US20100039695A1 - Methods for measurement and characterization of interferometric modulators - Google Patents

Methods for measurement and characterization of interferometric modulators Download PDF

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Publication number
US20100039695A1
US20100039695A1 US12/367,428 US36742809A US2010039695A1 US 20100039695 A1 US20100039695 A1 US 20100039695A1 US 36742809 A US36742809 A US 36742809A US 2010039695 A1 US2010039695 A1 US 2010039695A1
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interferometric modulator
voltage
mems
current
movable
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Alok Govil
Kasra Khazeni
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SnapTrack Inc
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Qualcomm MEMS Technologies Inc
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Publication of US20100039695A1 publication Critical patent/US20100039695A1/en
Assigned to SNAPTRACK, INC. reassignment SNAPTRACK, INC. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: QUALCOMM MEMS TECHNOLOGIES, INC.
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/12—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means
    • G01D5/14—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage
    • G01D5/24—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by varying capacitance
    • G01D5/241—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by varying capacitance by relative movement of capacitor electrodes
    • G01D5/2417—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using electric or magnetic means influencing the magnitude of a current or voltage by varying capacitance by relative movement of capacitor electrodes by varying separation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B81—MICROSTRUCTURAL TECHNOLOGY
    • B81C—PROCESSES OR APPARATUS SPECIALLY ADAPTED FOR THE MANUFACTURE OR TREATMENT OF MICROSTRUCTURAL DEVICES OR SYSTEMS
    • B81C99/00—Subject matter not provided for in other groups of this subclass
    • B81C99/0035—Testing
    • B81C99/0045—End test of the packaged device
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/28—Testing of electronic circuits, e.g. by signal tracer
    • G01R31/282—Testing of electronic circuits specially adapted for particular applications not provided for elsewhere
    • G01R31/2829—Testing of circuits in sensor or actuator systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/28—Testing of electronic circuits, e.g. by signal tracer
    • G01R31/2832—Specific tests of electronic circuits not provided for elsewhere
    • G01R31/2836—Fault-finding or characterising
    • G01R31/2837—Characterising or performance testing, e.g. of frequency response
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B81—MICROSTRUCTURAL TECHNOLOGY
    • B81B—MICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B2201/00—Specific applications of microelectromechanical systems
    • B81B2201/04—Optical MEMS
    • B81B2201/042—Micromirrors, not used as optical switches

Definitions

  • Microelectromechanical systems 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.
  • interferometric modulator or interferometric light modulator refers to a device that selectively absorbs and/or reflects light using the principles of optical interference.
  • 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.
  • 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.
  • 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.
  • a method of determining a restoring force of a movable layer of a microelectromechanical system (MEMS) device including applying a driving signal to the MEMS device, the MEMS device including a movable electrode and a fixed electrode, where the driving signal induces movement of the movable electrode relative to the fixed electrode, measuring a current through the MEMS device during movement of the movable electrode, identifying frequency components of the measured current, and utilizing the frequency components of the measured current to determine the restoring force acting on the movable electrode.
  • MEMS microelectromechanical system
  • a method of characterizing mechanical characteristics of a microelectromechanical system (MEMS) device including a movable layer including placing the MEMS device in a low-pressure environment, applying a driving signal to the MEMS device to induce movement of the movable layer, measuring a current through the MEMS device during movement of the movable layer, and determining a frequency at which the movable layer oscillates.
  • MEMS microelectromechanical system
  • a device including a microelectromechanical system (MEMS) device including a movable layer, circuitry configured to apply a driving signal to the MEMS device to induce movement of the movable layer, measure a current through the MEMS device, determine a frequency at which the movable layer oscillates, and determine a restoring force acting on the movable layer.
  • MEMS microelectromechanical system
  • a device including means for inducing movement of a movable layer of a microelectromechanical system (MEMS) device, means for measuring a current through the MEMS device, means for determining a frequency at which the movable layer oscillates, and means for determining a restoring force acting on the movable layer.
  • MEMS microelectromechanical system
  • a display module including a display including a plurality of microelectromechanical system (MEMS) devices, where the MEMS devices each include a movable electrode and a fixed electrode, driver circuitry configured to drive the MEMS-based display, and monitoring circuitry configured to apply a driving signal to at least one of the plurality of MEMS devices, where the driving signal induces movement of the movable electrode relative to the fixed electrode, measure a current through the at least one of the plurality of MEMS devices, determine a frequency at which the movable layer oscillates, and determine a restoring force acting on the movable layer.
  • MEMS microelectromechanical system
  • 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 relaxed 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. 4 is an illustration of a set of row and column voltages that may be used to drive an interferometric modulator display.
