Abstract:
A micro electro-mechanical system (MEMS) positioner, including an actuator and method for making the same, includes a stage formed within a first layer of semiconductor material, along with a series of beams, flexure hinges and controlled input thermal actuators. The actuators are operatively engaged with a second layer, and are selectively actuatable to effect longitudinal expansion thereof, so that relative actuation between individual ones of actuators spaced in the planar direction relative to one another is configured to generate controlled movement of the stage within the planar direction, and relative actuation between individual ones of actuators spaced orthogonally to the planar direction relative to one another is configured to generate controlled movement of the stage out of the planar direction. The relative position between the stage and the support is adjustable in each of six degrees of freedom, so that the compliant mechanism forms a quasi-static precision manipulator.

Description:
This application is related to U.S. patent application Ser. No. 10/175,415, filed on Jun. 19, 2002, entitled “Six Degree of Freedom Flexure Stage”. 
   BACKGROUND OF THE INVENTION 
   (1) Field of the Invention 
   The present invention relates generally to a MEMS (Micro Electro-Mechanical Systems) device, and more particularly, to a micro-scale alignment device capable of repeatedly aligning a stage portion relative to a support structure with a relatively high degree of accuracy and precision with up to six degrees of freedom. 
   (2) Background Information 
   There is a growing need for fine motion control and positioning at micro and nano scales, such as for the growing number of MEMS applications, including active alignment of fiber optic elements, x-y stages with nanometer level resolution, and machine elements for micro-scale machinery. Also, micro-mirrors, micro-resonators, and manipulation for bio molecules . . . etc will require multi-axis nano and micro-positioners. 
   Culpepper, in U.S. patent application Ser. No. 10/175,415, filed on Jun. 19, 2002, entitled “Six Degree of Freedom Flexure Stage”, (the ‘415 reference’) which is fully incorporated herein by reference, discloses an adjustable monolithic compliant mechanism. This compliant mechanism includes a stage which may be adjusted by displacing one or more tabs coupled thereto, to provide for controlled movement in six degrees of freedom. 
   Next generation applications (e.g., fiber optic alignment, optical switching, and the like) will require precision alignment devices capable of being fabricated on a micro- or nano-scale, e.g., as MEMS devices fabricated on a chip-level using many conventional semiconductor fabrication techniques, and which are capable of providing high resolution (i.e., nanometer/microradian) position control with six degrees of freedom (i.e., x, y, z, θ x , θ y , and θ z ). 
   Indeed, as shown in  FIG. 1 , a lateral misalignment as small as 0.001 mm have been shown to generate insertion losses in fiber optics of 1 dB. Likewise, angular misalignment as small as 0.001 rad (0.057 degree) may result in more than 1 dB loss. Unfortunately, conventional alignment devices typically require actuation along at least three mutually orthogonal axes in order to generate movement with six degrees of freedom. Such actuation, however, does not lend itself to the planar structures typically associated with semiconductor fabrication and MEMS devices. Therefore there exists a need for a micro-scale alignment device configured for fabrication using micro-scale wafer fabrication techniques. 
   SUMMARY OF THE INVENTION 
   One aspect of the present invention includes a micro electro-mechanical system (MEMS) positioner which includes a stage within a first layer of semiconductor material. The first layer also includes a series of beams, a series of first flexure hinges coupled to the stage and to the beams, and a plurality of first controlled input thermal actuators extending longitudinally therein. The first actuators are coupled to the first beams at spaced locations thereon. A second stage extends in a planar direction within a second layer of semiconductor material. The second layer also includes a series of second beams, a series of second flexure hinges coupled to the second stage and to the second beams, and a series of second controlled input thermal actuators extending longitudinally therein. The second actuators are coupled to the second beams at spaced locations thereon. The first layer is superposed with the second layer, which are coupled to one another by an intermediary layer which extends intermittently in the planar direction. Each of the first and second actuators are selectively actuatable to effect longitudinal expansion thereof, so that relative actuation between individual ones of actuators spaced in the planar direction relative to one another is configured to generate controlled movement of the stage within the planar direction, and so that relative actuation between individual ones of actuators spaced orthogonally to the planar direction relative to one another is configured to generate controlled movement of the stage out of the planar direction. The relative position between the stage and the support is adjustable in each of six degrees of freedom, so that the compliant mechanism forms a quasi-static precision manipulator. 
