Abstract:
An electrostatic actuator comprising: first and second comb arrays of electrodes arranged on a base, the electrodes of the first and second comb arrays being interleaved; a third comb array of electrodes spring mounted over the first and second comb arrays, the electrodes of the third comb array being essentially aligned with the electrodes of the second comb array; means for applying a first voltage to the third comb array and a second voltage to the first and second comb arrays to generate an attractive force acting on the third comb array to move the third comb array toward the second comb array; and, means for applying the first voltage to the second and third comb arrays and the second voltage to the first comb array to generate a repulsive force acting on the third comb array to move the third comb array away from the second comb array.

Description:
FIELD OF THE INVENTION  
       [0001]     The invention relates to the field of electrostatic actuators, and more particularly, to micro electrostatic actuators to be used in applications including optical MEMS devices, RF MEMS devices, and MEMS memory.  
       Background of the Invention  
       [0002]     Microelectromechanical systems (MEMS) are the integration of mechanical elements and electronics on the same chip using microfabrication technology similar to the IC process to realize high performance and low cost functional devices such as micro sensors and micro actuators.  
         [0003]     MEMS is becoming an enabling technology in many fields as it enables the construction of devices or systems characterized by high performance, small size, small weight and low cost. Typical MEMS applications include: inertial measurement units such as micro accelerometers and micro gyroscopes; optical MEMS such as digital light processing (DLP) systems, micro optical switches and micromirrors for adaptive optics; and, RF MEMS devices such as micro RF switches, micro oscillators and micro varactors.  
         [0004]     Micro actuators are important building blocks in constructing MEMS devices. There are four main actuation techniques used in MEMS, i.e., electrostatic, thermal, magnetic and piezoelectric. Among them the electrostatic actuation is the flexures cannot counteract the rapidly increasing nonlinear most used one because of its outstanding advantages such as low power consumption, simple structure, quick response, and especially high compatibility with IC fabrication technology. Micro electrostatic actuators can be categorized into two types, i.e., lateral (in-plane) actuators which move in the plane parallel to the substrate, and out-of-plane actuators which move in the plane perpendicular to the substrate. For lateral actuation or in-plane movement, combdrive types are preferred. The parallel-plate configuration is most suitable for vertical actuation or out-of-plane movement. Out-of-plane actuators are the subject of the present invention.  
         [0005]     A conventional out-of-plane electrostatic actuator uses attractive electrostatic force and consists of two parallel plate electrodes: a fixed electrode and a moving electrode. The moving electrode is pulled down toward the fixed electrode by an attractive electrostatic force when a potential is applied between the two electrodes and it moves back to its original position due to a restoring force from supporting flexures when the voltage is removed.  
         [0006]     The application of conventional parallel plate attractive electrostatic actuators is limited by the “pull-in” effect: when the displacement of the moving electrode exceeds ⅓ of the initial gap distance, the linear restoring force from the electrostatic attractive force between the fixed and moving electrodes, and as such the moving electrode sticks to the fixed electrode. A detailed explanation of the “pull-in” effect in conventional parallel-plate micro electrostatic actuator can be found in U.S. Pat. No. 5,753,911. Because of the “pull-in” effect the stroke of a conventional parallel-plate actuator is limited to less than one third of the initial gap distance between the fixed and moving electrodes.  
         [0007]     Surface micromachining is a mature and preferred technology for low cost batch production of MEMS devices. In conventional parallel-plate attractive micro electrostatic actuators fabricated by surface micromachining technology, the initial gap distance between the fixed and moving electrodes is formed by a sacrificial layer such as silicon oxide, which is normally limited to a thickness of less than 2-3 micrometers. Therefore, the stroke of a conventional parallel-plate micro electrostatic actuator is limited to less than one micrometer (⅓ the thickness of the sacrificial layer).  
         [0008]     In a number of MEMS applications, a stroke of the actuator as large as several micrometers is required. A significant effort has thus been dedicated to increasing the stroke of conventional parallel-plate electrostatic actuators. U.S. Patent Application Publication Nos. 2003/0103717 and 2004/0160118 present a method of using an elevation mechanism to raise the moving electrode to obtain a large initial gap between the fixed and moving electrodes, and therefore a larger stroke. By using the elevation mechanism a larger stroke is achieved at the price of increased fabrication complexity, lower space usage efficiency, lower production yield and higher driving voltage.  
         [0009]     Another method to increase the stroke of conventional parallel plate attractive electrostatic actuator was disclosed in U.S. Patent Application Publication Nos. 2003/0011955 and U.S.2003/0117152. The method is based on using a special control circuit to realize a linear relation between the driving voltage and the gap distance, and therefore allows a large displacement. The largest stroke achieved by using this special control circuit is the full initial gap distance, which is normally limited in the range of 2-3 micrometers when standard surface micromachining is used to fabricate the parallel plate electrostatic actuator. Moreover, the special control circuit increases the cost of the chip.  
