Lithography Resolution and Depth of Focus Calculator (Rayleigh)
Resolution and depth of focus pull in opposite directions in lithography. This calculator applies the Rayleigh equations so you can see the trade-off across wavelength, NA and process factor.
Your numbers
ArF immersion scanners reach about 1.35. Dry ArF is below 1. Current EUV scanners are 0.33 or 0.55.
Lower is harder. The single-exposure theoretical limit is 0.25.
Often between 0.5 and 1 depending on the definition of acceptable focus range.
Your results
The Rayleigh equations are first-order scaling rules. Real resolution depends on resist, illumination, mask type, OPC and the specific scanner. Use your lithography group's process window data for decisions.
Half-pitch and depth of focus vs NA
Sweeps Numerical aperture (NA) from 0.3 to 1.4, holding your other inputs fixed.
Process documents searchable on your own servers
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How to use the calculator
Pick the exposure wavelength from the standard sources, then enter the numerical aperture, the process factor k1 and the depth of focus factor k2. The tool returns the minimum half-pitch, the minimum pitch, the depth of focus and the margin of your k1 above the theoretical single-exposure limit of 0.25. The chart sweeps NA and shows how resolution improves while depth of focus collapses, which is why higher NA tools need flatter wafers and tighter focus control.
- Use a realistic k1 from your resist and illumination setup.
- Pitch is twice the half-pitch for a line-space pattern.
- Check k1 against 0.25 before planning a single exposure.
The Rayleigh equations
Resolution (the smallest half-pitch) is CD = k1 x lambda / NA. Depth of focus is DOF = k2 x lambda / NA squared. NA appears squared in the denominator of DOF, so doubling NA cuts DOF to a quarter while only halving CD. Wavelength reduction helps both: this is why the industry moved from i-line to KrF, ArF, immersion and then EUV. A k1 below 0.25 cannot be reached with a single exposure, and multiple patterning is needed.
Worked example
For ArF immersion at 193 nm, NA 1.35 and k1 of 0.32, the half-pitch is about 45.7 nm, and the pitch is about 91 nm. With k2 of 0.8, the depth of focus is 193 times 0.8 divided by 1.35 squared, which is about 85 nm. For a target pitch of 80 nm the required k1 would be 0.28 for half-pitch 40 nm, which is close to the 0.25 limit, so multiple patterning or EUV would be considered.
Common mistakes
A frequent mistake is quoting NA for an immersion system as if it were a dry system, or mixing pitch and half-pitch. Another is treating k1 as a constant of the scanner when it is a function of the whole process, including resist, mask, illumination and OPC. Finally, the DOF equation depends on how the user defines acceptable focus, so compare k2 values only when the definitions are the same.
Frequently Asked Questions
What is k1 in lithography?
k1 is a dimensionless factor that captures how aggressively the process pushes resolution. It includes resist performance, illumination, mask enhancement and OPC. Lower k1 means a harder process, with 0.25 as the physical limit for single exposure.
Why does depth of focus shrink as NA grows?
Depth of focus scales as 1 over NA squared, while resolution scales as 1 over NA. A higher NA captures steeper diffraction angles, which sharpens features but makes the image sensitive to small changes in wafer height.
Is half-pitch the same as critical dimension?
Not always. For equal line and space the half-pitch equals the line width, so the terms are used interchangeably in Rayleigh. For isolated lines or contacts, the printed CD can differ from the half-pitch.
Does this cover EUV?
Yes for first-order scaling. Choose 13.5 nm and the NA of your tool, for example 0.33 or 0.55. EUV has additional effects, such as stochastics and mask 3D effects, that the Rayleigh equations do not capture.
If your process recipes, masks and equipment records are spread across systems, Netray can help build a private search layer over those documents, running on your own hardware.
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