane. The direction along the Z axis indicated by the arrow will be referred to as the +Z direction or the +z side, and the direction opposite thereto will be referred to as the −Z direction or the −Z side. This also applies to the X axis direction and the Y axis direction. In connection with this, the plus side of the Z axis direction will sometimes be referred to as the upper side, and the minus side of the Z axis direction will sometimes be referred to as the lower side. 
     As shown in  FIG. 1 , this optical switch system has the optical switch array  1 , m light input optical fibers  2 , m light output optical fibers  3 , n light output optical fibers  4 , an external control circuit  6  as an control portion that supplies, in response to an optical path switching state command signal, a control signal for achieving the optical path switching state prescribed by the optical path switching state command signal to an optical switch array  1 . In the case shown in  FIG. 1 , m=3 and n=3, but m and n may be arbitrary numbers respectively. 
     The optical switch array  1  includes the substrate  11  and m×n mirrors  12  arranged on the substrate  11 . The m light input optical fibers  2  are arranged in a plane parallel to the XY plane so as to guide incident light from one side of the Y axis direction relative to the substrate  11  in the Y axis direction. The m light output optical fibers  3  are disposed on the other side relative to the substrate  11  so as to be opposed to the m light input optical fibers  2  respectively and arranged in a plane parallel to the XY plane so that light that travels in the Y axis direction without being reflected by any mirror  12  in the optical switch array  1  is incident thereon. The n light output optical fibers  4  are arranged in a plane parallel to the XY plane so that light that is reflected by any mirror  12  in the optical switch array  1  and travels in the X axis direction is incident thereon. The m×n mirrors  12  are arranged on the substrate  11  in a two dimensional matrix pattern in such a way that they can be moved along the Z axis direction so as to be moved to and removed from the intersection points of the exit optical paths from the m light input optical fibers  2  and the incident optical paths to the m light output optical fibers  4  respectively by microactuators that will be described later. In this embodiment, the orientation of the mirrors  12  is arranged in such a way that the normal line thereof and the X axis form an angle of 45 degrees in a plane parallel to the XY plane. The operation principle of optical path switching in this optical switch system per se is the same as the operation principle of optical path switching in conventional two-dimensional optical switches. 
     Next, the configuration of one optical switch used as a unit element of the optical switch array  1  shown in  FIG. 1  will be described with reference to  FIGS. 2 to 5 .  FIG. 2  is a schematic plan view of the optical switch.  FIG. 3  is a schematic cross sectional view taken along line Y 3 -Y 4  in  FIG. 2 .  FIG. 4  is a schematic cross sectional view taken along line X 1 -X 2  in  FIG. 2 .  FIG. 5  is a cross sectional view equivalent to  FIG. 3 , but shows a state in which the mirror  12  is retained at a lower position. In This connection,  FIGS. 3 and 4  show a state in which the mirror  12  is retained at an upper position. 
     This optical switch has, besides the above described mirror  12  and the above described substrate  11 , a movable plate  21  serving as the movable portion that is provided in such a way as to be movable relative to the substrate  11 . The substrate  11  is provided with a recessed portion  13  that constitutes a region which the movable plate  21  enters. In this embodiment, the substrate  11  used is a semiconductor substrate such as a silicon substrate. Insulating films  14 ,  15  such as silicon oxide films are layered on the substrate  11 . Two electrodes  16   a ,  16   b  that constitute a fixed electrode portion  16  serving as the first electrode portion and wiring patterns  17   a ,  17   b  therefor are formed between the insulating films  14  and  15 . To the electrodes  16   a ,  16   b  are applied an identical electric potential through the wiring patterns  17   a ,  17   b . The electrodes  16   a ,  16   b  and wiring patterns  17   a ,  17   b  may be made of, for example, a metal film such as an Al film. In this embodiment, the fixed portion includes the substrate  11 , the insulating films  14 ,  15 , the fixed electrode portion  16  and the wiring patterns  17   a ,  17   b.    
     The movable plate  21  is made of thin films and has a lower insulating film  22 , two electrodes  23   a ,  23   b  that constitute a movable electrode portion  23  serving as the second electrode portion formed on the lower insulating film  22  and portions of wiring patterns  24   a ,  24   b  for the electrodes  23   a ,  23   b  formed on the lower insulating film  22  and an upper insulating film  25  covering the upper surface of them. An electrostatic force can be created between the movable electrode portion  23  and the fixed electrode portion  16  by a voltage between the movable electrode portion  23  and the fixed electrode portion  16 . For example, the insulating films  22 , 25  may be made of silicon oxide films or the like, and the electrodes  23   a ,  23   b  and the wiring patterns  24   a ,  24   b  may be made of metal films such as Al films. 
     Although the electrodes  23   a ,  23   b  and the wiring patterns  24   a ,  24   b  are covered with the upper insulating film  25  and should normally be drawn as hidden lines in  FIG. 2  accordingly, the portions hidden by the upper insulating film  25  are also drawn in solid lines for the convenience of graphical illustration. The electrodes  16   a ,  16   b  and the wiring patterns  17   a ,  17   b  are drawn as hidden lines. 
     In this embodiment, both end portions of the movable plate  21  with respect to the X axis direction are mechanically connected to the peripheral portion of the recessed portion  13  of the substrate  11  via flexure portions  27   a ,  27   b  as spring portions having a spring characteristic and anchor portions  28   a ,  28   b  in the mentioned order. The flexure portions  27   a ,  27   b  and the anchor portions  28   a ,  28   b  are constituted by the lower insulating film  22 , the remainder of the aforementioned wiring patterns  24   a ,  24   b  and the upper insulating film  25  that extend continuously from the movable plate  21  without change. Although not shown in the drawings, the wiring patterns  24   a ,  24   b  are electrically connected to wiring patterns (not shown) formed between the insulating films  14 ,  15  via holes (not shown) formed on the insulating films  22 ,  15  at the anchor portions  28   a ,  28   b  and electrically connected commonly through them, and a desired electric potential can be applied to the wiring patterns  24   a ,  24   b.    
     The flexure portions  27   a ,  27   b  have quadrilateral shapes in the plan view as shown in  FIG. 2 . Thus, the movable plate  21  is adapted to be movable in the up and down directions (i.e. along the Z axis). Specifically, in this embodiment, the movable plate  21  is adapted to be movable between an upper position (or the second position) (see  FIGS. 3 and 4 ) to which it tends to be returned by a spring force (restoring force) of the flexure portions  27   a ,  27   b  and a lower bound position (or the first position) (not shown) at which the movable plate  21  having entered the recessed portion  13  of the substrate  11  comes in contact with the bottom of the recessed portion  13  (or, strictly speaking, with the insulating film  15  on the recessed portion  13  of the substrate  11 ). In this embodiment, however, the movable plate  21  does not come in contact with the bottom of the recessed portion  13 , but when the movable plate  21  is retained on the lower side, it is retained at a lower position shown in  FIG. 5  between the aforementioned upper position and the aforementioned lower bound position as will be described later. 
     The movable plate  21  and the flexure portions  27   a ,  27   b  are plane symmetric in shape and structure with respect to the plane that contains line X 1 -X 2  and is parallel to the X-Z plane and with respect to the plane that contains line Y 1 -Y 2  and is parallel to the Y-Z plane respectively. 
     The fixed electrode portion  16  and the movable electrode portion  23  are arranged in such a way that a first force that biases the movable plate  21  downwardly (or in the −Z direction) according to the electrostatic force acting between the electrode portions  16  and  23  that is generated when the voltage between the electrode portions  16  and  23  is constant reaches a peak when the movable plate  21  is at a third position between the lower bound position (or the first position) at which the movable plate  21  is in contact with the bottom of the recessed portion  13  and the upper position (or the second position) shown in  FIGS. 3 and 4 . 
     In this embodiment, such an arrangement is realized by arranging the two electrodes  16   a ,  16   b  that constitute the fixed electrode portion  16  and the two electrodes  23   a ,  23   b  that constitute the movable electrode portion  23  in such a way that they do not overlap in the plan view as seen in the direction of the Z axis (or the direction of movement of the movable plate  21 ) as shown in  FIG. 2 . 
