Patent Publication Number: US-2013241903-A1

Title: Optical stack for clear to mirror interferometric modulator

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This disclosure claims priority to U.S. Provisional Patent Application No. 61/612,163, filed on Mar. 16, 2012, entitled “Electro-Mechanical Systems Based Display Device Including Clear to Mirror Optical Stack,” and assigned to the assignee hereof. The disclosure of the prior application is considered part of, and is incorporated by reference in, this disclosure. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to the field of display devices and more particularly to electromechanical systems based display devices. 
     DESCRIPTION OF THE RELATED TECHNOLOGY 
     Electromechanical systems 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 having 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. 
     Devices including electromechanical systems may be used for a variety of purposes including as displays for electronic systems. Such devices may be transmissive, reflective or transflective. Implementations that enhance the transmittance and/or reflectance properties of such devices are desirable. 
     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 an electromechanical device comprising a substrate, an optical stack disposed over the substrate and a movable layer disposed over the optical stack. The optical stack includes an index matching layer and a first at least partially transmissive and at least partially reflective layer. The index matching layer is disposed between the substrate and the first layer. The movable layer and the optical stack define a cavity therebetween. The movable layer is configured to move through the cavity and includes a second at least partially transmissive and at least partially reflective layer, and a dielectric layer disposed on the second layer such that the second layer is between the cavity and the dielectric layer. The index of refraction of the first and the second layer can be greater than approximately 3.0. 
     In various implementations of the electromechanical device the first and the second layer can have an extinction coefficient characteristic less than approximately 0.1. In various implementations, the index matching layer can include aluminum oxide (Al2O3) and/or the first layer can include gallium phosphide (GaP) and/or the second layer can include gallium phosphide (GaP). In various implementations, the index matching layer can be configured to match the refractive index of the first layer with the refractive index of the substrate. In various implementations, the movable layer is movable between a first position when the cavity is collapsed to a second position when the cavity is not collapsed, the first position being closer to the optical stack than the second position. In various implementations, the device can be configured to reflect light incident on the substrate when the movable layer is in the first position. In various implementations, the device can be transmissive of light incident on the substrate when the movable layer is in the second position. In various implementations, the device can be configured to move the movable layer to the first and the second position by the application of electrostatic forces, mechanical forces or using vacuum. In various implementations the cavity can be an interferometric cavity. In various implementations, the thickness of the first and second layer can be between approximately 20 nanometers and approximately 40 nanometers. In various implementations, the index matching layer can have a thickness between approximately 60 nanometers and approximately 90 nanometers. In various implementations, the dielectric layer can have a thickness between approximately 60 nanometers and approximately 100 nanometers. In various implementations, the cavity can include an insulating layer between the movable layer and the fixed optical stack. In various implementations, the first and/or the second layer can be resistive. In various implementations the resistivity of the first and/or the second layer can be about 100 ohm-meter. 
     Another innovative aspect of the subject matter described in this disclosure can be implemented in an electromechanical device comprising a substrate, an optical stack disposed over the substrate and a movable layer disposed over the optical stack. The optical stack includes a means for refractive index matching and a first means for partially transmitting and partially reflecting light, wherein the refractive index matching means is disposed between the substrate and the first partially transmitting and partially reflecting means. The movable layer and the optical stack include a means for producing optical resonance therebetween, the movable layer is configured to move through the optical resonance producing means using a means for actuating the movable layer. The movable layer includes a second means for partially transmitting and partially reflecting light, and a dielectric layer disposed on the second partially transmitting and partially reflecting means such that the second partially transmitting and partially reflecting means is between the optical resonance producing means and the dielectric layer. The index of refraction of the first and second partially transmitting and partially reflecting means is greater than approximately 3.0. 
     In various implementations, the refractive index matching means can include a refractive index matching layer, or the first means for partially transmitting and partially reflecting light can include a partially transmissive and a partially reflective layer, or the second means for partially transmitting and partially reflecting light can include a partially transmissive and a partially reflective layer, or the optical resonance producing means can include an optical resonant cavity. In various implementations, the actuating means can include a device configured to provide an electrostatic force or a mechanical force. In various implementations, the first and second partially transmitting and partially reflecting means can have an absorption coefficient characteristic less than approximately 0.1. 
