Rama Nand Singh

Optimum Mask and Source Patterns to Print a Given Shape

New degrees of freedom can be optimized in mask shapes when the source is also adjustable, because required image symmetries can be provided by the source rather than the collected wavefront. The optimized mask will often consist of novel sets of shapes that are quite different in layout from the target IC patterns. This implies that the optimization algorithm should have good global convergence properties, since the target patterns may not be a suitable starting solution. We have developed an algorithm that can optimize mask and source without using a starting design. Examples are shown where the process window obtained is between 2 and 6 times larger than that achieved with standard RET methods. The optimized masks require phase shift, but no trim mask is used. Thus far we have only optimized 2D patterns over small fields (periodicities of approximately 1 micrometer or less). We also discuss mask optimization with fixed source, source optimization with fixed mask, and the re-targeting of designs in different mask regions to provide a common exposure level.

Optimum mask and source patterns to print a given shape

New degrees of freedom can be optimized in mask shapes when the source is also adjustable, because required image symmetries can be provided by the source rather than the collected wave front. The optimized mask will often consist of novel sets of shapes that are quite different in layout from the target integrated circuit patterns. This implies that the optimization algorithm should have good global convergence properties, since the target patterns may not be a suitable starting solution. We have developed an algorithm that can optimize mask and source without using a starting design. Examples are shown where the process window obtained is between two and six times larger than that achieved with standard reticle enhancement techniques (RET). The optimized masks require phase shift, but no trim mask is used. Thus far we can only optimize two-dimensional patterns over small fields (periodicities of ;1 mm or less), though patterns in two separate fields can be jointly optimized for maximum common window under a single source. We also discuss mask optimization with fixed source, source optimization with fixed mask, and the retargeting of designs in different mask regions to provide a common exposure level.

Contrast properties of reflective liquid crystal light valves in projection displays

Projectors that use reflective light valves must employ beam splitters or analogous components to separate bright-state light from dark-state light, since both states must propagate in the space above the light valve. Polarization ray tracing shows that such beam splitters will not usually achieve high rejection of dark-state light when the beam has the typical angular divergence of about ±10°. At such propagation angles, different rays in the beam will have appreciably different planes of incidence at tilted optical coatings in the system (because of the compound angles involved). If the light valve is mirrorlike in dark state, we show that to correct the depolarization resulting from compound incidence angles, it is necessary that the optics introduce no rotation in the illuminating polarization. To a reasonable approximation, such a rotation in polarization will double in the return pass through the optics. To the same approximation, induced ellipticity in the illuminating polarization will cancel in double pass, and pure rotation can be converted to pure ellipticity with a quarterwave retarder. An important qualification, however, is that a light valve can only be exactly mirrorlike in restricted cases [i.e., if linearly polarized input light remains exactly linearly polarized (though possibly rotated) at all wavelengths when it reaches the mirror backplane of the light valve, independent of small manufacturing errors]. We calculate contrast loss in the more realistic case of a reflective twisted nematic liquid crystal (TNLC) light valve interacting with tilted coatings in the projection optics over finite numerical aperture (NA), and discuss the impact on LC thickness tolerances and spectral bandwidth Δλ. We extend our results to apply to more general light valves and more general projection optics configurations. Dark-state background is found to scale as NA2 (or in some cases as ∼NA2Δλ2). Because of this interaction, the complete system almost always shows a lower contrast than the light valve alone.

Projection display throughput: efficiency of optical transmission and light-source collection

The optical system for a projection display based on three miniature reflective spatial light modulators (SLMs) is described. The total projection display light throughput is a function not only of the optical system efficiency but also of the light-collection and light-coupling efficiency referred to here as the lamp-SLM coupling. The optical system efficiency is the transmission of the optical components in the projection display. These are examined in detail through measurements and estimates of the components in the system. The various optical components include UV-IR filtering, illumination optics, polarization optics, color separation and recombination optics, SLM efficiency, and projection optics. The lamp-SLM coupling, which is the amount of usable light that can be collected from a particular lamp coupled to the projection optical system, is determined by the light-source luminance, the efficiency of the light-collection optics, and the optical system etendue. For small SLMs, less than 50 mm diagonal, for example, the lamp-SLM coupling efficiency falls off rapidly with SLM size and optical system f-number. The dependence of this coupling efficiency on SLM size is determined from measurements of the light-collection efficiency as a function of aperture size, where the apertures are used to simulate SLMs of the same dimensions. A variety of arc lamps were investigated for use in the projection display based on IBM reflective SLM devices. The lamp-SLM coupling dependence on arc gap was determined. The measurements are used to compare various lamps and to estimate directly the throughput for the complete projection system. The SLMs used in the projection display are liquid crystal devices which utilize only one polarization of light while discarding the second. Converting the discarded polarization into useful light can in principle double the throughput of the projector. However, polarization conversion results in doubling of the size of the light source and thus produces less efficient lamp-SLM coupling, particularly for long-arc-gap lamps. Measurements and analysis of throughput enhancement by polarization conversion are presented, and the dependence on arc gap and optical system etendue is discussed.