     In this embodiment, each of the electrodes  16   a ,  16   b ,  23   a  and  23   b  has a rectangular strip-like shape extending in the direction of X axis. The electrodes  16   a ,  16   b  that constitutes the fixed electrode portion  16  are arranged in a manner shown in  FIG. 2 , whereby the fixed electrode portion  16  has a shape that is plane symmetric with respect to the plane that contains line X 1 -X 2  and is parallel to the X-Z plane and with respect to the plane that contains line Y 1 -Y 2  and is parallel to the Y-Z plane. Similarly, the electrodes  23   a ,  23   b  that constitutes the movable electrode portion  23  are arranged in a manner shown in  FIG. 2 , whereby the movable electrode portion  23  has a shape that is plane symmetric with respect to the plane that contains line X 1 -X 2  and is parallel to the X-Z plane and with respect to the plane that contains line Y 1 -Y 2  and is parallel to the Y-Z plane. The electrodes  23   a  and  23   b  are arranged on the +Y side and the −Y side respectively with respect to the plane that contains line X 1 -X 2  and is parallel to the X-Z plane. In the plan view as seen in the Z axis direction, the electrode  16   a  is arranged on the +Y side of the electrode  23   a  side by side with a small spacing from the electrode  23   a , and both the electrodes do not overlap. In the plan view as seen in the Z axis direction, the electrode  16   b  is arranged on the −Y side of the electrode  23   b  side by side with a small spacing from the electrode  23   b , and both the electrodes do not overlap. 
     The mirror  12  is fixed perpendicularly on the upper surface of the movable plate  21 . As described before, the orientation of the reflecting surface of the mirrors  12  is arranged in such a way that the normal line thereof and the X axis form an angle of 45 degrees in a plane parallel to the XY plane. 
     In this embodiment, by controlling the voltage between the fixed electrode portion  16  and the movable electrode portion  23 , the state in which the mirror  12  is retained at the upper position (away from the substrate  11 ) (shown in  FIGS. 3 and 4 ) and the state in which the mirror  12  is retained at the lower position (close to the substrate  11 ) (shown in  FIG. 5 ) can be achieved as will be described in detail later. In this embodiment, this control is performed by the external control circuit  6  shown in  FIG. 1 . 
     In the state where the mirror  12  is retained at the upper position, incident light traveling in the Y axis direction is reflected by the mirror  12  as shown in  FIG. 3  to travel in the direction toward the front side of the drawing sheet of  FIG. 3 . In the state where the mirror  12  is retained at the lower position, incident light traveling in the Y axis direction is not reflected by the mirror  12  but passes through it without change to become exit light. 
     A microactuator that drives the mirror  12  is constituted by the components of the above described optical switch structure other than the mirror  12 . 
     The optical switch array  1  according to this embodiment can be manufactured using semiconductor manufacturing techniques such as forming and patterning of a film, etching, and forming and removal of a sacrificial layer, for example. The outline of an example of this manufacturing method will be briefly described. First, the recessed portions  13  are formed on the silicon substrate  1  by photolithographic etching. Then, the insulating film  14 , electrodes  16   a ,  16   b , wiring patterns  17   a ,  17   b  and insulating film  15  etc. are formed by film deposition and patterning. Then, a first resist as a sacrificial layer is formed to fill the recessed portions  13 , and flattening by CMP (Chemical Mechanical Polishing) or the like is performed to leave the aforementioned first resist only in the recessed portions  13 . Thereafter, the insulating film  22 , electrodes  23   a ,  23   b , wiring patters  24   a ,  24   b  and insulating film  25  etc. are formed by film deposition and patterning. Subsequently, recesses allocated for the mirrors  12  are formed by a second resist, and thereafter metal portions such as Au, Ai or the like that are to constitute mirrors  12  are grown by electrolytic plating as described in Japanese Patent the above mentioned Application Laid-Open No. 2001-42233. Finally, the aforementioned first and second resists are removed, whereby the optical switch array  1  is finished. In this embodiment, since the wiring patterns  17   a ,  17   b  are formed in such a way as to climb over the stepped wall portions of the recessed portions  13 , it may be difficult to form the wiring patterns  17   a ,  17   b  in manufacturing in some cases. In such cases, for example, the area other than the recessed portions  13  on the silicon substrate  1  may be restricted to the areas near the flexure portions  27   a ,  27   b  to enlarge the area of the recessed portions  13  in the silicon substrate  1 , and the wiring patterns  17   a ,  17   b  may be formed only within the area of the recessed portions  13   a.    
     In the following, the operation principle of the microactuator of one optical switch in the optical switch array  1  according to this embodiment will be described. 
     As shown in  FIGS. 3 and 4 , when a voltage is applied between the fixed electrode  16  and the movable electrode  23  in the state in which the movable plate  21  is retained at the upper position, an electrostatic force acts between these electrodes  16  and  23  (in particular, between electrodes  16   a  and  23   a  and between electrodes  16   b  and  23   b , in this embodiment). Since in the plan view as seen in the Z axis direction, the electrode  16   a  and the electrode  23   a  do not overlap, and electrode  16   b  and the electrode  23   b  do not overlap, the direction of electrostatic force acting between the electrodes  16   a  and  23   a  and the direction of the electrostatic force acting between the electrodes  16   b  and  23   b  are inclined with respect to the Z axis. However, thanks to the above described symmetry of the electrode portions  16  and  23 , the components of the electrostatic forces in the X axis direction and the Y axis direction are cancelled, and only the component of the generated electrostatic forces in the Z axis direction acts effectively on the movable plate  21 . Thus, a force that biases the movable plate  21  in the downward direction (−Z direction) is exerted on it by the electrostatic force generated between the electrode portions  16  and  23 . This causes the movable plate  21  to move in the downward direction. 
     When the movable plate  21  is displaced in the downward direction, the spring force of the flexure portions  27   a ,  27   b  acts as a restoring force in the upward direction (+Z direction) according to the displacement amount. At first, the magnitude of the downward biasing force by the aforementioned electrostatic force is larger than the magnitude of this spring force, and the movable plate  21  moves downward. 
     On the other hand, as the movable plate  21  moves downward and comes closer to the substrate  11 , the downward biasing force by the electrostatic force acting between the electrode portions  16  and  23  increases at first since the distance between the electrodes  16   a ,  23   a  and the electrodes  16   b  and  23   b  becomes shorter. However, as the movable plate  21  moves downward, the proportion of the Z direction component of the electrostatic force generated decreases, since the electrode  16   a  and the electrode  23   a  do not overlap and the electrode  16   b  and the electrode  23   b  do not overlap in the plan view as seen in the Z axis direction. In addition, the closer to the substrate  11  the movable plate  21  is, the larger the degree of this decrease becomes. For this reason, the downward biasing force by the electrostatic force acting between the electrode portions  16  and  23  reaches a peak when the movable plate  21  comes to a certain position, and as the movable plate  21  moves closer to the substrate  11  from that position, the downward biasing force by the electrostatic force acting between the electrode portions  16  and  23  decreases. Consequently, the downward biasing force by the electrostatic force acting between the electrode portions  16  and  23  is eventually in equilibrium with the upward spring force by the flexure portions  27   a ,  27   b  at a position before the movable plate  21  comes in contact with the bottom of the recessed portion  13  of the substrate  11 , and the movable plate  21  stops at that position. If the movable plate  21  is displaced downward from this stop position, the upward spring force becomes the stronger force and the movable plate  21  moves in the reverse direction or the upward direction, while if the movable plate  21  is displaced upward from the stop position, the downward biasing force by the electrostatic force becomes the stronger force, and the movable plate  21  moves in the reverse direction or the downward direction. For this reason, the movable plate  21  is retained stably at the aforementioned stop position.  FIG. 5  illustrates this state. 
