Abstract:
A micro-electro-mechanical system (MEMS) mirror device includes an mirror, bonding pads, springs, and beams connected to the mirror. The mirror has a width greater than 1000 and less than 1200 microns, a length greater than 4000 and less than 5500 microns, and a thickness greater than 240 microns. Each beam includes a plurality of rotational comb teeth and is connected by multiple springs to the bonding pads.

Description:
FIELD OF INVENTION 
   This invention relates to micro-electro-mechanical system (MEMS) devices, and more particularly to MEMS scanning mirrors. 
   DESCRIPTION OF RELATED ART 
   Various electrostatic comb actuator designs for MEMS scanning mirrors have been proposed. The extensive applications of these devices include barcode readers, laser printers, confocal microscopes, projection displays, rear projection TVs, and wearable displays. Typically a MEMS scanning mirror is driven at its main resonance to achieve a large scan angle. To ensure a stable operation, it is crucial to ensure the mirror and its associated movable structure will vibrate in the desired mode shape at the lowest and main resonant frequency. In many applications, the mirror size has to be large and the mirror surface has to be flat to ensure high optical resolution. The mirror vibration/scanning speed also has to be fast for many applications. It is known that when the mirror size and scanning speed increase, the mirror dynamic flatness deteriorates. Without a flat mirror surface, the scanning mirror is of little use to many applications. In addition, this main frequency has to be separated far from other structural vibration frequencies to avoid potential coupling between the desired and the undesired mode shapes. 
   The undesired structural vibrations will increase the mirror dynamic deformation and result in degraded optical resolution. Furthermore, some of the structural vibration modes may cause the rotationally movable and stationary comb teeth to come into contact and break the actuator all together. Two or more structural vibration modes with close resonant frequencies may be coupled to produce high vibration amplitude that leads to hinge failure. Thus, an apparatus and a method are needed in the design of MEMS scanning mirrors to effectively improve the vibration stability at resonance, and to ensure optical resolution of these devices. 
   SUMMARY 
   In one embodiment of the invention, a micro-electro-mechanical system (MEMS) mirror device includes a mirror, bonding pads, springs, and beams connected to the mirror. The mirror has a width greater than 1000 and less than 1200 microns, a length greater than 4000 and less than 5500 microns, and a thickness greater than 240 microns. Each beam includes a plurality of rotational comb teeth and is connected by multiple springs to the bonding pads. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1A ,  1 B,  1 C,  1 D,  1 E,  1 F, and  1 G illustrate a MEMS device in one embodiment of the invention. 
       FIGS. 1H ,  1 I,  1 J, and  1 K illustrate the MEMS device of  FIG. 1A  with different power schemes in embodiments of the invention. 
       FIG. 2  illustrates process for manufacturing the device of  FIG. 1A  in one embodiment of the invention. 
       FIGS. 3 ,  4 ,  5 ,  6 ,  7 , and  8  illustrate a MEMS device in another embodiment of the invention. 
       FIG. 9  illustrates process for manufacturing the device of  FIGS. 3 ,  4 ,  5 ,  6 ,  7 , and  8  in one embodiment of the invention. 
       FIG. 10  illustrates another rib structure for supporting the mirror of a MEMS device in another embodiment of the invention. 
   

