Patent Publication Number: US-7719500-B2

Title: Reflective display pixels arranged in non-rectangular arrays

Description:
RELATED APPLICATIONS 
     This application claims the benefit of priority under 35 U.S.C. §119(e) to U.S. Provisional Application 60/613,853, filed Sep. 27, 2004. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     The field of the invention relates to microelectromechanical systems (MEMS). More particularly, this application relates to interferometric display pixels in non-rectangular arrays. 
     2. Description of the Related Technology 
     Microelectromechanical systems (MEMS) include micro mechanical elements, actuators, and electronics. Micromechanical elements may be created using deposition, etching, 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 MEMS device is called an interferometric modulator. 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 certain embodiments, an interferometric modulator may comprise a pair of conductive plates, one or both of which may be transparent and/or reflective in whole or part and capable of relative motion upon application of an appropriate electrical signal. In a particular embodiment, one plate may comprise a stationary layer deposited on a substrate and the other plate may comprise a metallic membrane separated from the stationary layer by an air gap. As described herein in more detail, the position of one plate in relation to another can change the optical interference of light incident on the interferometric modulator. Such devices have a wide range of applications, and it would be beneficial in the art to utilize and/or modify the characteristics of these types of devices so that their features can be exploited in improving existing products and creating new products that have not yet been developed. 
     SUMMARY OF CERTAIN EMBODIMENTS 
     The system, method, and devices of the invention each have several aspects, no single one of which is solely responsible for its desirable attributes. Without limiting the scope of this invention, its more prominent features will now be discussed briefly. After considering this discussion, and particularly after reading the section entitled “Detailed Description of Certain Embodiments” one will understand how the features of this invention provide advantages over other display devices. 
     One embodiment includes a display apparatus having a number of interferometric modulators arranged in an at least partially curvilinear configuration, and a number of electrodes, where each electrode is electrically coupled to two or more interferometric modulators. 
     Another embodiment includes a display having a number of interferometric modulators arranged in an at least partially curvilinear configuration, a first electrode electrically coupled to a first group of interferometric modulators and a second electrode electrically coupled to a second group of interferometric modulators. Also, each of the first group and the second group of interferometric modulators contains at least one interferometric modulator in common, and contains at least one interferometric modulator not in common. 
     Still another embodiment includes a display having a plurality of interferometric modulators arranged in an at least partially curvilinear configuration, and a viewing surface having a number of regions, each region including an optically active area and an optically inactive area. Each region also has a ratio of the optically active area to the optically inactive area, wherein the ratio of any first region larger than a designated surface area is substantially the same as the ratio of any second region of the display larger than the designated area. 
     Yet another embodiment includes a display having an at least partially curvilinear edge, where the display also includes a number of interferometric modulators arranged in an at least partially curvilinear configuration of pixels. The pixels form a boundary, wherein the boundary corresponds to the edge. 
     Still another embodiment includes a display, a processor that is in electrical communication with the display and is configured to process image data, and a memory device in electrical communication with the processor. 
     Another embodiment includes a display device formed by a process. The process includes forming a number of interferometric modulators on the substrate, where the interferometric modulators are arranged in an at least partially curvilinear configuration. The process also includes forming a plurality of electrodes on the substrate, wherein each electrode is electrically coupled to two or more interferometric modulators. 
     Yet another embodiment includes a method of forming a display on a substrate. The method includes forming a plurality of interferometric modulators on the substrate so that the interferometric modulators are arranged in an at least partially curvilinear configuration. The method also includes forming a number of electrodes on the substrate, where each electrode is electrically coupled to two or more interferometric modulators. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an isometric view depicting a portion of one embodiment of an interferometric modulator display in which a movable reflective layer of a first interferometric modulator is in a released position and a movable reflective layer of a second interferometric modulator is in an actuated position. 
         FIG. 2  is a system block diagram illustrating one embodiment of an electronic device incorporating a 3×3 interferometric modulator display. 
