Patent Publication Number: US-7907325-B2

Title: Control methods for micromirror devices implemented with a single address electrode

Description:
This application is a Non-provisional application claiming a Priority date of Feb. 26, 2007 based on a previously filed Provisional Application 60/903,467 filed by the common Applicants of this application and the disclosures made in Provisional Application 60/903,467 are further incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a technology involving micromirror devices. More particularly, this invention relates to micromirror devices using mirror elements each controlled with a single address electrode. 
     2. Description of the Related Art 
     A micromirror is a microscopic mirror used in reflecting light. A deflectable micromirror device (DMD), that is, one composed of display elements implemented with a micro electromechanical system (MEMS) device configuration where an electric circuit is integrated on a silicon substrate and many micromirrors are arranged on the flat surface of the substrate, is generally known as a device using micromirrors. One can change the deflection angle of a micromirror surface on a conventional DMD by applying a voltage to two address electrodes positioned below each micromirror to generate a coulomb force F. Note that “deflection” referred to in this specification indicates the tilt of a micromirror surface.  FIG. 1  is a circuit diagram that shows two driving circuits configured with memory cells with an SRAM configuration, which are connected to two address electrodes according to the conventional method. 
     A DMD is composed primarily of a substrate, a plurality of micromirrors, address electrodes used in deflecting the angle of the micromirrors, and elastic hinges for supporting each of the micromirrors. The elastic hinges are arranged on the substrate to support the micromirrors. In one mirror element, two address electrodes are situated immediately below each micromirror on the substrate. These address electrodes are connected to an external circuit via driving circuits on the substrate, whereby voltages are applied to the address electrodes. 
     U.S. Pat. No. 5,285,407 discloses the driving circuits configured for the two address electrodes in one mirror element of a DMD. To control the micromirror of the mirror element, the deflection of each micromirror is achieved by generating coulomb Forces F between the micromirror and the address electrodes, with voltages applied to the address electrodes via the driving circuits. Since the elastic hinges support the micromirrors, the flat surface of each micromirror is normally held in the position of the initial state by the restoring force of each elastic hinge when there is no control voltage applied to the electrodes. 
     U.S. Pat. No. 5,214,420 discloses the projection system using the above-described DMD. This projection system controls light by reflecting incident light on or away from a projection optical path by deflecting each micromirror as described above. In this patented disclosure, the light almost entirely reflected on a projection optical path, and light reflected away from the projection optical path are referred to as ON light and OFF light respectively. Additionally, light partially reflected on the projection optical path, which is light reflected on the projection optical path at a particular ratio of the ON light to the OFF light, that is, light the quantity of which is smaller than that of the ON light is referred to as intermediate light in this specification. 
     However, DMDs employed in the configurations disclosed by the above-described patents require two address electrodes for one mirror element. Therefore, it is necessary to connect two driving circuits to the two address electrodes. This leads to the technical problem of the relatively large surface area taken up by the driving circuits connected to the address electrodes on the substrate. Accordingly, when many mirror elements must be arranged on the substrate in order to obtain an image with a high-definition resolution, such as hi-vision, the area occupied by the driving circuits on the substrate expands with an increase in the number of mirror elements, leading to an increase in the size of the substrate itself. As a result, the projection apparatus becomes larger and more expensive. 
     U.S. Pat. No. 6,266,178 discloses the driving circuit  21  connected to an address electrode on a substrate by using a memory cell with a DRAM configuration as a charge storage cell. Namely, U.S. Pat. No. 6,266,178 discloses the invention for downsizing the driving circuit  21  by using the charge storage cell  20  shown in  FIG. 2A . 
       FIG. 2B  shows the configuration of the two driving circuits  21  that use the charge storage cell  20  and are connected to the two address electrodes in one mirror element. However, in this scenario, the technical problem described above, in that the size of the substrate itself must be increased due to the large area occupied by the driving circuits on the substrate when many mirror elements are arranged to obtain an image with a high-definition resolution, remains. 
     U.S. Pat. No. 6,975,444 discloses the configuration for controlling a mirror element with one address electrode with a DRAM or SRAM configuration. This document discloses the embodiment where a mirror connected to a cover glass is deflected in only one direction with respect to a substrate. 
     U.S. Pat. No. 6,885,494 discloses the technology related to the deflection angle of a mirror element. U.S. Pat. No. 4,229,732 discloses the configuration where a hinge is situated on a mirror surface. U.S. Pat. No. 5,061,049 discloses the landing electrode with the same potential as a mirror. U.S. Pat. No. 5,671,083 discloses the memory configuration using a capacitor. U.S. Pat. No. 6,657,759 discloses the technology for holding a mirror at a predetermined angle. 
     As described in these patents above, in a DMD where two electrodes are provided on a substrate in one mirror element, the two driving circuits required for each of the two address electrodes occupy a large area on the substrate because the configuration of the two driving circuits corresponding to the two address electrodes is required. This imposes a severe restriction on the arrangement of a larger number of mirror elements on the substrate. Additionally, previous to this invention, there have been no methods for controlling one mirror element with a single address electrode in a micromirror device. Furthermore, there have been no methods disclosed for controlling a mirror element to deflect in two directions with high precision. 
     SUMMARY OF THE INVENTION 
     A first method for controlling a micromirror device according to the present invention is a method for controlling a micromirror device including a plurality of mirror elements each composed of a micromirror supported on a substrate by an elastic hinge, and an address electrode arranged across the deflection axis of the micromirror, and this controlling method comprises deflecting the micromirror by changing a potential to a predetermined waveform for the address electrode. In the first method for controlling the micromirror device, a potential changed to the predetermined waveform is, for example, a potential of a pulse waveform applied at predetermined operational timing. Additionally, the width of the pulse is shorter than a time period for deflecting the micromirror in one direction. 
     A second method for controlling a micromirror device according to the present invention is a method for controlling a micromirror device including a plurality of mirror elements each composed of a micromirror supported on a substrate by an elastic hinge, and an address electrode having first and second regions that are arranged across the deflection axis of the micromirror, the micromirror is deflected in a direction of the first region by applying a predetermined voltage to the address electrode in a initial state where the micromirror is not deflected, and this method comprises deflecting the micromirror in the direction of the second region by changing the potential of the address electrode to a predetermined waveform. 
     The second method for controlling the micromirror device comprises applying the pulse voltage to the address electrode at the predetermined operational timing of the micromirror, and further comprises applying the pulse voltage in a time period shorter than that for deflecting the micromirror in one direction. 
     A third method for controlling a micromirror device according to the present invention is a method for controlling a micromirror device including a plurality of mirror elements each comprising a micromirror supported on a substrate by an elastic hinge, and a address electrode having first and second electrode parts that have asymmetrical shapes and different properties with respect to the deflection axis of the micromirror, and are connected so that their potentials become equal, and this method comprises deflecting the micromirror in the direction of the second electrode after drawing the micromirror in the direction of the first electrode by changing the potential of the address electrode to a predetermined waveform. 
     In the third method for controlling the micromirror device according to the present invention, a micromirror that is supported on the substrate by the elastic hinge and has asymmetrical shapes or different properties with respect to the deflection axis may be used as a replacement for the address electrode having the first and the second electrode parts with asymmetrical shapes or different properties with respect to the deflection axis of the micromirror. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a circuit diagram that shows two driving circuits configured with memory cells with an SRAM configuration, which are connected to two address electrodes according to the conventional method; 
         FIG. 2A  is a circuit diagram that shows a driving circuit configured with a charge storage cell, which is connected to an address electrode, according to the conventional method; 
         FIG. 2B  is a schematic diagram that shows two driving circuits connected to two address electrodes provided in one mirror element; 
         FIG. 3  is a perspective view of mirror elements that are two-dimensionally arranged on a substrate in a micromirror device, according to a preferred embodiment of the present invention; 
         FIG. 4A  is a cross-sectional view of a mirror element in an initial state taken along a line IV-IV of  FIG. 3  in the micromirror device, according to the preferred embodiment of the present invention; 
         FIG. 4B  is a cross-sectional view of the mirror element shown in  FIG. 4A  and held in an ON light state; 
         FIG. 4C  is a cross-sectional view of the mirror element shown in  FIG. 4A  and held in an OFF light state; 
         FIG. 4D  is a schematic diagram that explains a method for controlling the intensity of light reflected on a projection optical path, with a total amount of reflection light by making a micromirror oscillate between the ON and the OFF light states in the mirror element shown in  FIG. 4A ; 
         FIG. 4E  is a schematic diagram that shows one driving circuit connected to a single address electrode situated in one mirror element shown in  FIGS. 4A to 4D ; 
         FIG. 5A  is a schematic diagram that shows the correspondence between the areas of a micromirror and an address electrode (beneath the mirror) when a mirror element is viewed in the direction Z of  FIG. 3 , in the case where the area sizes of first and second electrode parts differ in the single address electrode of one mirror element in a micromirror device, according to a preferred embodiment of the present invention; 
         FIG. 5B  is a cross-sectional view of the mirror element shown in  FIG. 5A  and taken along the line IV-IV of  FIG. 3 ; 
         FIG. 5C  is a schematic diagram that shows the correspondence between the areas of a micromirror and an address electrode (beneath the mirror) when a mirror element is viewed in the direction Z of  FIG. 3 , in the case where the area sizes of first and second electrode parts differ in the single address electrode of a mirror element, as an alternate embodiment of the present invention; 
         FIG. 5D  is a cross-sectional view of the mirror element shown in  FIG. 5C  and taken along the line IV-IV of  FIG. 3 ; 
         FIG. 6A  is a chart that exemplifies a method for controlling the micromirror to operate in a free oscillation state, where the micromirror moves between ON and OFF light states, in the case where the area sizes of the first and the second electrode parts differ in the single address electrode of a mirror element in the micromirror device, according to the present invention; 
         FIG. 6B  is a chart that exemplifies a method for controlling the micromirror to change from an intermediate light state, that is, the initial state, to the OFF light state, and further to the ON light state, in the case where the area sizes of the first and the second electrode parts differ in the single address electrode of a mirror element in the micromirror device, according to the present invention; 
         FIG. 6C  is a chart that exemplifies a method for controlling the micromirror to change from the intermediate light state, that is, the initial state, to the ON light state, and further to the OFF light state, in the case where the area sizes of the first and the second electrode parts differ in the single address electrode of a mirror element in the micromirror device, according to the present invention; 
         FIG. 6D  is a chart that exemplifies a method for controlling the micromirror to change from the OFF light state to the intermediate light state, that is, the initial state, in the case where the area sizes of the first and the second electrode parts differ in the single address electrode of a mirror element in the micromirror device, according to the present invention; 
         FIG. 6E  is a chart that exemplifies a method for controlling the micromirror to change from the ON light state to the intermediate light state, that is, the initial state, in the case where the area sizes of the first and the second electrode parts differ in the single address electrode of a mirror element in the micromirror device according to the present invention; 
         FIG. 7A  is a schematic diagram of one mirror element in the micromirror device that shows the correspondence between the areas of the micromirror and the address electrode (beneath the mirror) when the mirror element is viewed in the direction Z of  FIG. 3 , in the case where the heights of the first and the second electrode parts differ in the single address electrode, according to one preferred embodiment of the present invention; 
         FIG. 7B  is a cross-sectional view of the mirror element shown in  FIG. 7A  and taken along the line IV-IV of  FIG. 3 ; 
         FIG. 7C  is a schematic diagram of one mirror element in the micromirror device that shows the correspondence between the areas of a micromirror and an address electrode (beneath the mirror) when the mirror element is viewed in the direction Z of  FIG. 3 , in the case where the heights of the first and the second electrode parts differ in the single address electrode, as an alternate embodiment of  FIG. 7A ; 
         FIG. 7D  is a cross-sectional view of the mirror element shown in  FIG. 7C  and taken along the line IV-IV of  FIG. 3 ; 
         FIG. 7E  is a schematic diagram of one mirror element in the micromirror device that shows a mechanism for controlling the deflection of a micromirror to the ON and the OFF light states, in the case where the heights and the area sizes of the first and the second electrode parts differ in the single address electrode, according to one preferred embodiment of the present invention; 
         FIG. 8A  is a schematic diagram of one mirror element in the micromirror device that shows the tops of the first and the second electrode parts of a single address electrode configured with materials having different permittivities, according to one preferred embodiment of the present invention; 
         FIG. 8B  is a schematic diagram of one mirror element in the micromirror device that shows the arrangement of the single address electrode where either of the tops of the first or the second electrode parts of the address electrode is configured with a material having a different permittivity than that of the rest of the electrode, according to one preferred embodiment of the present invention; 
         FIG. 9  is a schematic diagram of one mirror element in the micromirror device that shows the configuration where two regions of the micromirror, which respectively face and correspond to the first and the second electrode parts of the single address electrode, are configured with materials having different permittivities, according to one preferred embodiment of the present invention; 
         FIG. 10  is a schematic diagram of one mirror element in the micromirror device that shows the configuration where an elastic hinge for applying a voltage is connected to one of the two partitioned regions of the micromirror, which respectively correspond to the first and the second electrode parts of the single address electrode, according to one preferred embodiment of the present invention; 
         FIG. 11  is a schematic diagram of one mirror element in the micromirror device that shows the configuration where the thicknesses of the regions of the micromirror, which respectively face and correspond to the first and the second electrode parts of the single address electrode differ, according to one preferred embodiment of the present invention; 
         FIG. 12  is a schematic diagram of one mirror element in the micromirror device that shows the configuration where the elasticity coefficients of the elastic hinge are different, respective to the different deflection directions of the micromirror, according to one preferred embodiment of the present invention; 
         FIG. 13A  is a schematic diagram of one mirror element in the micromirror device that shows the correspondence between the areas of the micromirror and the address electrode (beneath the mirror), and the position of an elastic hinge when the mirror element is viewed in the direction of Z of  FIG. 3 , in the case where the elastic hinge supporting the micromirror is arranged in a position offset from the center of the micromirror, according to one preferred embodiment of the present invention; 
         FIG. 13B  is a cross-sectional view of the mirror element shown in  FIG. 13A  taken along the line IV-IV of  FIG. 3 ; 
         FIG. 14  is a schematic diagram of one mirror element in a micromirror device that shows the configuration implemented by adding an electrode for detecting the position of the micromirror or for changing the operation of the micromirror to one side of the element shown in  FIG. 4A , according to one preferred embodiment of the present invention; 
         FIG. 15A  is a chart that exemplifies a method for controlling the micromirror to change from the OFF to the ON light state by applying a multilevel voltage to the address electrode and/or the micromirror of a mirror element in the micromirror device, according to the present invention; 
         FIG. 15B  a charts that exemplifies a method for controlling the micromirror to be held in the ON light state by applying a multilevel voltage to the address electrode and/or the micromirror of a mirror element in the micromirror device, according to the present invention; 
         FIG. 15C  is a chart that exemplifies a method for controlling the micromirror to change from the intermediate light state to the ON light state by applying a multilevel voltage to the address electrode and/or the micromirror of a mirror element in the micromirror device, according to the present invention; and 
         FIGS. 15D and 15E  are charts that exemplify a method for controlling the micromirror to change from the ON light state to the OFF light state by applying a multilevel voltage to the address electrode and/or the micromirror of a mirror element in the micromirror device, according to the present invention; 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention discloses micromirror devices that include a plurality of mirror elements, with each mirror element controlled by a single address electrode and one driving circuit connected to the address electrode on a substrate. 
