Abstract:
A micromirror driver for simultaneously and independently controlling a resonant frequency and an amplitude of a micromirror. A micromirror having a plurality of grooves is supported in rotation by an elastic body. Base electrodes having a comb shape are affixed to the grooves and along an edge of the micromirror. A plurality of driver electrodes also having a comb shape are respectively engaged with the base electrodes in a gear like arrangement to electrostatically interact with the micromirror in response to applied voltages. An amplitude and a frequency of the micromirror are controlled by varying a magnitude or a waveform of one or more electrode voltages or by varying a phase between voltages applied to at least two electrodes. Accordingly, greater driving forces, a larger rotation angle of the micromirror, and independent control of amplitude and resonant frequency of the micromirror are obtained.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
         [0001]    This application claims the benefit of Korean Application Nos. 2001-10916 and 2001-10917, both filed Mar. 2, 2001, in the Korean Patent Office, the disclosures of which are incorporated herein by reference.  
         BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The present invention relates to a micromirror driver, and more particularly, to a micromirror driver which controls a resonant frequency and an amplitude of a micromirror as the micromirror rotates due to electrostatic forces, and increases a rotation angle of the micromirror using a lower voltage, and to a method of controlling the micromirror driver.  
           [0004]    2. Description of the Related Art  
           [0005]    In general, micromirror drivers are operated by electrostatic forces and switch a path, along which light beams are reflected, using a rotation angle of a micromirror.  
           [0006]    Referring to FIG. 1, a conventional micromirror driver comprises a frame  5 , a trench  10  formed in the frame  5 , a micromirror  20  received in the trench  10  and having a base electrode  15 , a torsion spring  25  which supports the micromirror  20  in rotation, and an electrode  30  which interacts with the base electrode  15  to rotate the micromirror  20 .  
           [0007]    The micromirror  20  rotates about the torsion spring  25  due to electrostatic forces generated between the base electrode  15  and the electrode  30 , as shown in FIG. 2. If the micromirror sufficiently rotates with a predetermined rotation angle, the micromirror  20  is restored to a horizontal state due to elastic restoring forces of the torsion spring  25 . The micromirror  20  repeatedly rotates in the above-described manner. It is possible to allow a rotating body, such as the micromirror  20 , to rotate with a greater rotation angle with a use of less voltage, taking advantage of resonance characteristics of an oscillating body. In other words, it is possible to effectively operate an oscillating body with less driving forces if the oscillating body is operated with a frequency, which is the same as a resonant frequency of the oscillating body.  
           [0008]    A conventional method of adjusting the resonant frequency of a micromirror increases or decreases a mass of the micromirror and a spring constant of a torsion spring. However, such a mass of the micromirror and the spring constant of a torsion spring are set in accordance with manufacturing conditions and may vary according to an environment, in which the micromirror is manufactured or is driven. Accordingly, it is difficult to obtain a precise resonant frequency of the micromirror due to variations in the manufacture of the micromirror. Thus, various efforts have been made to control the resonant frequency of a micromirror after manufacturing the micromirror.  
           [0009]    The resonant frequency f of an oscillating body can be expressed by Equation (1).  
             f   =       1     2      π                K   t     I                 (   1   )                               
 
           [0010]    In Equation (1), K t  represents a spring constant, and I represents an inertia moment.  
           [0011]    The equation of motion concerning the micromirror  20  rotating with a predetermined rotation angle (θ) is shown below as Equation (2).  
                         I                   θ   ¨       +       C   t          θ   .       +       K   t        θ       =     τ        (     θ   ,   V     )                   =       1   2                              θ            (     C                   V   2       )                           (   2   )                               
 