  • FIG. 5A illustrates one exemplary frame of display data in the 3 ⁇ 3 interferometric modulator display of FIG. 2 .
  • FIG. 5B illustrates one exemplary timing diagram for row and column signals that may be used to write the frame of FIG. 5A .
  • FIG. 7A is a cross section of the device of FIG. 1 .
  • FIG. 7D is a cross section of yet another alternative embodiment of an interferometric modulator.
  • FIG. 8C is a plot of voltage versus time during the transition period of FIG. 8A for a specific source current.
  • FIG. 14 is a plot illustrating a driving step signal applied to an interferometric modulator, and the measured current in response.
  • FIG. 17A is a plot of a driving voltage signal as a function of time.
  • FIG. 17B is a plot of position of an interferometric modulator as a function of time when the driving signal of FIG. 17A is applied.
  • FIG. 18C is a plot of position of an interferometric modulator as a function of time when the driving signal of FIG. 18A is applied.
  • FIG. 18F is a plot of the Fourier transform of the current signal of FIG. 18E .
  • FIG. 1 One interferometric modulator display embodiment comprising an interferometric MEMS display element is illustrated in FIG. 1 .
  • the pixels are in either a bright or dark state.
  • the display element In the bright (“relaxed” or “open”) state, the display element reflects a large portion of incident visible light to a user.
  • the dark (“actuated” or “closed”) state When in the dark (“actuated” or “closed”) state, the display element reflects little incident visible light to the user.
  • 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.
  • 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 gap with at least one variable dimension.
  • one of the reflective layers may be moved between two positions. In the first position, referred to herein as the relaxed position, the movable reflective layer is positioned at a relatively large distance from a fixed partially reflective layer.
  • the processor 21 is also configured to communicate with an array driver 22 .
  • the array driver 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 .
  • FIG. 2 illustrates a 3 ⁇ 3 array of interferometric modulators for the sake of clarity, the display array 30 may contain a very large number of interferometric modulators, and may have a different number of interferometric modulators in rows than in columns (e.g., 300 pixels per row by 190 pixels per column).
  • FIG. 3 is a diagram of movable mirror position versus applied voltage for one exemplary embodiment of an interferometric modulator of FIG. 1 .
  • the row/column actuation protocol may take advantage of a hysteresis property of these devices as illustrated in FIG. 3 .
  • An interferometric modulator 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.
  • 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.
  • 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.
  • a frame of an image may be created by sending a set of data signals (each having a certain voltage level) across 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 a first row electrode, actuating the pixels corresponding to the set of data signals.
  • the set of data signals is then changed to correspond to the desired set of actuated pixels in a second row.
  • a pulse is then applied to the second row electrode, actuating the appropriate pixels in the second row in accordance with the data signals.
  • the first row of pixels are unaffected by the second row pulse, and remain in the state they were set to during the first row pulse. This may be repeated for the entire series of rows in a sequential fashion to produce the frame.
  • the frames are refreshed and/or updated with new image 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 image frames may be used.
  • 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 .
  • actuating a pixel involves setting the appropriate column to ⁇ V bias , and the appropriate row to + ⁇ V, 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 + ⁇ V, 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.
  • the pixels Prior to writing the frame illustrated in FIG. 5A , the pixels can be in any state, and in this example, all the rows are initially 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.
  • FIGS. 6A and 6B 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.
  • 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 45 , an input device 48 , and a microphone 46 .
  • the housing 41 is generally formed from any of a variety of manufacturing processes, including injection molding, and vacuum forming.
  • 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 includes removable portions (not shown) that may be interchanged with other removable portions of different color, or containing different logos, pictures, or symbols.
  • the components of one embodiment of exemplary display device 40 are schematically illustrated in FIG. 6B .
  • the illustrated exemplary display device 40 includes a housing 41 and can include additional components at least partially enclosed therein.
  • 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 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 provides power to all components as required by the particular exemplary display device 40 design.
  • 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 .
  • the transceiver 47 can be replaced by a receiver.
  • 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 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.
  • 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 driver 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 driver 22 .
  • 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 driver 22 .
  • the array driver 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's x-y matrix of pixels.
  • driver controller 29 is a conventional display controller or a bi-stable display controller (e.g., an interferometric modulator controller).
  • array driver 22 is a conventional driver or a bi-stable display driver (e.g., an interferometric modulator display).
  • a driver controller 29 is integrated with the array driver 22 .
  • 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 .
  • 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.
  • 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.
  • power supply 50 is a rechargeable battery, such as a nickel-cadmium battery or a lithium ion battery.
  • power supply 50 is a renewable energy source, a capacitor, or a solar cell, including a plastic solar cell, and solar-cell paint.
  • power supply 50 is configured to receive power from a wall outlet.
  • 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 driver 22 .