       FIG. 3  is a perspective view of the micromirror device  30  according to the present invention where a plurality of mirror elements  38  is two-dimensionally arranged on a substrate  32 . As shown in  FIG. 3 , the micromirror device  30  is fundamentally formed by two-dimensionally (vertically and horizontally) arranging on a substrate  32  the mirror elements  38  each composed of an address electrode (not shown), an elastic hinge (not shown), and a micromirror  31  supported by the elastic hinge. According to the present invention, a single address electrode in each mirror element  38  controls the micromirror  31 . The micromirror  31  may be square, or some other similar shape. Preferably, the size of the micromirror  31  (or the pitch between the centers of the mirrors) is 4 μm to 10 μm, in consideration of the number of pixels ranging from 2K×4K of super hi-vision to the number of pixels of hi-vision, and the size of the micromirror device. More preferably, the size (or the pitch between the centers of the mirrors) of the micromirror  31  is 4 μm to 8 μm. 
       FIG. 3  shows the configuration where the square mirror elements  38  are vertically and horizontally arranged at predetermined intervals on the substrate  32 . However, the intervals between the mirror elements are not always required to be predetermined intervals. It is preferable, though, that the number of micromirrors  31  and driving circuits, which drive the micromirrors  31 , are arranged on the substrate  32  ranging from 1,000,000 for hi-vision to 8,000,000 for super hi-vision of 2K×4K. In  FIG. 3 , a deflection axis  39  for deflecting each mirror is represented with a dashed line. 
     A mirror element  38  in a micromirror device  30  according to the present invention is described in detail below with reference to the cross-sectional view of the mirror element  38  taken along the line IV-IV in the micromirror device  30  shown in  FIG. 3 . 
     First Preferred Embodiment 
       FIG. 4A  is a cross-sectional view of the mirror element  38  held in the initial state taken along the line IV-IV of  FIG. 3  in the micromirror device according to the present invention. The configuration and the initial state of one mirror element in the micromirror device according to the present invention are described below with reference to  FIG. 4A . In this configuration of one mirror element in the micromirror device according to the present invention, an insulation layer  40  is provided on a substrate  32 . The mirror element also includes one driving circuit  37 , for driving the micromirror, and one elastic hinge  36 , which is situated on the insulation layer  40 . The elastic hinge  36  supports one micromirror  31 , and an address electrode  33  connected to the driving circuit  37  is situated below the micromirror  31 . The address electrode  33  and the driving circuit  37 , which is connected to the address electrode  33 , electrically control the micromirror  31 . The elastic hinge  36  is connected to a hinge electrode  34  through an opening (not shown) in the insulation layer  40 . The hinge electrode  34  is grounded or held at a predetermined voltage. One mirror element of the micromirror device, according to the present invention, is configured as described above. Arranging multiple mirror elements  38 , as described above, on the substrate  32 , as shown in  FIG. 3 , can configure a micromirror device. 
     In this invention, the right and the left regions of the single address electrode, which protrude from the substrate and are positioned on both sides of the elastic hinge or the deflection axis of the micromirror, are referred to as first and second electrode parts, respectively, unless otherwise noted, and a coulomb force is generated between the first or the second electrode part and the micromirror by applying a voltage to the address electrode  33 . The use of the term, “applying a voltage”, referred to in this specification, is a paraphrase of changing a potential to a predetermined waveform. 
     The coulomb forces vary depending on the right and the left regions of the micromirror, and, in this way, the micromirror can be deflected to the right and the left sides of the elastic hinge and the deflection axis. When the micromirror is deflected to the right and the left sides of the deflection axis, it is preferable that the angles formed between the mirror surface and the vertical axis of the substrate in the position of the elastic hinge are symmetrical with respect to the vertical axis of the substrate in the position of the elastic hinge. 
     In the mirror element  38 , the micromirror  31  is formed, for example, with a metal of high reflectivity, or a dielectric multi-layer film, and the whole or part (such as the root, the top, and a middle portion) of the elastic hinge  36  for supporting the micromirror  31  is formed with a metal having a restoring force or a semiconductor material such as Si, etc. In this specification, the elastic hinge  36  is described based on the assumption that the elastic hinge  36  is implemented as a cantilever type and has elasticity for enabling the micromirror  31  to freely oscillate. The elastic hinge  36  can be implemented as a composite configuration composed of a torsion hinge and a cantilever or simply as a torsion hinge. For the address electrode  33 , for example, Al, Cu, or W, etc. may be used as a conductor. For the insulation layer  40 , SiO2, SiC, Si, etc. are available. As the substrate  32 , an 8-inch Si wafer is may be utilized. 
     The materials and the shapes of the constituent elements of the micromirror device, according to the present invention disclosed in this specification, may be varied depending on the purpose. The configuration and the controlling method shown in  FIGS. 4A to 4E  are described based on the assumption that the size of the right and the left regions of the single address electrode  33  and the micromirror  31  are configured asymmetrically with respect to the elastic hinge and the deflection axis 
     As is evident from the cross-sectional view of one mirror element shown in  FIG. 4A  and taken along the line IV-IV of  FIG. 3 , the initial state of the micromirror device  30  is the state in which the micromirror  31  is supported in a horizontal position to the substrate  32 .  FIGS. 4A to 4C  are described below based on the assumption that the initial state is the intermediate light state. 
       FIG. 4B  is a cross-sectional view of the mirror element  38  shown in  FIG. 4A , which is held in the ON light state, in the micromirror device, according to one preferred embodiment of to the present invention. In  FIG. 4B , coulomb forces F are applied between the first electrode part and the corresponding region of the micromirror  31 , and between the second electrode part and the corresponding region of the micromirror  31  by applying a voltage to the address electrode  33  in the initial state of  FIG. 4A . However, if the area size of the second electrode part is larger than that of the first electrode part, the Coulomb force applied between the second electrode part and the corresponding region of the micromirror  31  becomes higher than that of the Coulomb force applied between the first electrode part and the corresponding region of the micromirror. Accordingly, the micromirror  31  tilts to the side of the second electrode part. The deflection of the micromirror  31 , whereby incident light can be reflected as ON light, is changed by applying the voltage to the address electrode  33  as described above. 
       FIG. 4C  is a cross-sectional view of the mirror element shown in  FIG. 4A  and held in the OFF light state in the micromirror device, according to one preferred embodiment of the present invention. In  FIG. 4B , the micromirror  31  freely oscillates with the elasticity of the elastic hinge  36 . This oscillation is achieved by stopping the voltage applied to the address electrode  33  when the micromirror  31  is held in the ON light state. During the free oscillation, the micromirror  31  moves between the deflection angles for the ON light and the deflection angle for the OFF light. 
     The OFF light state is obtained by the timely reapplication of the voltage to the address electrode  33  when the distance r between the freely oscillating micromirror and the OFF light side, that is, the first electrode part of the address electrode  33 , is at a minimum. Coulomb forces F are applied between the first electrode part and the corresponding region of the micromirror, and between the second electrode part and the corresponding region of the micromirror. The Coulomb force F is inversely proportional to the square of the distance. Therefore, the coulomb force applied between the first electrode and the corresponding region of the micromirror is more intense than that of the force applied between the second electrode part and the corresponding region of the micromirror because the area size of the second electrode part is larger than that of the first electrode side when the distance between the first electrode part and the corresponding region of the micromirror decreases, and the distance between the second electrode part and the corresponding region of the micromirror increases. Accordingly, the micromirror  31  is drawn to the side of the first electrode part and contacts the address electrode  33 , whereby the micromirror is held in this position and the OFF light is obtained. 
     When the micromirror  31  is restored from the free oscillation state to the initial state, where the micromirror  31  is held horizontal to the substrate  32 , the oscillation of the micromirror  31  can be stopped by applying to the address electrode  33  a pulsed voltage of a predetermined waveform for a designated duration when the freely oscillating micromirror  31  is in suitable position. In an alternate method for restoring the micromirror  31  to the initial state, an additional electrode for stopping the oscillation of the micromirror  31  may be provided. In this configuration, suitable voltages may be applied to the two address electrodes to apply an equivalent coulomb force F. The present invention enables the micromirror  31  to be restored to the initial state by employing a single address electrode  33  and by using a pulsed voltage. 
     As described with reference to  FIGS. 4A to 4C , incident light can be controlled to be reflected as ON and OFF light beams by controlling the voltage to the single address electrode  33 . In comparison with conventional techniques, this new technique can reduce the number of address electrodes  33  necessary for controlling the micromirrors  31 , and the micromirrors  31  can be independently controlled. Additionally, since one address electrode  33  is required, the number of driving circuits  37 , each connected to an address electrode  33 , can also be reduced to one per micromirror  31 . 
     In an alternative to this preferred embodiment, the ON and OFF light states may be reversed in reference to the two parts of the address electrode  33 . The state where the micromirror  31  is deflected to the side of the second electrode part by applying the voltage to the single electrode may be defined as the OFF light state, and the state where the micromirror  31  is deflected to the side of the first electrode may be defined as the ON light state respectively in  FIGS. 4A to 4C , when the initial state is assumed to be the intermediate light state. 
       FIG. 4D  shows means for controlling the intensity of light reflected on the projection optical path in the intermediate light state, in which the surface of the micromirror freely oscillates between the ON, the intermediate, and the OFF light states. In the configuration shown in  FIG. 4D , the total amount of light reflected on the projection optical path can be adjusted to the intensity of intermediate light between the ON and the OFF light beams by causing the micromirror to repeat its free oscillation between the ON, the intermediate, and the OFF light states. In this way, one micromirror  31  can be controlled to deflect in the ON light, the intermediate light, and the OFF light states with a single address electrode  33 , and the quantity of light reflected on the projection optical path can be suitably adjusted. Accordingly, a higher gray scale can be achieved. Alternatively, the micromirror  31  can be changed to the intermediate light state or the OFF light state by applying the voltage to the address electrode when the initial state is assumed to be, for example, the ON light state by changing the heights of the first and the second electrode parts of the single address electrode  33  shown in  FIGS. 4A to 4D , or by adding a stopper or other similar component. 