   Another aspect of the invention includes a micro electro-mechanical system (MEMS) positioner including a stage and at least one beam extending in a planar direction, with a series of flexure hinges coupled to the stage and to the beams. A series of controlled input thermal actuators extend longitudinally within a first planar layer, being coupled to the beam at spaced locations thereon. A series of members extend longitudinally within a second planar layer, and are coupled to the beam at spaced locations thereon. The first layer is superposed with the second layer. Each of the actuators are selectively actuatable to effect longitudinal expansion thereof, so that actuation of the actuators is configured to generate controlled movement of the stage out of the planar direction and the compliant mechanism forms a quasi-static precision manipulator. 
   A further aspect of the invention includes a micro electro-mechanical system (MEMS) actuator assembly including a first actuator extending longitudinally in a first planar layer of semiconductor material, to form an electrical pathway therethrough, having a relatively high resistance portion and a relatively low resistance portion. A similar second actuator extends longitudinally in a second planar layer of semiconductor material, so that the first and second layers are superposed with one another with the low resistance portions being coupled to one another, and with the high resistance portions being free of one another. Each of the first and second actuators are configured for selective actuation by selectively conveying electric current therethrough, to generate thermal expansion of the relatively high resistance portions thereof, so that common actuation of both the first and second actuators is configured to generate movement of the actuator system within a planar direction; and actuation of one relative to the other of the first and second actuators is configured to generate controlled movement of the system out of the planar direction. 
   Another aspect of the invention includes a micro electro-mechanical system (MEMS) actuator assembly including a thermal actuator extending longitudinally in a first planar layer, the actuator forming an electrical pathway therethrough. A member extends longitudinally in a second planar layer, so that the first layer and the second layer are parallel to one another, and the actuator and member are coupled to one another. The actuator is configured for actuation by selective application of electricity thereto, to generate expansion thereof, so that actuation of the actuator is configured to generate controlled movement of the system out of the planar direction. 
   A yet further aspect of the invention includes a method of fabricating a positioner. The method includes providing a semiconductor wafer having at least two device layers alternately superposed with at least two oxide layers, applying a mask layer to the uppermost device layer, etching exposed portions of the uppermost device layer, and etching exposed portions of the uppermost oxide layer. The method further includes removing the mask layer, applying a metallization layer onto exposed portions of the device layers, masking portions of the metallization layer, to mask a desired contact area, etching the metallization layer to remove unwanted portions thereof, and removing the mask from remaining metallization to reveal contact areas. Additional steps include masking exposed areas of the wafer, etching exposed portions of the exposed device layer, etching exposed portions of the exposed oxide layer, etching exposed portions of exposed device layer, and masking the underside of the wafer and protecting the topside of the wafer. The underside of the wafer is then etched to an oxide layer, followed by applying a vaporized etchant to the wafer to remove exposed portions of oxide layer; and removing the mask. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a chart showing typical insertion losses associated with fiber optic misalignment; 
       FIG. 2  is a perspective schematic view of a typical fiber optic alignment application; 
       FIG. 3  is a schematic plan view of an exemplary embodiment of a positioner of the present invention; 
       FIG. 4  is a schematic perspective view of an actuator, on an enlarged scale, of the embodiment of  FIG. 3 ; 
       FIG. 5  is a schematic cross-sectional view, taken along  5 - 5  of  FIG. 3 ; 
       FIG. 6A  is a view similar to that of  FIG. 3 , with the positioner actuated to generate rotational movement about the z-axis; 
       FIG. 6B  is a view similar to that of  FIG. 3 , with the positioner actuated to generate translational movement along the y-axis; 
       FIG. 6C  is an elevational schematic view of the embodiment of  FIGS. 6A &amp; 6B , actuated to generate translational movement along the z-axis; 
       FIG. 7  is a graphical representation of the temperature profile of a portion of the embodiment of  FIG. 5 ; 
       FIGS. 8A-8F  are views similar to those of  FIGS. 6A &amp; 6B , of various alternate embodiments of the present invention actuated to generate translational movement in the x-direction; 
       FIG. 9  is a chart showing simulated results for the embodiments of  FIGS. 8A-8F ; 
       FIGS. 10A-10C  are cross-sectional elevational views similar to that of  FIG. 5 , of optional structures being applied to an embodiment of the present invention; 
       FIG. 11  is a table of cross-sectional elevational views similar to those of  FIGS. 10A-10C , of various steps in the fabrication of the embodiment of  FIGS. 3 and 5 ; 
       FIGS. 12A and 12B  are graphical representations of theoretical vs. actual test results of an embodiment of the present invention; 
       FIG. 13  is a plan view of a portion of an alternate embodiment of the present invention; 
       FIG. 14  is a chart of test results comparing aspects of various embodiments of the subject invention; and 
       FIG. 15  is a view similar to that of  FIG. 3 , of an alternate embodiment of the present invention including various optional aspects. 
   