     Another innovative aspect of the subject matter described in this disclosure can be implemented in a method of manufacturing an electromechanical device, the method comprises providing a substrate, providing an optical stack and providing a movable layer disposed over the optical stack. The optical stack is disposed over the substrate and includes a refractive index matching layer and a first at least partially transmissive and partially reflective, the refractive index matching layer disposed between the substrate and the first partially transmissive and partially reflective layer. The movable layer and the optical stack include a cavity therebetween. The movable layer is configured to move through the cavity, the movable layer includes a second at least partially transmissive and a partially reflective layer having a refractive index greater than approximately 3.0 and an absorption coefficient characteristic less than approximately 0.1, and a dielectric layer disposed on the conducting layer such that the second partially transmissive and partially reflective layer is between the cavity and the dielectric layer. 
     In various implementations, the first partially transmissive and partially reflective layer can be formed by a process including at least one of: physical vapor deposition, chemical vapor deposition, plasma-enhanced chemical vapor deposition, thermal chemical vapor deposition and spin-coating. In various implementations, the second partially transmissive and partially reflective layer can be formed by a process including at least one of: physical vapor deposition, chemical vapor deposition, plasma-enhanced chemical vapor deposition, thermal chemical vapor deposition and spin-coating. In various implementations, the method can further comprise providing a conducting frame around the movable layer, the conducting frame configured for use in actuating the movable layer. 
     Another innovative aspect of the subject matter described in this disclosure can be implemented in a display device comprising a substrate, an optical filter disposed over the substrate, an optical stack disposed over the optical filter and a movable layer disposed over the optical stack. The optical stack includes an index matching layer and a first at least partially transmissive and partially reflective layer, the index matching layer is disposed between the substrate and the first layer. The movable layer and the optical stack define a cavity therebetween. The movable layer is configured to move through the cavity when actuated and includes a second at least partially transmissive and partially reflective layer, the second layer having an refractive index characteristic greater than approximately 3.0 and an absorption coefficient characteristic less than approximately 0.1 and a dielectric layer disposed on the second layer such that the second layer is between the cavity and the dielectric layer. The movable layer is movable to a first position in an actuated state and to a second position in an unactuated state, the first position being closer to the optical stack than the second position. The movable layer and the optical stack are configured to be substantially transmissive when the movable layer is in the second position and substantially reflective when the movable layer is in the first position. 
     In various implementations, when the device is in the reflective first position, a color displayed on the display device can be substantially the same hue within a viewing angle of approximately 60 degrees with respect to a normal to a plane defined by a portion of the substrate. In various implementations, the substrate can include a black backing layer such that the display device will appear black when the movable layer is positioned in the second position. In some implementations, the optical stack can include a diffuser such that the display device will appear white when the movable layer is in the first position. In various implementations, the device can be an interferometric modulator. 
     Another innovative aspect of the subject matter described in this disclosure can be implemented in a display device, comprising a substrate, a means to filter light, the filtering means disposed over the substrate, an optical stack disposed over the substrate, and a movable layer disposed over the optical stack. The optical stack includes a means for refractive index matching and a first at least partially transmissive and partially reflective layer. The refractive index matching means is disposed between the substrate and the first at least partially transmissive and partially reflective layer. The movable layer and the optical stack include a cavity therebetween. The movable layer is configured to move through the cavity when actuated and includes a second at least partially transmissive and partially reflective layer having a refractive index characteristic greater than approximately 3.0 and an absorption coefficient characteristic less than approximately 0.1, and a dielectric layer disposed on the second layer such that the second layer is between the cavity and the dielectric layer. The movable layer is movable to a first position in an actuated state and to a second position in an unactuated state, the first position being closer to the optical stack than the second position. The movable layer and the optical stack are configured to be transmissive when the movable layer is in the second position and reflective when the movable layer is in the first position. In various implementations, the filtering means can include an optical filter and/or the refractive index matching means can include a refractive index matching layer. 