     The three states of the micromirror  31  shown in  FIGS. 4A to 4D , the initial state of the micromirror, the state in which the micromirror is deflected to the first electrode part, and the state in which the micromirror is deflected to the second electrode part of the single address electrode  33  may all be defined as any of the ON light state, the OFF light state, and the intermediate light states in this specification. Additionally, using the elastic hinge  36  with a restoring force suitable for the purpose can control the free oscillation. 
       FIG. 4E  shows the circuit configuration where the driving circuit is connected to the single address electrode in one mirror element in the micromirror device according to the present invention shown in  FIGS. 4A to 4D . Since the present invention requires a single address electrode, the amount of wiring can be reduced, in comparison with that required by the conventional configuration of the two address electrodes shown in  FIG. 2B . 
     As described above, in  FIGS. 4A to 4D , incident light can be controlled to be reflected as the ON, the intermediate, and the OFF light beams by controlling the micromirror  31  with the single address electrode  33  in one mirror element  38  in the micromirror device according to the present invention. Therefore, the number of address electrodes  33  can be reduced from two to only one. Unlike the conventional techniques of applying two address electrodes for controlling the deflection angle of the micromirror. Instead, the number of driving circuits  37  connected to the address electrodes  33  can be reduced. As a result, the circuit configuration of the mirror element  38  can also be reduced to half of the conventional configuration (two circuits). Accordingly, the area occupied by the driving circuits  37  on the substrate  32  can be reduced. As a result, the area occupied by the driving circuits  37  on the substrate  32  becomes smaller, or a larger number of mirror elements can be arranged on the substrate  32  of the same size as a conventional one. When the same number of micromirror devices as that of a conventional device is arranged on a substrate, the substrate can be downsized, leading to reductions in the size of the micromirror device itself. As a matter of course, two completely separated electrodes may still be provided, and one memory provided for the driving circuit may apply voltages to the two electrodes, for example, as shown in  FIG. 2B . 
     Furthermore, one large capacitor can be arranged below the micromirror, and the area of the capacitor plate determines the amount of the applied voltage. Alternatively, two separated capacitors may be arranged. As a result, the voltage applied to the electrode can be further increased, thus eliminating the influence of the voltage drop of the capacitor. Also, the influence of the photoelectric effect exerted by illumination light can be reduced. 
     Accordingly, the micromirror device according to the present invention is applicable to exemplary embodiment for a future super hi-vision with a high-definition resolution, a face-mounted display, an electric viewfinder, etc., and can reduce the sizes of the display device with 4K2K and 8K4K resolutions. Furthermore, according to the present invention, the configuration of the driving circuit can be made simpler than the conventional complicated configuration of two driving circuits, enabling the production of the micromirror device at lower cost. 
     The following descriptions are for the second to fourth preferred embodiments according to the present invention to disclose micromirror devices configured by arranging on a substrate multiple mirror elements each comprising one micromirror that is deflectable in multiple directions and supported by one elastic hinge, a single address electrode that corresponds to each micromirror and has shapes or properties asymmetrical with respect to the deflection axis of the micromirror, and one driving circuit that is connected to the address electrode and intended to control the micromirror to deflect in at least two directions. 
     Second Preferred Embodiment 
     According to the second preferred embodiment, the ON or the OFF light state can be implemented by tilting the micromirror with mutually different coulomb forces generated respectively between the micromirror and the first electrode part, and between the micromirror and the second electrode part by applying a voltage to the single address electrode based on the assumption that the initial state is the intermediate light state. 
     The second preferred embodiment of the present invention discloses the micromirror device including a plurality of mirror elements with each micromirror controlled to deflect to the ON and the OFF light states by forming an address electrode as one component of one mirror element, and by making the areas of the right and the left regions of the single address electrode asymmetrical with respect to the deflection axis of the micromirror. 
       FIGS. 5A to 5D  show a method for controlling the micromirror  31  to deflect to the ON and the OFF light states by making the sizes of the first and the second electrode parts of the single address electrode  33  with different sizes in one mirror element  38  in the micromirror device according to one preferred embodiment of the present invention. The configurations and the controlling methods shown in  FIGS. 5A to 5D  and  6 A to  6 E are described based on the assumption that the mirror element  38  is configured symmetrically with respect to the elastic hinge  36  or the deflection axis of the micromirror  31  except that the area sizes of the first and the second electrode parts of the single address electrode  33  are different and asymmetrical. 
     A method for controlling the micromirror  31  to deflect to the ON or the OFF light state when the area sizes of the first and the second electrode parts differ in the single address electrode  33  as shown in  FIGS. 5A to 5D  in one mirror element  38  in the micromirror device according to the present invention is described with reference to  FIGS. 6A to 6E . 
       FIG. 5A , viewed in the direction Z of  FIG. 3 , shows the correspondence between the areas of the micromirror  31  and the address electrode  33  when the mirror element  38  is configured by making the areas and the shapes of the first and the second electrode parts of the single address electrode  33  different in order to vary the positions in which coulomb forces F is applied between the micromirror and the electrode parts of the address electrode. 
       FIG. 5B  is a cross-sectional view of the mirror element  38  taken along the line IV-IV of  FIG. 3  in the micromirror device shown in  FIG. 5A .  FIG. 5A  shows the configuration where the single address electrode  33  is arranged below the micromirror  31  and the area sizes of the first electrode part  33   a  and the second electrode part  33   b  of the address electrode  33  differ and are formed as one piece across the elastic hinge  36  or the deflection axis in one mirror element  38 . In  FIG. 5A , the area of the first electrode part  33   a  on the left side of the elastic hinge  36  is larger than that of the second electrode part  33   b  of the address electrode  33  on the right side of the elastic hinge  36 .  FIG. 5B  is a cross-sectional view of the configuration of the mirror element taken along the line IV-IV of  FIG. 3  in the micromirror device shown in  FIG. 5A . This figure shows the configuration where the single address electrode  33  is arranged as one piece below one micromirror  31  on the substrate  32 . 
       FIG. 5C , viewed in the Z direction of  FIG. 3 , shows the correspondence between the areas of the micromirror and the address electrode when the mirror element  38  configured with different area sizes of the first and the second electrode parts of the address electrode as an alternate embodiment of  FIG. 5A .  FIG. 5D  is the cross-sectional view of the mirror element  38  taken along the line IV-IV of  FIG. 3  in the micromirror device shown in  FIG. 5C . 
     This figure shows a single address electrode  33  linked within the substrate  32  arranged below the micromirror  31  so that the area sizes of the first and the second electrode parts  33   c  and  33   d  of the address electrode  33 , which protrude from the substrate  32 , are different. Except for the difference between the area sizes, the configuration of the mirror element in this figure is the same as that of the mirror element shown in  FIG. 5A . In the configuration shown in  FIG. 5C , the area  33   c  of the first electrode part of the address electrode is larger than the area  33   d  of the second electrode part of the address electrode. 
       FIG. 5D  is a cross-sectional view of the mirror element  38  shown in  FIG. 5C  and taken along the line IV-IV of  FIG. 3 . This figure shows the configuration where the two parts of the single address electrode  33  arranged below the micromirror protrude from the substrate  32  as the first and the second electrode parts  33   c  and  33   d . The two parts of the single address electrode  33 ,  33   c  and  33   d , are linked as one piece within the substrate  32  and their area sizes differ. In this case, the address electrode  33  may be transformed into another shape, such as the shape of a donut, in order to make the area sizes of the first and the second electrode parts of the address electrode  33  different. 
     A method for controlling the single micromirror  31  in one mirror element  38  in the micromirror device to deflect to the ON and the OFF light states when the area sizes of the first and the second electrode parts of the address electrode  33  differ according to the present invention is described. This specification assumes that the initial state where the micromirror  31  is horizontal to the substrate  32  is the intermediate light state, and that the larger electrode part of the address electrode, namely, the first electrode part  33   a  or  33   c  shown in  FIG. 5A  or  5 C, is the deflection direction of the mirror for reflecting the OFF light, and that the smaller electrode part, namely, the second electrode part  33   b  or  33   d  shown in  FIG. 5A  or  5 C, is defined as the deflection direction of the mirror for reflecting the ON light. A method for controlling the micromirror  31  to change from the initial state to the OFF light state, and further to the free oscillation state is described with reference to  FIG. 6A  showing a chart that represents the position of the micromirror  31 , and a chart that represents the voltage of the address electrode  33  during the same time period. 
     In  FIGS. 6A to 6E , the vertical axis of the chart that represents the position of the micromirror  31  indicates a move to the side of the ON light state or the OFF light state with respect to the intermediate light state as the initial state. The vertical axis of the chart that represents the voltage of the address electrode  33  indicates the state where the voltage is applied as the ON light state with respect to the initial state of 0V, that is, the state where the voltage is not applied. The horizontal axes of both of the charts indicate a time axis t that represents the same time period. 
     In  FIG. 6A , the position of the micromirror  31  is held in the initial state, that is, the intermediate light state up to a time t 1 , and the voltage is not applied to the address electrode  33  during this time period. When the micromirror  31  is deflected from the initial state to the OFF light state, the micromirror  31  is tilted toward the first electrode part  33   a  (of  FIG. 5A ) or  33   c  (of  FIG. 5C ) of the address electrode  33  by applying the voltage to the address electrode  33  as indicated by the time t 1  to a time t 2 . As a result, the micromirror  31  can be controlled to deflect to the OFF light state. This can be understood according to the principle that the coulomb force F represented by the following equations (1) and (2) is more intensified and applied between the first electrode part  33   a  or  33   c  with the larger area of the address electrode  33  and the micromirror  31 , since the electrode part  33   a  or  33   c  with the larger area can store a larger amount of charge, than the electrode part  33   b  (of  FIG. 5A ) or  33   d  (of  FIG. 5D ) with the smaller area when the distance r between the micromirror  31  and the first electrode part  33   a  or  33   c  on the OFF light side of the address electrode  33  is the same as that between the micromirror  31  and the second electrode part  33   b  or  33   d  on the ON light side of the address electrode  33  in the initial state. [[NOTE: please re-read this paragraph as I&#39;m not sure what it&#39;s saying]] 
                   F   =         1     4   ⁢   π   ⁢           ⁢     r   2         ·     1   ɛ       ⁢     q   1     ⁢     q   2               (   1   )               
Where r is the distance between the address electrode  33  and the micromirror  31 , ε is permittivity, and q 1  and q 2  are the amounts of charge stored.
 
     The Coulomb force F can be also represented by the following equation (2).
 
 F=k′e SV   2 /2 h   2   (2)
 
where S is the area size of the address electrode  33   a ( 33   c ) or  33   b ( 33   d ), h is the distance between the mirror  31  and address electrode  33   a ( 33   c ) or  33   b ( 33   d ), e is the permittivity between the mirror  31  and address electrode  33   a ( 33   c ) or  33   b ( 33   d ), V is the voltage applied to the address electrode  33   a ( 33   c ) or  33   b ( 33   d ), and k′ is a correction coefficient.
 
     When the voltage of the address electrode  33  is reduced to 0V in the OFF light state of the micromirror  31 , namely, when the application of the voltage is stopped, the coulomb force for deflecting the micromirror  31  to the OFF light state is lost, and the micromirror  31  enters the free oscillation state where the micromirror  31  deflects to the opposite side for deflecting the micromirror  31  to the ON light state with the elasticity of the elastic hinge  36  after passing through the position horizontal to the substrate in the initial state, and the micromirror  31  is restored to the OFF light state. This free oscillation state continues while its amplitude is being gradually reduced with attenuation caused by air resistance and a conversion into thermal energy by the elastic hinge. In a short time of 1/30 sec or shorter that is the standard period for one frame display on a display device, this attenuation can be set to a level that can reduce its influence. 
     The series of operations for causing the micromirror  31  to freely oscillate by tilting the micromirror  31  in the initial state, namely, the operations for causing the micromirror  31  to freely oscillate after tilting the micromirror  31  from the state horizontal to the substrate  32  is hereinafter referred to as “initial operations” in this specification. 
     A method for controlling the micromirror  31  to change from the initial state to the OFF light state, and further to the ON light state is described next with reference to  FIG. 6B  showing a chart that represents the position of the micromirror  31  along with a chart that represents the voltage of the address electrode  33  during the same time period, as indicated by the time axis t. 
     Similar to  FIG. 6A , the position of the micromirror  31  is controlled to be held in the initial state that is the intermediate light state up to a time t 3  also in  FIG. 6B , and the voltage is not applied to the address electrode  33  in this time period. 
     When the micromirror  31  is deflected from the initial state to the OFF light state, the micromirror  31  is tilted toward the first electrode part  33   a  or  33   c  of the address electrode  33  by applying the voltage to the address electrode  33  as indicated by the duration of time t 3  to a time t 4 . As a result, the micromirror  31  can be deflected to the OFF light state. 