   DETAILED DESCRIPTION 
   Referring to the accompanying figures, the present invention is directed to a micro-scale alignment device (e.g., nanopositioner) adapted to provide six-axis alignment (i.e., movement with six degrees of freedom) in microsystems such as MEMS devices. For example, with reference to  FIG. 2 , an embodiment of the present invention shown as nanopositioner  20 , may be installed within a fiber alignment device  22  to align optics  24  with a fiber  26 . As shown in  FIG. 3 , in this embodiment, nanopositioner  20  is a planar, monolithic, micro-scale device which generates controlled displacements/motions via compliance of the device&#39;s structure. This device  20  includes an inner stage  30  supported via hinges  32  by beams  34 . Beams  34  are coupled, e.g., at opposite ends thereof, to distal ends of actuators  36 . Proximal ends of actuators  36  are secured to ground  38 . 
   Advantageously, nanopositioner  20  does not require joints and therefore avoids the friction, wear and hysteresis errors associated with conventional macro-scale devices, and which tend to preclude their use in nanomanipulation (e.g., MEMS) applications. Moreover, this device  20  provides desired six-axis alignment, including both in-plane and out-of-plane movement, using only in-plane actuators. As will be discussed in greater detail hereinbelow, embodiments of the present invention accomplish this movement using an unorthodox multiple layer approach which generates out-of-plane motion without the use of out-of-plane actuators. As typically used, and as used herein, ‘in-plane’ motion refers to motion in the x, y, and θ z  directions ( FIG. 3 ), while ‘out-of-plane’ motion refers to motion in the θ x , θ y , and z directions. 
   Examples of device  20  have been shown to achieve six-axis alignment in a work volume (i.e., work envelope) as small as 5×5×2 μm 3 , with nanometer/micro-radian resolution (e.g., resolution of 0.015 μm with repeatability of 5 nanometers and a force of approximately 150 μN from a device with a 1 mm 2  device footprint. These embodiments are easily scalable, and additional examples, e.g., having footprints of 1.2, 1.5 and 3 mm 2  have been built. Moreover, exemplary devices having a work volume of 6×6×10 μm 3  have been shown to generate up to 500 μN of force, to exhibit a force ratio of approximately 80 μN of force for each 1 μm of in plane work envelope. The combination of these abilities makes embodiments of the present invention capable of practical, six-axis alignment of small-scale components. These embodiments may thus be used in many micro-scale applications, such as MEMS, fiber optic components including wave guides and sources/receivers, and micro-photonic components/chips. In addition, embodiments of the present invention may be configured to provide for long term fixation without power. 
   These and other advantages of this invention will become evident in light of the following detailed discussion of various embodiments thereof. 
   Turning now to  FIG. 4 , embodiments of the present invention are provided with a generally U-shaped actuator  36 . Actuator  36  extends longitudinally along a length L within a first planar layer of thickness H as shown. This actuator is fabricated from, or otherwise includes electrically conductive or semiconductive material(s) so that it effectively forms a U-shaped electrical pathway extending between contacts disposed proximate to first and second grounded end portions  40 ,  42 , respectively. In particular embodiments, actuator  36  is fabricated from a semiconductor material as discussed hereinbelow. In these embodiments, the electrical pathway is formed by a relatively narrow, and high resistance, portion  44  separated by a gap G from a relatively wide, and low resistance, portion  46 . An open neck portion  48  facilitates displacement as discussed hereinbelow. 
   During operation, current passing through actuator  36  along the U-shaped electrical pathway tends to heat up high resistance portion  44 , while low resistance portion  46  remains relatively cool. This action generates longitudinal expansion of the portion  44  relative to portion  46 , which displaces actuator  36  in the direction of displacement D as shown. 