           [0012]    In Equation (2), I represents an inertia moment, C t  represents capacitance between the base electrode  15  of the micromirror  20  and the electrode  30 , K t  represents the spring constant of the torsion spring  25 , and τ represents a rotation moment (torque). Where V 0 , α, and V represent an initial voltage of the electrode  30 , an arbitrary coefficient, and a driving voltage of the electrode  30 , respectively, and V=(V 0 +αθ), Equation (2) can be rearranged into Equation (3)  
                       I                   θ   ¨       +       C   t          θ   .       +       K   t        θ       =         1   2               C          θ            V   2       +       1   2          C        (     2      V     )                 V          θ                       =         1   2               C          θ            (       V   0   2     +     2        V   0        αθ     +       α   2          θ   2         )       +       1   2          C2        (       V   0     +   αθ     )          α                     (   3   )                               
 
           [0013]    by substitution of V=(V 0 +αθ).  
           [0014]    The capacitance C t  is linearly varied with respect to the rotation angle θ of the micromirror  20 , as shown in FIG. 3. In other words, as the rotation angle θ of the micromirror  20  increases, the distance between the base electrode  15  and the electrode  30  increases, and thus the capacitance C t  linearly decreases. Accordingly, a variation of the capacitance C t  with respect to a variation of the rotation angle θ becomes a constant γ. The constant γ can be expressed as  
              C          θ       =     γ   .                           
 
           [0015]    Accordingly, C=C 0 +γθ where C 0  represents a capacitance value when θ=0. Equation (3) can be rearranged into Equation (4) by substitutions of  
              C          θ       =   γ                         
 
           [0016]    and C=C 0 +γθ.  
                 I                   θ   ¨       +       C   t          θ   .       +       K   t        θ       =       1   2          [         (       γ                   V   0       +     2      α                   C   0         )          V   0       +       (       4      γα                   V   0       +     2        α   2          C   0         )        θ     +     3        γα   2          θ   2         ]               (   4   )                               
 