     A controlling method for deflecting the micromirror  31  from the OFF light state to the ON light state is described next. The micromirror  31  that is deflected from the initial state to the OFF light state enters the free oscillation state by temporarily reducing the voltage of the address electrode  33  to 0V for the duration of time t 4  to time t 5 . The operations described up to this point are the initial operations described with reference to  FIG. 6A . By the timely application of the voltage to the second electrode part  33   b  or  33   d  with the smaller area on the ON light side of the address electrode at the time t 5  when the micromirror  31  becomes close to the second electrode part  33   b  or  33   d , the micromirror  31  can be held on the ON light side. As a result, the micromirror  31  can be held in the ON light state. 
     This is implemented as follows: the coulomb force F represented by the equation (1) is more intensified by the square of the distance r than by the amounts of charge q 1  and q 2 , and a higher coulomb force F is applied to the side of the shorter distance r between the address electrode  33  and the micromirror  31  by suitably adjusting both the area sizes of the ON and the OFF light sides of the single address electrode  33  even when the area size of the second electrode part of the address electrode is smaller than that of the first electrode part, whereby the micromirror  31  can be deflected to the ON light side. In this way, the micromirror  31  can be controlled to change from the initial state to the OFF light state, and further to the ON light state. 
     A method for controlling the micromirror  31  to change from the initial state to the ON light state, and further to the OFF light state is described next with reference to  FIG. 6C  showing the chart that represents the position of the micromirror  31  along with the chart that represents the voltage of the address electrode  33  during the same time period, as indicated by the time axis t. 
     In  FIG. 6C , the micromirror  31  is held in the initial state that is the intermediate light state up to a time t 6 , and a voltage is not applied. When the micromirror  31  is deflected from the initial state to the ON light state, the micromirror  31  is tilted toward the first electrode part  33   a  or  33   c  with the larger area of the address electrode  33  by temporarily applying the voltage to the address electrode  33  as indicated by the time t 6  to a time t. As a result, the micromirror  31  enters the OFF light state. This operation is required to cause the micromirror  31  to freely oscillate by tilting the micromirror  31  from one side to another. Alternatively, the mirror can be deflected in the reverse direction by reducing the voltage applied to the address electrode  33  to a lower level or to 0V when the required elastic spring force remains even if the micromirror is not completely deflected to the OFF light state, or before the micromirror  31  is deflected to the OFF light state. The micromirror tilted from the initial state to the OFF light state enters the free oscillation state by temporarily reducing the voltage of the address electrode  33  to 0V from the time t 7  to a time t 8 . By timely applying the voltage to the second electrode part  33   b  or  33   d  with the smaller area on the ON light side of the address electrode  33  at the time t 8  when the micromirror  31  becomes close to the second electrode part  33   b  or  33   d  on the ON light side during the free oscillation, the micromirror  31  can be held on the ON light side. As a result, the micromirror  31  can be deflected to the ON light state. Specifically, the Coulomb force F is applied when the micromirror  31  is changed from the OFF light state to the ON light state in  FIG. 6B . Inversely, when the micromirror is controlled to deflect from the ON light state to the OFF light state, the micromirror  31  reenters the free oscillation state by reducing to 0V the voltage of the address electrode  33  of the micromirror  31  held in the ON light state as indicated by a time t 9  to a time t 10 . 
     The micromirror  31  is controlled and held in the OFF light state by applying the voltage to the address electrode  33  when the micromirror  31  becomes close to the side of the second electrode part  33   b  or  33   d  inversely to the case where the micromirror is changed to the ON light state. Because the distance r between the address electrode  33  and the micromirror  31  predominantly functions over the area size of the first or the second electrode part of the address electrode  33  in the equation (1) as in the description of the coulomb force F applied when the micromirror  31  is deflected from the OFF light state to the ON light state as shown in  FIG. 6B . In this way, the micromirror  31  can be controlled to change from the initial state to the ON light state, and further to the OFF light state. 
     A method for controlling the micromirror  31  to change from the OFF light state of the micromirror  31  to the initial state is described next with reference to  FIG. 6D  showing the chart that represents the position of the micromirror  31  along with the chart that represents the voltage of the address electrode  33  during the same time period, as indicated by the time axis t. 
     Assume that the micromirror  31  is held in the OFF light state up to a time t 11  by applying the voltage to the address electrode  33  in  FIG. 6D . When the micromirror  31  is restored from the OFF light state to the initial state, a suitable pulsed voltage is applied as indicated by the time t 11  to a time t 13 . In this case, the micromirror  31  enters the free oscillation state by reducing the voltage of the address electrode  33  to 0V at the time t 11  in the OFF light state of the micromirror  31 , and the micromirror  31  can be restored to the initial state by generating a coulomb force F that draws the micromirror  31  to the OFF light side, namely, by generating the force reverse to the moving direction of the micromirror  31  by temporarily applying the suitable voltage to the address electrode  33  in a suitable distance r between the address electrode  33  and the micromirror  31  while the micromirror  31  is moving from the OFF light state to the ON light state. Accordingly, the micromirror  31  can be restored to the initial state by applying the pulsed voltage to the single address electrode  33 . If the micromirror  31  cannot be completely restored to the initial state by applying the pulsed voltage only once, such a control may be repeated multiple times. 
     As described above, the micromirror  31  can be controlled to restore from the OFF light state to the initial state. 
     A method for restoring the micromirror  31  from the ON light state to the initial state (the inverse of  FIG. 6D ) is described with reference to  FIG. 6E  showing the chart that represents the position of the micromirror  31  along with the chart that represents the voltage of the address electrode  33  during the same time period, as indicated by the time axis t. 
     In  FIG. 6E , the micromirror  31  is controlled and held in the ON light state up to a time t 14  by applying the voltage to the address electrode  33 . When the micromirror  31  is restored from the ON light state to the initial state, a suitable pulsed voltage is applied as indicated by the time t 14  to a time t 16 . This is implemented as follows: the micromirror starts to freely oscillate by reducing the voltage of the address electrode  33  to 0V at time t 14  in the OFF light state of the micromirror  31 , and an acceleration reverse to the moving direction of the micromirror  31  is generated by causing the coulomb force F to draw the micromirror  31  back to the ON light side by temporarily applying a suitable voltage to the address electrode at a time t 15  when the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point while the freely oscillating micromirror is moving from the ON light side to the OFF light side, whereby the micromirror can be restored to the initial state quickly or within a predetermined time. This is because the distance r between the address electrode  33  and the micromirror  31  predominantly functions over the area size of the first or the second electrode part of the address electrode  33  in the equation (1) in a similar manner as in  FIG. 6B . Accordingly, the micromirror  31  can be restored to the initial state by applying the pulsed voltage to the single address electrode  33 . In this way, the micromirror  31  can be restored from the ON light state to the initial state. 
       FIGS. 6D and 6E  show the nearly linear changes of the micromirror  31  from the deflection state to the horizontal initial state. However, the locus of the change of the micromirror  31  may be a locus representing that the micromirror  31  changes toward the initial state after being again deflected in the same direction. 
     The micromirror  31  can therefore be stopped in a shorter time than that required for restoring the micromirror to the initial state by being naturally attenuated after the micromirror  31  starts to freely oscillate. The techniques of the present invention is not limited to the loci of the micromirror  31  and the waveforms of the applied voltage shown in  FIGS. 6D and 6E . 
     As described for  FIGS. 6A to 6E , the micromirror  31  can be controlled to change to the OFF light state after the initial operations by applying the voltage to the address electrode  33  when the micromirror  31  becomes close to the electrode part on the OFF light side. In contrast, the micromirror  31  can be controlled to change to the ON light state by applying the voltage to the address electrode  33  when the micromirror  31  becomes close to the electrode part on the ON light side. Furthermore, the micromirror  31  can be restored from the free oscillation state to the initial state by applying the pulsed voltage to the address electrode  33 . 
     The configurations and the controlling methods according to the present invention shown in  FIGS. 5A to 5D  and  6 A to  6 E are characterized in that the area sizes of the first and the second electrode parts of the single address electrode  33  are made different and asymmetrical in order to implement the initial operations for causing the micromirror  31  to freely oscillate. Furthermore, the micromirror  31  can be controlled to change to the ON and the OFF light states by applying the voltage when the freely oscillating micromirror  31  becomes close to the ON or the OFF light side that is the first or the second electrode part of the address electrode  33 . 
     The initial state, the deflection state for deflecting the micromirror  31  of the first electrode part  33   a  or  33   c  with the larger area of the address electrode, and the deflection state for deflecting the micromirror  31  to the second electrode part  33   b  or  33   d  with the smaller area of the address electrode may be made to correspond to any of the ON, the OFF, and the intermediate light states as needed. However, it is preferable to make the OFF and the ON light states correspond to the deflection state for deflecting the micromirror  31  to the electrode part with the larger area. Also, it preferable to control the deflection state for deflecting the micromirror  31  to the electrode part with the smaller area respectively as in this preferred embodiment. This is because the micromirror  31  must be once deflected to the ON light state as the initial operations for causing the micromirror  31  to freely oscillate if the ON light state is made to correspond to the deflection state for deflecting the micromirror  31  to the electrode part with the larger area of the single address electrode, and light that is not originally related to image projection is projected due to the incidence of light to the projection optical path at this time. This is not preferable for image projection. 
     Third Preferred Embodiment 
     The third preferred embodiment discloses the micromirror device that includes a plurality of mirror elements in each of which the micromirror can be controlled to deflect to the ON and the OFF light states by making the right and the left regions of the address electrode with different heights. The address electrode is formed as one piece and arranged across the elastic hinge or the deflection axis of the micromirror. 
       FIGS. 7A to 7D  show a method for controlling the micromirror  31  to deflect to the ON or the OFF light state with the first and the second electrode parts of the single address electrode  33  have different heights in one mirror element  38  in the micromirror device according to the present invention. The mirror element  38  shown in  FIGS. 7A to 7D  is described for a configuration that the first and the second electrode parts of the address electrode  33  are symmetrically placed with respect to the elastic hinge or the deflection axis of the micromirror  31 . But the first and the electrode parts have different heights. 
       FIG. 7A  shows the correspondence between the sizes of the areas of the micromirror and the address electrode by viewing the mirror element  38  in the direction Z of  FIG. 3 . The first and the second electrode parts of the single address electrode  33  have different heights in one mirror element  38  in the micromirror device according to the present invention.  FIG. 7B  is a cross-sectional view of the mirror element  38  shown in  FIG. 7A  and taken along the line IV-IV of  FIG. 3 . 
     In  FIG. 7A  the first electrode part  33   e  and the second electrode part  33   f  are arranged below the micromirror  31  with the first electrode part  33   e  and the second electrode part  33   f  have different heights while their area sizes are equal. The single address electrode is configured as one piece across the elastic hinge  36  or the deflection axis of the micromirror. Specifically, the second electrode part  33   f  on the right side of the elastic hinge  36  is higher than the first electrode part  33   e  on the left side of the elastic hinge. 
       FIG. 7B  is a cross-sectional view of the mirror element  38  shown in  FIG. 7A  and taken along the line IV-IV of  FIG. 3  in the micromirror device. The single address electrode  33  positioned below the micromirror  31  is configured as one piece on the substrate  32 . The first electrode part  33   e  and the second electrode part  33   f  have different heights.  FIG. 7C  shows the correspondence between the sizes of the areas of the micromirror and the address electrode by viewing the mirror element  38  in the direction Z of  FIG. 3 . The mirror element  38  includes the first electrode part  33   g  and the second electrode part  33   h  of the single address electrode have different heights as an alternate embodiment of  FIG. 7A .  FIG. 7D  is a cross-sectional view of the mirror element  38  shown in  FIG. 7C  and taken along the line IV-IV of  FIG. 3  in the micromirror device according to the third preferred embodiment of the present invention. 
       FIG. 7C  shows the single address electrode linked within the substrate  32  below the micromirror  31  with the first electrode part  33   g  and the second electrode part  33   h  protruding from the substrate  32  have different heights. Specifically, the height of the second electrode part  33   h  of the single address electrode is higher than that of the first electrode part  33   g.    
       FIG. 7D  shows the configuration where the first electrode part  33   g  and the second electrode part  33   h  protruding from the substrate  32  have different heights and both of the electrode parts are linked within the substrate in the single address electrode  33  positioned below the micromirror  31 . 
     The address electrode  33  may be reconfigured to make the first and the second electrode parts of the address electrode  33  have different heights as needed. When the sizes or the positions of the right and the left regions of the address electrode are symmetrical and only their heights are different, micromirror  31  deflects to the right and the left regions with different angles. With this configuration, the deflection angles to the right and the left sides of the micromirror  31  can be made equal with a protrusion stopper in the electrode part with a lower height. 