     Another innovative aspect of the subject matter described in this disclosure can be implemented in a method of manufacturing an electromechanical display device, the method comprises providing a substrate, providing an optical filter disposed over the substrate, providing an optical stack disposed over the substrate and providing a movable layer disposed over the optical stack. The optical stack includes a refractive index matching layer and a first at least partially transmissive and partially reflective layer, the refractive index matching layer is disposed between the substrate and the first layer. The movable layer and the optical stack include an optical resonant cavity therebetween. The movable layer is configured to move through the cavity and includes a second at least partially transmissive and partially reflective layer having a refractive index greater than approximately 3.0 and an absorption coefficient characteristic less than approximately 0.1, and a dielectric layer disposed on the second layer such that the second layer is between the cavity and the dielectric layer. 
     In various implementations, the first partially transmissive and partially reflective layer can be formed by a process including at least one of: physical vapor deposition, chemical vapor deposition, plasma-enhanced chemical vapor deposition, thermal chemical vapor deposition and spin-coating. In various implementations, the second partially transmissive and partially reflective layer can be formed by a process including at least one of: physical vapor deposition, chemical vapor deposition, plasma-enhanced chemical vapor deposition, thermal chemical vapor deposition and spin-coating. In various implementations, the method further comprises providing a conducting frame around the movable layer, the conducting frame can be configured for use in actuating the movable layer. 
     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. 
         FIGS. 9A-9D  illustrate implementations of an electromechanical systems device, which can include an interferometric modulator, that can be switched between a transmissive state and a reflective state. 
         FIGS. 10A-10D  illustrate implementations of a display element that include an electromechanical systems device. 
         FIG. 11  illustrates a simulated reflectance spectrum of an implementation of a display element similar to the display element illustrated in  FIGS. 10A-10D . 
         FIGS. 12A and 12B  illustrate simulated chromaticity diagram of an implementation of a display device including a plurality of display elements similar to the display element illustrated in  FIGS. 10A-10D . 
         FIGS. 13A and 13B  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.g., 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 (e.g., MEMS and non-MEMS), aesthetic structures (e.g., 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. 
     As discussed below, in certain implementations, an electromechanical systems device includes a fixed layer disposed on a substrate, and a movable layer disposed over the fixed layer. The device can be configured such that the device is transmissive allowing visible light incident on the substrate to propagate through the device when the movable layer is positioned at a location (a first position) a certain distance away from the fixed layer. The device can be further configured such that the device reflects visible incident light when the movable layer is positioned at a location (a second position) which is closer to the fixed layer than the first position. In some implementations, the electromechanical systems device can transmit incident light when the movable layer is placed at a location a first distance from the fixed layer (e.g., a first position). In such a “clear” state, the device can appear clear to a viewer viewing the device. In certain implementations, the electromechanical systems device can reflect almost all the incident light when the movable layer is placed at a location a second distance from fixed layer (a second position) such that the device appears highly reflective and mirror-like to a viewer viewing the electromechanical systems device through the substrate. The light transmission and light reflection capacity of the electromechanical systems device can be enhanced by including a layer of material (for example, gallium phosphide (GaP)) having a refractive index (n) greater than approximately three (3) and an absorption coefficient (k) less than about 0.1 in the device structure. In various implementations, the absorption coefficient (k) can be approximately zero (0). 
     In certain implementations, an electromechanical systems device that can be switched from a transmissive (or “clear”) state to a reflective (or “mirror”) state can be used in a display device to display a variety of colors. For example, the electromechanical systems device can be configured to display a black color in the transmissive state by providing a black backing on a side of the electromechanical systems device opposite the substrate away from a side of the device exposed for viewing. As another example, the electromechanical systems device can be configured to display a white color in the reflective state by providing a diffuser. As yet another example, the electromechanical systems device can be configured to display a color (for example, red, green, blue, yellow, etc.) in the reflective state by providing an optical color filter. 
     Particular implementations of the subject matter described in this disclosure can be implemented to realize one or more of the following potential advantages. Electromechanical systems devices that are capable of switching from a transmissive (clear) state to a reflective (mirror) state can be included in window panes to control the amount of light entering a room. Such devices can also be used in privacy screens, as a camera shutter or in any other application where it is desirable to control the amount of light transmitted or reflected. In display devices, such electromechanical systems devices can be used to switch from displaying black color to displaying white color so as to provide grey scale control. Such electromechanical systems devices can also be configured to display a bright white. In some implementations, a display device including the electromechanical systems devices described herein can be approximately 30% brighter than other available display devices. In various implementations, the view angle dependence of the color displayed by display devices that include such electromechanical systems devices may be reduced to provide display devices that are viewable over a wide angular range. The materials for the various layers of the electromechanical systems devices and their thickness can be selected to achieve a reflectance spectrum that is flat for wavelengths in the visible spectral region. This can enable the display devices that include such electromechanical systems devices to have reduced or almost no color shift when viewed over a wide angular width. 
