Patent Publication Number: US-2012044562-A1

Title: Actuation and calibration of charge neutral electrode

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This disclosure claims priority to U.S. Provisional Patent Application No. 61/374,539, filed Aug. 17, 2010, entitled “ELECTROSTATIC ACTUATION AND CALIBRATION OF CHARGE NEUTRAL ELECTRODE,” and assigned to the assignee hereof. The disclosure of the prior application is considered part of, and is incorporated by reference in, this disclosure. This application is related to U.S. patent application Ser. No. ______, entitled “Actuation and Calibration of Charge Neutral Electrode,” filed Aug. 16, 2011 (Attorney Docket No. QCO.357A/092491U2), which is assigned to the assignee of the present invention. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to actuation of electrodes in electromechanical systems. 
     DESCRIPTION OF THE RELATED TECHNOLOGY 
     Electromechanical systems (EMS) include devices having electrical and mechanical elements, actuators, transducers, sensors, optical components (e.g., mirrors) and electronics. Electromechanical systems can be manufactured at a variety of scales including, but not limited to, microscales and nanoscales. For example, microelectromechanical systems (MEMS) devices can include structures having sizes ranging from about a micron to hundreds of microns or more. Nanoelectromechanical systems (NEMS) devices can include structures baying sizes smaller than a micron including, for example, sizes smaller than several hundred nanometers. Electromechanical elements may be created using deposition, etching, lithography, and/or other micromachining processes that etch away parts of substrates and/or deposited material layers, or that add layers to form electrical and electromechanical devices. 
     One type of electromechanical systems device is called an interferometric modulator (IMOD). As used herein, the term interferometric modulator or interferometric light modulator refers to a device that selectively absorbs and/or reflects light using the principles of optical interference. In some implementations, an interferometric modulator may include a pair of conductive plates, one or both of which may be transparent and/or reflective, wholly or in part, and capable of relative motion upon application of an appropriate electrical signal. In an implementation, one plate may include a stationary layer deposited on a substrate and the other plate may include a reflective membrane separated from the stationary layer by an air gap. The position of one plate in relation to another can change the optical interference of light incident on the interferometric modulator. Interferometric modulator devices have a wide range of applications, and are anticipated to be used in improving existing products and creating new products, especially those with display capabilities. 
     Some interferometric modulators include bi-stable display elements having two states: a relaxed state and an actuated state. In contrast, analog interferometric modulators can reflect a range of colors. For example, in one implementation of an analog interferometric modulator, a single interferometric modulator can reflect a red color, a green color, a blue color, a black color, and a white color. In some implementations, an analog modulator can reflect any color within a given range of wavelengths. 
     SUMMARY 
     The systems, methods and devices of the disclosure each have several innovative aspects, no single one of which is solely responsible for the desirable attributes disclosed herein. 
     One innovative aspect of the subject matter described in this disclosure can be implemented in a device for modulating light that includes a display element. The display element includes a first electrode and a second electrode spaced apart from the first electrode by a gap. The display element also includes a movable third electrode disposed between the first electrode and the second electrode and at least one electrical contact. The first electrode and the second electrode are configured to produce an electric field therebetween capable of moving the movable third electrode when the movable third electrode is electrically isolated and charge neutral when a voltage is applied across the first electrode and the second electrode. The third electrode is configured to move within the gap between an electrically isolated first position, an electrically connected second position, and an electrically isolated third position. The third electrode is in electrical communication with the at least one electrical contact at the electrically connected second position. The electrical contact is configured to change an electrical charge on the third electrode when the third electrode is in the electrically connected second position. The third electrode is also configured to move to the third position after the electrical charge on the third electrode has been changed. 
     Another implementation is a device for modulating light including a display element. The device includes means for producing a non-uniform electric field. The device also includes a movable electrode disposed between a first electrode and a second electrode forming a gap therebetween, the movable electrode being configured to move within the gap between an electrically isolated first position, a second position, and an electrically isolated third position. The device also includes means for changing an electrical charge on the movable electrode when the movable electrode is in the second position. 
     Yet another implementation includes a method of actuating a device for modulating light. The method includes applying a charging actuation voltage across a first electrode and a second electrode to produce an electric field in a gap between the first electrode and second electrode in order to move an electrically isolated, charge-neutral third electrode, positioned in the gap, towards the first electrode from a first position to a second position. The method also includes electrically connecting the third electrode with an electrical contact when the third electrode is in the second position. The method further includes changing an electrical charge on the third electrode when the third electrode is in the second position until a mechanical restorative force on the third electrode exceeds an electric force of the electric field on the third electrode. 
     Another implementation is a method of calibrating an analog interferometric modulator in a display. The method includes applying a calibration voltage across a first electrode and a second electrode to produce an electric field in a gap between the first electrode and the second electrode to move a third electrode, positioned in the gap, towards the first electrode from an electrically isolated first position to an electrically connected second position, the third electrode being subject to a mechanical restorative force. The method further includes electrically connecting the third electrode to one or more conductive posts electrically connected to the first electrode, to change an electric charge on the third electrode when the third electrode is in the second position, until a mechanical restorative force on the third electrode exceeds an electric field force on the third electrode such that the third electrode moves to an electrically isolated third position, the third position being farther away from the first electrode than the second position. In some implementations, the first electrode includes an upper electrode and a complementary electrode aligned laterally relative to the upper electrode and the method also includes electrically connecting the complementary electrode to the upper electrode to form a compound electrode. The calibration voltage can then be applied across the compound electrode and the second electrode. 
     Yet another implementation is device for modulating light that includes a display element. The display element includes a first electrode and a second electrode spaced apart from the first electrode by a gap, the first electrode and the second electrode configured to produce a non-uniform electric field therebetween when an actuation voltage is applied across the first electrode and the second electrode during an actuation procedure. The display element further includes a complementary electrode aligned laterally relative to the first electrode, the complementary electrode configured to be electrically isolated from the first electrode during the actuation procedure and electrically connected to the first electrode to form a compound electrode during a calibration procedure, the compound electrode and the second electrode configured to produce a uniform electric field therebetween when a calibration voltage is applied across the compound electrode and the second electrode during the calibration procedure. The display element also includes at least one electrical contact disposed on the complementary electrode and a movable third electrode disposed between the first electrode and the second electrode, the third electrode being configured to move within the gap between an electrically isolated first position, a second position in electrical communication with the at least one electrical contact, and an electrically isolated third position. The electrical contact is configured to change an electrical charge on the third electrode when the third electrode is in the second position, and the third electrode is configured to move to the third position after the electrical charge on the third electrode has been changed. 
     Still a further implementation includes a device for modulating light that includes a display element. The display element includes means for producing a non-uniform electric field and means for producing a uniform electric field. The display element further includes a movable electrode disposed between a first electrode and a second electrode forming a gap therebetween, the movable electrode being configured to move within the gap between an electrically isolated first position, a second position, and an electrically isolated third position. The display element also includes means for changing an electrical charge on the movable electrode when the movable electrode is in the second position. In some implementations, the means for producing a non-uniform electric field includes the first electrode and the second electrode. The first electrode and the second electrode have different surface areas. In some implementations, the means for producing a uniform electric field includes the first electrode and the second electrode, where the first electrode includes an upper electrode electrically connected to a complementary electrode aligned laterally relative to the upper electrode. 
     Details of one or more implementations of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages will become apparent from the description, the drawings, and the claims. Note that the relative dimensions of the following figures may not be drawn to scale. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example of an isometric view depicting two adjacent pixels in a series of pixels of an interferometric modulator (IMOD) display device. 
         FIG. 2  shows an example of a system block diagram illustrating an electronic device incorporating a 3×3 interferometric modulator display. 
         FIG. 3  shows an example of a diagram illustrating movable reflective layer position versus applied voltage for the interferometric modulator of  FIG. 1 . 
         FIG. 4  shows an example of a table illustrating various states of an interferometric modulator when various common and segment voltages are applied. 
         FIG. 5A  shows an example of a diagram illustrating a frame of display data in the 3×3 interferometric modulator display of  FIG. 2 . 
         FIG. 5B  shows an example of a timing diagram for common and segment signals that may be used to write the frame of display data illustrated in  FIG. 5A . 
         FIG. 6A  shows an example of a partial cross-section of the interferometric modulator display of  FIG. 1 . 
         FIGS. 6B-6E  show examples of cross-sections of varying implementations of interferometric modulators. 
         FIG. 7  shows an example of a flow diagram illustrating a manufacturing process for an interferometric modulator. 
         FIGS. 8A-8E  show examples of cross-sectional schematic illustrations of various stages in a method of making an interferometric modulator. 
         FIG. 9  shows an example of a flowchart illustrating one method for actuating and calibrating a charge neutral electrode of an analog interferometric modulator. 
         FIG. 10  shows an example of a cross-section of an interferometric modulator having a three layer or electrode design. 
         FIG. 11A  shows an example of a cross-section of another analog interferometric modulator with a control circuit. 
         FIG. 11B  shows an example of a schematic of charge pump circuitry to place a charge on an electrode of an interferometric modulator. 
         FIG. 12  shows an example of a perspective view of an analog interferometric modulator which includes a middle electrode that can be moved between two charged electrodes. 
         FIG. 13  shows an example of an equivalent circuit of the analog interferometric modulator shown in  FIG. 12 . 
         FIG. 14  shows an example of a graph illustrating how the net upward electric force acting on the middle electrode of the analog interferometric modulator of  FIG. 12  varies with the distance between an upper electrode and the middle electrode. 
         FIG. 15A  shows an example of a cross-sectional schematic of an analog interferometric modulator which includes a middle electrode that can be moved between two charged electrodes. 
         FIG. 15B  shows an example of the analog interferometric modulator of  FIG. 15A  after a compound electrode has been formed. 
         FIG. 16  shows an example of a schematic characterizing the analog interferometric modulator configuration shown in  FIG. 15A  as an equivalent circuit. 
         FIG. 17  shows an example of a graph illustrating the magnitude of the net upward force acting on the middle electrodes in the analog interferometric modulators of  FIGS. 12 and 15A . 
         FIG. 18  shows an example of a plan view of a complementary electrode and an upper electrode shown in  FIG. 15A . 
         FIG. 19  shows an example of a plan view of another electrode configuration. 
         FIG. 20  shows an example of a plan view of yet another electrode configuration. 
         FIG. 21  shows an example of a cross-section of yet another analog interferometric modulator which includes a middle electrode that can be moved between two charged electrodes. 
         FIG. 22  shows an example of a flowchart illustrating one method for providing charge onto the middle electrode of the analog interferometric modulator of  FIG. 21 . 
         FIG. 23  shows an example of a cross-section of the analog interferometric modulator of  FIG. 21  illustrating the middle electrode in a second position. 
         FIG. 24  shows an example of a cross-sectional schematic of still a further analog interferometric modulator which includes a middle electrode that can be moved between two charged electrodes. 
         FIG. 25  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 24  illustrating the middle electrode in a second position. 
         FIG. 26  shows an example of a cross-sectional schematic of an analog interferometric modulator which includes a middle electrode that can be calibrated. 
         FIG. 27  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 26  illustrating the middle electrode in a first position. 
         FIG. 28  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 26  after the middle electrode is actuated toward a second position. 
         FIG. 29  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 26  illustrating the middle electrode in the second position. 
         FIG. 30  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 26  illustrating the middle electrode in a third position. 
         FIG. 31  shows an example of a flowchart illustrating one method for calibrating charge on the middle electrode of the analog interferometric modulator of  FIG. 26 . 
         FIG. 32  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 26  illustrating the middle electrode in the second position during a calibration procedure. 
         FIG. 33  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 26  illustrating the middle electrode in the third position following a calibration procedure. 
         FIG. 33A  shows an example of a cross-sectional schematic of an analog interferometric modulator having a middle electrode with a calibrated charge that is related to the stiffness of springs supporting the middle electrode. 
         FIG. 34  shows an example of a cross-sectional schematic of yet another analog interferometric modulator which includes a middle electrode that can be calibrated. 
         FIG. 35  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 34  illustrating the middle electrode in a first position. 
         FIG. 36  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 34  after the middle electrode is actuated toward a second position. 
         FIG. 37  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 34  illustrating the middle electrode in the second position. 
         FIG. 38  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 34  illustrating the middle electrode in a third position. 
         FIG. 39  shows an example of a flowchart illustrating one method of calibrating charge on the middle electrode of the analog interferometric modulator of  FIG. 34 . 
         FIG. 40  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 34  illustrating the middle electrode in the second position during a calibration procedure. 
         FIG. 41  shows an example of a cross-sectional schematic of the analog interferometric modulator of  FIG. 34  illustrating the middle electrode in the third position following a calibration procedure. 
         FIGS. 42A and 42B  show examples of system block diagrams illustrating a display device that includes a plurality of interferometric modulators. 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     The following detailed description is directed to certain implementations for the purposes of describing the innovative aspects. However, the teachings herein can be applied in a multitude of different ways. The described implementations may be implemented in any device that is configured to display an image, whether in motion (e.g., video) or stationary (e.g., still image), and whether textual, graphical or pictorial. More particularly, it is contemplated that the implementations may be implemented in or associated with a variety of electronic devices such as, but not limited to, mobile telephones, multimedia Internet enabled cellular telephones, mobile television receivers, wireless devices, smartphones, bluetooth devices, personal data assistants (PDAs), wireless electronic mail receivers, hand-held or portable computers, netbooks, notebooks, smartbooks, tablets, printers, copiers, scanners, facsimile devices, GPS receivers/navigators, cameras, MP3 players, camcorders, game consoles, wrist watches, clocks, calculators, television monitors, flat panel displays, electronic reading devices (e-readers), computer monitors, auto displays (e.g., odometer display, etc.), cockpit controls and/or displays, camera view displays (e.g., display of a rear view camera in a vehicle), electronic photographs, electronic billboards or signs, projectors, architectural structures, microwaves, refrigerators, stereo systems, cassette recorders or players, DVD players, CD players, VCRs, radios, portable memory chips, washers, dryers, washer/dryers, parking meters, packaging (for example electromechanical systems (EMS), MEMS and non-MEMS applications), aesthetic structures (for example, display of images on a piece of jewelry) and a variety of electromechanical systems devices. The teachings herein also can be used in non-display applications such as, but not limited to, electronic switching devices, radio frequency filters, sensors, accelerometers, gyroscopes, motion-sensing devices, magnetometers, inertial components for consumer electronics, parts of consumer electronics products, varactors, liquid crystal devices, electrophoretic devices, drive schemes, manufacturing processes, and electronic test equipment. Thus, the teachings are not intended to be limited to the implementations depicted solely in the Figures, but instead have wide applicability as will be readily apparent to a person having ordinary skill in the art. 
     Methods and devices to actuate, charge, and calibrate movable electrodes in analog interferometric modulators are described herein. For example, various methods and devices are provided to actuate a charge-neutral, electrically isolated electrode (“middle electrode”) disposed in a gap between two charged electrodes such that the charge-neutral electrode is actuated and moves toward one of the charged electrodes. In one implementation, at least two charged electrodes are configured to produce an electric field therebetween capable of moving the electrically isolated, charge neutral middle electrode when a voltage V is applied across the charged electrodes. In such implementations, there can be at least two charged electrodes having different dimensions and/or surface areas. The middle electrode can be disposed between such electrodes. In another implementation, the charge-neutral, electrically isolated middle electrode is actuated by applying an electric field between charged electrodes having different surface areas, where a complementary electrode is aligned laterally relative to one of the charged electrodes. 
