Abstract:
A micromechanical device comprising one or more electronically movable structure sets comprising for each set a first electrode supported on a substrate and a second electrode supported substantially parallel from said first electrode. Said second electrode is movable with respect to said first electrode whereby an electric potential applied between said first and second electrodes causing said second electrode to move relative to said first electrode a distance X, (X), where X is a nonlinear function of said potential, (V). Means are provided for linearizing the relationship between V and X.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     The present invention claims priority to U.S. Provisional Application Ser. No. 60/363,139 commonly owned with the application. 
     
    
     STATEMENT REGARDING FEDERALY SPONSORED RESEARCH OR DEVELOPMENT  
       [0002]     This invention was made with Government Support under Contract Number W-7405-ENG-48 awarded by the Department of Energy. The Government has certain rights in the invention. 
     
    
     BACKGROUND OF THE INVENTION  
       [0003]     Among the applications for micromechanical devices are planar actuators comprising one or typically an array of actuators in a two-dimensional matrix in which individual elements of the array need to be individually and rapidly displaced.  
         [0004]     In one application of such actuators to the deflection of radiation, an array of actuators includes mirrors activated by micromechanical electrostatic motivators to provide rapid displacement of the mirror positions in the array in order to alter the phase delay of incoming radiation wavefronts and thereby adjust the phase of the reflected light or the angle of reflection.  
         [0005]     In modern high-speed systems such as scanners and pattern recognition systems, the demands for rapid adjustment of the phase of reflected light or beam angle continue to increase, placing severe demands upon control circuitry for an array of large dimensions to precisely and individually control each of hundreds or thousands of mirror elements in the array.  
         [0006]     An additional problem encountered in controlling such actuators is the nonlinearity between displacement and applied control voltage due to the mathematical relationship between displacement and applied potential in what is essentially a parallel-plate capacitor geometry. To deal with the nonlinearity in order to provide accurate beam reflection, a heavy demand is placed upon processing electronics to accomplish any adjustment to the hundreds or thousands of individual actuators for controlling the position on an ongoing, rapid sequence basis.  
       BRIEF SUMMARY OF THE INVENTION  
       [0007]     The present invention provides for an effective way of linearizing the response between desired position and applied potential that takes advantage of and places structured designs directly into the micromechanical structure. It is operative directly in response to digital signals, avoiding the complexity and delay of looped processing to accomplish the mathematical linearization.  
         [0008]     According to the present invention, at least one electrode of each of the parallel plate actuator elements is divided into a plurality of electrode segments of varying area, from a minimum first area to a maximum, nth area of greatest value, through a plurality of areas increasing from one to the other by a factor of two. Each of the electrode segments is individually addressed through voltage gates that are controlled by binary ones and zeroes directly representative of the applied voltage potential. The resulting nonlinear transfer function that relates the applied potential to the effective displacement caused by the applied potential counteracts some or all of the nonlinearity in the relationship or transfer function between applied potential and actuator displacement.  
         [0009]     The nonlinearity in the transfer characteristic between applied potential and actuator displacement is completely eliminated by adjusting the applied voltage that is applied to each of the electrode segments through the use of a plurality of current sources each of magnitude varying from a low minimum first magnitude corresponding to and activated with activation of the first electrode segment and varying, one to the other, by factor of two up to the largest or nth current source, corresponding to and activated simultaneously with activation of the largest or nth electrode segment.  
         [0010]     The resulting system utilizes a simple structure not requiring time-consuming electronic processing of the applied potential in order to produce a linear relationship between displacement and input value, but nevertheless linearizing its relationship with respect to the displacement value it causes. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]     The present invention is more fully understood with respect to the drawings of which:  
         [0012]      FIGS. 1A and 1B  are perspective views of first and second examples of a planar actuator of the type to which the present invention is applied;  
         [0013]      FIG. 2  is a schematic diagram of a single element of an actuator array of the type illustrated in  FIGS. 1A and 1B ;  
         [0014]      FIGS. 3A and 3B  are graphs representing the transfer function between the desired deflection represented by either a voltage or a digital number versus the actual displacement in an actuator of the type illustrated in  FIG. 2 , being respectively nonlinear and linearized transfer functions.  
         [0015]      FIG. 4  is a diagram illustrating the operation of a planar array in reflecting the rays of a light beam;  
         [0016]      FIG. 5  is a schematic diagram illustrating a circuit according to the invention for controlling individual actuator elements of a planar activator array;  
         [0017]      FIG. 6  illustrates the linearization of the transfer function relating the digital input signal and the displacement;  
         [0018]      FIG. 7  is a diagrammatic illustration of a system for controlling a planar array using circuitry of the type illustrated in  FIG. 5 . 
     