   Turning now to  FIG. 5 , device  20  is provided with a multiple layer construction, to include a first set of actuators  36  disposed on the first layer, and a second layer of actuators  36 ′ disposed on a second layer. In the embodiment shown, a spacer layer  37  is used to physically join, while separating and thermally insulating, the first and second layers to effectively form a three-layer construction. Stage  30 ,  30 ′ may be optionally provided with a central bore  31 ,  31 ′ to facilitate some positioning applications. 
   The multi-layer architecture, while tending to be counter-intuitive for the reasons discussed below, advantageously provides device  20  with both in-plane and out-of-plane motion. For example, simultaneous actuation of both superposed first and second actuators  36  and  36 ′ generates movement of stage  30 ,  30 ′ ‘in-plane’ such as shown in  FIGS. 6A &amp; 6B . In  FIG. 6A , alternate pairs of actuators  36  and  36 ′ have been actuated to generate in-plane rotation of stage  30  around the z-axis. In  FIG. 6B , all but two of the actuator pairs  36 ,  36 ′ have been actuated to displace stage  30  along the y-axis. 
   Out-of-plane motion may be generated by activating actuators  36 ,  36 ′ independently of one another, (or energizing them with different power levels to achieve combinations of in-plane and out-of-plane displacement). As shown in  FIG. 6C , actuators  36  have been activated without activating actuators  36 ′, to move stage  30  in the −z direction. 
   Those skilled in the art will recognize that nominally any combination of actuators  36 ,  36 ′ may be activated to generate movement of stage  30  in any one or more of six degrees of freedom, i.e., x, y, z, θ x , θ y , θ z , alone or in combination. 
   Advantageously, this multi-layered construction enables both in-plane and out-of-plane motion solely by use of in-plane actuators. This aspect facilitates fabrication on a micrometer scale, e.g., on a semiconductor wafer, for MEMS and other micro-scale applications, using many conventional semiconductor/integrated circuit (IC) fabrication techniques, despite conventional wisdom in this regard. Conventional wisdom generally indicates that the bond formed between layers fabricated using techniques such as chemical vapor deposition, microlithography, and etching (e.g., deep reactive ion etching (DRIE)) would likely fail due to shear when subjected to the out-of-plane loading described herein. Surprisingly, however, finite element simulations and tests of the multi-layered silicon-based embodiments of the present invention have demonstrated out-of-plane movement of stage  30 ,  30 ′ without buckling or delamination. 
   Yet another unexpected advantage of the multi-layered construction of embodiments of the present invention is the ability to achieve a high degree of flatness. Flatness is a quality that is highly desirable for micro-scale precision manipulators such as device  20 , but is relatively difficult to achieve in MEMS devices. While not wishing to be tied to any particular theory, applicants suspect that embodiments hereof attain their high degree of flatness because residual stresses inherent in each single layer as a result of conventional MEMS fabrication techniques, tend to offset one another. Thus, any stresses within one of the two outer layers are effectively balanced by those of the other outer layer. The flatness of the central stage has been shown to be as small as a +/−1 μm deviation over 3 mm size. 
   Another factor tending to militate against the multi-layered approach of the instant invention is the high thermal conductivity of silicon and other semiconductors. It would thus be expected that the heat generated during activation of actuator  36  would tend to transfer readily to its mirror image actuator  36 ′ and prevent the creation of a thermal gradient between the layers sufficient to generate the required out-of-plane movement. The instant applicants, have, however, overcome this difficulty through the use of the aforementioned intermediary layer (e.g., SiO2). 
   In this regard, attention is directed to  FIG. 7 , which is a simulated, representative thermal profile taken through the high resistance portions ( FIG. 4 ) of an activated actuator  36 , an adjacent inactive actuator  36 ′, and an intermediate layer of SiO 2  disposed therebetween. This profile indicates that even in the event that a portion of actuator  36  were as high as 900 degrees K, a corresponding portion of actuator  36 ′, separated from actuator  36  by only a one micron thickness of SiO 2 , would remain at or below approximately 380 degrees K to provide a significant thermal gradient. Moreover, an air gap, such as provided between portions (e.g., high resistance portions) of adjacent actuators  36 ,  36 ′ is expected to provide even greater thermal isolation for an even greater thermal gradient. 
