Patent Publication Number: US-2021171339-A1

Title: Cellular Array Electrostatic Actuator

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a utility conversion and claims priority to U.S. Ser. No. 62/945,561, filed Dec. 9, 2019, the contents of which are incorporated herein by reference in their entirety for all purposes. 
    
    
     BACKGROUND INFORMATION 
     1. Field 
     The present disclosure relates generally to electrostatic actuators. More particularly, the present disclosure relates to an electrostatic actuator comprising an array of cells that is microfabricated and has microscale feature sizes. 
     2. Background 
     An actuator is a component of a machine that is used to move the machine, a component of the machine, or another object. An electromechanical actuator is one example of an actuator. An electromechanical actuator is capable of converting electrical energy into mechanical motion. Electromechanical actuators are used in various applications, ranging from consumer electronics, optical systems, instrumentation and robotics to the automotive industry. 
     Different types of electromechanical actuators may be used in various different applications to provide different types of movement at various different scales. Electric motors and solenoids, piezoelectric actuators, and electrostatic actuators are examples of different types of electromechanical actuators. Electric motors and solenoids produce movement based on electromagnetic forces generated by electric current in wire coils. Piezoelectric actuators produce movement based on the piezoelectric effect, the internal generation of a mechanical strain resulting from an applied electric field in some materials. 
     An electrostatic actuator produces movement based on the electrostatic force that is generated between two conducting electrodes when a voltage is applied between them. Depending on the arrangement of the electrodes, various types of electrostatic actuators are possible. It may be desirable to improve on the capability provided by current electrostatic actuators and increase the number of applications for which electrostatic actuators may be used. 
     Therefore, there may be a need for an apparatus and method that take into account at least some of the issues discussed above, as well as other possible issues. 
     SUMMARY 
     The illustrative embodiments provide an electrostatic actuator comprising a framework and a plurality of electrodes. The framework comprises walls defining a plurality of cells forming an array of cells. The plurality of electrodes comprise an electrode in each cell in the plurality of cells. A gap separates the electrode in each cell from the walls of the cell. The framework is configured to contract in response to an electrical signal applied between the framework and the plurality of electrodes. 
     Illustrative embodiments also provide a method of operating an electrostatic actuator. An electrical signal is applied between a framework and a plurality of electrodes of the electrostatic actuator to cause the framework to contract. The framework comprises walls defining a plurality of cells forming an array of cells. The plurality of electrodes comprise an electrode in each cell in the plurality of cells. The electrode in each cell is separated from the walls of the cell by a gap. 
     Illustrative embodiments also provide a method of making an electrostatic actuator. Trenches are formed in a substrate to form walls of a framework. The walls define a plurality of cells forming an array of cells. A sacrificial layer is formed on the walls. The trenches are filled with a layer of polysilicon to form electrodes in the cells. The sacrificial layer is then removed to form gaps between the walls and the electrodes in the cells. 
     Further objects, features, and advantages will be apparent from the following detailed description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The novel features believed characteristic of the illustrative embodiments are set forth in the appended claims. The illustrative embodiments, however, as well as a preferred mode of use, further objectives and features thereof, will best be understood by reference to the following detailed description of an illustrative embodiment of the present disclosure when read in conjunction with the accompanying drawings, wherein: 
         FIG. 1  is a schematic block diagram of a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 2  is a perspective view illustration of a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 3  is a close-up perspective view illustration of a portion of a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 4  is a close-up plan view illustration of a portion of a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 5  is a cross-section view illustration of a cell in a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 6  is an illustration of a stress profile of a cellular array electrostatic actuator upon the application of an electrical signal to the cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 7  is a schematic cross-section side view of a cellular array electrostatic actuator upon the application of an electrical signal to the cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 8  is a flow chart diagram of a process of making a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIGS. 9 a -9 h    are cross-sectional views of a portion of an electrostatic actuator at various points during the making of the electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 10  is a flow chart diagram of a process of using a cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 11  is a scanning electron microscope, SEM, image plan view of a fabricated cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 12  is a close-up scanning electron microscope image plan view of a portion of a fabricated cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 13  is a further close-up scanning electron microscope image plan view of a portion of a fabricated cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 14  is a close-up scanning electron microscope image plan view of an air gap in a portion of a fabricated cellular array electrostatic actuator in accordance with an illustrative embodiment; 
         FIG. 15  is a scanning electron microscope image view of a fabricated cellular array electrostatic actuator with an electrical signal applied thereto in accordance with an illustrative embodiment; 
         FIG. 16  is a close-up scanning electron microscope image view of a portion of a fabricated cellular array electrostatic actuator with an electrical signal applied thereto in accordance with an illustrative embodiment; and 
         FIG. 17  is an illustration of an electrostatic actuator lifting an object in accordance with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The illustrative embodiments recognize and take into account various considerations. For example, the illustrative embodiments recognize and take into account various limitations of electric motors and solenoids and piezoelectric actuators. 
