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

[kololo]

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?

 

[berkeman]

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

 

[kololo]

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.

 

[berkeman]

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

 

[kololo]

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