Abstract:
A micromirror actuator includes: a substrate; spring units elastically supported by protrusion formed on the substrate; a micromirror connected to the spring units and formed to be capable of rotating; trenches formed in the substrate at either side of the protrusions to correspond to the surface of the micromirror; and lower electrodes formed in each of the trenches. Accordingly, it is possible to expand the range of the driving angle of the micromirror with the use of a lower voltage.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a micromirror actuator and, more particularly, to a micromirror actuator, which can be driven by attractive electrostatic forces and can have a wide range of driving angles with the use of a low driving voltage. 
     This application is based on Korean Patent Application No. 2001-36092 filed on Jun. 23, 2001, the disclosure of which is incorporated herein by reference in its entirety. 
     2. Description of the Related Art 
     Micromirrors are generally used in various fields including an optical communication field. For example, micro-optical cross connects (MOXCs) are devices for selecting an optical path and thus allowing an optical signal to be transmitted from an input terminal to a predetermined output terminal, and micromirrors are the most important components of MOXC. 
     Micromirror actuators, which can maintain a micromirror at a predetermined angle, have been manufactured by using many different methods and having various structures. FIGS. 1A and 1B are views illustrating a conventional micromirror actuator using attractive electrostatic forces and including an elastic element, such as a torsion spring. Referring to FIGS. 1A and 1B, a micromirror  14  is formed horizontally, over a substrate  11  with a spring unit  13  supported by a protrusion  12  formed on the substrate  11 . The micromirror  14  is formed to be capable of rotating, and a lower electrode  15  is formed under the micromirror  14 . If external voltage is applied to the micromirror  14  and the lower electrode  15 , attractive electrostatic forces are generated between the micromirror  14  and the lower electrode  15 , as shown in FIG.  1 B. Due to the electrostatic forces, the micromirror  14  supported by the spring unit  13  inclines over the substrate  11  at a predetermined angle. 
     The range, in which the driving angle of the micromirror actuator driven by attractive electrostatic forces can be controlled by external voltage, is strictly restricted due to the special characteristics of the method of driving the micromirror actuator. In other words, if a voltage not less than a predetermined level, i.e., threshold voltage, is applied between the spring unit  13  and the micromirror  14 , attractive electrostatic force generated by the applied voltage is always stronger than the elastic restoring force of the spring unit  13 . Thus, the distance between the micromirror  14  and the lower electrode  15  becomes shorter. This can be described more thoroughly with reference to Equation (1).              F   =       ɛ                   AV   2         d   2               (   1   )                                
     In Equation (1), F represents an attractive electrostatic force, ε represents a dielectric constant, A represents the area of an electrode, V represents a potential difference, and d represents the distance between the electrodes. In general, the intensity of the attractive electrostatic force acting between the electrodes is inversely proportional to the square of the distance between the electrodes but is proportional to the square of a voltage applied to the electrodes. Accordingly, as the distance d between the electrodes decreases, the influence of the voltage applied to the electrodes on the attractive electrostatic force between the electrodes increases. In addition, the range, in which the driving angle of a micromirror can be controlled by the voltage applied to the electrodes, becomes very sensitive to a potential difference between the electrodes. 
     On the other hand, as the distance d between the electrodes increases, the influence of the voltage applied to the electrodes on the attractive electrostatic force between the electrodes, decreases, and the range, in which the driving angle of a micromirror can be controlled by the voltage applied to the electrodes, expands. However, the voltage applied to the electrodes must be increased to obtain a desired angle of the micromirror, and the height of a sacrificial layer formed in manufacturing of a micromirror actuator must be increased. 
     SUMMARY OF THE INVENTION 
     To solve the above-described problems, it is an aspect of the present invention to provide a micromirror actuator, which is capable of obtaining a larger driving angle with the use of a lower driving voltage by forming a stepped electrode in a trench (thus lower than in FIGS. 1A and B) so as to make the difference between the lower electrode and a micromirror vary. 