     Electric motors and solenoids are relatively bulky and heavy, due, for example, to the metal core and wire windings used in such devices. Electric motors and solenoids also may be relatively noisy and power inefficient. Electric motors and solenoids may be especially power inefficient in applications that require very low speed or stop and hold operation, such as robotics. 
     Piezoelectric material, such as bulk piezoelectric lead zirconate titanate, PZT, may be used as actuators in relatively high precision positioning systems. Such piezoelectric actuators typically may reach a maximum strain of approximately 0.1%, for example, approximately 10 micrometer displacement for a 1 centimeter long block of material. Typical piezoelectric actuators may require actuation voltages in excess of 100 volts to reach such strains. 
     The illustrative embodiments also recognize and take into account that microelectromechanical actuators with relatively large displacement ranges may be useful for various applications. For example, without limitation, microelectromechanical actuators with relatively large displacement ranges may be used in robotics and microrobotics, miniature lens positioning for automatic focusing, zooming or optical image stabilization, micro-positioning stages, and other applications. Such applications may require displacement ranges from tens of micrometers to millimeters and actuation forces in the mN range. 
     The illustrative embodiments also recognize and take into account that electrostatic actuators are relatively energy efficient and have relatively fast response time. The relatively low structural stiffness of electrostatic actuators allows relatively wide displacement ranges. 
     Illustrative embodiments also recognize and take into account that the electrostatic force between electrodes in an electrostatic actuator is inversely related to the square of the distance between the electrodes. Therefore, the force generated by an electrostatic actuator may be significantly increased by shrinking the gap between the electrodes. Furthermore, smaller gaps can withstand much larger electric fields than larger scale gaps. For example, smaller gaps in the range of a few micrometers and below may withstand relatively large electric fields of hundreds of MV/m compared to the known breakdown field of air for larger scale gaps of approximately 3 MV/m. 
     Illustrative embodiment also recognize and take into account, however, that the maximum displacement of an electrostatic actuator is limited to the distance between electrodes. Therefore, reducing the gap between the electrodes in an electrostatic actuator to increase the force generated also reduces the maximum displacement of the actuator. 
     Illustrative embodiments recognize the potential for microelectromechanical electrostatic actuators to realize high energy density with relatively simple structures, materials and fabrication. Illustrative embodiments provide a cellular array electrostatic actuator that is inspired by the cellular structure of biological muscles and that may be made by micromachining. A cellular array electrostatic actuator in accordance with an illustrative embodiment bypasses the trade-off between maximum displacement and generated force by summing up displacements from many cascaded actuator cells with individual submicrometer displacements. Cellular array electrostatic actuators in accordance with an illustrative embodiment combine larger range of motion and scalability along with larger force and energy densities compared to conventional electrostatic actuators. 
     Microelectromechanical electrostatic actuators in accordance with illustrative embodiments may be adopted for a wide range of applications. Cellular array electrostatic actuators in accordance with illustrative embodiments offer orders of magnitude larger displacement and work densities compared to conventional electromagnetic and piezoelectric actuators. Cellular array electrostatic actuators in accordance with illustrative embodiments may replace piezoelectric and electromagnetic actuators in some existing applications. For example, without limitation, cellular array electrostatic actuators in accordance with illustrative embodiments may be used in compact optical systems and camera modules, robotics, microrobotics, surgical devices, precision positioning systems and instrumentation, and other appropriate applications. As a further example, a cellular array electrostatic actuator in accordance with an illustrative embodiments may be used to move the lens of a compact camera module, such as the lens of a smartphone camera, for focusing and zooming, as well as optical image stabilization. Such actions are currently performed by electromagnetic coils which consume significantly more power than electrostatic actuators. 
     Turning to  FIG. 1 , a schematic block diagram of a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Cellular array electrostatic actuator  100  includes framework  102  comprising array of cells  104 . Framework  102  may be made of an appropriate conductive material. For example, without limitation, framework  102  may be made of an appropriate metal, doped semiconductor, or another appropriate conductive material. 
     Array of cells  104  comprises a plurality of cells  110 . In accordance with an illustrative embodiment, cells  110  in array of cells  104  are hollow cells formed between walls  112 . Walls  112  completely surround and thus define the hollow portions of cells  110 . 
