LithoBench-PDE

A benchmark dataset for PDE-based computational lithography simulation, constructed by generating high-fidelity 3D reference simulations for photomasks from the LithoBench dataset. Each sample contains intermediate 2D and 3D field data from the lithography simulation pipeline, providing ground-truth input-output pairs for three PDE learning tasks corresponding to three governing PDEs of photolithography.

PDE Learning Tasks

For each photomask, the reference simulation pipeline generates three ground-truth input-output pairs:

Task	PDE	Mapping	Input	Output	Shape
Mask diffraction	Maxwell's equations	M → E	M (photomask)	E (diffracted near field)	[H, W] → [2, 2, H, W] (complex64)
Post-exposure bake	Reaction-diffusion equation	h → m	h (photoacid concentration)	m (deprotection image)	[25, H, W] → [25, H, W]
Development	Eikonal equation	R → T	R (development rate)	T (development time)	[25, H, W] → [25, H, W]

• M → E: Given a 2D photomask pattern, solve Maxwell's equations to predict the diffracted near field (DNF), represented as a 2×2 Jones matrix of the electric field (complex-valued). Reference solutions are computed by rigorous coupled wave analysis (RCWA).
• h → m: Given a 3D photoacid concentration volume (25 z-slices), solve the reaction-diffusion equation governing the deprotection reaction during post-exposure bake (PEB) to produce the deprotection image. Reference solutions are computed by the finite difference method (FDM).
• R → T: Given a 3D development rate field (25 z-slices), solve the eikonal equation to obtain the development time field, whose isosurface defines the 3D developed photoresist structure. Reference solutions are computed by the fast marching method (FMM).

All data are generated under a fixed nominal condition of a 193 nm, NA 0.85, 4x-reduction projection system with an annular source (σ 0.7–0.9), 0 nm focus, and 30 mJ/cm² dose. The exposure is stochastic (photon and photoacid shot noise); the random seed of every sample is listed in LithoBench_PDE/seed_manifest.json. The grid spacing is 4 nm on the wafer plane and 16 nm on the photomask plane.

Photomask Categories

Category	Samples	Spatial Size	Description
Metal_I	1,600	512×512	Curvilinear metal photomasks obtained by inverse lithography
Metal_T	1,600	512×512	Rectilinear metal target layouts used directly as photomasks
Metal_P	61	512×512	Packed Metal: central crops of Metal_T clips composed by rectangle packing
Standard	216	512×512	Standard patterns in five families: isolated line (8), line-space (16), multiple bars (64), vertical lines with horizontal space (64) and vertical lines with horizontal line (64)
Contact_I	163	512×512	Curvilinear contact photomasks
Contact_T	163	512×512	Rectilinear contact target layouts
Metal_L	5	512×512 to 1024×1024	Large-area masks packed from Metal_T unit clips, side lengths 512, 640, 768, 896 and 1024 px

Total: 3,808 samples (~436 GB)

The file names of the standard patterns encode the family and its parameters (L: line width, S: space, N: number of bars, H: gap or bridge height, w: isolated line width; wafer-scale nm).

Data split used in the paper

Split	Samples
Training / validation	Metal_I and Metal_T: the first 1,500 cells (cell0 to cell1500; cell705 does not exist) and Metal_P: all 61, split 80 / 20 at random with seed 0, so that the Metal_I and Metal_T versions of a cell always fall into the same subset. Standard: all 216, training only.
Test	Metal_I and Metal_T cells 1501 to 1600 (100 each, in distribution), Contact_I and Contact_T (163 each, out of distribution), Metal_L (5, large area)

train_val_split and test_paths in neurolitho/data.py of the NeuroLitho code implement this split.

The photomask plane is represented on an 8192 nm × 8192 nm domain (512 × 512 grid at 16 nm spacing), which the 4x-reduction projection lens images onto a 2048 nm × 2048 nm wafer field. 3D photoresist fields are represented on a 2048 nm × 2048 nm × 100 nm domain (512 × 512 × 25 grid at 4 nm spacing). The DNF E is represented with four complex electric field components E_UV (U, V ∈ {x, y}), where E_UV denotes the U component of the electric field for incident light polarized in V direction; M and E share the photomask-plane grid. Metal_L tiles use the same spacings on larger N × N grids (N = 512 to 1024, 2.048 to 4.096 µm on the wafer).

Additional Files

• checkpoints/SONO/{maxwell,reaction_diffusion,eikonal}.pt: the trained NeuroLitho neural-operator stages for the three tasks (params, state_dict and normalization stats per file), used by the NeuroLitho code (see Code).
• fig_data/: the data behind the paper figures, rendered by the notebooks in vis/: f3_pred/<case>/{pred.pt, ref.pt} (prediction and reference of five example cases), f4_PW/{ref,pred}/ (process-window sweeps: developed bottom / top resist patterns and emulated SEM images for every dose and defocus of three illumination settings) and f5_SMO/w{10,01,00}/ (source-mask optimization checkpoints, their reference evaluation and stochastic exposure trials).

System Requirements

Software dependencies

The loader and visualization code are pure Python and run on CPU.