     This invention thus discloses a method for controlling the micromirror  31  to deflect to the ON and the OFF light state when the ON and the OFF light sides that are the first and the second electrode parts, respectively, differ in height in the single address electrode  33  of one mirror element  38  in the micromirror device. The method for controlling the micromirror  31  to deflect to the ON and the OFF light states in this preferred embodiment can also be understood according to the controlling method described with reference to  FIGS. 6A to 6E . 
     The method for controlling the mirror element according to the third preferred embodiment is briefly described below. By applying a voltage, the micromirror  31  is deflected from the initial state; the micromirror is tilted to the higher second electrode part  33   f  or  33   h  of the address electrode  33  according to the equation (1). Specifically, a higher coulomb force F is applied between the second electrode part  33   f  with a greater height or  33   h  of the address electrode  33  and the micromirror  33  because their distance r becomes shorter than that between the lower first electrode part  33   e  or  33   g  and the micromirror  31  in the initial state of the micromirror  31 . 
     A method for controlling the micromirror  31  to deflect to the OFF or the ON light state is described next. The micromirror  31  when tilted from the initial state and enters the free oscillation state, the voltage of the address electrode  33  is temporarily reduced to 0V. By timely applying the voltage during the free oscillation when the micromirror  31  comes close to the first electrode part  33   e  or  33   g  or the second electrode part  33   f  or  33   h  that is the ON or the OFF light side, the micromirror  31  can be controlled and held on the ON or the OFF light side. As a result, the micromirror  31  is controlled and held in the ON or the OFF light state. In this case, the coulomb force F represented by the equation (1) is more intensified by the distance r between the micromirror  31  and the address electrode  33 , and a higher coulomb force F is therefore applied to the side of the shorter distance r. Thus, the micromirror  31  can be deflected to the ON or the OFF light side. In this way, the micromirror is deflected from the initial state to the OFF or the ON light state. 
     Also a method for restoring the micromirror  31  from the OFF or the ON light state to the initial state in this preferred embodiment can also be implemented according to the controlling method described with reference to  FIGS. 6A to 6E . Namely, by applying a suitable pulsed voltage in the ON or the OFF light state of the micromirror  31 , the micromirror can be restored to the initial state. Specifically, by temporarily reducing the voltage of the address electrode  33  to 0V, the micromirror  31  starts to freely oscillate. An acceleration reverse to the moving direction of the micromirror  31  is generated. The coulomb force F to draws the micromirror  31  to the side opposite to the side to which the micromirror  31  is moving when the voltage to the address electrode  33  is temporarily reduced and the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point in the moving direction of the freely oscillating micromirror  31 . Thus the micromirror  31  is restored to the initial state. Accordingly, by applying a pulsed voltage of a predetermined duration of time to the single address electrode  33 , the micromirror  31  is restored from the ON or the OFF light state to the initial state. 
       FIG. 7E  shows the configuration to control the micromirror  31  to deflect to the ON and the OFF light states when the first electrode part  33   i  and the second electrode part  33   j  of the single address electrode  33  across the elastic hinge  36  or the deflection axis of the micromirror have different heights and area sizes as one preferred embodiment of the mirror element in the micromirror device according to the present invention. In  FIG. 7E , the mirror element  38  is configured symmetrically with respect to the elastic hinge  36  or the deflection axis of the micromirror. But the first electrode part  33   i  and the second electrode part  33   j  of the single address electrode  33  have different heights and the areas. 
       FIG. 7E  shows the configuration implemented by combining the configurations shown in  FIGS. 5A and 5C , and  7 A and  7 C. This configuration is characterized in that the first electrode part  33   i  and the second electrode  33   j  of the single address electrode  33  have different area sizes and heights of the ON and the OFF light sides 
     A person having ordinary skill in the art can easily understand the controlling method used in the configuration shown in  FIG. 7E  according to the controlling method described with reference to  FIGS. 5A to 5D ,  6 A to  6 E, and  7 C to  7 D. 
     Fourth Preferred Embodiment 
     The fourth preferred embodiment discloses the configuration to control the micromirror to deflect to the ON or the OFF light state with a coulomb force. The top surfaces of the right and the left regions of the single address electrode formed as one piece and arranged across the elastic hinge  36  or the deflection axis of the micromirror have layers with different permittivities in one mirror element in the micromirror device according to the fourth preferred embodiment of the present invention. 
       FIG. 8A  shows the configuration where the micromirror  31  is controlled to deflect to the ON or the OFF light state by forming the top surfaces of the first and the second electrode parts of the address electrode  33  in one mirror element  38  in the micromirror device as one preferred embodiment of the present invention with materials  81   a  and  81   b  have different permittivities. The mirror element  38  is configured symmetrically with respect to the elastic hinge  36 . But the materials  81   a  and  81   b  on the tops of the first and the second electrode parts of the single address electrode  33  have different permittivities. 
       FIG. 8A  shows the cross-section of the configuration where the materials  81   a  and  81   b  on the tops of the first and the second electrode parts of the single address electrode  33  positioned below the micromirror  31  in one mirror element in the micromirror device according to this preferred embodiment of the present invention have different permittivities. 
     The address electrode  33  may be suitably reconfigured with the materials  81   a  and  81   b  on the tops of the first and the second electrode parts of the address electrode  33  have different permittivities. For example, metals such as Si, SiC, Si3N4, Al203, and HfO 2  that is referred to as a high-k material and has been attracting attention in recent years as a material with high permittivity available to the shrinkage of a semiconductor are suitably selected and used as the materials  81   a  and  81   b . This material with different permittivities may be selected for the right and the left regions of the address electrode  33 . Alternatively, the thicknesses and the materials of films for protecting the electrodes may be varied respectively for the right and the left regions. 
     This invention thus discloses a method for controlling the micromirror  31  to deflect to the ON and the OFF light states by forming the tops of the first and the second electrode parts of the single address electrode  33  with the materials  81   a  and  81   b  have different permittivities in one mirror element  38  in the micromirror device. Specifically, the method to control the micromirror  31  in this preferred embodiment is described with reference to  FIGS. 6A to 6E . The method for controlling the micromirror in the mirror element in the fourth preferred embodiment is briefly described below. 
     When the micromirror  31  is deflected from the initial state, the micromirror is tilted to the side of the address electrode  33  configured with a material with low permittivity, according to the equation (1) by applying a voltage to the address electrode  33 . Because the permittivity ε of the side of the address electrode  33  is configured with the material of low permittivity than that of the side of the address electrode  33  configured with the material with high permittivity. A higher coulomb force F is therefore applied to the side of the address electrode  33  configured with the material with low permittivity. 
     By temporarily reducing the voltage of the address electrode  33  to 0V, the micromirror  31  is tilted from the initial state and starts to freely oscillate. When the freely oscillating micromirror  31  becomes close to the ON or the OFF light side of the address electrode, by timely applying a suitable voltage to the address electrode  33 , the micromirror  31  can be held on the ON or the OFF light side that is the first or the second electrode part. As a result, the micromirror  31  is controlled to deflect to the ON or the OFF light state. Because the Coulomb force F represented by the equation (1) is more intensified by the square of the distance r between the micromirror  31  and the address electrode  33  than by the permittivity ε of the address electrode  33 . A higher coulomb force F is therefore applied to the side of the shorter distance r between the address electrode  33  and the micromirror  31 , whereby the micromirror  31  is tilted to the ON or the OFF light side of the address electrode  33  with the shorter distance r from the micromirror  31 . Therefore, the micromirror  31  is controlled to change from the initial state to the OFF or the ON light state. 
     According to the controlling method described with reference to  FIGS. 6A to 6E , a method for controlling the micromirror  31  to restore from the OFF or the ON light state to the initial state is described. Namely, by applying a suitable voltage in the ON or the OFF light state of the micromirror  31 , the micromirror  31  can be restored from the ON or the OFF light state to the initial state. 
     Specifically, by temporarily reducing to 0V the voltage of the electrode part of the address electrode  33  holding the micromirror  31  when the micromirror  31  starts to freely oscillate, an acceleration reverse to the moving direction of the micromirror  31  is generated thus causing the coulomb force F to draw the micromirror  31  back to the side opposite to the side. By temporarily applying the voltage to the address electrode  33  when the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point, the freely oscillating micromirror  31  is moving from the side that holds the micromirror  31  toward the opposite side, whereby the micromirror  31  can be restored to the initial state. In this way, the micromirror  31  can be restored from the ON or the OFF light state to the initial state by applying the pulsed voltage to the single address electrode  33 . 
       FIG. 8B  shows a mirror configuration to control the micromirror  31  to deflect to the ON or the OFF light state. A material  82  with a permittivity different from that of the address electrode  33  at the top of one of the electrode parts of the single address electrode  33  in one mirror element  38  in the micromirror device. 
       FIG. 8B  depicts the mirror element  38  configured symmetrically with respect to the elastic hinge  36  or to the deflection axis of the micromirror, While the top surfaces of the address electrode  33  on either of the tops of the ON and the OFF light sides of the single address electrode  33  are formed with different dielectric materials in the mirror element  38  in the micromirror device as one preferred embodiment of the present invention. 
     The configuration shown in  FIG. 8B  is characterized in that either of the tops of the electrode parts of the single address electrode  33  is formed with material  82  that has a permittivity different from that of the address electrode  33  as an alternate embodiment of the configuration of one mirror element  38  in the micromirror device according to the present invention shown in  FIG. 8A . 
     According to the controlling method described with reference to  FIG. 8A , a person having ordinary skill in the art can easily understand a method for controlling the micromirror  31  to deflect to the ON or the OFF light state with the single address electrode  33  in the mirror element  38  in the micromirror device shown in  FIG. 8B . 
     The fifth to seventh preferred embodiments of the present invention disclose the micromirror devices supported on a substrate. The substrate includes a plurality of mirror elements each comprising at least one elastic hinge that can deflect a micromirror in a plurality of directions. One micromirror has shapes or properties asymmetrical with respect to the deflection axis. The mirror further includes a single address electrode and one driving circuit connected to the address electrode to control the micromirror to deflect in at least two directions. 
     Fifth Preferred Embodiment 
     The fifth preferred embodiment discloses the micromirror device where the micromirror is controlled to deflect to the ON and the OFF light states with a coulomb force. The regions of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode across the elastic hinge or the deflection axis of the micromirror are formed with materials with different permittivities. 
       FIG. 9  depicts the mirror element  38  configured symmetrically with respect to the elastic hinge  36  while the regions respectively face and correspond to the first and the second electrode parts of the single address electrode  33  of the micromirror, are formed with materials  91   a  and  91   b  with different permittivities.  FIG. 9  shows the regions of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33 , are configured with the materials  91   a  and  91   b  with different permittivities in one mirror element  38  in the micromirror device according to the fifth preferred embodiment of the present invention. A micromirror  92  is formed as one piece to totally cover the surface of the micromirror by combining the materials  91   a  and  91   b  with different permittivities, which respectively correspond to the first and the second electrodes of the address electrode, is stacked on the surface of the micromirror positioned immediately below the micromirror  92  in order to enable the micromirror to reflect incident light. The materials  91   a  and  91   b  have different permittivities may be implemented to reflect the incident light to configure as a reflection mirror. Alternatively, a plate made of a material with high or low permittivity may be formed on either of the right and the left regions of the micromirror. 
     According to the fourth preferred embodiment of the present invention, a method for controlling the micromirror to deflect to the ON and the OFF light states is disclosed. In one mirror element  38  in the micromirror device the regions of the micromirror respectively correspond to the first and the second electrode parts of the single address electrode  33 , are configured with the materials  91   a  and  91   b  with different permittivities. The controlling method according to this preferred embodiment is disclosed according to the controlling method described with reference to  FIGS. 6A to 6E . The controlling method in the mirror element according to the fifth preferred embodiment is briefly described below. 
     The micromirror is deflected from the initial state with the micromirror held horizontally relative to the surface of the substrate  32  in the mirror element  38 .  FIG. 9  shows the micromirror is tilted to the side of the material with lower permittivity of the micromirror according to the equation (1) by applying a voltage to the address electrode  33 . Because in the initial state of the micromirror 
     A higher coulomb force F is applied to the side of the material with lower permittivity in comparison with the side of the material with higher permittivity. By temporarily reducing the voltage of the address electrode  33  to 0V, the micromirror is tilted from the initial state and starts to freely oscillate. By timely applying the voltage to the address electrode  33  when the micromirror becomes close to the first or the second electrode part during the free oscillation, the micromirror can be controlled to deflect to the ON or the OFF light side. As a result, the micromirror can be controlled to be held in the ON or the OFF light state. 
     In this case, the coulomb force F represented by the equation (1) is more intensified inversely proportional to the square of the distance r between the micromirror and the address electrode  33  than by the permittivity ε of the material  91   a  or  91   b  with a different permittivity. The higher coulomb force is therefore applied to the side of the shorter distance r between the micromirror and the address electrode  33 , whereby the micromirror is tilted to the ON or the OFF light side. Thus the micromirror can be controlled to deflect from the initial state to the OFF or the ON light state. 