   Use of the same reference numbers in different figures indicates similar or identical elements. 
   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1A  illustrates a MEMS scanning mirror device  400  in one embodiment of the invention. Device  400  includes a top layer  402  bonded atop but electrically insulated from a bottom layer  404 . 
     FIGS. 1B and 1C  illustrate the details of top layer  402 . Top layer  402  includes a top mirror layer  406  having an oval shape. Top mirror layer  406  includes trenches/grooves  408  on its top surface. Trenches  408  reduce the mass of top mirror layer  406 , which in turn minimizes the total dynamic deformation. By minimizing the total dynamic deformation, the optical resolution of device  400  is improved. Although shown to run along the entire top surface, trenches  408  may be most effective when placed along the outer perimeter of top mirror layer  406  away from a rotational axis  414 . As described later, trenches  408  can be etched at the same time as other components by controlling their width so they are not etched through top mirror layer  406 . Alternatively, a shadow mask can be used to protect top mirror layer  406  during etching to prevent trenches  408  from etching through. The positions and the number of trenches  408  can be refined through finite element analysis. Gaps  409 A and  409 B separate top mirror layer  406  from the surrounding components in top layer  402 . As described later, the width of gaps  409 A and  409 B is designed to be greater than the widths of the gaps around more fragile components so that any trapped gas can escape around top mirror layer  406  instead of the fragile components during the etching process. 
   Opposing sides of top mirror layer  406  are connected by multiple support attachments  410  to the proximate ends of beam-like structures  412 A and  412 B. By connecting top mirror layer  406  at multiple locations to beams  412 A and  412 B, the dynamic deformation of top mirror layer  406  is minimized. The positions and the number of support attachments  410  can be refined through finite element analysis. 
   Opposing sides of beams  412 A and  412 B about a rotational axis  414  are connected to rotational comb teeth  416 . Rotational comb teeth  416  each has a tapered body that consists of an end rectangular section that has a smaller cross-section than a base rectangular section. By reducing the size and thus the weight of rotational comb teeth  416  at its ends, the inertia of the entire structure is reduced. By reducing the structural inertia, the scanning speed can be increased or/and the driving voltage can be reduced. In one embodiment, rotational comb teeth  416  provide the electrostatic biasing force used to increase the driving efficiency of the movable structure by tuning its modal frequency. In another embodiment, rotational comb teeth  416  provide the electrostatic driving force to drive the mirror. In yet another embodiment, rotational comb teeth  416  provide both the electrostatic biasing force and the electrostatic driving force. 
   Beams  412 A and  412 B are connected by serpentine springs to bonding pads mounted atop bottom layer  404 . Specifically, beam  412 A has a distal end connected by a serpentine spring  422 - 1  to a bonding pad  424 , and a midsection connected by serpentine springs  422 - 2  and  422 - 3  to a bonding pad  426  formed within beam  412 A. Similarly, beam  412 B has a distal end connected by a serpentine spring  428 - 1  to a bonding pad  430 , and a midsection connected by serpentine springs  428 - 2  and  428 - 3  to a bonding pad  432  formed within beam  412 B. Thus, beams  412 A and  412 B are connected by springs in a distributed manner along rotational axis  414  of top mirror layer  406 . Beams  412 A and  412 B may include holes  433  to reduce their mass. 
   By carefully adjusting the distribution of the stiffness and the location of the springs, all modal frequencies of the movable structure can be effectively separated and the desired rotational mode can be designed at the lowest resonance frequency. Since the main resonant frequency is the lowest and far apart from other structural modal frequencies, the mirror rotation will not excite any other undesired vibration mode. By using multiple springs, the maximum stress and strain on each spring are lower than conventional scanning mirror designs supported by only a pair of torsional beams. Since the stress and strain on each spring are reduced, the reliability of each spring is improved and the rotational angle is increased. 
   Top layer  402  may include stationary comb teeth  434  that are interdigitated in-plane with rotational comb teeth  416 . Stationary comb teeth  434  may have a tapered body like rotational comb teeth  416 . In one embodiment, stationary comb teeth  434  provide the electrostatic biasing force used to increase the driving efficiency of the movable structure by tuning its modal frequency. In another embodiment, stationary comb teeth  434  provide the electrostatic driving tree to drive top mirror layer  406 . In yet another embodiment, stationary comb teeth  434  provide both the electrostatic biasing force and the electrostatic driving force. Stationary comb teeth  434  are connected to bonding pad  436  mounted atop bottom layer  404 . 