     When switching from the state in which the movable plate  21  is retained at the lower position as shown in  FIG. 5  to the state shown in  FIGS. 3 and 4 , it is sufficient to stop generation of the electrostatic force by changing the voltage between the electrode portions  16  and  23  equal to zero. Then, as a result, the movable portion  21  returns to the upper position shown in  FIGS. 3 and 4  by the upward spring force by the flexure portions  27   a ,  27   b.    
     According to this embodiment, as described above, since when an electrostatic force is generated by application of a voltage between the electrode portions  16  and  23 , the movable portion  21  is stably retained at a position before it comes in contact with the fixed portion as shown in  FIG. 5 , the pull-in state, which have occurred in the past, can be prevented from occurring. Since the movable plate  21  does not come in contact with the fixed portion, the possibility that the movable plate  21  sticks to the fixed portion to become inoperable or cause operation delay is eliminated. 
     In the following, a comparative example to be compared with the embodiment will be described with reference to  FIGS. 6 to 8 .  FIG. 6  is a schematic plan view showing an optical switch of the comparative example.  FIGS. 7 and 8  are schematic cross sectional views taken along line Y 5 -Y 6  in  FIG. 6 .  FIG. 7  shows a state in which the mirror  12  is retained at an upper position, and the  FIG. 8  shows a state in which the mirror  12  is retained at a lower position.  FIGS. 6 to 8  are equivalent to  FIGS. 2 ,  3  and  5  respectively. In  FIG. 6 , however, illustration of the mirror  12  is omitted. In  FIGS. 6 to 8 , elements the same as or equivalent to elements in  FIGS. 2 ,  3  and  5  are designated by the same reference signs, and redundant descriptions thereof will be omitted. 
     What is different in the optical switch of this comparative example from the optical switch according to the embodiment is only that in the comparative example, the fixed electrode portion is composed of an electrode  216  that has a quadrilateral shape in the plan view as seen in the Z axis direction, and the movable electrode portion is composed of an electrode  223  that just overlaps the electrode  216  in the plan view as seen in the Z axis direction. 
     In this comparative example, when a voltage is applied between the electrodes  216  and  223  in the state in which the movable plate  21  is retained at the upper position as shown in  FIG. 7 , an electrostatic force acts between the two electrodes  216  and  223  in the −Z direction. This causes the movable plate  21  to move in the downward direction (or −Z direction). 
     As the movable plate  21  is displaced in the downward direction, a spring force of the flexure portions  27   a ,  27   b  acts as a restoring force in the upward direction (+Z direction) according to the displacement amount. Since the magnitude of the electrostatic force is larger than the magnitude of this spring force, the movable plate  21  moves downward. 
     In this comparative example, since the electrodes  216  and  233  just overlap each other in the plan view as seen in the Z axis direction (the situation is the same in cases where most part of them overlap even if there is a non-overlapping part), the electrostatic force in the −Z direction simply increases as the movable plate  21  moves downward and comes closer to the substrate  11 , and it does not have a peak. Therefore, the downward force acting on the movable plate  21  by the aforementioned electrostatic force will not be in equilibrium with the upward spring force by the flexure portions  27   a ,  27   b , and the movable plate  21  will not stop until it comes in contact with the bottom of the recessed portion  13  of the substrate  11 , as shown in  FIG. 8 . Once the movable plate  21  comes in contact with the bottom of the recessed portion  13  of the substrate  11  as shown in  FIG. 8 , it is kept in that state. Thus the pull-in state occurs. 
     In connection with this, if the voltage between the electrodes  216  and  223  is decreased when the movable plate  21  comes close to the substrate  11 , there is a position at which the downward electrostatic force and the upward spring force by the flexure portions  27   a ,  27   b  are in equilibrium. However, even if the movable plate  21  once stops at this equilibrium position, the downward electrostatic force becomes stronger than the upward spring force if the movable plate  21  is displaced downward from that position. Therefore, the movable plate  21  cannot be at rest in a stable state at the aforementioned equilibrium position, and when a small positional displacement of the movable plate  21  occurs, downward movement of the movable plate  21  cannot be suppressed only by the upward spring force by the flexure portions  27   a ,  27   b , and the movable plate  21  cannot become stationary until it comes in contact with the bottom of the recessed portion  13  of the substrate  11  after all. 
     When to switch from the state in which the movable plate  21  is retained at the lower position as shown in  FIG. 8  to the state shown in  FIG. 7 , the voltage between the electrode portions  216  and  223  is changed equal to zero to stop generation of the electrostatic force. Then, as a result, the movable portion  21  should return to the upper position shown in  FIGS. 3 and 4  by the upward spring force by the flexure portions  27   a ,  27   b . However, in this comparative example, since the pull-in state as shown in  FIG. 8  occurs as described above, the movable plate  21  sticks to the bottom of the recessed portion  13  of the substrate  11  to disable switching to the state shown in  FIG. 7  in some cases. Even if such an inoperable state does not occur, detaching the movable plate  21  from the fixed portion takes time and causes operation delay. 
     By the way, analysis of operation of an actual element requires advanced mathematical techniques such as a finite element method. In the following, to promote understanding of the above described operation principle of the actuator used in this embodiment, a model of the actuator used in this embodiment will be formulated to make the calculation simpler, and the relationship between the position of the movable plate  21  and the force effectively acting on the movable plate  21  will be determined based on that model. 
       FIG. 9  shows a model of the actuator used in this embodiment. The two electrodes  16   a ,  16   b  that constitute the fixed electrode portion  16  and the two electrodes  23   a ,  23   b  that constitute the movable electrode portion  23  actually have flat plate shapes, but they are assumed to be bar members having a circular cross section (i.e. cylinders) extending in the X axis direction. 
     It is assumed that all the electrodes  16   a ,  16   b ,  23   a ,  23   b  have the same shape and dimensions; their length along the X axis direction is represented by L and the radius of the upper surface and the lower surface is represented by R. The distance between the centers of the electrodes  23   a  and  23   b  in a plane parallel to the Y-Z plane is represented by 1, the distance between the centers of the electrodes  16   a  and  23   a  along the Y axis direction and the distance between the centers of the electrodes  16   b  and  23   b  along the Y axis direction are both represented by d, the distance between the centers of the electrodes  16   a  and  23   a  along the Z axis direction and the distance between the centers of the electrodes  16   b  and  23   b  along the Z direction axis are both represented by z, and the angle that the line connecting the centers of the electrodes  16   a  and  23   a  forms with the Y axis direction and the angle that the line connecting the centers of the electrodes  16   b  and  23   b  forms with the Y axis direction are both represented by θ. The position of the movable plate  21  will be represented by distance z. It is assumed that R&lt;&lt;z, R&lt;&lt;d, z&lt;&lt;L and d&lt;&lt;L hold. 
     It is assumed that the distance  1  between the electrodes  23   a  and  23   b  is sufficiently long, so that when a voltage V is applied between the fixed electrode  16  and the movable electrode  23 , the electrostatic force acts only between the electrodes  16   a  and  23   a  and between the electrodes  16   b  and  23   b . The magnitude of the electrostatic force acting between the electrodes  16   a ,  23   a  when the voltage V is applied is represented by F 1 , and the magnitude of the electrostatic force acting between the electrodes  16   b ,  23   b  when the voltage V is applied is represented by F 2 . The electrodes  16   a  and  16   b  are kept at an identical electric potential, and the electrodes  23   a  and  23   b  are kept at an identical electric potential. 
     In the model shown in  FIG. 9 , the spring force by the flexure portions  27   a ,  27   b  in the +Z direction is represented by Fk. 
     In this model, under the assumptions R&lt;&lt;z, R&lt;&lt;d, z&lt;&lt;L and d&lt;&lt;L, the capacitance C 0  between the electrodes  23   a  and  23   b  is expressed approximately by formula 1 shown below. In formula 1, ε0 is the permittivity of vacuum. In this connection, the permittivity of the Si substrate and the insulator in the movable portion is assumed to be equal to ε0 to facilitate calculation. 
     