     According to the present invention, a micromirror actuator comprises a substrate, spring units elastically supported by protrusions formed on the substrate, a micromirror connected to the spring units and capable of rotating, trenches formed in the substrate at either side of the protrusions to correspond to the surface of the micromirror and lower electrodes formed in each of the trenches. Lower electrodes may include an electrode formed at the bottom and sidewall of each of the trenches or between the trenches. Trenches may have vertical, slanted or stepped sidewalls. Further, in order to enlarge the range of the driving angle of the micromirror, the distance between the lower electrodes and the micromirror is varied as well as the distance between the lower electrodes and their size. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above aspects and advantages of the present invention will become more apparent by describing in detail illustrative and non-limiting embodiments thereof with reference to the accompanying drawings, in which: 
     FIG. 1A is a perspective view of a conventional micromirror actuator; 
     FIG. 1B is a cross-sectional view of the micromirror actuator, taken along line  1 B— 1 B of FIG. 1A; 
     FIG. 2A is a perspective view of a micromirror actuator according to a first illustrative and non-limiting embodiment of the present invention; 
     FIG. 2B is a cross-sectional view of the micromirror actuator according to a first illustrative and non-limiting embodiment of the present invention, taken along line  2 B— 2 B of FIG. 2; 
     FIG. 3 is a view illustrating the operational principle of the micromirror actuator according to a first illustrative and non-limiting embodiment of the present invention; 
     FIGS. 4A through 4D are cross-sectional views of micromirror actuators, which have almost the same structure as the micromirror actuator shown in FIGS. 1A and 1B and are different from one another in the length of the electrodes and the vertical distance between the micromirror and the electrodes, which is varied in order to obtain the operating modes of the present invention; 
     FIGS. 5A through 5D are graphs showing variations of torque induced by the repulsive force of a spring and torque generated between a micromirror and a lower electrode with respect to the rotation angle of the micromirror during operation of each of the micromirror actuators shown in FIGS. 4A through 4D, respectively; 
     FIG. 6A is a cross-sectional view of a micromirror actuator according to a first illustrative and non-limiting embodiment of the present invention, which is formed to have the same variable values as the micromirror actuator shown in FIG. 4D; 
     FIG. 6B is a graph showing variations of torque induced by attractive electrostatic force and torque induced by the repulsive force of a spring with respect to the rotation angle of a micromirror; 
     FIG. 7 is a cross-sectional view of a micromirror actuator according to a second illustrative and non-limiting embodiment of the present invention; and 
     FIG. 8 is a cross-sectional view of a micromirror actuator according to a third illustrative and non-limiting embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention will now be described in detail by describing illustrative, non-limiting embodiments thereof with reference to the accompanying drawings. In the drawings, the same reference characters denote the same elements. 
     FIGS. 2A and 2B are views showing a micromirror actuator according to a first illustrative and non-limiting embodiment of the present invention. Specifically, FIG. 2A is a perspective view of a micromirror actuator according to a first illustrative and non-limiting embodiment of the present invention, and FIG. 2B is a cross-sectional view of the micromirror actuator according to the first embodiment of the present invention, taken along line  2 B— 2 B of FIG.  2 A. As shown in FIG. 2A, protrusions  22  are formed on a substrate  21 , in which trenches  25  are formed, and a micromirror  24  is formed to be capable of rotating due to spring units  23  elastically supported by the protrusions  22 . Lower electrodes  26  are formed in the trenches  25 , i.e., at the bottom and the sidewall of the trenches  25 . Also, the lower electrode  26  may be formed on the substrate  21  between the trenches  25 . 
     The micromirror actuator according to the present invention is driven by attractive electrostatic force, and the attractive electrostatic force is induced by a potential difference between the micromirror  24  and the lower electrodes  26 . The operational principle of the micromirror actuator having such a structure will be described as follows. 
     If external voltage is applied to the micromirror  24  and the lower electrode  26 , attractive electrostatic force is generated between the micromirror  24  and the lower electrodes  26  and thus the micromirror  24  begins to rotate. The rotation angle of the micromirror  24  is determined by mechanical equilibrium between the intensity of the attractive electrostatic force affecting the micromirror  24  and the restoring torque of the spring-unit  23  supported by the protrusions  22 . 
     Here, torque induced by the attractive electrostatic force generated between the micromirror  24  and the lower electrodes  26  are determined as the sum of torques induced by horizontal and vertical electrodes included in the lower electrodes  26 . In addition, torques induced by the horizontal electrodes are determined as the sum of torques induced by electrodes formed at the bottom of the trenches  25  and on the substrate  21  between the trenches  25 . The restoring torque of the spring units  23  is determined as the spring constant of the spring units  23  multiplied by the rotation angle of the micromirror  24 . These relations mentioned above will be described with reference to FIG. 3, and torque induced by attractive electrostatic force generated between the horizontal electrodes and the micromirror  24  can be expressed by Equation (2A).                           T   h     =                    ∫   0   L            F   h        x           A         =         ∫   0     L   a              F   h        x           A         +       ∫     L   a     L            F   h        x           A                         =                    ɛ                   WV   2         2                   θ   2              {           L   a        sin                 θ         g   ·     L   a          sin                 θ       +     ln        (     1   -         L   a        sin                 θ     g       )       +       L                 sin                 θ       d   +   g   -     L                 sin                 θ         +                                    ln        (     1   -       L                 sin                 θ       d   +   g         )       -     (           L   a        sin                 θ       d   +   g   -       L   a        sin                 θ         +     ln        (     1   -         L   a        sin                 θ       d   +   g         )         )       }                   (     2      A     )                                
     In Equation (2A), T h  represents torque induced by attractive electrostatic force generated between horizontal electrodes  34  and  35 , and a micromirror  32 , shown in FIG. 3. F h  represents attractive electrostatic force generated by the horizontal electrodes  34  and  35 , L represents the distance from the rotation axis of the micromirror  32  and either end of the micromirror  32 , ε represents a dielectric constant (of lower electrodes), θ represents the rotation angle of the micromirror  32 , d represents the depth of a trench  33 , and g represents the vertical distance between the micromirror  32  and a substrate  31 . 
