The past decade has experienced a remarkable synergy between Resolution Enhancement Technologies (RET) in Optical Lithography and Optical Proximity Correction (OPC). This heterogeneous array of patterning solutions ranges from simple rule-based to more sophisticated model-based corrections, including sub-resolution assist features, partially transmitting masks and various dual mask approaches. A survey of the evolutionary development from the early introduction of the first OPC engines in 1996 to the debut of Immersion Lithography in 2006 reveals that the convergence of RET and OPC has also enabled a progressive selection and fine-tuning of Geometric Design Rules (GDR) at each technology node, based on systematic adoption of lithographic verification. This paper describes the use of "full-chip" lithography verification engines in current Design For Manufacturing (DFM) practices and extends the analysis to identify a set of key technologies and applications for the 45, 32 and 22 nm nodes. As OPC-derived tools enter the stage of maturity, from a software standpoint, their use-model is being greatly broadened from the back-end mask tape-out flow, upstream, directly integrated into physical design verification. Lithography awareness into the physical design environment, mediated by new DFM verification tools and flows, is driving various forms of manufacturable physical layout implementation: from Restricted Design Rules and Flexible Design Rules to Regular Circuit Fabrics. As new lithography solutions, such as immersion lithography and EUV, will have to be deployed within a complex technology framework, the paper also examines the trend towards "layout design regularization" and its implications for patterning and next generation lithographies.

From an optical imaging perspective, photomask design and topography have evolved over the past 10 years from optically thin, light-blocking apertures to optically thick, volumetric scattering elements. The reduction in mask feature size to the sub-wavelength regime coupled with increases in exposure system numerical aperture will continue to push the optics of a photomask toward a more complex and detailed physical model. Moreover, aggressive implementation of resolution enhancement methods in state of the art lithography create mask layouts that resemble diffractive optical elements rather than the electronic circuit patterns the mask is intended to reproduce. In this paper, we address some of the optical characteristics of photomasks for current lithographic technologies as well as new trends driven by a continued reduction in mask feature size and increased numerical aperture enabled by immersion lithography. As a general conclusion, we find the photomask is best treated and characterized as a true and integrated optical component of the imaging system. By considering the mask from this vantage point, many imaging related issues in advanced lithography may be anticipated and potentially optimized.

The history of Nikon's projection lens development for optical microlithography started with the first "Ultra Micro-Nikkor" in 1962, which was used for making photo-masks. Nikon's first wafer stepper "NSR-1010G" was developed with a g-line projection lens in 1980. Since then, many kinds of projection lenses have been developed for each generation of stepper or scanner. In addition to increasing numerical aperture (NA) and field size, there have been many technical transitions for the projection lens, such as shortening the wavelength, controlling Zernike aberrations with phase measurement interferometry (PMI) for low k1 lithography, using aspherical lenses, applying kinematic optomechanical mounts, and utilizing free asphere re-polishing steps in the lens manufacturing process. The most recent advancement in projection lens technology is liquid immersion and polarization control for high NA imaging. NA now exceeds 1.0, which is the theoretical limit for dry (in air) imaging. At each transition, the amount of information that goes through the projection lens has been increased. In this paper, the history of the microlithographic lens is reviewed from several different points of view, such as specification, optical design, lens manufacturing, etc. In addition, future options of the projection lens are discussed briefly.

We present a systematic analysis of the imaging performance for a 0.93 numerical aperture (NA) state-of-the-art immersion lithography scanner and we compare this performance to its dry NA=0.93 counterpart. The increased depth of focus (DOF) enabled by immersion lithography presents a set of advantages for semiconductor manufacturing which we explore in this article. First, we show that 0.93 NA immersion prevents, for a 65nm gate-level process, the need for imposing pitch restrictions with an attenuated-PSM solution; something not possible with an equivalent "dry" process. Second, we demonstrate the superior critical dimension uniformity (CDU) of an immersion process in the presence of realistic focus variations typically encountered in semiconductor manufacturing. Third, we confirm that the through-pitch behavior of "wet" and "dry" scanners is well matched, enabling the possibility of transferring optical proximity corrections (OPC) between the two types of lithography scanners. The transferability of OPC is key to enabling a fast insertion of immersion lithography into the manufacturing process for the 65nm and 45nm nodes. Finally, we conclude that, from an imaging perspective, immersion is ready for high-volume manufacturing.

Immersion Lithography is now the most important technique for extending optical lithography's capabilities and meeting the requirements of the Semiconductor Industry Association (SIA) roadmap. The introduction of water as an immersion fluid will allow optical lithography to progress as far as the 45nm (half pitch) node using ArF scanning systems such as the XT1700i. Developments are under way to explore the use of immersion lithography beyond this performance level and toward the 32nm (half pitch) node. This paper examines the progress that has been made, particularly with the use of 2^nd-generation immersion fluids. The requirements of the exposure system are defined. Issues associated with achieving the requirements are reviewed and discussed. Special attention is given to clarifying the optical materials and the issues associated with extending optical designs to hyper-numerical aperture (NA) levels. A number of threshold levels for the numerical apertures are set by the refractive index of the available materials in the lithographic film stack. These are defined. The requirements of high refractive index fluids are detailed. The performance of experimental samples is compared to system requirements. Fluid interaction with photoresists and topcoats are examined. The results of stain tests and soak tests for fluid samples on resist are reported. Data is supplied on resist imaging for 32nm line and space L/S.

Semiconductor manufacturers are in the midst of the next technology node C045 (65nm half-pitch) development. The difference this time is that the heavy lifting is being done while swimming. Generally, for the C065 node (hp90), critical layers will be processed using 193-nm scanners with numerical apertures up to 0.85. It is also clear that the capabilities and potential benefits of immersion lithography (at this wavelength and NA) should to be examined, in addition to the development of immersion lithography for the C045 and C032 technology generations. The potential benefits of immersion lithography; increased DOF in the near term and hyper-NA imaging in the next phase, have been widely reported. A strategy of replacing conventional "dry" lithographic process steps with immersion lithographic process steps would allow the benefits of immersion to be realized much earlier. To fully realize this advantage a direct comparison of immersion lithography's benefits and therefore speed learning is needed. However, such an insertion should be "transparent": i.e. the "immersion process" should run with the same reticles (OPC) and resists, as the conventional process. In an effort to gain this knowledge about the immersion processes, we have chosen a path of optimizing and ramping-up the lithographic process for the C065 technology node. In this paper, we report on the compatibility of inserting immersion lithography processes into an established C065 process running in a pilot manufacturing line. We will present an initial assessment of some critical parameters for the implementation of immersion lithography. This assessment includes: OPC compatibility, imaging, process integration, and defectivity all compared to the dry process of record. Finally, conclusions will be made as to the overall readiness of immersion to support C065 node processing in direct transfer from dry and its extendibility to C045. In this work, the C045 technology node (hp65) is the main target vehicle. However, a successful introduction of immersion technology may allow a strategy change complementary with the previous (C065) technology node (i.e. run C065 immersion in production and benefit from larger process windows).