     FIGS. 1D ,  1 E,  1 F, and  1 G illustrate the details of bottom layer  404 . Bottom layer  404  includes a bottom mirror layer  460  having a protrusion  462  from an oval plate  464 . A gap  465  separates bottom mirror layer  460  from the surrounding components in bottom layer  404 . As shown in  FIG. 1F , the bottom surface of plate  464  serves as the reflecting surface and other structures can be aligned with the mirror using assembly alignment marks  466  on the bottom surface of bottom layer  404 . The top surface  467  of bottom mirror layer  460  is bonded with the bottom surface of top mirror layer  406  to form the final mirror. As shown in  FIG. 1G , the final mirror has an I-beam like structure where top mirror layer  406  forms the top flange, protrusion  462  forms the web, and plate  464  forms the bottom flange. The I-beam like structure removes most of the mirror mass and stiffens the mirror structure. Therefore, it minimizes the dynamic deformation of the bottom mirror surface. By minimizing the total dynamic deformation of bottom mirror surface, the optical resolution of device  400  is improved. The shape of the I-beam like structure can be refined through finite element analysis. 
   Bottom layer  404  includes surfaces for anchoring the bonding pads of the movable structure in top layer  402 . Specifically, anchoring pads  468  and  470  provide surfaces for mounting corresponding bonding pads  426  and  432 , and anchoring pad  472  provides a surface for mounting bonding pads  424 ,  430 , and  436 . 
   Bottom layer  404  includes stationary comb teeth  474  that are out-of-plane interdigitated with rotational comb teeth  416 . In other words, they are interdigitated when viewed from above or when the final mirror is rotated. Stationary comb teeth  474  may have a tapered body like comb teeth  416  and  434 . Referring to  FIG. 1E , a gap  482  is provided between stationary comb teeth  474  and anchoring pad  472 . Gap  482  has a width greater than gaps  484  between adjacent stationary comb teeth  474  so that gap  482  is etched deeper into bottom layer  404  than gaps  484 . A deeper gap  482  allows rotational comb teeth  416  to rotate at a greater angle without contacting bottom layer  404 . In one embodiment, stationary comb teeth  474  provide the electrostatic driving force to drive the final mirror. In another embodiment, stationary comb teeth  474  provide the electrostatic biasing force used to increase the driving efficiency of the movable structure. In another embodiment, stationary comb teeth  474  provide both the electrostatic driving force and the electrostatic biasing force. In yet another embodiment, the capacitance between rotational comb teeth  416  and stationary comb teeth  474  is sensed to determine the rotational position of the mirror. 
     FIG. 2  illustrates a method  500  for making device  400  in one embodiment of the invention. The process starts at a step  0  with a silicon wafer  502  having a silicon dioxide layer  504  formed on the top surface and a silicon dioxide layer  506  formed on the bottom surface. Wafer  502  is used to form bottom layer  404  ( FIG. 1E ) of device  400 . 
   In step  1 , a photoresist  508  is deposited on oxide layer  506 , exposed, and developed in a lithographic process to define one or more lithographic alignment marks  511  (shown in step  3 ). 
   In step  2 , the bottom surface of wafer  502  is etched to remove portions of oxide layer  506  left unprotected by photoresist  508 . In one embodiment, oxide layer  506  is dry etched. The top surface of wafer  502  is deposited with a photoresist  510  to protect it from the etching of the bottom surface. 
   In step  3 , the bottom wafer surface of wafer  502  is etched to remove portions of wafer  502  left unprotected by oxide layer  506  to form lithography alignment marks  511 . After the silicon dry etch, the remaining photoresists  508  and  510  are stripped. 
   In step  4 , photoresist  510  is reapplied and is exposed and developed in a lithographic process to define bottom mirror layer  460  ( FIG. 1E ), surfaces  468 ,  470 , and  472  ( FIG. 1E ), and stationary comb teeth  474  ( FIG. 1E ) on the top surface of wafer  502 . The mask used is aligned with the lithographic alignment marks  511  on the bottom wafer surface. 
   In step  5 , the top surface of wafer  502  is etched to remove portions of oxide layer  504  left unprotected by photoresist  510 . In one embodiment, oxide layer  504  is dry etched. 
   In step  6 , the top surface of wafer  502  is etched to remove portions of wafer  502  left unprotected by oxide layer  504  to form bottom mirror layer  460  ( FIG. 1E ), surfaces  468 ,  470 , and  472 , and stationary comb teeth  474  ( FIG. 1E ). Afterwards, the remaining photoresist  510  is stripped and oxide layers  504  and  506  are removed by a wet or dry etch. 
   In step  7 , a silicon wafer  512  is bonded to the top surface of wafer  502 . Wafer  512  has a silicon dioxide layer  514  formed on the top wafer surface and a silicon dioxide layer  516  formed on the bottom wafer surface. Wafer  512  is used to form top layer  402  ( FIG. 1C ) of device  400 . In one embodiment, wafers  512  and  502  are bonded by silicon fusion. 
   In step  8 , a photoresist  518  is deposited on oxide layer  514 , exposed, and developed in a lithographic process to define the components of top layer  402  ( FIG. 1C ). The mask used is aligned with lithographic alignment marks  511  on the bottom wafer surface. Also defined in step  8  are one or more lithographic alignment marks  521  (shown in step  10 ) and a separation trench  519  (shown in step  10 ). In order to etch trenches  408  ( FIG. 1C ), which are etched into wafer  512  at a particular depth, along with the gaps that surround the other components, which are etched through wafer  512 , the dimensions of trenches  408  and the gaps of the other components are differentiated. 
   In step  9 , the top surface of wafer  512  is etched to remove portions of oxide layer  514  left unprotected by photoresist  518 . In one embodiment, oxide layer  514  is dry etched. Afterwards, the remaining photoresist  518  is stripped. 