     Torque induced by attractive electrostatic force generated between a vertical electrode  36  and the micromirror  32  can be expressed by Equation (2B).                           T   v     =                    ∫     g   a     L            F   v             A         =       ∫     g   a     L              ɛ                   WV   2           [         (       x   2     -   θ     )        x     -     (       π   2     -     θ   A       )       ]     2          x           x                       =                  B       A   2          (     AL   +   B     )         +       1     A   2            Ln        (     AL   +   B     )         -     B       A   2          (       Ag   a     +   B     )         -       1     A   2            ln        (       Ag   a     +   B     )                         (     2      B     )                                  
     In Equation (2B), T v  represents torque induced by the vertical electrode  36 , and F v  represents attractive electrostatic force generated between the vertical electrode  36  and the micromirror 32. In addition,            g   a     =         L   a   2     +     g   2           ,       θ   a     =       tan     -   1            (     g     L   a       )         ,       and                 B     =         g   a          (       θ   A     -     θ   2       )       .                              
     Accordingly, supposing that T t  represents torque affecting the micromirror  32 , T t =T h +T v , and the rotation angle of the micromirror  32  is determined when T t =T r . 
     The operation of the micromirror actuator according to the present invention will be described below. In a state where external voltage is not applied to the micromirror  32  and the lower electrodes  34 ,  35 , and  36 , in other words, in a state where no external force is applied between the micromirror  32  and the lower electrodes  34 ,  35 , and  36 , the micromirror  32  is kept in a horizontal position. On the other hand, if external voltage is applied to the micromirror  32  and the lower electrodes  34 ,  35 , and  36 , attractive electrostatic force is generated between the micromirror  32  and the lower electrodes  34 ,  35 , and  36  and thus the micromirror  32  begins to rotate so that the micromirror  32  comes close to the lower electrodes  34 ,  35 , and  36 . As the micromirror  32  comes closer to the trench  33 , attractive electrostatic force generated between the vertical electrode formed on the sidewall of the trench  33  and the micromirror  32  becomes stronger so that the micromirror  32  can further rotate. As described above, the micromirror  32  rotates due to an attractive electrostatic force between the micromirror  32  and the lower electrodes  34 ,  35 , and  36 . Finally, if the restoring torque of the spring unit  32  increases to be equal to torque induced by the attractive electrostatic force generated between the micromirror  32  and the lower electrodes  34 ,  35 , and  36 , the micromirror  32  maintains a predetermined rotation angle θ. 
     FIGS. 4A through 4D are cross-sectional views of micromirror actuators, which are slightly different from the conventional micromirror actuator shown in FIGS. 1A and 1B in that the position of a lower electrode  43  and the distance between the lower electrode  43  and the micromirror  42  is different. FIGS. 5A through 5D are graphs showing variations of torque T t  induced by attractive electrostatic force between the lower electrode  43  and the micromirror  42  and torque T r  induced by the repulsive force of a spring with respect to the rotation angle θ of the micromirror  42  when a predetermined external voltage (V=V 0 =55 V) is applied to the micromirror actuators of FIGS. 4A through 4D, respectively. 
     These simulations are performed to find the operational modes of micromirror actuators according to the present invention. 
     In the case of the micromirror actuator shown in FIG. 4A, the lower electrode  43  is formed to be longer than the lower electrode  15  shown in FIG. 1B so that the area of the opposing surface of each of the lower electrode  43  and the micromirror  42  can be enlarged. As shown in FIG. 5A, torque T t  induced by attractive electrostatic force generated between the lower electrode  43  and the micromirror  42  is always stronger than torque T r  induced by the repulsive force of a spring, and thus there is no equilibrium point between the torques T t  and T r , in which case it is impossible to control the rotation angle of the micromirror  42 . 