           [0017]    In the right side of Equation (4), (γV 0 +2αC 0 ) affects the rotation amplitude of the micromirror  20 , (4γαV 0 +2α 2 C 0 ) affects the resonant frequency f of the micromirror  20 , and 3γα 2  affects both the amplitude and the resonant frequency of the micromirror  20 . Here, if the resonant frequency f of the micromirror  20  is controlled by adjusting α, the voltage V of the driving voltage of the electrode  30  is varied because V=(V 0 +αθ). If the initial voltage V 0  of the electrode  30  is varied, α is also varied. Thus, it is impossible to simultaneously control the frequency f and the amplitude of the micromirror  20 . In other words, elements required to control the frequency f and the amplitude of the micromirror  20  are dependent on each other, and thus if one of the elements is controlled, the other element is affected by the controlled element and cannot be controlled simultaneously or independently.  
         SUMMARY OF THE INVENTION  
         [0018]    To solve the above-described problems, it is an object of the present invention to provide a micromirror driver, in which a frequency controlling electrode and an amplitude controlling electrode operate independently and thus a resonant frequency and an amplitude of a micromirror are independently and simultaneously controllable, allowing the micromirror to rotate with a larger rotation angle by decreasing a spring constant of a rotation axis of the micromirror. Another object of the present invention is to provide a method of controlling a micromirror driver.  
           [0019]    Additional objects and advantages of the invention will be set forth in part in the description which follows, and, in part, will be obvious from the description, or may be learned by practice of the invention.  
           [0020]    Accordingly, to achieve the above and other objects of the invention, according to one aspect of the present invention, there is provided a micromirror driver. The micromirror driver comprises a micromirror having at least one groove, an elastic body which supports the micromirror in rotation, and at least one electrode which receives a voltage to generate electrostatic forces to rotate the micromirror through interaction of the electrostatic forces with the micromirror. The amplitude and frequency of the micromirror are controlled by varying one of a magnitude and a waveform of the voltage of the at least one electrode.  
           [0021]    Each groove is formed in a respective peripheral area of the micromirror and is arranged near a rotation axis of the micromirror.  
           [0022]    Preferably, a first electrode controls the frequency of the micromirror during rotation of the micromirror, a second electrode controls the amplitude of the micromirror during the rotation of the micromirror, and the second electrode operates independently of the first electrode.  
           [0023]    A voltage V of the at least one electrode satisfies the equation, V 2 =V 0 +αθ, where V 0  represents an initial voltage of the at least one electrode, α represents an arbitrary coefficient, and θ represents a rotation angle of the micromirror. A voltage V 1  of the first electrode satisfies the equation, V 1   2 =V 0 ,and a voltage V 2  of the second electrode satisfies the equation, V 2   2 =V 0 .  
           [0024]    A base electrode is formed on the micromirror and the base electrode and the first and second electrodes are formed in a comb shape and the combs of the first and second electrodes and the comb of the base electrode are arranged gear-like so that an effective area of opposing surfaces of the electrodes is maximized.  
           [0025]    Preferably, a plurality of grooves are formed in the micromirror and arranged symmetrically with respect to the rotation axis of the micromirror.  
           [0026]    In order to achieve the above and other objects of the present invention, according to another aspect of the present invention, there is provided a micromirror driver. The micromirror driver comprises a micromirror having at least one groove and a base electrode formed at the groove, an elastic body which supports the micromirror in rotation, and at least two electrodes which drive the micromirror in rotation by generating electrostatic forces through interaction of the at least two electrodes with the base electrode and, the at least two electrodes operating independently of each other.  
           [0027]    One of the at least two electrodes is used to control the frequency of the micromirror by varying a waveform of a voltage applied to the one electrode.  
           [0028]    The other of the at least two electrodes is used to control the amplitude of the micromirror by varying the magnitude of the voltage applied to the other of the at least two electrodes.  
           [0029]    In order to achieve the above and other objects of the present invention, according to another aspect of the present invention, there is provided a method of controlling a micromirror driver, which comprises a micromirror, an elastic body supporting the micromirror in rotation, and at least one electrode. The method comprises: generating electrostatic forces between the micromirror and the at least one electrode; a voltage V of the at least one electrode to satisfy an equation, V 2 =V 0 +αθ where V 0  represents an initial voltage of the at least one electrode, α represents an arbitrary coefficient, and θ represents a rotation angle of the micromirror; and controlling a frequency and/or an amplitude of the micromirror by varying the initial voltage V 0  of the at least one electrode and the arbitrary coefficient α.  
           [0030]    Preferably, a second electrode controls a resonant frequency f of the micromirror by varying the arbitrary coefficient α in an equation, V 2 =αθ, and the resonant frequency f of the micromirror is expressed by the equation,  
       f   =       1     2      π                  K   t     -       γ   2        α       I                               
 
           [0031]    wherein K t  represents the spring constant of the elastic body, I represents an inertia moment of the micromirror, and γ2 represents a variation of capacitance with respect to a variation of the rotation angle θ of the micromirror.  
           [0032]    The second electrode controls the resonant frequency f of the micromirror by varying the arbitrary coefficient a in the equation, V 2 =αθ, and in a case where a voltage with a phase difference of π/2 is applied to the first and second electrodes, the resonant frequency f of the micromirror can be expressed by the equation,  
       f   =       1     2      π                  K   t     +       γ   2        α       I                               
 