         [0010]     Other methods were also developed to increase the stroke of conventional parallel plate micro electrostatic actuators such as using second-order flexures (e.g., D. M. Burns and V. M. Bright, “Nonlinear flexures for stable deflection of an electrostatically actuated micromirror,” Proc. SPIE Conf. Vol. 3226, 1997) and a dual-gap structure (e.g., Jun Zou, et al., “Development of a wide tuning range MEMS tunable capacitor for wireless communication systems.” International Electron Devices Meeting 2000).  
         [0011]     All the attempts mentioned above to increase the stroke of conventional parallel-plate attractive electrostatic actuators, are either not adequate to achieve a stroke large enough for many applications or are not compatible with standard surface micromachining technology and thus are difficult to implement in a batch-production process.  
         [0012]     U.S. Pat. No. 5,541,465 discloses a design of special electrode arrangements for constructing cantilever actuators. This design has a serious drawback which limits it from being widely used as a bi-directional large stroke electrostatic actuator in MEMS devices, namely, the moving electrodes require electric potentials with opposite polarities thereby a movable insulation layer such as silicon nitride or silicon oxide has to be added to physically constrain and electrically insulate all the moving electrodes. These requirements complicate the fabrication process, lead to a deterioration of the performance of the component, and add wiring complexity. Moreover no moving insulation layer is available in many commercial MEMS fabrication processes such as MUMPS (Multi User MEMS Processes), SUMMIT (Sandia Ultra planar Multilevel MEMS Technology), and so on.  
         [0013]     An electrostatic actuator utilizing both attractive and repulsive forces can provide bi-directional movement of the electrodes. The total stroke of such a bi-directional electrostatic actuator includes two parts, i.e., the displacement of the moving electrode in the direction toward the fixed electrode and that in the direction away from the fixed electrode. Therefore the stroke is not limited by the initial gap distance. Hence, a large stroke can be achieved by the bidirectional electrostatic actuator. Bi-directional electrostatic actuator can separate sticking surfaces, thereby is able to make reprogrammable MEMS nonvolatile memory.  
         [0014]     A bi-directional electrostatic actuator of the comb-drive type has been disclosed and is the subject of U.S. Pat. No. 6,771,001. As is common with the comb-drive configuration, the disclosed device provides large in-plane motion while minimizing out-of-plane motion.  
         [0015]     A need therefore exists for an improved electrostatic actuator. Consequently, it is an object of the present invention to obviate or mitigate at least some of the above mentioned disadvantages.  
       SUMMARY OF THE INVENTION  
       [0016]     In accordance with one aspect of the present invention, there is provided a method of operating an electrostatic actuator comprising the steps of: providing a base containing a plurality of electrodes; providing a movable element being movably connected to the base, the moveable element including a plurality of electrodes, one or more of the plurality of electrodes having a corresponding aligned electrode on the base, and each aligned electrode on the base being disposed adjacent to at least one non-aligned electrode disposed on the base; and generating one, or both at different intervals, of: a repulsive electrostatic force by applying a voltage of V 1  to the electrodes on the movable element, V 1  to the aligned electrodes on the base and V 2  to the non-aligned electrodes on the base; and/or an attractive electrostatic force by applying a voltage of V 1  to the electrodes on the moveable element, and V 2  to the aligned and non-aligned electrodes on the base. In accordance with another aspect of the invention, a method is provided for electrostatic actuation in a micro-electro-mechanical system, related to the aforesaid method.  
         [0017]     In accordance with another aspect of the present invention, there is provided an electrostatic actuator comprising: a base containing a plurality of electrodes; a movable element being movably connected to the base, the moveable element including a plurality of electrodes, one or more of the plurality of electrodes having a corresponding, aligned electrode on the base, and each aligned electrode on the base being disposed adjacent to at least one non-aligned electrode disposed on the base; and a means for applying voltage to the electrostatic actuator, said means being operable to generate one, or both at different intervals, of: a repulsive electrostatic force by applying a voltage of V 1  to the electrodes on the movable element, V 1  to the aligned electrodes on the base and V 2  to the non-aligned electrodes on the base; or an attractive electrostatic force by applying a voltage of V 1  to the electrodes on the moveable element, and V 2  to the aligned and non-aligned electrodes on the base.  
         [0018]     In yet another aspect of the present invention, a micro-electro-mechanical system is provided that includes at least one of the aforesaid electrostatic actuator.  
         [0019]     The present invention provides a parallel-plate type electrostatic actuator having a large stroke out-of-plane motion achieved through a bi-directional capability and through a combined attractive-repulsive principle of operation. Advantageously, the present invention can be fabricated by mature standard surface micromachining technology.  
         [0020]     In particular, the invention provides a repulsive electrostatic actuator by arranging electrodes to generate, when a repulsive force is desired, an asymmetric field around the moving electrodes leading to a net repulsive force. Moreover, the invention provides a bi-directional electrostatic actuator which combines both attractive and repulsive forces to drive the moving electrodes toward and away from the fixed electrodes, thereby increasing the total stroke of conventional parallel plate attractive electrostatic actuators. The invention relies on a special arrangement of electrodes whereby the moving electrodes are subject to either an attractive or a repulsive force depending on the voltage applied. In general, the invention provides a bi-directional electrostatic actuator with a simple structure, e.g., only two conductive layers are needed such that it can be easily incorporated with MEMS devices without adding extra fabrication complexity and is compatible with standard surface micromachining technology.  