     Array of cells  104  may include any appropriate number of cells  110  having any appropriate size, shape  114 , and arrangement  116 . As used herein, including in the claims, unless explicitly stated otherwise, shape  114  of cells  110  refers to the shape of cells  110  in a plane that extends through cells  110  perpendicular to all of walls  112  forming cells  110 . Similarly, as used herein, including in the claims, unless explicitly stated otherwise, arrangement  114  of cells  110  refers to the arrangement of cells  110  in a plane that extends through cells  110  perpendicular to all of walls  112  forming cells  110 . For example, all walls  112  forming cells  110  in array of cells  104  may extend substantially parallel to each other in a first direction. In this case, shape  114  of cells  110  is the shape of cells  110  in a plane that extends through cells  110  perpendicular to the first direction and arrangement  116  of cells  110  is the arrangement of cells  110  in the plane that extends through cells  110  perpendicular to the first direction. 
     For example, without limitation, shape  114  of cells  110  in array of cells  104  may be substantially rectangular  118 . In this case, arrangement  116  of cells  110  in array of cells  104  may form brick wall pattern  120 . Any other appropriate shape  114  and arrangement  116  of cells  110  may be used to form array of cells  104 . Shape  114  and arrangement  116  of cells  110  in array of cells  104  may be substantially the same across array of cells  104 . Alternatively, cells  110  in different parts of array of cells  104  may have different shapes, different arrangements, or different shapes and arrangements. 
     Points in framework  102  comprise nodes  122 . For example, without limitation, nodes  112  may comprise points in framework  102  at which walls  112  forming cells  110  in array of cells  104  are connected together. During operation of cellular array electrostatic actuator  100 , walls  112  of cells  110  are deformed, leading to contraction of framework  102  as a whole. However, deformation at nodes  122  of framework  102  during operation of cellular array electrostatic actuator  100  is less than the deformation of other portions of walls  112  during operation of cellular array electrostatic actuator  100 . Preferably, there may be almost no deformation at nodes  122  of framework  102  during operation of cellular array electrostatic actuator  100 . 
     Cellular array electrostatic actuator  100  further comprises plurality of electrodes  124  in cells  110  in array of cells  104 . For example, without limitation, electrodes  124  may be made of polysilicon  126  or another appropriate material. The shape and arrangement of electrodes  124  preferably corresponds to shape  114  and arrangement  116  of the corresponding cells  110  in which electrodes  124  are positioned. 
     Electrodes  124  may be electrically connected together by electrical interconnects  128 . Electrical interconnects  128  may be implemented in any appropriate manner. However, electrical interconnects  128  between electrodes preferably are flexible  130  so that the whole network of interconnected electrodes  124  is able to contract along with framework  102  during operation of cellular array electrostatic actuator  100 . 
     Electrodes  124  are preferably attached to framework  102  at nodes  122 , where there is preferably little or no deformation during operation of cellular array electrostatic actuator  100 . Attaching electrodes  124  to framework  102  at nodes  122  provides adequate stiffness for electrodes  124  to pull walls  112  toward electrodes  124  during the operation of cellular array electrostatic actuator  100  without electrodes  124  being deformed or pulled into contact with walls  112 . 
     Each cell  132  in array of cells  104  thus is defined by walls  134 , and electrodes  124  include electrode  136  in each cell  132  in array of cells  104 . Electrode  136  is located in the hollow portion of cell  132  that is surrounded and defined by walls  134  of cell  132  and is separated from walls  134  of cell  132  by gap  138 . For example, without limitation, each cell  132  in array of cells  104  may comprise two submicrometer wide high aspect ratio capacitive gaps between walls  134  of cell  132  and electrode  136 . 
     The width of gap  138 , that is, the distance between walls  134  of cell  132  and electrode  136 , may be selected as appropriate for the desired electrostatic force to be generated and displacement to be provided by cell  132 . Gap  138  having a larger width will provide for greater displacement but less force. Gap  138  having a smaller width will provide for less displacement but more force. 
     Gap  138  may be filled with air, in which case gap  138  may be referred to as an air gap. However, gap  138  may contain any other appropriate dielectric gas, fluid, or flexible material. For example, without limitation, gap  138  may be filled with a dielectric liquid or an elastomer. The material filling gap  138  may be selected as appropriate for a particular application of cellular array electrostatic actuator  100  in accordance with an illustrative embodiment. The material filling gap  138  may be advantageously selected to obtain force proportional to the dielectric constant of the material. Gap  138  may contain a vacuum in some applications. 
     Walls  134  of cell  132  preferably may be covered with dielectric film  140 . Dielectric film  140  preferably is located on walls  134  between walls  134  and gap  138  between walls  134  and electrode  136 . Dielectric film  140  may comprise silicon nitride  142 , such as low stress silicon nitride, or any other appropriate dielectric material. 
     Dielectric film  140  prohibits short circuits between electrodes  124  biased at high voltages and framework  102  upon contact between electrodes  124  and framework  102 . Dielectric film  140  also may increase the breakdown field of gap  138  by blocking flow of electrons due to field emission or tunneling. In addition, silicon nitride  142  is known to lower stiction between touching surfaces. Therefore, dielectric film  140  comprising silicon nitride  142  may reduce the possibility of electrodes  124  sticking to framework  102  upon contact. 