   Turning now to  FIGS. 8A-8F , various embodiments of the invention desirably utilize actuators that are relatively stiff in their lateral directions, while providing compliant support for stage  30  in the longitudinal direction. Device  20  provides the requisite lateral stiffness through the use of actuators  36 ,  36 ′, as shown and described hereinabove, while the desired longitudinal compliance is provided by beams  34  ( FIG. 3 ). Although the configuration of device  20  has been found to meet these requirements, many other configurations may be devised to provide the desired functionality. Examples of various alternate configurations are shown in  FIGS. 8A-8E , with device  20  shown in  FIG. 8F . In these figures, each embodiment is shown with its actuators selectively activated to generate displacement in the x-direction. 
   Simulated results for each of the embodiments of  FIGS. 8A-8F  are shown in  FIG. 9 . These results indicate that device  20  ( FIG. 8F ) provides the highest maximum displacement of the center of its stage, and the highest transmission ratio. As used herein, ‘transmission ratio’ refers to the ratio of the movement of the center of stage  30 ,  30 ′ to the movement at the distal end of actuators  36 ,  36 ′. While these embodiments provide a transmission ratio ranging from about 0.05 to about 0.8, in light of the disclosures herein, the skilled artisan will recognize that embodiments of the present invention may be configured with a transmission ratio within a range extending from much smaller than one, e.g., on the order of 0.05, to orders of magnitude larger, e.g., on the order of 10-50. Turning now to  FIGS. 10A-10C , as an additional option, a fixation layer  50  may be utilized. For clarity of exposition, and for convenience, fixation layer  50  is shown and described as being applied to a device  20 , of which only the upper layer thereof, including actuators  36  and stage  30 , is shown. It is to be understood that a similar fixation layer may be applied to any of the embodiments shown and described herein. 
   Fixation layer  50  serves to maintain the relative position of stage  30 ,  31 ′, without requiring a continuous supply of power to the device  20 . Fixation layer  50  may be fabricated from the same material as that of device  20 , e.g., using similar fabrication techniques. 
   For example, layer  50  may be patterned, e.g., using conventional etching/masking techniques, to produce a heater portion  53  supported by a spacer layer  51 , to extend in spaced, superposed orientation with device  20 . A portion of layer  50  may also be deposited onto stage  30 , e.g., atop a suitably sized portion of spacer layer  51  as shown, to form a collar  52 . Clearance sufficient to permit normal operation of device  20  is provided between collar  52  and terminal ends  54  of ground portions  53  as shown. Solder  56  is deposited on terminal ends  54 . 
   In operation, device  20  is operated as described hereinabove, to move stage  30  ( 30 ′) to a desired position, such as shown in  FIG. 10B . Thereafter, heater portions  53  are heated, e.g., by passing electric current therethrough in a conventional manner, to melt solder  56 , so that the solder flows between terminal ends  54  and collar  52 . Facing surfaces of ends  54  and collar  52  may be optionally metallized to facilitate flow of the melted solder into the position shown in  FIG. 10C . 
   Heater portions  53  may then be deactivated to permit solder  56  to solidify while actuators  36 ,  36 ′ maintain stage  30 ,  30 ′ in the desired position. In this regard, because the actuators are disposed relatively far away from solder  56  and from stage  30  (see, e.g.,  FIG. 3 ), heat generated by the actuators should not prevent solidification of solder  56  in most applications. Once solder  56  has solidified, the actuators may be powered down, wherein the solder  56  will maintain stage  30 ,  30 ′ in the desired position. In the event re-alignment is desired, heater portions  53  may be re-heated to re-melt solder  56 , whereupon stage  30 ,  30 ′ may be moved to a new position. 
