August 31, 2011 — The introduction of extreme ultraviolet (EUV) lithography into the semiconductor fabrication process will enable a continuation of Moore’s law below the 22nm technology node. It also introduces new patterning distortions — flare along with proximity effects — that must be accurately modeled and corrected on the reticle [1]. Flare caused by scattered light in the projection optics could result in several nanometers of on-wafer dimensional variation, if left uncorrected. Previous work by the authors has focused on combinations of model-based and rules-based approaches to modeling and correction of flare in EUV lithography. New work focuses on an all model-based approach to flare compensation, which offers both model and optical proximity correction (OPC) accuracy. Designers will need to consider the benefits and tradeoffs of all-model versus hybrid OPC approaches, which include correction time, accuracy, and data volume.
EUV is positioned as the leading technology for continued scaling beyond the 22nm node. The 10x reduction in wavelength in EUV can bring k1 back up to 0.5 or above. This technology still faces many challenges, however, primarily in the needed source power, resist characteristics, and availability of defect-free masks.
Although imaging becomes easier with EUV, users must correct for flare, the incoherent light produced by scattering from imperfections in the optical system. Local pattern density on the mask also affects the magnitude of flare; clear, open, low-density regions suffer the most.
OPC’s success for EUV litho depends on the ability to accurately model and correct for flare. Recently developed software strikes at that target.
Modeling for EUV flare
Flare in EUV systems is caused by surface roughness in the mirrors. Incident light is scattered in multiple directions in addition to the specular direction (Fig. 1).
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| Figure 1. EUV light scattering from surface roughness. |
Scattering is inversely proportional to the wavelength squared, thus it is more prominent for 13.5nm EUV than in the deep ultraviolet (DUV) systems currently in use for wafer fab. Because of reflections, the light must travel twice across the interface.
The scattering is captured by the statistical signal processing function called power spectral density (PSD). The final effect on the aerial image is modeled by the pedestal model shown in Eq. 1.
The factor Io accounts for the effects of the partial coherence. Total integrated scatter (TIS) is the overall flare, or the loss of light energy. The overall energy available for coherent image formation is decreased to the amount 1-TIS. The local flare is obtained by convolving the flare PSF (FPSF) with the intensity Io.
The flare PSF is the flare response of a point source. It can be obtained by Kirk test patterns or from the PSD in the optics. The scattering into the mid-spatial frequency makes it a very long range function, ranging from a few hundred nanometers to several millimeters. It can be approximated by a fractal form. Several fractals will most likely be required to approximate it well, however. The TIS can be found by integrating the PSF over the brightfield area.
The long range of the flare PSF makes it impractical to compute the flare for OPC with a direct convolution of the aerial image with the PSF. However, it has been found that convolving the PSF with an average mask density grid can yield enough accuracy [2]. To speed up the computation, variable size grids are used. To include flare in the OPC model, Mentor’s Calibre tool first divides the original layout into a 1