3 ms·

Could you not simply take the 2D fourier transform of the desired on-chip pattern and use that as the mask? It seems like the diffraction pattern of the "long"

Could you not simply take the 2D fourier transform of the desired on-chip pattern and use that as the mask? It seems like the diffraction pattern of the "long" wave laser would give you exactly what you want on the chip... and if you are putting hundreds of chips on a single wafer, it seems like you might not even need to worry too much about ringing at the edges.

HelloNurse 5y ago
You might be confusing the somewhat similar shapes arising from the Fourier transform of step functions etc. or from diffraction from an individual hole or obstacle. Unlike the Fourier transform, which is a purely mathematical operation, diffraction has no "inverse": if you add more diffraction you just add more waves to the projected pattern. The only ways to defeat diffraction are reducing it with shorter wavelengths and compensating it with multiple exposures with different patterns in which light and dark fringes compensate each other: exactly the two general approaches (EUV and multipatterning) taken by the semiconductor industry.
- labcomputer 5y ago
  I don't think I am, actually. In the far field with a narrow bandwidth coherent light source (i.e., a laser), the projected image should be the FT of the aperture. That limiting condition is sometimes known as Fraunhofer diffraction, and generalizes to arbitrary apertures (not just a single hole). Consider a narrow-band laser incident upon a diffraction grating for example. It produces a single point (well, two or three points, mirrored across the grating), not the uniform smudge that you'd expect by naively adding up the diffraction patterns of a bunch of slits. You should actually try this experiment for yourself! The only trick is that you need a collimated laser and you need it to illuminate the entire inverse-FT-chip-grating aperture at once. This deck has some nice examples of multi-hole apertures on slides 20 and 22: https://www.brown.edu/research/labs/mittleman/sites/brown.edu.research.labs.mittleman/files/uploads/lecture30_0.pdf https://www.brown.edu/research/labs/mittleman/sites/brown.ed...

HelloNurse 5y ago

You might be confusing the somewhat similar shapes arising from the Fourier transform of step functions etc. or from diffraction from an individual hole or obstacle. Unlike the Fourier transform, which is a purely mathematical operation, diffraction has no "inverse": if you add more diffraction you just add more waves to the projected pattern. The only ways to defeat diffraction are reducing it with shorter wavelengths and compensating it with multiple exposures with different patterns in which light and dark fringes compensate each other: exactly the two general approaches (EUV and multipatterning) taken by the semiconductor industry.

labcomputer 5y ago
I don't think I am, actually. In the far field with a narrow bandwidth coherent light source (i.e., a laser), the projected image should be the FT of the aperture. That limiting condition is sometimes known as Fraunhofer diffraction, and generalizes to arbitrary apertures (not just a single hole). Consider a narrow-band laser incident upon a diffraction grating for example. It produces a single point (well, two or three points, mirrored across the grating), not the uniform smudge that you'd expect by naively adding up the diffraction patterns of a bunch of slits. You should actually try this experiment for yourself! The only trick is that you need a collimated laser and you need it to illuminate the entire inverse-FT-chip-grating aperture at once. This deck has some nice examples of multi-hole apertures on slides 20 and 22: https://www.brown.edu/research/labs/mittleman/sites/brown.edu.research.labs.mittleman/files/uploads/lecture30_0.pdf https://www.brown.edu/research/labs/mittleman/sites/brown.ed...