  • the above-described optimization may be implemented in any number of hardware and/or software components and in various configurations.
  • FIGS. 7A-7E illustrate five different embodiments of the movable reflective layer 14 and its supporting structures.
  • FIG. 7A is a cross section of the embodiment of FIG. 1 , where a strip of metal material 14 is deposited on orthogonally extending supports 18 .
  • the moveable reflective layer 14 of each interferometric modulator is square or rectangular in shape and attached to supports at the corners only, on tethers 32 .
  • the moveable reflective layer 14 is square or rectangular in shape and suspended from a deformable layer 34 , which may comprise a flexible metal.
  • FIG. 7E an extra layer of metal or other conductive material has been used to form a bus structure 44 . This allows signal routing along the back of the interferometric modulators, eliminating a number of electrodes that may otherwise have had to be formed on the substrate 20 .
  • the interferometric modulators function as direct-view devices, in which images are viewed from the front side of the transparent substrate 20 , the side opposite to that upon which the modulator is arranged.
  • the reflective layer 14 optically shields the portions of the interferometric modulator on the side of the reflective layer opposite the substrate 20 , including the deformable layer 34 . This allows the shielded areas to be configured and operated upon without negatively affecting the image quality. For example, such shielding allows the bus structure 44 in FIG. 7E , which provides the ability to separate the optical properties of the modulator from the electromechanical properties of the modulator, such as addressing and the movements that result from that addressing.
  • Display devices like those based on interferometric modulator technology may be measured and characterized with one or more optical, electronic and/or mechanical techniques. Depending on the display technology, these measurements can form a part of calibration of the display module (the display “module” referred to herein includes the display panel, the display driver, and associated components such as cabling, etc.), and the measurement parameters may be stored into a non-volatile memory (e.g., NVRAM) in the display module for future use.
  • NVRAM non-volatile memory
  • Each of the five voltage difference ranges has a title reflecting its effect on the state of the interferometric modulator.
  • the five voltage difference ranges are: 1) negative actuate (“Actuated”); 2) negative hold (“Stability Window”); 3) release (“Relaxed”); 4) positive hold (“Stability Window”); and 5) positive actuate (“Actuated”).
  • approximate values of the thresholds between these input voltage difference ranges may be known, but in order to more optimally operate the interferometric modulator array, the threshold voltages can be measured with more precision.
  • the thresholds may vary from device to device, lot to lot, over temperature, and/or as the device ages. Threshold values may accordingly be measured for each manufactured device or group of devices, but doing so across the entire operational envelope may be difficult or impractical, and may not provide a real-time indication of the operational performance of the interferometric modulator.
  • One method of measuring the threshold voltages is to apply inputs of various voltage differences while monitoring the state of the interferometric modulators through observation of the optical characteristics of the interferometric modulators. This may be accomplished, for example, through human observation or by use of an optical measurement device. Additionally or alternatively, the state of the interferometric modulators may be monitored through electronic response measurement.
  • the array driver 22 of the display array 30 discussed above, may be configured to measure electrical responses of display elements in order to determine the state and/or operational characteristics of the display elements according to the methods discussed below.
  • Display devices may have one or more electrical parameters that change in relation to the optical response or optical state.
  • the interferometric modulator is set to an actuated state when the electrostatic attraction between the reflective layer and the optical stack is great enough to overcome the mechanical restorative forces working to hold the reflective layer in the relaxed state. Because the reflective layer, the optical stack, and the gap between them form two conductive plates separated by a dielectric in some embodiments, the structure has a capacitance.
  • the capacitance of the structure varies according to the distance between the two plates, the capacitance of the structure varies according to the state of the interferometric modulator. Therefore, an indication of the capacitance can be used to determine the state of the interferometric modulator.
  • such characterizations may be done after fabrication of the interferometric modulators, as a quality control measure or as a part of a refinement of a manufacturing process. In other embodiments, the characterizations may be done during normal operation of the interferometric modulator, in order to determine whether certain characteristics have changed over time or in response to changes in operating conditions.
  • FIG. 8B depicts a plurality of simulated voltage measurements as functions of time for a plurality of different source currents I 0 ranging between 1 ⁇ A and 0.1 mA.
  • FIG. 8C depicts a simulated voltage for a particular source current 108 b between 1 ⁇ A and 0.1 mA.
  • the source current I 0 can be selected based upon the characteristics of the interferometric modulator, as well as the desired response for testing purposes. For example, for an ideal interferometric modulator having a load capacitance of 1 pF, ignoring inductive or resistive effects, a constant source current of 1 ⁇ A will charge the device to the 10 V range in 10 ms, and a 10 ⁇ A will charge the device to the 10 V range in 1 ms. Thus, for an expected voltage range within which the transition voltage is expected to be identified and a desired time period, an appropriate source current value can be selected. As described with respect to FIG. 8B , the source current may also be selected such that the first peak at the beginning of the transition voltage will correspond to the actuation voltage of the interferometric modulator.