Immersion lithography is rapidly approaching the manufacturing phase. A production-quality exposure tool system with NA=1.07 (Nikon NSR-S609B) was constructed to target the start of immersion lithography for IC manufacturing in 2006. Its projection optics have very small wavefront aberration and lowest local flare levels. The overlay issue has been analyzed, and its cause was found to be evaporation cooling. With the tandem stage and local fill nozzle implemented in the S609B, we have successfully avoided the evaporation cooling so that the good wet-to-dry mix-and-match overlay data have been obtained. The major part of immersion specific defects is caused by dried water-droplets, i.e. water-marks. The local fill nozzle has eliminated this defectivity by avoiding air flow in the nozzle. In the future, water immersion with NA=1.30 optics will be used for half-pitch 45nm manufacturing. Finer pattern imaging down to 32nm seems to need high-index material immersion or nonlinear double patterning, but these have several issues and concerns to be solved.

Defectivity has been one of the largest unknowns in immersion lithography. It is critical to understand if there are any immersion specific defect modes, and if so, what their underlying mechanisms are. Through this understanding, any identified defect modes can be reduced or eliminated to help advance immersion lithography to high yield manufacturing. Since February 2005, an ASML XT:1250Di immersion scanner has been operational at IMEC. A joint program was established to understand immersion defectivity by bringing together expertise from IMEC, ASML, resist vendors, IC manufactures, TEL, and KLA-Tencor. This paper will cover the results from these efforts. The new immersion specific defect modes that will be discussed are air bubbles in the immersion fluid, water marks, wafer edge film peeling, and particle transport. As part of the effort to understand the parameters that drive these defects, IMEC has also developed novel techniques for characterizing resist leaching and water uptake. The findings of our investigations into each immersion specific defect mechanism and their influencing factors will be given in this paper, and an attempt will be made to provide recommendations for a process space to operate in to limit these defects.

New applications of evanescent imaging for microlithography are introduced. The use of evanescent wave lithography (EWL) has been employed for 26nm resolution at 1.85NA using a 193nm ArF excimer laser wavelength to record images in a photoresist with a refractive index of 1.71. Additionally, a photomask enhancement effect is described using evanescent wave assist features (EWAF) to take advantage of the coupling of the evanescent energy bound at the substrate-absorber surface, enhancing the transmission of a mask opening through coupled interference.

The introduction of immersion step and scan systems has opened the road for hyper-NA lenses (NA > 1). At these NA's polarization control becomes a key parameter in imaging. Application of polarized illumination leads to an increase of contrast and exposure latitude. The resulting resolution enhancement offered by polarized illumination enables 45nm node lithography with an ArF, NA=1.2 system. Hyper-NA systems utilizing polarized illumination must be fully compatible with all requirements for a volume production tool: maintaining imaging performance at full throughput, overlay and focus control; flexibility and ease-of-use are essential features. Adequate polarization control is realized by employing polarization-preserving optics, and by automated in-line metrology to optimize the system for any selected polarization state. In this paper we address the improvements of polarization for the 65nm and 45nm imaging node applications. Experimental results describing the imaging effects while using polarized illumination on high-NA (NA=0.93) and hyper-NA (NA=1.2) exposure tools will be shown. These data will also be compared to simulations. In addition, this paper includes a short section that deals with the issues of reticle birefringence. Finally, system control and in-line metrology under high-volume production conditions will be discussed.

For an ultra-high numerical aperture (NA), such as that exceeding 0.9, the p-polarized component of light that has passed through a region at the limit of the NA of a high-NA lithography tool, degrades contrast because of the so-called vector imaging effect, and is therefore detrimental to the formation of optical images. Polarized illumination removes the effect of the p-polarized light component and provides illumination light composed of s-polarized light. The higher the NA, the greater are the benefits of polarized illumination. Therefore, in lithography at the 45-nm node and below, polarized illumination is viewed as an indispensable technology. We explore the applicability of polarized illumination to device manufacturing processes at the 45-nm node and beyond, with a focus on the utilization of azimuthally polarized illumination, which enables one mask exposure. The data used in this research were obtained through imaging simulations and experiments using a dry lithography tool equipped with a 0.92-NA projection lens. In imaging simulations using a lithography simulator, the application of azimuthally polarized illumination improved image contrast in resists by approximately 20% for half pitch (HP) 65-nm dense patterns. As a result, device patterns showed enhanced robustness with respect to exposure dose error; extended process windows; and reduced mask error enhancement factor (MEEF), line edge roughness (LER), and line end shortening (LES). This paper examines the results of experiments conducted using imaging simulations and lithography tools on other product device like patterns (besides special patterns in which benefits can clearly be expected, including dense (L/S) patterns), and reports the results.

The initial experimental verification of a polarization monitoring technique is presented. A series of phase shifting mask patterns produce polarization dependent signals in photoresist and are capable of monitoring the Stokes parameters of any arbitrary illumination scheme. Experiments on two test reticles have been conducted. The first reticle consisted of a series of radial phase gratings (RPG) and employed special apertures to select particular illumination angles. Measurement sensitivities of about 0.3 percent of the clear field per percent change in polarization state were observed. The second test reticle employed the more sensitive proximity effect polarization analyzers (PEPA), a more robust experimental setup, and a backside pinhole layer for illumination angle selection and to enable characterization of the full illuminator. Despite an initial complication with the backside pinhole alignment, the results correlate with theory. Theory suggests that, once the pinhole alignment is corrected in the near future, the second reticle should achieve a measurement sensitivity of about 1 percent of the clear field per percent change in polarization state. This corresponds to a measurement of the Stokes parameters after test mask calibration, to within about 0.02 to 0.03. Various potential improvements to the design, fabrication of the mask, and experimental setup are discussed. Additionally, to decrease measurement time, a design modification and double exposure technique is proposed to enable electrical detection of the measurement signal.

