Abstract

Reflective displays that rely on ambient light as opposed to an internal light source have been making inroads for a variety of important applications, especially those involving mobility where power usage must be aggressively controlled. The underlying color rendering strategies for both reflective and emissive displays have largely been the same, combining three fixed, primary color subpixels to compose the rich gamut that users expect. The result, for reflective color displays, is unfavorable brightness/gamut performance since each of the color subpixels absorbs roughly 2/3 of the incident white light. We demonstrate a new technology that we call the single mirror interferometric display that overcomes such limitations with pixels whose reflectance properties can tune through a continuum of colors, including high contrast black and white reflectance states. We use an effect that we call interferometric absorption in which a thin absorbing metal layer in front of a highly reflective mirror surface selectively absorbs different colors, depending on the gap that separates the two. The gap is controlled by electrostatic actuation in a relatively simple micro-electro-mechanical-system structure. We describe this elegant and powerful color rendering principle and present experimental results for the basic pixel device as well as early system demonstrations.

© 2015 Optical Society of America

1. INTRODUCTION

A display system consists of a spatial array of pixels whose optical properties (reflection or emission) can be controlled to render two-dimensional color images. A system is needed to realize this in practice, as illustrated by the active matrix backplane system of Fig. 1, where each pixel element can be addressed via a thin film transistor switch, allowing row-by-row updating of the visual information. The optical state of each pixel is set by a voltage or current, and a given row of pixels is selected by a corresponding row of pixel switches and energized by the column drivers. Most display devices assign the primary color components of an image pixel to separate but adjacent device pixels so that three physical pixels are needed to render a single image pixel, as illustrated. Reflective display technologies have used this architecture, including the first generation micro-electro-mechanical-system (MEMS) display [1], color E-ink [2], and reflective LCD [3]. Variations on this theme for emissive technologies include RGBW subpixels [4], where the addition of a white pixel allows for added flexibility in the image rendering and, in some cases, power savings. In the case of organic light emitting diodes (OLEDs), PenTile and related arrangements use a lower density of blue and red subpixels compared to the green subpixels (RGBG) with the claim that the higher-density green subpixels can be used to specify the resolution of the display [5].

 figure: Fig. 1.

Fig. 1. Display system architecture.

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The single mirror interferometric (SMI) display takes a completely different approach in rendering an image. As opposed to having a collection of primary color subpixels to represent each image pixel, all of the device pixels on the SMI panel are identical. Each device pixel can tune its reflective color continuously across the visible spectrum and also provide high contrast black and white states. Instead of limiting the primaries to three or four choices, the SMI palette has potentially a large number of primaries to choose from.

RGB-based reflective displays exhibit less than ideal brightness and gamut performance. The brightness problem is straightforward and illustrated in Fig. 2. In order to represent a particular primary color, the other two primaries must be black, which means that only 1/3 of the incident light can at best be reflected back toward the viewer (assuming that the incident light has a flat spectrum and each color pixel reflects 1/3 of the total spectrum). This generalizes to the rendering of any color or white. The latter will be at best a neutral gray with maximum reflectivity of 33% (in most reflective LCDs, there is an additional 50% loss due to the polarizer that is needed). The lowered gamut is less obvious and has to do with leakage from the subpixels that are turned off and supposed to be black. The black state leakage, along with scattered light from imperfections and other surface reflections, conspire to degrade the saturation of colors. In the SMI display, however, the 2/3 brightness penalty is avoided since every pixel can render the correct primary color. The gamut, likewise, is not degraded by unwanted black state leakage.

 figure: Fig. 2.

Fig. 2. RGB versus SMI color rendering.

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There is one difficulty, however, in the inability of the SMI pixel to realize grayscale modulation. The rendering of full color with grayscale modulation requires spatial and/or temporal dithering where dithering artifacts must be carefully controlled. This is discussed in some detail in a later section.

In what follows, we explain how the reflective colors are realized in the SMI display system using a novel combination of interferometric absorption and MEMS actuation devices. Developmental system demonstrations are given to prove the basic principles of operation.

2. COLOR BY INTERFEROMETRIC ABSORPTION

Interferometric absorption takes place in an optical configuration that requires a mirror, a thin metallic absorbing layer, and an air gap that separates the two. Such a system, which we call the interferometric modulator (IMOD), is illustrated in Fig. 3 where the incident light first passes through the thin layer of metal before reflecting off a mirror and passing back through the same metal to the observer. The metallic layer is sufficiently thin so as to allow partial absorption and partial transmission of the light. In Appendix A, we present a simple theory that specifies the essential characteristics of the absorbing layer. The incident and reflected light interfere with one another, and the constituent spectral components in the light set up standing-wave interference patterns that differ in periodicity, following the component’s wavelength. The IMOD is essentially a programmable reflection filter that achieves its color (wavelength) selectivity by moving the mirror to align the node (null) in the interference pattern with the absorber layer. The movement of the mirror is achieved through MEMS technology, as is explained later.

 figure: Fig. 3.