   In step  10 , the top surface of wafer  512  is etched to remove portions of wafer  512  left unprotected by oxide layer  514  to form the components of top layer  402  ( FIG. 1C ). In one embodiment, wafer  512  is etched using a DRIE process down to the etch stop formed by oxide layer  516 . When the top of device  400  is etched through, gas trapped between the bonded wafers  502  and  512  may escape and damage fragile components such as the comb teeth. To prevent such damage, gaps  409 A and  409 B ( FIG. 1C ) around top mirror layer  406  ( FIG. 1C ) are designed to be larger than the gaps around the other components so that oxide layer  516  beneath gaps  409 A and  409 B are etched through before the other gaps. This allows the air to escape around top mirror layer  406 , which is a structurally strong component. 
   In step  11 , the top surface of the mirror is protected by a shadow mask surface  522  to prevent the top mirror layer  406  from being etched through. This step is optional if inertia-reducing trenches  408  have a width that is smaller than other gaps so they are not etched through. However, the shadow mask may be preferred to create inertia-reducing trenches  408  having greater width, thereby removing more mass and further reducing the inertia of the rotating structure. 
   In step  12 , a photoresist  520  is deposited on the bottom surface of wafer  502 , exposed, and developed on the bottom surface of wafer  502  to define assembly alignment marks  466  ( FIG. 1F ), separation trench  509  (shown in step  13 ), and gap  465  ( FIG. 1E ) for separating bottom mirror layer  460  ( FIG. 1E ) from bottom layer  404  ( FIG. 1E ). The mask used is aligned with lithographic alignment marks  521  on the top wafer surface. 
   In step  13 , the bottom surface of wafer  502  is etched to remove portions of wafer  502  left unprotected by photoresist  520  to form assembly alignment marks  466  ( FIG. 1F ) and separation trench  509 , and to separate bottom mirror layer  460  ( FIG. 1E ) from layer  404  ( FIG. 1E ). In one embodiment, wafer  502  is etched using a DRIE process. 
   In step  14 , portions of oxide layer  516  are removed from the structure to release the various components of device  400  while maintaining the bonds between the corresponding bonding and anchoring pads. In one embodiment, portions of oxide layer  516  are removed using a hydrofluoric acid wet etch. 
   In step  15 , the bottom surface of bottom mirror layer  460  ( FIG. 1F ) is deposited with a reflective material (e.g., aluminum) to create a mirror surface. In one embodiment, a shadow mask is used to define areas to be deposited with the reflective material. 
   In step  16 , devices  400  made from wafers  502  and  512  are singulated. In one embodiment, wafers  502  and  512  are singulated by dicing through separation trenches  509  and  519  (shown in step  15 ). 
   Referring to  FIG. 1A , the operation of device  400  in one embodiment is explained hereafter. Rotational comb teeth  416  are coupled via bonding pad  424  to receive a reference voltage from a voltage source  476  (e.g., ground). Stationary comb teeth  434  are coupled via bonding pad  436  to receive a steady voltage from a voltage source  478  (e.g., a DC voltage source). Stationary comb teeth  474  ( FIGS. 1D and 1E ) are coupled via bonding pad  472  to receive an oscillating voltage from a voltage source  480  (e.g., an AC voltage source). Thus, a steady voltage difference between rotational comb teeth  416  and stationary comb teeth  434  changes the natural frequency of device  400 , whereas an AC voltage difference between rotational comb teeth  416  and stationary comb teeth  474  ( FIGS. 1D and 1E ) oscillates the mirror at the desired scanning frequency and at the desired scanning angle. 
   Referring to  FIG. 1H , the operation of device  400  in another embodiment is explained hereafter. Rotational comb teeth  416  are coupled via bonding pad  424  to receive a steady voltage from voltage source  476  (e.g., a DC voltage source). Stationary comb teeth  434  are coupled via bonding pad  436  to receive an oscillating voltage from AC voltage source  480 . Stationary comb teeth  474  ( FIGS. 1D and 1E ) are coupled via bonding pad  472  to receive a steady voltage from DC voltage source  478 . Between rotational comb teeth  416  and stationary comb teeth  434 , a steady voltage difference changes the natural frequency and the rotation amplitude of device  400  while an AC voltage oscillates the mirror at the desired scanning frequency and at the desired scanning angle. Furthermore, a steady voltage difference between rotational comb teeth  416  and stationary comb teeth  474  ( FIGS. 1D and 1E ) can also be used to change the amplitude of the rotational angle of device  400 . The capacitance between rotational comb teeth  416  and stationary comb teeth  474  can also be sensed through respective bonding pads  436  and  472  to determine the rotational angle of device  400 . 
   Referring to  FIG. 11 , the operation of device  400  in another embodiment is explained hereafter. Rotational comb teeth  416  are coupled via bonding pad  424  to receive an oscillating voltage from AC voltage source  480 . Stationary comb teeth  434  are coupled via bonding pad  436  to receive a steady voltage from DC voltage source  476 . Stationary comb teeth  474  ( FIGS. 1D and 1E ) are coupled via bonding pad  472  to receive a steady voltage from DC voltage source  478 . Between rotational comb teeth  416  and stationary comb teeth  434 , a steady voltage difference changes the natural frequency and the rotation amplitude of device  400  while an AC voltage difference between rotational comb teeth  416  and stationary comb teeth  434  oscillates the mirror at the desired scanning frequency and at the desired scanning angle. A steady voltage difference between rotational comb teeth  416  and stationary comb teeth  474  ( FIGS. 1D and 1E ) can also be used to change the amplitude of the rotational angle of device  400 . The capacitance between rotational comb teeth  416  and stationary comb teeth  474  can also be sensed through respective bonding pads  436  and  472  to determine the rotational angle of device  400 . 