           [0033]    wherein K t  represents the spring constant of the elastic body, I represents the inertia moment of the micromirror, and γ2 represents a variation of capacitance with respect to a variation of the rotation angle θ of the micromirror.  
           [0034]    In order to achieve the above and other objects, according to another aspect of the present invention, there is provided a method of controlling a micromirror driver, which comprises a micromirror, an elastic body supporting the micromirror in rotation, and at least one electrode which rotates the micromirror by generating electrostatic forces through interaction with the micromirror. The method includes the step of comprising controlling the resonant frequency of the micromirror by varying the waveform of the driving voltage of the at least one electrode. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0035]    The above objects and advantages of the present invention will become more apparent by describing in detail an embodiment thereof with reference to the attached drawings in which:  
         [0036]    [0036]FIG. 1 is a schematic plan view of a conventional micromirror driver;  
         [0037]    [0037]FIG. 2 is a diagram illustrating rotation of a conventional micromirror;  
         [0038]    [0038]FIG. 3 is a graph showing a variation of capacitance with respect to a rotation angle of a conventional micromirror;  
         [0039]    [0039]FIG. 4A is a plan view of a micromirror driver according to an embodiment the present invention;  
         [0040]    [0040]FIG. 4B is an enlarged view of a portion of FIG. 4A, showing an engagement of a first portion of a base electrode and a driver electrode;  
         [0041]    [0041]FIG. 4C is an enlarged view of a portion of FIG. 4A, showing an engagement of a second portion of the base electrode and another driver electrode;  
         [0042]    [0042]FIG. 5 is a graph showing a relationship between a driving voltage and motion of a micromirror according to an embodiment of the present invention; and  
         [0043]    [0043]FIG. 6 is a graph showing a variation of the driving voltage of the micromirror with respect to a rotation angle of the micromirror. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0044]    Reference will now be made in detail to the present embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout.  
         [0045]    Referring to FIGS. 4A, 4B and  4 C, a micromirror driver according to the present invention comprises a frame  100 , a micromirror  110 , a trench  108  having sufficient space in which to rotate the micromirror  110 , an elastic body  105  which elastically supports the micromirror in rotation, and at least one electrode to drive the micromirror  110 .  
         [0046]    The micromirror  110  comprises a reflector  110   a , by which light beams incident on the micromirror  110  are reflected, and at least one groove  110   b  formed in a peripheral area of the reflector  110   a.    
         [0047]    A first electrode  115 , controls a rotation amplitude of the micromirror  110  according to a magnitude of a first voltage applied to the first electrode  115 , and second electrodes  120 ,  121 ,  122 , and  123 , control a resonant frequency f of the micromirror  110  by controlling a waveform of a second voltage applied to at least one of the second electrodes  120 , 121 ,  122  and  123 , the second electrodes operating independently of the first electrode  115 . The first electrode  115  is located at a side or both sides of the trench  108  in a direction parallel with the elastic body  105 . Preferably, the second electrodes  120 ,  121 ,  122 , and  123  are each located to be inserted into a respective groove  110   b.    
         [0048]    A base electrode  113 , which interacts with the first electrode  115  and the second electrodes  120 ,  121 ,  122 , and  123  to generate electrostatic forces, is located to face the first electrode  115  and the second electrodes  120 , 121 , 122 , and  123 . In particular, since the base electrode  113  is formed at sidewalls of the groove  110   b  of the micromirror  110 , the effective area where the driving force of the micromirror is primarily obtained is maximized. That is, a larger area for interaction of the electrodes is obtained, which serves to enhance the driving force of the micromirror, where the groove  110   b  is formed around the micromirror  110  as compared with a conventional micromirror formed in a plate shape without a groove. In order to maximize the area of the opposing surface of the base electrode  113  and the first and second electrodes  115 , and  120  through  123 , the first electrode  115 , the second electrodes  120  through  123 , and the base electrode  113  are formed in a comb shape. The first electrode  115  comprises a plurality of projections  115   a  as shown in FIG. 4B and the second electrodes  120  through  123  each comprise a plurality of projections of which the projections  122   a  shown in FIG. 4C are exemplary. The base electrode  113  comprises a plurality of projections  113   a  which are arranged to be in gear with the projections  115   a  of the first electrode  115  or the projections of each of the second electrodes  120  through  123 . The reflector  110   a  may be formed to have a minimum surface area as long as the reflector  110   a  does not lose a function of reflection of light beams. Preferably, the grooves  10   b  are formed to be symmetrical with respect to a rotation axis C of the micromirror  110 .  
         [0049]    Next, a method of controlling a micromirror driver having structure as described with reference to FIG. 4 will be described below.  
         [0050]    The micromirror  110  is rotated due to electrostatic forces generated by interaction between the base electrode  113  and the first and second electrodes  115 , and  120  through  123 . Here, a voltage V of the electrodes used to drive the micromirror  110  is expressed by a term for determining the magnitude of the voltage V and a term for determining a waveform of the voltage V. For example, the driving voltage V of the micromirror  110  is formed into V 2 =V 0 +αθ where V 0  represents an initial voltage and α represents an arbitrary coefficient.  
         [0051]    [0051]FIG. 5 is a graph showing time to apply a driving voltage V and variation of the waveform of the driving voltage V with respect to an arbitrary coefficient α according to the motion of the micromirror  110 . Here, a critical angle θc represents the maximum angle, by which the micromirror  110  is rotated due to electrostatic forces. As shown in FIG. 5, the waveform of the voltage varies in accordance with a variations.  
         [0052]    [0052]FIG. 6 is a graph showing variation of a driving voltage V 2  with respect to a rotation angle θ. As shown in FIG. 6, the driving voltage V 2  is proportional to the rotation angle θ of the micromirror  110 , and accordingly, a depends on an initial voltage V 0  when the driving voltage V 2  reaches a predetermined level. In other words, if the initial value V 0  is varied when the driving voltage V 2  reaches a predetermined level, a also varies.  
         [0053]    In a case where V 2 =V 0 +αθ and only one electrode is used, Equation (2) can be rearranged into Equation (5) by substitution of V 2 .  
                         I                   θ   ¨       +       C   t          θ   .       +       K   t        θ       =       1   2                              θ            (     C                   V   2       )                   =         1   2                 C                       θ            V   2       +       1   2        C                 V   2                         θ                       =         1   2                 C                       θ            (       V   0     +   αθ     )       +       1   2        C                 α                           (   5   )                               
 