Fig. 3. IMOD pixel—optical components to harness interferometric absorption.

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Referring to the illustration in Fig. 4(a), incident light at wavelength λ will interfere with its own reflection from the mirror to create a standing wave with local peaks and nulls. The first null is λ/2 from the mirror, and subsequent nulls are placed at λ/2 intervals. For that wavelength, a very thin absorber placed at one of the null positions will absorb very little energy. When the absorber is placed at the null of the red interference pattern [Fig. 4(b)], other colors are absorbed, reflecting the red with high efficiency. As the absorber moves closer to the mirror, the reflection color turns green, then blue, then black, where the colors across the visible spectrum are absorbed nearly uniformly, and finally white, when the absorber is collapsed onto the mirror, where no part of the visible spectrum is absorbed.

 figure: Fig. 4.

Fig. 4. Standing-wave electric field diagram.

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3. SOME OPTICAL DETAILS

The illustration shown in Fig. 4 indicates that the absorber is in contact with the mirror for the white state. In practice, the mirror is not a perfect reflector, and even for the most reflective metals, the light partially penetrates into the surface so that the first-order node is inside the metal near the surface (the skin depth effect). Additionally, some lubricating surface treatment is often needed to prevent the contacting surfaces from sticking to one another (or an air gap imposed by mechanical stops). Furthermore, a passivation layer is required to protect the metal absorber from contacting the metal mirror for electrostatic actuation. As such, the first-order node cannot be made coincident with the absorber for the white state. For example, when a 9 nm Al2O3 passivation and 10 nm air gap is applied, the white state reflectance is very low (45%) because the standing-wave field intensity is quite high at the absorber. Therefore, the second-order node should be used as the white state absorber location. To reduce the spatial separation of the nodes of different wavelengths, we can use a high index/low index pair of layers with appropriate thicknesses as illustrated in Fig. 5, where the secondary null can be accessible for the white state with approximate alignment across an appreciable fraction of the visible spectrum. At the black state, minimum reflection across the entire visible spectrum is desired. Again, the simple absorber layer on its own does not achieve the best performance because of the effects of dispersion (in the absorber and the mirror materials), and impedance matching layers of high/low dispersion dielectric materials can be incorporated into the design.

 figure: Fig. 5.

Fig. 5. Dielectric coatings to enhance the interferometric absorptive colors. The red/green/blue curves indicate the electric field intensities for 630, 530, and 440 nm light. Light enters from the right, and the mirror reflective surface (AlCu) is on the left side of the figure.

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By using well-established thin film optimization procedures [6], we arrive at a prescription for dielectric layers for the mirror as well as the impedance matching layers for the absorbing layer, as shown in Fig. 5. The corresponding reflectivities for various gap values are plotted in Fig. 6. The reflective spectra can also be characterized by a corresponding plot on a colorimetric diagram—this time with the air gap as a parameter as illustrated in Fig. 7. The spiral of colors straddles the sRGB color periphery (the blue triangle), as the air gap varies from 10 to 640 nm. As the air gap is further increased, the colors become more and more saturated to a point until either the interference pattern becomes washed out due to coherence limits or multiple higher-order colors start to mix.

 figure: Fig. 6.

Fig. 6. Reflectivity at various gap values.

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 figure: Fig. 7.

Fig. 7. Interferometric colors plotted on uv as a function of air gap (the trajectory starts near the X-marked location and spirals clockwise as the air gap is increased from 10 to 640 nm with a 5 nm step).

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These colors thus characterized correspond to light incident normal to the mirror surface. The SMI pixel by itself behaves as a colored mirror and would have significant viewing issues without an adequate diffuser that would enable the rendered color to be viewed across a range of viewing angles. In addition, a diffuser with sufficient haze is needed to partially compensate for a shift in the reflective spectrum that is common to interferometric optical devices.

If a diffuser is placed on the display, between the reflective pixel and the viewer, incident light is scattered before passing through the pixel optics and the reflected light is scattered once more before reaching the observer, thus widening the viewing angle range. An optical diffuser can be characterized by its haze value, which represents the percentage of incident light power scattered more than 2.5° away from a collimated incident beam [7]. As the haze is increased, the viewing angle range increases at the cost of reduced color saturation. Figure 8 shows the desaturating characteristic (calculated) of using a diffuser with a haze of 78% for the viewing condition where the viewing direction is 8° from surface normal and the illumination is a 50/50 mixture of diffuse and collimated (directed 20° off normal of surface) light. The diffuser haze of 78% does not materially affect the stated 343 ppi resolution, with the display substrate glass thickness of 0.5 mm.

 figure: Fig. 8.

