IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

The phase-shifting mask consists of a normal transmission mask that has been coated with a transparent layer patterned to ensure that the optical phases of nearest apertures are opposite. Destructive interference between waves from adjacent apertures cancels some diffraction effects and increases the spatial resolution with which such patterns can be projected. A simple theory predicts a near doubling of resolution for illumination with partial incoherence σ < 0.3, and substantial improvements in resolution for σ < 0.7. Initial results obtained with a phase-shifting mask patterned with typical device structures by electron-beam lithography and exposed using a Mann 4800 10× tool reveals a 40-percent increase in usuable resolution with some structures printed at a resolution of 1000 lines/mm. Phase-shifting mask structures can be used to facilitate proximity printing with larger gaps between mask and wafer. Theory indicates that the increase in resolution is accompanied by a minimal decrease in depth of focus. Thus the phase-shifting mask may be the most desirable device for enhancing optical lithography resolution in the VLSI/VHSIC era.

Improving resolution in photolithography with a phase-shifting mask

Optical proximity correction (OPC) is one of the most widely used resolution enhancement techniques (RET) in nanometer designs to improve subwavelength printability. Conventional model-based OPC assumes nominal process conditions without considering process variations because of the lack of variational lithography models. A simple method to improve OPC results under process variations is to sample multiple process conditions across the process window, which requires long run times. We derive a variational lithography model (VLIM) that can simulate across the process window without much run-time overhead compared to the conventional lithography models. To match the model to experimental data, we demonstrate a VLIM calibration method. The calibrated model has accuracy comparable to nonvariational models, but has the advantage of taking process variations into consideration. We introduce the variational edge placement error (VEPE) metrics based on the model, a natural extension to the edge placement error (EPE) used in conventional OPC algorithms. A true process-variation aware OPC (PVOPC) framework is proposed used the VEPE metric. Due to the analytical nature of VLIM, our PVOPC is only about 2 to 3× slower than the conventional OPC, but it explicitly considers the two main sources of process variations (exposure dose and focus variations) during OPC. Thus our post-PVOPC results are much more robust than the conventional OPC ones, in terms of both geometric printability and electrical characterization under process variations.

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True process variation aware optical proximity correction with variational lithography modeling and model calibration

Optical proximity correction (OPC) and phase-shifting mask (PSM) are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. Traditional RETs, however, fix the source thus limiting the degrees of freedom during the optimization of the mask patterns. To overcome this restriction, a set of simultaneous source and mask optimization (SMO) methods have been developed recently where the resulting source and mask patterns fall well outside the realm of known design forms. This paper focuses on developing computationally efficient, pixel-based, simultaneous source mask optimization methods for both OPC and PSM designs, where the synergy is exploited in the joint optimization of source and mask patterns. The Fourier series expansion model is applied to approximate the partially coherent system as a sum of coherent systems. Cost sensitivity is used to drive the output pattern error in the descent direction. In order to influence the solution patterns to have more desirable manufacturability properties, topological constraints are added to the optimization framework. Several illustrative simulations are presented to demonstrate the effectiveness of the proposed algorithms.

Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography

ACKNOWLEDGEMENTS My sincere gratitude to Professor Dennis Sylvester for providing me the opportunity to study at the University of Michigan. Without his vision, encouragement and continuous support, this dissertation was impossible. Professor Sylvester was always around to listen and to give advice. He not only taught me how to ask questions and express my ideas, also taught me to be a careful and meticulous researcher. He always provided timely responses for proof reading and commenting my papers and chapters, extremely patient even after I had made many revisions. A special thank goes to Dr. Luigi Capodieci, who has always been very supportive and responsible for helping me complete the challenging research that lies behind this dissertation. He was always there listening to my ideas and giving me feedbacks and guidelines that help me go through my problems at many critical moments. I'm also deeply indebted to the rest of my thesis committee: Professor David Blaauw, Professor Ken Wise, for their insightful comments, hard questions, constructive suggestions and numerous encouragement. During the course of this work, I was part of the GSRC and SRC program. I would like to thank the sponsors for their continuous support of the projects. A warm hug to my research fellows for their very valuable inputs and contributions for various projects: Peng. They have made my life at UM very pleasant and memorable: Last, but not least, my utmost thanks to my family: my parents Yinxiang Yang and Xiumei Zhang, for giving me life in the first place, for educating me with aspects from both arts and sciences, for teaching me how to be a good person and for their unconditional support and encouragement to pursue my interests. Their patient love enabled me to complete this work.

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Manufacturability Aware Design.

With the continuous shrink of feature sizes the pitch of the mask comes closer to the wave length of light. It has been recognized that in this case polarization effects of the mask become much more pronounced and deviations in the diffraction efficiencies from the well known Kirchhoff approach can no longer be neglected. It is not only the diffraction efficiencies that become polarization dependent, also the phases of the diffracted orders tend to deviate from Kirchhoff theory when calculated rigorously. This also happens for large structures, where these phase deviations can mimic polarization dependent wave front aberrations, which in the case of polarized illumination can lead to non-negligible focus shifts that depend on the orientation and the features size themselves. This orientation dependence results in a polarization induced astigmatism offset, which can be of the same order of magnitude or even larger as polarization effects stemming from the lens itself. Hence, for correctly predicting polarization induced astigmatism offsets, one has to both consider lens and mask effects at the same time. In this paper we present a comprehensive study of polarized induced phase effects of topographic masks and develop a simple theoretical model that accurately describes the observed effects.

