2D cosine law simulation

Overview

In thin-film deposition processes such as evaporation or directional PVD, the spatial distribution of deposited material is often approximated using a cosine-law model.

This repository provides a 2D cosine-law deposition simulation tool for estimating relative thickness (or flux) distributions on a substrate based on simple geometrical assumptions.

The tool is intended as a baseline model for quick evaluation of deposition uniformity before detailed simulation or experimental validation.

All simulation parameters are defined in a CSV configuration file, enabling repeatable and code-independent parametric studies.

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Included Tools

2D cosine law simulation.py

• Main simulation script for 2D cosine-law deposition map
• Reads all parameters from settings.csv
• Generates numerical results and plots automatically

settings.csv

• Configuration file defining geometry, model parameters, and output settings
• No modification of the source code is required

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Instructions

1. Place 2D cosine law simulation.py in a directory
2. Place settings.csv in the same directory
3. Edit parameters in settings.csv as needed
4. Run the script

Model and Parameter Definition

Geometrical Model

The deposition source is approximated as a point source located at height H above the substrate.

For each substrate position x:

• Distance
  r = √( H² + (x − x₀)² )

• Incident angle
  cosθ = H / r

• Relative intensity
  I(x) ∝ (cosθ)ⁿ × (1 / r²) (optional)

where n is an empirical cosine exponent and x₀ is the lateral source offset.

This tool provides relative distributions, not absolute thickness values.

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Data and Parameter Definition

The following conventions are used in this repository:

• All length units are in millimeters (mm)
• Angles are handled implicitly through geometry
• Substrate region is defined symmetrically as ± substrate_half_width_mm
• Parameter values are read as strings and internally cast to numeric types

Key Parameters in settings.csv

Key	Description
H_mm	Source-to-substrate distance
x_min_mm, x_max_mm	Calculation range
dx_mm	Spatial resolution
x_source_offset_mm	Lateral source offset
cosine_n	Cosine-law exponent
include_r2	Enable 1 / r² attenuation
normalize_to_peak	Normalize peak intensity to 1
scale_factor	Scaling factor after normalization
substrate_half_width_mm	Half-width of substrate
output_dir	Output directory name
output_basename	Output file prefix

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Typical Use Cases

• Early-stage process window exploration
• Sensitivity studies for source height or offset
• Comparison of cosine exponent (n) effects
• Pre-evaluation of thickness uniformity
• Educational or conceptual demonstrations of cosine-law deposition

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Input / Output Format

Input Format

• settings.csv defines all simulation parameters

Output Format

Generated files are saved to the specified output directory:

• <basename>.csv

  • x_mm, intensity_raw, intensity_scaled

• <basename>_metrics.csv

  • mean, min, max, peak-to-peak / mean, sigma / mean

• <basename>.png

  • 2D deposition map plot

Original input files are not modified.

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Notes and Limitations

• Point-source approximation
• No re-emission, scattering, or plasma interactions
• Cosine exponent (n) is empirical

For quantitative prediction or equipment design, more advanced simulations or experimental validation are required.

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Related tools

• 1D cosine law simulation
  A 1D cosine-law deposition simulation tool for estimating relative thickness or flux distributions using point-source geometry.