The use of immersion technology extends the lifetime of optical lithography by enabling ultra-high NA much greater than 1.0. Ultra-high NA application for low k₁ imaging strongly demands an adoption of polarization illumination as a resolution enhancement technology. It is typically assumed that the transmitted wavefront has uniform amplitude and a constant polarization state across the pupil. This assumption is not valid any more for the level required for low k₁ imaging. This paper considers methods of polarization analysis including polarization aberration theory. Definitions of basic polarization phenomena and review of matrix representation are included in this discussion. Finally we propose Pauli spin matrix representation as preferred method to describe polarization aberration.

Polarization is becoming very important technology in micro-lithography at the higher NA lithography for much smaller design. The wide and intensive studies to apply the polarization technology into lithography application have been achieved. Source polarization, mask polarization and projection lens polarization could make different printing results compared to non-polarization cases. Especially k1 factor below 0.3 needs aggressive resolution enhancement techniques. Environmental parameters such as mask CD, lens aberration, stray light, image plane deviation and resist characteristic make CD controllability worse in the very low k1 regime. The polarization technology can contribute to getting better imaging performance. This experiment is challenging k1 factor down to 0.29 with the source polarization function. The source polarization effect on real device will be shown through the simulation and actual printing process using 6% attenuated PSM. The related OPC strategy with the polarized source will also be discussed.

In our previous work we have shown that as the NA of a lithographic projection system increases some of the simulation assumptions that are traditionally made - such as the so-called Hopkins assumption, i.e. the assumption that diffraction at the mask is independent of the angle of incidence of the illuminating light waves - break down, at least in some cases. Reliable simulation results will then only be obtained if this Hopkins assumption is eliminated, i.e. when the diffraction effect is reevaluated for each incident direction. The differences in the results between two such simulations, one using the Hopkins approach, the other with this assumption removed, have been demonstrated to be very significant in some case, but today there is no clear understanding when the removal of the Hopkins assumption is essential: a systematic study is not available. As simulations without the Hopkins approximation are significantly more time consuming than simulations done under the Hopkins assumption, a better understanding of which model can or must be used under which circumstances, would be of significant practical importance. The aim of this paper is to provide such a more systematic study for the case of 6% attenuated PSM with line/space structures targeting at a 45 nm resist linewidth for a variety of pitches, for a NA = 1.2 water immersion system. Standard lithographic metrics such as process windows will be used to compare the two simulation approaches. All this work will be done taking the mask topography and optical material parameters into account. As the polarization state of the mask-illumination will also greatly affect the imaging quality at hyper-NA, we will compare the results for different polarization states and illumination modes.

This paper extends our previous work on globally optimizing source shapes for lithography. A key extension is our global optimization against metrics that involve process window through focus. For example, the user can determine the particular source shape which maximizes the area of the ED window (common exposure-defocus window) across all patterns. In nominal terms, integrated process window is a highly nonlinear objective function; for example, ED window is defined in terms of fractional (i.e. percentage or relative) exposure latitude, and dose is proportional to the reciprocal of intensity, which means that when ED window is calculated the source variables appear in both numerator and denominator of a ratio of reciprocals. In addition, exposure and focus latitudes are defined in terms of the common window as bounded by all features, and the determination of which features are gating is a conditional and non-differentiable function of the source variables. Also, the focus integration should only extend to the plane where ED window first closes down to zero; this limit also depends on the variables in a nonlinear way. However, despite these complexities, it proves possible under quite benign approximations to reformulate ED window maximization as a near-linear-programming problem that can be solved globally, in polynomial time. The algorithm can be extended in several ways, e.g. to account for effects like mask linewidth errors (MEF). In some cases MEF-optimized sources can substantially reduce the sensitivity to mask error, and may differ appreciably from sources optimized for individual perturbed masks. Resist effects can be approximated by influence/diffusion kernels operating on the exposing image within the film. The area of an inscribed rectangular process band can be optimized in place of the full ED window. Source pixelation can be structured to account for finite illuminator resolution and constraints on minimum pole size. Multiple exposures can also be handled, and polarization can be selected optimally on a pixel-by-pixel basis.

In this paper, we expand on previous work in which we investigated algorithms and cost functions for dense OPC. We explore using multiple contours at different process conditions in order to generate "process window OPC". We analyze and discuss the computational cost of the dense OPC approach in comparison to sparse OPC. We also discuss the flexibility to use any possible resist model inside a dense OPC system. We show how the dense OPC system can be used together with dense, contour-based verification for the 45nm node. The dense verification and OPC tools provide a framework for lithography friendly design and DFM for the 45nm manufacturing node.

The most important task in the OPC (optical proximity correction) process is to make a model database which can simulate optical behavior, while the characterization of resist development is still performed empirically. The previous approaches to lithography model generation heavily rely on 1 dimensional CD (critical dimension) measurements containing hundreds of features representing different sizes, shapes and pitches. Despite the huge amount of experiment data, there still can be a significant model error due to mismatching between measurement points and simulation points in 2 dimensional structures such as line ends, contact, and corners. Since the large number of data is required, it is quite natural that there require a huge computational effort to get the model. Our approach in this paper is based on the fitting model with 2D images, i.e., SEM image or a rigorous simulation image. It would not be an overstatement to say that a 2D wafer image is worth thousands of CD measurements. This approach is able to cover the symmetric as well as the non-symmetric patterns and prevents the threshold level from an inappropriate swing at the CTR (constant threshold resist) model. This paper aims to show how to extract the information of the wafer image, how to optimize the OPC modeling with quickness, and how to increase the modeling accuracy for the entire pattern. In addition, this paper shows the excellent agreement between the simulation image and the wafer image for the critical layout of the sub 70 nm technology node memory devices.

Tolerancing of lithographic imaging systems is a crucial step in the design of these lens systems. Usually a metric such as maximum RMS wavefront error is specified, and lens surface error budgets (curvature, tilt, decenter,...) are derived to ensure the specification is satisfied. Simple compensation schemes are then used to optimize "yield", that is, to maximize the chances of achieving the designed value of the RMS wavefront error. Software that performs these computations has been available to the lens design community for many years. The concept of tolerancing can be applied to other merit functions as well, but with the advent of hyper-NA, immersion systems for sub-90 nm lithography, questions arise about the efficacy of using RMS wavefront error as an accurate predictor of performance change. For example, nontrivial Jones matrices across the exit pupil give rise not only to scalar phase and transmission variations across the pupil, but also differential changes to transmission ("diattenuation") and phase ("retardance") that are not taken into account in standard wavefront error calculations, and depend upon the incident polarization. However, a merit function based on such quantities is not very useful to the lithographer on the fab floor. For the lithographer, it is desirable to build the system based on more direct metrics, such as across-chip-linewidth-variation (ACLV) or H-V bias, provided the metrics are based on fundamental properties of the imaging system, and are not excessively dependent on process specific information. We have developed software to determine manufacturing and alignment tolerances of a lens using a set of merit functions that are based on linewidth predictions. These include across-chip linewidth variation (ACLV), H-V bias, LR bias, overlay error and telecentricity error. The calculation of these quantities includes a simple resist development model. In this paper, we will show results of a tolerancing study on a hyper-NA immersion lens that uses this software.