     The electrostatic attracting force for parallel plates with dielectric covered walls is given by: 
     
       
         
           
             
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     where ε 0  is the permittivity of free space (8.85*10 −12  F/m), A is the electrode area, V act  is the actuation voltage, g is the width of the gap, t di  is the dielectric thickness, and ε r  is the relative permittivity of the dielectric film. 
     Cellular array electrostatic actuator  100  may include appropriate electrical connections  144  for providing electrical signal  146  between framework  102  and electrodes  124  to operate cellular array electrostatic actuator  100 . Electrical connections  144  may be implemented in any appropriate manner. 
     For example, without limitation, electrical signal  146  may comprise an actuation voltage applied between framework  102  and electrodes  124 . Upon application of this electrical signal  146  between framework  102  and electrodes  124 , lateral electrostatic forces will pull walls  112  of cells  110  toward electrodes  124 , causing framework  102  as a whole to contract. 
     Electrical signal  146  to operate cellular array electrostatic actuator  100  may be provided in any appropriate manner. For example, electrical signal  146  may be generated and provided to cellular array electrostatic actuator  100  by controller  148 . Controller  148  may be implemented in any appropriate manner to generate and provide electrical signal  146  for operation of cellular array electrostatic actuator  100 . For example, without limitation, controller  148  may be implemented in hardware or in hardware in combination with software. 
     Electrical connections  144  may be configured such that electrical signal  146  may be provided independently to various different sub-regions  150  of cellular array electrostatic actuator  100 . Sub-regions  150  may include various different portions of framework  102  that include subsets of cells  110  in array of cells  104  and corresponding subsets of electrodes  124 . Sub-regions  150  may or may not overlap, such that any particular cell  132  in array of cells  104  may be included in one or more sub-regions  150 . By providing electrical signal  146  independently to different sub-regions  150  of cellular array electrostatic actuator  100 , various different portions of framework  102  may be made to contract at different times, in different ways, or both, to cause framework  102  as a whole to move in a desired manner. 
     Framework  102  of cellular array electrostatic actuator  100  may be attached to support structure  152 . For example, without limitation, support structure  152  may include any appropriate structure whereby cellular array electrostatic actuator  100  may be mounted for use. Framework  102  may be attached to support structure  152  such that framework  102  contracts with respect to support structure  152  during operation of cellular array electrostatic actuator  100 . For example, without limitation, framework  102  may be attached to support structure  152  along one side of framework  102  such that framework  102  extends from support structure  152 . 
     Support structure  152  may be made and framework  102  may be attached to support structure  152  in any appropriate manner. For example, without limitation, framework  102  may be integrally formed attached to support structure  152  during a process for making cellular array electrostatic actuator  100  by micromachining. 
     Appropriate portions of electrical connections  144  may be provided on support structure  152  for providing electrical signal  146  to cellular array electrostatic actuator  100 . For example, without limitation, metal pads or other appropriate structures for connecting wires to cellular array electrostatic actuator  100  may be provided on support structure  152 . 
     Framework  102  may be attached to base  154 . For example, base  154  may comprise a relatively thin flexible film that extends across all or a portion of one side of framework  102  to connect together one side of all or a portion of cells  110  in array of cells  104 . Cells  110  that are attached to base  154  will contract less on the side that is attached to base  154  than on the side that is not attached to base  154 . Therefore, base  154  causes framework  102  to bend when framework  102  contracts during operation of cellular array electrostatic actuator  100 . For example, without limitation, base  154  may be configured to cause framework  102  to bend in a desired manner when framework  102  contracts during operation of cellular array electrostatic actuator  100 . 
     Base  154  may be made and framework  102  may be attached to base  154  in any appropriate manner. For example, without limitation, base  154  may comprise a residual thin film that is formed on one side of framework  102  during a process for making cellular array electrostatic actuator  100  by micromachining. 
     Cellular array electrostatic actuator  100  may be used to move object  156 . For example, without limitation, object  156  may be a component of a machine or any other appropriate object. Object  156  may be moved by connecting object  156  in any appropriate manner to framework  102  such that the contraction, or bending and contraction, of framework  102  during operation of cellular array electrostatic actuator  100  moves object  156  in a desired manner. Framework  102  may be configured to include an appropriate structure for connecting object  156  to be moved to framework  102 . 
     Cellular array electrostatic actuator  100  may be made in any appropriate manner. For example, without limitation, cellular array electrostatic actuator  100  may be made by micromachining. An example of a process for making a cellular array electrostatic actuator by micromachining is described below with reference to  FIGS. 8 and 9 . 