     Methods and devices to provide charge onto movable electrodes in analog interferometric modulators are also described herein. For example, various methods and devices can provide a charge to a charge-neutral, electrically isolated middle electrode after it has been actuated or moved toward a charged electrode. In one implementation, charge is placed on the middle electrode when the middle electrode moves toward a charged electrode and makes direct electrical contact with conductive posts on the charged electrode. The middle electrode develops a net charge until the electric force acting on the middle electrode is overcome by the opposing mechanical spring force acting on the middle electrode. The middle electrode then moves away from the charged electrode, breaking electrical contact and electrically isolating the charge that has been placed on the middle electrode. In another implementation, the middle electrode is inductively charged when the middle electrode moves toward a charged electrode and electrically contacts conductive posts on a complementary electrode aligned laterally relative to the charged electrode, where the complementary electrode is electrically isolated from the charged electrode and connected to electrical ground. 
     Methods and devices to calibrate the charge that is provided to a movable electrode in an analog interferometric modulator are also described herein. In one implementation using a “switch” configuration, one or more switches are closed to electrically connect a complementary electrode and a charged electrode to form a compound electrode. A calibration voltage is applied between the compound electrode and the opposing charged electrode, causing the charged middle electrode to move toward the compound electrode and to change its charge by, for example, electrically contacting at least one conductive structure (for example conductive posts) on the compound electrode. In one implementation, the electrical contact causes charge on the middle electrode to change until the electric force acting on the middle electrode is overcome by the opposing mechanical spring force acting on the middle electrode. The middle electrode then moves away from the compound electrode, breaking electrical contact and electrically isolating the charge that remains onto the middle electrode. Upon release, the amount of charge on the middle electrode is related to the mechanical spring force acting on the middle electrode. The structure that holds the middle electrode and provides the mechanical spring force can be, for example, springs of various configurations or the structure of the middle electrode itself that opposes deformation of the electrode. For clarity of disclosure, structure that provides a mechanical spring force on the middle electrode is referred to herein as a “spring” whether such force is provided by the electrode material itself or a structure connected to the middle electrode. 
     Another implementation uses a “switchless” configuration to calibrate charge that has been placed on a movable electrode. A calibration voltage is applied between two charged electrodes having different surface areas. The charged middle electrode moves toward the charged electrode having the smaller surface area and electrically contacts conductive posts electrically connected to the charged electrode. The electrical contact causes charge on the middle electrode to change until the electric force acting on the middle electrode is overcome by the opposing mechanical spring force acting on the middle electrode. The middle electrode then moves away from the charged electrode, breaking electrical contact and electrically isolating the charge that remains on the middle electrode. Upon release, the amount of charge on the middle electrode is related to the stiffness of the springs holding the middle electrode. 
     Particular implementations of the subject matter described in this disclosure can be implemented to realize one or more of the following potential advantages. A three-terminal electromechanical device (for example, an interferometric modulator) can include a movable middle electrode disposed in a gap between two electrodes, for example, an upper electrode and a lower electrode. Implementations of the devices and methods described herein can move an electrically isolated middle electrode having net zero charge, so that the middle electrode contacts the upper (or lower) electrode. The middle electrode can become charged through this contact, solving drawbacks associated with typical three-terminal devices. Devices and methods are disclosed to charge the middle electrode once it contacts the upper (or lower) electrode. Once charge is provided to the middle electrode, the middle electrode can then be released from the contacting electrode, which isolates charge on the electrode. The charge on the middle electrode can then be calibrated to account for the particular mechanical spring force acting on the middle electrode. Methods and systems for calibrating a charge placed onto the middle electrode are described, for example, with reference to  FIGS. 31-33  and  39 - 41 . Calibrating each of the middle electrodes across an array of three-terminal devices with a desired amount of charge can allow for movement of all of the middle electrodes to the same location upon application of the same voltage across all of the devices. Following calibration, the plurality of calibrated modulators in the array can be in an operationally ready state. Additionally, the actuation, charging, and calibration procedures described herein can be repeated where useful and adjusted to account for variances in the rate of charge leakage from the middle electrodes over the lifetime of the device. 
     An example of a suitable EMS or MEMS device, to which the described implementations may apply, is a reflective display device. Reflective display devices can incorporate interferometric modulators (IMODs) to selectively absorb and/or reflect light incident thereon using principles of optical interference. IMODs can include an absorber, a reflector that is movable with respect to the absorber, and an optical resonant cavity defined between the absorber and the reflector. The reflector can be moved to two or more different positions, which can change the size of the optical resonant cavity and thereby affect the reflectance of the interferometric modulator. The reflectance spectrums of IMODs can create fairly broad spectral bands which can be shifted across the visible wavelengths to generate different colors. The position of the spectral band can be adjusted by changing the thickness of the optical resonant cavity, i.e., by changing the position of the reflector. 
       FIG. 1  shows an example of an isometric view depicting two adjacent pixels in a series of pixels of an interferometric modulator (IMOD) display device. The IMOD display device includes one or more interferometric MEMS display elements. In these devices, the pixels of the MEMS display elements can be in either a bright or dark state. In the bright (“relaxed,” “open” or “on”) state, the display element reflects a large portion of incident visible light, e.g., to a user. Conversely, in the dark (“actuated,” “closed” or “off”) state, the display element reflects little incident visible light. In some implementations, the light reflectance properties of the on and off states may be reversed. MEMS pixels can be configured to reflect predominantly at particular wavelengths allowing for a color display in addition to black and white. 
     The IMOD display device can include a row/column array of IMODs. Each IMOD can include a pair of reflective layers, i.e., a movable reflective layer and a fixed partially reflective layer, positioned at a variable and controllable distance from each other to form an air gap (also referred to as an optical gap or cavity). The movable reflective layer may be moved between at least two positions. In a first position, i.e., a relaxed position, the movable reflective layer can be positioned at a relatively large distance from the fixed partially reflective layer. In a second position, i.e., an actuated position, the movable reflective layer can be positioned more closely to the partially reflective layer. Incident light that reflects from the two layers can interfere constructively or destructively depending on the position of the movable reflective layer, producing either an overall reflective or non-reflective state for each pixel. In some implementations, the IMOD may be in a reflective state when unactuated, reflecting light within the visible spectrum, and may be in a dark state when unactuated, absorbing and/or destructively interfering light within the visible range. In some other implementations, however, an IMOD may be in a dark state when unactuated, and in a reflective state when actuated. In some implementations, the introduction of an applied voltage can drive the pixels to change states. In some other implementations, an applied charge can drive the pixels to change states. 
     The depicted portion of the pixel array in  FIG. 1  includes two adjacent interferometric modulators  12 . In the IMOD  12  on the left (as illustrated), a movable reflective layer  14  is illustrated in a relaxed position at a predetermined distance from an optical stack  16 , which includes a partially reflective layer. The voltage V 0  applied across the IMOD  12  on the left is insufficient to cause actuation of the movable reflective layer  14 . In the IMOD  12  on the right, the movable reflective layer  14  is illustrated in an actuated position near or adjacent the optical stack  16 . The voltage V bias  applied across the IMOD  12  on the right is sufficient to maintain the movable reflective layer  14  in the actuated position. 
     In  FIG. 1 , the reflective properties of pixels  12  are generally illustrated with arrows  13  indicating light incident upon the pixels  12 , and light  15  reflecting from the pixel  12  on the left. Although not illustrated in detail, it will be understood by a person having ordinary skill in the art that most of the light  13  incident upon the pixels  12  will be transmitted through the transparent substrate  20 , toward the optical stack  16 . A portion of the light incident upon the optical stack  16  will be transmitted through the partially reflective layer of the optical stack  16 , and a portion will be reflected back through the transparent substrate  20 . The portion of light  13  that is transmitted through the optical stack  16  will be reflected at the movable reflective layer  14 , back toward (and through) the transparent substrate  20 . Interference (constructive or destructive) between the light reflected from the partially reflective layer of the optical stack  16  and the light reflected from the movable reflective layer  14  will determine the wavelength(s) of light  15  reflected from the pixel  12 . 
     The optical stack  16  can include a single layer or several layers. The layer(s) can include one or more of an electrode layer, a partially reflective and partially transmissive layer and a transparent dielectric layer. In some implementations, the optical stack  16  is electrically conductive, partially transparent and partially reflective, and may be fabricated, for example, by depositing one or more of the above layers onto a transparent substrate  20 . The electrode layer can be fainted from a variety of materials, for example various metals, for example indium tin oxide (ITO). The partially reflective layer can be formed from a variety of materials that are partially reflective, for example various metals, e.g., chromium (Cr), semiconductors, and dielectrics. The partially reflective layer can be formed of one or more layers of materials, and each of the layers can be formed of a single material or a combination of materials. In some implementations, the optical stack  16  can include a single semi-transparent thickness of metal or semiconductor which serves as both an optical absorber and electrical conductor, while different, electrically more conductive layers or portions (e.g., of the optical stack  16  or of other structures of the IMOD) can serve to bus signals between IMOD pixels. The optical stack  16  also can include one or more insulating or dielectric layers covering one or more conductive layers or an electrically conductive/optically absorptive layer. 
     In some implementations, the layer(s) of the optical stack  16  can be patterned into parallel strips, and may form row electrodes in a display device as described further below. As will be understood by one having ordinary skill in the art, the term “patterned” is used herein to refer to masking as well as etching processes. In some implementations, a highly conductive and reflective material, for example aluminum (Al), may be used for the movable reflective layer  14 , and these strips may form column electrodes in a display device. The movable reflective layer  14  may be formed as a series of parallel strips of a deposited metal layer or layers (orthogonal to the row electrodes of the optical stack  16 ) to form columns deposited on top of posts  18  and an intervening sacrificial material deposited between the posts  18 . When the sacrificial material is etched away, a defined gap  19 , or optical cavity, can be formed between the movable reflective layer  14  and the optical stack  16 . In some implementations, the spacing between posts  18  may be approximately 1-1000 um, while the gap  19  may be less than 10,000 Angstroms (Å). 
     In some implementations, each pixel of the IMOD, whether in the actuated or relaxed state, is essentially a capacitor formed by the fixed and moving reflective layers. When no voltage is applied, the movable reflective layer  14  remains in a mechanically relaxed state, as illustrated by the pixel  12  on the left in  FIG. 1 , with the gap  19  between the movable reflective layer  14  and optical stack  16 . However, when a potential difference, a voltage, is applied to at least one of a selected row and column, the capacitor formed at the intersection of the row and column electrodes at the corresponding pixel becomes charged, and electrostatic forces pull the electrodes together. If the applied voltage exceeds a threshold, the movable reflective layer  14  can deform and move near or against the optical stack  16 . A dielectric layer (not shown) within the optical stack  16  may prevent shorting and control the separation distance between the layers  14  and  16 , as illustrated by the actuated pixel  12  on the right in  FIG. 1 . The behavior is the same regardless of the polarity of the applied potential difference. Though a series of pixels in an array may be referred to in some instances as “rows” or “columns,” a person having ordinary skill in the art will readily understand that referring to one direction as a “row” and another as a “column” is arbitrary. Restated, in some orientations, the rows can be considered columns, and the columns considered to be rows. Furthermore, the display elements may be evenly arranged in orthogonal rows and columns (an “array”), or arranged in non-linear configurations, for example, having certain positional offsets with respect to one another (a “mosaic”). The terms “array” and “mosaic” may refer to either configuration. Thus, although the display is referred to as including an “array” or “mosaic,” the elements themselves need not be arranged orthogonally to one another, or disposed in an even distribution, in any instance, but may include arrangements having asymmetric shapes and unevenly distributed elements. 
       FIG. 2  shows an example of a system block diagram illustrating an electronic device incorporating a 3×3 interferometric modulator display. The electronic device includes a processor  21  that may be configured to execute one or more software modules. In addition to executing an operating system, the processor  21  may be configured to execute one or more software applications, including a web browser, a telephone application, an email program, or any other software application. 
     The processor  21  can be configured to communicate with an array driver  22 . The array driver  22  can include a row driver circuit  24  and a column driver circuit  26  that provide signals to, e.g., a display array or panel  30 . The cross section of the IMOD display device illustrated in  FIG. 1  is shown by the lines  1 - 1  in  FIG. 2 . Although  FIG. 2  illustrates a 3×3 array of IMODs for the sake of clarity, the display array  30  may contain a very large number of IMODs, and may have a different number of IMODs in rows than in columns, and vice versa. 
       FIG. 3  shows an example of a diagram illustrating movable reflective layer position versus applied voltage for the interferometric modulator of  FIG. 1 . For MEMS interferometric modulators, the row/column (i.e., common/segment) write procedure may take advantage of a hysteresis property of these devices as illustrated in  FIG. 3 . An interferometric modulator may use, in one example implementation, about a 10-volt potential difference to cause the movable reflective layer, or mirror, to change from the relaxed state to the actuated state. When the voltage is reduced from that value, the movable reflective layer maintains its state as the voltage drops back below, in this example, 10 volts, however, the movable reflective layer does not relax completely until the voltage drops below 2 volts. Thus, a range of voltage, approximately 3 to 7 volts, in this example, as shown in  FIG. 3 , exists where there is a window of applied voltage within which the device is stable in either the relaxed or actuated state. This is referred to herein as the “hysteresis window” or “stability window.” For a display array  30  having the hysteresis characteristics of  FIG. 3 , the row/column write procedure can be designed to address one or more rows at a time, such that during the addressing of a given row, pixels in the addressed row that are to be actuated are exposed to a voltage difference of about, in this example, 10 volts, and pixels that are to be relaxed are exposed to a voltage difference of near zero volts. After addressing, the pixels can be exposed to a steady state or bias voltage difference of approximately 5 volts in this example, such that they remain in the previous strobing state. In this example, after being addressed, each pixel sees a potential difference within the “stability window” of about 3-7 volts. This hysteresis property feature enables the pixel design, for example that illustrated in  FIG. 1 , to remain stable in either an actuated or relaxed pre-existing state under the same applied voltage conditions. Since each IMOD pixel, whether in the actuated or relaxed state, is essentially a capacitor formed by the fixed and moving reflective layers, this stable state can be held at a steady voltage within the hysteresis window without substantially consuming or losing power. Moreover, essentially little or no current flows into the IMOD pixel if the applied voltage potential remains substantially fixed. 
     In some implementations, a frame of an image may be created by applying data signals in the form of “segment” voltages along the set of column electrodes, in accordance with the desired change (if any) to the state of the pixels in a given row. Each row of the array can be addressed in turn, such that the frame is written one row at a time. To write the desired data to the pixels in a first row, segment voltages corresponding to the desired state of the pixels in the first row can be applied on the column electrodes, and a first row pulse in the form of a specific “common” voltage or signal can be applied to the first row electrode. The set of segment voltages can then be changed to correspond to the desired change (if any) to the state of the pixels in the second row, and a second common voltage can be applied to the second row electrode. In some implementations, the pixels in the first row are unaffected by the change in the segment voltages applied along the column electrodes, and remain in the state they were set to during the first common voltage row pulse. This process may be repeated for the entire series of rows, or alternatively, columns, in a sequential fashion to produce the image frame. The frames can be refreshed and/or updated with new image data by continually repeating this process at some desired number of frames per second. 
     The combination of segment and common signals applied across each pixel (that is, the potential difference across each pixel) determines the resulting state of each pixel.  FIG. 4  shows an example of a table illustrating various states of an interferometric modulator when various common and segment voltages are applied. As will be understood by one having ordinary skill in the art, the “segment” voltages can be applied to either the column electrodes or the row electrodes, and the “common” voltages can be applied to the other of the column electrodes or the row electrodes. 
     As illustrated in  FIG. 4  (as well as in the timing diagram shown in  FIG. 5B ), when a release voltage VC REL  is applied along a common line, all interferometric modulator elements along the common line will be placed in a relaxed state, alternatively referred to as a released or unactuated state, regardless of the voltage applied along the segment lines, i.e., high segment voltage VS H  and low segment voltage VS L . In particular, when the release voltage VC REL  is applied along a common line, the potential voltage across the modulator pixels (alternatively referred to as a pixel voltage) is within the relaxation window (see  FIG. 3 , also referred to as a release window) both when the high segment voltage VS H  and the low segment voltage VS L  are applied along the corresponding segment line for that pixel. 
     When a hold voltage is applied on a common line, for example a high hold voltage VC HOLD     —     H  or a low hold voltage VC HOLD     —     L , the state of the interferometric modulator will remain constant. For example, a relaxed IMOD will remain in a relaxed position, and an actuated IMOD will remain in an actuated position. The hold voltages can be selected such that the pixel voltage will remain within a stability window both when the high segment voltage VS H  and the low segment voltage VS L  are applied along the corresponding segment line. Thus, the segment voltage swing, i.e., the difference between the high VS H  and low segment voltage VS L , is less than the width of either the positive or the negative stability window. 