• Operating system. Developed and tested on Linux x86_64 (Ubuntu). The code is OS-independent and should also run on macOS and Windows (untested).
• Python 3.9 or newer (tested on 3.12).
• Python packages (see requirements.txt)

Hardware

No special hardware is needed. A CUDA-capable GPU is recommended for further computation on the data such as training models.

Installation

# (optional) create a clean environment
conda create -n lithobench-pde python=3.12 -y
conda activate lithobench-pde

# install dependencies
pip install -r requirements.txt

Or install the packages directly:

pip install "torch>=2.0" "numpy>=1.23" "huggingface_hub>=0.20" \
            "plotly>=5.0" "scikit-image>=0.20" "matplotlib>=3.5"

Download

Option 1: Download individual .pt files

from huggingface_hub import hf_hub_download

path = hf_hub_download(
    "AISDL-SNU/LithoBench-PDE",
    "LithoBench_PDE/Contact_I/INV_X8__0_0.pt",
    repo_type="dataset",
    local_dir="./data",
)

# Or using the CLI
huggingface-cli download AISDL-SNU/LithoBench-PDE LithoBench_PDE/Contact_I/INV_X8__0_0.pt --repo-type dataset --local-dir ./data

Option 2: Download an entire category folder

from huggingface_hub import snapshot_download

snapshot_download(
    "AISDL-SNU/LithoBench-PDE",
    repo_type="dataset",
    allow_patterns="LithoBench_PDE/Contact_I/*",
    local_dir="./data",
)

Usage

Quick start (load a sample)

import torch
from huggingface_hub import hf_hub_download

path = hf_hub_download(
    "AISDL-SNU/LithoBench-PDE",
    "LithoBench_PDE/Contact_I/INV_X16__0_0.pt",
    repo_type="dataset",
)
sample = torch.load(path, map_location="cpu")
for k in ["M", "E", "h", "m", "R", "T"]:
    print(k, tuple(sample[k].shape), sample[k].dtype)

Expected output (a few seconds once the file has downloaded):

M (512, 512) torch.float32
E (2, 2, 512, 512) torch.complex64
h (25, 512, 512) torch.float32
m (25, 512, 512) torch.float32
R (25, 512, 512) torch.float32
T (25, 512, 512) torch.float32

Dataset class

The LithoBenchPDE class in LithoBench_PDE.py loads the data and can select the per-task input and target tensors.

from LithoBench_PDE import LithoBenchPDE
from torch.utils.data import DataLoader

# From the Hub (downloads .pt files to ./data) or a local directory
ds = LithoBenchPDE.from_hub("AISDL-SNU/LithoBench-PDE", categories=["Contact_I"])
ds = LithoBenchPDE("./data/LithoBench_PDE", categories=["Contact_I", "Metal_I"])
# sample keys: M, E, h, m, R, T, sample_id, category
# The default categories are the six 512 x 512 ones; request Metal_L (512 to 1024 px tiles) explicitly.

# Filter to a single PDE task -> samples become {"input", "target", "sample_id", "category"}
ds = LithoBenchPDE.from_hub("AISDL-SNU/LithoBench-PDE", task="maxwell")  # or "reaction_diffusion", "eikonal"

for batch in DataLoader(ds, batch_size=4, shuffle=True):
    inputs, targets = batch["input"], batch["target"]

Visualization

The notebooks in vis/ render the data and prediction examples from the bundled fig_data/. They run on CPU and need no GPU or model checkpoints. Open a notebook and run all cells, which takes about 30 to 60 seconds each on a normal desktop CPU. Figures render inline, and vis_data.ipynb also saves an interactive .html export. The helper functions in vis/plot.py (vis_mask, vis_field, and others) also work on your own tensors of the same shape.

Notebook	Data	Content
vis/vis_data.ipynb	LithoBench_PDE/, fig_data/f3_pred	dataset samples and prediction examples
vis/vis_PW.ipynb	fig_data/f4_PW	process window
vis/vis_SMO.ipynb	fig_data/f5_SMO	source-mask optimization

File Format

Each .pt file is a Python dictionary saved with torch.save() containing:

{
    "M": torch.Tensor,  # [H, W] float32        - photomask pattern
    "E": torch.Tensor,  # [2, 2, H, W] complex64 - diffracted near field
    "h": torch.Tensor,  # [25, H, W] float32     - photoacid concentration
    "m": torch.Tensor,  # [25, H, W] float32     - deprotection image
    "R": torch.Tensor,  # [25, H, W] float32     - development rate
    "T": torch.Tensor,  # [25, H, W] float32     - development time
}

Code

The NeuroLitho code (training of the checkpoints, inference with a comparison against the reference, process-window sweeps) is available as a Code Ocean capsule, which becomes public with its DOI when the paper is published; the DOI will be added here.

License

• Dataset (LithoBench_PDE/, checkpoints/, fig_data/) is released under the Creative Commons Attribution 4.0 International (CC-BY-4.0) license.
• Software (the LithoBench_PDE.py loader and the vis/ code) is released under the MIT License.

The Metal, Contact, Packed Metal and Metal_L layouts are derived from the LithoBench dataset, Copyright (c) 2023 Su Zheng, used under the MIT License; its copyright and permission notice is reproduced in LICENSE-LithoBench. The standard patterns were generated for this dataset.

Citation

TBA