Increase in numerical aperture leads to a decrease in line width?

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Discussion Overview

The discussion revolves around the relationship between numerical aperture (NA) and minimum line width in the context of semiconductor lithography. Participants explore how changes in NA affect optical resolution and feature size, examining both theoretical and practical implications.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that an increase in numerical aperture leads to a decrease in minimum line width, suggesting improved resolution.
  • Others question this assertion, proposing that higher numerical aperture may actually result in a larger illuminated area, potentially increasing the minimum line width.
  • A participant cites their school notes indicating that the illuminated area affects the feature size on the substrate, leading to confusion about the relationship between NA and minimum line width.
  • One participant emphasizes that minimum line width refers to the smallest width of features that can be reliably imaged, which may contradict the earlier claims about illuminated area.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between numerical aperture and minimum line width, with no consensus reached on how these concepts interrelate.

Contextual Notes

There are unresolved aspects regarding the definitions of minimum line width and illuminated area, as well as the assumptions underlying the application of the formula relating NA to resolution.

kololo
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According to the formula, an increase in numerical aperture leads to a decrease in minimum line width and thus better resolution.
However, if were to draw it out, given the same depth of focus, why does the minimum line width increase with higher numerical aperture?
 
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kololo said:
View attachment 348515
According to the formula, an increase in numerical aperture leads to a decrease in minimum line width and thus better resolution.
However, if were to draw it out, given the same depth of focus, why does the minimum line width increase with higher numerical aperture?
Can you post a link to where you got that figure? It looks like it is confusing minimum line width (optical resolution) and illuminated area.

See if this link about NA and optical resolution helps:

https://www.photometrics.com/learn/microscopy-basics/resolution-and-numerical-aperture
 
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Thank you for your reply.

It was from notes provided by my school (semiconductor lithography).
It suggests the illuminated area. When the positive resist on the substrate is exposed to light, it becomes soluble and is washed off. This leaves a feature on the substrate. The line width was defined as the minimum feature size, which is the length of the resist that was washed off.

So, in the case of high NA, a larger area will be exposed to light. Hence, the feature printed will be larger (larger line width). This suggests that the line width corresponds to the illuminated area.

However, the formula suggests otherwise. It seems like I am either missing something to link these two theories together, or my understanding is wrong.
 
kololo said:
So, in the case of high NA, a larger area will be exposed to light. Hence, the feature printed will be larger (larger line width). This suggests that the line width corresponds to the illuminated area.
No. In my experience with semiconductor fabrication, the "minimum line width" or "minimum feature size" pertains to the smallest horizontal width of metal or poly that you can reliably image. So when we say that our process is 10 nanometer, that means that the thinnest trace widths and thinnest transistor channels that we can reliably image and make are 10 nanometers wide.

https://en.wikipedia.org/wiki/Semiconductor_device_fabrication

1721396648081.png
 
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Ohh, I must have misunderstood the definition of minimum linewidth. Thank you for the clarification.
 
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