     The illustration of cellular array electrostatic actuator  100  in  FIG. 1  is not meant to imply physical or architectural limitations to the manner in which illustrative embodiments may be implemented. Other components or structures, in addition to or in place of the ones illustrated, may be used. Some components or structures may be optional. Also, the blocks are presented to illustrate some functional components or structures. One or more of these blocks may be combined, divided, or combined and divided into different blocks when implemented in an illustrative embodiment. 
     Turning to  FIG. 2 , a perspective view illustration of a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Cellular array electrostatic actuator  200  is an example of one implementation of cellular array electrostatic actuator  100  in  FIG. 1 . 
     Cellular array electrostatic actuator  200  includes silicon framework  202  comprising walls defining a plurality of cells forming an array of cells. In this example, polysilicon electrodes  204  extend into the cells in framework  202  from a top side of framework  202 . Flexible polysilicon base  206  is on the bottom side of framework  202 , on the opposite side of framework  202  from where polysilicon electrodes  204  extend into the cells. 
     Framework  202  is attached to and extends from support structure  208  such that framework  202  is suspended from support structure  208 . In this example, electrical connections  210  are provided on support structure  208 . Electrical connections  210  may be configured to have wires attached thereto for providing electrical signals to cellular array electrostatic actuator  200  for operation thereof in the manner described herein. 
     Turning to  FIG. 3 , a close-up perspective view illustration of a portion of a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment.  FIG. 3  is a close-up view of the portion of cellular array electrostatic actuator  200  indicated by box  3  in  FIG. 2 . 
     Turning to  FIG. 4 , a close-up plan view illustration of a portion of a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment.  FIG. 4  is a close-up plan view of the portion of cellular array electrostatic actuator  200  indicated by box  4  in  FIG. 2 . 
     In this example, cells  300  in framework  202  are rectangular in shape and arranged in a brick wall pattern. Polysilicon electrical interconnects  302  provide electrical connections between electrodes  204  in cells  300 . Interconnect anchoring points  401  are represented by circles. 
     Turning to  FIG. 5 , a cross-section view illustration of a cell in a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Cell  500  is an example of one implementation of cell  132  in cellular array electrostatic actuator  100  in  FIG. 1 . 
     Walls  502  and  504  of a framework define the hollow portion of cell  500 . Polysilicon electrode  506  extends into the hollow portion of cell  500  between walls  502  and  504 . In this example, electrode  506  is attached to walls  502  and  504  at anchor points  508  and  510 , respectively. Anchor points  508  and  510  preferably are located at nodes in the framework where there is little or no deformation during operation of the cellular array electrostatic actuator. 
     Electrode  506  is separated from walls  502  and  504  by gap  512  and silicon nitride dielectric film  514  on walls  502  and  504 . Walls  502  and  504  are pulled into gap  512  toward electrode  506  in response to applying an electrical signal between walls  502  and  504  and electrode  506 , thereby contracting cell  500  and the framework that cell  500  is a part of. Dielectric film  514  prevents a short circuit between walls  502  and  504  and electrode  506  and sticking of walls  502  and  504  to electrode  506  if walls  502  and  504  are pulled into contact with electrode  506 . Dielectric film  514  also may increase the breakdown field of gap  512 . 
     Turning to  FIG. 6 , an illustration of a stress profile of a cellular array electrostatic actuator upon the application of an electrical signal to the cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment.  FIG. 6  is an illustration of cellular array electrostatic actuator  200  in  FIG. 2  with an actuation voltage applied to cellular array electrostatic actuator  200 . 
     Framework  202  contracts in response to applying an electrical signal between framework  202  and electrodes  204  in cellular array electrostatic actuator  200 . Base  206  on the bottom side of framework  202  causes the bottom side of framework  202  to contract less than the top side of framework  202 . Therefore, framework  202  bends upward in response to applying the electrical signal to cellular array electrostatic actuator  200  in this example. 
     Turning to  FIG. 7 , a schematic cross-section side view of a cellular array electrostatic actuator upon the application of an electrical signal to the cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Cellular array electrostatic actuator  700  is another example of one implementation of cellular array electrostatic actuator  100  in  FIG. 1 . 
     Cellular array electrostatic actuator  700  includes a framework comprising walls  702  defining a plurality of cells forming an array of cells. Each of the cells includes electrode  704 . Electrode  704  in each cell is located between walls  702  of the cell and is separated from walls  702  by gap  706 . In this example, the framework of cellular array electrostatic actuator  700  is attached to support structure  708  and the bottom side of the framework is attached to flexible base  710 . 
     Walls  702  and electrode  704  of each cell in cellular array electrostatic actuator  700  are pulled together, in the directions indicated by arrows  712 , in response to applying an electrical signal between walls  702  and electrode  704 , thereby partially closing gap  706  between walls  702  and electrode  704  and causing the framework as a whole to contract. Base  710  on the bottom side of the framework causes the bottom side of the framework to contract less than the top side of the framework. Therefore, the framework bends upward in response to applying the electrical signal to cellular array electrostatic actuator  700  in this example. 
