Stochastic effects are an area of increasing focus and concern for EUV lithographers. John Biafore, Research Scientist in the PROLITH group at KLA-Tencor, provided an in-depth view of the many sources of these problematic effects as well as potential mitigation strategies at the Nikon symposium earlier this year.
Lithography modeling strategies have historically favored the continuum approximation, in which one assumes that local fluctuations from quantum effects are small. However, these methods are not as accurate when either the length scale of features is comparable to the molecular sizes or when the number of photons absorbed in proximity to a feature are small enough that local fluctuations affect lithography, producing feature edge roughness (LER), feature CD variability or non-uniformity (LWR and LCDU), as well as missing or failed features (Figure 1A). To accurately model current effects in EUV and other resists, PROLITH builds the quantization of light and matter into their lithography models.
Biafore explained that stochastic effects in lithography are observed as local, random variabilities or failures in the after-develop resist image (ADI). They can be caused optically by uncertainty in the absorbed photon number, as well as by physical-chemical causes including uncertainties in the release of photoproducts (both amount and position), and by diffusional blur during post-processing or development (Figure 1B).
Reliance on continuum modeling to predict EUV lithography carries significant risk. For instance, hot spots may appear or disappear randomly due to stochastic effects (Figure 2A). Studies of stochastics in EUV have been a focus area for over a decade, and the origin of the troublesome variability is in the resist exposure and uncertainty in the amount of energy absorbed. This is because the exposure process is the single connection between the projection image and the resist; the resist cannot compensate for inherent statistical effects, a.k.a. photon shot noise (PSN), in photon absorption (Figure 2B). The photon shot noise effect is compounded by other stochastic effects occurring in the resist.
To see this, Biafore first compared continuum and stochastic simulations of a single edge looking at the incident and absorbed photons using EUV with 30 nm film thickness, 20 mJ/cm2 dose, and image blur = 0. The thin EUV resist film typically only absorbs a fraction (20%) of the incident photons; given the photon shot-noise effects from that combined with the stochastic nature of photoacid generation and reaction-diffusion, the simulations highlight that even for a perfect edge the photoproduct (acid) and protected polymer (M) after reaction-diffusion (RxD) shows an edge roughness greater than zero (Figure 3). The PSN produces uncertainty in the number of photoproducts, while exposure blur from the photoelectric effect produces uncertainty in their position as well.
To see blur effects, Biafore shared stochastic simulations of single edges after exposure and reaction-diffusion using EUV with 30 nm film thickness, 35 mJ/cm2 dose, and comparing image blur = 0 nm vs. 10 nm. The addition of image blur had a negative effect on the roughness and positioning (Figure 4A); whereas subsequent simulations showed improvements were gained by increasing dose and decreasing image blur (Figure 4B).
Inclusion of all these effects produces more accurate prediction of hotspots; after that, it is necessary to understand the mechanism that causes failures like missing contacts or shorts, whether they are “hard” repeaters that always print, or stochastic or “soft” repeaters that sometimes print. Lithography simulation should be used to find and diagnose the root cause of the failures, determine a repair strategy, and identify weak points on the wafer that require close monitoring (Figure 5A). E-beam inspection techniques can evaluate 8 wafers in 24 hours with ~0.01% of the wafer area inspected, whereas optical inspection can evaluate 24 wafers in 24 hours with ~97% of the wafer checked. A combination of optical and e-beam wafer inspection methods (Figure 5B) is necessary to effectively monitor locations of stochastic weak points.
Stochastics continue to challenge the EUV lithography community, and Biafore underscored that accurate simulations are essential for cost-effective EUV process characterization. Many factors conspire to produce stochastic effects, and mitigation may require: increasing image contrast, raising the dose, improving resist mechanics, better understanding and optimization of properties affecting exposure blur, as well as increasing the absorption by a factor of two in organic CARs. In the meantime though, Biafore concluded that whatever cannot be repaired using simulation must be monitored, and he warned that verification of stochastic weak points may require full wafer inspection to monitor millions, if not billions or more sites.