  • the measured voltage during the transition period can be used to provide an indication of the value of the change in capacitance. Because each of the source current, the transition time, and the transition voltage are either known or can be determined from the measured voltage, the shape of the voltage plot in the transition region can provide an indication of the amount of capacitance change during the actuation, and can be compared to predicted values for the capacitance change.
  • Such an embodiment of a characterization method enables the identification of transition voltages without the need for (but may allow for) an optical measurement instrument to determine the state of the interferometric modulator, and can be done using relatively simple testing equipment.
  • the testing process can be done over a substantially long period of time relative to the actuation time of the interferometric modulator, and does not require (but may allow for) the identification of a short-term discontinuity in a measured parameter such as current.
  • this characterization method can be used to test the actuation voltages of an array of interferometric modulators connected in parallel.
  • actuation of one interferometric modulator will drive others away from concurrent actuation as charge is drawn to the actuating modulator(s). This will reduce the charge on the non-actuated modulators and may cause the movable layer of the non-actuated modulators to move slightly away from the fixed electrode.
  • the voltage across the array of interferometric modulators will remain substantially constant as the modulators in the array successively actuate, until all modulators have actuated.
  • the actuation voltage of an array of interferometric modulators can thus be determined from an analysis of the voltage across the array as a function of time, in similar fashion to that described above.
  • the plot 110 contains a pre-transition region 112 , a transition region 114 , and a post transition region 116 .
  • the discontinuity within the transition region 114 may be used to identify an actuation voltage Va.
  • controlled impedance may be used to drive an interferometric modulator while voltage across the modulator is measured.
  • FIG. 10 schematically depicts a circuit 130 including a voltage source 132 , a resistor 134 , and an interferometric modulator 136 which functions as a variable capacitor.
  • the use of a resistor 134 in the circuit 130 which is sufficiently large will keep the impedance substantially constant in the path of the voltage drive and the interferometric modulator, regardless of the state of the interferometric modulator.
  • the interferometric modulator 136 shown in FIG. 10 may be an array of interferometric modulators arranged in parallel.
  • FIG. 11A is a plot 140 of voltage across such an array of interferometric modulators as a function of charge.
  • a voltage sufficient to drive the interferometric modulators to a collapsed state is provided via voltage source 132 , the voltage across the interferometric modulators increases as charge accumulates, as can be seen in section 142 of the plot.
  • the actuation voltage is reached, one or more of the interferometric modulators in the array will begin to actuate.
  • the voltage across a large array e.g.
  • interferometric modulator elements greater than 100 interferometric modulator elements of interferometric modulators will remain substantially constant during this actuation period 144 , as the overall charge on the interferometric modulators is increasing and actuating interferometric modulators pull charge from other non-actuating interferometric modulators. Once the array of modulators have all actuated, the voltage continues to increase, as can be seen in section 146 of the plot.
  • the voltage across the interferometric modulators decreases until the release voltage is reached, as can be seen in region 148 .
  • the voltage remains substantially constant as the charge decreases, as can be seen in region 150 .
  • the voltage across the interferometric modulator during actuation may not remain substantially constant, but may instead decrease slightly during actuation before continuing to increase after actuation.
  • a plot 160 of voltage across an interferometric modulator as a function of time is shown in FIG. 11B . It can be seen from the figure that the increase in voltage is initially steep, as the capacitance of the unactuated interferometric modulator is lower than the capacitance of the actuated interferometric modulator. After an actuation period during which the voltage decreases somewhat, the voltage continues to increase. After actuation, the increase is less steep than when the interferometric modulator was unactuated, as the capacitance is higher in the actuated state than in the non-actuated state.
  • FIGS. 12A and 12B are plots of voltage as a function of time over a large array of interferometric modulators driven in parallel, where a large resistor is placed in series with the array.
  • a large resistor may have a resistance of 1 M ⁇ , although resistors having a higher or lower resistance may be used, and multiple resistors may be used to provide a desired level of resistance.
  • the square driving waveform 172 a spans both the positive and negative hysteresis windows of the interferometric modulator, and the measured voltage response is shown as signal 174 a.
  • FIG. 12A the square driving waveform 172 a spans both the positive and negative hysteresis windows of the interferometric modulator, and the measured voltage response is shown as signal 174 a.
  • the driving waveform 172 b spans only the positive hysteresis windows of the interferometric modulators, and the measured voltage response is shown as signal 174 b.
  • periods of substantially constant voltage over time such as sections 176 of the figures are indicative of transition voltages, as discussed above.