     Turning to  FIG. 8 , a flow chart diagram of a process of making a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Process  800  is an example of one implementation of a method of making cellular array electrostatic actuator  100  in  FIG. 1 . With reference to  FIGS. 9 a -9 h   , schematic cross-sectional views of a portion of a cellular array electrostatic actuator are depicted at various points during making of the cellular array electrostatic actuator by process  800  in  FIG. 8 . For example, the schematic cross-sectional views in  FIGS. 9 a -9 h    may correspond generally to cross-sectional views taken in the general area and direction indicated by arrow  9  at various points during the making of cellular array electrostatic actuator  200  in  FIG. 2 . 
     Process  800  may begin with providing substrate  900  on which a cellular array electrostatic actuator in accordance with an illustrative embodiment will be fabricated (operation  802 ). With reference to  FIG. 9 a   , a schematic cross-section view of an example of substrate  900  is depicted in accordance with an illustrative embodiment. For example, substrate  900  may be a silicon-on-insulator substrate comprising handle layer  902 , buried oxide, BOX, layer  904  on handle layer  902 , and silicon device layer  906  on buried oxide layer  904 , such that buried oxide layer  904  is between silicon device layer  906  and handle layer  902 . For example, without limitation, silicon device layer  906  may be an approximately 25 micrometer thick layer of low resistivity p-type semiconductor and buried oxide layer  904  may be approximately 4 micrometers thick. Substrate  900  comprising other appropriate materials, having other appropriate dimension, or comprising other appropriate materials and dimensions may be used for fabricating a cellular array electrostatic actuator in accordance with an illustrative embodiment. 
     Vertical trenches  908  are formed in silicon device layer  906  of substrate  900  to form the walls of a framework that define an array of cells for a cellular array electrostatic actuator in accordance with an illustrative embodiment (operation  804 ). Trenches  908  preferably extend all the way through silicon device layer  906  to buried oxide layer  904 . For example, trenches  908  may be formed by deep reactive ion etching, DRIE, of silicon device layer  906  or by another appropriate process. Trenches  908  correspond to the interior space between the walls of the cells in a cellular array electrostatic actuator. Operation  804  forms silicon device layer  906  into the walls that define the cells of a cellular array electrostatic actuator, while keeping silicon device layer  906  intact between different actuator arrays. With reference to  FIG. 9 b   , a schematic cross-sectional view of an example of trenches  908  formed in silicon device layer  906  substrate  900  is depicted in accordance with an illustrative embodiment. 
     Buried oxide layer  904  then may be removed from underneath trenches  908  formed in silicon device layer  906  (operation  806 ). For example, buried oxide layer  904  may be removed from underneath trenches  908  by wet etching via a dip in hydrofluoric acid, HF, or in another appropriate manner. With reference to FIG.  9   c , a schematic cross-sectional view of substrate  900  with buried oxide layer  904  removed from underneath trenches  908  in silicon device layer  906  is depicted in accordance with an illustrative embodiment. 
     Dielectric film  910  then may be formed on the walls of trenches  908  in silicon device layer  906  (operation  808 ). For example, without limitation, operation  808  may comprise depositing an approximately 500 nm thick conformal layer of low stress silicon nitride via low-pressure chemical vapor deposition, LPCVD, to cover the walls of trenches  908  in silicon device layer  906 . Other appropriate materials, dimensions, and methods of forming dielectric film  910  may be used. 
     Sacrificial layer  912  then may be formed over dielectric film  910  (operation  810 ). Sacrificial layer  912  defines the transduction air-gaps for the actuator cells. For example, without limitation, operation  810  may comprise depositing an approximately 450 nm thick conformal layer of silicon dioxide via low-pressure chemical vapor deposition. Other appropriate materials, dimensions, and methods of forming sacrificial layer  912  may be used. With reference to  FIG. 9 d   , a schematic cross-section view of substrate  900  with dielectric film  910  deposited on the walls of trenches  908  and sacrificial layer  912  deposited over dielectric film  910  is depicted in accordance with an illustrative embodiment. In a variation of the method described herein, a second dielectric layer may be formed over sacrificial layer  912 . 
     Trenches  908  then may be filled with first layer of polysilicon  914  (operation  812 ). First layer of polysilicon  914  in trenches  908  forms the electrodes for the actuator cells. First layer of polysilicon  914  also fills the empty space underneath trenches  908  that is created after the removal of buried oxide layer  904  in operation  806 . For example, without limitation, operation  812  may comprise depositing an approximately 3.5 micrometer thick layer of p-type doped polysilicon via low-pressure chemical vapor deposition. Other appropriate materials, dimensions, and methods of filling trenches  908  with first layer of polysilicon  914  may be used. 