       
         
           
             
               
                 
                   
                     C 
                     0 
                   
                   ≅ 
                   
                     
                       
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                         ⁢ 
                         
                             
                         
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                         ln 
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                                 d 
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                                 2 
                               
                             
                           
                           / 
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                         ) 
                       
                     
                     · 
                     L 
                   
                 
               
               
                 
                   [ 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     When a voltage V is applied between the electrodes  16   a  and  23   a , an electrostatic force F 1  is generated between the electrodes  16   a  and  23   a . The electrostatic force F acting between the two electrodes is expressed by formula 2 shown below in terms of the capacitance C, the voltage V between the electrodes and the distance S between the electrodes. Accordingly the electrostatic force F 1  acting between the electrodes  16   a  and  23   a  is expressed by formula 3 shown below. 
     
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       1 
                       2 
                     
                     · 
                     
                       
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     Since the direction of the electrostatic force F 1  is inclined by the aforementioned angle θ from the Y axis direction, the Y axis component F 1   y  and the Z axis component F 1   z  of the electrostatic force F 1  are expressed by formula 4 and formula 5 shown below respectively. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     The electrostatic force F 2  acting between the electrodes  16   b  and  23   b  when a voltage V is applied has the same magnitude as the electrostatic force F 1 , and only the direction is different. Accordingly, the Y axis component F 2   y  and the Z axis component F 2   z  of the electrostatic force F 2  are expressed by formula 6 and formula 7 shown below respectively.
 
 F   2y   =−F   1   y   [Formula 6]
 
F 2z =F 1z   [Formula 7]
 
     Therefore, the Y axis component Fey and the Z axis component Fez of the resultant force Fe of the electrostatic force F 1  and the electrostatic force F 2  are expressed by formula 8 and formula 9 shown below respectively. 
     
       
         
           
             
               
                 
                   
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     In the final analysis, the Y axis component Fly of the electrostatic force F 1  and the Y axis component F 2   y  of the electrostatic force F 2  cancel each other, and the force Fe that effectively acts on the movable plate  21  by the generated electrostatic forces is the Z axis component Fez of the resultant force of the electrostatic force F 1  and the electrostatic force F 2 . 
     On the other hand, it is assumed that the flexure portions  27   a ,  27   b  obey Hooke&#39;s law, and the spring constant thereof is represented by k. It is assumed that the state in which no electrostatic force is acting on the movable plate  21  is equivalent to the state of a coil spring in its natural length, and the position of the movable plate  21  in that state is represented by z 0 . Then, the spring force Fk by the flexure portions  27   a ,  27   b  in the +Z direction is expressed by formula 10 shown below.
 
 F   k   =k ( z   ( )   −z )  [Formula 10]
 