   Referring to  FIG. 1J , the operation of device  400  in another embodiment is explained hereafter. Rotational comb teeth  416  are coupled via bonding pad  424  to receive a steady voltage from DC voltage source  476 . Stationary comb teeth  434  are coupled via bonding pad  436  to receive an oscillating voltage from an AC voltage source  480 A. Stationary comb teeth  474  ( FIGS. 1D and 1E ) are coupled via bonding pad  472  to receive an oscillating voltage from an AC voltage source  480 B. The oscillating voltage provided by AC voltage source  480 B is out of phase (e.g., 180 degrees out of phase) with the oscillating voltage provided by voltage source  480 A. Between rotational comb teeth  416  and stationary comb teeth  434 , a steady voltage difference changes the natural frequency and the rotation amplitude of device  400  while an AC voltage difference oscillates the mirror at the desired scanning frequency and at the desired scanning angle. An AC voltage difference between rotational comb teeth  416  and stationary comb teeth  474  ( FIGS. 1D and 1E ) can also be used to oscillate the mirror at the desired scanning frequency and at the desired scanning angle. The capacitance between rotational comb teeth  416  and stationary comb teeth  474  can also be sensed through respective bonding pads  436  and  472  to determine the rotational angle of device  400 . 
   Referring to  FIG. 1K , the operation of device  400  in another embodiment is explained hereafter. Rotational comb teeth  416  are coupled via bonding pad  424  to receive an oscillating voltage from AC voltage source  480 A. Stationary comb teeth  434  are coupled via bonding pad  436  to receive a steady voltage from DC voltage source  476 . Stationary comb teeth  474  ( FIGS. 1D and 1E ) are coupled via bonding pad  472  to receive an oscillating voltage from AC voltage source  480 B. Between rotational comb teeth  416  and stationary comb teeth  434 , a DC voltage difference changes the natural frequency and the rotation amplitude of device  400  while an AC voltage difference oscillates the mirror at the desired scanning frequency and at the desired scanning angle. Between rotational comb teeth  416  and stationary comb teeth  474  ( FIGS. 1D and 1E ), a DC voltage difference can also be used to change the amplitude of the rotational angle of device  400  while an oscillating voltage difference can also be used to oscillate the mirror at the desired scanning frequency and at the desired scanning angle. The capacitance between rotational comb teeth  416  and stationary comb teeth  474  can also be sensed through respective bonding pads  436  and  472  to determine the rotational angle of device  400 . 
     FIGS. 3 ,  4 ,  5 ,  6 ,  7  and  8  illustrate a MEMS scanning mirror device  600  in one embodiment of the invention. Device  600  includes a top layer  602  ( FIGS. 3 and 4 ) bonded atop but electrically insulated from a bottom layer  604  ( FIGS. 6 and 7 ). 
   Referring to  FIGS. 3 and 4 , top layer  602  includes an oval mirror  606  with a width A and a length B. Mirror  606  is separated from the surrounding components (e.g., bonding pad  636 ) by gaps  609 A and  609 B having a width C. Width C of gaps  609 A and  609 B is designed to be greater than the widths of the gaps around more fragile components so that any trapped gas can escape around mirror  606  instead of the fragile components during the etching process. Alignment marks  666  are formed in bond pad  636  for aligning other components to device  600 . 
   Opposing sides of mirror  606  are connected by multiple support attachments  610  to the proximate ends of beam-like structures  612 A and  612 B. By connecting mirror  606  at multiple locations to beams  612 A and  612 B, the dynamic deformation of mirror  606  is minimized. The position and the number of support attachments  610  can be further refined through finite element analysis. Each of beams  612 A and  612 B has a length D and a width E. 
   Opposing sides of beams  612 A and  612 B about a rotational axis  614  are connected to rotational comb teeth  616  (shown enlarged in  FIG. 5 ). Rotational comb teeth  616  each has a tapered body consisting of a base width F, an end width ( 3 , a length H, and a pitch W. By reducing the size and thus the weight of rotational comb teeth  616  at its ends, the inertia of the entire structure is reduced. By reducing the structural inertia, the scanning speed can be increased or/and the driving voltage can be reduced. In one embodiment, rotational comb teeth  616  provide the electrostatic biasing force used to increase the driving efficiency of the movable structure by tuning its modal frequency. In another embodiment, rotational comb teeth  616  provide the electrostatic driving force to drive the mirror. In yet another embodiment, rotational comb teeth  616  provide bath the electrostatic biasing force and the electrostatic driving force. 
   Beams  612 A and  612 B are connected by serpentine springs (also known as “hinges”) to bonding pads mounted atop bottom layer  604 . Specifically, beam  612 A has a distal end connected by a serpentine spring  622 - 1  to a bonding pad  624 . Furthermore, beam  612 A has a midsection connected by (1) serpentine springs  622 - 2  and  622 - 3  to a bonding pad  626 - 1  formed within beam  612 A, (2) serpentine springs  622 - 4  and  622 - 5  to a bonding pad  626 - 2  formed within beam  612 A, (3) serpentine springs  622 - 6  and  622 - 7  to a bonding pad  626 - 3  formed within beam  612 A, and (4) serpentine springs  622 - 8  and  622 - 9  to a bonding pad  626 - 4  formed within beam  612 A. 