         [0021]     According to one particular aspect of the invention, there is provided in one embodiment of the invention a bi-directional actuator comprising two arrays of electrodes: one array of moving electrodes positioned opposite another array of fixed electrodes. Each moving electrode has, in accordance with this embodiment, a corresponding and aligned fixed electrode. Each fixed electrode has two “adjacent” fixed electrodes not aligned with a moving electrode, in accordance with this particular embodiment. The adjacent electrodes are in the same plane as the fixed electrodes. In general, the number of fixed electrodes is 2n+1 where n is the number of moving electrodes. Voltages can be applied in different ways as follows: 1) when a voltage V 1  is supplied to the moving electrodes and a voltage V 2  is supplied to all the fixed electrodes, where V 1 =V 2 , an attractive force is generated to move the moving electrodes towards the fixed electrodes; 2) when the moving electrodes and their corresponding aligned fixed electrodes are supplied with a voltage V 1 , and the adjacent fixed electrodes are supplied with a voltage V 2 , a repulsive force is generated to move the moving electrodes away from the fixed electrodes; and, 3) when a voltage V 1  is supplied to the moving electrodes and a voltage of V 2  is supplied to all the “adjacent” fixed electrodes, which are not aligned with any moving electrodes, an attractive force is generated to move the moving electrodes towards the fixed electrodes if all the moving electrodes are wider than the aligned fixed electrodes.  
         [0022]     In accordance with a particular embodiment of the invention, the adjacent fixed electrodes are elevated through support posts to be in the same plane as the moving electrodes when no voltage is applied. When the moving electrodes and the elevated adjacent fixed electrodes are supplied with a voltage V 1 , and the aligned fixed electrodes are supplied with a voltage V 2 , where V 1 =V 2 , an attractive force is generated to move the moving electrodes towards the aligned fixed electrodes. When the aligned electrodes in both arrays are supplied with a voltage V 1 , and the elevated unaligned adjacent fixed electrodes are supplied with V 2 , a repulsive force is generated to move the moving electrodes away from the fixed electrodes. Preferably, the moving electrodes are only subject to a single voltage, thereby eliminating any requirement for additional insulating layers on the moveable element or any wiring complexity. Preferably, the moveable element has only two structural layers.  
         [0023]     Advantageously, the bi-directional large-stroke electrostatic actuator of the present invention can be implemented with standard surface micromachining techniques and easily incorporated into MEMS devices such as optical switches, RF switches, tunable capacitors, micromirrors, micro gyroscopes, and the like.  
         [0024]     According to another particular aspect of the invention, there is provided an electrostatic actuator comprising: first and second comb arrays of electrodes arranged on a base, the electrodes of the first and second comb arrays being interleaved; a third comb array of electrodes spring mounted over the first and second comb arrays, the electrodes of the third comb array being essentially aligned with the electrodes of the second comb array; and, means for applying a first voltage to the third comb array and a second voltage to the first and second comb arrays to generate an attractive force acting on the third comb array to move the third comb array toward the second comb array.  
         [0025]     Preferably, the means is adapted for applying the first voltage to the second and third comb arrays and the second voltage to the first comb array to generate a repulsive force acting on the third comb array to move the third comb array away from the second comb array.  
         [0026]     Preferably, the means is adapted for applying the first voltage to the third comb array and the second voltage to the first comb array to generate an attractive force acting on the third comb array to move the third comb array toward the second comb array.  
         [0027]     Preferably, the electrostatic actuator further includes posts for elevating the electrodes of the first comb array with respect to the electrodes of the second comb array. Preferably, the electrodes of the first and third comb arrays are coplanar.  