It is well accepted to judge imaging capability of an exposure tool primarily on printing equal line-spaces, at a minimum ½ pitch. Further on, combining line-space minimum ½ pitches with scanner maximum NA, defines the process k₁. From a lithographer viewpoint, flash memory device is the perfect candidate to achieve lowest k₁ lithography for a given NA. This is justified by flash layout specific, with regular and relative simple 1-D topology of the critical layers that look like line-space gratings. In reality, flash layout presents a subtle topology and cannot be considered a simple 1-D line-space problem. Uniqueness to flash layout is the array-end zones, where pattern regularity is broken up by features with dimensions and separation of n x ½ pitch, where n is an integer number that we used in this work to manipulate litho process latitudes. Integrated lithography concept seeks to tweak flash pattern details and tune it with scanner control parameters. We introduce feature-center placement through focus and dose as the metric to characterize a cross-coupling phenomena occurring between adjacent features located at array-end of typical flash poly wordline layer. We comparedthe metric behavior with usual litho process window parameters and identified interactions with scanner CDU control parameters. We show how feature-center placement errors are direct functions of optical and physical characteristics of mask materials, attenuated PSM or binary, and of layout array-end topology. Imaging at extreme low-k₁, effects from layout specifics and mask materials are best characterized by full vector, rigorous EM simulation, instead of scalar approach, typically used for OPC treatment. Predicted CDU performance of 1.2NA scanner, based on integrated lithography concept, matched very well the experimental results in printing 45nm ½ pitch flash wordline layer. Results show that 1.2NA scanner, operating at 0.28 k₁ could be an effective lithography solution for 45nm flash designs.

Alternating Phase Shift Mask (APSM) Technology has been developed and successfully implemented for the poly gate of 65nm node Logic application at Intel. This paper discusses the optimization of the mask design rules and fabrication process in order to enable high volume manufacturability. Intel's APSM technology is based on a dual sided trenched architecture. To meet the stringent OPC requirements associated with patterning of narrow gates required for the 65nm node, Chrome width between the Zero and Pi aperture need to be minimized. Additionally, APSM lithography has an inherently low MEEF that furthermore, drives a narrower Chrome line as compared to the Binary approach. The double sided trenched structure with narrow Chrome lines are mechanically vulnerable and prone to damage when exposed to conventional mask processing steps. Therefore, new processing approaches were developed to minimize the damage to the patterned mask features. For example, cleaning processes were optimized to minimize Chrome & quartz damage while retaining the cleaning effectiveness. In addition, mask design rules were developed which ensured manufacturability. The narrow Chrome regions between the zero and Pi apertures severely restrict the tolerance for the placement of the second level resists edges with respect to the first level. UV Laser Writer based resist patterning capability, capable of providing the required Overlay tolerance, was developed, An AIMS based methodology was used to optimize the undercut and minimize the aerial image CD difference between the Zero and Pi apertures.

The understanding of focus variation across a wafer is crucial to CD control (both ACLV and AWLV) and pattern fidelity on the wafer and chip levels. This is particularly true for the 65nm node and beyond, where focus margin is shrinking with the design rules, and is turning out to be one of the key process variables that directly impact the device yield. A technique based on the Phase-Shift Focus Monitor (PSFM) is developed to measure realistic across-wafer focus errors on materials processed in actual production flows. With this technique, we are able to extract detailed across-wafer focus performance at critical pattern levels from the front end of line (FEOL) all the way through the back end of line (BEOL). Typically, more than 8,000 data points are measured across a wafer, and the data are decomposed into an intra-field focus map, which captures the across chip focus variation (ACFV), and an inter-field focus map, which describes the across wafer focus variation (AWFV). ACFV and AWFV are then analyzed to understand various components in the overall focus error, including; across slit lens image field, reticle shape and dynamic scan components, local wafer flatness, wafer processing effect, pattern density, and edge die abnormality. The intra-field ACFV lens component is compared with TI's ScatterLith and ASML's FOCAL techniques. Results are consistent with the predictions based on the on-board lens aberration data. Inter-field AWFV is the most interesting, due to lack of detailed understanding of the process impact on scanner focus and leveling. PSFM data is used to characterize the effect of wafer processing such as etch, deposition, and CMP on across wafer focus control. Comparison and correlation of PSFM focus mapping with the wafer height and residual moving average (MA) maps generated by the scanner's optical leveling sensors shows a good match in general. Process induced focus errors are clearly observed on wafers of significant film stack variation and/or pattern density variation. Implications on total focus control and depth of focus (DOF) requirements for 65nm mass production are discussed in this paper using a quantitative pattern yield model. The same technique can be extended to immersion lithography.

It is well understood from previous work performed by Nikon and several others that the optical proximity effect (OPE) behavior of a litho tool will depend on the details in the partial coherence pattern projected by the tool's illuminator. While there are several other areas of influence, including the lens numerical aperture (NA), laser bandwidth, and simple parameters like focus and dose, the contribution of pupil fill cannot be ignored. This becomes especially significant when different tools, sometimes from varied manufacturers, are used to execute the same critical process. While measurements of pupil fill are readily available, the decision of what to do with the data can be frustrating. Lithographers cannot be expected to re-run their modeling for every small change in the pupil fill from one tool to another, or for changes due to small illuminator adjustments. A streamlined characterization technique is needed. This need becomes especially acute when we consider the exotic pupil fills to be used in pushing the performance envelope of immersion tools. At Nikon, we have already assessed the importance of the pupil fill. Therefore, we turn our attention to techniques that can be used to fully characterize it. We have developed several different characterization methods, including not only the derivation of "effective" sigma terms, but also a more direct analysis using a modulation transfer function. These diverse methods, and their correlation with vital litho parameters like iso-nested bias and HV bias, will be presented.