   Similarly, beam  612 B has a distal end connected by a serpentine spring  628 - 1  to a bonding pad  630 . Furthermore, beam  612 B has a midsection connected by (1) serpentine springs  628 - 2  and  628 - 3  to a bonding pad  632 - 1  formed within beam  612 B, (2) serpentine springs  628 - 4  and  628 - 5  to a bonding pad  632 - 2  formed within beam  612 B, (3) serpentine springs  628 - 6  and  628 - 7  to a bonding pad  632 - 3  formed within beam  612 B, and (4) serpentine springs  628 - 8  and  628 - 9  to a bonding pad  632 - 4  formed within beam  612 B. 
   Thus, beams  612 A and  612 B are connected by springs in a distributed manner along rotational axis  614  of mirror  606 . Each of serpentine springs  622  and  628  has a width I ( FIG. 4 ) and consists of five sections having length J. Each of bonding pads  626  and  632  has a height K and width L. 
   By carefully adjusting the distribution of the stiffness and the location of the springs, all modal frequencies of the movable structure can be effectively separated and the desired rotational mode can be designed at the lowest resonance frequency. Since the main resonant frequency is the lowest and far apart from other structural modal frequencies, the mirror rotation will not excite any other undesired vibration mode. By using multiple springs, the maximum stress and strain on each spring are lower than conventional scanning mirror designs supported by only a pair of torsional beams. Since the stress and strain on each spring are reduced, the reliability of each spring is improved and the rotational angle is increased. 
   Top layer  602  further includes stationary comb teeth  634  (shown enlarged in  FIG. 5 ) that are interdigitated in-plane with rotational comb teeth  616 . Stationary comb teeth  634  each has a tapered body consisting of a base width M, an end width N, a length O, a constant spacing P with rotational comb teeth  634 , and a pitch W. In one embodiment, stationary comb teeth  634  provide the electrostatic biasing force used to increase the driving efficiency of the movable structure by tuning its modal frequency. In another embodiment, stationary comb teeth  634  provide the electrostatic driving force to drive mirror  606 . In yet another embodiment, stationary comb teeth  634  provide both the electrostatic biasing force and the electrostatic driving force. Stationary comb teeth  634  are connected to bond pad  636  mounted atop bottom layer  604 . 
   A pad  652  is defined after top layer  602  is etched to form bonding pads  624  and  636 . Pad  652  is separated by a distance AJ from bonding pads  624  and  636 . Furthermore, bonding pad  636  has a width AK near gaps  609 A and  609 B. 
   Referring to  FIGS. 6 and 7 , bottom layer  604  includes a rib  660 , which is bonded to the bottom surface of mirror  606 . Rib  660  serves to stiffen mirror  606  without significantly increasing the mirror mass. Therefore, it minimizes the dynamic deformation of mirror  606 . By minimizing the total dynamic deformation of mirror  606 , the optical resolution of device  600  is improved. Rib  660  is separated from the components of bottom layer  604  by a gap  665 . Rib  660  has an oval shape with horizontal crossbeams interconnected with vertical crossbeams. The shape of rib  660  can be further refined through finite element analysis. 
   Bottom layer  604  includes surfaces for anchoring the bonding pads in top layer  602 . Specifically, (1) anchoring pads  668 - 1 ,  668 - 2 ,  668 - 3 ,  668 - 4  provide surfaces for mounting corresponding bonding pads  626 - 1 ,  626 - 2 ,  626 - 3 , and  626 - 4  ( FIG. 3 ), (2) anchoring pads  670 - 1 ,  670 - 2 ,  670 - 3 , and  670 - 4  provide surfaces for mounting corresponding bonding pads  632 - 1 ,  632 - 2 ,  632 - 3 , and  632 - 4  ( FIG. 4 ), and (3) anchoring pad  672  provides a surface for mounting bonding pads  624 ,  630 ,  636 , and  652  ( FIGS. 3 and 4 ). 
   Bottom layer  604  includes opposing stationary comb teeth  674  and  675  (shown enlarged in  FIG. 8 ) that are out-of-plane interdigitated with rotational comb teeth  616 . In other words, they are interdigitated when viewed from above or when mirror  606  is rotated. Stationary comb teeth  674  each has a tapered body with a base width Q, an end width R, a length S, and a pitch W. The ends of stationary comb teeth  674  are located a distance X from a centerline  615 , which coincides with rotational axis  614 . Stationary comb teeth  675  each has a tapered body with a base width T, an end width U, a length V, and a pitch W. The ends of stationary comb teeth  675  are located a distance Y from centerline  615 . A gap  682  is provided between stationary comb teeth  674  and  675  and anchoring pad  672 . Gap  682  has a width greater than gaps between adjacent stationary comb teeth  474  so that gap  682  is etched deeper into bottom layer  604 . A deeper gap  682  allows rotational comb teeth  616  to rotate at a greater angle without contacting bottom layer  604 . 
   In one embodiment, the capacitances between rotational comb teeth  616  and stationary comb teeth  674  and  675  are sensed to determine the rotational position of the mirror. In one embodiment, stationary comb teeth  674  has greater surface area than stationary comb teeth  675  so that the capacitance generated when rotational comb teeth  616  rotates into stationary comb teeth  674  is larger than the capacitance generated when rotational comb teeth  616  rotates into stationary comb teeth  675 . Thus, the direction of the mirror rotation can be detected. 
     FIG. 9  illustrates a method  800  for making device  600  in one embodiment of the invention. The process starts at a step  0 ′ with a silicon wafer  802  having a silicon dioxide layer  804  formed on the top surface and a silicon dioxide layer  806  formed on the bottom surface. Wafer  802  is used to form bottom layer  604  ( FIGS. 6 and 7 ) of device  600 . Silicon wafer  802  has a thickness Z, silicon dioxide layer  804  has a thickness AA, and silicon dioxide layer  806  has a thickness AB. 