       FIG. 10  is a graph, drawn according to the above formula 9 and formula 10, showing the relationship between the position z of the movable plate  21  and the electrostatic force Fe and the spring force Fk in the model shown in  FIG. 9 . In the case shown in  FIG. 10 , it is assumed that R=1 μm, d=10 μm, L=100 μm, V=75 V, k=1 mN/m and z 0 =100 μm. 
     In the following, the aforementioned operation principle of the actuator used in this embodiment will be described using  FIG. 10 . 
     As shown in  FIG. 10 , as the position z of the movable plate  21  changes from z=0 to z=z 0 , the force Fe in the −Z direction acting on the movable plate  21  by the electrostatic force passes points A to F and has a peak at point C. On the other hand, the spring force Fk in the +Z direction acting on the movable plate  21  is represented by a downward sloping straight line. In the case shown in  FIG. 10 , the curve representing the force Fe and the line representing the spring force Fk intersect at points B, D and E. 
     In the case shown in  FIG. 10 , since Fk&gt;Fe holds in the section of the position z of the movable plate  21  corresponding to the section from point D to point E, even if the force Fe is generated by applying the voltage V=75 V, which was used in drawing the graph shown in  FIG. 10 , in the state in which the position z of the movable plate  21  is z 0 , the movable plate  21  cannot be moved below the position of point E only by that. In view of this, in this embodiment, the voltage applied is made larger than that in the above described case so that Fk&lt;Fe holds in all over the section of the position z of the movable plate  21  from point C to point F in  FIG. 10  to thereby move the movable plate  21  to a position between point A and point D, and thereafter V=75 V is applied. Then, if the movable plate  21  is at a position between point A and point B, the movable plate  21  moves in the upward direction (or +Z direction) toward point B since the Fk&gt;Fe holds, and when the movable plate  21  comes to point B, both the forces are in equilibrium since Fk=Fe. Thus, the movable plate  21  is at rest at point B. Conversely, if the movable plate  21  is at a position between point B and point D, the movable plate  21  moves in the downward direction (or −Z direction) toward point B since the Fk&lt;Fe holds, and when the movable plate  21  comes to point B, both the forces are in equilibrium since Fk=Fe. Thus, the movable plate  21  is at rest at point B. In the vicinity of point B, since the relation of the forces Fk&gt;Fe that causes the movable plate  21  to move upward holds at positions below point B, and the relation of the forces Fk&lt;Fe that causes the movable plate  21  to move downward holds at positions above point B, the movable plate  21  is stably retained at point B. 
     In the above description, a case in which a relatively low voltage that realizes values shown in  FIG. 10  is applied after a relatively high voltage is applied to move the movable plate  21  from position z 0  to the position of point B and retain it at point B has been described by way of example. This is because in retaining the movable plate  21 , a lower applied voltage is more preferable in terms of power consumption etc. However, the aforementioned relatively high voltage may be continuously applied without changing it into a relatively low applied voltage even while continuously retaining the movable plate  21 . In this case, the stable retaining position of the movable plate  21  corresponding to point B in  FIG. 10  is displaced a little from point B in  FIG. 10 . This will be understood from the fact that when the value of the force Fe at each position is changed in proportion to the square of the applied voltage while leaving the force Fk unchanged, the intersection point is displaced. 
     In the case where the applied voltage is made higher so that the movable plate  21  is moved to point D, the movable plate  21  remains at point D and does not move toward point B even if the voltage V is changed to V=75 V. To be precise, movement toward point B occurs when the position is below the position of point D. 
     As described before, when the voltage applied is changed, the stable retaining position of the movable plate  21  corresponding to point B in  FIG. 10  is displaced a little from point B in  FIG. 10 . Therefore, in the actuator used in this embodiment, an analogue-based position control of the movable plate  21  with which the stable retaining position of the movable plate  21  is changed to a desired position according to the magnitude of the voltage applied can be performed. Accordingly, the actuator according to the present invention can be used in various applications in which analogue-based position control of a movable portion is required while still utilizing electrostatic force. Nonetheless, in this embodiment, since the actuator is used in the optical switch as shown in  FIGS. 3 and 5  with which digital-based position control is acceptable, it is not necessary to change the applied voltage to perform analogue-based position control of the movable plate  21 . 
     Next, a model of the actuator of the comparative example shown in  FIGS. 6 to 8  will be formulated and the relationship between the position of the movable plate  21  and the force effectively acting on the movable plate  21  will be determined in a similar manner as the case of  FIG. 9 . 
       FIG. 11  shows a model of the actuator of the comparative example shown in  FIGS. 6 to 8 . In this model also, the spring force Fk in the +Z direction by the flexure portions  27   a ,  27   b  is the same as  FIG. 9 . In the model shown in  FIG. 11 , the electrode  216  constituting the fixed electrode portion and the electrode  223  constituting the movable electrode portion are constructed as parallel flat plates unlike with the model shown in  FIG. 9 . In the model shown in  FIG. 11 , the electrostatic force in the −Z direction acting between the electrodes  216  and  223  when a voltage V is applied is represented by Fe′. 
       FIG. 12  is a graph, drawn according to a known formula expressing the electrostatic force between parallel flat plates and formula 10 shown before, showing the relationship between the position z of the movable plate  21  (or the distance between the electrodes  216  and  223 , in this case) and the electrostatic force Fe′ in the −Z direction and the spring force Fk in the model shown in  FIG. 11 . In the case shown in  FIG. 12 , it is assumed that the width of the electrodes  216 ,  223  in the Y axis direction is 10 μm, the length of the electrodes  216 ,  223  in the x axis direction is 100 μm, and the voltage V applied is 20 V. 
     As shown in  FIG. 12 , as the position z of the movable plate  21  changes from z=0 to z=z 0 , the electrostatic force Fe′ in the −Z direction acting on the movable plate  21  does not have a peak unlike with the force Fe in  FIG. 10 . In addition, the line representing the electrostatic force Fe′ and the line representing the spring force Fk intersects at point G. When the movable plate  21  is located below point G, the relationship of forces Fk&lt;Fe′ that causes the movable plate  21  to move downward holds, and when the movable plate is located above point G, the relationship of forces Fk&gt;Fe′ that causes the movable plate  21  to move upward holds. 
     A case in which a voltage higher than the voltage applied in the state shown in  FIG. 12  is applied in the state in which the position z of the movable plate  21  is z 0  to realize the relationship Fk&lt;Fe′ to move the movable plate  21  downward will be considered. In this case, if the relatively high voltage is continued to be applied, the relationship Fk&lt;Fe′ is maintained even when the movable plate  21  comes to point G or located below point G in  FIG. 12 , and the movable plate  21  comes in contact with the fixed portion and retained in the contact state to cause the pull-in state. If the voltage applied is changed to the relatively low voltage in the state shown in  FIG. 12  when the movable plate  21  comes to point G in  FIG. 12 , both forces are in equilibrium since Fk=Fe′ holds at point G. However, if a small positional displacement of the movable plate  21  in the upward direction from the position of point G occurs, then Fk&gt;Fe′ holds, whereby the movable plate  21  is moved upward to return to position z 0 . On the other hand, if a small positional displacement of the movable plate  21  in the downward direction from the position of point G occurs, then Fk&lt;Fe′ holds, whereby the movable plate  21  is moved downward to come in contact with the fixed portion and retained in the contact state to cause the pull-in state. 
     As above, in this comparative example, trying to retain the movable plate  21  at a lower position results in the pull-in state, and it is impossible to retain the movable plate  21  stably at an intermediate position between the position z 0  and the contact position. 
     In this comparative example, analogue-based control of the movable plate  21  is quite impossible even if the voltage applied is changed, since the pull-in state occurs. 
     Although in the embodiment, the fixed electrode portion  16  and the movable electrode portion  23  are arranged in such a way that the fixed electrode portion  16  and the movable electrode portion  23  do not overlap at all in the plan view as seen in the Z axis direction as described before, they may be arranged in such a way as to overlap partly to some extent so long as a peak like point C in  FIG. 10  is present. 