Fig. 8. Reflective color spiral with the application of a diffuser in a typical indoor illumination condition (50% diffused and 50% collimated light).

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The materials used in fabricating the IMOD pixels are widely available, and processes for their deposition and etch do not present significant challenges for manufacturing, with one exception. The in-plane stresses and vertical stress gradients must be properly controlled so as to keep the mirror relatively flat. This is discussed in the next section.

4. ELECTROMECHANICS OF THE PIXEL

The requirements for the electromechanics of the pixel are to (1) allow accurate control of the mirror movement by balancing the applied electrostatic force against mechanical restoration forces (i.e., hinges) and (2) maintain mirror flatness so as to not adversely impact the color gamut. The electrostatic control of a two-plate capacitive structure is well known and was used in the first interferometric absorptive color display [1].

The SMI shown in Fig. 9 is configured as a three-terminal device to minimize the mirror curvature for a given actuation range and to linearize the displacement-voltage actuation curve. If the mirror is not sufficiently thick, the structure will bend during actuation, which will result in desaturation of the reflective colors since different parts of the bent mirror will have different gaps to the absorber, giving rise to different colors. The mirror, which is the center terminal, is driven by TFT electronics to position it at the desired location somewhere in between the two voltage-biased outer terminals, which have fixed positions. Equilibrium between the electrostatic and mechanical forces exists when

F=K(xx0)(VdVb)22ϵAx2+Vd22ϵA(dx)2=0,
where the voltages and displacements are defined in Fig. 9. K is the restoring force on the mirror provided by the hinges shown in Fig. 10, A is the area of the mirror, and ϵ is the dielectric permittivity of air. This equilibrium state is stable only if
0>Fx=K+ϵA(VdVb)2x3+ϵAVd2(dx)3,
thus limiting the range across which the mirror can be stably controlled.

 figure: Fig. 9.

Fig. 9. Three-terminal configuration of SMI pixel. The mirror is in between the top (common) and bottom (bias) electrical terminals and driven through the TFT switch. Although not shown, the top terminal and absorber are fixed to a thick dielectric layer on the top and the substrate, respectively, and do not move, while the mirror is suspended by mechanical hinges to a quiescent position.

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 figure: Fig. 10.

Fig. 10. Three-dimensional exploded view of the SMI MEMS. The mirror is suspended by four hinges and has a stiffener in the middle to maintain flatness. The top terminal consists of a metal layer covered by a thick dielectric to form a mechanical platform for TFT electronics.

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The mirror is suspended by hinges on all fours sides and is rotationally symmetric (four-fold) to resist tilting. The center portion of the mirror is thicker than the hinges due to the addition of a stiffener to decouple the requirement of maintaining a very flat and stiff mirror and the requirement of having adequately compliant hinges to maintain low-power operation. Since the mirrors have multiple optical coatings, the stresses of the thin films must be precisely controlled to maintain flatness throughout all operating conditions.

To drive the mirror to a specific position, a voltage is applied to the mirror through the TFT that is controlled by a row select pulse of duration less than (FrNr)1, where Fr is the refresh rate of the display and Nr is the number of rows in the display. The mirror movement is comparatively slower than the row select pulse due to the significant squeezed-film damping at such small gaps. Since the mirror has not yet settled by the time the TFT isolates the mirror from the data lines, the voltage on the mirror varies as the mirror is moving since the three-terminal device functions as a capacitive divider. This provides a form of negative feedback that increases the stable travel range of this electromechanical actuator by reducing the quadratic increase in electrostatic forces as electrical terminals are brought together. Figure 11 shows the mirror position as a function of applied voltage for the cases in which (1) the mirror voltage is held constant until the mirror settles and (2) the mirror voltage is pulsed briefly and then isolated and allowed to settle to the voltage level determined by the capacitive divider.

 figure: Fig. 11.

Fig. 11. Mirror position as a function of voltage applied.

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The kink in the response curve at the 140 nm mirror position is due to the compound spring effect when a specifically designed feature of the mirror hinge contacts the absorber terminal first before the mirror makes full contact with the absorber, thus increasing the mechanical restoring force to aid mirror peel back.

In order to monitor the characteristics of the pixel to account for variations in the manufacturing process and aging, a circuit measures the current flowing into a group of SMI pixels that is actuated by a voltage ramp. The circuit shown in Fig. 12 uses a high-precision voltage-controlled-current-source that is driven in a closed loop to minimize noise. The output of the op-amp, which indicates the amount of current going into the group of SMI pixels, is used to infer the position of the mirror as a function of voltage. Small regions of the display panel are scanned systematically to determine the uniformity and aging of the panel over time and environmental conditions.

 figure: Fig. 12.