   In step  1 ′, a photoresist  808  is deposited on oxide layer  806 , exposed, and developed in a lithographic process to define one or more lithographic alignment marks  811  (shown in step  3 ′). 
   In step  2 ′, the bottom surface of wafer  802  is etched to remove portions of oxide layer  806  left unprotected by photoresist  808 . In one embodiment, oxide layer  806  is dry etched. The top surface of wafer  802  is deposited with a photoresist  810  to protect it from the etching of the bottom surface. 
   In step  3 ′, the bottom wafer surface of wafer  802  is etched to remove portions of wafer  802  left unprotected by oxide layer  806  to form lithography alignment marks  811 . After the silicon dry etch, the remaining photoresists  808  and  810  are stripped. 
   In step  4 ′, photoresist  810  is reapplied and is exposed and developed in a lithographic process to define rib  660  ( FIG. 6 ), anchoring pads  668 - 1  to  668 - 4 ,  670 - 1  to  670 - 4 , and  672  ( FIGS. 6 and 7 ), and stationary comb teeth  674  and  675  ( FIGS. 6 ,  7 , and  8 ) on the top surface of wafer  802 . The mask used is aligned with the lithographic alignment marks  811  on the bottom wafer surface. 
   In step  5 ′, the top surface of wafer  802  is etched to remove portions of oxide layer  804  left unprotected by photoresist  810 . In one embodiment, oxide layer  804  is dry etched. 
   In step  6 ′, the top surface of wafer  802  is etched to remove portions of wafer  802  left unprotected by oxide layer  804  to form rib  660  ( FIG. 6 ), anchoring pads  668 - 1  to  668 - 4 ,  670 - 1  to  670 - 4 , and  672  ( FIGS. 6 and 7 ), and stationary comb teeth  674  and  675  ( FIGS. 6 ,  7 , and  8 ). Rib  660  is etched free from the other components while anchoring pads  668 - 1  to  668 - 4 ,  670 - 1  to  670 - 4 , and  672  are etched to a height AC, and comb teeth  674  and  675  are etched to a height AD. Afterwards, the remaining photoresist  810  is stripped and oxide layers  804  and  806  are removed by a wet or dry etch. 
   In step  7 ′, a silicon wafer  812  is bonded to the top surface of wafer  802 . Wafer  812  has a silicon dioxide layer  814  formed on the top wafer surface and a silicon dioxide layer  816  formed on the bottom wafer surface. Wafer  812  is used to form top layer  602  ( FIGS. 3 and 4 ) of device  600 . Silicon wafer  812  has a thickness AE, silicon dioxide layer  814  has a thickness AF, and silicon dioxide layer  816  has a thickness AG. In one embodiment, wafers  812  and  802  are bonded by silicon fusion. 
   In step  8 ′, a photoresist  818  is deposited on oxide layer  814 , exposed, and developed in a lithographic process to define the components of top layer  602  ( FIGS. 3 ,  4 , and  5 ). The mask used is aligned with lithographic alignment marks  811  on the bottom wafer surface. Also defined in step  8 ′ are one or more lithographic alignment marks  821  (shown in step  11 ′) and a separation trench  819  (shown in step  11 ′). 
   In step  9 ′, the top surface of wafer  812  is etched to remove portions of oxide layer  814  left unprotected by photoresist  818 . In one embodiment, oxide layer  814  is dry etched. Afterwards, the remaining photoresist  818  is stripped. 
   In step  10 ′, the top surface of wafer  812  is etched to remove portions of wafer  812  left unprotected by oxide layer  814  to form the components of top layer  602  ( FIGS. 3 ,  4 ,  5 ). In one embodiment, wafer  812  is etched using a DRIE process down to the etch stop formed by oxide layer  816 . When the top of device  600  is etched through, gas trapped between the bonded wafers  802  and  812  may escape and damage fragile components such as the comb teeth and serpentine springs. To prevent such damage, gaps  609 A and  609 B ( FIG. 3 ) around mirror  606  ( FIG. 3 ) are designed to be larger than the gaps around the other components so that oxide layer  816  beneath gaps  609 A and  609 B are exposed before the other gaps. This allows the air to escape around mirror  606 , which is a structurally strong component. 
   In step  11 ′, a photoresist  820  is deposited on the bottom surface of wafer  802 , exposed, and developed on the bottom surface of wafer  802  to define separation trench  809  (shown in step  12 ′) and gap  665  ( FIG. 6  and step  12 ′) for separating rib  660  ( FIG. 6 ) from bottom layer  604  ( FIG. 6 ). The mask used is aligned with lithographic alignment marks  821  on the top wafer surface. 
   In step  12 ′, the bottom surface of wafer  802  is etched to remove portions of wafer  802  left unprotected by photoresist  820  to form separation trench  809  and to separate rib  660  ( FIG. 6 ) from bottom layer  604  ( FIG. 6 ). Separation trench  809  has a depth of AH. In one embodiment, wafer  802  is etched using a DRIE process. 
   In step  13 ′, portions of oxide layer  816  are removed from the structure to release the various components of device  600  while maintaining the bonds between the corresponding bonding and anchoring pads, and between the mirror and the rib. In one embodiment, portions of oxide layer  816  are removed using a hydrofluoric acid wet etch. 
   In step  14 ′, the top surface of mirror  606  ( FIG. 3 ) is deposited with a reflective material (e.g., aluminum) to create a mirror surface. In one embodiment, a shadow mask is used to define areas to be deposited with the reflective material. 
   In step  15 ′, devices  600  made from wafers  802  and  812  are singulated. In one embodiment, wafers  802  and  812  are singulated by dicing through separation trenches  809  and  819  (shown in step  14 ′). 
   In one embodiment of the invention, the dimensions of device  600  are as follows: 
   