     An example of a suitable 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 actuated, reflecting light outside of the visible range (e.g., infrared light). 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 indicating light  13  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 formed from a variety of materials, such as various metals, for example indium tin oxide (ITO). The partially reflective layer can be formed from a variety of materials that are partially reflective, such as 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 conductor, while different, 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 a conductive/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 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, such as 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, e.g., 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 require, for example, 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, e.g., 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, 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 10-volts, and pixels that are to be relaxed are exposed to a voltage difference of near zero volts. After addressing, the pixels are exposed to a steady state or bias voltage difference of approximately 5-volts 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, e.g., 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 readily 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 (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, such as 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, such as 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 always 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. 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 the, e.g., 3×3 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, e.g., 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 necessary 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, such as 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.  6 A- 6 E 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, such as 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, such as, 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, such as 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 arranged. 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, such as voltage addressing and the movements that result from such addressing. Additionally, the implementations of  FIGS. 6A-6E  can simplify processing, such as, e.g., 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, e.g., interferometric modulators of the general type illustrated in  FIGS. 1 and 6 , in addition to 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 such as 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 ,  16   b  can be configured with both optically absorptive and conductive properties, such as the combined conductor/absorber sub-layer  16   a . Additionally, one or more of the sub-layers  16   a ,  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 ,  16   b  can be an insulating or dielectric layer, such as 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. 
     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 such as 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 design size. Deposition of the sacrificial material may be carried out using deposition techniques such as 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 e.g., a post  18  as 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 (e.g., a polymer or an inorganic material, e.g., silicon oxide) into the aperture to form the post  18 , using a deposition method such as 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 such as 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, e.g., reflective layer (e.g., aluminum, aluminum alloy) 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 ,  14   c  as shown in  FIG. 8D . In some implementations, one or more of the sub-layers, such as sub-layers  14   a ,  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  may also 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, e.g., cavity  19  as 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 such as Mo or amorphous Si may be removed by dry chemical etching, e.g., by exposing the sacrificial layer  25  to a gaseous or vaporous etchant, such as 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. 
     As discussed above, in various implementations, the interferometric modulator can be actuated between two positions, or at least two positions in some implementations, such that the interferometric modulator appears non-reflective (in the visible range, for example, dark, dark blue, dark purple or black) in one state and reflective to display a color (for example, red, blue, green) in another state. In some implementations, instead of displaying a color in the reflective state, the interferometric modulator can be configured to display white in the reflective state by reflecting almost uniformly all the wavelengths in the visible region. Such an interferometric modulator that can be switched from appearing dark or black in the non-reflective state to appearing white in the reflective state may be advantageous to provide grey scale control in display devices. 
       FIGS. 9A-9D  illustrate implementations of an electromechanical systems device  900 , which can include an interferometric modulator, that can be switched between a transmissive state and a reflective state. In various implementations, the electromechanical systems device  900  can include an interferometric modulator that operates in accordance with the principles set forth above. The electromechanical systems device  900  can include a substrate  901 , an index matching layer  902 , at least partially transmissive and partially reflective layers  903 ,  906  and a dielectric layer  907 . The index matching layer  902  and the at least partially transmissive and partially reflective layer  903  together can form at least a portion of an optical stack  916  that is disposed over the substrate  901 . In various implementations, the optical stack  916  can be similar to the optical stack  16  discussed above. The at least partially transmissive and partially reflective layer  906  is supported over the substrate  901  by posts  904  such that the layer  906  is separated from the layer  903  by a gap  905 . Such posts  904  can include, but is not limited to, such structure as is illustrated in  FIGS. 6   a - 6 E. 