     When an addressing, or actuation, voltage is applied on a common line, for example a high addressing voltage VC ADD     —     H  or a low addressing voltage VC ADD     —     L , data can be selectively written to the modulators along that line by application of segment voltages along the respective segment lines. The segment voltages may be selected such that actuation is dependent upon the segment voltage applied. When an addressing voltage is applied along a common line, application of one segment voltage will result in a pixel voltage within a stability window, causing the pixel to remain unactuated. In contrast, application of the other segment voltage will result in a pixel voltage beyond the stability window, resulting in actuation of the pixel. The particular segment voltage which causes actuation can vary depending upon which addressing voltage is used. In some implementations, when the high addressing voltage VC ADD     —     H  is applied along the common line, application of the high segment voltage VS H  can cause a modulator to remain in its current position, while application of the low segment voltage VS L  can cause actuation of the modulator. As a corollary, the effect of the segment voltages can be the opposite when a low addressing voltage VC ADD     —     L  is applied, with high segment voltage VS H  causing actuation of the modulator, and low segment voltage VS L  having no effect (i.e., remaining stable) on the state of the modulator. 
     In some implementations, hold voltages, address voltages, and segment voltages may be used which produce the same polarity potential difference across the modulators. In some other implementations, signals can be used which alternate the polarity of the potential difference of the modulators from time to time. Alternation of the polarity across the modulators (that is, alternation of the polarity of write procedures) may reduce or inhibit charge accumulation which could occur after repeated write operations of a single polarity. 
       FIG. 5A  shows an example of a diagram illustrating a frame of display data in the 3×3 interferometric modulator display of  FIG. 2 .  FIG. 5B  shows an example of a timing diagram for common and segment signals that may be used to write the frame of display data illustrated in  FIG. 5A . The signals can be applied to a 3×3 array, similar to the array of  FIG. 2 , which will ultimately result in the line time  60   e  display arrangement illustrated in  FIG. 5A . The actuated modulators in  FIG. 5A  are in a dark-state, i.e., where a substantial portion of the reflected light is outside of the visible spectrum so as to result in a dark appearance to, for example, a viewer. Prior to writing the frame illustrated in  FIG. 5A , the pixels can be in any state, but the write procedure illustrated in the timing diagram of  FIG. 5B  presumes that each modulator has been released and resides in an unactuated state before the first line time  60   a.    
     During the first line time  60   a : a release voltage  70  is applied on common line  1 ; the voltage applied on common line  2  begins at a high hold voltage  72  and moves to a release voltage  70 ; and a low hold voltage  76  is applied along common line  3 . Thus, the modulators (common  1 , segment  1 ), ( 1 , 2 ) and ( 1 , 3 ) along common line  1  remain in a relaxed, or unactuated, state for the duration of the first line time  60   a , the modulators ( 2 , 1 ), ( 2 , 2 ) and ( 2 , 3 ) along common line  2  will move to a relaxed state, and the modulators ( 3 , 1 ), ( 3 , 2 ) and ( 3 , 3 ) along common line  3  will remain in their previous state. With reference to  FIG. 4 , the segment voltages applied along segment lines  1 ,  2  and  3  will have no effect on the state of the interferometric modulators, as none of common lines  1 ,  2  or  3  are being exposed to voltage levels causing actuation during line time  60   a  (i.e., VC REL −relax and VC HOLD     —     L −stable). 
     During the second line time  60   b , the voltage on common line  1  moves to a high hold voltage  72 , and all modulators along common line  1  remain in a relaxed state regardless of the segment voltage applied because no addressing, or actuation, voltage was applied on the common line  1 . The modulators along common line  2  remain in a relaxed state due to the application of the release voltage  70 , and the modulators ( 3 , 1 ), ( 3 , 2 ) and ( 3 , 3 ) along common line  3  will relax when the voltage along common line  3  moves to a release voltage  70 . 
     During the third line time  60   c , common line  1  is addressed by applying a high address voltage  74  on common line  1 . Because a low segment voltage  64  is applied along segment lines  1  and  2  during the application of this address voltage, the pixel voltage across modulators ( 1 , 1 ) and ( 1 , 2 ) is greater than the high end of the positive stability window (i.e., the voltage differential exceeded a predefined threshold) of the modulators, and the modulators ( 1 , 1 ) and ( 1 , 2 ) are actuated. Conversely, because a high segment voltage  62  is applied along segment line  3 , the pixel voltage across modulator ( 1 , 3 ) is less than that of modulators ( 1 , 1 ) and ( 1 , 2 ), and remains within the positive stability window of the modulator; modulator ( 1 , 3 ) thus remains relaxed. Also during line time  60   c , the voltage along common line  2  decreases to a low hold voltage  76 , and the voltage along common line  3  remains at a release voltage  70 , leaving the modulators along common lines  2  and  3  in a relaxed position. 
     During the fourth line time  60   d , the voltage on common line  1  returns to a high hold voltage  72 , leaving the modulators along common line  1  in their respective addressed states. The voltage on common line  2  is decreased to a low address voltage  78 . Because a high segment voltage  62  is applied along segment line  2 , the pixel voltage across modulator ( 2 , 2 ) is below the lower end of the negative stability window of the modulator, causing the modulator ( 2 , 2 ) to actuate. Conversely, because a low segment voltage  64  is applied along segment lines  1  and  3 , the modulators ( 2 , 1 ) and ( 2 , 3 ) remain in a relaxed position. The voltage on common line  3  increases to a high hold voltage  72 , leaving the modulators along common line  3  in a relaxed state. 
     Finally, during the fifth line time  60   e , the voltage on common line  1  remains at high hold voltage  72 , and the voltage on common line  2  remains at a low hold voltage  76 , leaving the modulators along common lines  1  and  2  in their respective addressed states. The voltage on common line  3  increases to a high address voltage  74  to address the modulators along common line  3 . As a low segment voltage  64  is applied on segment lines  2  and  3 , the modulators ( 3 , 2 ) and ( 3 , 3 ) actuate, while the high segment voltage  62  applied along segment line  1  causes modulator ( 3 , 1 ) to remain in a relaxed position. Thus, at the end of the fifth line time  60   e , the 3×3 pixel array is in the state shown in  FIG. 5A , and will remain in that state as long as the hold voltages are applied along the common lines, regardless of variations in the segment voltage which may occur when modulators along other common lines (not shown) are being addressed. 
     In the timing diagram of  FIG. 5B , a given write procedure (i.e., line times  60   a - 60   e ) can include the use of either high hold and address voltages, or low hold and address voltages. Once the write procedure has been completed for a given common line (and the common voltage is set to the hold voltage having the same polarity as the actuation voltage), the pixel voltage remains within a given stability window, and does not pass through the relaxation window until a release voltage is applied on that common line. Furthermore, as each modulator is released as part of the write procedure prior to addressing the modulator, the actuation time of a modulator, rather than the release time, may determine the line time. Specifically, in implementations in which the release time of a modulator is greater than the actuation time, the release voltage may be applied for longer than a single line time, as depicted in  FIG. 5B . In some other implementations, voltages applied along common lines or segment lines may vary to account for variations in the actuation and release voltages of different modulators, for example modulators of different colors. 
     The details of the structure of interferometric modulators that operate in accordance with the principles set forth above may vary widely. For example,  FIGS. 6A-6E  show examples of cross-sections of varying implementations of interferometric modulators, including the movable reflective layer  14  and its supporting structures.  FIG. 6A  shows an example of a partial cross-section of the interferometric modulator display of  FIG. 1 , where a strip of metal material, i.e., the movable reflective layer  14  is deposited on supports  18  extending orthogonally from the substrate  20 . In  FIG. 6B , the movable reflective layer  14  of each IMOD is generally square or rectangular in shape and attached to supports at or near the corners, on tethers  32 . In  FIG. 6C , the movable reflective layer  14  is generally square or rectangular in shape and suspended from a deformable layer  34 , which may include a flexible metal. The deformable layer  34  can connect, directly or indirectly, to the substrate  20  around the perimeter of the movable reflective layer  14 . These connections are herein referred to as support posts. The implementation shown in  FIG. 6C  has additional benefits deriving from the decoupling of the optical functions of the movable reflective layer  14  from its mechanical functions, which are carried out by the deformable layer  34 . This decoupling allows the structural design and materials used for the reflective layer  14  and those used for the deformable layer  34  to be optimized independently of one another. 
       FIG. 6D  shows another example of an IMOD, where the movable reflective layer  14  includes a reflective sub-layer  14   a . The movable reflective layer  14  rests on a support structure, for example support posts  18 . The support posts  18  provide separation of the movable reflective layer  14  from the lower stationary electrode (i.e., part of the optical stack  16  in the illustrated IMOD) so that a gap  19  is formed between the movable reflective layer  14  and the optical stack  16 , for example when the movable reflective layer  14  is in a relaxed position. The movable reflective layer  14  also can include a conductive layer  14   c , which may be configured to serve as an electrode, and a support layer  14   b . In this example, the conductive layer  14   c  is disposed on one side of the support layer  14   b , distal from the substrate  20 , and the reflective sub-layer  14   a  is disposed on the other side of the support layer  14   b , proximal to the substrate  20 . In some implementations, the reflective sub-layer  14   a  can be conductive and can be disposed between the support layer  14   b  and the optical stack  16 . The support layer  14   b  can include one or more layers of a dielectric material, for example, silicon oxynitride (SiON) or silicon dioxide (SiO 2 ). In some implementations, the support layer  14   b  can be a stack of layers, for example a SiO 2 /SiON/SiO 2  tri-layer stack. Either or both of the reflective sub-layer  14   a  and the conductive layer  14   c  can include, e.g., an aluminum (Al) alloy with about 0.5% copper (Cu), or another reflective metallic material. Employing conductive layers  14   a ,  14   c  above and below the dielectric support layer  14   b  can balance stresses and provide enhanced conduction. In some implementations, the reflective sub-layer  14   a  and the conductive layer  14   c  can be formed of different materials for a variety of design purposes, for example achieving specific stress profiles within the movable reflective layer  14 . 
     As illustrated in  FIG. 6D , some implementations also can include a black mask structure  23 . The black mask structure  23  can be formed in optically inactive regions (e.g., between pixels or under posts  18 ) to absorb ambient or stray light. The black mask structure  23  also can improve the optical properties of a display device by inhibiting light from being reflected from or transmitted through inactive portions of the display, thereby increasing the contrast ratio. Additionally, the black mask structure  23  can be conductive and be configured to function as an electrical bussing layer. In some implementations, the row electrodes can be connected to the black mask structure  23  to reduce the resistance of the connected row electrode. The black mask structure  23  can be formed using a variety of methods, including deposition and patterning techniques. The black mask structure  23  can include one or more layers. For example, in some implementations, the black mask structure  23  includes a molybdenum-chromium (MoCr) layer that serves as an optical absorber, a layer, and an aluminum alloy that serves as a reflector and a bussing layer, with a thickness in the range of about 30-80 Å, 500-1000 Å, and 500-6000 Å, respectively. The one or more layers can be patterned using a variety of techniques, including photolithography and dry etching, including, for example, carbon tetrafluoride (CF 4 ) and/or oxygen (O 2 ) for the MoCr and SiO 2  layers and chlorine (Cl 2 ) and/or boron trichloride (BCl 3 ) for the aluminum alloy layer. In some implementations, the black mask  23  can be an etalon or interferometric stack structure. In such interferometric stack black mask structures  23 , the conductive absorbers can be used to transmit or bus signals between lower, stationary electrodes in the optical stack  16  of each row or column. In some implementations, a spacer layer  35  can serve to generally electrically isolate the absorber layer  16   a  from the conductive layers in the black mask  23 . 
       FIG. 6E  shows another example of an IMOD, where the movable reflective layer  14  is self supporting. In contrast with  FIG. 6D , the implementation of  FIG. 6E  does not include support posts  18 . Instead, the movable reflective layer  14  contacts the underlying optical stack  16  at multiple locations, and the curvature of the movable reflective layer  14  provides sufficient support that the movable reflective layer  14  returns to the unactuated position of  FIG. 6E  when the voltage across the interferometric modulator is insufficient to cause actuation. The optical stack  16 , which may contain a plurality of several different layers, is shown here for clarity including an optical absorber  16   a , and a dielectric  16   b . In some implementations, the optical absorber  16   a  may serve both as a fixed electrode and as a partially reflective layer. 
     In implementations such as those shown in  FIGS. 6A-6E , the IMODs function as direct-view devices, in which images are viewed from the front side of the transparent substrate  20 , i.e., the side opposite to that upon which the modulator is formed. In these implementations, the back portions of the device (that is, any portion of the display device behind the movable reflective layer  14 , including, for example, the deformable layer  34  illustrated in  FIG. 6C ) can be configured and operated upon without impacting or negatively affecting the image quality of the display device, because the reflective layer  14  optically shields those portions of the device. For example, in some implementations a bus structure (not illustrated) can be included behind the movable reflective layer  14  which provides the ability to separate the optical properties of the modulator from the electromechanical properties of the modulator, for example voltage addressing and the movements that result from such addressing. Additionally, the implementations of  FIGS. 6A-6E  can simplify processing, for example patterning. 
       FIG. 7  shows an example of a flow diagram illustrating a manufacturing process  80  for an interferometric modulator, and  FIGS. 8A-8E  show examples of cross-sectional schematic illustrations of corresponding stages of such a manufacturing process  80 . In some implementations, the manufacturing process  80  can be implemented to manufacture an electromechanical systems device, for example interferometric modulators of the general type illustrated in  FIGS. 1 and 6 . The manufacture of an electromechanical systems device can also include other blocks not shown in  FIG. 7 . With reference to  FIGS. 1 ,  6  and  7 , the process  80  begins at block  82  with the formation of the optical stack  16  over the substrate  20 .  FIG. 8A  illustrates such an optical stack  16  formed over the substrate  20 . The substrate  20  may be a transparent substrate, for example glass or plastic, it may be flexible or relatively stiff and unbending, and may have been subjected to prior preparation processes, e.g., cleaning, to facilitate efficient formation of the optical stack  16 . As discussed above, the optical stack  16  can be electrically conductive, partially transparent and partially reflective and may be fabricated, for example, by depositing one or more layers having the desired properties onto the transparent substrate  20 . In  FIG. 8A , the optical stack  16  includes a multilayer structure having sub-layers  16   a  and  16   b , although more or fewer sub-layers may be included in some other implementations. In some implementations, one of the sub-layers  16   a  and  16   b  can be configured with both optically absorptive and electrically conductive properties, for example the combined conductor/absorber sub-layer  16   a . Additionally, one or more of the sub-layers  16   a  and  16   b  can be patterned into parallel strips, and may form row electrodes in a display device. Such patterning can be performed by a masking and etching process or another suitable process known in the art. In some implementations, one of the sub-layers  16   a  and  16   b  can be an insulating or dielectric layer, for example sub-layer  16   b  that is deposited over one or more metal layers (e.g., one or more reflective and/or conductive layers). In addition, the optical stack  16  can be patterned into individual and parallel strips that form the rows of the display. It is noted that  FIGS. 8A-8E  may not be drawn to scale. For example, in some implementations, one of the sub-layers of the optical stack, the optically absorptive layer, may be very thin, although sub-layers  16   a  and  16   b  are shown somewhat thick in  FIGS. 8A-8E . 
     The process  80  continues at block  84  with the formation of a sacrificial layer  25  over the optical stack  16 . The sacrificial layer  25  is later removed (e.g., at block  90 ) to form the cavity  19  and thus the sacrificial layer  25  is not shown in the resulting interferometric modulators  12  illustrated in  FIG. 1 .  FIG. 8B  illustrates a partially fabricated device including a sacrificial layer  25  formed over the optical stack  16 . The formation of the sacrificial layer  25  over the optical stack  16  may include deposition of a xenon difluoride (XeF 2 )-etchable material, for example molybdenum (Mo) or amorphous silicon (a-Si), in a thickness selected to provide, after subsequent removal, a gap or cavity  19  (see also  FIGS. 1 and 8E ) having a desired size. Deposition of the sacrificial material may be carried out using deposition techniques, for example physical vapor deposition (PVD, e.g., sputtering), plasma-enhanced chemical vapor deposition (PECVD), thermal chemical vapor deposition (thermal CVD), or spin-coating. 
     The process  80  continues at block  86  with the formation of a support structure, for example post  18 , illustrated in  FIGS. 1 ,  6  and  8 C. The formation of the post  18  may include patterning the sacrificial layer  25  to form a support structure aperture, then depositing a material (for example, a polymer or an inorganic material, for example, silicon oxide) into the aperture to form the post  18 , using a deposition method, for example PVD, PECVD, thermal CVD, or spin-coating. In some implementations, the support structure aperture formed in the sacrificial layer can extend through both the sacrificial layer  25  and the optical stack  16  to the underlying substrate  20 , so that the lower end of the post  18  contacts the substrate  20  as illustrated in  FIG. 6A . Alternatively, as depicted in  FIG. 8C , the aperture formed in the sacrificial layer  25  can extend through the sacrificial layer  25 , but not through the optical stack  16 . For example,  FIG. 8E  illustrates the lower ends of the support posts  18  in contact with an upper surface of the optical stack  16 . The post  18 , or other support structures, may be formed by depositing a layer of support structure material over the sacrificial layer  25  and patterning portions of the support structure material located away from apertures in the sacrificial layer  25 . The support structures may be located within the apertures, as illustrated in  FIG. 8C , but also can, at least partially, extend over a portion of the sacrificial layer  25 . As noted above, the patterning of the sacrificial layer  25  and/or the support posts  18  can be performed by a patterning and etching process, but also may be performed by alternative etching methods. 