         [0028]     Preferably, the third comb array is at least one of translatable and rotatable with respect to the first and second comb arrays. Preferably, the electrostatic actuator further includes a spacing material between the third comb array and first and second comb arrays, wherein the spacing material is one of a vacuum and a fluid. Preferably, the electrodes are one of straight and curved. Preferably, the electrodes have one of equal and unequal widths. Preferably, the electrodes have a width that is larger than a height of the electrodes. Preferably, a distance between the electrodes of the third comb array and the electrodes of the first and second comb arrays is zero. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0029]     Embodiments of the invention may best be understood by referring  10  the following description and accompanying drawings. In the description and drawings, like numerals refer to like structures or processes. In the drawings:  
         [0030]      FIG. 1  is a perspective view illustrating a bi-directional electrostatic actuator in accordance with an embodiment of the invention;  
         [0031]      FIG. 2  is a perspective view illustrating the electrical connection of the electrodes of the actuator of  FIG. 1  in accordance with an embodiment of the invention;  
         [0032]      FIG. 3  is a section view illustrating the actuator of  FIG. 1  in accordance with an embodiment of the invention;  
         [0033]      FIG. 4  is a table illustrating modes of actuation of the bi-directional electrostatic actuator of  FIG. 1  as a function of voltage applied to the various sets of electrodes, in accordance with an embodiment of the invention;  
         [0034]      FIG. 5  is a graph illustrating the attractive force generated in the bi-directional actuator of  FIG. 1 ;  
         [0035]      FIG. 6  is a graph illustrating the repulsive force produced in the bi-directional actuator of  FIG. 1 ;  
         [0036]      FIG. 7  is a graph illustrating the total force produced in the bi-directional electrostatic actuator of  FIG. 1  during bidirectional operation;  
         [0037]      FIG. 8  is a graph illustrating the displacement of the bi-directional electrostatic actuator of  FIG. 1  during bi-directional operation;  
         [0038]      FIG. 9 ( a ) is a perspective view illustrating the electrical connection of the electrodes of the actuator of  FIG. 1  for operation as a “unidirectional large stroke attractive actuator” having a stroke of the full initial gap, in accordance with an embodiment of the invention;  
         [0039]      FIG. 9  ( b ) is a section view illustrating the electrodes of the actuator of  FIG. 1  for operation as a “unidirectional large stroke attractive actuator” having a stroke of the full initial gap, in accordance with an embodiment of the invention;  
         [0040]      FIG. 9 ( c ) is a table illustrating the mode of actuation of the actuator of  FIG. 1  when operating as a “unidirectional large stroke attractive actuator” having a stroke of the full initial gap, in accordance with an embodiment of the invention;  
         [0041]      FIG. 10  is a graph illustrating the relationship between the attractive force versus the gap distance of the actuator of  FIG. 1  when operating as a “unidirectional large stroke attractive actuator” having a stroke of the full initial gap;  
         [0042]      FIG. 11  is a graph illustrating the relationship between the driving voltage versus the gap distance of the actuator of  FIG. 1  when operating as a “unidirectional large stroke attractive actuator” having a stroke of the full initial gap;  
         [0043]      FIG. 12  is a top view illustrating a prototype of a micromirror driven by the electrostatic actuator of  FIG. 1  in accordance with an embodiment of the invention;  
         [0044]      FIG. 13  is a top view illustrating the electrodes of the micromirror of  FIG. 12  in accordance with an embodiment of the invention;  
         [0045]      FIG. 14  is a graph illustrating numerical simulation results and experimental measurement results for micromirror of  FIG. 12 ;  
         [0046]      FIG. 15  is a perspective view illustrating a second bidirectional electrostatic actuator in accordance with an embodiment of the invention;  
         [0047]      FIG. 16  is a perspective view illustrating the electric connections within the bi-directional electrostatic actuator of  FIG. 15  in accordance with an embodiment of the invention;  
         [0048]      FIG. 17  ( a ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 15  in accordance with an embodiment of the invention;  
         [0049]      FIG. 17  ( b ) is a table illustrating the mode of actuation of the bi-directional electrostatic actuator of  FIG. 15  as a function of voltage applied to the various sets of electrodes, in accordance with an embodiment of the invention;  
         [0050]      FIG. 18  is a graph illustrating the attractive force produced in the bi-directional electrostatic actuator of  FIG. 15 ;  
         [0051]      FIG. 19  is a graph illustrating the repulsive force produced in the bi-directional electrostatic actuator of  11 ;  
         [0052]      FIG. 20  is a graph illustrating the total force produced in the bi-directional electrostatic actuator of  FIG. 15  while in a bi-directional operation mode;  
         [0053]      FIG. 21  is a graph illustrating the displacement of the bidirectional electrostatic actuator of  FIG. 15  while in a bidirectional operation mode;  
         [0054]      FIG. 22  ( a ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 1  where electrodes in the moving array are essentially aligned with or overlapped by corresponding electrodes in the fixed array, in accordance with an embodiment of the invention;  
         [0055]      FIG. 22 ( b ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 1  where the aligned fixed electrodes have more than one adjacent unaligned fixed electrode on each side and where the number of unaligned fixed electrodes could be equal to or larger than 1, in accordance with an embodiment of the invention;  
         [0056]      FIG. 22 ( c ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 1  where electrodes in the moving array are essentially but not completely aligned with corresponding electrodes in the fixed array, in accordance with an embodiment of the invention;  