     Also, according to the controlling method described with reference to  FIGS. 6A to 6E , a method for controlling the micromirror to restore from the OFF or the ON light state to the initial state is disclosed. Namely, the micromirror can be restored from the ON or the OFF light state with the micromirror tilted and held to the initial state by applying a suitable pulsed voltage. This is implemented as follows: the micromirror  31  starts to freely oscillate by temporarily reducing the voltage of the side of the address electrode  33  holding the micromirror to 0V. Specifically, this is achieved by grounding the address electrode  33 . It causes an acceleration reverse to the moving direction of the micromirror  31  and causing the coulomb force F to draw the micromirror back to the side opposite to the side to which the micromirror is moving when temporarily applying the voltage to the address electrode  33  as the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point in the moving direction of the micromirror. Therefore, the micromirror can be restored to the initial state. By applying the pulsed voltage to the single address electrode  33  in this way, the micromirror can be restored from the ON or the OFF light state to the initial state. 
     Sixth Preferred Embodiment 
     The sixth preferred embodiment discloses the micromirror device including a plurality of mirror elements in each of which the micromirror can be controlled to deflect to the ON or the OFF light state with a coulomb force. The Coulomb force is generated by connecting an electrode to which a predetermined voltage is applicable to either of the regions of the micromirror. The regions of the electrode respectively face and correspond to the first and the second electrode parts that are respectively positioned on the right and the left sides of the deflection axis in the single address electrode disposed across the elastic hinge or the deflection axis of the micromirror. 
       FIG. 10  shows the micromirror that deflects to the ON or the OFF light state by respectively insulating the regions  91   a  and  91   b  of the micromirror. The regions  91   a  and  91   b  respectively face and correspond to the first and the second electrode parts of the single address electrode  33 . With a hinge  101   b  and by applying a predetermined voltage and a grounded hinge  101   a  to function as the two hinges respectively connected to the regions  91  and  91   b  of the micromirror in one mirror element  38  in the micromirror device according to the sixth preferred embodiment. 
       FIG. 10  depicts the mirror element  38  configured symmetrically with respect to the elastic hinge or the deflection axis of the micromirror while that the regions  91   a  and  91   b  of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33 , are implemented as conductor layers. The conductor layers are insulated almost at the middle of the micromirror in order for their separation. The two hinges such as the grounding hinge  101   a  and the hinge  101   b  to which the predetermined voltage is applicable are respectively connected to the regions  91   a  and  91   b  of the micromirror. An electrode  102  for applying the predetermined voltage is connected to the hinge  101   b . A driving circuit  104   c  connected to the electrode  102  is provided in the micromirror device according to the sixth preferred embodiment of the present invention. Furthermore, the mirror element  38  may be made asymmetrical with respect to the elastic hinge or the deflection axis of the micromirror. 
       FIG. 10  shows the regions  91  and  91   b  of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33 , are insulated to prevent them from being electrically continuous, and the two hinges such as the grounding hinge  101   a  and the hinge  101   b  to which the predetermined voltage is applicable are respectively connected to the regions  91   a  and  91   b  of the micromirror. The hinge  101   b  is further connected to the electrode  102  for applying the predetermined voltage via the driving circuit  104  in one mirror element in the micromirror device according to the sixth preferred embodiment of the present invention. 
     Additionally, an insulator  103  formed as one piece for covering the micromirror regions  91   a  and  91   b  on the ON and the OFF light sides is stacked on the surface of the micromirror configured with the micromirror regions  91   a  and  91   b . These regions respectively correspond to the first and the second electrode parts of the address electrode  33 . The micromirror  92  is further stacked on the insulator  103  in order to enable the micromirror  92  to reflect incident light. The insulator  103  may be configured with a reflective material and implemented as a reflection mirror. Furthermore, the micromirror regions  91   a  and  91   b  may be implemented as reflection mirrors with a surface for reflection. 
     According to the sixth preferred embodiment of present invention, a method for controlling the micromirror  92  to deflect to the ON or the OFF light state in one mirror element  38  is described. The method is achieved by connecting the two hinges such as the grounding hinge  101   a  for the micromirror region  91   a , and the hinge  101   b  that can apply the predetermined voltage to the other micromirror region respectively to the regions  91   a  and  91   b  of the micromirror. These two regions respectively face and correspond to the first and the second electrode parts of the single address electrode  33 , in the micromirror device The controlling method according to this preferred embodiment is briefly described based on the controlling method described with reference to  FIGS. 6A to 6E . 
     When the micromirror  92  is deflected from the initial state, predetermined voltages are applied to the electrode  102  and the address electrode  33  in order to apply a voltage to the micromirror region  91  on one side of the micromirror via the hinge  101   b . By applying to the electrode  102  the voltage with the same polarity as that applied to the address electrode  33 , the micromirror can be tilted in the side opposite to the side to which the voltage is applied. Because the potential difference between the address electrode  33  and the micromirror region to which the voltage is applied becomes smaller than that applied between the address electrode  33  and the micromirror region. The voltage is not applied in the micromirror to the regions respectively correspond to the first and the second electrode parts of the address electrode  33 , in the initial state, and the amount of charge q in the equation (1) therefore becomes small, whereby a higher coulomb force F is applied to the opposite side. 
     Because even when the voltage applied to the electrode  102  is equal to or lower than that applied to the electrode  33 , a reduction in the drawing force implemented by the Coulomb force F is required. Additionally, the micromirror region  91   b  acts as the address electrode. The micromirror can be controlled by applying no voltage to the electrode  102  when the micromirror is deflected to the side of the region  91   b  and stopped by making contact with the electrode  33 , or by applying the same voltage as the electrode  33  to the electrode  102  (or by reducing the drawing force implemented by the coulomb force) when the micromirror is deflected to the opposite side. Additionally, the micromirror can be switched on/off by suitably addressing the electrodes  33  and  102  according to an image signal corresponding to each mirror pixel. 
     Furthermore, a person having ordinary skill in the art can easily understand that the micromirror can be controlled in the aforementioned way also by implementing a configuration where the region  91   b  made to act as the electrode corresponding to the address electrode  33  is extended to the side of the region  91   a . When the voltage according to an address signal from an image signal is applied the address voltage from the image signal is prevented from being applied by grounding the electrode  33 . 
     At this time, the micromirror can be controlled to deflect to the ON or the OFF light side by generating a difference between coulomb forces F by applying the voltages to both the micromirror and the address electrode  33 . The micromirror tilted from the initial state starts to freely oscillate by temporarily reducing the voltages of the micromirror and the address electrode to 0V. By timely applying the voltages to the address electrode  33  and/or the micromirror via the hinge  10   b  that is connected to the micromirror and can apply the predetermined voltage when the micromirror  31  becomes close to the first or the second electrode part of the address electrode  33  during the free oscillation. The micromirror  31  can be held on the ON or the OFF light side. As a result, the micromirror can be controlled to deflect to the ON or the OFF light state. 
     This is implemented as follows: the square of the distance r between the micromirror and the address electrode  33  is a dominant factor in the equation (1). The higher coulomb force is therefore applied to the side of the shorter distance r between the address electrode  33  and the micromirror, whereby the micromirror can be titled to the ON or the OFF light side. In this way, the mirror element in the sixth preferred embodiment is controlled to change from the initial state to the OFF or the ON light state. 
     Also, according to the controlling method described with reference to  FIGS. 6A to 6E , a method for controlling the micromirror to restore from the OFF or the ON light state to the initial state is disclosed. Namely, by temporarily reducing the potential difference between the micromirror and the address electrode to 0V in the ON or the OFF light state, the micromirror starts to freely oscillate where the micromirror is tilted and held. Then, the coulomb force F draws the micromirror back to the side opposite to the side to which the micromirror is moving by temporarily applying a suitable voltage to the address electrode  33  and/or the hinge  101   b  connected to the micromirror and can apply the predetermined voltage when the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point in the moving direction of the freely oscillating micromirror. An acceleration that is reverse to the moving direction of the micromirror is generated, whereby the micromirror can be restored to the initial state. Namely, the micromirror  31  can be restored from the ON or the OFF light state to the initial state by applying a pulsed voltage to the address electrode  33  and/or the hinge  101   b  that is connected and can apply the predetermined voltage. 
     Seventh Preferred Embodiment 
     The seven preferred embodiment according to the present invention discloses the micromirror device that can control the micromirror to deflect to the ON or the OFF light state with a coulomb force by forming an address electrode as one piece in one mirror element. The micromirror has flat surface for reflecting incident light. The regions of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode across the elastic hinge or the deflection axis of the micromirror have different thickness. 
       FIG. 11  shows the micromirror  31  controlled to deflect to the ON or the OFF light state with regions  111   a  and  111   b  of the r micromirror. The regions  111   a  and  111   b  respectively face and correspond to the first and the second electrode parts of the single address electrode  33  across the elastic hinge or the deflection axis of the micromirror.  FIG. 11  depicts the mirror element  38  configured symmetrically with respect to the elastic hinge  36  or the deflection axis of the micromirror while that the regions  111   a  and  111   b  of the regions of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33  have different thicknesses. 
     In the configuration shown in  FIG. 11 , the regions  111   a  and  111   b  of the regions of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33  have different thicknesses the mirror element in the micromirror device according to the seventh preferred embodiment of the present invention. The lower surface of the micromirror may be reconfigured to make the regions  111   a  and  111   b  of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33  have different thicknesses. 
     According to the seventh preferred embodiment of the present invention, a method for controlling the micromirror  31  to deflect to the ON or the OFF light state is disclosed. The regions  111   a  and  111   b  of the micromirror respectively face and correspond to the first and the second electrode parts of the single address electrode  33  across the elastic hinge or the deflection axis of the micromirror have different thicknesses in one mirror element  38  in the micromirror device. The controlling method for the micromirror  31  in this preferred embodiment is described according to the controlling method described with reference to  FIGS. 6A to 6E . The controlling method in the mirror element in the seventh preferred embodiment is briefly described below. 
     According to the equation (1), by applying a voltage to the address electrode  33 , the micromirror  31  is deflected from the initial state and tilted to the thicker side  11   b  of the region of the micromirror corresponding to the address electrode  33 . This is because the square of the distance r between the micromirror  31  and the address electrode  33  functions as a dominant factor in the equation (1). A higher coulomb force F is therefore applied to the side of the shorter distance r between the address electrode  33  and the thicker side  111   a  of the micromirror in comparison with the thinner side  111   a  of the micromirror in the initial state. The micromirror tilted form the initial state starts to freely oscillate by temporarily reducing the voltage of the address electrode  33  to 0V. The micromirror  31  can be held on the ON or the OFF light side that is the first or the second electrode by timely applying a suitable voltage to the address electrode  33  when the freely oscillating micromirror  31  becomes close to the ON or the OFF light side of the address electrode, whereby the micromirror can be deflected to the ON or the OFF light state. Specifically, the coulomb force F represented by the equation (1) is more intensified by the square of the distance r between the micromirror  31  and the address electrode  33 . A higher coulomb force F is applied to the side of the shorter distance r between the address electrode  33  and the micromirror  31 , whereby the micromirror  31  can be tilted to the ON or the OFF light side. In this way, the micromirror  31  can be controlled to deflect from the initial state to the OFF or the ON light state. 
     With reference to  FIGS. 6A to 6E , a method for controlling the micromirror  31  to restore from the OFF or the ON light state to the initial state is disclosed. Namely, by applying a suitable pulsed voltage in the ON or the OFF light state of the micromirror  31 , the micromirror  31  can be restored to the initial state. This is implemented as follows: the micromirror  31  starts to freely oscillate by temporarily reducing to 0V the voltage applied to the address electrode  33  while holding the micromirror  31  to 0V. An acceleration reverse to the moving direction of the micromirror  31  is generated because the Coulomb force F that draws the micromirror  31  back to the side opposite to the side to which the freely oscillating micromirror is moving. By temporarily applying the voltage to the address electrode  33  when the distance r between the address electrode  33  and the micromirror reaches a suitable point while the micromirror  31  is moving from the electrode side holding the micromirror  31  to the other electrode side, the micromirror  31  can be restored to the initial state. Accordingly, by applying the pulsed voltage to the single address electrode  33 , the micromirror  31  can be restored from the ON or the OFF light state to the initial state. 
     Eighth Preferred Embodiment 
     The eighth preferred embodiment discloses the micromirror device where the micromirror can be controlled to deflect to the ON or the OFF light state. A coulomb force is combined with the elasticity of elastic hinges by using elastic members with different elasticity coefficients respectively for the deflection directions of the micromirror. The address electrode across the elastic hinge or the deflection axis of the micromirror is formed as one piece in one mirror element. 