         FIG. 3  is a diagram of movable mirror position versus applied voltage for one exemplary embodiment of an interferometric modulator of  FIG. 1 . 
         FIG. 4  is an illustration of a set of row and column voltages that may be used to drive an interferometric modulator display. 
         FIGS. 5A and 5B  illustrate one exemplary timing diagram for row and column signals that may be used to write a frame of display data to the 3×3 interferometric modulator display of  FIG. 2 . 
         FIG. 6A  is a cross section of the device of  FIG. 1 . 
         FIG. 6B  is a cross section of an alternative embodiment of an interferometric modulator. 
         FIG. 6C  is a cross section of another alternative embodiment of an interferometric modulator. 
         FIG. 7  is a perspective view depicting a wrist watch with an enlarged illustration of a non-rectangular pixel array used on the face thereof. 
         FIG. 8  is an illustration of a non-rectangular pixel array in which each pixel has substantially the same area. 
         FIG. 9A  is an illustration of a non-rectangular pixel array in which each pixel contains a single interferometric modulator. 
         FIG. 9B  is an illustration of a non-rectangular pixel array in which each pixel contains four interferometric modulators that are substantially the same shape. 
         FIG. 9C  is an illustration of a non-rectangular pixel array in which each pixel contains multiple interferometric modulators that are substantially the same size and substantially the same shape. 
         FIG. 10A  is a system block diagram illustrating an embodiment of a display device. 
         FIG. 10B  is a system block diagram illustrating an embodiment of a display device. 
     
    
    
     DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS 
     The following detailed description is directed to certain specific embodiments of the invention. However, the invention can be embodied in a multitude of different ways. In this description, reference is made to the drawings wherein like parts are designated with like numerals throughout. As will be apparent from the following description, the embodiments 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 or pictorial. More particularly, it is contemplated that the embodiments may be implemented in or associated with a variety of electronic devices such as, but not limited to, mobile telephones, wireless devices, personal data assistants (PDAs), hand-held or portable computers, GPS receivers/navigators, cameras, MP3 players, camcorders, game consoles, wrist watches, clocks, calculators, television monitors, flat panel displays, computer monitors, auto displays (e.g., odometer display, etc.), cockpit controls and/or displays, display of camera views (e.g., display of a rear view camera in a vehicle), electronic photographs, electronic billboards or signs, projectors, architectural structures, packaging, and aesthetic structures (e.g., display of images on a piece of jewelry). MEMS devices of similar structure to those described herein can also be used in non-display applications such as in electronic switching devices. 
     One interferometric modulator display embodiment comprising an interferometric MEMS display element is illustrated in  FIG. 1 . In these devices, the pixels are in either a bright or dark state. In the bright (“on” or “open”) state, the display element reflects a large portion of incident visible light to a user. When in the dark (“off” or “closed”) state, the display element reflects little incident visible light to the user. Depending on the embodiment, the light reflectance properties of the “on” and “off” states may be reversed. MEMS pixels can be configured to reflect predominantly at selected colors, allowing for a color display in addition to black and white. 
       FIG. 1  is an isometric view depicting two adjacent pixels in a series of pixels of a visual display, wherein each pixel comprises a MEMS interferometric modulator. In some embodiments, an interferometric modulator display comprises a row/column array of these interferometric modulators. Each interferometric modulator includes a pair of reflective layers positioned at a variable and controllable distance from each other to form a resonant optical cavity with at least one variable dimension. In one embodiment, one of the reflective layers may be moved between two positions. In the first position, referred to herein as the relaxed, the movable layer is positioned at a relatively large distance from a fixed partially reflective layer. In the second position, the movable layer is positioned more closely adjacent to the partially reflective layer. Incident light that reflects from the two layers interferes constructively or destructively depending on the position of the movable reflective layer, producing either an overall reflective or non-reflective state for each pixel. 