The quality of model-based OPC (MBOPC) depends on both modeling and correction accuracy. As the k1 process factor decreases and design complexity increases, the correction accuracy becomes more important. Especially, in case of high NA immersion lithography with strong off-axis illumination (OAI) such as dipole and cross-pole illumination, mask error enhancement factor (MEEF) and normalized intensity log-slope (NILS) vary seriously according to the pattern directions and shapes, so that the normal correction method, which uses the constant damping value, causes the divergence of correction and can hardly define optimum bias. Therefore, we developed design rule (D/R) constraints and new correction method to prevent the divergence and to reduce the OPC run time for sub-60nm device. In this paper, D/R constraints derived from MEEF are introduced to reduce MEEF across the full chip. In addition, we propose new methods to achieve the global OPC convergence of low-k1 lithography by MEEF-based correction combined with proportion-integral-derivative (PID) controller. The PID controller can prevent the divergence because it considers the derivative term between EPEs (edge placement error) of previous and current iteration. Since MEEF-based correction uses the variable damping value derived from MEEF of each pattern fragment, it is effective for the convergence of the memory bit-line layer composed of the complicated 2D patterns. MEEF-based correction combined with PID controller merges the merits of each method and is found to be a stable correction method for k1 factor smaller than 0.27. Applying the proposed method, we could remove the process weak points having more than 20% CD variation caused by the divergence and achieve sufficient process margin for sub-60nm memory device. OPC run time is also reduced by 40% compared with the normal correction method.

Immersion lithography with ArF light and Ultra Pure Water (UPW) is the most promising technology for semiconductor manufacturing with 65 nm hp design and below. Since Nikon completed the first full-field immersion scanner, the Engineering Evaluation Tool (EET, NA=0.85) at the end of 2004, Toshiba and Nikon have investigated overlay accuracy with the EET which uses the local fill nozzle. EET successfully demonstrated immersion tools are comparable in single machine overlay accuracy to dry tools, and immersion-dry matching has the same level overlay matching accuracy as dry-dry matching. EET also made it clear that overlay accuracy is independent of scanning speed, and both solvent-soluble topcoats, as well as developer-soluble topcoats can be used without degradation of overlay accuracy. We investigated the impact of the thermal environment on overlay accuracy also, assuming that a key technology of overlay with immersion tools must achieve thermal stabilities similar to dry tools. It was found that the temperature of supply water and loading wafer are stable enough to keep the overlay accuracy good. As for evaporation heat, water droplets on the backside of the wafer lead to overlay degradation. We have decided to equip the wafer holder of S609B, the first immersion production model, with an advanced watertight structure.

Immersion lithography allows the semiconductor industry to create next-generation devices without requiring a large shift in infrastructure, making it an appealing extension to optical lithography. Improved resolution is enabled by placing an immersion fluid with a high refractive index between the final lens of the optical system and the resist-coated wafer. Several engineering challenges accompany the insertion of the immersion fluid in a production tool, one of the most important being the confinement of a relatively small amount of liquid to the under-lens region. The semiconductor industry demands high throughput, leading to relatively large wafer scan velocities and accelerations. These result in large viscous and inertial forces on the three-phase contact line between the liquid, air, and substrate. If the fluid dynamic forces exceed the resisting surface tension force then residual liquid is deposited onto the substrate. Liquid deposition is undesirable; as the droplets evaporate, they will deposit impurities on the substrate. In an immersion lithography tool, these impurities may result in defects. An experimental investigation was undertaken to study the static and dynamic contact angle under conditions that are consistent with immersion lithography. A semi-empirical model is described here to predict the velocity at which liquid loss occurs. This model is based on fluid physics and correlated to measurements of the dynamic and static contact angles. The model describes two regimes, an inertial and a capillary regime, characterized by two distinct liquid loss processes. The semi-empirical model provides the semiconductor industry with a useful predictive tool for reducing defects associated with film pulling.

This paper discusses the types and formation of immersion defects. It is shown that drying stains and water marks are the main immersion defects. The immersion defects are related to resist leaching, water penetration and droplet formation. It is shown that scanner immersion hood design based on an actuated air gap and air curtain droplet clean-up minimizes defect counts. Additionally, pre-and post soaks steps in the track can reduce drying stains and water marks. The defect performance is evaluated on XT:1250i and XT:1400i systems. It is shown that the immersion defect density can go as low as 0.01 /cm², which is well below the ITRS 2005 number of 0.03 /cm².

To evaluate the effect of water exposure to a resist stack a set of experiments was designed that introduce a pre- and post-exposure wetting time to a coated wafer. The ASML 1150i α-immersion scanner, integrated with a TEL-Lithius coater track, was used to investigate the formation of defects related to the extended wetting. In the first approach, wetting was achieved using a dynamic DI-water rinse in the developer module of the track. For the second approach the immersion hood was positioned over the wafer at a fixed position and time, subjecting the wafer area below the immersion hood to the flowing water. We investigated various resists and topcoats. Defect inspections were performed on these film stacks after imaging.

The immersion effects on lithography-system performance have been investigated using a ASML TWINSCAN XT:1250Di immersion-ArF scanner (NA=0.85) and Tokyo Electron CLEAN TRACK ACT12 at IMEC. Effects of immersion-induced-temperature change and effects of material-top surface are discussed in this paper. The wafer-stage temperature is measured during the leveling-verification tests and compared with the observed residual-focus-error change. The results indicate that stage-temperature change under an immersion environment can induce a focus change. In this paper, it was proved that the improved-temperature-control stage is effective to mitigate the immersion-specific focus change. The immersion effect on overlay is also investigated as a function of material top surface. It was demonstrated that the effect of material-receding-contact angles on the grid-residual errors (non-correctable errors) is small in the latest-immersion-hardware configuration of the scanner. However, there was a tendency that material with a smaller-receding-contact angle has a larger-wafer scaling although it is a correctable parameter. This can be caused by the first-layer wafer shrinkage due to more water evaporation on the more-hydrophilic surface. The immersion effect on scanner-dynamic performance is then investigated by changing the material-top surface and the scan speed of the scanner. It was turned out that the scan synchronization is not much affected by differences of material receding-contact-angles for the new configuration of the scanner. Moving-standard deviation of the synchronization error in scanning direction (y-direction) is slightly more affected by increased scanning speed, although it stays within specification even at a maximum scan speed of 500 mm/sec. Finally the immersion effects on resist-profile uniformity are examined. It was found that lower-leaching-film stacks (with a top coat or a lower leaching resist) seem to mitigate the variation of resist-profile uniformity.