     In the embodiment, both the fixed electrode portion  16  and the movable electrode portion  23  have a plane symmetric shape with respect to the plane that contains line X 1 -X 2  and is parallel to the X-Z plane and the plane that contains line Y 1 -Y 2  and is parallel to the YZ plane as described before. However, such symmetry is not essentially required in the present invention. For example, the above mentioned symmetry is not essentially required in the case where the movable portion is guided by guide means and the moving direction of the movable portion is determined regardless of the direction of the force acting on the movable portion accordingly. 
     Modifications of the First Embodiment 
     The fixed electrode portion  16  and the movable electrode portion  23  in the above described first embodiment may be modified in the manners illustrated in  FIGS. 13 to 16  respectively. 
       FIGS. 13 to 16  are schematic plan views equivalent to  FIG. 2  that show modifications of the above described first embodiment respectively. In  FIGS. 13 to 16 , elements the same as or equivalent to the elements in  FIG. 2  are designated by the same reference signs, and redundant descriptions thereof will be omitted. In  FIGS. 13 to 16 , illustration of the mirror  12  is omitted. 
     In every embodiment, both the fixed electrode portion  16  and the movable electrode portion  23  have a plane symmetric shape with respect to the plane that contains line X 1 -X 2  and is parallel to the X-Z plane and the plane that contains line Y 1 -Y 2  and is parallel to the YZ plane. 
     In the modification shown in  FIG. 13 , the fixed electrode portion  16  is composed of one rectangular strip-like electrode  16   c  extending in the X axis direction. The movable electrode  23  is composed of two rectangular strip-like electrodes  23   c ,  23   d  extending in the X axis direction. The electrode  16   c  is arranged in such a way as to extend along line X 1 -X 2  in the plan view as seen in the Z axis direction. In the plan view as seen in the Z axis direction, the electrodes  23   c  and  23   d  are arranged on the +Y side and the −Y side of the electrode  16   c  respectively side by side with a small spacing from the electrode  16   c , and they do not overlap the electrode  16   c . Although the wiring pattern for the electrode  16   c  is not illustrated in  FIG. 13 , the wiring pattern overlaps the electrode  23   c  (or  23   d ) in the plan view as seen in the Z axis direction. However, the overlapping area is small, and there is no problem in producing a peak like point C in  FIG. 10 . 
     In the modification shown in  FIG. 14 , the fixed electrode portion  16  is composed of two rectangular strip-like electrodes  16   e ,  16   f  extending in the X axis direction. The movable electrode portion  23  is composed of one rectangular strip-like electrode  23   e  extending in the X axis direction. The electrode  23   e  is arranged in such a way as to extend along line X 1 -X 2  in the plan view as seen in the Z axis direction. In the plan view as seen in the Z axis direction, the electrodes  16   e  and  16   f  are arranged on the +Y side and the −Y side of the electrode  23   e  respectively side by side with a small spacing from the electrode  23   e , and they do not overlap the electrode  23   e . Although the wiring patterns for the electrodes  16   e  and  16   f  is not illustrated in  FIG. 14 , the wiring pattern does not overlap the electrode  23   e  in the plan view as seen in the Z axis direction. 
     In the modification shown in  FIG. 15 , the fixed electrode portion  16  is composed of three rectangular strip-like electrodes  16   g ,  16   h ,  16   i  extending in the X axis direction. The movable electrode portion  23  is composed of two rectangular strip-like electrode  23   g ,  23   h  extending in the X axis direction. The electrode  16   g  is arranged in such a way as to extend along line X 1 -X 2  in the plan view as seen in the Z axis direction. In the plan view as seen in the Z axis direction, the electrodes  23   g  and  23   h  are arranged on the +Y side and the −Y side of the electrode  16   g  respectively side by side with a small spacing from the electrode  16   g , and they do not overlap the electrode  16   g . In the plan view as seen in the Z axis direction, the electrode  16   h  is arranged on the +Y side of the electrode  23   g  side by side with a small spacing from the electrode  23   g , and it does not overlap the electrode  23   g . In the plan view as seen in the Z axis direction, the electrode  16   i  is arranged on the −Y side of the electrode  23   h  side by side with a small spacing from the electrode  23   h , and it does not overlap the electrode  23   h . Although the wiring patterns for the electrodes  16   g ,  16   h  and  16   i  are not illustrated in  FIG. 15 , the wiring pattern for the electrode  16   g  overlaps the electrode  23   g  (or  23   h ) in the plan view as seen in the Z axis direction. However, the overlapping area is small, and there is no problem in producing a peak like point C in  FIG. 10 . 
     In the modification shown in  FIG. 16 , the fixed electrode portion  16  is composed of an electrode  16   j  having an annular portion and rectangular strip-like portions extending from its +X side and −X side of the X axis direction in the +X direction and −X direction respectively. The movable electrode portion  23  is composed of two band-like electrodes  23   j ,  23   k  extending on the +X side and −X side of the electrode  16   j  respectively with a small spacing from the electrode  16   j  while conforming to the shape of the electrode  16   j  in the plan view as seen in the Z axis direction. The electrodes  23   j  and  23   k  do not overlap the electrode  16   j . Although the wiring pattern for the electrode  16   j  is not illustrated in  FIG. 16 , the wiring pattern overlaps the electrode  23   j  (or  23   k ) in the plan view as seen in the Z axis direction. However, the overlapping area is small, and there is no problem in producing a peak like point C in  FIG. 10 . 
     Second Embodiment 
       FIG. 17  is a general diagram schematically showing an example of an optical system (that is, in this embodiment, an optical switch system) provided with an optical switch array  101  that constitutes an optical switch apparatus as an optical apparatus according to the second embodiment of the present invention. In  FIG. 17 , elements the same as or equivalent to elements in  FIG. 1  are designated by the same reference signs, and redundant descriptions thereof will be omitted. 
     What is different in the optical system shown in  FIG. 17  from the optical system shown in  FIG. 1  is only that an optical switch array  101  is used in place of the optical switch array  1 , the external control circuit  6  operates in a different way accordingly, and a magnet  5  serving as a magnetic field generation portion that generates a magnetic field for the optical switch array  101  is additionally provided as will be described later. 
     In this embodiment, the magnet  5  is disposed beneath the optical switch array  101  as shown in  FIG. 17  and generates a magnetic field illustrated by magnetic lines of force  5   a  for the optical switch array  101 . Specifically, the magnet  5  generates a substantially uniform magnetic field directed along the X axis direction toward the plus side thereof for the optical switch array  101 . 
       FIG. 18  is a general plan view schematically showing the optical switch array  101  in  FIG. 17 . The optical switch array  101  is provided with a substrate  111  (not shown in  FIG. 18 ), m×n movable plates  112  arranged two dimensionally on the substrate  111  and, mirrors  12  provided on the respective movable plates  112 . The portion of the optical switch array  101  other than the mirrors  12  constitutes a microactuator array as a microactuator apparatus. 
     Next, the structure of one optical switch as a unit element of the optical switch array  101  shown in  FIG. 17  will be described with reference to  FIGS. 19 to 25 . 
       FIG. 19  is a general plan view schematically illustrating one optical switch as a unit element of the optical switch array  101  shown in  FIG. 17 .  FIG. 20  is a schematic cross sectional view taken along line M-M′ in  FIG. 19 . Please note that  FIG. 20  shows the cross section of only the movable plate  112 .  FIG. 21  illustrates the shape of the pattern of an Al film  122  when the movable plate  112  in  FIG. 19  is seen from above. To facilitate understanding, the area of the Al film  122  is hatched in  FIG. 21 . In  FIG. 21 , a fixed electrode portion  323  and a wiring pattern  324  for it are additionally illustrated.  FIGS. 22 and 24  are schematic cross sectional views taken along line N-N′ in  FIGS. 19 and 21  respectively as seen from the +Y side in the −Y direction. Please note that  FIGS. 22 and 24  additionally show the mirror  12  as seen in the −Y direction.  FIGS. 23 and 25  are schematic cross sectional views taken along line K-K′ in  FIG. 21 .  FIGS. 22 and 23  show a state in which the mirror  12  is retained at a upper position at which it is present in an optical path, and  FIGS. 24 and 25  show a state in which the mirror  12  is retained at a lower position at which the mirror  12  is away from the optical path. In  FIGS. 22 and 25 , for the convenience of graphical illustration, illustration of a protruding portion  124  that will be described later is omitted, as if there were not a difference in height associated with the protruding portion  124 . 