  • FIG. 12C illustrates an alternate driving signal 178 which may be used in such an embodiment.
  • the signal 178 alternates between an upper voltage 179 a which may be greater than the positive actuation voltage of the interferometric modulator, a bias voltage 179 b which may be between the positive release voltage of the interferometric modulator and the negative release voltage of the interferometric modulator, and a lower voltage 179 c which may be lower than the negative actuation voltage of the interferometric modulator.
  • the driving voltage will span both the positive hysteresis window and the negative hysteresis window of the interferometric modulator, and may facilitate the identification of release voltages, as the voltage remains at the bias voltage for an extended period of time, in contrast to the driving signal 172 a of FIG. 12A .
  • the bias voltage may be substantially zero, but any suitable bias voltage may be used.
  • the current through an interferometric modulator can be measured and analyzed in order to characterize the dynamic behavior of the interferometric modulator.
  • the capacitance of the interferometric modulator changes according to the position of the movable membrane with respect to other conducting membranes, which may be fixed conducting membranes. The change of capacitance will result in the generation of current through a suitably chosen circuit when a non-zero voltage is applied across the interferometric modulator.
  • the current as a function of time may be monitored and used to determine information such as the position of the movable membrane as a function of time.
  • a trans-impedance amplifier may be used to measure current by converting an input current to a voltage output proportional to the input current. The voltage signal can then be recorded, and because the relationship between the input current and the voltage output are known based upon design of the trans-impedance amplifier, the current as a function of time can readily be determined.
  • FIGS. 13A , 13 B, and 13 C illustrate various circuit designs which may be utilized in such a characterization process.
  • FIG. 13A schematically illustrates a circuit 180 comprising an interferometric modulator 182 , resistors 184 a, 184 b, 184 c, and an amplifier 186 .
  • resistors 184 a and 184 b may comprise 1 ⁇ resistors
  • resistor 184 c may comprise a 260 ⁇ resistor
  • amplifier 186 may comprise an Analog Devices AD8041 amplifier, although other suitable value or components may also be utilized, and may depend upon expected characteristics of the interferometric modulator 182 .
  • Circuit 180 functions as a non-inverting operational amplifier with gain. Output from the interferometric modulator 182 is applied to the non-inverting input of operational amplifier 186 .
  • FIG. 13B schematically illustrates an alternative circuit 190 comprising an interferometric modulator 192 , resistors 194 a, 194 b, 194 c, 194 d, 194 e, 194 f, amplifiers 196 a and 196 b, and capacitors 198 a and 198 b.
  • resistors 194 a and 194 b may comprise 27 k ⁇ resistors
  • resistor 194 c may comprise a 260 k ⁇ resistor
  • resistor 194 d may comprise a 200 k ⁇ resistor
  • resistor 194 e may comprise a 1 k ⁇ resistor
  • resistor 194 f may comprise a 15 k ⁇ resistor
  • amplifiers 196 a and 196 b may comprise Analog Devices AD8041 amplifiers
  • capacitor 198 a may comprise an 8.2 pF capacitor
  • capacitor 198 b may comprise a 100 pF capacitor, although other suitable values or components may also be utilized.
  • FIG. 13C schematically illustrates another alternative circuit 200 comprising an interferometric modulator 202 , resistors 204 a - 204 l, amplifiers 206 , capacitors 208 , signal generator 210 and signal analysis module 212 (e.g., an oscilloscope or other signal analysis circuitry and/or logic).
  • an interferometric modulator 202 comprising an interferometric modulator 202 , resistors 204 a - 204 l, amplifiers 206 , capacitors 208 , signal generator 210 and signal analysis module 212 (e.g., an oscilloscope or other signal analysis circuitry and/or logic).
  • resistors 204 a and 204 f may comprise 51 ⁇ resistors
  • resistors 204 b and 204 c may comprise 680 ⁇ resistors
  • resistors 204 d and 204 l may comprise 8.2 ⁇ resistors
  • resistor 204 e may comprise a 1 ⁇ resistor
  • resistor 204 f may comprise a 51 ⁇ resistor
  • resistors 204 g and 204 i may comprise 510 ⁇ resistors
  • resistor 204 h may comprise a 62 ⁇ resistor
  • resistor 204 j may comprise a 68 ⁇ resistor
  • resistor 204 k may comprise a 620 ⁇ resistor.
  • capacitors 208 may comprise 1 ⁇ F capacitors
  • amplifiers 206 may comprise Analog Device AD811 amplifiers. Other suitable values and components may also be utilized.
  • Circuit 200 functions as a two stage circuit.
  • a first stage 214 applies a signal to the interferometric modulator 202 , which may comprise a signal applied from signal generator 210 or a signal proportional to Vdc shown in FIG. 13C .
