Localized and cascading secondary electron generation as causes of stochastic defects in extreme ultraviolet projection lithography

Abstract

Projection lithography using extreme ultraviolet (EUV) light at 13-nm wavelength is expected to achieve production of integrated circuits below 10 nm design-rules. In pursuit of further miniaturization, however, stochastic pattern defect problems have arisen. Here, we discuss the possible impact of spatially inhomogeneous secondary electron (SE) generation on stochastic defects. Two mechanisms are investigated: (1) accidental connections of photon shot noises enhanced by densely localized SE generation and (2) cascading SE generation along photoelectron trajectory traveling from pattern edge into a dark region. Since such defect probabilities are extremely low (typically 10 −4 to ∼10 −12), results of Monte Carlo simulation based on classical optical image and electron scattering simulations are converted into probability functions for densities of physical/chemical events such as photon absorption, SE generation, and elementary reaction in chemically amplified resists. Probabilities of pattern formation and of defect generation are modeled using these functions. Results of performance optimization using a multiobjective genetic algorithm show higher stochastic defects probability in EUV than in conventional deep-UV exposure due to larger spatial inhomogeneity in reaction density and existence of SE generation strings. Defect probabilities are strongly dependent on absolute pattern sizes in the two mechanisms, regardless of the resolution capability of imaging systems. Guidelines for suppressing stochastic defects are suggested, such as homogenization of reaction density, material composition for increasing scattering crosssection, and suppression of pattern edge fluctuation.

Estimating extremely low probability of stochastic defect in extreme ultraviolet lithography from critical dimension distribution measurement

“…Before discussing the defect prediction, here, we briefly review our model. 8,9 We start from generating numbers of physical/chemical events in a resist film, such as photon absorption, secondary electron generation, chemical reaction, and solubility flipping of resist polymer/molecule using coupled Monte-Carlo simulation, which combines simulations for optical imaging, photoelectron scattering, and chemical amplification with acid diffusion [ Fig. 1(a)].…”

“…Assuming one-dimensional pattern for simplicity, the stochastic pattern defect probability (for mechanism A in Ref. 8) is obtained as the probability that the spot film defects cover the area between the main pattern edge at x edge and the point x d representing defect area as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 3 2 6 ; 7 5 2…”

“…Please see Ref. 8 for details. A 20% increase in irradiation dosage shifts the mean CD by 20% (corresponding to a 1.5-nm shift in edge position) with changing the histogram profiles [ Fig.…”

“…We previously introduced the probabilistic model for stochastic defects generation based on two mechanisms, cascading shot noises and long-range scattered photoelectrons. 8,9 In this paper, we apply this model to predict an extremely low probability of stochastic defect generation on real wafers.…”

Cascade and cluster of correlated reactions as causes of stochastic defects in extreme ultraviolet lithography

“…We previously calculated stochastic defects probabilities and their dependences on imaging and material conditions by combining fully coupled a Monte Carlo method and probabilistic models, pointing out that a wide range of variations in photoelectron trajectories and resulting SE distributions have also impact on defect generations. [17][18][19] However, this has not fully taken account of resist factor of stochastics. Mack 20 analytically compared the impacts of photon and resist (acid in CAR) factors on LCDU, and relationships of resist compositions and defect probabilities have also been pointed out.…”