     The optical switch as the unit element of optical switch array  101  has one movable plate  112  serving as a movable portion that is provided on the substrate  111  such as a silicon substrate and constitutes one microactuator together with the substrate  111  and the mirror  12  as an optical element serving as a driven member mounted on the movable plate  112 . 
     The movable plate  112  is plane symmetric in shape and structure with respect to the plane that contains line X 101 -X 102  and is parallel to the X-Z plane as shown in  FIGS. 19 and 21 . 
     The movable plate  112  is made of thin films and includes a lower silicon nitride film (SiN film)  121  extending all over the planar shape of the movable plate  112 , an upper SiN film  123  and an intermediate Al film  122  partly provided between these films  121  and  123  as shown in  FIGS. 19 to 25 . Thus, the movable plate  112  includes a portion composed of a two layered film in which the SiN films  121  and  123  are layered in order from the bottom and a portion composed of a three layered film in which the SiN film  121 , Al film  122  and SiN film  123  are layered in order from the bottom. The pattern shape of the Al film  122  as shown in  FIG. 21  will be described later. The movable plate  112  is formed according to predetermined film thickness and film forming conditions so that it is bent upward (in the +Z direction) relative to the substrate  111  as shown in  FIG. 22  by internal stress caused by a difference in the thermal expansion coefficient between the SiN films  121 ,  123  and the Al film  122  and internal stress caused upon film formation. 
     The movable plate  112  includes a mirror mount plate  112   a  having a rectangular shape as a mount portion on which the mirror  12  is mounted (i.e. a supporting base for the mirror  12 ) and two band-like support plates  112   b  connected to an end of the mirror mount plate  112   a  as shown in  FIG. 19 . In this embodiment, the two support plates  112   b  are two beam portions that are mechanically connected to each other in parallel. Each of the support plates  112   b  has leg portions  112   c  and  112   d  at the end thereof. Both the leg portions  112   c  and  112   d  are fixed on the substrate  111 . In the movable plate  112 , the leg portions  112   c  and  112   d  provide a fixed end, and the mirror mount plate  112   a  side can be raised as shown in  FIG. 22 . As above, in this embodiment, the movable plate  112  is a movable portion having a cantilever structure with the fixed end at the leg portions  112   c  and  112   d . In this embodiment, the substrate  111 , insulating films  113 ,  114  and the fixed electrode portion  323  etc. layered thereon that will be described later constitute the fixed portion. 
     As shown in  FIG. 19 , the movable plate  112  has the protruding portion  124  that is provided thereon in such a way as to surround the portion of the movable plate  112  on which the mirror  12  is mounted. The protruding portion  124  is produced by shaping the multi-layered film constituting the movable plate  112  to form a protrusion. Since providing the protruding portion  124  in this way creates a difference in height, bending by the internal stress is suppressed in the region of the movable plate  112  surrounded by the protruding portion  124  and the region of the movable plate  112  in which the protruding portion  124  is provided and flatness can be maintained in these regions. For this reason, in the movable plate  112 , the portion on which the mirror  12  is mounted is planar even in the state in which the mirror  12  is raised to an upper position by bending caused by the internal stress as shown in  FIG. 22 , and accordingly the shape of the mirror  12  mounted thereon can be kept unchanged. 
     As above, in the movable plate  112 , bending is suppressed in the region surrounded by the protruding portion  124  and the region in which the protruding portion  124  is provided, but the protruding portion  124  is not provided in the region near the leg portions  112   d  of the support plate  112   b . Accordingly, in the movable plate  112 , the mirror mount plate  112   a  side thereof can be raised by bending of the region of the support plate  112   b  in which the protruding portion is not provided with the leg portions  112   c ,  112   d  serving as the fixed end, as shown in  FIG. 22 . In addition, the region of the support plate  112   b  near the leg portions  112   d  constitutes a plate spring portion as an elastic portion because the protruding portion  124  is not provided in that region. 
     In the following, the shape of the Al film  122  in the movable plate  112  will be described with reference to  FIG. 21 . In this embodiment, since the movable plate  112  is driven using both Lorentz force and electrostatic force as driving forces, the Al film  122  is patterned in the shape shown in  FIG. 21 . A pattern  122   a  in the Al film  122  extends from each of the two leg portions  112   d  to the end side (or the +X side) of the movable plate  112  along the outer peripheral edge of the movable plate  112  and are connected to a linear pattern  122   c  extending in the Y axis direction along the side  112   e  at the end of the movable plate  112 . The pattern  122   c  constitutes a current path (or current path for Lorentz force) that is disposed in a magnetic field to generate a Lorentz force as a driving force when electric current is supplied thereto. Hereinafter, the pattern  122   c  will be referred to as the Lorentz force current path  122   c  in some cases. The pattern  122   c  is also a pattern included in the Al film  122 . The patterns  122   a  are wiring patterns for supplying a current to the Lorentz force current path  122   c . As shown in  FIGS. 22 and 24 , the pattern  122   a  is connected to a wiring pattern for Lorentz force  142  made of an Al film via contact holes in the insulating film  114  and the SiN film  121  at the +Y side leg portion  112   d , and connected to another wiring pattern for Lorentz force  142  at the −Y side leg portion in the same manner. A current serving as a drive signal for Lorentz force is supplied from the wiring pattern for Lorentz force  142  to the pattern  122   a  via the leg portions  112   d . The Lorentz force current path  122   c  is in a magnetic field directed in the X axis direction generated by the magnet  5  shown in  FIG. 17 . Therefore, when a current is supplied to the Lorentz force current path  122   c  via the pattern  122   a , a Lorentz force in the +Z direction or −Z direction acts on the Lorentz force current path  122   c  according to the direction of the current. 
     As shown in  FIGS. 22 to 24 , on the substrate  111  are layered insulating films  113  and  114  such as silicon oxide films in order from the substrate  111  side, and the wiring pattern for Lorentz force  142  is formed between the insulating films  113  and  114 . 
     A pattern  122   b  in the Al film  122  extends from each of the two leg portions  112   c  to the vicinity of the base side (or the −X side) of the mirror mount plate  112   a  of the movable plate  112  along the inner edges of the two band-like support plates  112   b  of the movable plate  112  and is connected to a movable electrode portion  322  provided near the base of the mirror mount plate  112   a  to constitute a wiring pattern for the movable electrode portion  322 . An electrostatic force can be created between the movable electrode portion  322  and a fixed electrode portion  323  that will be described later by a voltage between the movable electrode portion  322  and the fixed electrode portion  323 . 
     As shown in  FIGS. 21 ,  23  and  25 , the movable electrode portion  322  is composed of four rectangular strip-like electrodes  122   f ,  122   g ,  122   h ,  122   i  extending in the X axis direction in the plan view as seen in the Z axis direction. The +X side ends of the electrodes  122   f ,  122   g ,  122   h  and  122   i  are connected one another by a wiring pattern  122   j . The two wiring patterns  122   b  are connected to the −X side end of the electrode  122   f  and the −X side end of the electrode  122   i  respectively. The electrodes  122   f ,  122   g ,  122   h ,  122   i  and the wiring pattern  122   j  are also patterns included in the Al film  122 . 
     With the arrangement of the electrodes  122   f ,  122   g ,  122   h ,  122   i  that constitute the movable electrode portion  322  as shown in  FIG. 21 , the movable electrode portion  322  has a plane symmetric shape with respect to the plane that contains line X 101 -X 102  and is parallel to the X-Z plane. 
     The pattern  122   b  is connected to a wiring pattern for the movable electrode (not shown) via contact holes in the insulating film  114  and the SiN film  121  at the leg portions  112   c , and a voltage (a voltage for electrostatic force, or a drive signal for electrostatic force) is applied between it and the fixed electrode portion  323 . 
     The fixed electrode portion  323  is composed of three rectangular strip-like electrodes  323   a ,  323   b ,  323   c  extending in the X axis direction as shown in  FIGS. 21 ,  23  and  25  and is provided between the insulating films  113  and  114  on the substrate  111  with a wiring pattern  324  for the fixed electrode portion  323 . The fixed electrode portion  323  and the wiring pattern  324  are made of continuously formed integral Al film. With the arrangement of the electrodes  323   a ,  323   b ,  323   c  that constitute the fixed electrode portion  323  as shown in  FIG. 21 , the fixed electrode portion  323  has a plane symmetric shape with respect to the plane that contains line X 101 -X 102  and is parallel to the X-Z plane. 