     In the case of the micromirror actuator shown in FIG. 4B, the lower electrode  43  is located relatively far away from the rotation axis of the micromirror  42  so that the area of the opposing surface of each of the lower electrode  43  and the micromirror  42  is small. As shown in FIG. 5B, there is no equilibrium point between the torques T t  and T r , like in FIG.  5 A. 
     In the case of the micromirror actuator shown in FIG. 4C, the lower electrode  43  is located relatively close to the rotation axis of the micromirror  42  so that the area of the opposing surface of each of the lower electrode  43  and the micromirror  42  is small. Referring to FIG. 5C, equilibrium points exist between the torque T t  induced by attractive electrostatic force generated between the lower electrode  43  and the micromirror  42  and the torque T r  induced by the repulsive force of a spring, and thus an equilibrium state, in which the micromirror  42  stops rotating and maintains a predetermined rotation angle, exists. However, in the equilibrium state, the rotation angle of the micromirror  42  is approximately below 2 degrees, and the micromirror actuator is not considered useful. 
     The micromirror actuator shown in FIG:  4 D is the same as the micromirror actuator shown in FIG. 4A except for the vertical distance g between the micromirror  42  and a substrate  41 . In other words, the vertical distance g between the micromirror  42  and the substrate  41  of the micromirror actuator shown in FIG. 4D is longer than the vertical distance g between the micromirror  42  and the substrate  41  of the micromirror actuator shown in FIG.  4 A. Referring to FIG. 5D, an equilibrium point exists between the torque T t  induced by attractive electrostatic force generated between the lower electrode  43  and the micromirror  42  and the torque T r  induced by the repulsive force of a spring, unlike in FIG.  5 A. However, in this case, the rotation angle of the micromirror  42  is very small. Accordingly, in order to achieve an equilibrium state of the rotation angle of the micromirror  42 , the voltage applied to the micromirror  42  and the lower electrode  43  must be increased to about 90 V, as shown in FIG.  5 D. 
     FIG. 6A is a cross-sectional view of a micromirror actuator according to a first, illustrative and non-limiting embodiment of the present invention, which is formed to have the same variable values as the micromirror actuator shown in FIG.  4 D. FIG. 6B is a graph showing torque T t  induced by attractive electrostatic force and torque T r  induced by the repulsive force of a spring. As shown in FIGS. 6A and 6B, an equilibrium point exists between the torque T t  induced by an attractive electrostatic force generated between a micromirror  62  and a lower electrode  63  and the torque T r  induced by the repulsive force of a spring. At this point the rotation angle of the micromirror  62  is about 6 degrees and is greater than in the prior art. The rotation angle of the micromirror  62  can be increased more considerably by adjusting the vertical distance g between the micromirror  62  and a substrate  61  and by varying the depth of a trench  64 . 
     FIG. 7 is a cross-sectional view of a micromirror actuator according to a second, illustrative and non-limiting embodiment of the present invention. In the second embodiment, unlike in the first embodiment, trenches  74  are formed in a substrate  71  to have a slanted sidewall, and lower electrodes  73  are formed along the slanted sidewall of the trench  74 . In the second, illustrative and non-limiting embodiment, the distance between the micromirror  72  and the lower electrodes  73  is shorter during the rotation of the micromirror  72  than the distance between the micromirror  62  and the lower electrode  64  in the first embodiment, and thus the range, within the driving angle of the micromirror  72  can be varied, can be enlarged more considerably. 
     FIG. 8 is a cross-sectional view of a micromirror actuator according to a third, illustrative and non-limiting embodiment of the present invention. Referring to FIG. 8, a trench  84  is formed in a substrate  81  to have a stepped sidewall so that the distance between a lower electrode  83  formed along the stepped sidewall of the trench  84  and a micromirror  82  can be shorter than the distance between the lower electrode  73  and the micromirror  72  in the second embodiment, and thus the area of the opposing surface of each of the lower electrode  83  and the micromirror  82  can be expanded more. 
     According to the present invention, a microactuator is formed to include a trench, and electrodes are formed at the bottom and sidewall of the trench. Thus, it is possible to reduce voltage necessary to rotate a micromirror with a predetermined rotation angle. In addition, it is possible to realize a micromirror actuator having a wide range of driving angles by adjusting the voltage applied to the micromirror actuator. The micromirror actuator according to the present invention may be used in various fields including an optical communication field. For example, the micromirror actuator according to the present invention may be applied to devices using optical signals, such as a scanner, a display device, or an optical switch. 
     The above and other features of the invention including various and novel details of construction and combination of parts has been particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular construction and combination of parts embodying the invention is shown by way of illustration only and not as a limitation of the invention. The principles and features of this invention may be employed in varied and numerous embodiments without departing from the scope of the invention.