pyoptics.litho

Lithography imaging toolbox.

The building blocks of a lithographic imaging simulation, each one exchangeable:

  • illumination: Illumination sources (coherent, conventional, annular, dipole, quadrupole, quasar, custom maps) for any sigma and any polarization (x, y, TE/azimuthal, TM/radial, unpolarized, Jones or Stokes vectors, partially polarized via a degree of polarization),

  • mask: a MaskLayout (geometry of one period: lines and spaces, isolated lines, dense and isolated contact holes, any set of rectangles, Manhattan polygons via MaskLayout.from_polygons) and a mask stack (ThinMask: Kirchhoff transmissions such as binary or attenuated PSM; FilmMask: transmissions of the absorber computed with pyoptics.thin_films, angle and polarization dependent; RigorousMask: RCWA of the patterned absorber for 1D layouts), the thin ones optionally with a polarization dependent boundary layer at the edges (BoundaryLayer) as an approximation to thick mask effects,

  • Projector: the projection lens (NA, wavelength, immersion, vectorial or scalar model, Zernike aberrations, apodization (e.g. apodization Zernikes), a Jones pupil, defocus),

  • WaferStack: optional resist on a thin film stack (BARC, substrate, top coat), computed with pyoptics.thin_films for TE and TM, with standing waves; without it the aerial image in the immersion medium is computed,

  • LithoSimulation: puts them together and computes images (Abbe’s method, exact sum over diffraction orders on any rectilinear grid), focus-exposure matrices and process windows,

  • metrics: contrast, ILS/NILS, threshold CDs, dose to size, Bossung curves, exposure latitude vs. depth of focus, MEEF,

  • lens: aberrations of a ray traced lens (pyoptics.raytrace) as Zernikes, distortion and telecentricity per field point, CD, placement and best focus across a scanner slit, Zernike sensitivities; geometric and energetic telecentricity and the real (apodized) pupil of a coated lens,

  • hopkins: Hopkins imaging with transmission cross coefficients (TCC) and their SOCS decomposition, exact against Abbe for thin masks and fast for many masks with the same optics,

  • wafer: also swing curves (reflectance, absorbed energy through resist thickness) and BARC optimization over the angles of the image,

  • resist: a chemically amplified resist in an x-z cross section: exposure, post-exposure bake (acid diffusion, quencher, amplification), Mack development with a fast marching front, resist profiles, dose to size and dose to clear,

  • rcwa: rigorous mask diffraction of 1D layouts (RCWA), RigorousMask for Abbe and Hopkins imaging, calibration of the boundary layer model,

  • jones_pupil: polarization of the lens as Jones pupils, in the representations of the literature (Jones-Zernike, Pauli-Zernike, retardance and diattenuation in orientation Zernike polynomials), with the polar decomposition; lens.lens_jones_pupil traces it through a coated or uncoated lens, optionally with CaF2 elements (materials.CubicCrystal), on top of raytrace.System.trace_polarization,

  • source_opt: source optimization of a pixelated (freeform) source for a set of clips by linear programming on the Abbe responses,

  • opc: optical proximity correction of Manhattan polygons: bias tables through pitch, SRAF rules, fragments and edge placement errors, model-based OPC,

  • illuminator: a ray traced KrF illuminator (KrFIlluminator) for the Caldwell lens: zoom-axicon (US 5,675,401), glass rod and REMA objective (US 5,982,558); conventional and annular settings, the pupil fill at any field point as an Illumination, field uniformity and the telecentricity against the projection lens,

  • plot: source, mask, pupil fill, images, Bossung plots, process windows.

All lengths are image-side (wafer scale) values; mask dimensions are given at wafer scale as well (1x), the reduction ratio of the projector is only used to obtain the angles of incidence at the mask.

Convention: fields vary as exp(i(k.r - omega*t)).

References

C. Mack, “Fundamental Principles of Optical Lithography: The Science of Microfabrication”, Wiley (2007).

    1. Levinson, “Principles of Lithography”, 4th ed., SPIE Press (2019).

A. Erdmann, “Optical and EUV Lithography: A Modeling Perspective”, SPIE Press (2021).

A. K.-K. Wong, “Resolution Enhancement Techniques in Optical Lithography”, SPIE Press (2001).