High-numerical-aperture optical designs

This paper is an overview of the designs of high-numerical-aperture lenses for optical projection lithography at the IBM Thomas J. Watson Research Center.

Yield estimation of SRAM circuits using "Virtual SRAM Fab"

Static Random Access Memories (SRAMs) are key components of modern VLSI designs and a major bottleneck to technology scaling as they use the smallest size devices with high sensitivity to manufacturing details. Analysis performed at the “schematic” level can be deceiving as it ignores the interdependence between the implementation layout and the resulting electrical performance. We present a computational framework, referred to as “Virtual SRAM Fab”, for analyzing and estimating pre-Si SRAM array manufacturing yield considering both lithographic and electrical variations. The framework is being demonstrated for SRAM design/optimization in 45nm nodes and currently being used for both 32nm and 22nm technology nodes. The application and merit of the framework are illustrated using two different SRAM cells in a 45nm PD/SOI technology, which have been designed for similar stability/performance, but exhibit different parametric yields due to layout/lithographic variations. We also demonstrate the application of Virtual SRAM Fab for prediction of layout-induced imbalance in an 8T cell, which is a popular candidate for SRAM implementation in 32–22nm technology nodes.

Correction of contrast in projection systems by means of phase-controlled prism coatings and band-shifted twist compensators

Projectors that use LCOS lightvalves face special contrast requirements. Most configurations for reflective light valves employ tilted beam-dividing coatings that see both bright and dark polarization states. The optics must then be designed to eliminate polarization mixing at these coatings, which ordinarily arises when the S and P planes for different rays are non-parallel. We show how phase- controlled coatings can exploit the double-pass symmetry of the Plumbicon tri-prism geometry to correct this effect, reducing cross-polarized reflectivity to approximately 1E-3 when the light valve is mirror-like in black-state. Though contrast in different rays varies as a function of both ray skew component and coating angle of incidence, we show that for NA <EQ 0.2 the computation involved in calculating beam contrast is essentially equivalent to tracing a single ray. Light valves that use a normally-black TN mode exhibit a non-mirror-like phase dispersion in their black-state, complicating contrast control in the optics. Scatter depolarization at the edges of pixel electrodes is enhanced in these light valves, because the inherent twist causes the backplane polarization to be rotated out of alignment with pixel edges. We show that all of these contrast degradation mechanisms can be addressed by incorporating into the light valve a compensating layer having opposite birefringence to the black-state TN active layer. Moreover, when the compensating layer and driven layer are blue-shifted to a shorter LC thickness than would ordinarily be appropriate for the wavelength band of interest, a highly achromatic response is obtained at all gray levels.

43.1: Color Filterless Liquid Crystal Display Illuminated with LEDs

We have prototyped a 13.3-inch diagonal color filterless LCD illuminated with LEDs. A new color directional backlight combined with a microlens attached liquid crystal cell plate shows the feasibility of a new power efficient LCD with better color and lead-free features.

Failure prediction across process window for robust OPC

In conventional Optical and Process Correction (OPC), models are calibrated with the CD measurement from the “good” printable patterns. Predictions of process window loss are based on extrapolation from the “good” region into the failure region. The extrapolation is always a less accurate process than interpolation. In this paper, we utilize the experimental pass/fail data to build models that accurately identify and predict printing failures. We developed a methodology and a formal apparatus for failure modeling. It is found that two or more aerial image shape parameters are required to describe all failure mechanisms for a sub-100nm process. This empirical failure model is currently applied to Optical Rule Checking (ORC) of the post-OPC layout. It also can be used to constrain layout corrections in the future.

Projection optics for reflective light valves

Reflective x-Si backplanes allow projection displays to evolve toward higher pixel count and greater miniaturization, extending the range of competitive application. As light valve area A is reduced, projector output into solid angle S equalsV (pi) NA2 can in many cases be considered to decrease roughly as approximately (A*S)0.5, with the 0.5 exponent representing typical microdisplay operating in a regime that is neither purely brightness-limited nor purely power-limited. Polarization modulation entails a modified scaling approximately (A*S/2)0.5; color sequential operation, approximately (1/3)*(A*S)0.5; spatially divided single-light-valve RGB projection, approximately (A*S/3)0.5. Projection lenses for three-light-valve system must provide an increased working distance to accommodate a color recombiner. Zoom lens are often required in front projectors, and rear projection usually entails a short lens-to-screen distance. It has become cost-effective to use plastic aspherical elements to meet these requirements. Periodic strip-PBS arrays have been widely adopted for polarization recycling, but aperiodic homogenizers are sometimes used to correct the uneven magnification and symmetry limitations of conic reflectors. Bright-state and dark-state beams must occupy distinct etendues in the half space above a reflective light valve, creating a vulnerability to crosstalk. Crosstalk from a polarizing beamsplitter gives rise to a residual background intensity approximately 0.3*NA2, unless a quarterwave corrector is used. Crosstalk can also arise from stress birefringence in prism substrates. Stray light makes an indirect contribution to background, but can sometimes be corrected by filtering.