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:

Build the Transmission Cross-Coefficient (TCC) matrix from the illumination source and pupil function
Eigendecompose the TCC to obtain SOCS kernels and eigenvalues
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

Lithosim

Install / Use

README