BY RYAN PEARMAN, D2S, Inc., San Jose, CA
There are big changes on the horizon for semiconductor mask manufacturing, including the imminent first production use of multi-beam mask writers, and the preparation of all phases of semiconductor manufacturing for the introduction of extreme ultra-violet (EUV) lithography within the next few years. These changes, along with the increasing use of multiple patterning and inverse- lithography technology (ILT) with 193i lithography, are driving the need for more detailed and more accurate modeling for mask manufacturing.
New solutions bring new mask modeling challenges
Both EUV and multi-beam mask writing provide solutions to many long-standing challenges for the semiconductor industry. However, they both create new challenges for mask modeling as well. Parameters once considered of negligible impact must be added to mask models targeted for use with EUV and/or multi-beam mask writers. In particular, the correct treatment of dose profiles has emerged as a critical component for mask models targeting these new technologies. This is in addition to scattering effects, such as the well-known EUV mid-range scatter, that must be included in mask models to accurately predict the final mask results. Gaussian models, which form the basis for most traditional mask models, will not be sufficient as many of these new parameters are more properly represented with arbitrary point-spread functions (PSFs).
The most obvious – and most desperately needed – benefit of EUV lithography is greater accuracy due to its enhanced resolution. However, this benefit comes along with a mask-making challenge: wafer-printing defects due to mask errors will appear more readily because of this enhanced resolution. Therefore, the introduction of EUV will require the mean-to-target (MTT) variability on photomasks to become smaller. From a mask manufacturability perspective, all sources of printing errors, systematic and random, must be improved. This means that mask models must also be more accurate, not only in predicting measurements, but also in predicting variability.
A well-known challenge for EUV mask modeling is the EUV mid-range scatter effect. The more complex topology of EUV masks leads to broader scattering effects. In addition to “classical” forward- and back-scatter effects, which dominate 193i lithography, there is a mid-range (1μm) scatter that now requires modeling. This phenomenon is non-Gaussian in nature, so cannot be simulated accurately with simple Gaussian (“1G”) models. In combination with better treatment of resist effects, a PSF-based model is a much better represen- tation of the critical lithography process.
The eagerly anticipated introduction of EUV will demand a lower-sensitivity resist to be used for EUV masks due to the smaller size of EUV features. This is one of the reasons why multi-beam mask writers have emerged as the replacement for variable shaped beam (VSB) tools for the next generation of mask writers. Slower resists require higher currents, and VSB tools today are limited thermally in ways the massively parallel multi-beam tools are not. In addition to thermal effects, VSB mask writers are runtime-limited by shot count; we are already approaching the practical limit for many advanced masks. Shot count is only expected to grow in the future as pitches shrink and complex small features become prevalent in EUV masks – and even in 193i masks due to increased use of ILT to improve process windows for 193i lithography.
In contrast to VSB mask writers, which use shaped apertures to project the shapes (usually rectangles) created by optical-proximity correction (OPC) onto the mask, multi-beam mask writers rasterize the desired mask shapes into a field of pixels, each of which are written by one of hundreds of thousands of individual beamlets (FIGURE 1). This enables multi-beam mask writers to write masks in constant time, no matter how complicated the mask shapes. Each of these beamlets can be turned on and off independently to create the desired eBeam input, which enables the fine resolution of smaller shapes. However, it also means that the dose profiles for the multi-beam writers are far more complex, leading to the need for more advanced, separable dose and shape modeling.
Since the beamlets of a multi-beam tool are smaller than the primary length-scale of the dose blur, a key second advantage of multi-beam writers emerges: the patterns written are intrinsically curvilinear. In contrast, VSB mask writers can only print features with limited shapes – principally rectangular and 45-degree diagonals, although some tools enable circular patterns. The critical process-window enhancements for ILT also rely on curvilinear mask shapes, so a synergy appears: better treatment of curved edges at the mask writing step will lead to better wafer yield.
Dose and shape: New requirements for multi- beam and EUV mask models
Multi-beam mask writers, EUV masks, and even the proliferation of ILT will require mask models to change substantially. Until very recently, curvi-linear mask features have been ignored when characterizing masks, and models, when used, have assumed simplicity. Primary electron blur (“forward scattering”), including chemically amplified resist (CAR) effects, historically have been assumed to be a set of Gaussians, with length scales between 15nm and 300nm. All other effects of the mask making processes – long-range electron scattering (“back-scatter” and “fogging”), electron charging, devel- opment, and plasma-etching effects – have either been assumed to be constant regardless of mask shape or the dose applied, or have been accounted for approxi- mately by inline corrections in the exposure tool.
To meet the challenges posed by both EUV and multi- beam writing – especially since they are likely to be employed together – mask models will need to treat dose and shape separately, and to explicitly account for the various scattering, fogging, etch, and charging effects (FIGURE 2).
When masks were written entirely at nominal dose, dose-based effects could be handled together with shape-based effects as a single term. Several years ago, overlapping shots were introduced by D2S for VSB tools to both improve margins and reduce shot-count for complex mask shapes. At this time, it became clear that dose modulation (including overlapping shots) required specific modeling. Some effects (like etch) varied only with respect to the resist contour shapes, while other print bias effects were based on differences in exposure slope near the contour edge. For all the complexity of VSB overlapping shots, all identical patterns were guaranteed to print in the same way. Today, with multi-beam writers, there are significant translational differences in features due to dose-profile changes as they align differently with the multi-beam pixel grid.