         [0054]    As described above, if  
                  C                       θ       =   γ     ,     C   =       C   0     +     γθ   .                               
 
         [0055]    Accordingly, Equation (5) can be rearranged into Equation (6) by the substitution of  
              C          θ       =       γ                 and                 C     =       C   0     +     γ                   θ   .                                 
 
                 I                     θ     ¨       +       C   t          θ   .       +       [       K   t     -     γ                 α       ]        θ       =       1   2          (       γ                   V   0       +     α                   C   0         )               (   6   )                               
 
         [0056]    Here, K t −γα affects the frequency of the micromirror  110 , and  
         1   2          (       γ                   V   0       +     α                   C   0         )                           
 
         [0057]    affects the amplitude of the micromirror  110 . According to Equation (6), the frequency f is controllable, while varying the coefficient α and amplitude of the micromirror  110 , and while varying the initial voltage V 0 .  
         [0058]    In a case where V 2 =V 0 +αθ, V 1   2 =V 0 , and V 2   2 =αθ (V 1  represents the voltage of the first electrode, and V 2  represents the voltage of the second electrodes), the driving voltage V of the micromirror  110  can be expressed by Equation (7).  
         
       V=V 
       1 
       2 
       +V 
       2 
       2  
     
           V   1   2   =V   0 ,  
           V   2   2 =αθ 
         [0059]    Equation (8) can be obtained by substituting Equation (7) into Equation (2) and rearranging Equation (2) with respect to the rotation angle θ of the micromirror  110 .  
                     I                     θ   ¨                    +     C   t                  θ   .                    +     K   t              θ     =                  1   2                              θ            (     C                   V   2       )                   =                    1   2          (            C                       θ       )          (       V   1   2     +     V   2   2       )       +       1   2        C                            θ            (       V   1   2     +     V   2   2       )                     =                    1   2          (            C                       θ       )          V   1   2       +       1   2          (            C                       θ       )          V   2   2       +       1   2          C        (            V   1   2            θ       )         +       1   2          C        (            V   2   2            θ       )                         (   8   )                               
 