It is well known that the refractive optics used in today's exposure tools are highly chromatic, meaning that small wavelength shifts will cause large focus shifts. Even a line-narrowed excimer laser has a large enough range of wavelengths that we can no longer think of an infinitely thin image plane. The concept of "focus blur" can be generalized to encompass the effect of laser bandwidth chromatic aberrations, vertical stage vibrations (MSDz) and stage tilts which cause focus to change during the scan. This paper will introduce a new parameter called Mean Absolute Defocus (MAD) that can characterize the focus blur, and will be shown to correlate with the lithographic effects. Focus blur can be incorporated into simulation models, in a manner similar to the way that stage vibration is modeled. New simulation results will illustrate the impact of focus blur on modern lithographic processes. Process stability and machine-to-machine matching issues will be discussed.

Phase Measurement Interferometers (PMI) are widely used during the manufacturing process of high quality lenses. Although they have an excellent reproducibility and sensitivity, the set-up is expensive and the accuracy of the measurement needs to be checked frequently. This paper discusses an alternative lens metrology method that is based on an aerial image measurement. We discuss the Extended Nijboer-Zernike (ENZ) method and its application to aberration measurement of a high-NA optical system of a wafer stepper. ENZ is based on the observation of the through-focus intensity point-spread function of the projection lens. The advantage of ENZ is a simple set-up that is easy to run and maintain and provides good accuracy. Therefore the method is useful during lens assembly in the factory. The mathematical framework of ENZ is shown and the experimental procedure to extract aberrations for a high-NA lens is demonstrated on a high-NA DUV lithographic lens. PMI data is given as reference data. It is shown that ENZ provides an attractive alternative to the interferometer.

An automated aberration extraction method is presented which allows extraction of lithographic projection lens' aberration signature having only access to object (mask) and image (wafer) planes. Using phase-wheel targets on a two-level 0/π phase shift mask, images with high sensitivity to aberrations are produced. Zernike aberration coefficients up to 9^th order have been extracted by inspection of photoresist images captured via top-down SEM. The automated measurement procedure solves a multi-dimensional optimization problem using numerical methods and demonstrates improved accuracy and minimal cross-correlation. Starting with a detailed procedure analysis, recent experimental results for 193-nm projection optics in commercial full field exposure tools are discussed with an emphasis on the performance of the aberration measurement approach.

The OPE signature of a lithographic stepper or scanner has become a very important characteristic of the tool, as it determines the OPC correction to be applied to reticles exposed on that tool. The signature depends on a variety of detailed information about the scanner lens and illuminator, which in turn depend on the characteristics of the illumination light from the laser. Specifically, changes in the laser bandwidth should impact OPE as the lens exhibits some chromatic aberration. Tool-to-tool differences and time fluctuation of the laser bandwidth could cause variations in OPE tool matching and stability. To assess this, a detailed study of laser bandwidth effects on OPE was performed. A sensitive spectrometer was connected to a litho laser, allowing careful measurements of both the FWHM and E₉₅ parameters of the laser spectral profile. Lithographic modeling using the chromatic response of the lens was run in order to predict effects. Exposures of CD through pitch were made to test the modeling. Finally, the bandwidth data was correlated with litho sensitivity to create a "bandwidth effect", put in context with the other common scanner parameters affecting OPE.

Double patterning lithography is very fascinating way of lithography which is capable of pushing down the k1 limit below 0.25. By using double patterning lithography, we can delineate the pattern beyond resolution capability. Target pattern is decomposed into patterns within resolution capability and decomposed patterns are combined together through twice lithography and twice etch processes. Two ways, negative and positive, of doing double patterning process are contrived and studied experimentally. In this paper, various issues in double patterning lithography such as pattern decomposition, resist process on patterned topography, process window of 1/4 pitch patterning, and overlay dependent CD variation are studied on positive and negative tone double patterning respectively. Among various issues about double patterning, only the overlay controllability and productivity seemed to be dominated as visible obstacles so far.

Today novel RET solutions are gaining more and more attention from the lithography community that is facing new challenges in attempting to meet the new requirement of the SIA roadmap. Immersion, high NA, polarization, and mask topography, are becoming common place terminology as lithographers continue to explore these areas. Here with, we compare a traditional 6% MoSi based EAPSM reticle and a high transmission solution made of a SiON/Cr film stack. Insights into the manufacturability of high transmission material are provided. Test patterns have been analyzed to determine the overall impact of imaging performance when used with immersion scanners and polarized light. Some wafer results provide reliability of simulations, which are used to make further investigation on polarization and immersion effects.

Patterning of random CH for the 65nm node and below has proven to be a very difficult task. As a rule of thumb, difficulties in contact patterning are driven by the low depth of focus towards isolated contacts and/or the lower contrast combined with higher mask error factor (MEEF) for denser contact arrays. In this work, we experimentally investigate the use of illumination modes consisting of the combination of annular plus conventional illumination, so-called "Bulls-Eye" illumination. This study is a search for the optimal sigma settings for the annular and conventional parts, with respect to process window and MEEF through pitch. Also, the extend to which the Bulls-Eye is advantageous is demonstrated by means of experimental comparison to wafer prints by conventional illumination. Besides regular grid CH arrays, the Bulls-Eye performance is evaluated for different 2D contact patterns. Experimental results are obtained on ASML ArF scanners at various NAs up to 0.93. Additionally, immersion lithography and Focus Drilling are considered at given exposure setting as techniques to increase the focal depth. The experiments show promising results, printing contacts from k₁ = 0.40 onwards with acceptable process, MEEF, and proximity through pitch, and this without side-lobe printing.

We explore technical and practical issues to apply EAPSM technology with high transmission into ArF lithography. This technique needs to be reviewed in the standpoint of process and device fabrication using short wavelength, high NA, OAI and OPC technology. In this paper, we analyze optical characteristics of multi-stacked film that composed of phase material like MoSi, Cr-SiON, Cr-SiO₂, and Ta-SiO₂. Three-dimensional analyses of film structure are to consider intensity variations and optical influence by n &k value, thickness and polarization light. The comparison will be focused on optimization or determination of each high T materials. Moreover, we specify CD impacts of mask CD error, variations of phase and transmission for various pattern size, and 3D structure. Polarization effect in this structure and high NA condition will be also interesting part to be studied impacts on process. In the device application of technology, we consider overall process margin to satisfy cell & periphery design rule and OPC treatment to improve process windows. Optimum SRAF design and tri-tone mask technology will be key issue to improve DOF margin of specific design rule in OPC treatment. For 65nm technology or less, intensity formation distributed on mask affects CD and process margin directly on wafer patterning process. High transmission EAPSM will have specifically differences with 6% EAPSM in OPC treatment and it will be required new OPC rule in ArF lithography. Using simulation and experiment, we find high transmission EAPSM has advantages in device manufacturing and approach technical issue to be solved in material, process and device application. This technique shows to improve exposure latitude & DOF margin, and to reduce MEEF in process. Finally it will be good candidate to satisfy lithography requirement of 65nm and 45nm node.

