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It has long been observed that certain pattern-failure phenomena manifest in an apparent random manner on wafer. Thus for a design pattern featuring multiple identical repeats in identical surrounding environments, some locations will at certain processing conditions result in failure, whereas identical patterns in direct proximity might not exhibit failure. Two examples of such are sub-resolution assist features (SRAF) printing and aspect-ratio dependent pattern collapse. SRAFs are of course designed to not print on the wafer, but it is observed that when SRAFs of a certain size or proximity to the main feature, at a specific dose and focus condition, are first observed to print on wafer, they do so in a random manner. The clearest demonstration of this is for a simple grating pattern with long running simple 1D lines interspersed with uniformly sized SRAF on the mask. Depending upon the resist system polarity, it is common to see splotches of partially printed SRAF dimples in the photoresist, or residual scum of photoresist appearing randomly along the length of the SRAM location. This behavior can be ascribed to the cumulative stochastic effects of exposure, PEB, and develop. A more complex phenomenon is pattern-collapse, which has been thoroughly researched and shown to be related to non-uniform capillary forces acting upon the newly developed photoresist pattern as well as the profile and bottom CD of those patterns. The result can again be an apparent randomness to the toppling of patterns which are nominally identical, especially when layout and process conditions are right at the onset of failure observation. Early experimental work in characterizing these two phenomena were often based on simple SEM image analysis, and demonstrated perhaps parts per thousand sensitivity. More sophisticated optical imaging techniques such as E-beam inspection can achieve perhaps parts per million sensitivity. With the advent of EUV lithography, there has been increased attention on stochastic effects, owing to the relatively few number of photons involved in the exposure of a single pattern. The result has been improved experimental methodologies for characterizing stochastic phenomena such as micropinching or micro-bridging, as well as improved simulation of these random behaviors. For 7 nm and below, the required sensitivity to protect yield is less than parts per billion. In this work, we report on the use of stochastic models to quantify the prediction of SRAF printing and pattern-collapse through the process window. Simple grating patterns with variable sized single SRAFs are used for characterization of the failure rate expressed in terms of percent of total SRAF mask layout area in the design block. For pattern collapse simulation, an array of photoresist posts are utilized, and as a proxy for pattern collapse, we use bottom CD area calculated from the randomized simulated contour. We use a range of different stochastic models to represent variable degrees of stochastic contribution and show the impact on main feature line edge roughness (LER) as well as pattern failure. Examples are shown for both EUV and 193i cases, and it is highlighted that stochastic failure is not relegated solely to EUV.
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