    
     DETAILED DESCRIPTION  
       [0019]      FIGS. 1A and 1B  illustrate planar arrays of actuators typical of those in which the present invention is operative. Each array includes a substrate  12  having thereon electrodes  14  on an insulating layer  13 . In typical micromechanical versions of the arrays, the substrate  12  is silicon, the insulating layer  13  silicon nitride, and electrodes  14  may be either metalizations or conductive diffusions, each with appropriate leads, typically metalizations, not shown to apply potential thereto. Above the substrate  12  a plurality of second electrodes  16  are supported by legs  18  in the case of  FIG. 1A  or monolithic structures  20  in the case of  FIG. 1B . In the case of  FIG. 1A , the electrodes  14  may be commonly connected whereas the second electrodes  16  are individually metallized and connected by supports  18  to individual circuit leads. In the case of  FIG. 1B , the first electrodes  14  will typically be individually connected to circuit leads while the electrodes  16  are commonly connected to a single lead.  
         [0020]     A reflective surface  22  is fastened above the second electrodes  16  via posts  24  in both versions of  FIGS. 1A and 1B .  
         [0021]      FIG. 2  illustrates in cross-section a single actuator  26  from the planar array illustrated in  FIG. 1B . In this case, the bottom electrodes  14  are individually connected through leads not shown to individually controlled sources of potential, such as the exemplary voltage source  28 , while the second, upper electrodes  16  are connected in common through supports  20 , typically to ground  30 . The dimensions illustrated in  FIG. 2  are exemplary only to identify the scale of the structures of micromechanical devices of this type and are not to be seen as limiting.  
         [0022]     The force created by the voltage source  28 , shown only for purposes of illustration of operation of such activators, produces along illustrated electrostatic field lines  32  a force between the electrodes  14  and  16 . As the voltage increases, the force increases, and the displacement in the direction X of the electrode  16  toward the electrode  32  increases. The relationship for such a structure is illustrated by the graph of  FIG. 3A  which shows a typical transfer function between applied voltage V and displacement X. The curve  36  representing that transfer function is dramatically nonlinear reflective of the fact that as the electrode  16  approaches the electrode  14 , the force due to the applied voltage increases such that for every unit increase in applied voltage the resulting displacement becomes larger than the displacement for units at lower levels of applied voltage. Such a situation makes for a complication in the ability to accurately control, typically in an open loop function such as in an image processor, the reflected phase or angle of deflection of an incident light beam.  
         [0023]      FIG. 4  illustrates for such a typical array  26  the physics of light beam reflection. As shown in this example, an incident beam  40  of radiation is reflected by the reflective or mirror elements  22  creating an output beam  42 . The input beam  40  has a wavefront  44  representing the locus of same phase radiation in the input beam  40 . The output beam  42  has a wavefront  46  again representing a locus of identical phase in the output beam  42 . In an unactivated situation the mirrors  22  lie in the same plane but diverge when activated by the application of a potential individually between the electrodes  14  and  16  of each actuator in array  26 . Upon activation selectively of the mirrors  22  by applying respectively different voltages between the electrodes  14  and  16 , the path length of the input beam and the output beam  42  can be varied over the entire area of the wavefront  44  delaying some sections relative to other sections which in turn causes the output beam wavefront  46  to be changed in phase resulting in a change in the phase of selected sections of the output beam itself.  
         [0024]     In order to change or steer the input beam  40  onto different trajectories for output beams  42  it is essential that a progressive change in displacement occur over the entire array of mirrors  22 . To accomplish that accurately with the transfer function illustrated in  FIG. 3A  requires an enormously complex processing scheme if it is done electronically before the application of the individual voltages V between the electrodes  14  and  16 . The present invention linearizes the effect of the applied voltage such that a transfer function between a digital number representing the desired deflection and the actual displacement  50  as illustrated in  FIG. 3B  is achieved. This is accomplished using a circuit of the type shown in  FIG. 5  which can be substantially integral with the micromechanical structure and thus does not require time-consuming electronic processing that would reduce the response speed of the structure.  
         [0025]     As illustrated in  FIG. 5 , each of the electrodes  14  is segmented into a plurality of electrode segments  60 ,  62  . .  64  each of increasing area with a ratio of increase between each successively larger segment being a factor of two, from the smallest, first electrode segment  60  to the largest, nth electrode segment  64 . While  FIG. 5  illustrates only three electrode segments  60 - 64  it is to be understood in the application of the invention to a real structure there could be a larger number of electrode segments depending upon the desired resolution and the acceptable expense for the array and distribution circuitry to convert the incoming voltage, typically in digital binary form to separate ones and zeroes for each electrode segment  60 - 64  application lead  66 . Each lead  66  is fed with a signal from corresponding data lines  70 ,  72  and  74 . For example, if an 8-bit data word or byte is used, representing 256 possible data states or voltage levels, there will be eight electrode segments  60 - 64  and corresponding data leads  70 - 74  corresponding to the individual zero and one bit positions in the data word. By activating a select combination of the electrode segments it is possible to achieve the corresponding voltage effect in 256 resolution steps. The digital ones and zeroes operate through control switches  80 ,  82  and  84  which may be integral to the structure. The digital ones and zeroes representing the desired deflection of said actuator  20  are carried on input lines  70 , 72 , 74  and are obtained from the output of a digital control device such as a computer, microprocessor, microcontroller, or logic circuit. The number of digital bits of said digital signal corresponds to the number of electrodes  60 - 64  included in the system. Each of the switches  80 - 92  is activated by one digital line  70 , 72 , 74  of the digital signal, with the line  70  corresponding to the least significant bit (LSB) connected to the switch  80  and, in turn, the electrode segment of smallest area, and the line  74  corresponding to the most significant bit (MSB) connected to the switch  84  and, in turn, the nth electrode segment of largest area.  
         [0026]     The effect of the linearization achieved through the use of switches  80 - 84  is to linearize the transfer function illustrated in  FIG. 3A  to the form illustrated by curve  90  in  FIG. 6 . This is linearized to the extent that the curve is substantially flattened and can be adjusted to have end points fitted to the end points of a fully linearized transfer function illustrated by curve  92 .  
         [0027]     To achieve a linearization corresponding to the curve  92  an adjustment in the reference voltage corresponding to the same digital word is provided by applying a varying load in the form of current sources  100 ,  102  and  104 , connected via switches  101 ,  103 , and  105  to a junction point  106  common with the application of voltage V o  from a source  108  through a resistor  110 . The sources  100 ,  102 ,  104  are connected to the common junction point  106  by switches  101 ,  103 , and  103  controlled through the same digital lines controlling the switches  80 - 84 . The magnitude of the current of each current source increases according to a series from a first current of lowest value corresponding to the LSB and the smallest electrode segment, increasing by a factor of two from current source to current source to the largest, nth current source corresponding to the MSB and largest area electrode segment. In this manner, a total linearization of the transfer function as illustrated in curve  92  can be achieved.  
         [0028]     The mathematics corresponding to this linearization operate as follows:  
         [0029]     Mechanical restoring force for a given displacement of the actuator electrode:
 