     The gap  905  can include a low refractive index substance having a refractive index lower than refractive index of the materials included in the substrate  901 , the index matching layer  902 , the at least partially transmissive and partially reflective layers  903 ,  906  and the dielectric layer  907 . In some implementations, one or more gases (e.g., gases air, nitrogen, and argon) can be disposed in the gap  905 . In some implementations, the gap  905  can be (at least partially) devoid of air or a gas, and be in a vacuum state. The at least partially transmissive and partially reflective layer  906  along with the dielectric layer  907  can together constitute a movable layer  914  that can be moved or actuated to switch the electromechanical systems device  900  from a transmissive state to a reflective. In various implementations, the movable layer  914  can be similar to the movable reflective layer  14  discussed above. The movement or actuation of the movable layer  914  can be accomplished by the application of a force, such as, for example, an electrostatic force or a mechanical force. In some implementations, the movement or actuation of the movable layer  914  can be accomplished using pressure differentials. For example, in some implementations a vacuum is used to move the movable layer  914 . 
     In other implementations, the movable layer  914  and the optical stack can include electrodes or conductor layers for moving the movable layer  914  using electrostatic forces, as described herein. As illustrated in  FIG. 9C , another implementation can have a frame  920   a , that includes a conductive material, disposed surrounding part or all of the movable layer  914 . The frame  920   a  can be configured as an electrode. In such implementations, another frame  920   b  that includes a conducting material can be disposed around the optical stack  916 , forming another electrode. The movable layer  914  can be actuated using electrostatic force generated between the two frames  920   a  and  920   b . The frames  920   a  and  920   b  can include a metal such as, for example, aluminum, copper, silver or gold. In various implementations, the frames  920   a  and  920   b  can include conducting materials other than metals. 
     The substrate  901  can be transparent and can include glass or a material that is transmissive to light (e.g., acrylic, plastic, etc.) so as to allow a viewer to see through the substrate  901 . The index matching layer  902  can include aluminum oxide (Al 2 O 3 ). The index matching layer  902  is used to match the refractive index of the at least partially transmissive and partially reflective layer  903  with the refractive index of the substrate  901 . The index matching layer  902  can have a thickness between approximately 60 nm and approximately 90 nm. The at least partially transmissive and partially reflective layers  903  and/or  906  can include a material that has a real part (n) of the complex index of refraction (n+ik) greater than approximately 3.0 and a low (for example, approximately 0 or less than 0.1) imaginary part (or extinction coefficient characteristic, k) of the complex index of refraction (n+ik). Materials having a high refractive index (n) and a low extinction coefficient characteristic (k) can be desirable since these materials can provide an increased front surface reflection and absorb a very small percentage of light. For example, almost 30% of the light incident on a front surface of the partially transmissive and partially reflective layers  903  and/or  906  can be reflected if the partially transmissive and partially reflective layers  903  and/or  906  includes a material having a refractive index (n) of approximately 3.0. In various implementations, the extinction coefficient characteristic, k can have a low value, for example, between approximately 0 and approximately 0.2 such that the at least partially transmissive and partially reflective layers  903  and  906  absorb a very small percentage of the incident light. For example, in some implementations, the at least partially transmissive and partially reflective layers  903  and  906  absorb less than 1% of the incident light. In various implementations, the at least partially transmissive and at least partially reflective layers  903  and  906  can include Gallium Phosphide (GaP), having the real part of the complex index of refraction equal to approximately 3.5 and the imaginary part of the complex index of refraction less than approximately 0.1 (for example, equal to approximately zero (0)). The imaginary part of the complex index of refraction, also known as the extinction coefficient, provides a measure of the absorption of light. Since, the extinction coefficient for GaP is equal to approximately zero (0), very little incident light is absorbed by GaP thus providing increased reflectance in the mirror state and increased transmittance in the clear state. In various implementations, the conductance of the at least partially transmissive and at least partially reflective layers  903  and  906  including GaP can be increased by doping GaP with impurities. The thickness of the at least partially transmissive and partially reflective layers  903  and/or  906  can be between approximately 20 nm and approximately 40 nm. In various implementations, the dielectric layer  907  can include silica (SiO 2 ). The thickness of the dielectric layer  907  can be between approximately 60 nm and approximately 100 nm. The dielectric layer  907  can provide a spring restoring force. The dielectric layer  907  can advantageously serve to provide stiffness to the device structure. The dielectric layer  907  can be useful in providing mechanical stability to the device structure. In various implementations, the dielectric layer  907  can be eliminated. In such devices, the layers  903  and  906  are designed to have a desired stiffness to provide the required spring restoring force. 