     The depicted portion of the pixel array in  FIG. 1  includes two adjacent interferometric modulators  12   a  and  12   b . In the interferometric modulator  12   a  on the left, a movable and highly reflective layer  14   a  is illustrated in a relaxed position at a predetermined distance from a fixed partially reflective layer  16   a . In the interferometric modulator  12   b  on the right, the movable highly reflective layer  14   b  is illustrated in an actuated position adjacent to the fixed partially reflective layer  16   b.    
     The fixed layers  16   a ,  16   b  are electrically conductive, partially transparent and partially reflective, and may be fabricated, for example, by depositing one or more layers each of chromium and indium-tin-oxide onto a transparent substrate  20 . The layers are patterned into parallel strips, and may form row electrodes in a display device as described further below. The movable layers  14   a ,  14   b  may be formed as a series of parallel strips of a deposited metal layer or layers (orthogonal to the row electrodes  16   a ,  16   b ) deposited on top of posts  18  and an intervening sacrificial material deposited between the posts  18 . When the sacrificial material is etched away, the deformable metal layers  14   a ,  14   b  are separated from the fixed metal layers by a defined gap  19 . A highly conductive and reflective material such as aluminum may be used for the deformable layers, and these strips may form column electrodes in a display device. 
     With no applied voltage, the cavity  19  remains between the layers  14   a ,  16   a  and the deformable layer is in a mechanically relaxed state as illustrated by the pixel  12   a  in  FIG. 1 . However, when a potential difference is applied to 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 voltage is high enough, the movable layer is deformed and is forced against the fixed layer (a dielectric material which is not illustrated in this Figure may be deposited on the fixed layer to prevent shorting and control the separation distance) as illustrated by the pixel  12   b  on the right in  FIG. 1 . The behavior is the same regardless of the polarity of the applied potential difference. In this way, row/column actuation that can control the reflective vs. non-reflective pixel states is analogous in many ways to that used in conventional LCD and other display technologies. 
       FIGS. 2 through 5  illustrate one exemplary process and system for using an array of interferometric modulators in a display application. 
       FIG. 2  is a system block diagram illustrating one embodiment of an electronic device that may incorporate aspects of the invention. In the exemplary embodiment, the electronic device includes a processor  21  which may be any general purpose single- or multi-chip microprocessor such as an ARM, Pentium®, Pentium II®, Pentium III®, Pentium IV®, Pentium® Pro, an 8051, a MIPS®, a Power PC®, an ALPHA®, or any special purpose microprocessor such as a digital signal processor, microcontroller, or a programmable gate array. As is conventional in the art, the processor  21  may be configured to execute one or more software modules. In addition to executing an operating system, the processor 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. 
     In one embodiment, the processor  21  is also configured to communicate with an array controller  22 . In one embodiment, the array controller  22  includes a row driver circuit  24  and a column driver circuit  26  that provide signals to a display array or panel  30 . The cross section of the array illustrated in  FIG. 1  is shown by the lines  1 - 1  in  FIG. 2 . For MEMS interferometric modulators, the row/column actuation protocol may take advantage of a hysteresis property of these devices illustrated in  FIG. 3 . It may require, for example, a 10 volt potential difference to cause a movable layer to deform from the relaxed state to the actuated state. However, when the voltage is reduced from that value, the movable layer maintains its state as the voltage drops back below 10 volts. In the exemplary embodiment of  FIG. 3 , the movable layer does not relax completely until the voltage drops below 2 volts. There is thus a range of voltage, about 3 to 7 V in the example illustrated in  FIG. 3 , where there exists 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 having the hysteresis characteristics of  FIG. 3 , the row/column actuation protocol can be designed such that during row strobing, pixels in the strobed 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 close to zero volts. After the strobe, the pixels are exposed to a steady state voltage difference of about 5 volts such that they remain in whatever state the row strobe put them in. After being written, each pixel sees a potential difference within the “stability window” of 3-7 volts in this example. This feature makes the pixel design illustrated in  FIG. 1  stable under the same applied voltage conditions in either an actuated or relaxed pre-existing state. Since each pixel of the interferometric modulator, 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 voltage within the hysteresis window with almost no power dissipation. Essentially no current flows into the pixel if the applied potential is fixed. 