Fig. 12. Circuit to measure current flowing into SMI pixels as it is actuated. A ramp is applied to the positive terminal of the op-amp to drive the mirror through its entire range. The output of the analog-to-digital converter is the current drawn by the group of SMI pixels.

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5. IGZO TFT/MEMS INTEGRATION

The SMI display panel architecture is described in Fig. 13, showing the active matrix backplane as an array of transistor switches that allows individual mirror connections to be made to the corresponding column electrode that is driven by a silicon CMOS circuit. Also shown is an integrated row driver circuit that is made directly on the glass using the same TFT process as for the backplane switches. This is common practice in the display industry using both low temperature poly silicon (LTPS) [8] and indium gallium zinc oxide (IGZO) [9,10] technologies. What is unique in our approach is the integration of the IGZO TFT and MEMS processes in a way that does not compromise the performance of either. A detailed discussion of the process integration techniques that were developed is outside the scope of this paper, but we describe the general fabrication process sequence, pointing out the key process steps that were optimized to yield the desired outcome. We also highlight the TFT performance characteristics that were achieved using our integrated process.

 figure: Fig. 13.

Fig. 13. SMI panel system architecture. IGZO TFT technology was developed to provide both the pixel switches as well as to implement an integrated row driver.

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The pixel architecture is shown schematically in Fig. 14, where the MEMS device layers are shown to be fabricated first, followed by the TFT sections that are built on top of the superstructure that houses the MEMS portions. Light enters through the transparent glass substrate and is reflected back through the absorber toward the viewer. The TFT is shielded from the light by the mirror and black matrix patches that block the light from entering the panel between the mirrors. All of the air gaps are defined during the process by a sacrificial material that is etched away as the last step before packaging by a vapor phase process. The sacrificial material that we used is sputtered Mo, and the etchant is XeF2. The top dielectric roof also serves as the platform on which the TFTs are built. The sequence of fabrication is important as the TFT device characteristics are known to be very sensitive to process temperature and ambient gas conditions. Building the MEMS first allows for minimal perturbation of the TFT, but care still needs to be taken since the release etch and subsequent encapsulation processes can adversely affect the device characteristics.

 figure: Fig. 14.

Fig. 14. Exploded view of the MEMS + IGZO TFT pixel built up starting from the viewing side.

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The TFT technology chosen is IGZO, which is a metal oxide semiconductor, typically prepared by sputter deposition using a compound indium-oxide–gallium-oxide–zinc-oxide target [11]. The device geometry used in our development is a bottom-gate configuration with etch stop layer as illustrated in Fig. 15. The transistor is an n-type field-effect transistor in which the application of a gate bias controls the current flow between the source and drain contacts.

 figure: Fig. 15.

Fig. 15. Bottom-gate configuration with etch stop layer (ESL). The ESL protects the IGZO surface (back-channel) from process damage during source and drain (S/D) metal etching.

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While many have reported on IGZO and related oxide transistors in the literature, we are the first, to the best of our knowledge, to report on a MEMS/TFT integrated process to implement both an active matrix backplane and integrated row drivers. The gate insulator is plasma enhanced chemical vapor deposition (PECVD) SiO2, and the metal contacts are made with sputtered molybdenum. The IGZO active channel is also sputtered. Typical device transfer characteristics (Ids versus Vgs at Vds=0.1 and 10.1 V) of the fabricated IGZO TFTs with W/L=4μm/8μm are shown in Fig. 16. The field-effect mobility (μsat) in the saturation regime is higher than 10cm2/V-sec, and the devices exhibit sharp switching characteristics (exceeding the display application requirements) as we can see the subthreshold slope (SS) of 150mV/dec. The inset table summarizes μsat, SS, and threshold voltage (Vth).

 figure: Fig. 16.

Fig. 16. Typical device transfer curves. The device dimensions are W/L=4μm/8μm, and nine devices in 6 glass wafer are plotted together. The inset table summarizes the TFT parameters. The curves taken from different parts of the wafer are overlaid together.

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6. SMI IMAGE RENDERING

To display images in full color, almost all displays, emissive or reflective, combine multiple display elements (more than one per image pixel to be rendered) to achieve the desired color appearance. These display elements can be subpixels for spatial mixing or pixels that are temporally modulated within each video frame to mix colors in the time domain. The human visual system has limited resolution, in terms of both spatial and temporal acuity. For instance, normal eyes cannot resolve pixels that are smaller than 50cycles/deg, which corresponds roughly to a pixel width of 43 μm, at a viewing distance of 0.25 m, nor track temporal fluctuations in excess of 30 Hz [12]. Therefore, when a displayed image is observed under normal viewing conditions, the human visual system blends the colors of those display elements, both spatially and temporally.