FM=−kx  (1)
 
 where k is a mechanical spring constant and x the displacement. 
 
         [0030]     Electrostatic force for a given applied voltage:  
               F   E     =         εA   TOT     ⁢     V   2         2   ⁢       (     g   -   x     )     2                 (   2   )             
 
 where g is the spacing between electrodes  14  and  16  at zero applied voltage, A TOT  their area of overlap as seen from a view perpendicular to the surface, and ε a physical constant called the permittivity. 
 
         [0031]     Equilibrium occurs when F M +F E =0:  
             kx   =             εA   TOT     ⁢     V   2         2   ⁢       (     g   -   x     )     2         ⁢   or   ⁢           ⁢   2   ⁢       kx   ⁡     (     g   -   x     )       2       =       εA   TOT     ⁢     V   2                 (   3   )             
 
         [0032]     Define a constant C=2k/ε, so that the above becomes:
 
 Cx ( g−x ) 2   =A   TOT   V   2   (4)
 
         [0033]     In one application of Eq. (4), one can keep the voltage V constant and adjust the area A TOT  by activating only some subset of the electrode segments A n . In such a case, solving Eq. (4) for the required A TOT  as a function of desired displacement x results in  
               A   TOT     =         C     V   2       ⁢       x   ⁡     (     g   -   x     )       2       =       C     V   2       ⁡     [       x   3     -     2   ⁢     gx   2       +       g   2     ⁢   x       ]                 (   5   )             
 
 This relationship is nonlinear and is undesirable for the reasons described previously. A desirable condition is one in which the displacement x is linearly proportional to the activation area A TOT , i.e., dx/dA, and therefore dA/dx, are constant. Taking the derivative of Eq. (5) with respect to x leads to  
               dA   dx     =       C     V   2       ⁡     [       3   ⁢     x   2       -     4   ⁢   gx     +     g   2       ]               (   6   )             
 
 Taking this equation&#39;s reciprocal results in:  
               dx   dA     =       V   2       C   ⁡     (       3   ⁢     x   2       -     4   ⁢   gx     +     g   2       )                 (   7   )             
 
         [0034]     One can then impose the additional constraint that V also be a function of the desired displacement x. Specifically, let V(x)=V o (g−x)/g, where V o  is the value of V at zero displacement, and where V is reduced as x approaches in value that of the gap spacing, g. The displacement equation, now a function of both area A TOT  and applied voltage V(x), becomes:  
               A   TOT     =         C     V   2       ⁢       x   ⁡     (     g   -   x     )       2       =         gC         V   0   2     ⁡     (     g   -   x     )       2       ⁢       x   ⁡     (     g   -   x     )       2       =       gC     V   0   2       ⁢   x                 (   8   )             
 
 The displacement x then becomes  
             x   =         V   0   2     ⁢     A   TOT       gC             (   9   )             
 
         [0035]      FIG. 7  illustrates an overall digital bit application system for use in the present invention. Voltage from a command system  120  is applied through and converted in a processor  121  which may be hard- or software operated, to apply a digital word  122  to a distribution system  124  which applies on busses  130 ,  132  . .  134 , voltages representing the binary bits 0 or 1 in some combination to individual actuators  140 . The busses  130 - 134  will typically contain multiple leads for the individual electrode segments to be activated as illustrated above with respect to  FIG. 5 .  
         [0036]     The above-described preferred embodiment is intended as exemplary only, the scope of the invention being described and limited only as shown in the following claims.