     In typical applications, a display frame may be created by asserting the set of column electrodes in accordance with the desired set of actuated pixels in the first row. A row pulse is then applied to the row  1  electrode, actuating the pixels corresponding to the asserted column lines. The asserted set of column electrodes is then changed to correspond to the desired set of actuated pixels in the second row. A pulse is then applied to the row  2  electrode, actuating the appropriate pixels in row  2  in accordance with the asserted column electrodes. The row  1  pixels are unaffected by the row  2  pulse, and remain in the state they were set to during the row  1  pulse. This may be repeated for the entire series of rows in a sequential fashion to produce the frame. Generally, the frames are refreshed and/or updated with new display data by continually repeating this process at some desired number of frames per second. A wide variety of protocols for driving row and column electrodes of pixel arrays to produce display frames are also well known and may be used in conjunction with the present invention. 
       FIGS. 4 and 5  illustrate one possible actuation protocol for creating a display frame on the 3×3 array of  FIG. 2 .  FIG. 4  illustrates a possible set of column and row voltage levels that may be used for pixels exhibiting the hysteresis curves of  FIG. 3 . In the  FIG. 4  embodiment, actuating a pixel involves setting the appropriate column to −V bias , and the appropriate row to +ΔV, which may correspond to −5 volts and +5 volts respectively Relaxing the pixel is accomplished by setting the appropriate column to +V bias , and the appropriate row to the same +ΔV, producing a zero volt potential difference across the pixel. In those rows where the row voltage is held at zero volts, the pixels are stable in whatever state they were originally in, regardless of whether the column is at +V bias , or −V bias . As is also illustrated in  FIG. 4 , it will be appreciated that voltages of opposite polarity than those described above can be used, e.g., actuating a pixel can involve setting the appropriate column to +V bias , and the appropriate row to −ΔV. In this embodiment, releasing the pixel is accomplished by setting the appropriate column to −V bias , and the appropriate row to the same −ΔV, producing a zero volt potential difference across the pixel. 
       FIG. 5B  is a timing diagram showing a series of row and column signals applied to the 3×3 array of  FIG. 2  which will result in the display arrangement illustrated in  FIG. 5A , where actuated pixels are non-reflective. Prior to writing the frame illustrated in  FIG. 5A , the pixels can be in any state, and in this example, all the rows are at 0 volts, and all the columns are at +5 volts. With these applied voltages, all pixels are stable in their existing actuated or relaxed states. 
     In the  FIG. 5A  frame, pixels ( 1 , 1 ), ( 1 , 2 ), ( 2 , 2 ), ( 3 , 2 ) and ( 3 , 3 ) are actuated. To accomplish this, during a “line time” for row  1 , columns  1  and  2  are set to −5 volts, and column  3  is set to +5 volts. This does not change the state of any pixels, because all the pixels remain in the 3-7 volt stability window. Row  1  is then strobed with a pulse that goes from 0, up to 5 volts, and back to zero. This actuates the ( 1 , 1 ) and ( 1 , 2 ) pixels and relaxes the ( 1 , 3 ) pixel. No other pixels in the array are affected. To set row  2  as desired, column  2  is set to −5 volts, and columns  1  and  3  are set to +5 volts. The same strobe applied to row  2  will then actuate pixel ( 2 , 2 ) and relax pixels ( 2 , 1 ) and ( 2 , 3 ). Again, no other pixels of the array are affected. Row  3  is similarly set by setting columns  2  and  3  to −5 volts, and column  1  to +5 volts. The row  3  strobe sets the row  3  pixels as shown in  FIG. 5A . After writing the frame, the row potentials are zero, and the column potentials can remain at either +5 or −5 volts, and the display is then stable in the arrangement of  FIG. 5A . It will be appreciated that the same procedure can be employed for arrays of dozens or hundreds of rows and columns. It will also be appreciated that the timing, sequence, and levels of voltages used to perform row and column actuation can be varied widely within the general principles outlined above, and the above example is exemplary only, and any actuation voltage method can be used with the systems and methods described herein. 
