A new, rigorous model for solving three-dimensional light-scattering problems in the optical lithography process of semiconductor manufacturing is introduced. The new model employs a hybrid approach to solve Maxwell's equations in the spatial frequency domain with the use of vector potentials. The model extends a successful two-dimensional lithography model and has been applied to the simulation of the patterning of light by three-dimensional (3-D) photomasks. The theory behind the new model is presented, and examples are given of the model's results and computational efficiency on an engineering workstation. The efficiency is highest for fully symmetric structures where the paraxial partial-coherence approximation is valid. The model can easily be extended to the efficient simulation of light scattering in 3-D optical alignment and photosensitive polymer problems.

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Triple patterning lithography (TPL) has received more and more attentions from industry as one of the leading candidate for 14nm/11nm nodes. In this paper, we propose a high performance layout decomposer for TPL. Density balancing is seamlessly integrated into all key steps in our TPL layout decomposition, including density-balanced semi-definite programming (SDP), density-based mapping, and densitybalanced graph simplification. Our new TPL decomposer can obtain high performance even compared to previous state-of-the-art layout decomposers which are not balanced-density aware, e.g., by Yu et al. (ICCAD'11), Fang et al. (DAC'12), and Kuang et al. (DAC'13). Furthermore, the balanced-density version of our decomposer can provide more balanced density which leads to less edge placement error (EPE), while the conflict and stitch numbers are still very comparable to our non-balanced-density baseline.

The upcoming 14nm logic node will require lithographic patterning of complex layout patterns with minimum pitches of approximately 44nm to 50nm. This requirement is technically feasible by reusing existing 20nm litho-etch-litho-etch (LELE) double patterning (DPT) methods with very strong restricted design rules. However, early indications are that the cost-effective design and patterning of these layouts will require lithographic methods with additional resolution, especially in two-dimensional configurations. If EUV lithography reaches maturity too late, the 14nm logic node will need other lithographic techniques and the corresponding physical design rules and EDA methodologies to be available. Triple patterning technology (TPT) is a strong option for 14nm node logic on both hole and line-space pattern layers. In this paper we study major implications of a 14nm logic TPT lithographic solution upon physical design, design rules, mask synthesis/EDA algorithms and their process interactions.

Self-aligned double pattering (SADP) has been adapted as a promising solution for sub-30nm technology nodes due to its lower overlay problem and better process tolerance. SADP is in production use for 1D dense patterns with good pitch control such as NAND Flash memory applications, but it is still challenging to apply SADP to 2D random logic patterns. The favored type of SADP for complex logic interconnects is a two mask approach using a core mask and a trim mask. In this paper, we first describe layout decomposition methods of spacertype double patterning lithography, then report a type of SADP compliant layouts, and finally report SADP applications on Samsung 22nm SRAM layout. For SADP decomposition, we propose several SADP-aware layout coloring algorithms and a method of generating lithography-friendly core mask patterns. Experimental results on 22nm node designs show that our proposed layout decomposition for SADP effectively decomposes any given layouts.