     
       
             
             
           
         
             
                 
             
             
               Reference number 
               Dimension (in microns) 
             
             
                 
             
           
           
             
               Width A of mirror 606 
               &gt;1000 &amp; &lt;1200 (e.g., 1110) 
             
             
               Length B of mirror 606 
               &gt;4000 &amp; &lt;5500 (e.g., 5000) 
             
             
               Width C of mirror gap 609 
               &gt;150 &amp; &lt;350 (e.g., (250) 
             
             
               Length D of beam 612 
               &gt;3000 &amp; &lt;9000 (e.g., 8000) 
             
             
               Width E of beam 612 
               &gt;800 &amp; &lt;1400 (e.g., 1240) 
             
             
               Base width F of rotational comb teeth 616 
               &gt;8 &amp; &lt;14 (e.g., 10.5) 
             
             
               End width G of rotational comb teeth 616 
               &gt;4 &amp; &lt;10 (e.g., 6) 
             
             
               Length H of rotational comb teeth 616 
               &gt;400 &amp; &lt;900 (e.g., 780) 
             
             
               Width I of spring 622 
               &gt;20 &amp; &lt;60 (e.g., 50) 
             
             
               Length J of spring 622 
               &gt;200 &amp; &lt;500 (e.g., 390) 
             
             
               Height K of bonding pads 626 and 632 
               &gt;350 &amp; &lt;700 (e.g., 640) 
             
             
               Width L of bonding pads 626 and 632 
               &gt;350 &amp; &lt;700 (e.g., 660) 
             
             
               Base width M of stationary comb teeth 
               &gt;8 &amp; &lt;14 (e.g., 11.5) 
             
             
               634 
             
             
               End width N of stationary comb teeth 634 
               &gt;4 &amp; &lt;10 (e.g., 7) 
             
             
               Length O of stationary comb teeth 634 
               &gt;400 &amp; &lt;900 (e.g., 780) 
             
             
               Spacing P between rotational comb teeth 
               &gt;8 &amp; 14 (e.g., 11.5) 
             
             
               616 and stationary comb teeth 636 
             
             
               Base width Q of stationary comb teeth 674 
               &gt;8 &amp; &lt;14 (e.g., 8) 
             
             
               End width R of stationary comb teeth 674 
               &gt;4 &amp; &lt;10 (e.g., 7) 
             
             
               Length S of stationary comb teeth 674 
               &gt;150 &amp; &lt;500 (e.g., 200) 
             
             
               Base width T of stationary comb teeth 675 
               &gt;6 &amp; &lt;14 (e.g., 7.5) 
             
             
               End width U of stationary comb teeth 675 
               &gt;4 &amp; &lt;10 (e.g., 7) 
             
             
               Length V of stationary comb teeth 675 
               &gt;150 &amp; &lt;500 (e.g., 100) 
             
             
               Comb teeth pitch W 
               &gt;30 &amp; &lt;50 (e.g., 40) 
             
             
               Distance X from stationary comb teeth 
               &gt;500 &amp; &lt;700 (e.g., 660) 
             
             
               674 to centerline 615 
             
             
               Distance Y from stationary comb teeth 
               &gt;500 &amp; &lt;700 (e.g., 660) 
             
             
               675 to centerline 615 
             
             
               Thickness Z of bottom wafer 802 used 
               &gt;450 &amp; &lt;550 (e.g., 525) 
             
             
               to form bottom layer 604 
             
             
               Thickness AA of top oxide layer 804 on 
               &gt;1 &amp; &lt;2 (e.g., 1.5) 
             
             
               bottom wafer 802 
             
             
               Thickness AB of bottom oxide layer 806 
               &gt;1 &amp; &lt;2 (e.g., 1.5) 
             
             
               on bottom wafer 802 
             
             
               Height AC of anchoring pads 668 and 
               &gt;300 &amp; &lt;450 (e.g., 400) 
             
             
               670 on bottom layer 604 
             
             
               Height AD of stationary comb teeth 
               &gt;250 &amp; &lt;450 (e.g., 300) 
             
             
               674 and 675 on bottom layer 604 
             
             
               Thickness AE of top wafer 812 used to 
               &gt;120 &amp; &lt;240 (e.g., 150) 
             
             
               form top layer 602 
             
             
               Thickness AF of top oxide layer 814 on 
               &gt;1 &amp; &lt;2 (e.g., 1.2) 
             
             
               top wafer 812 
             
             
               Thickness AG of bottom oxide layer 816 
               &gt;1 &amp; &lt;2 (e.g., 1.2) 
             
             
               on top wafer 812 
             
             
               Depth AH of separation trench 809 on 
               &gt;120 &amp; &lt;240 (e.g., 180) 
             
             
               bottom wafer 812 
             
             
               Minimum distance AJ from pad 152 to 
               &gt;120 &amp; &lt;240 (e.g., 200) 
             
             
               any of pads 624 and 636 
             
             
               Distance AK from pad 652 to gap 609 
               &gt;400 (e.g., 250) 
             
             
               around the mirror 
             
             
               Number of springs 
               2 to 20 (e.g., 18) 
             
             
               Number of bonding pads connected to 
               2 to 10 (e.g., 10) 
             
             
               springs 
             
             
               Total mirror thickness with rib 
               &gt;240 (e.g., 675) 
             
             
               Total hinge length for one spring 
               &gt;600 (e.g., 1900) 
             
             
                 
             
           
        
       
     
   
   The operation of device  600  in one embodiment is explained hereafter. Rotational comb teeth  616  are coupled via bonding pad  624  to receive a bias voltage (e.g., ground or a DC voltage) from a voltage source  676 . This is used to change the natural frequency of device  600 . Stationary comb teeth  634  are coupled via bonding pad  636  to receive a driving voltage (e.g., an AC voltage with or without a zero-offset) from a voltage source  678 . This is used to oscillate mirror  606  at the desired scanning frequency and at the desired scanning angle. Stationary comb teeth  674  and  675  are coupled via bonding pad  672  to a capacitance meter  680 . This is used to detect the angle of rotation of mirror  606 . 
     FIG. 10  illustrates another rib  1060  that can be used to stiffen mirror  606  without significantly increasing the mirror mass in one embodiment of the invention. Rib  1060  includes a midsection  1062  having three protruding beams  1064  on either side of midline  615 . Midsection  1062  also includes holes  1066  that reduces the mass of rib  1060 . The shape of rib  1060  can be further refined through finite element analysis. 
   Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention. For example, devices  400  and  600  can be used in laser printing, barcode scanning, and micro-display applications. Numerous embodiments are encompassed by the following claims.