       FIGS. 10A and 10B  are system block diagrams illustrating an embodiment of a display device  40 . The display device  40  can be, for example, a cellular or mobile telephone. However, the same components of display device  40  or slight variations thereof are also illustrative of various types of display devices such as televisions and portable media players. 
     The display device  40  includes a housing  41 , a display  30 , an antenna  43 , a speaker  44 , an input device  48 , and a microphone  46 . The housing  41  is generally formed from any of a variety of manufacturing processes as are well known to those of skill in the art, 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. In one embodiment the housing  41  includes 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  of exemplary display device  40  may be any of a variety of displays, including a bi-stable display, as described herein. In other embodiments, the display  30  includes a flat-panel display, such as plasma, EL, OLED, STN LCD, or TFT LCD as described above, or a non-flat-panel display, such as a CRT or other tube device, as is well known to those of skill in the art. However, for purposes of describing the present embodiment, the display  30  includes an interferometric modulator display, as described herein. 
     The components of one embodiment of exemplary display device  40  are schematically illustrated in  FIG. 10B . The illustrated exemplary display device  40  includes a housing  41  and can include additional components at least partially enclosed therein. For example, in one embodiment, the exemplary 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  44  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 controller  22 , which in turn is coupled to a display array  30 . A power supply  50  provides power to all components as required by the particular exemplary display device  40  design. 
     The network interface  27  includes the antenna  43  and the transceiver  47  so that the exemplary display device  40  can communicate with one ore more devices over a network. In one embodiment the network interface  27  may also have some processing capabilities to relieve requirements of the processor  21 . The antenna  43  is any antenna known to those of skill in the art for transmitting and receiving signals. In one embodiment, the antenna transmits and receives RF signals according to the IEEE 802.11 standard, including IEEE 802.11(a), (b), or (g). In another embodiment, the antenna transmits and receives RF signals according to the BLUETOOTH standard. In the case of a cellular telephone, the antenna is designed to receive CDMA, GSM, AMPS or other known signals that are used to communicate within a wireless cell phone network. The transceiver  47  pre-processes 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 processes signals received from the processor  21  so that they may be transmitted from the exemplary display device  40  via the antenna  43 . 
     In an alternative embodiment, the transceiver  47  can be replaced by a receiver. In yet another alternative embodiment, network interface  27  can be replaced by an image source, which can store or generate image data to be sent to the processor  21 . For example, the image source can be a digital video disc (DVD) or a hard-disc drive that contains image data, or a software module that generates image data. 
     Processor  21  generally controls the overall operation of the exemplary 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  then sends the processed data to the driver controller  29  or to 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. 
     In one embodiment, the processor  21  includes a microcontroller, CPU, or logic unit to control operation of the exemplary display device  40 . Conditioning hardware  52  generally includes amplifiers and filters for transmitting signals to the speaker  44 , and for receiving signals from the microphone  46 . Conditioning hardware  52  may be discrete components within the exemplary display device  40 , or may be incorporated within the processor  21  or other components. 
     The driver controller  29  takes the raw image data generated by the processor  21  either directly from the processor  21  or from the frame buffer  28  and reformats the raw image data appropriately for high speed transmission to the array controller  22 . Specifically, the driver controller  29  reformats 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 controller  22 . Although a driver controller  29 , such as a 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. They may be embedded in the processor  21  as hardware, embedded in the processor  21  as software, or fully integrated in hardware with the array controller  22 . 
     Typically, the array controller  22  receives the formatted information from the driver controller  29  and reformats the video data into a parallel set of waveforms that are applied many times per second to the hundreds and sometimes thousands of leads coming from the display&#39;s x-y matrix of pixels. 