     The process  80  continues at block  88  with the formation of a movable reflective layer or membrane, for example the movable reflective layer  14  illustrated in  FIGS. 1 ,  6  and  8 D. The movable reflective layer  14  may be formed by employing one or more deposition steps including, for example, reflective layer (e.g., aluminum, aluminum alloy, or other reflective layer) deposition, along with one or more patterning, masking, and/or etching steps. The movable reflective layer  14  can be electrically conductive, and referred to as an electrically conductive layer. In some implementations, the movable reflective layer  14  may include a plurality of sub-layers  14   a ,  14   b , and  14   c  as shown in  FIG. 8D . In some implementations, one or more of the sub-layers, for example sub-layers  14   a  and  14   c , may include highly reflective sub-layers selected for their optical properties, and another sub-layer  14   b  may include a mechanical sub-layer selected for its mechanical properties. Since the sacrificial layer  25  is still present in the partially fabricated interferometric modulator formed at block  88 , the movable reflective layer  14  is typically not movable at this stage. A partially fabricated IMOD that contains a sacrificial layer  25  also may be referred to herein as an “unreleased” IMOD. As described above in connection with  FIG. 1 , the movable reflective layer  14  can be patterned into individual and parallel strips that form the columns of the display. 
     The process  80  continues at block  90  with the formation of a cavity, for example cavity  19  illustrated in  FIGS. 1 ,  6  and  8 E. The cavity  19  may be formed by exposing the sacrificial material  25  (deposited at block  84 ) to an etchant. For example, an etchable sacrificial material, for example Mo or amorphous Si may be removed by dry chemical etching, for example, by exposing the sacrificial layer  25  to a gaseous or vaporous etchant, for example vapors derived from solid XeF 2 , for a period of time that is effective to remove the desired amount of material, typically selectively removed relative to the structures surrounding the cavity  19 . Other etching methods, e.g. wet etching and/or plasma etching, also may be used. Since the sacrificial layer  25  is removed during block  90 , the movable reflective layer  14  is typically movable after this stage. After removal of the sacrificial material  25 , the resulting fully or partially fabricated IMOD may be referred to herein as a “released” IMOD. 
     The interferometric modulators described above are bi-stable display elements having two states: a relaxed state and an actuated state. The following description relates to analog interferometric modulators. For example, in one implementation of an analog interferometric modulator, a single interferometric modulator can reflect a red color, a green color, a blue color, a black color, and a white color. In some implementations, an analog interferometric modulator can reflect any color within a range of wavelengths of light depending upon an applied voltage. Further, the optical stack of the analog interferometric modulator may differ from the bi-stable display elements described above. These differences may produce different optical results. For example, in some implementations of the bi-stable elements described above, the closed (actuated) state gives the bi-stable element a dark (for example black) reflective state. In some implementations, the analog interferometric modulator reflects white light when the electrodes are in a position analogous to the closed state of the bi-stable element. 
     A three-terminal electromechanical device (for example, an interferometric modulator) can include a movable middle electrode disposed in a gap between an upper and a lower electrode. In one approach, a three-terminal device can use a switch or a series capacitor to provide charge onto the middle electrode. Then, a voltage may be applied across the upper and lower electrodes, and the charged middle electrode can interact with the resulting electric field produced between the upper and lower electrodes. As a result, the charged middle electrode can be moved or displaced based upon the electric field produced by the applied voltage. However, using switches and capacitors to provide charge onto the middle electrode in this manner can lead to parasitic loading of the middle electrode. While it can be useful to provide charge onto a charge-neutral middle electrode that is not electrically connected to any external circuits and, thus, is electrically isolated, a charge-neutral middle electrode would ordinarily not respond to the applied electric field between the upper and lower electrodes. Accordingly, devices and methods for moving an electrically isolated middle electrode with net zero charge, so that it contacts an electrical contact (or electrode) thereby imparting a charge to the middle electrode, can be useful. Devices and methods to release a middle electrode after it receives charge can also be useful. 
       FIG. 9  shows an example of a flowchart illustrating one method for actuating and calibrating a charge neutral electrode of an analog interferometric modulator. The method  900  begins at block  951  in which an electrically isolated, charge neutral middle electrode is provided. The electrically isolated middle electrode can be charge neutral, for example, before being charged and/or calibrated, when a device is first powered on, or after the charge has been depleted as a result of leakage or a purposeful charge dissipation procedure. The method continues at block  952  in which the middle electrode is actuated, moving the middle electrode towards another electrode using an electrical force. Devices and methods to actuate the middle electrode when it is charge neutral are described below, for example, with reference to  FIGS. 12-20 . The method  900  continues at block  953  in which charge is provided to the middle electrode.  FIGS. 21-25  describe some general implementations of systems and methods for placing charge on such a middle electrode. Specifically, device and methods for charging the middle electrode by contact with an upper electrode are described with reference to  FIGS. 21-23 , and devices and method for charging the middle electrode by contact with an isolated, grounded complimentary electrode are described with reference to FIGS.  22  and  24 - 25 . In some implementations, the charge-neutral middle electrode may be charged using a switch configuration, as described with reference to  FIGS. 26-30 , while in other implementations, the middle electrode may be charged using a switchless configuration, as described with reference to  FIGS. 34-38 . 
     The method  900  includes block  954  in which the charge placed on the middle electrode is calibrated to account for the particular mechanical spring force acting on the middle electrode. Certain devices and methods for calibrating the charge using a switch configuration are described with reference to  FIGS. 31-33 . Additionally, some implementations of devices and methods for calibrating the charge using a switchless configuration are described with reference to  FIGS. 39-41 . Calibrating each of the middle electrodes across an array of three-terminal devices with a desired amount of charge can allow for reliable movement of all of the middle electrodes to the same location upon application of a selected voltage across all of the devices. This can help improve the accuracy of the color displayed in an analog interferometric modulator display. 
     The method  900  continues at block  955  in which a display including an array of analog interferometric modulators having calibrated middle electrodes is operated. In some aspects, operating the display includes actuating or moving the middle electrodes to various locations in the gap formed by the upper electrode  1002  and lower electrode  1010  (see  FIG. 10 ) to display an image. The location of the middle electrode helps to determine the reflected displayed color of an analog interferometric modulator pixel. The method  900  optionally continues at block  956  in which blocks  952 - 955  are repeated. In some implementations, before returning to block  952 , the middle electrode is rendered charge neutral. In some implementations, the middle electrode retains some charge when it is actuated at block  952 . 
       FIG. 10  shows an example of a cross-section of an analog interferometric modulator  1000  having a three layer or electrode design. The modulator  1000  includes an upper or first electrode  1002 . In one implementation, electrode  1002  is a plate made of metal. The upper electrode  1002  may be stiffened using a stiffening layer  1003 . In one implementation, the stiffening layer  1003  is a dielectric. The stiffening layer  1003  may be used to keep the upper electrode  1002  rigid and substantially flat. The modulator  900  also includes a lower or second electrode  1010 , and a middle or third electrode  1006 , which can also include metal. The three electrodes are electrically insulated by insulating posts  1004 . The insulating posts  1004  also serve to hold middle electrode  1006  between electrodes  1002  and  1010  in an equilibrium position when no electric forces are present. The middle electrode  1006  has a stiffening layer  1008  disposed thereon. In one implementation, the stiffening layer  1008  includes silicon oxynitride. 
     The middle electrode  1006  is configured to move in the area or gap between upper electrode  1002  and lower electrode  1010 . The stiffening layer  1008  helps to keep a portion of the middle electrode  1006  relatively rigid and flat as it moves between electrodes  1002  and  1010 . In one implementation, the stiffening layer  1008  is disposed on the central portion of the middle electrode  1006 . In this implementation, the side portions of the middle electrode  1006  are able to bend as the middle electrode  1006  moves. In  FIG. 10 , middle electrode  1006  is shown in an equilibrium position where the electrode is substantially flat. As the middle electrode  1006  moves away from this equilibrium position, the side portions of the middle electrode  1006  will deform or bend. The side portions of the middle electrode  1006  implement an elastic spring force that applies a force to move the middle electrode  1006  back to the equilibrium position (see, for example, springs  2634  in  FIGS. 26-33  and springs  3434  in  FIGS. 34-41 ). 
     The middle electrode  1006  also serves as a mirror to reflect light entering the structure through substrate  1012 . In some implementations, substrate  1012  is made of glass. In one implementation, the lower electrode  1010  is an absorbing chromium or chromium-containing layer. To remain at least partially transparent, the absorbing layer can be made relatively thin, as described above. The lower electrode  1010  has a passivation layer  1014  (now specifically shown as a separate layer) disposed thereon. In one implementation, the passivation layer  1014  is a thin dielectric layer. In another implementation, the upper electrode  1002  has a passivation layer disposed thereon. In some implementations, the passivation layer is a thin dielectric layer. 
       FIG. 11A  shows an example of a cross-section of an analog interferometric modulator  1100  with a control circuit  1120 . The analog interferometric modulator  1100  may be modulator  1000  or other similar design of analog interferometric modulator. Modulator  1100  includes an upper electrode  1102 , a middle electrode  1106 , and a lower electrode  1110 . The modulator  1100  further includes insulating posts  1104  that insulate electrodes  1102 ,  1106 , and  1110  from other structures. The modulator  1100  further includes resistive elements  1116  disposed on the upper electrode  1102 . The upper electrode  1102  has a stiffening layer  1103  disposed thereon. In one implementation, the upper electrode  1102  is a metal and the stiffening layer  1103  is a dielectric. The modulator  1100  also includes a thin dielectric passivation layer  1114  disposed on the lower electrode  1110  such that the dielectric passivation layer  1114  is disposed between the lower electrode  1110  and the middle electrode  1106 . The lower electrode  1110  is disposed on a substrate  1112 . Resistive elements  1116  provide a separator between upper electrode  1102  and middle electrode  1106 . When middle electrode  1106  is moved toward upper electrode  1102 , resistive elements  1116  prevent the middle electrode  1106  from coming into contact with the upper electrode  1102 . In one implementation, middle electrode  1106  includes an insulating layer (not shown) disposed on the bottom portion of the middle electrode  1106 . 
     The analog interferometric modulator  1100  also includes a control circuit  1120 . The control circuit  1120  is configured to apply a voltage across the upper electrode  1102  and the lower electrode  1110 . A charge pump circuit  1118  is configured to selectively apply a charge to the middle electrode  1106 . Using the control voltage  1120  and the charge pump circuit  1118 , actuation of the middle electrode  1106  is achieved. The charge pump circuit  1118  is used to provide the middle electrode  1106  with an electric charge. The charged middle electrode  1106  then interacts with the electric field created by control circuit  1120  between upper electrode  1102  and the lower electrode  1110 . The interaction of the charged middle electrode  1106  and the electric field causes the middle electrode  1106  to move between electrodes  1102  and  1110 . 
     One example of charge injection circuitry which can be implemented as a charge pump circuit  1118  to place an accurate quantity of charge onto IMOD is illustrated in the schematics of  FIG. 11B . In these schematics, the IMOD is depicted as variable capacitor. The Reset IMOD (left-side) schematic illustrates an example circuit configuration for resetting an IMOD. In this configuration, a switch S 3  is closed shorting the IMOD to dissipate the charge on the IMOD. Switches S 1  and S 2  are “open” isolating a voltage source V in  and a capacitor C in  from each other and from the IMOD. The Pre-charge C in  (center) schematic illustrates an example circuit configuration where switch S 1  is closed connecting the voltage source V in  to the capacitor C in , charging the capacitor C in . The switch S 2  is “open” isolating the capacitor C in  from the IMOD, and switch S 3  is open so that the IMOD is no longer shorted. In the Sample and Transfer Charge onto IMOD (right-side) schematic, switch S 1  is open, isolating the voltage source V in  from the rest of the circuitry, and switch S 2  is closed, connecting capacitor C in  to the virtual ground input of the op-amp which remains connected to the IMOD terminal  1  (left terminal). The op-amp output is connected in feedback to terminal  2  of the IMOD. This is a well-known switched capacitor circuit that accurately transfers charge from the input capacitor C in  to the capacitor in the feedback path, in this case, the IMOD. Other approaches resulting in incomplete charge transfer can be implemented using switches without an op-amp. 
     The middle electrode  1106  can be moved to various positions between electrodes  1102  and  1110  by varying the voltage applied by the control circuit  1120 . For example, a positive voltage V c  applied by control circuit  1120  causes the lower electrode  1110  to be driven to a positive potential with respect to the upper electrode  1102 , which repels the middle electrode  1106  if and when it is positively charged. Accordingly, a positive voltage V c  causes middle electrode  1106  to move toward upper electrode  1102 . Application of a negative voltage V c  by control circuit  1120  causes the lower electrode  1110  to be driven to a negative potential with respect to the upper electrode  1102 , which attracts the middle electrode  1106  when it is positively charged. Accordingly a negative voltage V c  causes middle electrode  1106  to move toward lower electrode  1110 . 
     A switch  1122  can be used to selectively connect or disconnect the middle electrode  1106  from the charge pump circuit  1118 . Other methods known in the art besides a switch may be used to selectively connect or disconnect the middle electrode  1106  from the charge pump circuit  1118 , for example, a thin film semiconductor, a fuse, an anti fuse, etc. 
     The analog interferometric modulator  1100  may be configured such that the middle electrode  1106  responds in linear proportion to a voltage driven across upper electrode  1102  and lower electrode  1110 . Accordingly, there is a linear relationship between the voltage used to control the movement of the middle electrode  1006  and the position of the middle electrode  1106  between electrodes  1102  and  1110 . 
     Using a switch  1122  to provide charge to the middle electrode  1106  can cause parasitic loading of the middle electrode  1106 . For example, if the middle electrode  1106  is not completely isolated electrically, a stored charge Q on the middle electrode  1106  may vary as its position between electrodes  1102  and  1110 . This variation in Q can affect the response of the middle electrode  1106  to a charge. When middle electrode  1106  is not completely isolated electrically, there are parasitic capacitances attached from it to each of the upper electrode  1102  and the lower electrode  1110 . In addition, a portion of the stored charge Q may leak from the middle electrode  1106  through the switch  1122  over time. 
     Various systems and methods can be used to account for the parasitic capacitances, for example those described in U.S. Pat. No. 7,990,604, issued Aug. 2, 2011, titled “Analog Interferometric Modulator.” For example, modulator  1100  may be configured to account for the parasitic capacitances by including a capacitor connected in series with middle electrode  1106  and in parallel with parasitic capacitances  1140  and  1142 . It would therefore be advantageous to provide charge, then isolate the charge, on the middle electrode  1106  without an electrical connection from the middle electrode  1106  to a switch or series capacitor. Such an electrically isolated electrode can reduce parasitic loading or charge leakage issues. 
     Actuating a Neutral, Electrically Isolated Electrode 
       FIG. 12  shows an example of a perspective view of an analog interferometric modulator  1200  which includes a middle electrode that can be moved, or actuated, between two charged electrodes without the use of a switch or series capacitor electrically connected to the middle electrode. As described in greater detail below with reference to  FIGS. 21-23 , the middle electrode can be moved toward either charged electrode to provide charge onto the middle electrode without the use of a switch or series capacitor electrically connected to the middle electrode. 
     The modulator  1200  includes an upper electrode  1202  and a lower electrode  1210  spaced apart from the upper electrode  1202  by a constant gap g. A movable middle electrode or plate  1206  is disposed in the gap g, and can be spaced a distance d 2  from the upper electrode  1202  and a distance d 1  from the lower electrode  1210 . The middle electrode  1206  may be a metal reflector or a mirror. The middle electrode  1206  can be electrically isolated, that is, it is not electrically connected to an external component, for example a switch, when the middle electrode  1206  is disposed in the gap g. The middle electrode  1206  is also charge neutral, having the same total number of positive charges as negative charges. In some implementations, the electrodes  1202 ,  1206 , and  1210  are thin film electrodes. In some aspects, for example, a lateral dimension of a thin film upper electrode  1202  is D and the thickness of the thin film upper electrode  1202  is one-tenth the lateral dimension or less (D/10 or less). In some implementations, each of the three electrodes have thicknesses that are thin compared to the separation distances d 1  and d 2 . For example, the thicknesses of each of the three electrodes can be one or more orders of magnitude thinner than the separation distances d 1  and d 2 . 
     The middle electrode  1206  may be mechanically connected to and/or supported by structures or components (not shown in  FIG. 12 ). However, such structure (or components) can be configured such that the middle electrode  1206  remains electrically isolated (for example, the structure may be formed from a material which helps to electrically isolate the middle electrode  1206 . As discussed in greater detail below with reference to  FIGS. 21 ,  26 , and  34 , such structures may include springs that exert a restorative mechanical force on the middle electrode  1206  to restore the middle electrode  1206  to a specific position in the gap g. 
     The uncharged, electrically isolated middle electrode  1206  can be actuated or moved toward either the upper electrode  1202  or the lower electrode  1210  upon application of an electric field between the upper electrode  1202  and the lower electrode  1210 . In one implementation, this is achieved by configuring one of the upper electrode  1202  and the lower electrode  1210  to be a different size than the other. For example, in the implementation illustrated in  FIG. 12 , the upper electrode  1202  has a surface area A 2  while the lower electrode  1210  has a surface area A 1  that is greater than A 2 . In other aspects, the lower electrode  1210  can have a surface area A 1  that is less than the surface area A 2  of the upper electrode  1202 . The middle electrode  1206  can have a surface area less than or about equal to the surface area of the lower electrode  1210 . 
     Applying a voltage V across the upper electrode  1202  and the lower electrode  1210  produces a non-uniform electric field between the two electrodes. Implementations of the modulator  1200  can include a control circuit configured to apply a voltage V across the upper electrode  1202  and the lower electrode  1210  to produce the non-uniform electric field. 
       FIG. 13  shows an example of an equivalent circuit of the analog interferometric modulator configuration shown in  FIG. 12 . C 1  represents the capacitance between the lower electrode  1210  and the middle electrode  1206 , while C 2  represents the capacitance between the upper electrode  1202  and the middle electrode  1206 . ΔV 1  represents the potential difference between the lower electrode  1210  and the middle electrode  1206 , and is given by the equation: 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       V 
                       1 
                     