   Although the sequence of operations shown and described with respect to  FIGS. 10A-10C  relate to fixation of an in-plane displacement, the skilled artisan should recognize that this fixation approach may be used to maintain nominally any position of stage  30 ,  30 ′, e.g., positions including any combination of translations and rotations with up to six degrees of freedom. 
   Having described various embodiments of the present invention, the following is a description of an exemplary method of fabrication thereof. This method is shown and described with respect to device  20 , with the understanding that the skilled artisan, in light of the teachings hereof, may apply it to any of the other embodiments shown and described herein. 
   Turning now to  FIG. 11 , at  60 , a double SOI (silicon on insulator) wafer is provided, having two device layers  80 ,  80 ′ (e.g., 8 μm thick), and two oxide layers  82 ,  82 ′ (e.g., 1 μm thick) on an insulator  84 . Although a double silicon wafer is used in this example, embodiments of this invention may be fabricated from nominally any material known to those skilled in the art, including semiconductors such as doped silicon and/or aluminum nitride (AlN), or nominally any other material which may be developed in the future. In this regard, it is anticipated that non-conductive materials, e.g., having conductive components embedded therein, may be used to fabricate various embodiments hereof. 
   At  62 , a photoresist  86  is applied and patterned to form a mask layer. At  64 , a shallow etchant is applied to remove the exposed portions of device layer  80 . A second etchant is then applied to remove the newly exposed portions of oxide layer  82 . Photoresist layer  86  is then removed, e.g., through the use of asher (oxygen plasma). 
   At  66 , electrical contacts  88 ,  88 ′ for the actuators ( 36 ,  36 ′  FIG. 5 ) are provided by applying (e.g., by sputtering, evaporating, or other means of depositing or growing) a metallization layer onto the wafer, i.e., onto exposed portions of layers  80  and  82 . A photoresist is applied and patterned to portions of the metallization layer, to mask the desired contact area. An aluminum etchant is then used to remove unwanted aluminum. The photoresist is then removed, e.g., with oxygen plasma. 
   At  68 , a relatively thick photoresist is applied to exposed surfaces of the wafer, and prebaked. The photoresist is patterned  70  into the desired topography of device  20  (e.g.,  FIG. 3 ). 
   At  72 , a shallow etchant is applied to remove the exposed portions of device layer  80 . A second (e.g., vaporized) etchant is then applied to remove the newly exposed portions of oxide layer  82 . A shallow etchant is again applied to remove the exposed portions of second device layer  80 ′. 
   At  74 , the underside of the wafer is patterned with a photoresist and etched to the oxide layer  82 ′. At  76 , a vaporized etchant (e.g., HF vapor) is used to remove exposed portions of oxide layer  82 ′. At  78 , the photoresist is removed, e.g., by use of oxygen plasma, to produce completed device  20 . 
   The following illustrative example is intended to demonstrate certain aspects of the present invention. It is to be understood that this example should not be construed as limiting. 
   EXAMPLE 
   An exemplary device  20  of 3 mm in diameter was fabricated substantially and shown and described with respect to  FIG. 11 . A double SOI wafer with two device layers of thickness 8 μm, and two oxide layers 1 μm (N type/Sb Doped/&lt;110&gt;/Resistivity=0.01˜0.1 ohm/cm) was used in step  60 . An Endura™ vapor deposition machine was used to sputter a 5000 Angstroms aluminum (Al+2% Si) metallization layer in step  66 . A vapor of concentrated HF (49%) was used to etch oxide layer  82 ′ in step  76 . 
   In-plane and out-of-plane tests were conducted on the resulting device  20  using a ZYGO™ white light interferometer and a Micro-vision™ system to view the static and dynamic functions. Displacement of the device was measured and plotted as a function of input current as shown in  FIGS. 12A and 12B . These test results indicated actual, non-calibrated displacement generally within 10 percent of theoretical, using finite element analysis (FEA). The working temperature is expected to be within the range of 300-900 K, with a resolution of approximately 0.015 μm and repeatability to within approximately 0.005 μm. The expected work volume for this embodiment, as indicated in terms of the range of motion in each of the aforementioned six degrees of freedom, measured at the center of stage  30 , is shown in the following Table 1. 
   