     In one embodiment, the driver controller  29 , array controller  22 , and display array  30  are appropriate for any of the types of displays described herein. For example, in one embodiment, driver controller  29  is a conventional display controller or a bi-stable display controller (e.g., an interferometric modulator controller). In another embodiment, array controller  22  is a conventional driver or a bi-stable display driver (e.g., an interferometric modulator display). In one embodiment, a driver controller  29  is integrated with the array controller  22 . Such an embodiment is common in highly integrated systems such as cellular phones, watches, and other small area displays. In yet another embodiment, display array  30  is a typical display array or a bi-stable display array (e.g., a display including an array of interferometric modulators). 
     The input device  48  allows a user to control the operation of the exemplary display device  40 . In one embodiment, input device  48  includes a keypad, such as a QWERTY keyboard or a telephone keypad, a button, a switch, a touch-sensitive screen, a pressure- or heat-sensitive membrane. In one embodiment, the microphone  46  is an input device for the exemplary display device  40 . When the microphone  46  is used to input data to the device, voice commands may be provided by a user for controlling operations of the exemplary display device  40 . 
     Power supply  50  can include a variety of energy storage devices as are well known in the art. For example, in one embodiment, power supply  50  is a rechargeable battery, such as a nickel-cadmium battery or a lithium ion battery. In another embodiment, power supply  50  is a renewable energy source, a capacitor, or a solar cell, including a plastic solar cell, and solar-cell paint. In another embodiment, power supply  50  is configured to receive power from a wall outlet. 
     In some implementations control programmability resides, as described above, in a driver controller which can be located in several places in the electronic display system. In some cases control programmability resides in the array controller  22 . Those of skill in the art will recognize that the above-described optimization may be implemented in any number of hardware and/or software components and in various configurations. 
     The details of the structure of interferometric modulators that operate in accordance with the principles set forth above may vary widely. For example,  FIGS. 6A-6C  illustrate three different embodiments of the moving mirror structure.  FIG. 6A  is a cross section of the embodiment of  FIG. 1 , where a strip of metal material  14  is deposited on orthogonally extending supports  18 . In  FIG. 6B , the moveable reflective material  14  is attached to supports at the corners only, on tethers  32 . In  FIG. 6C , the moveable reflective material  14  is suspended from a deformable layer  34 . This embodiment has benefits because the structural design and materials used for the reflective material  14  can be optimized with respect to the optical properties, and the structural design and materials used for the deformable layer  34  can be optimized with respect to desired mechanical properties. The production of various types of interferometric devices is described in a variety of published documents, including, for example, U.S. Published application 2004/0051929. A wide variety of known techniques may be used to produce the above described structures involving a series of material deposition, patterning, and etching steps. 
     Many displays, such as computer monitors, televisions, and displays for cell phones, calculators, and PDA&#39;s are rectangular. There are some display applications, a watch face, for example, where the display is not rectangular. The usual procedure for making these non-rectangular displays is to form a rectangular display, and then remove or cover the corners, as necessary. Part of the reason for exclusively rectangular displays is that many display element technologies, such as, for example that used in active matrix LCD&#39;s, require complex driving and addressing circuitry. Because the circuitry would have to match or at least compensate for irregular display geometries, only recti-linear geometries have been preferred. It can be appreciated that this can be a waste of material and thus an aspect of device cost that would be beneficial to eliminate. Additionally, aesthetic sacrifices are made at least at the perimeter when using a square display in a round application. 
     As described more fully below, interferometric modulators such as those described above are very suitable for the production of non-rectangular arrays of pixels. As discussed in reference to  FIG. 1 , an interferometric light modulating cavity is formed at the intersections of movable layer columns  14   a  and  14   b , and electrode rows  16   a  and  16   b . Because of less complex driving and addressing circuitry, display arrays comprising interferometric modulators described herein are not constrained to have linear rows and columns. When the general structure shown in  FIG. 1  is maintained, each movable layer column will be modulated by an electrode row intersecting it, at the intersection, regardless of the local or general shape of the rows or columns. Such modulation will happen as discussed above in reference to  FIGS. 5A and 5B . Accordingly, interferometric modulators may be formed according to the principles taught above having curvilinear shapes. This characteristic of interferometric modulators enables creation of display arrays in a wide variety of configurations. 