         [0060]    In the right side of Equation (8),  
       (            C                       θ       )                         
 
         [0061]    of the first term concerns the first electrode  115  and thus will be marked with subscript 1. On the other hand,  
       (            C                       θ       )                         
 
         [0062]    of the second term concerns the second electrodes  120  through  123  and thus will be marked with subscript 2. As described above, C varies linearly with respect to θ, and thus the differentiation terms of capacitance with respect to θ, concerning the first and second electrodes  115 , and  120  through  123 , can be represented by γ 1  and γ 2  respectively. Accordingly,  
           (            C                       θ       )     1     =     γ   1                           
 
         [0063]    and  
           (            C                       θ       )     2     =       γ   2     .                           
 
         [0064]    Equation (8) can be rearranged into Equation (9) by substitution of V 1   2 =V 0  and V 2   2 =αθ.  
               I                     θ   ¨                    +     C   t                  θ   .                    +     K   t              θ     =                    1   2          γ   1          V   0       +       1   2          γ   2        α                 θ     +       1   2          C   2        α               (   9   )                               
 
         [0065]    Equation (9) can be rearranged into Equation (10) by substitution of C 2 =C 20 +γ 2 θ where C 20  represents the value of C 2  when θ is 0.  
                     I                     θ   ¨                    +     C   t                  θ   .                    +     K   t              θ     =                    1   2          γ   1          V   0       +       1   2          γ   2        α                 θ     +       1   2          (       C   20     +       γ   2        θ       )        α                   =                    1   2          γ   1          V   0       +       γ   2        α                 θ     +       1   2          C   20        α                     (   10   )                               
 
         [0066]    Equation (10) can be rearranged with respect to the rotation angle θ of the micromirror  110  into Equation (11).  
                 I                         θ   ¨     +     C   t                                θ   .       +       (       K   t     -       γ   2                   α       )        θ       =       1   2          (         γ   1                     V   0       +     α                   C   20         )               (   11   )                               
 
         [0067]    (K t −γ 2 α) in the left side of Equation (11), which is the coefficient of θ, affects the resonant frequency f of the micromirror  110 , and  
         1   2          (         γ   1          V   0       +     α                   C   20         )                           
 
         [0068]    in the right side of Equation (11) affects the amplitude of the micromirror  110 . In other words, the resonant frequency f of the micromirror can be expressed by Equation (12) using Equations (1), (2), and (11).  
             f   =       1     2      π                  K   t     -       γ   2        α       I                 (   12   )                               
 
         [0069]    According to Equation (12), the resonant frequency f of the micromirror  110  is controllable by varying an arbitrary coefficient α. The amplitude of the micromirror  110  can be controlled by  
         1   2          (         γ   1          V   0       +     α                   C   20         )                           
 
         [0070]    of Equation (11). Where the resonant frequency f of the micromirror  110  is controlled by varying a, the amplitude of the micromirror  110  is also affected by the variation of α. However, the amplitude of the micromirror  110  is controllable by controlling V 0 . Here, since V 0  is an independent variable, which is not affected by the variation of α, the amplitude of the micromirror  110  is controllable independently of the control of the resonant frequency f of the micromirror  110 . Accordingly, the resonant frequency and amplitude of the micromirror  110  are satisfactorily controllable independently and simultaneously.  
         [0071]    In another method of controlling a micromirror driver, the resonant frequency f of the micromirror  110  is controllable by applying a voltage with a predetermined phase difference to the first and second electrodes  115 , and  120  through  123 . For example, if voltages with a phase difference of π/2 are applied to the first and second electrodes  115 , and  120  through  123 , γ 2 α has a negative value. Thus, the resonant frequency f of the micromirror  110  can be expressed by Equation (13).  
             f   =       1     2      π                  K   t     +       γ   2        α       I                 (   13   )                               
 