Each pixel in the SMI display is capable of changing its color across the visible spectrum, including the important black and white states. Because it does not have a gray level control capability, however, general images must be rendered through a spatial or temporal dithering (or a combination of the two) approach. Each pixel in a given source image is mapped onto the gamut volume that is accessible by the SMI system. Each SMI pixel is then assigned to one of the many available primaries (five is the minimum, consisting of R, G, B, black, and white, but can be as many as 16 in our current system as limited by the driver electronics) by halftone techniques such as error diffusion and vector screening [13] in which the difference between the source and human visual perception of rendered images is minimized following well-defined algorithms. Figure 17 shows a computer generated image rendering with a palette of 16 primary colors available in the SMI system, using spatial dithering.

 figure: Fig. 17.

Fig. 17. Computer simulation of a spatially dithered image using 16 SMI primary colors. This simulation used an error diffusion algorithm that included the splitting of the image into four subframes with equal duration to implement a spatio-temporal dither [14].

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7. DEMONSTRATIONS

Square panels of 384×384 pixels with a diagonal of 1.58 and 74 μm pixel pitch were made, implementing the full three-terminal MEMS mirror array integrated with an IGZO active matrix backplane and integrated row driver circuits, using both a 6 glass wafer process and a Gen 4.5 glass sheet process, with similar results. Figure 18 shows the reflected colors from a patch of mirrors driven with varying voltages, showing microscope images to demonstrate the relative flatness of the mirror structures. Figure 19 shows a close-up of the mirrors in an array. The flatness of each mirror is typically within 10 nm of maximum sag.

 figure: Fig. 18.

Fig. 18. Mirrors driven to several colors demonstrating the flatness and uniformity that is achievable.

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 figure: Fig. 19.

Fig. 19. Close-up image of mirrors exhibiting a maximum mirror sag of less than 10 nm across the 74 μm pitch.

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The panel without diffusers was characterized with an optical spectrum analyzer to compare the actual device with the theoretical predictions (see Fig. 7). The measurement result for 15 colors that were selected is shown in Fig. 20, where the encircled gamut is approximately 108% of sRGB. With the application of a diffuser (haze value 78), measured with a completely diffuse ambient light source (with the observer viewing 8° off surface normal), the color gamut decreases due to a number of factors, including the diffusive mixing of angle-dependent colors and additional reflective and scatter losses arising from front of screen optical components including the cover glass, frontlight, touch screen, and adhesive layers.

 figure: Fig. 20.

Fig. 20. Measured color gamut of 15 SMI colors.

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Figure 21 shows the complete panel driven with a silicon driver chip that was mounted onto the glass using well-established chip-on-glass techniques. The panel was driven with 60 Hz video content with no ghosting artifacts, proving the adequate response speed of both the MEMS structures and the associated TFT circuits. The photos were taken with a digital camera in an office lighting environment with a simple plastic diffuser that was laminated onto the display panel. The extremely low leakage backplane enabled by the IGZO transistors was also demonstrated by holding an image for 10 s without refreshing, during which time no degradation of the image was observed. This aspect of operation is a key enabler for mobile and wearable applications where the conservation of precious battery power is an important consideration.

 figure: Fig. 21.

Fig. 21. Initial SMI panel demonstrations. Both images and video were rendered at 60 Hz. The illumination used was the available light in an average, fluorescent lamp lit office environment.

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The off-axis viewing properties are illustrated in Fig. 22, for the same demonstration panel, viewed at angles of 10°, 20°, and 40° with respect to the surface normal. The lighting conditions are the same, an average office environment with office room light at near normal of the panel. The drop in brightness is due to the particular haze value that was used, and a shift in some of the colors can be seen at the extreme 40° angle.

 figure: Fig. 22.

Fig. 22. SMI off-axis viewing examples: (a) camera directed 10° off surface normal, (b) 20°, and (c) 40°.

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8. SUMMARY

A completely new approach to realizing color displays, breaking away from the RGB construct, was presented. The potential for a bright, high gamut display in a reflective mode using available ambient light for viewing was demonstrated. The physics of both the optical and electromechanical aspects of operation were discussed in detail, introducing the concept of interferometric absorption to provide a rich palette of colors at each mirror-pixel location.

APPENDIX A: SELECTING THE ABSORBER MATERIAL AND THICKNESS

Although the IMOD effect is typically analyzed by thin film modeling techniques wherein the layers are treated as discrete interfaces and a numerical procedure is used to track the multiple reflected and transmitted beam components, the transmission line analysis [15] approach offers important insights into how the absorber layer should be designed.