         [0057]      FIG. 23  ( a ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 15  where electrodes in the moving array are essentially aligned with or overlapped by corresponding electrodes in the fixed array, in accordance with an embodiment of the invention;  
         [0058]      FIG. 23  ( b ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 15  where the aligned fixed electrodes have more than one adjacent unaligned fixed electrode on each side and where the number of unaligned fixed electrodes could be equal to or larger than 1, in accordance with an embodiment of the invention;  
         [0059]      FIG. 23 ( c ) is a section view illustrating the electrodes in the bi-directional electrostatic actuator of  FIG. 15  where electrodes in the moving array are essentially but not completely aligned with corresponding electrodes in the fixed array, in accordance with an embodiment of the invention;  
         [0060]      FIG. 24 ( a ) is perspective view illustrating a translation micromirror driven by the bi-directional electrostatic actuator of  FIG. 1  in accordance with an embodiment of the invention;  
         [0061]      FIG. 24 ( b ) is a perspective view illustrating a translation micromirror driven by the bi-directional electrostatic actuator of  FIG. 15  in accordance with an embodiment of the invention;  
         [0062]      FIG. 25  ( a ) is a perspective view illustrating a RF switch (or RF varactor) driven by the bidirectional electrostatic actuator of  FIG. 1  in accordance with an embodiment of the invention;  
         [0063]      FIG. 25  ( b ) is a perspective view illustrating a RF switch (or RF varactor) driven by the bi-directional electrostatic actuator of  FIG. 15  in accordance with an embodiment of invention;  
         [0064]      FIG. 26 ( a ) is a perspective view illustrating a rotary micromirror driven by the bi-directional electrostatic actuator of  FIG. 1  in accordance with an embodiment of the invention;  
         [0065]      FIG. 26 ( b ) is a perspective view illustrating a rotary micromirror driven by the bi-directional electrostatic actuator of  FIG. 15  in accordance with an embodiment of the invention;  
         [0066]      FIG. 27 ( a ) is a perspective view illustrating a RF switch (or RF varactor) driven by the bi-directional electrostatic actuator of  FIG. 1  in accordance with an embodiment of the invention; and,  
         [0067]      FIG. 27 ( b ) is a perspective view illustrating a RF switch (or RF varactor) driven by the bi-directional electrostatic actuator of  FIG. 15  in accordance with an embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0068]     In the following description, numerous specific details are set forth to provide a thorough understanding of the invention. However, it is understood that the invention may be practiced without these specific details. In other instances, well-known structures and techniques have not been described or shown detail in order not to obscure the invention.  
         [0069]     The inventors of the present invention have conducted theoretical analysis and developed an analytical model to optimize parallel-plate actuator displacement as a function of applied voltage. (S. He and R. Ben Mrad, “A Novel Large Stroke Micro Electrostatic Actuator for Vertical Translation of Micromirrors Used in Adaptive Optics,” IEEE Transactions on Industrial Electronics—Special Issue on OptoMechatronics—in press; S. He and R. Ben Mrad, “A Novel MEMS Tunable Capacitor,” International Conference on MEMS, NANO and Smart Systems, Aug. 25-27, 2004, Banff, Alberta). The theoretical basis is that through electrode configuration, an asymmetric field around the moving electrodes can be generated to provide either a net repulsive force or a net attractive force while all the moving electrodes are subject to the same potential. Through their analysis, they have discovered that simple structures can be fabricated using conventional IC processes and microfabrication technology, to combine a repulsive force with an attractive force to provide electrostatic actuators with bi-directional movement that significantly improve their stroke.  
         [0070]     The present invention provides for a large stroke bi-direction electrostatic actuator which can be fabricated with conventional surface machining fabrication technology.  
         [0071]     Advantageously, the present invention provides actuators having a simple structure without complexities arising from special wiring and voltage control circuitry.  
         [0072]     The present invention may be better understood with references to  FIGS. 1 and 2 .  
         [0073]      FIG. 1  schematically illustrates the simplest form of an actuator in accordance with the invention, in accordance with one particular embodiment thereof. A base  10  contains an array of electrodes (also known as fixed electrodes) and a movable element  30  containing an array of electrodes  42  (also known as moving electrodes) is connected via springs  50  to the base  10 . Each moving electrode  42  has a corresponding and aligned fixed electrode  22  on the base  10 . Each aligned fixed electrode  22  has an adjacent electrode  24  which is unaligned with any moving electrode and located between two fixed aligned electrodes.  
         [0074]     The springs  50  are flexible in the direction perpendicular to the plane of the moving electrodes  42  and are very stiff in other directions, such that the moving electrodes  42  can essentially move only in the out-of-plane direction.  
         [0075]     In a working actuator the electrodes are electrically connected as shown in  FIG. 2 .  FIG. 3  only shows part of the electrodes in the actuator as shown in  FIG. 1 . The moving electrodes  42  are electrically connected to a voltage source  60 , the aligned fixed electrodes  22  on the base  10  are electrically connected to a voltage source  64 , and the non-aligned fixed adjacent electrodes  24  are electrically connected to a voltage source  66 .  
         [0076]     The preferred embodiments of the invention may now be illustrated by reference to the specific examples provided as Example 1 and Example 2. Clearly, other embodiments are also within the scope of this invention, but references to the preferred embodiments facilitate an explanation of the various aspects of the invention.  