     In this embodiment, the electrode  323   b  is arranged in such a way as to extend along line X 101 -X 102  in the plan view as seen in the Z axis direction. In the plan view as seen in the Z axis direction, the electrodes  122   g  and  122   h  are arranged on the +Y side and the −Y side of the electrode  323   b  respectively side by side with a small spacing from the electrode  323   b , and they do not overlap the electrode  323   b . In the plan view as seen in the Z axis direction, the electrode  323   a  is arranged on the −Y side of the electrode  122   h  side by side with a small spacing from the electrode  122   h , and the electrode  323   a  does not overlap the electrode  122   h . In the plan view as seen in the Z axis direction, the electrode  323   c  is arranged on the +Y side of the electrode  122   g  side by side with a small spacing from the electrode  122   g , and the electrode  323   c  does not overlap the electrode  122   g . In the plan view as seen in the Z axis direction, the electrode  122   f  is arranged on the +Y side of the electrode  323   c  side by side with a small spacing from the electrode  323   c , and the electrode  122   f  does not overlap the electrode  323   c . In the plan view as seen in the Z axis direction, the electrode  122   i  is arranged on the −Y side of the electrode  323   a  side by side with a small spacing from the electrode  323   a , and the electrode  122   i  does not overlap the electrode  323   a.    
     In this embodiment, by arranging the electrodes that constitute the fixed electrode portion  323  and the movable electrode portion  322  in the above described manner, a first force that biases the movable plate  112  downwardly (in the −Z direction) according to the electrostatic force acting between the electrode portions  323  and  322  when the voltage between the electrode portions  323  and  322  is constant is designed to have a peak when the movable plate  112  is at a third position between the lower bound position (or the first position) at which the movable plate  112  is in contact with the insulating film  114  of the substrate  111  and the upper position (or the second position) shown in  FIGS. 22 and 23 . 
     In this embodiment, by controlling the voltage between the fixed electrode portion  323  and the movable electrode portion  322  and the current supplied to the Lorentz force current path  122   c , the state in which the mirror  12  is retained at the upper position (away from the substrate  111 ) ( FIGS. 22 and 23 ) and the state in which the mirror  12  is retained at the lower position (close to the substrate  11 ) ( FIGS. 24 and 25 ) can be achieved as will be described in detail later. In this embodiment, this control is performed by the external control circuit  6  shown in  FIG. 17 . In  FIGS. 22 and 24 , T denotes the cross section of the optical path of the incident light in relation to the positions at which the mirror  12  has been brought. 
     A microactuator that drives the mirror  12  is constituted by the components of the above described optical switch structure other than the mirror  12 . 
     The optical switch array  101  according to this embodiment can be manufactured using semiconductor manufacturing techniques such as forming and patterning of a film, etching, and forming and removal of a sacrificial layer, for example. The mirror  12  can be manufactured by, for example, the method same as that in the above described first embodiment. 
     According to this embodiment, since the fixed electrode portion  323  and the movable electrode portion  322  are configured in the above described way, the relationship between the position of the movable plate  112  and the force effectively acting on the movable plate  112  by the electrostatic force acting between the electrode portions  323  and  322  when a constant voltage is applied between the electrode portions  323  and  322  is similar to the relationship shown in  FIG. 10  described above. 
     According to this embodiment, in the state in which the aforementioned electrostatic force and the aforementioned Lorentz force do not act, the state in which the support plate  112   b  is bent in the +Z direction by the stress (or spring force) of the plate spring portion constituted by the region of the support plate  112   b  that is close to the leg portions  112   d  (i.e. the region in which the protruding portion  124  is not provided) is restored, and the mirror  12  is retained at the upper position, as shown in  FIGS. 22 and 23 . Thus, the mirror  12  is brought into the optical path T to reflect light incident on the optical path. 
     When this state is to be switched to the state in which light incident on the optical path T is allowed to pass without change without being reflected by the mirror  12 , for example, the above mentioned Lorentz force is first applied to move the movable plate  112  downward against the spring force of the above mentioned plate spring portion of the support plate  112   b , whereby the movable plate  112  is moved by the above mentioned Lorentz force to an arbitrary position corresponding to the range from point A to point D in  FIG. 10 . In this state, application of the above mentioned Lorentz force is terminated, and the voltage associated with  FIG. 10  is applied between the fixed electrode portion  323  and the movable electrode portion  322 . As a result, the movable electrode portion  322  is stably retained at the position corresponding to point B in  FIG. 10  (that is, a position before the movable plate  112  comes in contact with the insulating film  114  on the substrate  111 ) in a similar manner as the above described first embodiment.  FIGS. 24 and 25  illustrate this state. 
     In the state in which the mirror  12  is retained at the lower position, the incident light passes though without change without being reflected by the mirror  12  to become exit light, since the mirror  12  stays out from the optical path T. 
     When to switch from the state in which the movable plate  112  is retained at the lower position as shown in  FIGS. 24 and 25  to the state shown in  FIGS. 22 and 23 , it is sufficient to stop generation of the electrostatic force by, for example, changing the voltage between the electrode portions  323  and  322  equal to zero. Then, as a result, the movable plate  112  returns to the upper position shown in  FIGS. 22 and 23  by the upward spring force by the above mentioned plate spring portion of the support plate  112   b.    
     According to this embodiment, as described above, since when an electrostatic force is generated by application of a voltage between the electrode portions  323  and  322 , the movable portion  112  is stably retained at a position before it comes in contact with the fixed portion as shown in  FIGS. 24  and  25 , the pull-in state, which have occurred in the past, can be prevented from occurring. Since the movable plate  112  does not come in contact with the fixed portion, the possibility that the movable plate  112  sticks to the fixed portion to become inoperable or cause operation delay is eliminated. 
     The time at which the Lorentz force applied is once disabled and a voltage is applied to the electrode portions  323  and  322  in switching from the state shown in  FIGS. 22 and 23  to the state shown in  FIGS. 24 and 25  may be either before the movable plate  112  is brought into contact with the fixed portion or after it is once brought into contact with the fixed portion by the Lorentz force. Even if the movable plate  112  is brought into contact with the fixed portion by the Lorentz force, the Lorentz force can be made smaller than the electrostatic force in the state shown in  FIG. 8  in the comparative example by far, and therefore the possibility that the movable plate  112  sticks to the fixed portion to become inoperable is almost eliminated. 
     In the actuator used in this embodiment also, an analogue-based position control of the movable plate  112  with which the stable retaining position of the movable plate  112  is changed to a desired position according to the magnitude of the voltage applied can be performed, as with the actuator used in the above described first embodiment. 
     Although embodiments and modifications of the present invention have been described, the present invention is not limited to these embodiments and modifications. 
     For example, in the above described second embodiment, patters similar to the patterns of the fixed electrode portion  16  and the movable electrode portion  23  in the above described first embodiment or any one of the modifications shown in  FIGS. 13 to 16  may be used as the patterns of the fixed electrode portion  323  and the movable electrode portion  322 . 
     According to the present invention, the above described second embodiment may be configured in such a way that a different force (such as a force utilizing a change in the stress of a thin film caused by thermal expansion or a force utilizing a piezoelectric effect) may be used in place of the Lorentz force as a force used besides the electrostatic force. 
     Furthermore, although a spring force is used as the force for returning the movable plate to the upper position in the above described first and second embodiments, a configuration in which a different force (e.g. a magnetic force) can be utilized in place of the spring force may be adopted in the present invention. 
     The microactuator according to the present invention can be used in optical apparatuses other than optical switches and other various applications.