                   
                   = 
                   
                     
                       
                         C 
                         2 
                       
                       
                         
                           C 
                           1 
                         
                         + 
                         
                           C 
                           2 
                         
                       
                     
                      
                     
                         
                     
                      
                     V 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     ΔV 2  represents the potential difference between the upper electrode  1202  and the middle electrode  1206 , and is given by the equation: 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       V 
                       2 
                     
                   
                   = 
                   
                     
                       
                         
                           C 
                           1 
                         
                          
                         
                             
                         
                       
                       
                         
                           C 
                           1 
                         
                         + 
                         
                           C 
                           2 
                         
                       
                     
                      
                     
                         
                     
                      
                     V 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Applying a voltage V to the upper electrode  1202  and the lower electrode  1210  provides an electrical charge on the upper electrode  1202  and the lower electrode  1210  which has the same magnitude. The electric force exerted on the middle electrode  1206  by either of these charged electrodes is inversely proportional to the surface area of the charged electrode. However, in this example, because the surface area of the upper electrode  1202  is less than that of the lower electrode  1210  in this example, the upper electrode  1202  exerts a larger electric force on the middle electrode  1206  than the lower electrode  1210 . In implementations where the surface area of the lower electrode  1210  is less than that of the upper electrode  1202 , the lower electrode  1210  will exert a larger electric force on the middle electrode  1206  than the upper electrode  1202 . 
     The net force acting on the middle electrode  1206  can be determined using the parallel plate approximation for the capacitances C 1  and C 2 . Because the upper electrode  1202  and the lower electrode  1210  are stationary, the net electric force on the middle electrode  1206  can be approximated as: 
     
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       
                         
                           ɛ 
                           0 
                         
                          
                         
                           
                             
                               A 
                               2 
                             
                              
                             
                               ( 
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   V 
                                   2 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                       
                         2 
                          
                         
                           d 
                           2 
                           2 
                         
                       
                     
                     - 
                     
                       
                         
                           ɛ 
                           0 
                         
                          
                         
                           
                             
                               A 
                               1 
                             
                              
                             
                               ( 
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   V 
                                   1 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                       
                       
                         2 
                          
                         
                           d 
                           1 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where ∈ 0  represents the dielectric permittivity of a vacuum, A 1  represents the surface area of lower electrode  1210 , A 2  represents the effective surface area of upper electrode  1202 , ΔV 1  represents the potential difference between the lower electrode  1210  and the middle electrode  1206 , ΔV 2  represents the potential difference between the upper electrode  1202  and the middle electrode  1206 , d 1  represents the distance between the middle electrode  1206  and the lower electrode  1210 , and d 2  represents the distance between the middle electrode  1206  the upper electrode  1202 . Let A 1 =A and A 2 =αA, where α is the area factor. The force equation then simplifies to: 
     
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       ɛ 
                       0 
                     
                      
                     α 
                      
                     
                         
                     
                      
                     
                       AV 
                       2 
                     
                      
                     
                       
                         ( 
                         
                           1 
                           - 
                           α 
                         
                         ) 
                       
                       
                         
                           2 
                            
                           
                             [ 
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     α 
                                   
                                   ) 
                                 
                                  
                                 
                                   d 
                                   2 
                                 
                               
                               + 
                               
                                 α 
                                  
                                 
                                     
                                 
                                  
                                 g 
                               
                             
                             ] 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Thus, the application of an electric field across electrodes having disparate areas results in a net upward force on the charge neutral, electrically isolated middle plate  1206 , causing it to move up towards the upper electrode  1202  in implementations where the surface area of the upper electrode  1202  is less than that of the lower electrode  1210 . The middle plate  1206  is configured to move upward such that it makes contact with the upper electrode  1202 , or with contacts (e.g., resistive contacts) on and/or in electrical communication with the upper electrode  1202 . As described in greater detail below with reference to  FIGS. 23 and 25 , the contact between the middle electrode  1206  and the upper electrode  1202  can change the charge on the middle electrode  1206 . 
       FIG. 14  shows an example of a graph illustrating how the net upward electric force acting on the middle electrode  1206  varies with the distance d 2  between the upper electrode  1202  and the middle electrode  1206  in the analog interferometric modulator configuration of  FIG. 12 . In this example, the voltage V applied between the upper electrode  1202  and the lower electrode  1210  is 100 volts, the area factor α is 0.25, the total gap distance g is 1,000 nm, and the pixel size is 53 μm resulting in an area A of 2809 μm 2  in this configuration. 
     In some implementations, the lower electrode  1210  can have an surface area A 2  that is less than the surface area A 1  of the upper electrode  1202 . In such cases, application of a voltage between the upper electrode  1202  and the lower electrode  1210  will result in a non-uniform electric field and a net downward force on the middle electrode  1206 , which can move the middle electrode  1206  to contact the lower electrode  1210 . As explained elsewhere, this can be exploited to charge the middle electrode  1206  by physical contact with the lower electrode  1210 . 
     The upper electrode  1202  and the lower electrode  1210  can be configured to produce an electric field therebetween capable of moving the electrically isolated, charge neutral middle electrode  1206  when a voltage V is applied across the upper electrode  1202  and the lower electrode  1210 . The series combination of two capacitors, C top  being the capacitance between the upper electrode and the middle electrode and C bot  being the capacitance between the middle electrode and the lower electrode is given by 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           C 
                           total 
                         
                         = 
                           
                          
                         
                           1 
                           
                             
                               1 
                               
                                 C 
                                 top 
                               
                             
                             + 
                             
                               1 
                               
                                 C 
                                 bot 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1 
                           
                             
                               
                                 d 
                                 2 
                               
                               
                                 
                                   ɛ 
                                   0 
                                 
                                  
                                 
                                   ɛ 
                                   top 
                                 
                                  
                                 
                                   A 
                                   1 
                                 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   g 
                                   - 
                                   
                                     d 
                                     2 
                                   
                                 
                                 ) 
                               
                               
                                 
                                   ɛ 
                                   0 
                                 
                                  
                                 
                                   ɛ 
                                   bot 
                                 
                                  
                                 A 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1 
                           
                             
                               
                                 d 
                                 2 
                               
                                
                               
                                 ( 
                                 
                                   
                                     1 
                                     
                                       
                                         ɛ 
                                         0 
                                       
                                        
                                       
                                         ɛ 
                                         top 
                                       
                                        
                                       
                                         A 
                                         1 
                                       
                                     
                                   
                                   - 
                                   
                                     1 
                                     
                                       
                                         ɛ 
                                         0 
                                       
                                        
                                       
                                         ɛ 
                                         bot 
                                       
                                        
                                       A 
                                     
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               g 
                               
                                 
                                   ɛ 
                                   0 
                                 
                                  
                                 
                                   ɛ 
                                   bot 
                                 
                                  
                                 A 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     where ∈ 0  is the permittivity of free space, ∈ top  is the relative dielectric constant filling a top gap between the upper electrode and the middle electrode, A 1  is the surface area of the upper electrode, ∈ bot  is the relative dielectric constant filling a lower gap between the lower electrode and the middle electrode, d 2  is the gap between the upper and middle electrodes, g is the total distance between the upper and lower electrodes, and A is the surface area of the other lower and middle electrodes. If the electrode areas and the filling dielectric constants are the same for both the top and bottom capacitive sections, then the total capacitance value is a constant, independent of the gap between the upper and lower electrodes (for example, the distance d 2 ). If there is an imbalance in the electrode sizes and/or the dielectric constants of the gap filling media, then the total capacitance becomes a function of where the middle electrode is placed between the upper and lower electrodes. The electrical system will seek to increase the capacitance by moving the middle electrode up or down monotonically and this imbalance in the incremental capacitance (incremental with gap distance) can be a force that acts on the isolated and uncharged middle electrode. 
     In one implementation described above with reference to  FIG. 12 , the upper electrode  1202  and the lower electrode  1210  having two different surface areas are configured to produce an electric field therebetween capable of moving the electrically isolated, charge neutral middle electrode  1206 . As explained above, the total capacitance is a function of where the middle electrode  1206  is placed between the upper electrode  1202  and lower electrode  1210 . Application of a voltage V across the upper electrode  1202  and the lower electrode  1210  produces a non-uniform electric field that can influence the middle electrode  1206  to move towards the upper electrode  1202  or the lower electrode  1210 . In another example, the electrically isolated, charge neutral middle electrode  1206  can be moved by an electric field generated between an upper and lower electrodes having different shapes. In one implementation, the upper and lower electrodes having different shapes have the same or substantially the same surface area. In another implementation, the upper and lower electrodes having different shapes have different surface areas. Such implementations may generate more electric field lines in certain areas between the upper and lower electrode, increasing the flux of the electric field in such areas. In another example discussed below with reference to  FIG. 15A , a voltage applied between an upper electrode and a lower electrode, with a grounded complimentary electrode near the upper electrode, can produce an electric field that can influence the electrically isolated, charge neutral middle electrode to move toward the upper electrode. In still another implementation, a lower and upper electrode configuration that cannot be approximated as a parallel plate electrode configuration can produce an electric field an electric field capable of moving the electrically isolated, charge neutral middle electrode. In yet a further implementation, an upper gap between an upper electrode  1202  and a middle electrode  1206  or a lower gap between a lower electrode  1210  and the middle electrode  1206  may be filled with a dielectric fluid or gas, or both the upper gap and the lower gap may be filled with a dielectric fluid or gas. The rate of change of capacitance as the upper gap changes differs from the rate of change of capacitance as the lower gap changes, causing the middle electrode  1206  to move towards the upper electrode  1202  or the lower electrode  1206  upon application of a voltage V across the upper electrode  1202  and the lower electrode  1210 . While certain implementations may be described as relating to a non-uniform electric field and/or certain capacitance characteristics, a person having ordinary skill in the art will understand there may be other ways to characterize and describe the electrical and physical properties of such implementations, and the included descriptions are not intended to be limiting. 
     Compound Electrode Configuration 
       FIG. 15A  shows an example of a cross-section of an analog interferometric modulator  1500  which includes a middle movable electrode  1506 , an upper electrode  1502 , and a lower electrode  1510  spaced apart from the upper electrode  1502  by a constant gap g. In a relaxed (or unactuated) position, the middle electrode  1506  is electrically isolated and is positioned within gap g. The middle electrode  1506  can have a net zero electrical charge in this implementation. 
     The modulator  1500  also includes a complementary electrode  1524  aligned laterally relative to the upper electrode  1502 . In the illustrated implementation, the complementary electrode  1524  is connected to electrical ground and electrically isolated from the upper electrode  1502 , such that the complementary electrode  1524  and the upper electrode  1502  are two electrically separate electrodes. 
     As illustrated in  FIG. 15B  and described in greater detail below with reference to  FIG. 32 , however, the upper electrode  1502  and the complementary electrode  1524  can be configured to be electrically connected during a calibration procedure to form a “compound” electrode  1526 .  FIG. 15B  shows an example of the analog interferometric modulator  1500  after the compound electrode  1526  has been formed. When referred to herein, a “compound electrode” refers to the two electrodes that are included in the compound electrode in a state when they are electrically connected. The compound electrode  1526  has a surface A 2  that, in some implementations, is the same or substantially the same as the surface area A 1  of the lower electrode  1510 . In one implementation, when the complementary electrode  1524  is electrically connected to the upper electrode  1502  to form a compound electrode  1526 , the compound electrode  1526  configured as a parallel plate, such that applying a voltage across the compound electrode  1526  and the lower electrode  1510  generates a generally uniform electric field. This uniform electric field can be used during normal IMOD operations to, for example, move the middle electrode  1506  to various positions to reflect various colors. Additionally, during actuation and calibration procedures described with reference to  FIGS. 26-33 , the complementary electrode  1524  can aid actuation and calibration of the middle electrode  1506  as described below. 
     In some implementations, the complementary electrode  1524  may be disposed below the middle electrode  1506  and aligned laterally relative to the lower electrode  1510 , such that the lower electrode  1510  and the complementary electrode  1524  may form a compound electrode  1526 . 
     Referring again to  FIG. 15A  in which the complementary electrode  1524  is connected to electrical ground and electrically isolated from the upper electrode  1502 , the electrode configuration illustrated in  FIG. 15A  can increase the upward electric force acting on the middle electrode  1506  for a given applied voltage V. The complementary electrode  1524  can induce a positive charge on the top side  1528  of the middle electrode  1506  at its right and left ends. Because the middle electrode  1506  is net charge neutral and electrically isolated, the lower electrode  1510  induces a smaller positive charge on the bottom side  1530  of the middle electrode  1506  than in the configuration illustrated in  FIG. 12 . As a result, the magnitude of the upward force acting on the middle electrode  1506  is increased compared to the configuration shown in  FIG. 12  where electric field non-uniformity is achieved solely through upper and lower electrodes of different areas. 
       FIG. 16  shows an example of a schematic characterizing the analog interferometric modulator configuration shown in  FIG. 15A  as an equivalent circuit. The forces acting on the middle electrode  1506  will now be further described in greater detail with reference to  FIG. 16 . In this implementation, the surface area of the lower electrode  1510  is A, the surface area of the upper electrode  1502  is αA, and the surface area of the grounded complementary electrode  1524  is (1−αa)A. The potential difference between the upper electrode  1502  and the middle electrode  1506  is given by the equation: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     The potential difference between the lower electrode  1510  and the middle electrode  1506  is given by the equation: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     The net force acting on the middle electrode  1506  is in an upward direction (e.g., toward the upper electrode  1502 ), and is given by the equation: 
     
       
         
           
             
               
                 