     
       
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
                 
               TABLE 1 
             
             
                 
                 
             
             
                 
               X 
               Y 
               Z 
               θ x   
               θ y   
               θ z   
             
             
                 
               [μm] 
               [μm] 
               [μm] 
               [degree] 
               [degree] 
               [degree] 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               Range 
               4.16 
               4.36 
               10.50 
               1.26 
               1.09 
               1.34 
             
             
                 
             
           
        
       
     
   
   Turning now to  FIGS. 13 and 14 , still another optional variation of the foregoing embodiments is shown and described. In the foregoing embodiments, actuators  36 ,  36 ′ were shown and described having high resistance portions  44  ( FIG. 4 ) of substantially uniform transverse cross-section. However, as shown in  FIG. 13 , alternative embodiments of the instant invention may be provided with actuators  136  having high resistance portions  144  of non-uniform, e.g., contoured, transverse cross-sections. 
   It has been found by the instant inventors that such a contoured transverse cross-section may generate improved output force and/or stroke. The inventors have found that by varying the width of beam ‘in-plane’, temperature distribution (thermal strain) in the beam portion  144  is enhanced, while the bending stiffness (potential to store energy) is reduced, relative to similar beam portions of uniform cross-section. As such, these portions  144  generally have improved mechanical efficiency (higher force and stroke) and improved utilization of actuating power relative to beam portions of uniform transverse cross-section. 
   In a particular exemplary embodiment, a finite element analysis (FEA) simulation of actuator performance for a constant width silicon beam (width: 22.5 μm) was compared with that of a contoured beam (width: 15-30 μm, averaging 22.5 μm). Each actuator beam had the same length of 1.6 mm and the same thickness of 30 μm. Both beams were tested in a conventional chevron configuration with an included taper angle of 1 degree. The same maximum temperature (680 K) was set for each actuator portion. The results of the simulation indicated that the contoured beam had a wider, more uniform temperature distribution. A more uniform temperature distribution generally means that more material along the length of the beam is at a higher temperature, so that the contoured beam exhibits a greater overall temperature-induced strain (i.e., displacement) than does the constant width beam. 
   A comparison of the performance of the two actuator types is provided in  FIG. 14 . This comparison indicates that the contoured beam generates approximately a 100% increase in stroke (displacement), a 50% reduction in response time, and a 10% reduction in power requirements relative to a similar beam portion of uniform cross-section. Moreover, preliminary experiments have shown the actuator has up to an 800 μm stroke, and is otherwise suitable for general MEMS actuator design. 
   The artisan of ordinary skill will readily recognize that there are many variable shapes and configurations for the various portions of the various embodiments of this invention that may be used to alter the repeatability, resolution, and position control capabilities, etc., thereof. 
   Moreover, although embodiments have been shown and described herein effectively having ‘mirror image’ actuators  36 ,  36 ′ superposed with one another, it should be recognized by those skilled in the art, that such mirror image actuators may be disposed in non-superposed or offset relationship from one another without departing from the spirit and scope of the present invention. For example, an alternate embodiment of the present invention shown as device  20 ′ in  FIG. 15 , may be configured substantially similarly to that of device  20 , though having the actuators of one of its layers shifted and/or rotated in plane relative to those of the other layer. As shown, actuator  36 ″ of a second layer is shifted in plane relative to its corresponding actuator  36 . In addition, or alternatively, an actuator  36 ′″ of the second layer may be rotated relative to its corresponding actuator  36  as also shown. 
   In addition, the skilled artisan should also recognize that various embodiments of the present invention may include substantially any type of layered MEMS actuator system, including two or more mutually distinct types of actuators, and/or non-activatable actuators (e.g., compliant substrates), to enable out of plane motion without departing from the spirit and scope of the present invention. 
   The modifications to the various aspects of the present invention described hereinabove are merely exemplary. Other variations, modifications, and other implementations of what is described herein will also occur to those of ordinary skill in the art without departing from the spirit and the scope of the invention as claimed. Accordingly, the invention is to be defined not just by the preceding illustrative description, but instead by the spirit and scope of the following claims.