In this paper we describe, from the user's point of view, how Inverse Lithography Technology (ILT) differs from Optical Proximity Correction (OPC). We discuss some specifics of ILT at chip-scale. We show simulation and experimental results from 90nm and 65nm semiconductor nodes, comparing results from ILT-generated masks and OPC-generated masks for real-life layouts, in a production environment. In addition, we discuss issues related to complexity and manufacturability of ILT-generated masks.

Our studies of second generation immersion fluid candidates are moving beyond the discovery phase, and into addressing issues for their commercial application. Thus, we continue work to examine and fundamentally understand fluid transparency and refractive index, to fully optimize these properties. At the same time, we are now examining other process concerns, including index variation with temperature, new imaging performance studies, fluid handling considerations, and fluid property maintenance with active recycle during lithographic exposure. The systems and procedures we have developed in these areas continue to show our fluids' promise for sub-45nm immersion lithography applications.

Leaching of resist components into the water has been reported in several studies. Potential effects of photo-acid generator (PAG) dissolved in water include photocontamination of the last optical surface and the formation of particulate defects on the wafer surface. In order to determine the impact of these phenomena on lithographic performance, such as optics lifetime and yield, we have initiated a set of controlled studies, where predetermined amounts of PAG were introduced into pure water and the results monitored quantitatively. One set of studies identified the complex, nonlinear paths leading to photocontamination of the optics. At concentrations typical of leached PAG, below 500 ppb, the in-situ self-cleaning processes prevent contamination of the optics. On the other hand, initial experiments with a nano-dropper show that micron-scale particles from the dissolved PAG are formed on the wafer surface when water evaporates. This phenomenon requires further systematic studies both at the fundamental science and the engineering levels.

In immersion lithography, water drop residue has been identified as the source of watermark defects. Many methods have been studied to reduce water drops outside of the immersion area. However, from a physical point of view, the wafer surface is very hard to keep dry after immersion exposure. The water drop residues easily cause watermark defects that ranges from micrometer-size circular defects to sub-micron scum defects. In this paper we describe a few new methods to understand watermark formation. We also describe our studies on various water drop sizes and their impact on CD and defects. Our results show that major watermark defects occur as a result of the presence of relatively small water drops. A few methods have also been studied to reduce the impact of watermarks in order to remove watermark-induced pattern defects on wafers. These methods include post-immersion exposure treatment as well as novel material and process improvement methods. By applying these methods, we are able to remove watermark defects without an additional resist protection layer while still maintaining good resist lithographic performance.

We report on our comprehensive survey of high-index UV optical materials that may enable extension of immersion lithography beyond a numerical aperture of 1.45. Band edge, refractive index, and intrinsic birefringence (IBR) at 193 nm determine basic viability. Our measurements of these properties have reduced the list of potential candidates to: ceramic spinel, lutetium aluminum garnet, and a class of germanium garnets. We discuss our measurements of the intrinsic properties of these materials and assess the present status of their material quality relative to requirements. Ceramic spinel has no significant IBR, but transmission and scatter for the best samples remain at least two orders of magnitude from specifications. Improving these would require a major development effort. Presently available lutetium aluminum garnet has material quality much closer to the specifications. However, the IBR is about three times the required value. The germanium garnets offer the possibility of a lower IBR, but a suitable candidate material has yet to be established.

We tried to investigate various kinds of metal fluoride materials which have higher gravity than CaF₂ and cubic crystal system, and we found out barium lithium fluoride (BaLiF₃) and potassium yttrium fluoride (KY₃F₁₀) as candidates for the last lens material. We have developed unique Czochralski (CZ) machines and techniques for the growth of large calcium fluoride single crystals. And we applied these technologies to the growth of fluoride high index materials. We have succeeded to grow the large BaLiF₃ single crystal with 120mm in diameter and a KY₃F₁₀ single crystal, and measured their basic properties such as refractive index, VUV transmittance, birefringence, and so on. As a result of our basic research, we found out that BaLiF₃ single crystal is transparent at VUV region, and the refractive index at 193nm is 1.64, and KY₃F₁₀ single crystal has the index of 1.59 at the wavelength of 193nm which is slightly higher than fused silica. We expect that these fluoride high index materials are useful for the last lens material of the next generation immersion lithography.

Mask defects are of increasing concern for future lithography generations. The improved resolution capabilities of immersion and EUV systems increase also the sensitivity of these systems with respect to small imperfections of the mask. Advanced mask technologies such as alternating phase shift masks (AltPSM), chromeless phase shift lithography (CPL), or "thick" absorbers on EUV masks introduce new defect types. The paper presents an application of rigorous electromagnetic field modeling for the study of typical defect printing mechanisms in ArF immersion lithography and in EUV lithography. For standard imaging and mask technologies, such as binary masks or attenuated phase shift masks, small defects usually print as linewidth or critical dimension (CD) errors with the largest effect at best focus. For AltPSM, CPL masks, and EUV masks this is not always the case. Several unusual printing scenarios were observed: placement errors due to defects can become more critical than CD-errors, defects may print more critical at defocus positions different from the center of the process window, the defect printing may become asymmetric through focus, and the risk of defect printing depends on the polarization of the used light source. Several simulation examples will demonstrate these effects. Rigorous EMF simulations in combination with vector imaging simulations are very useful to understand the origins of the observed defect printing mechanisms.

Today novel RET solutions are gaining more and more attention from the lithography community that is facing new challenges in attempting to meet the new requirement of the SIA roadmap. Immersion, high NA, polarization, and mask topography, are becoming common place terminology as lithographers continue to explore these areas. Here with, we compare a traditional 6% MoSi based EAPSM reticle and a high transmission solution made of a SiON/Cr film stack. Insights into the manufacturability of high transmission material are provided. Test patterns have been analyzed to determine the overall impact of imaging performance when used with immersion scanners and polarized light. Some wafer results provide reliability of simulations, which are used to make further investigation on polarization and immersion effects.