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     Comparing equation (8) to equation (4) above, it is evident that the magnitude of the net force shown in equation (8), corresponding to the implementation illustrated in  FIG. 15A , is larger than the magnitude of the net force acting on the middle electrode  1206  in the implementation illustrated in  FIG. 12 . 
       FIG. 17  shows an example of a graph illustrating on a logarithmic scale the magnitude of the net upward forces acting on the middle electrode  1206  in the  FIG. 12  configuration and the middle electrode  1506  in the  FIG. 15A  configuration, as a function of the distance d 2  between the upper electrode  1202 ,  1502  and the middle electrode  1206 ,  1506 . In both implementations, the voltage V applied between the upper electrodes  1202 ,  1502  and the lower electrodes  1210 ,  1510  is 100 volts and the area factor α is 0.25.  FIG. 17  demonstrates that the magnitude of the net force F acting on the middle electrode  1506  in the  FIG. 15A  configuration, in which the complementary electrode  1524  is connected to electrical ground and electrically isolated from the upper electrode  1502 , is greater than the magnitude of the net force F acting on the middle electrode  1206  for the single upper electrode  1202  configuration, where d 2  is less than 700 nm. Thus, the electrode configuration illustrated in  FIG. 15A  may increase the upward electric force acting on the middle electrode  1506  for a given voltage V. 
       FIGS. 18-20  illustrate various electrode configurations including an upper electrode and a complementary electrode that can be electrically isolated and/or connected to form a compound electrode.  FIG. 18  shows an example of a plan view of the complementary electrode  1524  and the upper electrode  1502  shown in  FIG. 15A . In this implementation, a compound electrode may be formed in a ring configuration when the circular upper electrode  1502  is electrically connected to the ring-shaped complementary electrode  1524 . The complementary electrode  1524  is aligned laterally relative to the upper electrode  1502 . In this configuration, the upper electrode  1502  is positioned laterally inside the ring-shaped complementary electrode  1524 . 
     Implementations of compound electrodes described herein are not limited to circular or ring shapes. For example,  FIG. 19  shows an example of another electrode configuration, including a square-shaped upper electrode  1902  electrically isolated and/or connected to a square-frame-shaped complementary electrode  1924 . The upper electrode  1902  is positioned laterally inside the square-shaped complementary electrode  1924 . When electrically connected, the upper electrode  1902  and the complementary electrode  1924  can form a compound electrode having a surface area that is substantially the same as the surface area of a lower electrode  1910 . 
       FIG. 20  shows an example of an interlocking configuration, where a complementary electrode  2024  is aligned laterally relative to an upper electrode  2002 . When electrically connected together, the electrodes  2002 ,  2024  can form a compound electrode that has a surface area that is substantially the same or substantially the same as the surface area of a lower electrode  2010 . A person of ordinary skill in the art will understand other shapes and configurations for compound electrodes are also possible. 
     Placing Charge on an Electrode 
     Implementations of analog interferometric modulators described above can actuate a charge-neutral, electrically isolated middle electrode such that the middle electrode moves toward the upper or the lower electrode in the presence of a non-uniform electric field. Methods of providing a charge to the middle electrode after actuating its movement will now be described with reference to  FIGS. 21-25 . 
     Direct Charging of the Electrode 
       FIG. 21  shows an example of a cross-section of an analog interferometric modulator  2100  which includes a middle electrode  2106  and an upper electrode  2102 , and a lower electrode  2110 . In this implementation, the upper electrode  2102  has a surface area that is less than the surface area of the middle electrode  2106  and the lower electrode  2110 . The middle electrode  2106  is illustrated prior to being actuated in the presence of a non-uniform electric field between the upper electrode  2102  and the lower electrode  2110 . Prior to being actuated, the middle electrode  2106  is disposed in a first position in the gap g between the upper electrode  2102  and the lower electrode  2110 . The middle electrode  2106  is electrically isolated in the first position as described in detail above with reference to  FIG. 12 . Prior to actuation, the middle electrode  2106  has a net neutral electric charge. The modulator  2100  can also include one or more electrical contacts, for example, one or more conductive posts  2132  disposed on the upper electrode  2102 . 
       FIG. 22  shows an example of a flowchart illustrating one method  2200  for providing charge onto a middle electrode of modulator  2100  in  FIG. 21 . The method  2200  begins at block  2202  in which a charging actuation voltage V charge  is applied to produce a non-uniform electric field between the upper (or first) electrode  2102  and the lower (or second) electrode  2110 . The voltage V charge  can be less than 100 volts in some implementations. The voltage V charge  can between about 10 and about 20 volts in other implementations. In some cases, the voltage V charge  is under about 20 volts. As described in greater detail above, the middle electrode  2106  can be actuated and moved toward either the upper electrode  2102  or the lower electrode  2110  under the influence of the non-uniform electric field between electrodes  2102  and  2110  having disparate areas. 
     At block  2204 , upon the application of the charging actuation voltage the middle electrode  2106  moves, within the gap g, towards the first or second electrode. The remainder of the description of  FIG. 22  will describe the process with reference to the upper (first) electrode, but it is understood that method  2200  may also be implemented using the lower electrode using an applied charging actuation voltage of the appropriate polarity. In implementations where the middle electrode  2106  moves towards the upper electrode  2102 , the middle electrode  2106  moves in an upward direction under the influence of the non-uniform electric field towards the upper electrode  2102 . In other words, the middle electrode  2106  moves away from the first position in the gap g towards a second position closer to the upper electrode  2103 . At block  2206 , the middle electrode  2106  moves to a second position in the gap g and contacts an electrically conductive structure (for example, conductive posts  2132 ) which is electrically connected to the upper electrode  2102 . An example where the middle electrode  2106  is in the second position in the gap g is shown in  FIG. 23 . 
       FIG. 23  shows an example of a cross-section of the modulator  2100  illustrating the middle electrode  2106  in the second position, after the middle electrode  2106  makes contact with the conductive posts  2132  on the upper electrode  2102 . When moved to the second position, the middle electrode  2106  contacts the conductive posts  2132 , and the middle electrode  2106  is electrically connected to the upper electrode  2102  (through the conductive posts  2132 ) and is no longer electrically isolated. 
     With reference again to  FIG. 22 , next at block  2208 , an electrical charge on the middle electrode  2106  is changed. After electrical contact is made, the middle electrode  2106  begins to lose some of its negative charge through the conductive posts  2132 , by dissipating or “leaking” of its charge. Thus, the middle electrode  2106  is not charge neutral in the second position, and becomes increasingly positively charged as leaking continues. In some implementations, the conductive posts  2132  are resistive posts that provide resistance to reduce the rate of change of the charge on the middle electrode  2106 . In some implementations, a resistor exists in a path between the conductive posts  2106  and ground. 
     Contact between the middle electrode  2106  and the upper electrode  2102  can be sensed such that the time at which charge begins to leak off of the middle electrode  2106  can be measured. In one implementation, the charging actuation voltage V charge  is decreased to a selected calibration voltage V cal  once charge on the middle electrode  2106  begins to change at block  2208 . Methods for determining a defined calibration voltage V cal  are discussed in greater detail below with reference to block  3104  in  FIG. 31 . 
     The rate at which a negative charge is dissipated from the middle electrode  2106  can also be measured. In one implementation (discussed in greater detail with reference to  FIG. 37 ), the rate of dissipation can be decreased by increasing the resistance of the conductive path between the middle electrode  2106  and the upper electrode  2102 . For example, the resistance may be increased by connecting the conductive posts  2132  to the upper electrode  2102  through a resistor. Alternatively, conductive posts  2132  may be made of a highly resistive material. 
     As the middle electrode  2106  develops a net positive charge, the net upward electric force acting on the middle electrode  2106  diminishes. The middle electrode  2106  eventually develops just enough net positive charge that the upward electric force acting on the middle electrode  2106  can no longer balance the downward mechanical force exerted on the middle electrode  2106  by the mechanical spring force acting on the middle electrode  2106 . 
     At block  2210 , the middle electrode  2106  breaks contact with the conductive posts  2132  and moves in a downward direction away from the upper electrode  2102  to a third position in the gap g. In one implementation, the middle electrode  2106  moves to a third position just below the conductive posts  2132  after breaking contact. As used herein, a middle electrode  2106  positioned “just below” a conductive post  2132  is not in physical contact with the conductive post  2132 . In one implementation, the middle electrode  2106  moves to a distance of approximately 10 nanometers below the conductive posts  2132  when the middle electrode  2106  moves to a third position just below the conductive posts  2132 . After breaking electrical contact with the conductive posts  2132 , the middle electrode  2106  is electrically isolated. In contrast to the net-neutral middle electrode  2106  in the first position, the middle electrode  2106  is positively-charged in the third position. 
     The method  2200  next moves to block  2212 , in which charge on the middle electrode  2106  is calibrated. Devices and methods for calibrating charge on the middle electrode  2106  are described below with reference to  FIGS. 39-41 . 
     When the middle electrode  2106  moves to the third position at block  2210 , the amount of positive charge on the middle electrode  2106  is related to the strength of the spring force (e.g., the stiffness of the springs) holding the middle electrode  2106 . The stronger the spring force, the sooner the middle electrode  2106  breaks contact with the conductive posts  2132  resulting in the middle electrode  2106  having less of a positive charge than if it were connected longer. In one implementation, for example, the springs supporting a first middle electrode A are relatively stiffer than the springs holding a second middle electrode B. As a result, less negative charge is leaked off of the first middle electrode A (and consequently less positive charge imparted to the first middle electrode A), before the relatively stronger spring mechanical force acts to move the first middle electrode A down away from the upper electrode  2102 . In contrast, more negative charge is leaked off of the second middle electrode B (and more positive charge imparted to the second middle electrode B), before the mechanical force imparted by the relatively weaker springs will overcome the upward electric force acting on the second middle electrode B. 
     Induction Charging of the Electrode 
       FIG. 24  shows an example of a cross-section of an analog interferometric modulator  2400  capable of providing charge onto a charge-neutral, electrically isolated middle electrode. The modulator  2400  is similar to the modulator  2100  shown in  FIG. 21  and includes a middle electrode  2406 , an upper electrode  2402 , and a lower electrode  2410 . In this implementation, the modulator  2400  includes a complementary electrode  2424  aligned laterally relative to the upper electrode  2402 . As described above with reference to the compound electrode  1526  illustrated in  FIG. 15B , the complementary electrode  2424  and the upper electrode  2402  can be electrically connected to form a compound electrode. In the implementation illustrated in  FIG. 24 , however, the complementary electrode  2424  is electrically isolated from the upper electrode  2402 , and is connected to electrical ground. 
     As illustrated, the middle electrode  2406 , prior to actuation, is disposed in a first position in the gap between the upper electrode  2402  and the lower electrode  2410 . The middle electrode  2406  is electrically isolated in the first position. Prior to actuation, the middle electrode  2406  has a net neutral electric charge. The modulator  2400  can also include one or more electrical contacts. For example, one or more conductive posts  2432  are disposed on the complementary electrode  2424 . 
     Implementations of the analog modulator  2400  can provide a charge to the middle electrode  2406  through induction in accordance with the method  2200  illustrated in  FIG. 22 . For example, a charging actuation voltage V charge  is applied to produce a non-uniform electric field between the upper or first electrode  2402  and the lower or second electrode  2410 . At block  2204 , the middle electrode  2406  moves in the gap in an upward direction towards the upper electrode  2402  under the influence of the non-uniform electric field. The middle electrode  2406  moves away from the first position in the gap towards a second position closer to the upper electrode  2402 . At block  2206 , the middle electrode  2406  moves to a second position in the gap and contacts the conductive posts  2432  on the complementary electrode  2424 , and the middle electrode  2406  receives a charge. 
       FIG. 25  shows an example of a cross-section of the modulator  2400  illustrating the middle electrode  2406  in the second position, after the middle electrode  2406  makes contact with the conductive posts  2432  on the complementary electrode  2424 . When the middle electrode  2406  contacts the conductive posts  2432 , the middle electrode  2406  is no longer electrically isolated and is directly electrically connected to the complementary electrode  2424  (through the conductive posts  2432 ) in the second position. This contact between the middle electrode  2406  and the complementary electrode  2424  provides a path to ground, which provides inductive charging of the middle electrode  2406 . 
     At block  2208  of  FIG. 22 , the electrical charge on the middle electrode  2406  is changed. After electrical contact is made, positive charges on the middle electrode  2406  begin to dissipate (or leak) through the conductive posts  2432 . Thus, the middle electrode  2406  is not charge neutral in the second position, and becomes increasingly negatively charged as leaking continues. The rate at which charge on the middle electrode  2406  is dissipated can be controlled. For example, in one implementation described with reference to  FIG. 29 , the rate of dissipation is decreased using a resistor (not illustrated in  FIGS. 24-25 ) connecting the complementary electrode  2424  and the conductive posts  2432  to ground. 
     The charging actuation voltage V charge  can be decreased to a selected calibration voltage V cal  once discharge begins at block  2208 . As discharge continues and the middle electrode  2406  develops a net negative charge, the attraction between the upper electrode  2402  and the middle electrode  2406  diminishes. The middle electrode  2406  eventually develops just enough net negative charge that the upward electric force acting on the middle electrode  2406  can no longer balance the downward mechanical force exerted on the middle electrode  2406  that positions the middle electrode  2406  in the gap. 