       EXAMPLE 1  
       [0077]     The bi-directional electrostatic actuator of this example is schematically shown as  FIG. 1 .  FIG. 2  shows part of the electrodes of the actuator shown in  FIG. 1 —The section view of electrodes is shown as  FIG. 3 . The width of the moving electrodes  42  and that of the fixed electrodes  22 ,  24  are not necessarily equal. Normally, the moving electrodes  42  are slightly narrower than the aligned fixed electrodes  22  in order to accommodate for any undesired displacement during operation and for misalignments due to fabrication in the plane parallel to the plane of the electrodes. The minimum number of moving electrodes  42  is 1 and the minimum number of fixed electrodes  22 ,  24  is 3. There is no limitation on the maximum number of moving and fixed electrodes.  
         [0078]     All the electrodes are made of electrically conductive material. As shown in  FIG. 3  all moving electrodes  42  in the actuator are electrically connected to a voltage source  60 . Aligned fixed electrodes  22  on the base  10  are electrically connected to voltage source  64 . Unaligned fixed adjacent electrodes  24  are connected and subject to voltage source  66 .  
         [0079]     The bi-directional electrostatic actuator of this example can work in two modes, i.e., the attractive mode and the repulsive mode. When working in the attractive mode, the electrodes are subject to potentials in the manner shown in  FIG. 4 : all the moving electrodes  42  are supplied with a voltage V 1  at  60  and all the electrodes  22 ,  24  on the base  10  are supplied with a voltage V 2  at  64 ,  66 , where V 1 ≠V 2 . A resultant attractive force is generated to drive the moving electrodes  42  towards the fixed electrodes  22 ,  24  on the base  10 . When working in the repulsive mode, the electrodes are supplied with voltages as follows: all the moving electrodes  42  and the aligned fixed electrodes  22  on the base  10  are subject to a voltage V 1  at  60 ,  64 . The remaining unaligned fixed adjacent electrodes  24  are subject to a voltage V 2  at  66 . A resultant repulsive force is generated to drive the moving electrodes  42  away from the fixed electrodes  22 ,  24  on the base  10 .  
         [0080]     The actuator of this example has the following structural parameters: thickness of all electrodes 1 micrometer, width of moving electrodes 5 micrometers, width of fixed moving electrodes 8 micrometers, and distance between two neighboring fixed electrodes 8 micrometers.  
         [0081]     The attractive force generated in the bi-directional actuator of this example is shown in  FIG. 5 .  FIG. 5  is calculated using a commercially available numerical simulation software package named Maxwell®. g 0  is the initial gap distance between the fixed  22 ,  24  and moving 42 electrodes. γ represents the distance between the fixed and moving electrodes when the actuator is in operation.  
         [0082]     The repulsive force generated in the bi-directional actuator of this example is shown in  FIG. 6  which is also obtained from numerical simulations using the software package Maxwell®. When working in the repulsive mode the actuator of this example can produce a repulsive force over a very large range of the distance between the fixed and moving electrodes, i.e., 0-g_max. g_max is the maximum distance between the fixed and moving electrodes, within which the bi-directional actuator can generate a repulsive force. g_max is much larger than the initial gap distance go. That means the bi-directional actuator of this example working under the repulsive mode can achieve a stroke much larger than the initial gap distance. g_max is determined by structural parameters of the actuator. In this example, g_max is 12 micrometers.  
         [0083]     One method of using this electrostatic actuator is in a bidirectional mode of operation. That is, by applying a voltage to the actuator in the attractive mode as shown in  FIG. 5  to move the moving electrodes from its static position toward the fixed electrodes and by applying a voltage in the repulsive mode as shown in  FIG. 6  to move the moving electrodes from its static position away from the fixed electrodes.  FIG. 7  shows the force produced in the bi-directional actuator of this example when operated in both the attractive and repulsive modes.  FIG. 8  shows the total stroke as g_attractive+g_max. g_attractive is the stroke achieved when working in the attractive mode and is about ⅓*gO.  
         [0084]     The bi-directional electrostatic actuator of this example can also function as a unidirectional actuator. The actuator of this example working in the attractive mode can produce a stroke of ⅓*gO. In the repulsive mode it can produce a stroke of g_max.  
         [0085]     The actuator of this example can work as a “unidirectional large stroke attractive actuator” having a stroke of the full initial gap if all the moving electrodes  42  are wider than the aligned fixed electrodes  22  and only the moving electrodes  42  and unaligned “adjacent” fixed electrodes are connected to voltage sources, as shown in  FIG. 9  ( a ),  FIG. 9  ( b ) and  FIG. 9 ( c ) where: all moving electrodes  42  are connected to a voltage source  60 , V 1  and all unaligned “adjacent” fixed electrodes  24  are connected to a voltage source of  66 , V 2 .  
         [0086]     The nonlinearity of the attractive electrostatic force produced in the electrostatic actuator of the present invention working as a “unidirectional large stroke attractive actuator” is significantly decreased compared to conventional parallel plate actuators. The attractive force in the “unidirectional large stroke attractive actuator” is numerically calculated by the software Maxwell and is shown in  FIG. 10 . The actuator has the following structural parameters: thickness of all electrodes 1 micrometer, width of moving electrodes 5 micrometers, width of fixed moving electrodes 3 micrometers, and distance between two neighboring fixed electrodes 3 micrometers.  
