Yuri Granik

Using OPC to optimize for image slope and improve process window

We use the gradient of the image slope and gradient of the edge placement error (EPE) in order to improve both slope and EPE during OPC. The EPE gradient taken with respect to edge position is normally called MEEF or the MEEF matrix. Use of the gradient of image slope with respect to change in edge position was introduced by Granik as the “contrast matrix.” Whereas traditional OPC techniques focus on EPE alone (pattern fidelity), we broaden the scope of OPC to maximize slope for improved image robustness and to maximize process window.

Model-based OPC using the MEEF matrix

This paper covers the topic of matrix-OPC. In matrix-OPC, we perform OPC edge movements, considering the cross-MEEF of all edges which affect the edge placement error (EPE) at each simulation site. This contrasts with standard model-based OPC methods. In the standard methods a simulation site is placed on each edge fragment. The EPE is monitored by simulation along all sites. The EPE is assumed to be controllable for each site by moving the position of its edge fragment. In matrix OPC, not just one fragment, but all fragments which influence the EPE are used to control the EPE for a given site. Matrix OPC has application to the following areas: (1) OPC on PSM where non-adjacent edges can have larger impact than adjacent edges, (2) dipole and other complex illumination schemes, and (3) when the assumption that the self-MEEF terms are dominant starts to break down or when MEEF becomes negative.

New concepts in OPC

In this paper, we will discuss two new concepts to be used in model-based OPC: model-based fragmentation, and model tagging to account for long-range proximity effects. In model-based fragmentation we create an initial fragmentation consisting of small fragmentation across the design. Then, specific fragments are removed according to image criteria in order to keep only those fragmentation points which affect the aerial image the most. Optical flare and long-range etch effects are challenging because they have long interaction ranges. We describe here an edge tagging technique that binds different models to different regions on the layout enabling aberration- or density- sensitive corrections. We show application of this technique on a layout section. We discuss how to implement these techniques in practice and what impact they have on OPC speed and accuracy.

CD variation analysis technique and its application to the study of PSM mask misalignment

We study the influence of process parameters on strong phase shifted and binary mask designs. The impact of a poly gate alternate phase shifting technique on CD control is analyzed for a microprocessor design. A combination of OPC and PSM tools are used to assess sensitivity of CD to the variations of defocus, exposure dose, and mask misalignment, with and without PSM. A simulation region of 640x310 microns with 20000 MOSFETs is cut out from a random logic design. The edge placement error measurement sites are assigned each 200 nm across the transistor channels to fine-monitor CD variations. Four additional measurement sites are put close to the channel ends to monitor these regions susceptible to the CD variation. We use fast simulation technique that employs optical SOCS (Sum of Coherent Systems) decomposition and Extended Variable Threshold model. Optical parameters settings are chosen to be different for the binary and PSM masks to ensure comparable CD distributions in the center of the process windows. The PSM design is a 2-mask strong phase shifter design for poly gate level. Model-based OPC is applied to all relevant layers of the design including trim masks. To explore exposure-dose-misalignment input parameter space we setup partial factorial DOE with more than 100 runs each resulting in an EPE distribution for a parameter combination. We analyzed EPE shift and EPE dispersion. A definition of an EPE-based process window is proposed to capture the “proximity signature” of the design and its dependence on the process parameters. Comparison of binary and PSM designs yielded reliable quantitative measures of the PSM design performance gain.

Improved modeling performance with an adapted vectorial formulation of the Hopkins imaging equation

The Hopkins imaging theory for partially coherent light is adapted to include vector EM field interference inside a resist film stack. The negligible on-axis component of the EM field before the entrance pupil is ignored and this form is suitable for modeling IC lithographic projection printing. A new module, called TCCcalc, that is part of the Mentor Graphics’ Calibre Workbench modeling suite includes the vector image model inside resist can faithfully capture all physical effects that take place. Reduced contrast of the TM polarization, induced spherical aberration and standing wave creation are identified through examples to be the most important effects at high NA imaging. Application of the new vector image model to experimental data leads to a 20% reduction in the error between simulation and experiment for NA up to 0.75.

OPC methods to improve image slope and process window

In this paper, we use the gradient of the image slope and gradient of the edge placement error (EPE) in order to improve both slope and EPE during OPC. The EPE gradient taken with respect to edge position is normally called MEEF or more generally, the MEEF matrix. Use of the gradient of image slope with respect to change in edge position is a relatively new concept, introduced by Granik as the “contrast matrix”. Whereas traditional OPC techniques focus on EPE alone (pattern fidelity), we broaden the scope of OPC to maximize slope for improved image robustness and to maximize process window.