         [0072]    Here, K t  represents the spring constant of the elastic body  105 , I represents inertia moment, and γ 2  represents a variation of capacitance with respect to a variation of the rotation angle θ of the micromirror  110 . According to Equation (13), the resonant frequency f of the micromirror  110  is controllable by controlling an arbitrary coefficient α, which determines the waveform of the voltage.  
         [0073]    As described above, since the micromirror  110  in the micromirror driver according to the present invention includes the groove  110   b  to maximize an area prepared for electrodes to be installed, the mass of the micromirror  110  can be reduced to less than a mass of a conventional plate-shaped micromirror. As the mass of the micromirror  110  decreases, the inertia moment I of the micromirror  110  decreases. If the inertia moment I of the micromirror  110  decreases, and the resonant frequency f of the micromirror  110  is maintained at a predetermined level, the spring constant K t  of the elastic body  105  decreases according to Equation (12). However, the micromirror  110  is driven against restoring elastic forces of the elastic body  105  having a predetermined spring constant K t . Thus, as the elastic body  105  has a lower spring constant K t , less driving force is required to rotate the micromirror  110  with a predetermined rotation angle. In other words, as the spring constant K t  of the elastic body  105  becomes lower, a larger rotation angle of the micromirror  110  is obtained with less driving force. Accordingly, the micromirror driver according to the present invention uses the groove  110   b  as an area prepared for electrodes to be installed and reduces the spring constant K t  of the elastic body  105  with the use of the groove  110   b.    
         [0074]    As described above, the base electrode  113  and the first and second electrodes  115 , and  120  through  123  are formed in a comb shape. Since the base electrode  113  is arranged to be in gear with the first or second electrodes  115 , or  120  through  123 , the area of the opposing surface of the base electrode  113  and the first or second electrodes  115 , and  120  through  123  is maximized, and thus effective electrostatic forces generated by interaction between the base electrode  113  and the first and second electrodes  115 , and  120  through  123  is maximized with the use of a predetermined voltage.  
         [0075]    In the meantime, as the distance L 1  (FIG. 3) between the rotation axis C of the micromirror  110  and the first or second electrodes  115 , or  120  through  123  decreases, the critical angle θ c  of the micromirror  110  increases. If the critical angle θ c  of the micromirror  110  increases, the degree, to which electrostatic forces affect the micromirror  110  increases, and thus the range, in which the resonant frequency f of the micromirror  110  is controllable, increases even when the micromirror  110  rotates with a very large rotation angle. In the present invention, since the first and second electrodes  115 , or  120  through  123  are arranged at the sidewalls of the groove, the distance L 1  between the rotation axis of the micromirror  110  and the first or second electrodes  115 , or  120  through  123  is minimized.  
         [0076]    As described above, since the micromirror driver according to the present invention includes a electrode which controls the resonant frequency of a micromirror and a second electrode which controls the amplitude of the micromirror, which operates independently of the resonant frequency controlling electrode and is not affected by the resonant frequency controlling electrode, the resonant frequency and the amplitude of the micromirror are controllable simultaneously and independently of each other.  
         [0077]    In addition, the micromirror driver according to the present invention obtains a large rotation angle of the micromirror by reducing the inertia moment of the micromirror and the spring constant of the elastic body, while maintaining the effective area of the micromirror.  
         [0078]    Finally, since an area which engages the resonant frequency controlling electrode and an area which engages the amplitude controlling electrode are prepared in the micromirror of the micromirror driver according to the present invention, greater driving forces are obtained with the use of less voltage. In addition, since the distance between the rotation axis of the micromirror and the controlling electrodes is reduced and the area of the opposing surface of electrodes interacting with each other is increased, the range, in which the resonant frequency of the micromirror is controllable, is expanded even where the micromirror rotates with a very large rotation angle.  
         [0079]    Although a few embodiments of the present invention have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.