         [0087]     In  FIG. 10  the curve  72  is the attractive force produced by a conventional parallel plate actuator and the curve  70  is the attractive force produced in the actuator of the present invention working as a “unidirectional large stroke attractive actuator”.  
         [0088]      FIG. 11  shows relations of voltage versus displacement in both conventional parallel plate actuator, i.e., curve  76  and in the “unidirectional large stroke attractive actuator”, i.e., curve  74 .  FIG. 11  shows that conventional parallel plate actuator can only achieve a stroke of ⅓ the initial gap distance gO while the “unidirectional large stroke attractive actuator” can achieve a stroke of full gap distance.  
         [0089]     Prototypes were fabricated to experimentally verify operation of the bi-directional electrostatic actuator of the present invention.  FIGS. 12 and 13  show prototypes of a rotary micromirror actuated by the electrostatic actuator of the present invention.  FIG. 14  shows both the numerical simulation result  78  by the Maxwell®software package and the experimental measurement results  80 . The parameters of the rotary micromirror prototype driven by the micro electrostatic actuator are: mirror size 300 μm×300 μm, number of moving fingers  40 , moving finger width 3 μm, fixed finger width 5 μm, distance between two fixed fingers 5 μm, finger length 70 μm. The micromirror driven by the novel actuator can achieve a rotation of 2.25 degrees while a surface micromachined micromirror of the same size driven by conventional attractive parallel plate actuator can only achieve a rotation of 0.1˜0.2 degree.  
       EXAMPLE 2  
       [0090]     The bi-directional electrostatic actuator of this example is schematically shown in  FIG. 15 .  FIG. 16  shows part of the electrodes of the actuator shown in  FIG. 15 . A section view of the electrodes is shown in  FIG. 17 ( a ).  
         [0091]     As shown in  FIG. 15 , the moving electrodes  42  have a set of aligned fixed electrodes  22  on the base  10 . The unaligned fixed adjacent electrodes  24  are elevated to the same plane as the moving electrodes  42  by supporting posts  52 .  
         [0092]     As shown in  FIGS. 16 and 17  ( a ), all moving electrodes  42  in the actuator are electrically connected to a voltage source  60 . Aligned fixed electrodes  22  on the base  10  are electrically connected to voltage source  64 . Unaligned fixed adjacent electrodes  24  are connected and subject to voltage source  66 .  
         [0093]     The bi-directional electrostatic actuator of this example can work in two modes, i.e., the attractive mode and the repulsive mode. When working in the attractive mode, the electrodes are subject to potentials in the manner shown in FIGS.  17 ( a ) and  17 ( b ): all the moving electrodes  42  are supplied with a voltage V 1  at  60 , all the aligned fixed electrodes  22  on the base  10  are supplied with a voltage V 2  at  64 , and all the elevated unaligned fixed electrodes  24  are supplied with a voltage V 1  at  66 , where V 1  # V 2 . A resultant attractive force is generated to drive the moving electrodes  42  towards the fixed aligned electrodes  22  on the base  10 . When working in the repulsive mode, the electrodes are supplied with voltages as follows: all the moving electrodes  42  and the aligned fixed electrodes  22  on the base  10  are subject to a voltage V 1  at  60 ,  64 . The remaining unaligned fixed adjacent electrodes  24  are subject to a voltage V 2  at  66 . A resultant repulsive force is generated to drive the moving electrodes  42  away from the aligned fixed electrodes  22  on the base  10 .  
         [0094]     The structural parameters of the bidirectional actuator of this example are as follows: thickness of all electrodes 1 micrometer, initial gap distance 2 micrometers, width of moving electrodes 5 micrometers, width of fixed moving electrodes 8 micrometers, and distance between two adjacent fixed electrodes 8 micrometers.  
         [0095]     The attractive force generated in the bi-directional actuator of this example is shown in  FIG. 18 . gO is the initial gap distance between the aligned fixed electrodes  22  and the moving electrodes  42 . γ represents the distance between the aligned fixed electrodes on the base  10  and the moving electrodes  42  when the actuator is in operation.  FIG. 18  is calculated using Maxwell®. The attractive force produced is nonlinear with respect to the distance between the fixed and moving electrodes. Hence, when operating the actuator in the attractive mode the actuator of this example operates like a conventional parallel-plate electrostatic actuator and can thus repeatedly achieve a stroke of ⅓ the initial gap distance.  
         [0096]     The repulsive force generated in the bi-directional actuator of this example is shown in  FIG. 19  which is also obtained from numerical simulations using the software package Maxwell. When working in the repulsive mode the actuator of this example can produce a repulsive force over a very large range of the distance between the aligned fixed electrodes on the base and the moving electrodes, i.e., 0-g_max. g_max is the maximum distance between the fixed and moving electrodes, within which the bi-directional actuator can generate a repulsive force. g_max is much larger than the initial gap distance g 0 . That means the bi-directional actuator of this example working under the repulsive mode can achieve a stroke much larger than the initial gap distance. g_max is determined by structural parameters of the actuator. In this example, g_max is 12 micrometers.  