     First layer of polysilicon  914  then may be etched back on the top surface to provide access to sacrificial layer  912  (operation  814 ). With reference to  FIG. 9 e   , a schematic cross-section view of substrate  900  with first layer of polysilicon  914  filling trenches  908  and etched back on the top surface to expose sacrificial layer  912  is depicted in accordance with an illustrative embodiment. 
     Sacrificial layer  912  is then selectively patterned and removed from certain areas on the top surface to form anchor points  916  where the electrodes are to be anchored onto the silicon framework (operation  816 ). Anchor points  916  are preferably located at nodes in the framework where deformation of the framework when the actuator is operated is close to zero. Any appropriate known method may be used to selectively pattern and remove sacrificial layer  912 . 
     Second layer of polysilicon  918  is then applied on the top surface (operation  818 ). For example, without limitation, operation  818  may comprise depositing an approximately 2 micrometer thick layer of doped polysilicon via low-pressure chemical vapor deposition. Other appropriate materials, dimensions, and methods of applying second layer of polysilicon  918  may be used. 
     Second layer of polysilicon  918  then may be patterned to form interconnects between the electrodes and to anchor the electrodes to the silicon framework at anchor points  916  (operation  820 ). For example, without limitation, second layer of polysilicon  918  may be patterned via reactive-ion etching, RIE, or in any other appropriate manner. Dielectric film  910  provides electrical isolation between the polysilicon electrodes and the silicon framework at anchor points  916 . With reference to  FIG. 9 f   , a schematic section view of substrate  900  with second layer of polysilicon  918  applied on the top surface and patterned to form interconnects between the electrodes and to anchor the electrodes to the silicon framework is depicted in accordance with an illustrative embodiment. 
     Array boundaries then may be defined by patterning silicon device layer  906  around the actuator frames (operation  822 ). For example, without limitation, operation  822  may comprise patterning silicon device layer  906  by a lithography step performed on the top side of substrate  900  followed by deep reactive ion etching of the silicon device layer all the way to the buried oxide layer. Other appropriate methods of patterning silicon device layer  906  around the actuator frames to define array boundaries may be used. 
     Handle layer  902  is then removed from underneath the actuator arrays so that they are released (operation  824 ). For example, without limitation, operation  824  may comprise performing a lithography step on the back side of substrate  900  followed by deep reactive-ion etching, DRIE, to remove handle layer  902 . Other appropriate methods of removing handle layer  902  from underneath the actuator arrays may be used. With reference to  FIG. 9 g   , a schematic cross-section view of substrate  900  with handle layer  902  removed from underneath the actuator arrays is depicted in accordance with an illustrative embodiment. 
     Sacrificial layer  912  then may be removed from between the silicon framework and the polysilicon electrodes to form gaps  920  (operation  826 ), with the process terminating thereafter. For example, without limitation, operation  826  may comprise removing sacrificial layer  912  by submersion in hydrofluoric acid for approximately 15 minutes or by another appropriate amount of time. Silicon nitride has a relatively very low etch rate in hydrofluoric acid. Therefore, most of the thickness of nitride dielectric film  910  covering the walls of the silicon framework will remain in place as sacrificial layer  912  is removed in this way. Other appropriate methods of removing sacrificial layer  912  may be used. With reference to  FIG. 9 h   , a schematic section view of substrate  900  with sacrificial layer  912  removed to form gaps  920  is depicted in accordance with an illustrative embodiment. 
     In a variation of the method described herein, another sacrificial layer and another dielectric layer may be formed between first layer of polysilicon  914  and second layer of polysilicon  918 . 
     Turning to  FIG. 10 , a flow chart diagram of a process of using a cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Process  1000  may be implemented using cellular array electrostatic actuator  100  to move object  156  in  FIG. 1 . 
     Process  1000  may begin with connecting an object to be moved to the framework of an electrostatic actuator, wherein the framework comprises walls defining a plurality of cells forming an array of cells (operation  1002 ). The object may comprise any appropriate object to be moved. The object may be connected to the framework of the electrostatic actuator in any appropriate manner. For example, the object may be connected to the framework of the electrostatic actuator either directly or indirectly via one or more intermediate structures between the object and the framework. 
     An electrical signal then may be applied between the framework and electrodes in the cells of the electrostatic actuator to cause the framework to contract to move the object (operation  1004 ), with the process terminating thereafter. The framework contracts in response to the application of the electrical signal as electrostatic forces pull the walls of the cells inward toward the electrodes in the cells. In accordance with an illustrative embodiment, different electrical signals may be applied independently to the framework and the electrodes in a plurality of different sub-regions of the electrostatic actuator. Applying different electrical signals independently to different sub-regions of the electrostatic actuator will cause different portions of the framework to contract independently to move the framework, and the object connected thereto, in a desired manner. 