The IMOD is modeled using a transmission line construct as illustrated in Fig. 23. The mirror is modeled as an electrical short, the air gap is a section of transmission line of characteristic impedance Z0=377Ω, the absorber is a very short transmission line of characteristic impedance ZM, and the substrate glass, on which the absorber is placed, is a transmission line of characteristic impedance ZS. In terms of material parameters, the refractive index of the substrate glass is ns, and the complex refractive index of the absorber metal is nc=njk, where n is the real part of the index, k is the so-called extinction coefficient (defined so that both n and k are real and positive), and j is the square root of 1.

 figure: Fig. 23.

Fig. 23. Transmission line model.

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The characteristic impedance of the absorber metal is given by

ZM=Z0njk.
The characteristic impedance of the substrate is given by
Zs=Z0ns.

The absorbing metal layer can be crudely modeled as a resistive load, but to actually derive the conditions for an optimum material choice and thickness prescription, the key function of the absorbing layer must be described. Intuitively, the condition for high reflectivity is a simple short termination behind the absorber, easily met by making the air gap zero to achieve a white state (for all wavelengths) or one half of the wavelength of the color desired for high reflectivity. The other constraint on the function of the absorber is to efficiently absorb the colors not desired in the reflection. To formulate a simple condition, we examine one wavelength at a time, and set the air gap between the absorber and the mirror to one quarter of the wavelength of the light component. Of course, all color components not matching the one quarter wavelength condition will also be absorbed to some degree. For the one quarter wavelength air gap, the short termination presented by the mirror is transformed to an open circuit condition for the absorber, and the effective impedance looking into the absorbing layer is given by

ZMQ=ZMjtan(βda)=Z0njkjtan(2π(njk)daλ)Z0j2π(njk)2daλ=Z0(2πdaλ)2nkj(n2k2)(n2+k2)2,
where da is the thickness of the absorbing layer and β is the complex propagation constant in the absorber. Maximizing absorption is tantamount to minimizing the reflection for light entering the absorber. Since the light enters from the substrate glass into the absorber, the effective impedance ZMQ must match that of the substrate glass, which is purely real. This yields two conditions. First, we seek metals for which the real and imaginary components of the complex refractive index are the same: n=k. This would set the reactive part of the load of the above equation to zero. Second, the remaining real part of the effective impedance should be set equal to the substrate impedance resulting in
Z0(2πdaλ)2nk(n2+k2)2=Z0nsdaλ=nknsπ(n2+k2)2.

This yields a wavelength-dependent thickness to ensure a matching condition for all wavelengths, which is not possible. We can instead choose a wavelength for which the matching is perfect and accept a degree of mismatch for others.

To compare some metals, the difference between the real and imaginary parts of the refractive index is plotted in Fig. 24. The more absorptive metals have the two components more closely matched than the highly reflective Ag. The best absorbing metals turn out to be MoCr and V among readily available lists, and the optimum thickness predicted by this theory is 6–7 nm, verified by our experimental experience.

 figure: Fig. 24.

Fig. 24. (nk) for various metals. Vanadium (V) and the alloy molybdenum chromium (MoCr) exhibit the closest match between the real and imaginary parts of the refractive index across the visible spectrum.

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References

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  1. M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
    [Crossref]
  2. P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).
  3. Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).
  4. M. Dong and L. Zhong, “Chameleon: a color-adaptive Web browser for mobile OLED displays,” IEEE Trans. Mob. Comput. 11, 724–738 (2012).
  5. B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).
  6. H. A. Macleod, Thin-Film Optical Filters (CRC Press, 2001).
  7. “Standard test method for haze and luminous transmittance of transparent plastics,” (ASTM International, 2013).
  8. J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.
  9. K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
    [Crossref]
  10. C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).
  11. H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
    [Crossref]
  12. J. P. Allebach, Selected Papers on Digital Halftoning (SPIE Optical Engineering, 1999).
  13. J. Russ, The Image Processing Handbook, 5th ed. (CRC Press, 2006).
  14. V. V. Gogh, “Irises,” photograph downloaded from http://www.getty.edu/art/gettyguide/artObjectDetails?artobj=947 under the Getty Open Content Program.
  15. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

2012 (1)

M. Dong and L. Zhong, “Chameleon: a color-adaptive Web browser for mobile OLED displays,” IEEE Trans. Mob. Comput. 11, 724–738 (2012).

2011 (1)

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

2006 (2)

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).

2004 (1)

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

2003 (2)

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

1998 (1)

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Abe, K.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Aiba, T.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Albert, J. D.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Allebach, J. P.

J. P. Allebach, Selected Papers on Digital Halftoning (SPIE Optical Engineering, 1999).

Batey, J.

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Choi, J.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Chui, C.

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Chung, K.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Comiskey, B.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Den, T.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Dong, M.

M. Dong and L. Zhong, “Chameleon: a color-adaptive Web browser for mobile OLED displays,” IEEE Trans. Mob. Comput. 11, 724–738 (2012).