We discussed earlier that multi-beam tools print curvi-linear shapes. We should point out that even Manhattan designs become corner-rounded on the actual masks at line ends, corners, and jogs. Why? Physics is almost never Manhattan, and treating it as such will be inaccurate, as in the case of etching effects computed in the presence of Manhattan jogs. We need to embrace the fact that all printed mask shapes will be curvilinear and ensure that any shape-based simulation is able to predict effects at all angles, not just 0 and 90.
Increasing mask requirements drive the need for mask model accuracy
As we continue to move forward to more advanced processes with ever-smaller feature sizes, the requirement for better accuracy increases. There is quite literally less room for any defects. This increased emphasis on accuracy and precision is what drives the adoption of new technologies such as EUV and multi-beam mask writing; it drives the increased need for better model performance as well.
We have already discussed several model parameters that will need to be re-evaluated and handled differently in order to achieve greater accuracy. Accuracy also requires a more rigorous approach to the calibration and validation of models with test chips that isolate specific physics effects with specific test structures. For example, masks that include complex shapes require 2D validation. Today’s VSB mask writers are Manhattan (1D) writing instruments, so models built using these tools are by definition 1D-centric. Inaccuracies in 1D models are exacerbated when tested against a 2D validation. Physics-based models are far more likely to extrapolate to 2D shapes, and are better for ILT.
As features shrink, the accuracy of individual shapes on the mask is impacted increasingly by their proximity to other shapes. The context for each shape on the mask becomes as important as the shape itself. The solution is to model each shape within the context of its surroundings. This is driving the need for simulation-based modeling and mask-correction methodologies.
GPU acceleration: Making simulation-based mask modeling practical
Historically, simulation-based processing of mask models resulted in unacceptably long simulation runtimes. The most common approach until recently has been to use model-based or rules-based methodologies that, while providing less accuracy, result in faster runtimes. The advent of GPU-accelerated mask simulation has changed this picture. GPU acceleration is particularly suited to “single instruction, multiple data” (SIMD) computing, which makes it a very good fit for simulation of physical phenomena, and enables full- reticle mask simulation within reasonable runtimes.
An additional advantage of GPU acceleration is the ability to employ PSFs without runtime impact (FIGURE 3). As we’ve already discussed, PSFs are a natural choice for the mask-exposure model, including EUV mask mid-range scattering effects, forward-scattering details, and modeling back-scattering by construction. Using PSFs, any dose effect of any type can be exactly modeled during simulation-based processing.
GPU acceleration opens the door for simulation-based correction of a multitude of complex mask effects based on physics-based models, affording practical simulation run times for these more complex models.
PLDC: New mask models at work in multi-beam mask writers
As with any big changes to the semiconductor manufacturing process, the industry has been preparing for EUV and multi-beam mask writing for several years. These preparations have required various members of the supply chain to work together to deploy effective solutions. One example of this collaboration in the mask-modeling realm is the introduction by NuFlare Technology of pixel-level dose correction (PLDC) in its MBM-1000 multi-beam mask writer. At the 2017 SPIE Photomask Japan conference, NuFlare and D2S jointly presented a paper  detailing the mask modeling – and GPU acceleration – used in this new inline mask correction.
PLDC manipulates the dose of pixels to perform short- range (effects in the 10nm scale to 3-5μm scale) linearity correction while improving the overall printability of the mask. In addition to the traditional four-Gaussian (4G) PEC model, PLDC combines for the first time an inline 10nm-100nm short-range linearity correction with a 1μm scale mid-range linearity correction (FIGURE 4). This mid-range correction is particularly useful for EUV mid-range scatter correction.
The dose-based effects portion of the D2S mask model, TrueModel, are expressed as a PSF for an interaction range up to 3-5μm, and with a 4G PEC model for interaction range up to 40-50μm. Being able to express any arbitrary PSF as the correction model allows smoothing of “shoulders” that are often present on multiple Gaussian models, and allows proper modeling of effects that are not fundamentally Gaussian in nature (such as the EUV mid-range scatter). This ability to model physical effects and correct for them inline with mask writing results in more accurate masks, including for smaller EUV shapes and for curvilinear ILT mask shapes.
PLDC is simulation-based, so it has the ability to be very accurate regardless of targeted shape, regardless of mask type (e.g., positive, negative EUV, ArF, NIL master) with the right set of mask modeling parameters.
GPU acceleration enables fast computing of PSF convo- lutions for all dose-based effects up to 3-5μm range, performed inline in the MBM-1000, which helps to maintain turnaround time in the mask shop.
Mask models need some significant adaptations to meet the coming challenges. The new EUV/multi-beam mask writer era will require mask models to be more detailed and more accurate. More complex dose profiles and more complex electron scattering require PSFs be added to the industry-standard Gaussian models. More rigorous mask models with specific dose and specific shape effects are now needed. Simulation-based mask processing, made practical by GPU acceleration, is necessary to take context-based mask effects into account.
The good news is that the mask industry has been preparing for these changes for several years and stands ready with solutions to the challenges posed by these new technologies. Big changes are coming to the mask world, and mask models will be ready.
1. Pearman, Ryan, et al, “EUV modeling in the multi-beam mask writer era,” SPIE Photomask Japan, 2017.
2. “GPU-accelerated inline linearity correction: pixel-level dose correction (PLDC) for the MBM-1000,” Zable, Matsumoto, et al, SPIE Photomask Japan, 2017.