In all imaging systems, the forward process introduces undesirable effects that cause the output signal to be a distorted version of the input. A typical example is of course the blur introduced by the aperture. When the input to such systems can be controlled, prewarping techniques can be employed which consist of systematically modifying the input such that it (at least approximately) cancels out (or compensates for) the process losses. In this paper, we focus on the optical proximity correction mask design problem for "optical microlithography," a process similar to photographic printing used for transferring binary circuit patterns onto silicon wafers. We consider the idealized case of an incoherent imaging system and solve an inverse problem which is an approximation of the real-world optical lithography problem. Our algorithm is based on pixel-based mask representation and uses a continuous function formulation. We also employ the regularization framework to control the tone and complexity of the synthesized masks. Finally, we discuss the extension of our framework to coherent and (the more practical) partially coherent imaging systems

Mask Design for Optical Microlithography—An Inverse Imaging Problem

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks.

https://iopscience.iop.org/article/10.1088/2040-8978/12/4/045601/pdf

Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

Optical lithography has enabled the printing of progressively smaller circuit patterns over the years. However, as the feature size shrinks, the lithographic process variation becomes more pronounced. Source-mask optimization (SMO) is a current technology allowing a co-design of the source and the mask for higher resolution imaging. In this paper, we develop a pixelated SMO using inverse imaging, and incorporate the statistical variations explicitly in an optimization framework. Simulation results demonstrate its efficacy in process robustness enhancement.

/pdf/pixelated-source-mask-optimization-for-process-robustness-in-498fazra2f.pdf

Pixelated source mask optimization for process robustness in optical lithography

Inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem. We show how the inverse lithography problem can be addressed as an obstacle reconstruction problem or an extended nonlinear image restoration problem, and then solved by a level set time-dependent model with finite difference schemes. We present explicit detailed formulation of the problem together with the first-order temporal and second-order spatial accurate discretization scheme. Experimental results show the superiority of the proposed level set-based ILT over the mainstream gradient methods.

Level-set-based inverse lithography for photomask synthesis

Optical Proximity Correction (OPC) has been widely adopted for resolution enhancement to achieve nanolithography. However, conventional rule-based and model-based OPCs encounter severe difficulties at advanced technology nodes. Inverse Lithography Technique (ILT) that solves the inverse problem of the imaging system becomes a promising solution for OPC. In this paper, we consider simultaneously 1) the design target optimization under nominal process condition and 2) process window minimization with different process corners, and solve the mask optimization problem based on ILT. The proposed method is tested on 32nm designs released by IBM for the ICCAD 2013 contest. Our optimization is implemented in two modes, MOSAIC_fast and MOSAIC_exact, which outperform the first place winner of the ICCAD 2013 contest by 7% and 11%, respectively.

/pdf/mosaic-mask-optimizing-solution-with-process-window-aware-544j329e4r.pdf

MOSAIC: Mask Optimizing Solution With Process Window Aware Inverse Correction

Inverse Lithography Technology (ILT) is a rigorous approach to determine the mask shapes that produce the desired on-wafer 
results. In this paper, we briefly describe an image (or pixel))-based implementation of ILT in comparison to OPC 
technologies, which are usually edge-based. Such implementation is more computationally scalable and avoids laborious 
segmentation script-writing, which becomes more complex for newer generations because of complicated proximity 
effects. In this paper, we will give an overview of ILT, present some simulation and wafer examples to demonstrate the 
benefit of ILT, clarify common myths about ILT, discuss and show examples to illustrate the impact in every step of the 
mask making process. Specifically, studies done with several leading mask shops around the world on mask 
manufacturability (including data fracturing, writing strategy and writing time, mask inspection), will be shown.

Inverse lithography technology (ILT): What is the impact to the photomask industry?

In this paper, we present the Luminescent's ILT approach that can rapidly solve for the optimal photomask design. We
will discuss the latest development of ILT at Luminescent in the areas of sub-resolution assist feature (SRAF)
generation, process-window-based ILT and mask rule compliance (MRC). Results collected internally and from
customers demonstrate that ILT is not only an R&D tool, but also a tool quickly maturing for production qualification at
advanced technology nodes. By enforcing the proper constraints while optimizing the masks, ILT can improve process
windows while maintaining mask costs at a reasonable level.

Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45-nm and 32-nm

In this paper we present unintuitive patterns generated by inverse lithography technology. We show examples of contact hole masks designed with ILT that enjoy larger process windows than OPC. We also show variations in ILT-generated masks as the pitch of the contact hole array changes. In another example, we show poly masks designed for better process window to be substantially different from poly masks designed for better fidelity at nominal exposure-defocus (ED) condition. The mask with better fidelity has broken lines in comparison to the original layout. In a third example, we show deep trench mask patterns designed with ILT that, at first glance, bear no resemblance to the original layout, yet provide high fidelity in optical images. These patterns, although complex at first sight, can be generated in substantially simpler form with proper constraints without losing the spirit of ILT masks.

Inverse lithography technology principles in practice: unintuitive patterns

In this paper, we present the Luminescent's ILT approach that can rapidly solve for the optimal photomask design. We
will discuss the latest development of ILT at Luminescent in the areas of sub-resolution assist feature (SRAF) generation
and optimization to improve process window, and mask rule compliance (MRC). Results collected internally and from
customers demonstrate that ILT is not only an R&D tool, but also a tool quickly maturing for production qualification at
advanced technology nodes. By enforcing the proper constraints while optimizing the masks, ILT can improve process
windows while maintaining mask costs at a reasonable level.

Inverse lithography technology (ILT): keep the balance between SRAF and MRC at 45 and 32 nm

In this paper, we present the first ILT approach that can rapidly solve for the optimal photomask design and that is suitable for use in a production environment. We will discuss the latest development of ILT at Luminescent, in particular, in the areas of sub-resolution assist feture (SRAF) generation, mask rule compliance (MRC), and hardware acceleration. Results collected internally and from customers demonstrate that ILT is no longer just an RD as the industry moves forward, optical diffraction and interference are becoming fundamental obstacles, not just second order effects. It has long been known that the best lithography that is theoretically possible can be achieved by considering the design of photomasks as an inverse problem -- and then solving the inverse problem to find the optimal photomask for a given process, using a rigorous mathematical approach. Inverse Lithography Technology (ILT) has been explored for many years[1-8]. Although these early approaches to ILT often resulted in superb lithography, they were generally impractical in a production environment. Run-times were many orders of magnitude too slow, and the resulting masks were often too complex to manufacture. By ILT we mean the following: given the known forward transformation of a lithography process, ILT mathematically determines the optimized mask which produces the desired wafer target with the best pattern fidelity and largest process window. The forward transformation is modeled accurately, which may take into account all of the elements of the transformation from mask to wafer: for example, the electromagnetics of the 3D mask, the optics of illumination and the lens, the behavior of the photoresist, the dose and focus conditions, aberrations, etc. However, the strict inverse problem is ill-posed; because the forward operator is many-to-one (that is, many different masks will yield identical on-wafer results), and the function has no well-defined inverse. Moreover, for typical target patterns (e.g., a drawn layout with Manhattan geometry and sharp corners), there does not exist any mask function which

Dan Abrams

Papers

Inverse lithography technology (ILT): What is the impact to the photomask industry?

Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45-nm and 32-nm

Inverse lithography technology principles in practice: unintuitive patterns

Inverse lithography technology (ILT): keep the balance between SRAF and MRC at 45 and 32 nm

Inverse Lithography Technology (ILT) and Its Readiness for Production in Advanced Technology Nodes