The tri-lateral challenge of resolution, photospeed, and LER: scaling below 50nm?

Abstract

A simple analytical model for line-edge roughness in chemically amplified resists is derived from an accounting of stochastic fluctuations of photon ("shot noise") and acid number densities. Statistics from this counting exercise are applied to a region defined by the effective acid diffusion length; these statistics are then modulated by the slope of the image intensity to produce a value for LER. The model produces the familiar dependence of LER on aerial image (more specifically on latent image) and dose also seen in many other models and data. The model is then applied to the special case of interference imaging, for which the aerial image is a simple, known analytic function. The resulting expression is compared to experimental data at both relatively large half-pitches, shot with 257nm, and sub-50nm half-pitches shot with 13.5nm and hyper-NA 193nm. The model captures the primary scaling trends seen at the larger length scales, however at the sub-50nm problems arise. It appears that additional effects not covered by counting photons and acids are becoming increasingly important as length scales drop below about 50nm. These additional effects will require increased attention in order to improve LER in lockstep with diminishing CD and pitch.

Neutron Reflectivity Characterization of the Photoacid Reaction-Diffusion Latent and Developed Images of Molecular Resists for Extreme Ultraviolet Lithography

“…Routes to reduce L d include varying the size of the photoacid as well as covalently bonding the PAG to the resist to restrict diffusion. − In the current demand for high-throughput, resists with higher sensitivity to lower exposure doses ( E o ) is also a design criterion. The following relationship was proposed to generalize resist resolution metrics and is related to the line-edge roughness (LER) − LER ≈ 1 α E normalo 1 ε 1 LILS · L normald normalΔ where α is the fraction of light absorbed by the resist film, ε is the PAG quantum efficiency, and Δ is predicted to be 1, 3 / 2 , or 3 . The photoacid diffusion length is related to the effective diffusion constant ( D eff ) by L d = (4 D eff t PEB ) 1/2 .…”

Polymer matrix effects on acid generation

“…The experimentally derived Dill C value can be used to calculate the quantum efficiency of PAG decomposition at different lithographic wavelengths through the use Equation (2) in which Φ is the quantum efficiency, NA is Avogadro's number, h is Planck's constant, c is the speed of light, C is the exposure rate constant, α is the absorption coefficient, and λ is the wavelength of exposure. 21 Unlike the Dill C parameter, where incident dose is used, the quantum efficiency only considers dose absorbed into the PAG.…”

Resist fundamentals for resolution, LER, and sensitivity (RLS) performance tradeoffs and their relation to micro-bridging defects

“…This supports the hypothesis that higher acid concentration is reducing LWR. From literature 16 , it is proposed that LWR relates to the acid concentration instead of the simplistic relationship to exposure dose. Our calculations support that LWR roughly correlates to 1/sqrt[acid] as shown in Figure 16.…”

“…The over-exposure of large reticle structures down to small lines (ie gate) generates more acid and typically lower LWR 15 . The importance of acid generation has led researchers to even propose that LWR scales with 1/srqt[acid concentration], instead of the historical shot noise correlation to 1/sqrt[dose] 2,16 .…”