Around the turn of the century, increasing densities with tighter dimensions drove the industry to require simulation-based processing and analysis in fabs and mask shops. Rule-based geometric manipulation became too approximate to be useful. In addition, the move to curvilinear mask shapes, motivated by 2X improvement in process windows and enabled by multi-beam mask writers, has significantly increased the need for simulation results to be accurate in 2D – not just 1D “critical dimensions” – both for wafer shapes and for mask shapes. But any simulation is only as accurate as the model used. “Garbage in, garbage out.”
D2S TrueModel® for Wafer and TrueModel for Mask are physics-based models that provide D2S solutions with the accuracy required for today’s leading-edge nodes. GPU acceleration has enabled simulation-based correction of a multitude of complex effects driven by the math of physics and chemistry in practical runtimes.
The D2S TrueModel Calibrator for Mask extracts models for each mask process. For each design, D2S TrueMask® mask products and D2S pixel-level dose correction (PLDC) use the extracted mask models to simulate, correct, enhance, and verify mask shapes to be written by a mask writer. TrueModel for Mask models dose-based effects, such as eBeam and resist blur, as well as geometric distance-, area-, or volume-based effects, such as etch bias or resist shrinking. The models are aware of all long-range effects corrected by the mask writers but focus on short- to mid-range effects in the 10nm to 100µm scales.
To create the models, a proprietary D2S test chip is printed and specified 1D and 2D measurements are taken at the mask shop. The measurements are input to TrueModel Calibrator, which then extracts the model parameters for that mask process. The extracted model parameters are then provided to, for example, D2S PLDC to perform model-based uniformity enhancement and linearity correction.
D2S uses GPU acceleration to make the computation of additional model elements negligible in terms of processing speed. GPU-acceleration enables >100X computation speeds in physics-based core computing, because nature is inherently single-instruction multiple data (SIMD), as are GPUs. D2S takes advantage of this to attain superior model accuracy in modeling and in simulation, correction, and verification.
With the D2S approach, nothing is rule-based. Everything is analyzed in both local and global contexts based on the physics and chemistry that drive each instance of every shape on the reticle. This eliminates extra margins that are required in “design rules” or “mask rules” to account for the possibility that the context of the instantiated shape might affect the shape differently in different locations across the reticle.
The latest improvement, particularly relevant for EUV masks, is the point-spread function (PSF) modeling in TrueModel Calibrator for dose-based parts of the mask models. In addition to modeling the dose-based effects with multiple Gaussians of different sizes and weights, TrueModel mask models now smooth out the “shoulders” at the transition in between the Gaussians. This is particularly relevant for EUV masks because EUV mid-range scatter of the electrons cast by the multi-beam mask writer increases the number of those shoulders, and because EUV masks need to be more precise. The improvement comes just in time for High-NA (.55 NA) EUV masks that need even more precision.
TrueModel wafer models are extracted by TrueModel Calibrator for wafer for each wafer process. For each design, TrueMask wafer products including TrueMask ILT (for multi-beam writing) use the extracted wafer models to simulate, correct, enhance, and verify that the mask shapes to be written by a mask writer in the mask shop will print the wafer as desired in nominal shapes and across the process window.
D2S TrueModel for Wafer models lithographic effects, resist effects including negative tone development (NTD), mask 3D (M3D) effects, and development and etching effects. Various parameters including the light sources and wafer measurements from a test chip are input to TrueModel Calibrator, which then extracts the model parameters for that wafer process. The extracted model parameters are then provided to, for example, TrueMask ILT to design Entirely Manufacturable™, and therefore entirely curvilinear, mask designs that produce the desired wafer shapes with the best process windows.