     In various implementations, the partially transmissive and partially reflective layers  903  and  906  can be conductive. In some implementations, the conductive partially transmissive and partially reflective layers  903  and  906  can be configured, and used, as electrodes to receive drive currents and/or voltages from a driver circuit for electrostatically actuating the movable layer  914 . In some implementations where the partially transmissive and partially reflective layers  903  and  906  are conductive, a layer of insulating material,  925 , for example, an oxide (e.g., SiO 2 ), can be disposed between the partially transmissive and partially reflective layers  903  and  906  to prevent an electrical short, as illustrated in  FIG. 9D . As illustrated in  FIG. 9D , the layer of insulating material  925  can be included in the optical stack  916 . Alternately, in some implementations, the layer of insulating material can be included in the movable layer  914 . In some implementations, the partially transmissive and partially reflective layers  903  and  906  can have a resistivity of approximately 100 ohm-meter such that the partially transmissive and partially reflective layers  903  and  906  can be brought into contact when actuated electrostatically in the absence of an insulating layer without causing an electrical short. 
     When the electromechanical systems device  900  is in the un-actuated state such that movable layer  914  is farther apart from the optical stack  916 , the electromechanical systems device  900  is in a transmissive state such that a ray of light  910  that is incident on the device  900  through the substrate  901  is transmitted through the optical stack  916  and movable layer  914  and out of the device  900 . In the transmissive state the device  900  appears clear to a viewer viewing the device  900  through the substrate  901 . In the actuated state as illustrated in  FIG. 9B , the movable layer  914  is brought closer to or against the optical stack  916  such that a ray of light  910  that is incident on the device  900  through the substrate  901  is reflected by the movable layer  914  such that the device appears reflective or “mirror like” to a viewer viewing the device  900  through the substrate  901 . 
     In various implementations, the materials for the various layers of the electromechanical systems device  900  and the thickness of the various layers of the electromechanical systems device  900  can be selected such that incident light over a wide wavelength range is reflected almost uniformly to provide a reflectance spectrum that is flat over a wide wavelength range. For example, the reflectance spectrum of the electromechanical systems device  900  can be flat over a bandwidth of approximately 100 nm. As another example, the reflectance spectrum of the electromechanical systems device  900  can be flat over a bandwidth of approximately 300 nm. In various implementations, the reflectance spectrum of the electromechanical systems device  900  can be flat over the entire visible region. In some implementations, the reflectance spectrum of the electromechanical systems device  900  can have a full width at half maximum (FWHM) of approximately 100 nm, approximately 200 nm or approximately 300 nm. In various implementations, a reflectance spectrum that is flat over the entire visible range can be obtained by bringing the partially transmissive and partially reflective layers  903  and/or  906  of the electromechanical systems device  900  into contact with each other. In various implementations, where the electromechanical systems device  900  is activated electrostatically, the width of the reflectance spectrum or the FWHM of the reflectance spectrum can be increased by reducing the thickness of the insulating layer (for example, the oxide layer) that is between the partially transmissive and partially reflective layers  903  and/or  906 . For example, an insulating layer having a thickness between approximately 20 nm and approximately 40 nm can be used to achieve a reflectance spectrum with a FWHM of at least 50 nm. As another example, in some implementations, the partially transmissive and partially reflective layers  903  and  906  can have a certain impedance characteristic, in addition to being conductive, such that they can be brought into contact without causing an electrical short. Accordingly, in some implementations the insulating layer between the partially transmissive and partially reflective layers  903  and  906  can be omitted to achieve a reflectance spectrum with a FWHM of at least 100 nm. 