Full-field ArF immersion scanners with NA above 1.20 are expected to be available in 2006. 45-nm-halfpitch lines and spaces (LS) are feasible by using these scanners with polarized dipole illumination. However, from the standpoint of design flexibility, using c-quadrupole or annular illumination is the better alternative to the dipole illumination. An attenuating phase-shifting mask (attPSM) has been widely used for device manufacturing to improve resolution because of the simple layer structure without rigid specifications for mask topography such as undercut biasing in case of alternating PSM. In this study the impact of the absorber thickness of single-layer and bi-layer attPSMs, i.e. MoSi, Cr/SiON, and Ta/SiO₂, on the imaging performance of ArF immersion lithography is investigated by using a rigorous electro-magnetic field simulator, Prolith version 9.0.1 with advanced mask package (KLA-Tencor), using a lumped parameter resist model. Exposure latitude (EL) of critical dimension (CD), depth of focus, mask-error-enhancement factor (MEEF), and sensitivity to polarization are compared to find an optimum mask structure for the c-quadrupole illumination in hyper- NA lithography. In the hyper-NA lithography, the standard absorber thickness giving 6% transmittance is not necessarily the optimum from the viewpoint of the imaging performance. For example, to delineate 45 nm 1:1 LS with NA of 1.20 by using the Cr/SiON attPSM, the aerial-image contrast in resist of the standard 25-nm-thick Chromium is 20% smaller than that of 50-nm-thick Chromium. Optimizing the Chromium thickness increases EL by 29%, though it has few impacts, less than 1%, on 65 nm 1:1 LS with NA of 0.85. The EL of a thickness-optimized Ta/SiO₂ attPSM is 33% larger than that of the standard 68-nm-thick MoSi. Supposing the dose error, the focus error, and wafer CD error, we can relax the specification of mask CD error by using the 30-nm-thick Tantalum. Ta/SiO₂ is 63% more sensitive to the polarization state of the incident light than MoSi, but the impact on CD is only 0.8 nm with a 10% change of the polarization. Calculating diffraction efficiencies for the 45 nm LS shows probable causes of the better imaging performance of Ta/SiO₂; intensity of the 0th- and 1st-order diffracted light becomes larger than for MoSi and Cr/SiON as the illumination angle increases, phase difference between the 0th and 1st order is smaller in the large illumination angle, and amount of the flare-like exposure by light sources of the c-quad illumination parallel to the LS is smaller. As a summary, the three attPSMs with the nominal 6% transmittance and 180o phase difference give different imaging performances. Optimizing mask materials and thicknesses is important to have better image quality at NA above 1.0.

In case drastic changes need to be made to tool configurations or blank specifications, it is important to know as early as possible under which conditions the tight image placement requirements of future lithography nodes can be achieved. Modeling, such as finite element simulations, can help predict the magnitude of structural and thermal effects before actual manufacturing issues occur, and basic experiments using current tools can readily be conducted to verify the predicted results or perform feasibility tests for future nodes. Using numerical simulations, experimental mask registration, and printing data, the effects on image placement of stressed layer patterning, pellicle attachment, blank dimensional and material tolerances, as well as charging during e-beam writing were investigated for current mask blank specifications. This provides an understanding of the areas that require more work for image placement error budgets to be met and to insure the viability of optical lithography for future nodes.

One of the enabling RET candidates for 45 nm robust imaging is high transmission (20-30%) EAPSM masks. However, the effectiveness of these masks is strongly affected by the electromagnetic field (EMF) that is ignored in most commercial full-chip OPC applications that rely on the Kirchhoff approximation. This paper utilizes new commercial software to identify and characterize points in a design that are especially sensitive to these EMF effects. Characterization of conventional 6% and 30% High Transmission photomasks were simulated and compared with experimental results. We also explored, via simulation-driven design of experiment, the impact of mask variations in transmission, phase, and SRAF placement and size to the imaging capability. The simulations are confirmed by producing a photomask including the experimental variations and printing the mask to silicon. Final analysis of the data will include exact mask measurements to confirm match to simulation assumptions of mask stack, and phase.

ArF immersion lithography has opened the road towards increased optical resolution at the 193nm wavelength. Consequently, keeping the same 4X optical demagnification factor, the dimensions on the mask scale down to sub-wavelength values when we enter the 45nm node. At such dimensions, mask topography, mask type and materials as well as the polarization state of the light will influence the diffraction spectrum of a layout. As a result the image from high NA lithographic systems depends on the polarization state and intensities of the interfering orders. In general, with smaller features on the mask stronger polarization changes occur. Apart from the polarization changes in diffraction orders the total intensity in a diffraction order is also different from that predicted by standard scalar-Kirchhoff diffraction approximation used in present OPC packages. The difference in intensities of diffraction orders due to different mask materials and topography is the more dominating factor leading to through pitch CD errors when the scalar-Kirchhoff model is used for layout adjustment. Based on findings and classification of topography induced effects, a deviation-driver from scalar diffraction model was identified. This paper discusses a solution to compensate for topography effects while using the scalar diffraction model for reticle treatment. The area of applicability of such a scalar model, its advantages and limitations are illustrated with simulations and experiments.

This paper describes a method to measure the dynamic behavior of resist leaching in the time domain that is relevant for immersion lithography. The total leaching amount as a function of the contact time between water and resist is obtained and successfully fitted using previously described kinetic equations. In this way valuable information is obtained for the understanding of the contribution of resist leaching to lens contamination, CD uniformity and defectivity. The procedure is further used to study the effectiveness of various leaching mitigation strategies. Top coats prove to be a very effective method to reach the leaching specifications of the tool vendors. Also immersion dedicated resist materials meet the specifications or come very close.

Many RET technologies, such as rule and model based OPC, the use of sub-resolution assist features, and various PSM methodologies, can be thought of as heuristics employed in an attempt to design improved photomasks. Unfortunately, these traditional approaches are running into severe difficulties at advanced technology nodes (90nm and beyond). We discuss how one can find the optimal photomask by rigorously solving the lithography inverse problem. The design of the optimal mask takes into consideration not only pattern fidelity under nominal conditions, but also the size of the process window and the constraints and costs of mask manufacturing. By formulating the problem in a rigorous mathematical framework, we find highly optimal solutions which do not arise from traditional ad hoc approaches. The resulting masks often provide substantially improved depth-of-focus and exposure latitude, enabling geometries that may be otherwise unattainable.