     With reference again to  FIG. 22 , after contact as shown in  FIG. 25 , at block  2210 , the middle electrode  2406  breaks contact with the conductive posts  2432  and moves in a downward direction away from the upper electrode  2402  to a third position in the gap. When the middle electrode  2406  is released at block  2210 , the amount of positive charge on the middle electrode  2406  is related to the stiffness of the springs holding the middle electrode  2406 , as described in greater detail above. 
     After breaking electrical contact with the conductive posts  2432  and moving to the third position, the middle electrode  2406  is again electrically isolated but is now negatively-charged. Implementations of analog interferometric modulators  2400  can thus inductively charge a net-neutral, electrically isolated middle electrode by subjecting the middle electrode to a non-uniform electric field and moving the middle electrode into electrical contact with a charged plate, for example, in the implementations described above, the complimentary electrode  2424 . 
     The method  2200  next moves to block  2212 , in which charge on the middle electrode  2406  is calibrated. Devices and methods for calibrating charge on the middle electrode  2406  are described below with reference to  FIGS. 31-33 . 
     A person of ordinary skill in the art will understand that actuation and charging methods and devices described herein are not limited to an upper electrode  2402  that is subject to an applied voltage. For example, in one implementation, the upper electrode  2402  is connected to ground, and a charging actuation voltage is applied between the complementary electrode  2424  and the lower electrode  2410  to produce a non-uniform electric field. Conductive posts  2432  can be disposed on the upper electrode  2402  in such an implementation. 
     Calibrating Charge on the Electrode 
     In addition to actuating and providing charge onto an electrode, implementations of analog interferometric modulators described herein can calibrate the charge that has been placed on the electrode. Calibrating the charge on the middle electrodes in an array of interferometric modulators can compensate for variances in the spring constants of the mechanical structures holding the middle electrodes. Following a calibration procedure described in detail below, a series of positively- or negatively-charged, electrically isolated middle electrodes are suspended between their respective upper and lower electrodes. The positive (or negative) charge on each calibrated middle electrode is a function of the stiffness of the particular springs holding that electrode. 
     For example, following calibration procedures described herein, a middle electrode E 1  supported by relatively weak springs will have less positive charge than a middle electrode E 2  supported by relative stronger springs. If one global voltage, for example 1 volt, is applied across the upper and lower electrodes associated with E 1  and E 2 , the resulting electric force acting on E 1  and E 2  from the applied electric field will be proportional to the charge on E 1  and E 2 . The force acting on E 2 , with a greater positive charge, will be greater than the force acting on E 1 , with a lesser positive charge. The larger electric force acting on E 2  can compensate for the larger mechanical force exerted by its stiffer springs, such that it will move to the same position as E 1  with the same applied voltage. Thus, calibration of charge on a series of middle electrodes can be used to move the electrodes to the same location despite variances in their associated spring constants. 
     Induction Charging and Calibration of the Electrode 
     Systems and methods for inductively charging and calibrating a charge-neutral, electrically isolated electrode will now be described in detail with reference to  FIGS. 26-33 . 
       FIG. 26  shows an example of a cross-section of an analog interferometric modulator  2600  capable of providing charge onto a charge-neutral, electrically isolated electrode and capable of then calibrating that charge to account for the particular mechanical spring force acting on the electrode. The modulator  2600  includes an upper or first electrode  2602  separated from a lower or second electrode  2610  by a gap g. The modulator  2600  also includes a complementary electrode  2624  aligned laterally relative to the upper electrode  2602 . The modulator  2600  also includes switches  2638  that allow the complementary electrode  2624  to be electrically connected to the upper electrode  2602  or, alternatively, switches  2638  allows the complementary electrode  2624  to be connected to ground. 
     The modulator  2600  also includes a middle electrode  2606  suspended in the gap g and supported by springs  2634 . When the middle electrode  2606  is suspended in the gap g in a first position as shown in  FIG. 26 , the middle electrode  2606  is electrically isolated. The middle electrode is also charge neutral in the first position. When the middle electrode  2606  moves away from the first position, mechanical restorative forces applied to the middle electrode  2606  by the springs  2634  act to restore the middle electrode  2606  to the first position. 
     The complementary electrode  2624  includes one or more conductive posts  2632 . In some implementations, the complementary electrode  2624  is initially electrically isolated from the upper electrode  2602 , and is connected to electrical ground through a resistive component  2636 . In one implementation, the resistive component  2636  is a resistor configured to reduce current flow through the conductive posts  2632 . As described below with reference to  FIG. 32 , the complementary electrode  2624  and the upper electrode  2602  can be electrically connected to form a compound electrode  2626 . 
       FIG. 27  shows an example of a cross-section of the modulator  2600  illustrating the middle electrode  2606  disposed in a first position in the gap g between the upper electrode  2602  and the lower electrode  2610 . A charging actuation voltage V charge  is applied to the upper electrode  2602  and the lower electrode  2610  to produce a non-uniform electric field between, as described in greater detail above with reference to  FIGS. 15 and 24 . 
       FIG. 28  shows an example of a cross-section of the modulator  2600  after the middle electrode  2606  is actuated under the influence of the non-uniform electric field. In this view, the middle electrode  2606  has moved upward away from the first position toward the upper electrode  2602 , but the middle electrode  2606  is still electrically isolated and charge neutral, having the same number of positive charges as negative charges. 
       FIG. 29  shows an example of a cross-section of the middle electrode  2606  in the second position, after it has made electrical contact with the conductive posts  2632  on the complementary electrode  2624 . As described in greater detail with reference to  FIG. 25 , the negative charges on the middle electrode  2606  are bound by the positive charges on the upper electrode  2602 , while the electrical contact between the middle electrode  2606  and the complementary electrode  2624  neutralizes positive charges on the middle electrode  2606 . The mechanical restoring force exerted on the middle electrode  2606  by the springs  2634  is less than the electric force exerted by the electric field between the upper electrode  2602  and the lower electrode  2610 . As positive charge on the middle electrode  2606  continues to dissipate through electrical contact with the conductive posts  2632 , the middle electrode  2606  becomes increasingly negatively charged. The description above and elsewhere in this disclosure assumes that a positive voltage is applied between the lower electrode  2610  and the upper electrode  2602 . However, in implementations where the applied charging actuation voltage is negative, the negative charge on the middle electrode  2606  will dissipate so that the middle electrode  2606  becomes increasingly positively charged. 
     The rate of dissipation of charge on the middle electrode can be controlled. For example, in one implementation, the rate of discharge is controlled and/or decreased by connecting the conductive posts  2632  and the complementary electrode  2624  to electrical ground through a resistor  2636 . The rate of discharge can be decreased by selecting a resistor  2636  having a specific or desired resistance to connect the conductive posts  2632  and the complementary electrode  2624  to electrical ground. 
       FIG. 30  shows an example of a cross-section of the middle electrode  2606  in the third position, after the restoring spring force overcomes the electric force acting on the middle electrode  2606  and pulls the middle electrode  2606  downward away from the upper electrode  2602 . The middle electrode is again electrically isolated, but is now negatively charged. The negative charge on the middle electrode  2606  is related to the stiffness of the springs  2634  supporting the middle electrode  2606 . 
     Methods of actuating and providing charge onto a middle electrode  2606  have been described with reference to  FIGS. 26-30 . Methods and systems for calibrating a charge placed onto the middle electrode  2606  will now be described with reference to  FIGS. 31-33 . 
       FIG. 31  shows an example of a flowchart illustrating one method  3100  for calibrating the amount of charge on a middle electrode using, for example, the modulator  2600  of  FIG. 26 . In the disclosure that follows, reference will be also be made to features illustrated in  FIGS. 32 and 33  as they relate to the blocks in the method  3100  illustrated in  FIG. 31 . The method  3100  begins at block  3102  in which the complementary electrode  2624  is electrically connected to the upper electrode  2602  to farm a compound electrode  2626 . In one implementation, the electrodes  2624  and  2602  are connected together with one or more switches  2638  configured to isolate or connect the electrodes  2624  and  2602 . In some aspects, each modulator  2600  includes 2 switches per pixel. In another implementation, the switches  2638  include transistors that can close to form the compound electrode  2626  or open to segment the compound electrode  2626  into two separate electrodes: complementary electrode  2624  and upper electrode  2602 . 
       FIG. 32  shows an example of a cross-section of the modulator  2600  after the one or more switches  2638  have closed to form a compound electrode  2626 , which includes the complementary electrode  2624  and the upper electrode  2602 . The complementary electrode  2624  is no longer electrically isolated from the upper electrode  2602 , but electrically connected to it through the resistor  2636 . Now, both the complementary electrode  2624  and the upper electrode  2602  are electrically isolated from ground. After the one or more switches  2638  are closed, the surface area of the compound electrode  2626  is the same as or substantially the same as the surface area of the lower electrode  2610 . 
     After the middle electrode  2606  is actuated and is charged, as described above with reference to  FIGS. 26-30 , the middle electrode  2606  remains in the third position in the gap between the compound electrode  2626  and the lower electrode  2610 . In some implementations, the position of the middle electrode  2606  at the beginning of the calibration procedure is referred to as a “first” position. One having ordinary skill in the art will understand that the middle electrode  2606  is in the same position in the gap g whether it is described as being in the “third” position at the end of a charging procedure or in a “first position” at the beginning of a calibration procedure. 
     With reference again to  FIG. 31 , in block  3104 , a voltage is applied between the lower electrode  2610  and the compound electrode  2626  equal to a selected calibration voltage, V cal . Unlike the charging actuation voltage discussed above to place a charge onto the middle electrode  2606 , the voltage V cal  applied between the lower electrode  2610  and the compound electrode  2626  is configured to create a uniform or substantially uniform electric field between the electrodes  2602  and  2626 . The voltage V cal  can be under 100 volts in some aspects. The voltage V cal  can between about 10 an about 20 volts in other aspects. In some cases, the voltage V cal  is under about 20 volts. A controller can be configured to apply the calibration voltage across the compound electrode  2626  and the lower electrode  2610  during a calibration procedure. 
     In some implementations, the calibration voltage V cal  is determined at the time of manufacture of the modulator  2600  or an array of modulators  2600 . For example, the mechanical spring force acting on the middle electrode  2606  in each modulator  2600  in an array of modulators can first be estimated to determine a range of mechanical spring forces in the array. This range can then be adjusted to account for anticipated changes in the mechanical spring forces due to aging, environmental factors, and other influences during the anticipated life of the array of modulators  2600 . A single calibration voltage V cal  to be applied to each modulator  2600  in the array can then be chosen based on this information. In one implementation, V cal  is chosen to ensure that the modulator  2600  having the strongest mechanical spring force in the array will move upward towards the second position in electrical contact with the compound electrode  2626 . In another implementation, V cal  is chosen to ensure that the middle electrode  2606  in each modulator  2600  in the array moves upward towards the second position in electrical contact with the compound electrode  2626  when V cal  is applied across the array to each modulator  2600 . 
     The method next moves to block  3106 , in which the negatively-charged middle electrode moves upward toward the compound electrode  2626  under the influence of the uniform electric field between the lower and compound electrodes  2610 ,  2626 . The electric force applied to the middle electrode  2606  by the electric field thus causes the middle electrode  2606  to move away from the first position towards a second position in electrical contact with the compound electrode  2626 . Next at block  3108 , the middle electrode  2606  reaches the second position and is electrically connected to the compound electrode  2626  through the one or more conductive posts  2632  on the complementary electrode  2624 . 
       FIG. 32  shows an example of a cross-section of the modulator  2600  illustrating the middle electrode  2606  in the second position and contacting the conductive posts  2632 . The middle electrode  2606  is no longer electrically isolated and is directly electrically connected to the compound electrode  2626  (through the conductive posts  2632 ) in the second position. 
     With reference again to  FIG. 31 , in block  3110 , the electrical charge on the middle electrode  2606  is changed. After the middle electrode  2606  contacts the compound electrode  2626 , some of the charge on the middle electrode  2606  is neutralized, until the middle electrode  2606  can no longer resist the mechanical restoring force of the springs  2634 . 
     Moving next to block  3112 , the middle electrode  2606  moves in a downward direction to a third position in the gap g when the mechanical restorative force exceeds the electric force applied to the third electrode  2606 . The third position in a calibration procedure, for example the third position referenced in block  3112  in  FIG. 31 , can be but is not necessarily the same as a third position in an actuation procedure, for example the third position referenced in block  2210  in  FIG. 22 .  FIG. 33  shows an example of a cross-section of the modulator  2600  after the middle electrode separates from the conductive posts  2632  and moves to the third position, thus isolating the negative charges which remain on the middle electrode  2606 . When the middle electrode  2606  is released at block  3112 , the amount of negative charge on the middle electrode  2606  is related to the stiffness of the springs holding the middle electrode  2606 . The modulator  2600  is now calibrated and in an operational range or operationally ready state. 
       FIG. 33A  shows an example of a cross-sectional schematic of an analog interferometric modulator having a middle electrode  2606  with a calibrated charge Q c . The calibrated charge Q c  is related to the stiffness of springs  2634  supporting the middle electrode  2606 . In one implementation, the relationship between the calibrated charge Q c  on the middle electrode  2606  and the stiffness of the springs  2634  supporting the middle electrode  2606  is shown in the following equation: 
     
