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

In this paper, we survey key design for manufacturing issues for extreme scaling with emerging nanolithography technologies, including double/multiple patterning lithography, extreme ultraviolet lithography, and electron-beam lithography. These nanolithography and nanopatterning technologies have different manufacturing processes and their unique challenges to very large scale integration (VLSI) physical design, mask synthesis, and so on. It is essential to have close VLSI design and underlying process technology co-optimization to achieve high product quality (power/performance, etc.) and yield while making future scaling cost-effective and worthwhile. Recent results and examples will be discussed to show the enablement and effectiveness of such design and process integration, including lithography model/analysis, mask synthesis, and lithography friendly physical design.

Design for Manufacturing With Emerging Nanolithography

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?

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 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

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.

Fast inverse lithography technology

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

This paper presents ILT masks written by a DUV laser writer and a VSB e-beam writer, and their corresponding wafer print results. ILT mathematically determine the mask features that produce the desired on-wafer results. ILT-generated masks sometimes are non-intuitive, and different than those produced by past approaches; therefore, their manufacturability must be understood. In this study ILT was applied to create binary chrome-on-glass (CoG) masks with feature sizes ranging from 130 nm to 45 nm (at the wafer scale). The masks were written with both DUV laser (AMAT Alta 4300) and electron beam (JEOL JBX-9000) pattern generators. Wafers were then printed on a 193 nm scanner (ASML 1400, NA = 0.75). Mask image quality and wafer image quality (SEM micrographs and focus-exposure CD performance) were collected. In addition, it was also demonstrated that ILT has the capability to tune the mask complexity by constraining fracture figure size and the minimum mask feature/space.

Laser and e-beam mask-to-silicon with inverse lithography technology (ILT)

An implementation of inverse lithography technology is studied with special attention to 
illustrating and analyzing the placement, accuracy, and efficacy of subresolution assist elements. 
One-dimensional placement through pitch is characterized, and 2D capability is demonstrated for 
repeated patterns. Differences between the methods of mask preparation afforded by this system 
as compared to current practices are described.

Linyong Pang

Papers

Fast inverse lithography technology

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

Inverse lithography technology principles in practice: unintuitive patterns

Laser and e-beam mask-to-silicon with inverse lithography technology (ILT)

Inverse lithography technology at low k1: placement and accuracy of assist features