       FIG. 7  shows a wristwatch  700  having a non-rectangular display, a portion of which is shown enlarged as display portion  702 . In this embodiment the array is comprised of movable layer columns  714  and curvilinear electrode rows  716 , wherein interferometric modulators are formed at row and column intersections. Although in this embodiment electrode rows  716  and movable layer columns  714  are discussed, it is understood that selection of row and column designation is arbitrary, and that either rows or columns can be formed by the interferometric modulator electrode or movable layer structures. It is further understood that the movable layer, despite being referred to as “movable layer” to distinguish it from the structure referred to as “electrode,” is, in fact, an electrode. It is still further understood that rows and columns may be linear or nonlinear or curvilinear. 
     In  FIG. 7 , rows  716  are shown as a series of concentric arcs, and the linear columns  714  extend radially from a common center point. The center point of the columns in the embodiment of  FIG. 7  is shared with a center point of the concentric arcs. And, as discussed above, interferometric modulator pixels are formed at the row  716  and column  714  intersections. 
     In some embodiments rows  716  and columns  714  may be concentric arcs or circles, or they may have different centers. They may have substantially identical or may have different amounts of curvature. They may be partially or wholly linear. They may curve in one or in multiple directions. They may have substantially the same or different widths. The width of a row  716  or column  714  may change along its length according to or not according to an amount of local curvature. Rows  716  and columns  714  may have substantially the same or differing curvature characteristics. Adjacent rows  716  or adjacent columns  714  may or may not appear substantially parallel. One portion of the display may have curvature characteristics which are substantially the same or different than another portion of the display. One portion of the display may not share a row  716  or column  714  or either with another portion of the display. The curvature of rows  716  and columns  714  may correspond to an overall shape of the entire display, or a portion thereof, or the shape of some other portion of the device comprising the display. The rows  716  and columns  714  may intersect at a range of angles ranging from substantially right angles to very acute angles. Such characteristics of rows  716  and columns  714  as curvature, angles, and widths may be manipulated to achieve a desired aesthetic result. A display may contain rows  716  and columns  714 , or may contain only rows  716  or columns  714 . Rows  716  and columns  714  may appear to intersect themselves, or to be continuous, having no end point. Electrical connections for the rows  716  and columns  714  may be made with vias to lower layers of the electronics. Such connections may occur singly or multiply, and may be formed at the end or not at the end of the rows  716  and columns  714 . 
     As the pixels are formed by intersections of rows  716  and columns  714 , the shapes of pixels will vary with the characteristics of rows  716  and columns  714 . Pixels may have straight and/or curved edges. They may be of substantially the same size and/or shape or may have different sizes and shapes. Some pixels may be triangular. 
     In the embodiment of  FIG. 7 , the rows  716  in the array are substantially equally spaced, resulting in all pixels having the same length along their column edges. As the rows  716  decrease in length toward the center, the width of the pixels along the row edges decreases, resulting in a decrease in the area of the pixels toward the center of the array. Thus,  FIG. 7  demonstrates one particular embodiment in which the area of different pixels in the array can vary. Additional configurations of the arrays can permit the area of the pixels to vary as desired. For example, varying the width of columns  714  in  FIG. 7  also results in pixels that vary in area. 
     Also contemplated herein are embodiments in which most or all of the pixels in the array can have substantially the same area.  FIG. 8  shows a portion of such an embodiment. By necessity, the columns  814  narrow as they approach the center. To compensate, the rows  816  widen, thereby keeping the area substantially constant throughout the array. Some pixels may also be formed to have a larger or smaller area than the majority of the pixels of the array. For example, in  FIG. 8 , the pixels nearest the center may be made smaller (e.g., divided in half) or larger (e.g., two united into one), while the remainder of the pixels in the array can be configured to have substantially the same area. 