     The electromechanical systems device  900  can be manufactured using a manufacturing process similar to process  80  illustrated in  FIGS. 8A-8E . For example, the partially transmissive and partially reflective layer  903  can be deposited on the index matching layer  902  using deposition techniques such as physical vapor deposition (PVD) (e.g., sputtering), plasma-enhanced chemical vapor deposition (PECVD), thermal chemical vapor deposition (thermal CVD), or spin-coating. As another example, the partially transmissive and partially reflective layer  906  can be deposited on a sacrificial layer  25  formed during manufacturing using deposition techniques such as PVD (e.g., sputtering), PECVD, thermal CVD, or spin-coating. 
     Such electromechanical systems devices can be used as a smart window that can be actuated electrically or mechanically to control the amount of light entering a window. Various implementations of the electromechanical systems devices operating in accordance with the principles set forth above can be used as privacy screens, camera shutter or any other application where it is desirable to control the amount of light transmitted. Various implementations of the electromechanical systems devices described herein can also be used in display devices as discussed below. 
       FIGS. 10A-10D  illustrate implementations of a display element that include an electromechanical systems device that operates in accordance with the principles set forth above. The electromechanical systems device  900  is modified by providing a black backing  1004  disposed rearward of the movable layer  914  and including an optical filter  1001  in the optical stack  916 . The electromechanical systems device  1000  illustrated in  FIGS. 10A and 10B  can switch between a dark state and a color state. Such a device  1000  can be used in various display applications. 
     For example, when the electromechanical systems device  1000  is in the un-actuated state, as illustrated in  FIG. 10A , such that the movable layer  914  is farther apart from the optical stack  916 , the electromechanical systems device  1000  is in a transmissive state. In the transmissive state, a viewer viewing the device  1000  through the substrate  901  can perceive the black backing  1004  such that the device  1000  appears black or dark to the viewer. In the actuated state, as illustrated in  FIG. 10B , the movable layer  914  is brought closer to/against the optical stack  916  such that light incident through the substrate  901  is filtered by the color filter  1001  and reflected by the movable layer  914 . Thus, the device  1000  appears colored to a viewer viewing the device  1000  through the substrate  901 . The color perceived by the viewer in the actuated state is the color transmitted by the color filter  1001 . For example, if the color filter  1001  is configured to transmit wavelengths in the red portion of the visible range, then the device  1000  will appear red to a viewer. As another example, if the color filter  1001  is configured to transmit wavelengths in the blue portion of the visible range, then the device  1000  will appear blue to a viewer. Accordingly, the device  1000  can be used as a display pixel, or part of a display pixel, in a display device. 
     As discussed above, the implementations shown in  FIGS. 10A-10D  function as direct-view devices, in which images are viewed from the front side of the substrate  901 , i.e., the side opposite to that upon which the movable layer  914  is arranged. In these implementations, the black backing  1004  which is behind or rearward of the movable layer  914  will not be visible in the actuated state and thus will not impact or negatively affect the image quality of the display device, because the movable layer  914  optically shields the black backing  1004  in the actuated state. 
       FIG. 10C  illustrates an implementation of an electromechanical systems device  1000  that is capable of switching between a dark state and a white state for use in display applications. In the implementation illustrated in  FIG. 10C , a diffuser  1007  is included in the optical stack  916  such that the device  1000  appears white to the viewer in the actuated state and black in the un-actuated state. Such a device  1000  can be useful in providing better grey scale control. Additionally, since the device  1000  can be designed to have a flat reflectance spectrum over the entire visible range and absorb a small percentage (for example, less than 1%) of the incident light, the device  1000  can appear very bright in the white state. In some implementations, the device  1000  can display a white state that is approximately 30% to approximately 60% brighter than the white state displayed by other available display devices. 
       FIG. 10D  illustrates an implementation of an electromechanical systems device  1000  that is capable of switching between a color state and a white state for use in display applications. In the implementation illustrated in  FIG. 10D , a diffuser  1007  is included in the optical stack  916  such that the device  1000  appears white to the viewer in the actuated state. A color filter  1001  (for example, a red, green or blue color filter) is provided rearward of the movable layer  914  such that the device  1000  appears colored in the un-actuated state. 