     In the configuration shown in  FIG. 12 , the micromirror  31  can be controlled to deflect to the ON or the OFF light state by using the elastic hinges  122   a  and  122   b  with different elasticity coefficients respectively for the first and the second electrode parts of the single address electrode  33  in one mirror element  38  of the micromirror device according to the eighth preferred embodiment of the present invention. 
       FIG. 12  depicts the mirror element  38  configured with the elastic hinges  122   a  and  122   b  with different elasticity coefficients respectively for the first and the second electrode parts of the single address electrode  33 . The mirror element  38  is configured asymmetrically with respect to the deflection axis of the micromirror. The elastic hinges  122   a  and  122   b  with different elasticity coefficients may be combined into one elastic hinge, or partitioned and used as a plurality of elastic hinges. 
     Specifically, the hinges disclosed in this preferred embodiment are of a vertical cantilever type. Therefore, the surfaces of the right and the left hinges expand or contract when the micromirror deflects to the right or the left side. These hinges are configured to transform into different shapes when deflected to different tilt angles. 
     According to the eighth preferred embodiment of the present invention,  FIG. 12  shows the elastic hinges with different forces for deflecting the micromirror to the right and the left sides are used respectively for the first and the second electrode parts of the address electrode  33  in the mirror element of the micromirror device. By forming the hinges with different elasticities respectively for the sides of the first and the second electrode parts of the single address electrode  33 , it becomes easier to deflect the micromirror  31  to one side. The sizes and the heights of the electrode parts of the address electrode can be significantly changed. According to the eighth preferred embodiment of the present invention, a method is described for controlling the micromirror  31  to deflect to the ON or the OFF light state when the elastic hinges with different elasticity coefficients are used respectively for the sides of the first and the second electrode parts of the single address electrode  33  in one mirror element  38  of the micromirror device 
     By applying a voltage to the address electrode  33 , the micromirror  31  is deflected from the initial state and the micromirror is tilted to the side of the electrode part with the larger area or height of the address electrode  33  arranged asymmetrically with the elastic hinge or the deflection axis of the micromirror. The micromirror  31  tilted from the initial state to one side starts to freely oscillate when temporarily reducing the voltage of the single address electrode  33  to 0V. By timely applying a suitable voltage to the single address electrode  33  when the freely oscillating micromirror  31  moves close to the electrode part on the ON or the OFF light side of the address electrode, the micromirror  31  can be held on the ON or the OFF light side closer to the first or the second electrode part side. As a result, the micromirror can be deflected to the ON or the OFF light state. 
     This is implemented as follows: the Coulomb force F represented by the equation (1) described with reference to  FIG. 6A  is reversely proportional the square of the distance r between the address electrode  33  and the micromirror  31 . A higher coulomb force is therefore applied by reducing the distance between the address electrode  33  and the micromirror  31 . Therefore, the micromirror  31  is tilted to the ON or the OFF light side when the distance r between the address electrode  33  and the micromirror  31  becomes short. As a result, the micromirror  31  can be controlled to deflect from the initial state to the OFF or the ON light state. 
     According to the controlling method described with reference to  FIG. 6D  or  6 E a method for controlling the micromirror  31  to restore from the OFF or the ON light state to the initial state is disclosed. Specifically, by applying a suitable pulsed voltage to the address electrode  33  in the ON or the OFF state of the micromirror  31 , the micromirror  31  can be restored to the initial state. 
     This is implemented as follows: the micromirror  31  starts to freely oscillate when temporarily reducing the voltage of the address electrode  33  part holding the micromirror  31  to 0V. An acceleration reverse to the moving direction of the freely oscillating micromirror  31  is generated by causing the coulomb force F to draw the micromirror  31  back to the side opposite to the side to which the micromirror  31  is moving because of temporarily applying the voltage to the address electrode  33 . When the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point while the freely oscillating micromirror  31  is moving from the side thus holding the micromirror  31  toward the other side, whereby the micromirror can be restored to the initial state. In this way, the micromirror  31  can be restored from the ON or the OFF light state to the initial state by applying the pulsed voltage to the single address electrode  33 . 
     It can be easily understood by those of ordinary skill in the art that the deflection speed of the micromirror or the length of time required for the micromirror to deflect at a maximum angle vary by each deflection direction since the elasticity coefficients are different depending on a deflection direction. With such a difference of the deflection speed or the length of time exerts an influence, the micromirror is controlled with special considerations concerning the timing of mirror control. The same applies also to the case where the shape of the micromirror, or the waveform of a voltage applied to the micromirror is asymmetrical with respect to the deflection axis of the micromirror. 
     Ninth Preferred Embodiment 
     The ninth preferred embodiment discloses the micromirror device where the address electrode is formed as one piece, The micromirror is controlled to deflect to the ON or the OFF light state with a coulomb force by arranging an elastic hinge for supporting the micromirror in a position away from the gravity center of the micromirror. 
       FIG. 13A  shows the correspondence between the areas of the micromirror and the elastic hinge when the mirror element  38  is viewed in the direction Z of  FIG. 3 . According to the ninth preferred embodiment of the present invention, the elastic hinge for supporting the micromirror is placed in the position that is away from the gravity center of the micromirror in the mirror element  38  in the micromirror device. 
       FIG. 13B  is a cross-sectional view of the mirror element  38  shown in  FIG. 13A  and taken along the line IV-IV of  FIG. 3 .  FIG. 13A  shows the address electrode  33  formed as one piece, and the elastic hinge for supporting the micromirror is formed in the position away from the gravity center of the micromirror in the mirror element.  FIG. 13B  is a cross-sectional view of the mirror element  38  shown in  FIG. 13A  and taken along the line IV-IV of  FIG. 3 . This figure shows the configuration where the single address electrode  33  positioned below the micromirror  31  is formed as one piece on the substrate  32 , and the elastic hinge for supporting the micromirror is formed in the position away from the gravity center of the micromirror. 
     In this configuration, the micromirror  31  and the address electrode  33  are configured symmetrically with respect to an axis that is parallel to the deflection axis of the micromirror and passes through the gravity center. The elastic hinge is formed in the position that is away from the gravity center of the micromirror  31 . The elastic hinge is made to support the micromirror. Even when the coulomb forces generated respectively between the micromirror  31  and the electrode parts of the address electrode  33  are made equal, mirror movements along either directions differ. Therefore, the force for deflecting the micromirror to the side including the gravity center is more intensified. This can make the forces for deflecting the micromirror to the right and the left sides of the elastic hinge different, whereby the micromirror can be controlled to deflect to the ON or the OFF light state with a controlling method similar to that executed when the coulomb forces are different. 
     In  FIGS. 13A and 13B , the mirror element  38  is configured symmetrically with respect to the axis that is parallel to the deflection axis of the micromirror device and passes through the gravity center. The elastic hinges for supporting the micromirror is formed in the position away from the gravity enter of the micromirror. The configuration shown in  FIGS. 13A and 13B  is described based on the assumption that both the micromirror and the address electrode have shapes or properties symmetrical with respect to the axis that is parallel to the deflection axis of the micromirror and passes through the gravity center. Furthermore, the areas, etc. of the address electrode may be made asymmetrical except that the elastic hinge for supporting the micromirror  31  is arranged in the position away from the gravity center of the micromirror. 
     According to the ninth preferred embodiment of the present invention, a method for controlling the micromirror to deflect to the ON or the OFF light state in the mirror element where the address electrode is formed as one piece, and the elastic hinge for supporting the micromirror is arranged in the position away from the gravity center is described. 
     When the micromirror  31  is deflected from the initial state, the micromirror  31  is tilted toward the side of the elastic hinge with larger moment when applying a voltage to the address electrode  33 . Then, the micromirror  31  starts to freely oscillate by temporarily reducing the voltage of the single address electrode  33  to 0V. By timely applying a suitable voltage to the single address electrode  33  when the freely oscillating micromirror  31  comes close to the ON or the OFF light side of the address electrode, the micromirror  31  can be held on the ON or the OFF light side that is the first or the second electrode part. As a result, the micromirror  31  can be deflected to the ON or the OFF light state. Because the micromirror  31  can be tilted to the ON or the OFF light side as shown in  FIG. 6A  by making the moment corresponding to the coulomb force F represented by the equation (1) of the electrode part on one side of the micromirror larger than that on the opposite side. Accordingly, the micromirror  31  can be controlled to deflect from the initial state to the OFF or the ON light state. 
     Also a method for controlling the micromirror  31  from the OFF or the ON light state to the initial state is therefore disclosed according to the controlling method described with reference to  FIG. 6D  or  6 E. Specifically, by applying a suitable pulsed voltage to the address electrode  33  in the ON or the OFF light state of the micromirror  31 , the micromirror  31  can be restored to the initial state. This is implemented as follows: the micromirror  31  starts to freely oscillate when temporarily reducing to 0V the voltage on the side of the address electrode  33  part holding the micromirror  31 . An acceleration reverse to the moving direction of the micromirror  31  is generated because the moment caused by the Coulomb force F that draws the micromirror back to the side opposite to the side of the freely oscillating micromirror  31 . This occurs when the distance r between the address electrode  33  and the micromirror  31  reaches a suitable point while the freely moving micromirror  31  is moving from the side holding the micromirror  31  toward the other side, whereby the micromirror  31  can be restored to the initial state. In this way, the micromirror  31  can be restored from the ON or the OFF light state to the initial state by applying the pulsed voltage to the single address electrode  33 . 
     According to the first to the ninth preferred embodiments described above, the mirror elements in the micromirror devices is controlled by applying the voltage to the single address electrode. A person having ordinary skill in the art can easily understand that the deflection of the micromirror can be controlled also by grounding the address electrode, and by applying the voltage to the micromirror implemented as a conductor. For example, by grounding the address electrode, and by applying the pulsed voltage to the micromirror at designated timing, the micromirror can be restored to the initial state. Additionally, a person having ordinary skill in the art can easily understand that the tilt of the micromirror can be controlled by applying voltages to both the single address electrode and the micromirror, and that the deflection of the micromirror can be controlled in a similar manner by providing the address electrode only on the back of the micromirror. 
     Tenth Preferred Embodiment 
     The tenth preferred embodiment discloses the configuration implemented by adding in the first to the ninth preferred embodiments an electrode for detecting the position of the micromirror or for determining the timing to change the operation of the micromirror when the micromirror makes contact with the electrode and further describes the principle for detecting the position of the micromirror. The detection of the position of the micromirror referred to in this invention is to detect that the micromirror is tilted to the ON or OFF light side, or neither of the sides, or to determine the timing for the micromirror in changing from the deflected state to another state. 
     The tenth preferred embodiment disclosed a micromirror that is tilted by the coulomb force generated between the first or the second electrode part and the address electrode when applying a voltage to the single address electrode, whereby the micromirror can be deflected to the ON or the OFF light state. 
     The configuration in the tenth preferred embodiment is implemented by further providing another electrode that has the height for enabling the micromirror to make contact when tilting. The electrode is dedicated to the position detection of the micromirror outside either or both of the ON and the OFF light sides in the mirror elements in the first to the ninth preferred embodiments. 
       FIG. 14  shows an example of the configuration where the electrode  141  that is dedicated to a function of position detection of the micromirror  31  or to determine the timing to change the operation of the micromirror when the micromirror contacts the electrode. This electrode for detection is added outside of the area of the address electrode in one mirror element in the micromirror device shown in  FIG. 4A . The position or the micromirror  31  can be detected or the timing to change the operation of the micromirror can be determined according to the principle of observing whether or not the micromirror  31  and the electrode  141  are electrically continuous or a slight change occurs in the potential difference when the micromirror  31  makes contact with the electrode  141  in the aforementioned arrangement. 
     Depending on the detection method, the electrode  141  may be grounded, or a voltage may be applied to make a predetermined current flow to the electrode  141  when the micromirror makes contact with the electrode. For example, the charge stored in the micromirror is discharged at the moment when the micromirror  31  makes contact with the electrode  141 . The Coulomb force applied between the address electrode  33  and the micromirror  31  is terminated whereby holding the micromirror in one deflection state can be prevented even when the micromirror deflects to the side including the electrode  141 . As a result, the micromirror  31  once deflected toward the electrode  141  can be deflected in the opposite direction when the micromirror  31  makes contact with the electrode  141 . It is possible to hold the micromirror in the deflection state by grounding the electrode  141 . This eliminates the need for strictly controlling, for example, the time T 7  shown in  FIG. 6C  at which the voltage applied to the electrode  33  is reduced to 0V. Moreover, the duration for holding the micromirror in a predetermined direction can be minimized. 
     Furthermore, the transfer speed of charge to the region of the electrode  141  with which the micromirror makes contact is adjusted by providing a protection film with high resistivity, etc., whereby the transfer time of charge stored in the micromirror  31  can be changed, and in turn the time required for changing the coulomb force can be adjusted. This is effective also when this configuration is used for an experiment, etc. of the control of the ON/OFF light of the micromirror  31 . 
