Lithography resolution and depth of focus calculator
Enter the exposure wavelength, the lens numerical aperture (NA) and the process factor k1 to get the smallest half-pitch one exposure can print and its depth of focus. Add a target pitch to see whether it fits in a single exposure or must be split.
Results
Resolution (half-pitch)
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Minimum pitch per exposure
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Depth of focus
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Pitch splits needed
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1 means a single exposure can print the target pitch. 2 or more means the pattern must be split across several exposures, for example with double patterning (a rough count; real flows also use SADP and SAQP).
Lithography generations compared (using your k1 and k2)
Source
λ
NA
Half-pitch
Depth of focus
NA values are typical high-end values for each generation. Immersion depth of focus uses the simple formula without the fluid's refractive-index gain.
See it as a graph
Other inputs stay at their current values while the chosen input varies from 1/4 to 4 times its current value. The red dot is the current value.
What the Rayleigh equation says
The smallest feature a single exposure can resolve is R = k1 × λ / NA, where λ is the wavelength, NA is the numerical aperture describing how wide a cone of light the lens collects, and k1 captures how close illumination, mask and resist tricks push toward the physical limit. For equal lines and spaces the theoretical limit is k1 = 0.25, and production typically runs at about 0.28 to 0.4. Resolution improves only by shortening the wavelength, raising NA or lowering k1.
The depth-of-focus trade-off
The height range over which the image stays acceptably sharp is the depth of focus, estimated as DOF = k2 × λ / NA². Raising NA improves resolution in proportion to NA but shrinks depth of focus with NA squared. For 13.5 nm EUV, going from NA 0.33 to 0.55 improves resolution by about 1.7 times while cutting depth of focus by about 2.8 times. That is why wafer flatness and resist thickness are so tightly controlled, and why CMP planarization and thinner resists matter.
How the generations progressed
Light sources moved from the mercury g-line (436 nm) and i-line (365 nm) to KrF (248 nm) and ArF (193 nm) excimer lasers. ArF immersion lithography filled the gap between lens and wafer with water to push NA above 1, up to 1.35, reaching a half-pitch of about 40 nm at k1 = 0.28. Finer patterns need multipatterning or 13.5 nm EUV. At NA 0.33, EUV reaches a half-pitch of about 16 nm at k1 = 0.4, and High-NA EUV at 0.55 reaches about 10 nm.
Techniques that lower k1
Lowering k1 lets the same scanner print finer patterns. The main techniques are optical proximity correction (OPC), which pre-distorts mask shapes to offset diffraction; phase-shift masks, which flip the phase of light to raise contrast; off-axis illumination; and high-contrast resists. As k1 approaches 0.25, however, dimensional variation and defects grow and the process window narrows.
AShorten the exposure wavelength and increase the numerical aperture (NA)
BLengthen the exposure wavelength and decrease NA
CLengthen the exposure wavelength and increase NA
Show answer and explanation
Answer: A. Shorten the exposure wavelength and increase the numerical aperture (NA)
From the Rayleigh equation R = k1·λ/NA, resolution improves with shorter wavelength λ, larger numerical aperture NA and lower k1. Sources have shrunk from g-line (436 nm) through i-line (365 nm), KrF (248 nm) and ArF (193 nm) to EUV (13.5 nm), while NA grew from about 0.3 to 1.35 with immersion. ArF immersion (NA 1.35, k1 0.27) gives R ≈ 39 nm; finer pitches require multiple patterning or EUV.
Depth of focus is DOF = k2·λ/NA², inversely proportional to NA squared, so raising NA shrinks it rapidly—to around 100 nm in leading-edge lithography. This tightens requirements on wafer flatness, topography and resist-thickness uniformity, which is one reason CMP planarization matters. Scanners measure wafer height and tilt for each shot and adjust focus automatically.
AIt reflects the difficulty of the process, with a theoretical minimum of 0.25 for a single exposure
BThe larger it is, the higher the resolution
CIt is always 1 or more
Show answer and explanation
Answer: A. It reflects the difficulty of the process, with a theoretical minimum of 0.25 for a single exposure
k1 summarizes the combined capability of resist, mask tricks and illumination; smaller values resolve finer patterns but narrow the process window. The theoretical single-exposure limit for periodic lines and spaces is 0.25. In the 1990s k1 was around 0.6, but resolution-enhancement techniques—off-axis illumination, phase-shift masks, OPC—have brought production values down to about 0.27–0.3.
FAQ
What is the resolution limit of ArF immersion lithography?
With NA 1.35 and k1 = 0.28 the half-pitch is about 40 nm, a pitch of about 80 nm. Finer patterns are made with multipatterning such as double patterning, or with EUV.
How does depth of focus change with NA?
Depth of focus falls with the square of NA. Raising NA from 0.33 to 0.55 at the same wavelength and k2 reduces depth of focus by about 2.8 times.
What is the theoretical minimum k1?
For equal lines and spaces printed in a single exposure, the theoretical limit is k1 = 0.25. Production usually stays around 0.28 to 0.4 to keep enough process margin.