Two-dimensional G-MEEF theory and applications

Mask errors increasingly contribute into the CD error budget degrading quality of empirical OPC models and fidelity of the OPC features. Though the importance of studying mask error enhancements for the various feature types is well understood, the traditional MEEF theory embraces only simple features like dense lines or contacts, with a single degree of the mask distortion freedom. Complex mask shapes, including those that are routinely generated by OPC, or interactions between neighboring mask errors, have proven extremely difficult to analyze by the traditional MEEF theory. Motivated by the necessity to extend the traditional 1D approach, in previous works the authors introduced G-MEEF (Generalized Mask Error Enhancement) theory to explore complex 2D mask distortions. In this theory, mask and correspondent wafer errors were expressed as contour distortion vectors. The error enhancement is described by MEEM (Mask Error Enhancement Matrix) that transforms mask errors into the wafer distortions. MEEM captures complex effects of the self- and cross- enhancements when neighboring mask features collectively contribute into the wafer errors. Here we concentrate on G-MEEF applications. We study G-MEEF of SRAF structures and hammerheads. Inversion of the MEEM matrix can be used to conduct strict OPC corrections. We discuss different forms of OPC algorithms based upon this conversion.

Challenges and opportunities in applying grapho-epitaxy DSA lithography to metal cut and contact/via applications

Directed self assembly has become a very attractive technology for Fin and contact/via applications. Some of the issues related to pattern placement error, defectivity rates and process integration are actively being addressed by the industry and have not faced significant roadblocks for contact-hole applications. While many DSA applications have been proposed, deploying DSA for Fin structures competes in cost and variability control with SADP techniques. Given the 1D nature of find structures, it is difficult to control fin placement with accuracy better than 4nm 3 sigma. In addition, a second patterning step is needed to remove the un-wanted sections of the grating and leaving behind only the required fin structures, therefore limiting its adoption. On the other hand, DSA applied to contact/via holes has demonstrated low defectivity rates due to improved polymerization and processing techniques, as well as an adequate control to reduce the placement error due to thermal fluctuations during the annealing and cylinder formation process. For that reason, the results from contact/via layers can extend to the metal cut layer printing with DSA grapho-epitaxy. In this paper, we show that DSA provides a promising cost-effective solution for the technology scaling by reducing mask number from N to N-1. It is shown that pxOPC may provide better guiding patterns than the conventional one. In addition, the practical grouping rules for DSA should avoid 2D grouping, avoid putting more than 3 features in a group with different pitches, and avoid grouping features with different sizes. Our recommendations to designers for DSA technology are the following: if the design is to be decomposed with 2 or more DSA masks, then the design rules should be set up in this way: first the minimum pitch is better to be on DSA material’s own natural pitch; second, for each DSA mask, singletons and bar-like grouping shapes with DSA’s natural pitch should be used as much as possible.

Phase aware proximity correction for advanced masks

In this paper we describe the use of sparse aerial image simulation coupled with process simulation, using the variable threshold resist (VTR) model, to do optical and process proximity correction (OPC) on phase shift masks (PSM). We will describe the OPC of PSM, including attenuated PSM, clear field PSM, and double exposure PSM. We will explain the method used to perform such OPC and show examples of critical dimension control improvements generated from such a technique. Simulations, PSM assignment and model based OPC corrections are performed with Calibre Workbench, Calibre DRC, Calibre PSMgate and Calibre OPCpro tools from Mentor Graphics. In conclusion we will show that PSM techniques need to be corrected by a phase aware proximity correction tool in order to achieve both pattern fidelity as well as small feature size on the wafer in a production environment.

Considerations for the use of defocus models for OPC

It has been published that there is potential benefit to utilizing an OPC model based upon defocus instead of best focus processing, to give more robust patterning. While this is true with respect to gross opens and bridging problems, the available CD budget and the anticipated manufacturing consumption of defocus budgets must be considered. The net result will almost certainly always be that for gate layer processing, defocus model based OPC is not desirable. For other layers there may be favorable yield implications to running in such a manner, but the average CD in manufacturing will deviate from the design target. This paper will explore the interplay between variable focus distributions in manufacturing and the required CD control, pointing to those conditions under which a defocus model is advisable, and where it is not. Furthermore, the optimum magnitude of defocus is a compromise and has implications for final electrical performance.