In projection printing the proximity effects between adjacent two-dimensional features such as concentric elbows can be the limiting factor in designing layout rules. An aerial image simulation code based on the imaging algorithms in SAMPLE has been developed and used to investigate these proximity effects. The program accepts arbitrary polygonal shapes constructed of rectangular and triangular patches. The image is calculated using Hopkins transmission cross coefficient formulation and uses rapid integral evaluation techniques. The cpu time for this FORTRAN F77 program depends on the size of the mask and the partial coherence factor as 0.25[(1 + σ) 2A(NA/λ)2]2 seconds on a DEC VAX 11/780 using double precision, where A is the mask area, σ the coherence factor, NA the numerical aperture and λ the wavelength. The output intensity can be displayed with graphics tools such as UNIGRAFIX or cross-sectioned for input to SAMPLE development simulation along critical paths. Proximity effects in critical regions between features such as nested elbows, contacts near contacts and lines, and lines near large pads are studied. For small contacts studies show that a contact hole can be placed as close as 0.5λ/NA microns to another contact hole. For nested elbows the critical effect is the variation in intensity in the straight regions just adjacent to the corner. This undesirable variation is primarily due to the intrafeature intensity interactions and is not greatly influenced by the proximity of another nested elbow. For general feature shapes the proximity effects are reduced by increasing the partial coherence factor to 0.5 or higher but at the cost of reducing contrast and peak intensity. For contact masks a partial coherence of 0.3 is recommended for higher edge slope and peak intensities. Proximity effects of small defects are also illustrated.
Philip D. Flanner,
Andrew R. Neureuther,
"Two-Dimensional Optical Proximity Effects", Proc. SPIE 0633, Optical Microlithography V, (20 August 1986); doi: 10.1117/12.963727; https://doi.org/10.1117/12.963727