  • a second stage 216 comprises non-inverting operational amplifiers with gain which are used to measure the current through the interferometric modulator 202 .
  • the current as a function of time I(t) through the interferometric modulator 202 can be measured, utilizing any suitable measurement apparatus, which may utilize one of the circuits described with respect to FIGS. 13A-13C .
  • the charge as a function of time Q(t) on the interferometric modulator can be determined by integrating the current as a function of time, yielding the following relationship:
  • the interferometric modulator is operated under damping conditions, where air located between the two layers will have a damping effect on the motion of the interferometric modulators. In other embodiments, however, the interferometric modulator may be operated substantially in a vacuum, so that the damping effect is negligible.
  • the initial current is dependent upon the initial state of the interferometric modulator. Subsequently, during the change of state of the interferometric modulator, the current changes in response to the change of state of the interferometric modulator device.
  • FIG. 14 is a plot 220 illustrating a driving voltage signal 222 and a measured current response 224 for an interferometric modulator as measured on an oscilloscope.
  • the vertical scale of the measured current response 224 is extended vertically relative to the driving signal 222 such that each vertical increment represents 2V per division for driving signal 222 , while each vertical increment represents 0.5V per division for current response 224 .
  • Each horizontal increment represents 0.1 ms for both signals.
  • the driving voltage signal 222 comprises a step function voltage change. Initial application of the driving voltage signal 222 causes a rapid and strong spike in the measured current response 224 . Actuation of the interferometric modulator occurs at the first dip 226 in the measured current response 224 .
  • integrating the current for the period of time before the interferometric modulator begins to move thus gives a measure of the initial state of the interferometric modulator. Further, integrating the current during the time when the interferometric modulator is moving gives a measure of the dynamic mechanical response of the interferometric modulator. As well, integrating the current for the entire time period gives a measure of the final state of the interferometric modulator.
  • the capacitance of the interferometric modulator as a function of time is given by the following:
  • the capacitance as a function of time can be determined. This can used to calculate the position of the membrane as a function of time x(t), using the following relationship, where ⁇ 0 is the permittivity of free space, A is the area of the interferometric modulator, and d e is the defined as d/k, where d is the height of the dielectric layer and k is the dielectric constant of the dielectric layer:
  • V offset is the offset voltage
  • K is the spring constant of the movable membrane
  • g off is the distance between the dielectric layer and the movable layer when the offset voltage is applied
  • m the mass of the movable membrane:
  • the dynamic characteristics of the interferometric modulator can be accurately determined. For instance, the position as a function of time can be utilized to determine, for example, the actuation time of an interferometric modulator. A wide variety of other parameters can be determined in this manner.
  • frequency analysis may be performed on measured currents resulting when an interferometric modulator is driven by an input voltage.
  • experimental circuit arrangements similar to those of FIGS. 13B and 13C may be utilized to drive the interferometric modulators and measure the resultant current, although a wide variety of suitable circuits may be utilized. Analysis of the measured currents may in some embodiments enable a determination of transition voltages for a MEMS device, and in other embodiments enable determination of a restoring force acting on a movable layer within a MEMS device.
  • the driving voltage may produce a non-linear response, due to movement of the movable membrane as the voltage changes.
  • the response of the interferometric modulator may be substantially linear.
  • the response of the interferometric modulator is substantially linear with little distortion, and it can be determined that the voltage range of the driving signal is outside of the hysteresis range of the interferometric modulator.
  • FIG. 15B is a plot 240 of the output of an oscilloscope output when another driving sinusoidal voltage 242 is used to drive the same testing circuit used with respect to FIG. 15A , illustrating the measured current response 244 .
  • the current response 244 of FIG. 15B shows significant distortion. This distortion is evident in the calculated FFT 246 of the measured current response 244 , which contains not only the expected peak 248 a at the driving frequency, but also several substantially large peaks 248 b, 248 c, 248 d, 248 e, 248 f, 248 g, 248 h, at each of the harmonics of the driving frequency.
  • This non-linear response is indicative that at least a portion of the range of the driving voltage is within the hysteresis window of the interferometric modulator.
  • frequency analysis of measured current may be utilized to determine the natural resonant frequency of an interferometric modulator. This, in turn, may be utilized to determine the restoring force of a movable layer of the interferometric modulator.
  • an interferometric modulator can be modeled as a spring attached to the top plate of a capacitor.
  • FIG. 16 schematically illustrates such a model 250 , where a voltage source 252 is applied across a resistor 254 and an interferometric modulator 256 , the movable membrane of the interferometric modulator 256 being supported by a spring 258 having a spring constant K s .