       FIG. 11  illustrates a simulated reflectance spectrum  1100  of an implementation of a display element similar to the display element illustrated in  FIGS. 10A-10D . The group of traces  1101  corresponds to the simulated reflectance of the display element in the blue region of the visible spectrum for different positions of the movable layer  914 . The group of traces  1102  corresponds to the simulated reflectance of the display element in the green region of the visible spectrum for different positions of the movable layer  914 . The group of traces  1103  corresponds to the simulated reflectance of the display element in the red region of the visible spectrum for different positions of the movable layer  914 . As observed from  FIG. 11 , almost 60% or higher of the light incident on the device in the blue, green and red regions of the visible spectrum is reflected by the display element in the reflective or actuated state. Accordingly, the color displayed by the display element can be brighter than the color displayed by other available display devices. It is also observed from  FIG. 11  that the reflectance is almost uniform in the blue, green and red regions of the visible spectrum illustrating that the display element has a flat reflectance spectrum over the entire visible range. 
       FIGS. 12A and 12B  illustrate simulated chromaticity diagram  1200  of an implementation of a display device including a plurality of display elements similar to the display element illustrated in  FIGS. 10A-10D . The chromaticity diagram  1200  illustrates the different colors that can be produced by the display device. A wide range of colors are produced in such a display device by varying the relative intensity of light produced by the plurality of display elements. A chromaticity diagram illustrates how a display may be controlled to generate the mixtures of colors such as red, green, and blue that is perceived by the human eye as other colors. The horizontal and vertical axes of  FIGS. 12A and 12B  define a chromaticity coordinate system (for example, a coordinate system corresponding to the CIE 1976 (L*, u*, v*) color space) on which color values may be depicted. For example, region  1203  corresponds to the various shades, tints, chroma and/or hues produced by the display element in the blue region of the visible spectrum. As another example, region  1205  corresponds to the various shades, tints, chroma and/or hues produced by the display element in the green region of the visible spectrum light. As yet another example, region  1207  corresponds to the various shades, tints, chroma and/or hues produced by the display element in the red region of the visible spectrum. The triangular trace  1201  encloses a region  1202  that corresponds to the range of colors that can be produced by mixing the light produced in regions  1203 ,  1205  and  1207 . This range of colors may be referred to as the color gamut of the display device. As observed from the color gamut  1202 , the display element can be configured to produce a white point corresponding to CIE Standard Illuminant D65 having a correlated color temperature of approximately 6500 K. 
       FIG. 12B  illustrate a simulated color gamut produced by the display when angle of incidence of the light incident on the display element varies from approximately 0 degrees with respect to a surface normal of the display element to approximately 60 degrees with respect to the surface normal. As can be observed in  FIG. 12B , the display element does not exhibit large deviations in the color produced as the angle of incidence varies. Accordingly, the color produced by the display element substantially remains the same as the angle of incidence varies. Conversely, a viewer viewing the display element perceives little shift in color as the view angle varies from close to the surface normal to approximately 60 degrees from the surface normal. This feature may be advantageous in display devices configured to be viewable over a wide angular width or range. 
       FIGS. 13A and 13B  show examples of system block diagrams illustrating a display device  40  that includes a plurality of interferometric modulators. In various implementations, the display device  40  can include a plurality of electromechanical systems device  900 ,  1000 . The display device  40  can be, for example, 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 such as televisions, e-readers 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, such as plasma, EL, OLED, STN LCD, or TFT LCD, or a non-flat-panel display, such as a CRT or other tube device. In addition, the display  30  can include an interferometric modulator display, as described herein. 
     The components of the display device  40  are schematically illustrated in  FIG. 13B . 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, such as 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, 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, such as 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 , such as 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 is common in highly integrated systems such as 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, such as 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 as are well known in the art. For example, the power supply  50  can be a rechargeable battery, such as a nickel-cadmium battery or a lithium-ion battery. 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 may also 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. 
     If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. The steps of a method or algorithm disclosed herein may be implemented in a processor-executable software module which may reside on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that can be enabled to transfer a computer program from one place to another. A storage media may be any available media that may be accessed by a computer. By way of example, and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that may be used to store desired program code in the form of instructions or data structures and that may be accessed by a computer. Also, any connection can be properly termed a computer-readable medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and blu-ray disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media. Additionally, the operations of a method or algorithm may reside as one or any combination or set of codes and instructions on a machine readable medium and computer-readable medium, which may be incorporated into a computer program product. 
     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 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.