     In some embodiments, pixels may consist of one interferometric modulator. In such instances, the shape and size of the pixel is the same as the shape and size of the interferometric modulator, as shown in  FIG. 9A . In other examples, a pixel can contain multiple interferometric modulators, as shown in  FIGS. 9B and 9C . An interferometric modulator can be formed in any selected shape (e.g., circular, oval, etc.) and size, according to the shape and size of the pixel desired, subject only to the state of manufacturing capabilities at the time of fabrication. 
       FIG. 9B  shows an example of multiple interferometric modulators within pixels of an array, where the number of interferometric modulators within each pixel is the same for multiple pixels in the array. To realize different sized pixels, different sized interferometric modulators are used.  FIG. 9C  shows an example of an array of pixels where the size of the interferometric modulators within each pixel is the same. To realize different sized pixels, more or fewer interferometric modulators are used. These embodiments are representative of a variety of configurations that can be designed by one skilled in the art. 
     The shape and size of interferometric modulators to be used in any particular embodiment can be selected according to the principles discussed herein, and principles known in the art, where the knowledge of one skilled in the art includes subject matter covered in U.S. Pat. Nos. 6,794,119, 6,741,377, 6,710,908 and 5,835,255. Design considerations include, but are not limited to the fabrication process of the interferometric modulators, the process for actuating the interferometric modulators, and desired properties of the display such as density of active area, brightness, size and shape. 
     Displays containing interferometric modulators discussed herein contain an optically active portion, of which the optical properties can be modified in response to signals applied to the interferometric modulators. The displays also contain an optically inactive portion of which the optical properties are not modified in response to signals applied to the interferometric modulators. Typically, most of or the entire inactive portion is the portion separating the interferometric modulators. 
     In some circumstances it is useful to compare various regions of a viewing area of a display, where regions of the display are any part of the display that contains a sufficient number of pixels so as to represent a generalized density of interferometric modulators. For example, a region must not be so small that it includes only the inactive area separating two interferometric modulators. Typically, a region includes at least four interferometric modulators, but can include any larger number of interferometric modulators, such as 100, 1000 or 10,000 interferometric modulators. The region also can be measured in terms of area, where a region is typically at least 0.0025 mm 2 , but can be larger, such as 0.1 mm 2 , 1 mm 2 , or 10 mm. 
     In some embodiments displays may be configured such that any region of the display having a sufficient area (e.g., as discussed above) has an area ratio of the active portion to inactive portion that is substantially the same as the area ratio of the active portion to inactive portion for any other region of the display having a sufficient area. Thus, in such embodiments, the area ratio of the active portion to inactive portion is substantially uniform throughout the entire surface of the display. The actual area ratio of the active portion to inactive portion of the displays discussed herein can be any of a broad variety of values, according to the desired appearance of the display. In many embodiments, the amount of active area is maximized. 
     In other embodiments, when a display with properties other than uniform area ratio of the active portion to inactive portion, is desired, such a display can be designed in accordance with the teachings discussed herein for ordering pixels in a non-rectangular array and for arranging interferometric modulators within those pixels. For example, for circular displays in which the outer portion is desired to have a greater area ratio of the active portion to inactive portion, a design such as that shown in  FIG. 7  may be used. The pixel size in this embodiment increases at the outer regions of the display. The principles described herein also can be used to create a display in which the inner portion of a circle has a greater area ratio of the active portion to inactive portion, or any of a variety of different configurations according to the desired shape and appearance of the display. 
     The embodiments discussed herein are those presently preferred and are described so that an understanding of the present invention can be gained. There are, however, many configurations of non-rectangular arrays containing interferometric modulators not specifically described herein but in which the present invention is embodied. The invention should therefore not be seen as limited to the particular embodiments described herein, but rather, it is understood that the present invention has wide applicability with respect to non-rectangular arrays containing interferometric modulators. The invention may be embodied within a form that does not provide all of the features and benefits set forth herein, as some features may be used or practiced separately from others. All modifications, variations, or equivalent arrangements and implementations that are within the scope of the attached claims should therefore be considered within the scope of the invention.