       
         
           
             
               
                 
                   
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     where ∈ 0  represents the dielectric permittivity of a vacuum, A represents the surface area of middle electrode  2606 , V c  represents the voltage charging the upper electrode  2602 , x c  represents the distance from the location of the middle electrode  2606  at the quiescent (relaxed) position to a conductive post  2632 , K represents the spring constant, and d 0  represents the distance of the gap g. 
     The calibration procedure described with reference to  FIG. 31  can be applied to a series of modulators  2600  in an array. Following the calibration procedure described in  FIG. 31 , a plurality of negatively-charged, electrically isolated middle electrodes are suspended between their respective upper and lower electrodes. The negative charge on each calibrated middle electrode is a function of the stiffness of the particular springs holding that electrode. The amount of negative charge on each calibrated middle electrode is also sufficient to ensure that each of the middle electrodes will reliably and consistently move to the same location when the same voltage is applied across all of the middle electrodes. Thus, calibration of charge on a series of middle electrodes can be used to move the electrodes to the same location despite variances in their associated spring constants. 
     The calibration procedure described herein can be used to calibrate modulators  2600  in a display. In one implementation, a display includes a plurality of analog interferometric modulators  2600  arranged in an array. Drive voltages can be applied across the plurality of modulators  2600  in the array to operate the display and display data. Operating the display can include actuating or moving the middle electrodes  2606  of the modulators in the array to various locations in the gap formed by the upper electrodes  2602  and lower electrodes  2610  to display an image and/or data. The location of the middle electrode  2606  in the gap helps to determine the reflected displayed color of an analog interferometric modulator pixel. Operating or driving the display can result in charge being dissipated from the middle electrode  2606  in each of the plurality of modulators  2600 . In some implementations, the middle electrodes  2606  become charge neutral after the display is operated. In other implementations, a charge remains on middle electrodes  2606  after the display is operated. In some implementations, a dissipation voltage may be applied to cause the middle electrode  2606  to contact a conductive post  2632  in order to dissipate all charge from the middle electrode  2606 . 
     The actuation, charging, and calibration procedures described with reference to  FIGS. 26-33  can then be performed in preparation to display data on the display a second time. The complementary electrode  2624  in each of the modulators  2600  can be electrically isolated from the upper electrode  2602  and connected to electrical ground. The actuation procedure described above with reference to  FIGS. 27-28  can then be performed. For example, a charging actuation voltage can be applied across the upper electrode  2602  and the lower electrode  2610  of each of the modulators  2600  to produce a non-uniform electric field in the gap between the upper electrode  2602  and the lower electrode  2610 . The charging actuation voltage may be the same or substantially the same as the drive voltage. As described with reference to  FIGS. 27-28 , the middle electrodes  2606  in each of the modulators  2600  will be actuated or moved toward the upper electrode  2602 . 
     The charging procedure described with reference to  FIGS. 29-30  can then be performed across all modulators  2600  in the array. As described with reference to  FIGS. 31-33 , a calibration procedure can then be performed on each modulator  2600  to calibrate the charge that has been placed on each middle electrode  2606 . In one implementation, the calibration voltage used to actuate the middle electrodes  2606  during the calibration procedure is less than the charging actuation voltage. Following the calibration procedure, the modulators  2600  are in an operationally ready state. Drive voltages can again be applied across the plurality of modulators to operate the display to display data, beginning the cycle again. In some implementations, before the cycle is begun again, a dissipation voltage may be applied to return the middle electrode  2606  to a charge-neutral state, as mentioned above, or the middle electrode  2606  can still retain some charge when it is further charged and then calibrated. It will be understood that the above-described cycle of operation (for example, data display), actuation, charging, and calibration can be repeated where useful and adjusted to account for variances in the rate of charge leakage from the middle electrodes  2606  over the lifetime of the device. 
     Switchless Charging and Calibration of the Electrode 
     Systems and methods for charging and calibrating a charge-neutral, electrically isolated electrode without the use of switches will now be described in detail with reference to  FIGS. 34-41 . 
       FIG. 34  shows an example of a cross-section of an analog interferometric modulator  3400  capable of providing a charge onto a charge-neutral, electrically isolated electrode, then calibrating that charge to account for the particular mechanical spring force acting on the electrode, using a switchless calibration geometry. The modulator  3400  includes an upper or first electrode  3402  separated from a lower or second electrode  3410  by a gap g. The modulator  3400  also includes a middle electrode  3406  suspended in the gap g and supported by springs  3434 . 
     When the middle electrode  3406  is suspended in the gap g in a first position as shown in  FIG. 34 , the middle electrode  3406  is electrically isolated. The middle electrode is also charge neutral in the first position. When the middle electrode  3406  moves away from the first position, mechanical restorative forces applied to the middle electrode  3406  by the springs  3434  act to restore the middle electrode  3406  to the first position. 
     The modulator  3400  includes one or more resistive contacts or posts  3432  aligned laterally relative to the upper electrode  3402 . The conductive posts  3432  are electrically connected to the upper electrode  3402  through a resistive component  3436 . In one implementation, the resistive component  3436  is a resistor configured to reduce current flow through the conductive posts  3432 . 
       FIG. 35  shows an example of a cross-section of the modulator  3400  at the beginning of an actuation and charging procedure. As shown in  FIG. 27 , the middle electrode  3400  is initially charge neutral. A charging actuation voltage V charge  is applied to produce a non-uniform electric field between the upper electrode  3402  and the lower electrode  3410  (such as described in greater detail above with reference to  FIGS. 12 and 23 ). In this implementation, the upper electrode  3402  has a positive charge and the lower electrode  3410  has a negative charge (relative to each other) as a result of the applied voltage V charge . 
       FIG. 36  shows an example of a cross-section of the modulator  3400  after the middle electrode  3406  is actuated under the influence of the non-uniform electric field, as described in greater detail with reference to  FIG. 23 . In this view, the middle electrode  3406  has moved upward away from the first position toward the upper electrode  3402 , but it is still electrically isolated and charge neutral. 
       FIG. 37  shows an example of a cross-section of the modulator  3400  illustrating the middle electrode  3406  in the second position, after it has made electrical contact with the conductive posts  3432 . As described in greater detail with reference to  FIG. 23 , the electrical contact between the middle electrode  3406  and the conductive posts  3432  decreases negative charges on the middle electrode  3406 . In one implementation, the rate of changing the charge on the middle electrode  3406  is controlled and/or decreased by connecting the conductive posts  3432  to the upper electrode  3402  through a resistor  3436 . For example, the rate of changing the charge on the middle electrode  3406  can be controlled and/or decreased by selecting a resistor  3436  having a specific or desired resistance to connect the conductive posts  3432  and the upper electrode  3402 . 
     The middle electrode  3406  is thus charged by direct contact with the conductive posts  3432 . The mechanical restoring spring force exerted on the middle electrode  3406  by the springs  3434  is less than the electric force exerted by the electric field between the upper and lower electrodes  3402 ,  3410 . As negative charge on the middle electrode  3406  dissipates through electrical contact with the conductive posts  3432 , the middle electrode  3406  becomes increasingly positively charged. 
       FIG. 38  shows an example of a cross-section of the modulator  3400  illustrating the middle electrode  3406  in the third position, after the restoring spring force overcomes the electric force acting on the middle electrode  3406  and pulls the middle electrode  3406  downward away from the conductive posts  3432 . The middle electrode is again electrically isolated, but is now positively charged. The positive charge on the middle electrode  3406  is related to the stiffness of the springs  3434  supporting the middle electrode  3406 . The middle electrode  3406  now has a charge and returns to an electrically isolated position in the gap g, prior to a calibration procedure to calibrate the charge. 
     Methods of actuating and directly providing charge onto a middle electrode  3406  have been described with reference to  FIGS. 34-38 . Methods and systems for calibrating the charge that has been placed on the middle electrode  3306  will now be described with reference to  FIGS. 39-41 . 
     At the end of the actuation and charging procedure described above with reference to  FIGS. 34-38 , the middle electrode  3406  remains in the third position in the gap g between the top electrode  3402  and the lower electrode  3410 . In some implementations, the position of the middle electrode  3406  at the beginning of the calibration procedure is referred to as a “first” position. 
       FIG. 39  shows an example of a flowchart illustrating one method  3900  for calibrating charge on a middle electrode using the modulator  3400  of  FIG. 34 . The method  3900  begins at block  3902  in which the voltage applied between the upper electrode  3402  is set to a selected calibration voltage V cal . Methods to determine V cal  are described in greater detail above with reference to block  3104  of  FIG. 31 . In some implementations, the polarity of the applied voltage is reversed, so that a negative voltage is applied to the upper electrode  3402  and a positive voltage is applied to the lower electrode  3410 . 
     At block  3904 , the positively-charged middle electrode moves upward toward the conductive posts  3432  under the influence of an electric field between the upper and lower electrodes  3402 ,  3410 . The force applied to the middle electrode  3406  by the electric field causes the middle electrode  3406  to move away from the first position towards a second position in electrical contact with the conductive posts  3432 . 
     Next at block  3906 , the middle electrode  3406  moves to the second position and is electrically connected to the conductive posts  3432 . 
       FIG. 40  shows an example of a cross-section of the modulator  3400  illustrating the middle electrode  3406  in the second position and contacting the conductive posts  3432 . The middle electrode  3406  is no longer electrically isolated and is directly electrically connected to the conductive posts  3432  in the second position. 
     Next at block  3908 , the electrical charge on the middle electrode  3406  is changed. As shown in  FIG. 40 , after electrical contact is made between the middle electrode  3406  and the conductive posts  3432 , some of the positive charge on the middle electrode  3406  is depleted until the middle electrode  3306  can no longer resist the mechanical restoring force of the springs  3434 . 
     Moving next to block  3910 , the middle electrode  3406  moves in a downward direction to a third position in the gap g when the mechanical restorative spring force exceeds the force applied to the third electrode  3406 .  FIG. 41  shows an example of a cross-section of the modulator  3400  after the middle electrode separates from the conductive posts  3432  and moves to the third position, thus isolating the positive charges which remain on the middle electrode  3406 . When the middle electrode  3406  releases at block  3910 , the amount of positive charge on the middle electrode  3406  is related to the stiffness of the springs holding the middle electrode  3406 , as described in greater detail above. The modulator  3400  is now calibrated and in an operational range or operationally ready state. 
     The calibration procedure described with reference to  FIG. 39  can be applied to a series of modulators  3400  in an array. Following the calibration procedure described in  FIG. 39 , a series of positively-charged, electrically isolated middle electrodes are suspended between their respective upper and lower electrodes. The positive charge on each calibrated middle electrode is a function of the stiffness of the particular springs holding that electrode. Calibration of charge on a series of middle electrodes can be used to move the electrodes to the same location for a given applied voltage despite variances in their associated spring constants. 
     The calibration procedure described with reference to  FIG. 39  can be used to calibrate modulators  3400  in a display. In one implementation, a display includes a plurality of analog interferometric modulators  3400  arranged in an array. Drive voltages can be applied across the plurality of modulators  3400  in the array to operate the display and display data. Operating the display can include actuating or moving the middle electrodes  3406  of the modulators in the array to various locations in the gap formed by the upper electrodes  3402  and lower electrodes  3410  to display an image and/or data. Operating the display can result in charge being dissipated from the middle electrode  3406  in each of the plurality of modulators  3400 . In some implementations, operating the display can result in charge being dissipated from the middle electrode  3406  in each of the plurality of modulators  3400 , such that the middle electrodes  3306  have an uncalibrated charge. In some implementations, the charge is purposefully dissipated from the middle electrode  3406  by applying a dissipation voltage. 
     The actuation, charging, and calibration procedures described with reference to  FIGS. 34-41  can then be performed in preparation to display data on the display a second time. To begin, the actuation procedure described above with reference to  FIGS. 35-36  can be performed. For example, a charging actuation voltage can be applied across the upper electrode  3402  and the lower electrode  3410  of each of the modulators  3400  to produce a non-uniform electric field in the gap between the upper electrode  3402  and the lower electrode  3410 . The charging actuation voltage may be the same or substantially the same as the drive voltage. As described with reference to  FIGS. 35-36 , the middle electrodes  3406  in each of the modulators  3400  will be actuated or moved toward the upper electrode  3402 . 
     The charging procedure described with reference to  FIGS. 37-38  can then be performed across all modulators  3400  in the array. As described with reference to  FIGS. 39-41 , a calibration procedure can then be performed on each modulator  3400  to calibrate the charge that has been placed on each middle electrode  3406 . In one implementation, the calibration voltage used to actuate the middle electrodes  3406  during the calibration procedure is less than the charging actuation voltage. Following the calibration procedure, the modulators  3400  are in an operationally ready state. Drive voltages can again be applied across the plurality of modulators to operate the display to display data, beginning the cycle again. In some implementations, multiple drive voltages are applied on any given modulator to display different colors at different points in time before it is actuated, charged, and calibrated once again. In some implementations, before the cycle is begun again, a dissipation voltage may be applied to return the middle electrode  3406  to a charge-neutral state, as mentioned above, or the middle electrode  3406  can still retain some charge when it is further charged and then calibrated. The above-described cycle of operation (for example, data display), actuation, charging, and calibration can be repeated where useful and adjusted to account for variances in the rate of charge leakage from the middle electrodes  3406  over the lifetime of the device. 
     The voltage to actuate the middle electrode in order to calibrate charge on the middle electrode in the “switchless” implementation illustrated in  FIG. 34  will be greater than the voltage to actuate the middle electrode for calibration in the implementation illustrated in  FIG. 26 . The upper electrode  3402  in the “switchless” implementation illustrated in  FIG. 34  has a smaller surface area than the compound electrode  2626  in the implementation illustrated in  FIG. 32 . As described above with reference to  FIG. 17 , the force exerted by the smaller upper electrode  3402  in the “switchless” implementation illustrated in  FIG. 34  will generally be less than the force exerted by the compound electrode  2626  in the implementation illustrated in  FIG. 32 , thus a higher voltage will generally be used to actuate the middle electrode. It will also be understood that the capacitance between the upper electrode  3402  and the lower electrode  3410  in the implementation illustrated in  FIG. 34  is not a constant, but a function of the position of the middle electrode  3406 . As a result, the capacitance between the upper electrode  3402  and the lower electrode  3410  is a nonlinear function of the displacement of the middle electrode  3406 . The degree of nonlinearity is governed by the disparity in area between the upper electrode  3402 , the middle electrode  3406 , and the lower electrode  3410 . 
     The actuation, charging, and calibration methods and systems described herein are not limited to electromechanical systems devices, or MEMS devices. The methods and systems described herein can be used in any display device involving actuation, placement of charge, or calibration of charge on electrodes, for example OLED or LCD devices. The devices, methods, and systems described herein can also be implemented in devices having torsional mirrors or electrodes. For example, an electrically isolated, charge neutral torsional mirror or electrode can be actuated to move rotationally under the influence of a non-uniform field. 
       FIGS. 42A and 42B  show examples of system block diagrams illustrating a display device  40  that includes a plurality of interferometric modulators. The display device  40  can be, for example, a smart phone or a cellular or mobile telephone. However, the same components of the display device  40  or slight variations thereof are also illustrative of various types of display devices, for example televisions, e-readers, hand-held devices, and portable media players. 
     The display device  40  includes a housing  41 , a display  30 , an antenna  43 , a speaker  45 , an input device  48 , and a microphone  46 . The housing  41  can be formed from any of a variety of manufacturing processes, including injection molding, and vacuum forming. In addition, the housing  41  may be made from any of a variety of materials, including, but not limited to: plastic, metal, glass, rubber, and ceramic, or a combination thereof. The housing  41  can include removable portions (not shown) that may be interchanged with other removable portions of different color, or containing different logos, pictures, or symbols. 
     The display  30  may be any of a variety of displays, including a bi-stable or analog display, as described herein. The display  30  also can be configured to include a flat-panel display, for example plasma, EL, OLED, STN LCD, or TFT LCD, or a non-flat-panel display, for example a CRT or other tube device. In addition, the display  30  can include an interferometric modulator display, as described herein. For example, the display can include analog interferometric modulator pixels that are operated, actuated, charged, and/or calibrated using methods described herein. 
     The components of the display device  40  are schematically illustrated in  FIG. 42B . The display device  40  includes a housing  41  and can include additional components at least partially enclosed therein. For example, the display device  40  includes a network interface  27  that includes an antenna  43  which is coupled to a transceiver  47 . The transceiver  47  is connected to a processor  21 , which is connected to conditioning hardware  52 . The conditioning hardware  52  may be configured to condition a signal (e.g., filter a signal). The conditioning hardware  52  is connected to a speaker  45  and a microphone  46 . The processor  21  is also connected to an input device  48  and a driver controller  29 . The driver controller  29  is coupled to a frame buffer  28 , and to an array driver  22 , which in turn is coupled to a display array  30 . A power supply  50  can provide power to all components as required by the particular display device  40  design. 
     The network interface  27  includes the antenna  43  and the transceiver  47  so that the display device  40  can communicate with one or more devices over a network. The network interface  27  also may have some processing capabilities to relieve, e.g., data processing requirements of the processor  21 . The antenna  43  can transmit and receive signals. In some implementations, the antenna  43  transmits and receives RF signals according to the IEEE 16.11 standard, including IEEE 16.11(a), (b), or (g), or the IEEE 802.11 standard, including IEEE 802.11a, b, g or n. In some other implementations, the antenna  43  transmits and receives RF signals according to the BLUETOOTH standard. In the case of a cellular telephone, the antenna  43  is designed to receive code division multiple access (CDMA), frequency division multiple access (FDMA), time division multiple access (TDMA), Global System for Mobile communications (GSM), GSM/General Packet Radio Service (GPRS), Enhanced Data GSM Environment (EDGE), Terrestrial Trunked Radio (TETRA), Wideband-CDMA (W-CDMA), Evolution Data Optimized (EV-DO), 1xEV-DO, EV-DO Rev A, EV-DO Rev B, High Speed Packet Access (HSPA), High Speed Downlink Packet Access (HSDPA), High Speed Uplink Packet Access (HSUPA), Evolved High Speed Packet Access (HSPA+), Long Term Evolution (LTE), AMPS, or other known signals that are used to communicate within a wireless network, for example a system utilizing 3G or 4G technology. The transceiver  47  can pre-process the signals received from the antenna  43  so that they may be received by and further manipulated by the processor  21 . The transceiver  47  also can process signals received from the processor  21  so that they may be transmitted from the display device  40  via the antenna  43 . 
     In some implementations, the transceiver  47  can be replaced by a receiver. In addition, in some implementations, the network interface  27  can be replaced by an image source, which can store or generate image data to be sent to the processor  21 . The processor  21  can control the overall operation of the display device  40 . The processor  21  receives data, for example compressed image data from the network interface  27  or an image source, and processes the data into raw image data or into a format that is readily processed into raw image data. The processor  21  can send the processed data to the driver controller  29  or to the frame buffer  28  for storage. Raw data typically refers to the information that identifies the image characteristics at each location within an image. For example, such image characteristics can include color, saturation, and gray-scale level. 
     The processor  21  can include a microcontroller, CPU, or logic unit to control operation of the display device  40 . The conditioning hardware  52  may include amplifiers and filters for transmitting signals to the speaker  45 , and for receiving signals from the microphone  46 . The conditioning hardware  52  may be discrete components within the display device  40 , or may be incorporated within the processor  21  or other components. 
     The driver controller  29  can take the raw image data generated by the processor  21  either directly from the processor  21  or from the frame buffer  28  and can re-format the raw image data appropriately for high speed transmission to the array driver  22 . In some implementations, the driver controller  29  can re-format the raw image data into a data flow having a raster-like format, such that it has a time order suitable for scanning across the display array  30 . Then the driver controller  29  sends the formatted information to the array driver  22 . Although a driver controller  29 , for example an LCD controller, is often associated with the system processor  21  as a stand-alone Integrated Circuit (IC), such controllers may be implemented in many ways. For example, controllers may be embedded in the processor  21  as hardware, embedded in the processor  21  as software, or fully integrated in hardware with the array driver  22 . 
     The array driver  22  can receive the formatted information from the driver controller  29  and can re-format the video data into a parallel set of waveforms that are applied many times per second to the hundreds, and sometimes thousands (or more), of leads coming from the display&#39;s x-y matrix of pixels. 
     In some implementations, the driver controller  29 , the array driver  22 , and the display array  30  are appropriate for any of the types of displays described herein. For example, the driver controller  29  can be a conventional display controller or a bi-stable display controller (e.g., an IMOD controller). Additionally, the array driver  22  can be a conventional driver or a bi-stable display driver (e.g., an IMOD display driver). Moreover, the display array  30  can be a conventional display array or a bi-stable display array (e.g., a display including an array of IMODs). In some implementations, the driver controller  29  can be integrated with the array driver  22 . Such an implementation can be useful in highly integrated systems including cellular phones, watches and other small-area displays. 
     In some implementations, the input device  48  can be configured to allow, e.g., a user to control the operation of the display device  40 . The input device  48  can include a keypad, for example a QWERTY keyboard or a telephone keypad, a button, a switch, a rocker, a touch-sensitive screen, or a pressure- or heat-sensitive membrane. The microphone  46  can be configured as an input device for the display device  40 . In some implementations, voice commands through the microphone  46  can be used for controlling operations of the display device  40 . 
     The power supply  50  can include a variety of energy storage devices. For example, the power supply  50  can be a rechargeable battery, for example a nickel-cadmium battery or a lithium-ion battery. In implementations using a rechargeable battery, the rechargeable battery may be chargeable using power coming from, for example, a wall socket or a photovoltaic device or array. Alternatively, the rechargeable battery can be wirelessly chargeable. The power supply  50  also can be a renewable energy source, a capacitor, or a solar cell, including a plastic solar cell or solar-cell paint. The power supply  50  also can be configured to receive power from a wall outlet. 
     In some implementations, control programmability resides in the driver controller  29  which can be located in several places in the electronic display system. In some other implementations, control programmability resides in the array driver  22 . The above-described optimization may be implemented in any number of hardware and/or software components and in various configurations. 
     The various illustrative logics, logical blocks, modules, circuits and algorithm steps described in connection with the implementations disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. The interchangeability of hardware and software has been described generally, in terms of functionality, and illustrated in the various illustrative components, blocks, modules, circuits and steps described above. Whether such functionality is implemented in hardware or software depends upon the particular application and design constraints imposed on the overall system. 
     The hardware and data processing apparatus used to implement the various illustrative logics, logical blocks, modules and circuits described in connection with the aspects disclosed herein may be implemented or performed with a general purpose single- or multi-chip processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, or, any conventional processor, controller, microcontroller, or state machine. A processor also may be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some implementations, particular steps and methods may be performed by circuitry that is specific to a given function. 
     In one or more aspects, the functions described may be implemented in hardware, digital electronic circuitry, computer software, firmware, including the structures disclosed in this specification and their structural equivalents thereof, or in any combination thereof. Implementations of the subject matter described in this specification also can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions, encoded on a computer storage media for execution by, or to control the operation of, data processing apparatus. 
     Various modifications to the implementations described in this disclosure may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other implementations without departing from the spirit or scope of this disclosure. Thus, the claims are not intended to be limited to the implementations shown herein, but are to be accorded the widest scope consistent with this disclosure, the principles and the novel features disclosed herein. The word “exemplary” is used exclusively herein to mean “serving as an example, instance, or illustration.” Any implementation described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other possibilities or implementations. Additionally, a person having ordinary skill in the art will readily appreciate, the terms “upper” and “lower” are sometimes used for ease of describing the figures, and indicate relative positions corresponding to the orientation of the figure on a properly oriented page, and may not reflect the proper orientation of the IMOD as implemented. 
     Certain features that are described in this specification in the context of separate implementations also can be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation also can be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Further, the drawings may schematically depict one more example processes in the form of a flow diagram. However, other operations that are not depicted can be incorporated in the example processes that are schematically illustrated. For example, one or more additional operations can be performed before, after, simultaneously, or between any of the illustrated operations. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results.