  • the distance from the bottom plate of the capacitor to the top plate is defined as x
  • the thickness of the dielectric layer (not shown) which sets that minimum gap between the top and bottom plates
  • d the maximum distance from the top plate to the bottom plate
  • D the maximum distance from the top plate to the bottom plate
  • V 2 2 ⁇ ⁇ K s ⁇ 0 ⁇ A ⁇ ( D - x min ) ⁇ [ d ⁇ ( 1 k - 1 ) + x min ] 2 . ( 10 )
  • the small-amplitude natural frequency vibration f of the top plate around x min can be defined as follows, where m represents the mass of the top plate:
  • FIG. 17A depicts a driving voltage as a function of time. It can be seen that the voltage increases from 0 to 5 volts in roughly 5 ⁇ s.
  • the voltage across the interferometric modulator is calculated to be that shown in FIG. 17E . It can be seen that the voltage across the interferometric modulator is substantially similar to the applied voltage, and that the interferometric modulator moves to a stable position x min , as can be calculated by equation (10), even in the absence of damping. It can also be seen that the distance travelled by the interferometric modulator is only a small portion of the distance D, so the interferometric modulator is not fully actuated.
  • FIG. 18A depicts an alternative driving voltage as a function of time. As can be seen, although the voltage increases to the same level as the driving voltage of FIG. 17A , the voltage of FIG. 18A increases from 0 to 5 volts in a shorter period of time, in roughly 0.5 ⁇ s.
  • FIG. 18B illustrates the calculated voltage across the interferometric modulator, which as before, is roughly the same as the driving voltage.
  • FIG. 18C illustrates the calculated position as a function of time
  • FIG. 18D illustrates the calculated charge as a function of time
  • FIG. 18E illustrates the calculated current as a friction of time.
  • FIG. 18F illustrates the Fourier transform of the current, from which the frequency of this oscillation can be readily determined, and which is approximately equal to that predicted by equation (11).
  • the resistance may be increased to 10 M ⁇ from 10,000 ⁇ .
  • FIG. 19A the driving voltage 260 and the measured voltage 262 across the interferometric modulator are shown. It can be seen that, although the driving voltage is similar to the driving voltage of FIG. 18A , the measured voltage in FIG. 19A now lags the driving voltage, due to the increase in resistance and resulting increase in RC time constant of the circuit.
  • FIG. 19B illustrates the calculated position as a function of time
  • FIG. 19C illustrates the charge as a function of time
  • FIG. 19D illustrates the current as a function of time.
  • the Fourier transform of the current shown in FIG. 19E , again allows determination of the frequency f.
  • Analysis of the resonant frequency of the interferometric modulators may be performed as an initial quality control measurement, and/or may be used for ongoing monitoring of the dynamic characteristics of the interferometric modulator, since the restoring force and resonant frequency may change over time, due to a change in operating conditions, may be different between interferometric modulators within an array or across different interferometric modulator arrays, or the like.
  • the analysis may be performed via a test burst, or may be performed during normal activation of the display device. In certain embodiments, one or a small number of the interferometric modulators in an array may be analyzed in this manner. Other changes to the above methods may be made, as well.
  • the capacitance of an interferometric modulator or interferometric modulator array may be measured.
  • the circuitry utilized to make such measurements may be integrated into the driver circuitry of an interferometric modulator device, such as an interferometric modulator-based display, although this measurement may be done via any other suitable circuitry, and need not be integrated into driver circuitry.
  • a periodic electrical stimulus such as a sinusoidal voltage waveform is applied across the interferometric modulator.
  • This signal may be applied by itself, or may alternately be added to a regular drive waveform, which may in certain embodiments be a DC voltage, or any other suitable interferometric modulator drive scheme.
  • This periodic sinusoidal voltage V IMOD may be represented as follows:
  • the current through the interferometric modulator as a functions of time I(t) may be defined as follows, where C IMOD is the capacitance of the interferometric modulator and V IMOD is the voltage across the interferometric modulator:
  • I IMOD C IMOD ⁇ ⁇ V IMOD ⁇ t . ( 15 )
  • I IMOD 2 ⁇ fC IMOD V 0 cos(2 ⁇ ft ).
  • the resulting current is periodic, having the same frequency as the input voltage, but 90° out of phase with the input signal.
  • V CORR V 1 cos(2 ⁇ ft ).
  • the voltage output from the mixer contains both a constant term and a time-varying term.
  • the voltage output from the mixer can be filtered in order to reduce or eliminate the time-varying term, yielding the following:
  • V FILTER ⁇ fC IMOD kV 0 V 1 . (20)
  • the resultant voltage output from the filter is thus proportional to the capacitance of the interferometric modulator.
  • the capacitance of the interferometric modulator can be determined based upon the voltage output from the filter.