Drzaic, P.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Feeney, R.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Gally, B.

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Ha, Y.-M.

J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.

Hirano, M.

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

Hong, M.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Hosono, H.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

Jacobson, J.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Jang, J.-W.

J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.

Jeong, S.-H.

J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.

Kamiya, T.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

Kang, C. K.

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

Kida, Y.

Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).

Kim, B. H.

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

Kim, C.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Kim, S.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Kim, S. S.

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

Kim, T.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Kim, Y.-S.

J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.

Kothari, M.

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Kumomi, H.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Larson, E.

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Lee, B.-W.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Lee, S.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Loxley, A.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (CRC Press, 2001).

Maki, Y.

Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).

Miles, M.

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Mo, Y. G.

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

Nakajima, Y.

Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).

Nomura, K.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

Oh, J.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Ohta, H.

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

Park, C.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Park, J.-D.

J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.

Park, S. I.

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

Park, Y. S.

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

Russ, J.

J. Russ, The Image Processing Handbook, 5th ed. (CRC Press, 2006).

Sakong, D.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Sano, M.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Takagi, A.

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

Teranishi, Y.

Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).

Van Duzer, T.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

Yabuta, H.

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

Yang, Y.

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Zhang, L.

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Zhong, L.

M. Dong and L. Zhong, “Chameleon: a color-adaptive Web browser for mobile OLED displays,” IEEE Trans. Mob. Comput. 11, 724–738 (2012).

Appl. Phys. Lett. (1)

H. Yabuta, M. Sano, K. Abe, T. Aiba, T. Den, H. Kumomi, K. Nomura, T. Kamiya, and H. Hosono, “High-mobility thin-film transistor with amorphous InGaZnO4 channel fabricated by room temperature rf-magnetron sputtering,” Appl. Phys. Lett. 89, 112123 (2006).
[Crossref]

IEEE Trans. Mob. Comput. (1)

M. Dong and L. Zhong, “Chameleon: a color-adaptive Web browser for mobile OLED displays,” IEEE Trans. Mob. Comput. 11, 724–738 (2012).

J. Soc. Inf. Disp. (1)

M. Miles, E. Larson, C. Chui, M. Kothari, B. Gally, and J. Batey, “Digital paper™ for reflective displays,” J. Soc. Inf. Disp. 11, 209–215 (2003).
[Crossref]

Nature (1)

K. Nomura, H. Ohta, A. Takagi, T. Kamiya, M. Hirano, and H. Hosono, “Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors,” Nature 432, 488–492 (2004).
[Crossref]

SID Int. Symp. Dig. Tech. Pap. (1)

C. K. Kang, Y. S. Park, S. I. Park, Y. G. Mo, B. H. Kim, and S. S. Kim, “Integrated scan driver with oxide TFTs using floating gate method,” SID Int. Symp. Dig. Tech. Pap. 42, 25–27 (2011).

SID Symp. Dig. Tech. Pap. (3)

P. Drzaic, B. Comiskey, J. D. Albert, L. Zhang, A. Loxley, R. Feeney, and J. Jacobson, “A printed and rollable bistable electronic display,” SID Symp. Dig. Tech. Pap. 29, 1131–1134 (1998).

Y. Nakajima, Y. Teranishi, Y. Kida, and Y. Maki, “Ultra-low-power LTPS TFT-LCD technology using a multi-bit pixel memory circuit,” SID Symp. Dig. Tech. Pap. 37, 1185–1188 (2006).

B.-W. Lee, C. Park, S. Kim, T. Kim, Y. Yang, J. Oh, J. Choi, M. Hong, D. Sakong, K. Chung, S. Lee, and C. Kim, “TFT-LCD with RGBW color system,” SID Symp. Dig. Tech. Pap. 34, 1212–1215 (2003).

Other (7)

H. A. Macleod, Thin-Film Optical Filters (CRC Press, 2001).

“Standard test method for haze and luminous transmittance of transparent plastics,” (ASTM International, 2013).

J.-D. Park, J.-W. Jang, Y.-S. Kim, S.-H. Jeong, and Y.-M. Ha, “Implementation of 2.2 In. QVGA LTPS TFT-LCDs with the integration of p-type driving circuitry,” in International Display Workshop (2003), pp. 479–482.

J. P. Allebach, Selected Papers on Digital Halftoning (SPIE Optical Engineering, 1999).

J. Russ, The Image Processing Handbook, 5th ed. (CRC Press, 2006).

V. V. Gogh, “Irises,” photograph downloaded from http://www.getty.edu/art/gettyguide/artObjectDetails?artobj=947 under the Getty Open Content Program.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1984).