Polarization-induced astigmatism caused by topographic masks

Long write times have been an industry wide concern regarding rising mask costs. The purpose of this study is to develop a simple model that can predict mask write time precisely, without an e-beam writer. With a good understanding of the trade-offs between design complexity and write time, mask makers can work with mask designers more closely to simplify design and minimize mask cost. This work compared several basic models including calculations based on write area with a fixed e-beam shot size, a software estimation with a pre-set exposure, and a mask stage settling time. Our proposed model uses a completely different approach to examine the correlation between layout complexity (vertices count, total line edge, figure, etc.) through a CATS layout segmentation and actual write time. It is found that write time is a strong function of layout figure, vertex count and total line edge. Errors between actual write time and estimated write time from the new model reduced from 7% on average on the current production software to 3%. Additionally, the new model can operate independent of the writer type and without fractured data being transferred onto a writer. Also provided are a few case studies to evaluate the interaction between write time and basic shape/OPC (optical proximity correction). Using a simple design shape and a better data snapping strategy can reduce write time up to 10 fold for applications in nano-imprint template manufacturing. Several strategies to reduce mask cost are proposed.

Mask cost analysis via write time estimation

Mask inspection has become a major bottleneck in the manufacturing flow taking up as much as 40% of the total mask manufacturing time. In this paper, we explore techniques to improve the reticle inspection flow by increasing its design awareness. We develop an algorithm to locate nonfunctional features in a postoptical proximity correction layout without using any design information. Using this, and the timing information of the design (if available), the smallest defect size that could cause the design to fail is assigned to each reticle feature. The criticality of various reticle features is then used to partition the reticle such that each partition is inspected at a different pixel size and sensitivity so that the false and nuisance defect count is reduced without missing any critical defect. We also develop an analytical model to estimate the false and nuisance defect count. Using those models, our simulation results show that this design-aware mask inspection can reduce the false and nuisance defect count for a critical polysilicon layer from 80 defects down to 49 defects, leading to substantial reduction in defect review load. We also develop a model to estimate first pass yield (FPY) and show that our method can improve the FPY for a polysilicon layer from 11% to 30%. Apart from the polysilicon layer, the potential benefit of this approach is analyzed for active, contact and all the metal/via layers.

Design-Aware Mask Inspection

Keywords: Hyper NA, High NA, polarization, imaging, immersion, 193nm, low k1, mask birefringence, Stokes parameters ABSTRACT The introduction of polarized light in high NA lithography re quires additional characterization metrics for illumination systems. It has been shown that the percentage of the total light intensity that is polarized in the desired direction is a metric that can be closely related to wafer CD. On ASML sy stems, this quantity is called IPS (Intensity in Preferred State). Illuminators are characterized in terms of the mi nimum IPS found somewhere across the illuminated area and the IPS Range. In case the mask has a finite birefringe nce, there is an additional impact on th e effective IPS. After passing through the mask blank, the IPS of the light will have changed and hence, there will be a response for wafer CD. Mask birefringence in conjunction with IPS introduces an additional contribution for the CD budget. This work will focus on the impact of mask birefringence on wafer CD for different scenarios of polarized illumination. We will show that the angle of the fast axis of birefringence can have a much greater impact on CD than the maximum birefringence magnitude itself. Based on these results we will derive a requirement for mask birefringence which has its foundation on CD. We will present measurements of the birefringence distributions of mask blanks, patterned masks, and masks with pellicles to investigate the contribution of the mask process flow starting from substrate, material deposition, processing, and final pellicle application. In addition to the material properties of the pellicle, the mounting of the pellicle to the substrate may induce additional stress birefringence. 1. Introduction Since the beginning of optical lithography, the scalar approximation for the description of optical imaging has been used. For low numerical apertures (NA) of the imaging optics and for mask feat ures sizes well above the wavelength, imaging is largely independent of the polarization properties of the light hence, in this regime it is very well justified to omit the vector (polarized) nature of light for the description of the imaging process. Early light sources used (Hg g-line and i-line) were unpolarized, which can be understood as an incoherent superposition of two orthogonal polarization states. The use of laser light sources in lithography introduced polarized light, however most imaging systems destroyed (scrambled) the fixed polarization to offer unpolarized light at the reticle plane. In the scalar (or unpolarized) approxima tion, the concept of birefringence is meaningless. However, lens manufacturers were the first to be aware that birefringence has an impact on imaging. As k

The impact of mask birefringence on hyper-NA (NA>1.0) polarized imaging

Progress in photomask technology, exposure system flexibility and lithographic computation has enabled the practical exploration of jointly optimized lithographic imaging variables. The interaction between certain components, such as mask and illuminator, allows co-optimized solutions to frequently achieve better results when compared with sequential, single factor optimizations. In this work, we focus on the automated co-optimization of embedded phase shift mask transmission factor and exposure system illumination source profile for improving image based merit functions. Algorithm descriptions are provided and the critical interaction of optimization parameters with mask layout is highlighted. Our co-optimization algorithm is exercised on the more challenging random logic case and the concept of manipulating or restricting layout conditions to improve the achieved merit function is studied. Finally, suggestions for the experimental prototyping of solutions are provided and an assessment on deviating from the industry accepted 6% transmission discussed.

Chris Progler

Papers

Polarization-induced astigmatism caused by topographic masks

Mask cost analysis via write time estimation

Design-Aware Mask Inspection

The impact of mask birefringence on hyper-NA (NA>1.0) polarized imaging

Layout and source dependent transmission tuning