     In this embodiment, the electrode  141  is dedicated to the function of position detection of the micromirror  31  and is placed outside the address electrode  33 . However, the electrode  141  may be arranged inside and used as a stopper. 
     Alternatively, the position of the micromirror  31  can be detected by adding the address electrode dedicated to the position detection of the micromirror to the conventional configuration where two address electrodes are used in one mirror element. 
     With the micromirror controlled in this way, the tilting position of the micromirror can be securely controlled against a possible change in the tilting state caused by a disturbance (such as a physical impact caused by a hit, a drop, etc.) of the micromirror. Furthermore, the micromirror may be controlled and held in the ON or the OFF light state according to the timing of the voltage applied to the address electrode. 
     Eleventh Preferred Embodiment 
     The eleventh preferred embodiment discloses the micromirror device where the micromirror is controlled to tilt with the coulomb force generated between the first or the second electrode part of the single address electrode to which the voltage is applied. The micromirror is controlled to always tilt to a particular ON or OFF light state regardless of the current state of the micromirror. 
     The eleventh preferred embodiment also discloses a method for controlling the micromirror to always deflect to the ON or the OFF light state by making a voltage applied to the address electrode or micromirror multilevel regardless of the current state of the micromirror. 
     According to the eleventh preferred embodiment of the present invention, a method for controlling the micromirror to always deflect to a particular deflection state regardless of the currently tilting state of the micromirror, and a method for controlling the micromirror by making a voltage multilevel in one mirror element in the micromirror device are described below. 
     According to the first to the tenth preferred embodiments,  FIGS. 15A to 15D  are charts for representing the controlling method to hold the micromirror in the ON light state regardless of the current state such as the ON light state of  FIG. 15A , the OFF light state of  FIG. 15B , or the intermediate light state of  FIG. 15C  of the micromirror by using a multilevel voltage. 
       FIGS. 15A to 15D  assume that the address electrode or the micromirror is configured so that the coulomb force applied between the electrode part on the ON light side of the address electrode and the micromirror becomes higher than that applied between the electrode part on the OFF light side of the address electrode and the micromirror. In order to apply the multilevel voltage to the micromirror, the address electrode may be grounded. 
       FIG. 15A  shows a method to control the micromirror to deflect from the OFF light state to the ON light state.  FIG. 15  shows a method for controlling the micromirror to deflect from the ON light state again to the ON light state as shown in  FIG. 15B .  FIG. 15C  shows a method for controlling the micromirror to deflect from the initial state that is the intermediate light state to the ON light state.  FIG. 15D  shows a method for controlling the micromirror to deflect from the ON light state to the OFF light state. The control method are implemented by using the multilevel voltage is described with reference to  FIGS. 15A to 15D  showing the chart that represents the position of the micromirror along with the chart that represents the voltage of the address electrode in the same elapse of time indicated by a time axis t. 
     The vertical axis of the chart that represents the position of the micromirror indicates a move to the side of the ON or the OFF light state with respect to the intermediate light state as the initial state. The vertical axis of the chart represents the voltage of the address electrode indicates the state where the voltage is applied to the address electrode as the ON state with respect to the initial state of 0V. The horizontal axes of both of the charts are the time axis t indicating the elapse of time. 
       FIG. 15A  shows a controlling method for deflecting the micromirror from the OFF to the ON light state by making the voltage applied to the address electrode and/or the micromirror multilevel. The method for controlling the micromirror to deflect from the OFF to the ON light state is described below with reference to the charts of  FIG. 15A . With this method, the micromirror is held in the OFF light state up to a time t 18  by applying the voltage to the address electrode and/or the micromirror after the initial operations described in the second preferred embodiment are performed. The micromirror starts to freely oscillate and when the voltage of the address electrode and/or the micromirror is reduced to 0V. 
     A lower voltage than that used in the initial state of the micromirror is applied to the address electrode and/or the micromirror at a time t 19  when the distance between the OFF light side of the address electrode and the micromirror becomes shorter than that between the ON light side of the address electrode and the micromirror. The voltage is applied when the freely oscillating micromirror is moving away from the ON light side of the address electrode. The sum of the inertial force of the micromirror and the coulomb force applied between the ON light side of the address electrode and the micromirror becomes larger than the coulomb force applied between the OFF light side of the address electrode and the micromirror. Therefore, the micromirror is tilted toward the ON light side of the address electrode while its speed is being slowed down, whereby the micromirror can be deflected to the ON light state. In this way, a multilevel voltage applied to the address electrode is implemented for controlling the micromirror. 
       FIG. 15B  shows a controlling method for holding the micromirror in the ON light state by making the voltage applied to the address electrode and/or the micromirror multilevel. 
     Similar to  FIG. 15A , the micromirror is held in the ON light state up to the time t 18  by applying the voltage to the address electrode and/or the micromirror after the initial operations described in the second preferred embodiment. The micromirror starts to freely oscillate thereafter when reducing the voltage of the address electrode and/or the micromirror to 0V. A lower voltage than that used in the initial state is applied to the address electrode and/or the micromirror at the time t 19  when the distance between the ON light side of the address electrode and the micromirror becomes shorter than that between the OFF light side of the address electrode and the micromirror. The freely oscillating micromirror is moving away from the ON light side of the address electrode toward the OFF light side of the address electrode. The micromirror can be controlled to restore to the ON light state. This can be also understood according to the above principle described with reference to  FIG. 15A . Similar operations can be started in the OFF light state. 
       FIG. 15C  shows the controlling method for changing the micromirror from the initial state to the ON light state, and for holding the micromirror in the ON light state. This is achieved by applying a multilevel voltage to the address electrode and/or the micromirror.  FIG. 15C  is a timing diagram for showing the method for controlling the micromirror  31  to deflect from the initial state to the ON light state and for holding the micromirror in the ON light state is described below with reference to the charts. 
     The micromirror initially operates at an intermediate light state up to the time t 17 , with no voltage applied to the address electrode and/or the micromirror. Thereafter, the micromirror is deflected to the ON light state by applying the voltage to the address electrode and/or the micromirror at the time t 17 . The micromirror is held in the ON light state up to the time t 18 . The micromirror starts to freely oscillate when reducing the voltage of the address electrode and/or the micromirror to 0V at the time t 18 . Then, a lower voltage than that used for the micromirror to deflect from the initial state to the ON light state is timely applied at the time t 19  when the distance between the ON light side of the address electrode and the micromirror is shorter than the distance between the OFF light side of the address electrode and the micromirror. This takes place when the freely oscillating micromirror is moving away from the ON light side of the address electrode toward the OFF light side of the address electrode, whereby the micromirror can be controlled to deflect to the ON light state. This can be also understood according to the principle described with reference to  FIG. 15A . Moreover, a person having ordinary skill in the art can easily understand that a generally called stiction can be prevented from occurring when the micromirror is in contact with the electrode by holding the micromirror at a low voltage. 
     With the operations described with reference to  FIGS. 15A to 15C , the micromirror can be controlled to always deflect to either of the sides of the ON and the OFF light states regardless of the current state such as the ON, the OFF, or the initial state that is the intermediate light state of the micromirror. The control is achieved by applying a lower voltage than that applied in the initial state to the address electrode and/or the micromirror at particular timing. Such a controlling method for changing the applied voltage is also applicable to the controlling method described with reference to  FIGS. 6A to 6E . 
       FIG. 15D  shows a controlling method for deflecting the micromirror  31  from the ON light state to the OFF light state, and further to the ON light state by applying a multilevel voltage to the address electrode  33  and/or the micromirror  31 . A method for controlling the micromirror  31  to deflect from the ON light state to the OFF light state, and further to the ON light state is described with reference to the charts shown in  FIGS. 15D and 15E .  FIG. 15D  shows the state where the micromirror oscillates between the ON and the OFF light states, or with attenuated oscillation.  FIG. 15E  shows the state where the micromirror fully oscillates between the ON and the OFF light states. A person having ordinary skill in the art can easily understand that the difference between these states varies depending on the initial settings of the strength of the elastic spring force of the mirror element, or the position of a time point t. 
     In  FIGS. 15D and 15E , the micromirror  31  is held in the ON light state up to a time t 20  by applying the voltage to the address electrode  33  and/or the micromirror  31  after the initial operations described in the second preferred embodiment. The micromirror  31  starts to freely oscillate when reducing the voltage of the address electrode  33  and/or the micromirror  31  to 0V. A voltage lower than that used in the initial state is applied to the address electrode  33  and/or the micromirror  31  at a time t 21  when the freely oscillating micromirror  31  oscillates closest to the OFF light side of the address electrode  33  to control the micromirror  31  to deflect to the OFF light state. 
     In this case, the coulomb force F represented by the equation (1) is stronger because of the square of the distance r between the micromirror  31  and the address electrode  33 . The voltage as high as that for the initial state is not required because the distance r between the address electrode  33  and the micromirror  31  is shorter than that at the time of the initial operations when the freely oscillating micromirror  31  moves close to the OFF light side of the address electrode  33 . Therefore, the micromirror  31  is operated in the OFF light state by applying the voltage lower than that required for the initial state. 
     In this way, the micromirror  31  is controlled by applying a multilevel voltage to the address electrode  33  and/or the micromirror  31 . For example, the micromirror can be held in the ON or the OFF light state by applying a voltage to the address electrode and/or the micromirror is made at least bi-level except for the state where the voltage is not applied, and a voltage is applied at designated timing, whereby. 
     As described above, the micromirror can be controlled to change to a particular deflection state regardless of the current tilting state of the micromirror. The deflection of the micromirror is also controllable by applying a multilevel voltage to the address electrode and/or the micromirror. Furthermore, the deflection of the micromirror is more conveniently controllable by using the electrode  141  described in the tenth preferred embodiment. 
     According to the aforementioned preferred embodiments, it is preferable to apply the voltage of 3V to 15V to the micromirror or the electrode as the controlling method executed in one mirror element in the micromirror devices. Moreover, the voltage applied to the micromirror or the electrode may be a constant or multilevel voltage. When a memory circuit for driving to apply a voltage to the electrode has a DRAM configuration, the voltage can be easily adjustable by implementing a charge pump, or the like in a capacitor that is implemented as part of the circuit. 
     Additionally, when the micromirror and the electrode are implemented as address electrodes, a plurality of memories may be provided for each of the address electrodes. 
     It may be necessary to consider differences among the deflection speeds and the deflection times of mirror elements caused by variations of the micromirrors especially considering the fact that the micromirrors are controlled with the timing implemented to drive the micromirrors in all the mirror elements. Moreover, the micromirror can be controlled with higher precision when a multilevel voltage is applied to the electrode or by using the method described in the tenth preferred embodiment. 
     Up to this point, the first to the eleventh preferred embodiments have disclosed the micromirror devices including a plurality of mirror elements supported on a substrate. The micromirror is deflectable in a plurality of directions and supported by an elastic hinge. An address electrode corresponds to the micromirror and has shapes or properties asymmetrical with respect to the deflection axis of the micromirror. A driving circuit for controlling the micromirror is connected to the address electrode to deflect in at least two directions. The micromirror device further includes a plurality of mirror elements supported on a substrate. Each micromirror is deflectable in a plurality of directions and supported by an elastic hinge. The micromirror device further includes address electrode corresponding to the micromirror, and a driving circuit for controlling the micromirror connected to the address electrode to deflect in at least two directions. 
     This specification has disclosed the exemplary embodiments of the micromirror devices with detail descriptions. However, it is evident that various modifications and changes may be made to these embodiments without departing from the sprit and the scope of the present invention. Accordingly, this specification and the drawings are not to be taken in a limiting sense but to be regarded as specific embodiments. 
     Additionally, by employing the present invention, the micromirror devices used to provide an image with a hi-definition resolution may be downsized, leading to reductions in size and cost in comparison with conventional devices. Additionally, the micromirrors can be controlled with higher precision than in the conventional devices. Note that the present invention does not preclude the configuration for controlling a single address electrode and a circuit as in the above described preferred embodiments while controlling the ON/OFF light reflected by a micromirror by arranging two address electrodes for one mirror element on a substrate as shown in  FIG. 2B , and a configuration implemented by further comprising the electrode and the circuit disclosed by the preferred embodiments. The present invention is applied to the conventional methods for controlling a micromirror to deflect in two directions, whereby the micromirror can be controlled to stop, oscillate, or operates in many different other manners. Moreover, the micromirror can be controlled in a more complicated manner because of more flexible variations of the controlling methods. As a result, the present invention is expected to and is applicable to a face-mounted display, an electric viewfinder, a cinema projection system, etc. Moreover, the present invention has the advantage that the wiring and the configurations of the driving circuits and the address electrodes employed in the configurations according to the present invention are significantly simplified to achieve highly valued economic benefits.