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Figures (24)

Fig. 1.
Fig. 1. Display system architecture.
Fig. 2.
Fig. 2. RGB versus SMI color rendering.
Fig. 3.
Fig. 3. IMOD pixel—optical components to harness interferometric absorption.
Fig. 4.
Fig. 4. Standing-wave electric field diagram.
Fig. 5.
Fig. 5. Dielectric coatings to enhance the interferometric absorptive colors. The red/green/blue curves indicate the electric field intensities for 630, 530, and 440 nm light. Light enters from the right, and the mirror reflective surface (AlCu) is on the left side of the figure.
Fig. 6.
Fig. 6. Reflectivity at various gap values.
Fig. 7.
Fig. 7. Interferometric colors plotted on u v as a function of air gap (the trajectory starts near the X-marked location and spirals clockwise as the air gap is increased from 10 to 640 nm with a 5 nm step).
Fig. 8.
Fig. 8. Reflective color spiral with the application of a diffuser in a typical indoor illumination condition (50% diffused and 50% collimated light).
Fig. 9.
Fig. 9. Three-terminal configuration of SMI pixel. The mirror is in between the top (common) and bottom (bias) electrical terminals and driven through the TFT switch. Although not shown, the top terminal and absorber are fixed to a thick dielectric layer on the top and the substrate, respectively, and do not move, while the mirror is suspended by mechanical hinges to a quiescent position.
Fig. 10.
Fig. 10. Three-dimensional exploded view of the SMI MEMS. The mirror is suspended by four hinges and has a stiffener in the middle to maintain flatness. The top terminal consists of a metal layer covered by a thick dielectric to form a mechanical platform for TFT electronics.
Fig. 11.
Fig. 11. Mirror position as a function of voltage applied.
Fig. 12.
Fig. 12. Circuit to measure current flowing into SMI pixels as it is actuated. A ramp is applied to the positive terminal of the op-amp to drive the mirror through its entire range. The output of the analog-to-digital converter is the current drawn by the group of SMI pixels.
Fig. 13.
Fig. 13. SMI panel system architecture. IGZO TFT technology was developed to provide both the pixel switches as well as to implement an integrated row driver.
Fig. 14.
Fig. 14. Exploded view of the MEMS + IGZO TFT pixel built up starting from the viewing side.
Fig. 15.
Fig. 15. Bottom-gate configuration with etch stop layer (ESL). The ESL protects the IGZO surface (back-channel) from process damage during source and drain (S/D) metal etching.
Fig. 16.
Fig. 16. Typical device transfer curves. The device dimensions are W / L = 4 μm / 8 μm , and nine devices in 6 glass wafer are plotted together. The inset table summarizes the TFT parameters. The curves taken from different parts of the wafer are overlaid together.
Fig. 17.
Fig. 17. Computer simulation of a spatially dithered image using 16 SMI primary colors. This simulation used an error diffusion algorithm that included the splitting of the image into four subframes with equal duration to implement a spatio-temporal dither [14].
Fig. 18.
Fig. 18. Mirrors driven to several colors demonstrating the flatness and uniformity that is achievable.
Fig. 19.
Fig. 19. Close-up image of mirrors exhibiting a maximum mirror sag of less than 10 nm across the 74 μm pitch.
Fig. 20.
Fig. 20. Measured color gamut of 15 SMI colors.
Fig. 21.
Fig. 21. Initial SMI panel demonstrations. Both images and video were rendered at 60 Hz. The illumination used was the available light in an average, fluorescent lamp lit office environment.
Fig. 22.
Fig. 22. SMI off-axis viewing examples: (a) camera directed 10° off surface normal, (b) 20°, and (c) 40°.
Fig. 23.
Fig. 23. Transmission line model.
Fig. 24.
Fig. 24. ( n k ) for various metals. Vanadium (V) and the alloy molybdenum chromium (MoCr) exhibit the closest match between the real and imaginary parts of the refractive index across the visible spectrum.

Equations (6)

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F = K ( x x 0 ) ( V d V b ) 2 2 ϵ A x 2 + V d 2 2 ϵ A ( d x ) 2 = 0 ,
0 > F x = K + ϵ A ( V d V b ) 2 x 3 + ϵ A V d 2 ( d x ) 3 ,
Z M = Z 0 n j k .
Z s = Z 0 n s .
Z M Q = Z M j tan ( β d a ) = Z 0 n j k j tan ( 2 π ( n j k ) d a λ ) Z 0 j 2 π ( n j k ) 2 d a λ = Z 0 ( 2 π d a λ ) 2 n k j ( n 2 k 2 ) ( n 2 + k 2 ) 2 ,
Z 0 ( 2 π d a λ ) 2 n k ( n 2 + k 2 ) 2 = Z 0 n s d a λ = n k n s π ( n 2 + k 2 ) 2 .

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