Konstantinos Adam

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.

Modeling of electromagnetic effects from mask topography at full-chip scale

Polarization and other complex electromagnetic effects that arise because of mask topography are becoming increasingly more important to model. Commercial lithography simulation tools that operate on small layout areas of order 1-10μm2 have advanced models requiring solution of Maxwell’s three-dimensional boundary problem. However, this technique is not viable for full-chip modeling. Here, we show results that demonstrate the accuracy of domain decomposition method adapted for full-chip modeling of mask topography effects. The intensity error relative to the complete 3D solution is shown to be < 3%.

Understanding the impact of rigorous mask effects in the presence of empirical process models used in optical proximity correction (OPC)

Some practical aspects of integrating a mask modeling solution into the Optical Proximity Correction (OPC) framework are discussed. Specifically, investigations were performed to understand to what degree empirical process models used in OPC can compensate for mask effects when a Kirchhoff mask model is used. It is shown that both Constant Threshold Resist (CTR) models as well as more complex variable threshold process models can both compensate for mask effects at a single plane of focus. However, when looking through process window, neither process model can predict the focal behavior of Electro-Magnetic Field (EMF) simulators. The impact of mask effects will therefore need to be modeled in OPC, since process models cannot fully compensate for their effects. Heuristic approaches to modeling mask effects, like a constant biasing of feature edges, are then investigated and compared to more complex mask modeling solutions like Domain Decomposition Methods (DDM). It is shown that these heuristic approaches can be effective at single planes of focus to partially mitigate mask effects, however, do not provide complete solutions to predict and compensate for mask effects. DDM stands in stark contrast to heuristic methods, correctly predicting the through focus behavior of EMF simulations for the tested pitches and CDs. The impact of optical diameter (periodic boundary conditions) is also investigated to understand how the introduction of mask periodicity effects from optical diameter degrades the benefits derived from mask modeling. It is shown that as much as a 33% reduction in CD predictability is observed from an optical model with a 1um optical diameter compared to a 2.56um optical diameter. Finally, both a Kirchhoff mask model and a DDM mask model are compared to see which mask model more accurately explains experimental CD measurement data from a 65nm process. The DDM model generally reduces the edge placement error (EPE) on the calibrated focal data by 0.3-1.0nm.

Polarization effects in immersion lithography

Optical proximity correction (OPC) tools are already equipped with the most advanced models for image formation and are capable of thin-film modeling, vector diffraction modeling, and polarization modeling. Accurate simulation of immersion lithography, even in the context of OPC, does not pose any particular difficulty. We use the optical simulator of a commercial OPC software to study source polarization and its impact in process latitude and in proximity and linearity curves. More than a 10-nm difference in both curves is observed versus source polarization at an immersion numerical aperture (NA)>1, projected to print the 45-nm node. Simulation of large and arbitrary layout snippets confirms these results and demonstrates the feasibility of using advanced models in the context of OPC. Also, dry and water-immersion lithography are compared at the same NA<1 and the main differences in imaging are highlighted. The depth-of-focus (DOF) increase in immersion is confirmed in both the ambient medium and the available DOF in resist. The DOF simulation results correlate closely with recent experimental work from other researchers.

3D mask modeling for EUV lithography

In this work, 3D mask modeling capabilities of Calibre will be used to assess mask topography impact on EUV imaging. The EUV mask absorber height and the non-telecentric illumination at mask level, modulate the captured intensity from the shadowed mask area through the reflective optics on to the wafer, named as the mask shadowing effect. On the other hand, thinning the mask absorber height results in unwanted background intensity, or called flare. A true compromise has to be taken into account for the height parameter of a EUV mask absorber. We will discuss the state-of-the-art 3D mask modeling capabilities, and will present methodologies to tackle the described EUV mask shadowing effect in Calibre software. The findings will be validated against experiments on ASMLs NXE:3100 EUV scanner at imec. Masks with two different absorber heights will be evaluated on various combinations of features containing line/space and contact-hole.