lithosim

A lithography simulator with GDS layout support and physically-based optical/resist models.

Features

• GDS/OASIS input via gdstk — rasterize any layer from real layout files
• Bitmap input — PBM, PNG, or any Pillow-supported image format
• Hopkins partially-coherent imaging via SOCS (Sum of Coherent Systems) decomposition of the Transmission Cross-Coefficients (TCC)
• Illumination sources: conventional (disk), annular, dipole (x/y), quadrupole
• Pupil function with Zernike polynomial aberrations
• Defocus simulation via Zernike Z(2,0) coefficient
• Resist model: lumped parameter (Gaussian acid-diffusion blur + threshold)
• Pixel-based OPC via simulated annealing
• Fully-coherent mode (Jinc/Airy kernel) for fast approximate simulation

Installation

Requires Python 3.9+. Uses uv for dependency management:

uv sync

Dependencies: numpy, scipy, pillow, gdstk.

Usage

# Basic simulation (coherent, bitmap input)
uv run python lithosim.py tests/tiny.pbm results/sim

# Partial coherence with conventional source
uv run python lithosim.py --sigma 0.75 tests/tiny.pbm results/sim

# GDS input, specific layer
uv run python lithosim.py --layer 1/0 --nm-per-pixel 4 layout.gds results/layer1

# Annular illumination
uv run python lithosim.py --source annular --sigma-inner 0.5 --sigma-outer 0.9 layout.gds results/ann

# Defocus + resist blur
uv run python lithosim.py --defocus 50 --resist-blur 30 tests/tiny.pbm results/defocus

# OPC
uv run python lithosim.py --opc tests/tiny.pbm results/opc

Options

Option	Default	Description
--na	0.95	Numerical aperture
--wavelength	193.0	Exposure wavelength (nm)
--nm-per-pixel	8.0	Grid resolution (nm/pixel)
--source	conventional	Source type: coherent, conventional, annular, dipole_x, dipole_y, quadrupole
--sigma	0.75	Partial coherence factor
--sigma-inner	0.5	Annular source inner radius
--sigma-outer	0.9	Annular source outer radius
--n-kernels	auto	Number of SOCS kernels to retain
--defocus	0	Defocus (nm)
--threshold	0.2	Resist clearing threshold
--resist-blur	0	Acid diffusion length (nm, Gaussian sigma)
--layer	first found	GDS layer/datatype (e.g. 1/0)
--padding	20	Padding around GDS bounding box (pixels)
--opc	off	Run pixel-based OPC optimization

Output files

For a given <prefix>, the simulator writes:

• <prefix>_aerial.png — aerial image intensity
• <prefix>_resist.png — resist image (after diffusion blur)
• <prefix>_contour.pbm — binary contour (thresholded resist)
• <prefix>_opc_mask.pbm — OPC-optimized mask (if --opc)

Optical Model

The simulator implements Hopkins partially-coherent imaging via SOCS decomposition:

1. Build the Transmission Cross-Coefficient (TCC) matrix from the illumination source and pupil function
2. Eigendecompose the TCC to obtain SOCS kernels and eigenvalues
3. Compute the aerial image as a weighted sum of coherent images: I(x,y) = Σ λ_i |φ_i ⊛ mask|²

This accurately models partial coherence effects that the original fully-coherent (single Jinc kernel) model could not capture.

References

• A. Poonawala, P. Milanfar, "A Pixel-Based Regularization Approach to Inverse Lithography", Microelectronic Engineering, 84 (2007) pp. 2837–2852
• H. H. Hopkins, "On the diffraction theory of optical images", Proc. R. Soc. A, 217 (1953)
• Y. C. Pati, T. Kailath, "Phase-shifting masks for microlithography: automated design and mask requirements", JOSA A, 11 (1994)

Example Results

Simulation

Mask, Aerial Image, Contours

OPC

OPC Mask, OPC Aerial Image, OPC Contours