  • the output is proportional to the capacitance even when the measured interferometric modulator is “leaky” and thus has a resistive component in its impedance.
  • the output is proportional to the resistive component of the impedance of the interferometric modulator.
  • the periodic input voltage may be applied in conjunction with any drive signal, and the measurement can be made at multiple DC voltage values, such as in conjunction with a DC voltage sweep, in order to determine the capacitance or impedance at various voltage levels.
  • interferometric modulator properties such as capacitance may vary depending on the state of the interferometric modulator, capacitance measurements over a variety of DC voltage levels may be made, and then used to identify transition voltages by noting changes in capacitance due to actuation or release of the interferometric modulator.
  • the input and correlation voltages may not be sinusoidal signals, but may be any other type of signals, including but not limited to square waves or triangular waves.
  • appropriate mixers may be provided utilizing only switches, simplifying the circuit design.
  • FIG. 21 schematically depicts an exemplary circuit 270 which integrates the correlation circuitry with driver circuitry.
  • This circuit may, for example, form a part of a MEMS-based display module.
  • Circuit 270 comprises an interferometric modulator array 272 along with driver circuitry configured to drive the interferometric modulator array 272 .
  • Digital logic 274 controls digital-to-analog converters 276 a and 276 b configured to provide the static (or quasi-static) driving voltages to the interferometric modulator array. Individual rows and columns of the interferometric modulator array may in certain embodiments be addressed via switches 278 a and 278 b.
  • circuit 270 comprises additional circuitry, which may be used to, for example, perform the method discussed above.
  • An additional signal such as the input signal discussed above, may be generated via a direct digital synthesis block 280 a may be used to generate an additional signal, which may be used in conjunction with an additional digital-to-analog converter 276 c.
  • the current through the interferometric modulator may be measured via a trans-impedance amplifier 282 , which may be used in conjunction with a digital-to-analog converter 276 d.
  • the output from trans-impedance amplifier may be mixed via mixer 284 a with a correlation signal generated by a direct digital synthesis block 280 b or by a digital-to-analog converter.
  • a filter 286 a may be used to filter the periodic portion of the resultant signal, and an analog-to-digital converter 288 may be used to digitize the filtered or unfiltered resultant signal.
  • mixer 284 b may be used to mix the measured current with, for example, the input signal, and filter 286 b may be used to filter the signal.
  • Measurement circuitry configured to determine either actual or average power use may be integrated into devices, particularly mobile devices or other devices where power consumption is important, in order to provide a determination of such information regarding power usage.
  • spread spectrum techniques may be utilized in the measurement of the capacitance of interferometric modulators, although these techniques may be used in the measurement of other interferometric modulator characteristics, as well.
  • a known input parameter may be applied to a system, and a resultant output signal may be used to determine an output parameter.
  • the output signal is dependent not only on the known input parameter, but also on any undesirable noise or interference in this system, complicating the measurement of the output parameter.
  • measurement of the capacitance of an interferometric modulator may be done through the measurement of current, and the capacitance calculated from the resultant current.
  • the resultant capacitance may be used to determine, for example, the hysteresis curve of the interferometric modulator.
  • the measured current may be affected by noise or interference
  • a spread-spectrum technique may be utilized to minimize the effect of this noise or interference on the measured current.
  • the output parameter determined using the measured current will be undesirably affected by this noise or interference, making the determined output parameter less accurate.
  • a known signal which has a high amount of randomness is modulated with the driving voltage applied to the interferometric modulator.
  • the known signal may be a known pseudo-random signal.
  • the known signal may be a purely random signal which is measured to obtain a known signal.
  • FIG. 22A illustrates a modulated driving voltage 290 to be applied across an interferometric modulator, wherein the driving voltage has been modulated with a known random or pseudo-random signal.
  • FIG. 22D shows an ideal demodulated current 296 resulting from the demodulation of ideal resultant current 292 using the time integral of the modulation signal as the demodulation signal.
  • FIG. 22E shows a noisy demodulated current 298 resulting from demodulation of resultant current 294 , as well as the time average 299 of the noisy demodulated current 298 . It can be seen that the time average 299 is very close to the ideal demodulated current 296 , despite the introduction of additive noise.
  • the time average 299 of the demodulated current 298 provides a measurement which can be used to determine the capacitance of an interferometric modulator.
  • this method may be performed via components integrated with the driver circuitry of an interferometric modulator array, such as an interferometric modulator display device.
  • application of unrelated pseudo-random functions for modulation and demodulation does not result in a change to the output.
  • multiple such measurements are performed simultaneously within the same system using different orthogonal pseudo-random functions, they do not interfere with each other, permitting multiple simultaneous measurements to be made on the same system.
  • the capacitance of multiple interferometric modulator pixels within an array may be simultaneously measured.

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