         [0097]     One method of using this electrostatic actuator is in a bidirectional mode of operation. That is, by applying a voltage to the actuator in the attractive mode as shown in  FIG. 18  to move fixed the moving electrodes from its static position toward the electrodes and by applying a voltage in the repulsive mode as shown in  FIG. 19  to move the moving electrodes from its static position away from the fixed electrodes.  FIG. 20  shows the force produced in the bi-directional actuator of this example when operated in both the attractive and repulsive modes.  
         [0098]      FIG. 21  shows the total stroke as g_attractive+g_max. g_attractive is the stroke achieved when working in the attractive mode and is about ⅓*gO.  
         [0099]     The bi-directional electrostatic actuator of this example can also function as a unidirectional actuator. The actuator of this example working in the attractive mode can produce a stroke of ⅓*gO. In the repulsive mode it can produce a stroke of g_max.  
         [0100]     The bi-directional electrostatic actuators in the above examples can produce an attractive and a repulsive force, and can therefore achieve a bi-directional movement and a large stroke, which is not limited by the initial gap. They need only two conductive layers and can be easily fabricated by standard surface micromachining technology.  
         [0101]     Above, a simplified and generalized arrangement of electrodes was described. The term “aligned” was used to include alignment as well as overlap because exact alignment is not required for the operation of the invention. Also, for ease of understanding, regular arrays of electrodes were described. While regularity is preferred for optimal performance, it is not necessary for operation of the invention. Generally the invention includes: (a) an array of electrodes in a moving element having a corresponding array in a fixed element which contains a set of electrodes that essentially align or overlap those in the moving element, wherein a correspondence of 1:1 is desired but is not essential; and, (b) each of the electrodes in the fixed element described in (a) further has at least one adjacent fixed electrode on each side.  
         [0102]     To illustrate,  FIG. 22  ( a ) shows the configuration of  FIG. 1  where electrodes in the moving array are essentially aligned or overlapped by corresponding electrodes in the fixed array.  FIG. 22 ( b ) shows the configuration of  FIG. 1  where the aligned fixed electrodes have more than one adjacent unaligned fixed electrode  90  on each side and where the number of unaligned fixed electrodes  90  could be equal to or larger than 1. And,  FIG. 22 ( c ) shows the configuration of  FIG. 1  where electrodes in the moving array are essentially but not completely aligned with corresponding electrodes in the fixed array.  
         [0103]     In addition,  FIG. 23 ( a ) shows the configuration of  FIG. 15  where electrodes in the moving array are essentially aligned with or overlapped by corresponding electrodes in the fixed array.  FIG. 23 ( b ) shows the configuration of  FIG. 15  where the aligned fixed electrodes have more than one adjacent unaligned fixed electrode  90  on each side and where the number of unaligned fixed electrodes  90  could be equal to or larger than 1. And,  FIG. 23 ( c ) shows the configuration of  FIG. 15  where electrodes in the moving array are essentially but not completely aligned with corresponding electrodes in the fixed array.  
         [0104]     Applications of the Invention. Translation micromirrors as shown in FIGS.  24  ( a ) and  24 ( b ) are constructed by using two or four bi-directional electrostatic actuators of either the  FIG. 1  or  FIG. 15  type. Translation micromirrors based on the present invention can achieve a much larger stroke compared with conventional parallel-plate electrostatic actuators.  
         [0105]     Based on the same design as these translation micromirrors, by adding an electrode or microstrip underneath the mirror plate, an RF varactor or RF switch driven by the novel actuators of the present invention is formed, as shown in FIGS.  25 ( a ) and  25 ( b ). An RF varactor based on the present invention can achieve a tuning ratio larger than 4:1, while conventional parallel-plate actuator based varactors can achieve only 1.5:1.  
         [0106]     The present invention can also be used to realize rotation to drive either a rotary micromirror as shown in FIGS.  26 ( a ) and  26 ( b ) or an RF switch (or RF varactor) as shown in FIGS.  27 ( a ) and  27 ( b ).  
         [0107]     The electrostatic actuator of the present invention can also be used to realize  3 D rotation by constructing a structure that uses multiple actuators and a multi degree of freedom suspension system.  
         [0108]     Another application of the present invention is MEMS programmable nonvolatile memory. MEMS memory devices need two surfaces, which are able to come in contact and then separate even when there is no mechanical restoring force or the mechanical restoring force is very inadequate. Conventional electrostatic actuators provide only an attractive force which can drive the two surfaces to come in contact but can not separate them. The present invention, by providing a bidirectional electrostatic actuator, can provide both attractive force and repulsive force to drive the two surfaces in the MEMS memory to come in contact and then separate.  
         [0109]     Although preferred embodiments of the invention have been described herein, it will be understood by those skilled in the art that variations may be made thereto without departing from the spirit of the invention or the scope of the appended claims.