     Turning to  FIG. 11 , a scanning electron microscope image plan view of a fabricated cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment. Cellular array electrostatic actuator  1100  is another example of an implementation of cellular array electrostatic actuator  100  in  FIG. 1 . 
     The cells in cellular array electrostatic actuator  1100  are rectangular in shape and arranged in a brick wall pattern. Cellular array electrostatic actuator  1100  includes 450 cells arranged in 100 alternating rows of four cells or five cells in each row. Each cell is approximately 95 micrometers long and 10 micrometers wide. The overall size of the array of cells is approximately 1050 micrometers by 475 micrometers. 
     Turning to  FIG. 12 , a close-up scanning electron microscope image plan view of a portion of a fabricated electrostatic actuator is depicted in accordance with an illustrative embodiment.  FIG. 12  is a magnified view of a portion of cellular array electrostatic actuator  1100  in  FIG. 11 . 
     Cellular array electrostatic actuator  1100  includes silicon framework  1200  comprising walls defining an array of cells. Polysilicon electrodes  1202  are located in the cells in framework  1200 . Polysilicon electrical interconnects  1204  provide electrical connections between electrodes  1202  in the cells of framework  1200 . Electrodes  1202  are attached to framework  1200  by polysilicon isolated anchors at anchor points  1206 . 
     Turning to  FIG. 13 , a further close-up scanning electron microscope image plan view of a portion of a fabricated cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment.  FIG. 13  is a further magnified view of a portion of cellular array electrostatic actuator  1100  in  FIG. 11 .  FIG. 13  shows in more detail examples of portions of framework  1200 , polysilicon electrode  1202 , and anchor point  1206  in  FIG. 12 . 
     Turning to  FIG. 14 , a close-up scanning electron microscope image plan view of an air gap in a portion of a fabricated cellular array electrostatic actuator is depicted in accordance with an illustrative embodiment.  FIG. 14  is a further magnified view of portion  14  of cellular array electrostatic actuator  1100  in  FIG. 13 . 
       FIG. 14  shows in more detail portions of framework  1200  and polysilicon electrode  1202 . Air gap  1400  between framework  1200  and electrode  1202  also is shown. 
     Turning to  FIG. 15 , a scanning electron microscope image view of a fabricated cellular array electrostatic actuator with an electrical signal applied thereto is depicted in accordance with an illustrative embodiment.  FIG. 15  shows cellular array electrostatic actuator  1100  in  FIG. 11  upon application of a 90 volt actuation signal. 
     Upon application of the electrical signal, the framework of cellular array electrostatic actuator  1100  contracts and curves upward, taking the shape of an arch. The framework experiences a substantially uniform bending moment along its length, with slight periodic variations due to alternating rows with four and five cells. Vertical displacement at distal end  1500  of actuator  1100  is estimated from the scanning electron microscope image view to be approximately 230 micrometers in this example. Based on the measured displacement, the radius of curvature for actuator  1100  is 2.4 millimeters, corresponding to a 25.0 degree arch angle. To achieve such curvature, the top surface of actuator  1100  contracted by 11 micrometers. Each of the air gaps in each cell of actuator  1100  thus contracted by approximately 110 nanometers at the top surface of actuator  1100 . Using the equation presented above, the electrostatic force acting on the walls of the individual cells in actuator  1100  is approximately 0.4 mN. The electrostatic force acting on a row of four or five cells is thus 1.6 mN to 2.0 mN, with an average force of 1.8 mN per row. With estimated flexural stiffness of 1.3 N/m at distal end  1500  of actuator  1100 , and vertical displacement of 230 micrometers, the vertical force at distal end  1500  of actuator  1100  is estimated to be around 0.3 mN. 
     Turning to  FIG. 16 , a close-up scanning electron microscope image view of a portion of a fabricated cellular array electrostatic actuator with an electrical signal applied thereto is depicted in accordance with an illustrative embodiment.  FIG. 16  is a magnified view of portion  16  of cellular array electrostatic actuator  1100  upon application of a 90 volt actuation signal in  FIG. 15 . 
     Turning to  FIG. 17 , a scanning electron microscope image view of a cellular array electrostatic actuator lifting an object is depicted in accordance with an illustrative embodiment.  FIG. 17  shows cellular array electrostatic actuator  1100  in  FIG. 11  lifting object  1700 . 
     In this example, object  1700  is a piece of copper with a mass of approximately 1.2 mg. Object  1700  in this example is about forty times heavier than cellular array electrostatic actuator  1100 . Object  1700  is lifted approximately 45 micrometers by applying an approximately 30 volt activation voltage to actuator  1100 . Object  1700  was thrown away from actuator  1100  upon sudden application of an approximately 40 volt activation voltage. 
     The descriptions of the various embodiments have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiment, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed here.