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Correlation length has nowadays become of common use in lithographic applications. Together with the Hurst parameter, the power spectral density curve and the PSD(0), the correlation length ξ enables a full comprehension of the roughness along the edges of the features after lithography and after process (i.e. etch).
The correlation length can be intuitively defined by how much different points along the same feature’s edge know each other’s position. Behind this simple definition, ξ wraps multiple physical properties and parameters of the whole lithographic process:
1. Source or exposure dose, which set the lowest roughness values – like the PSD(0) – in the lower frequency ranges, before the optical frequency cut-off and resist reaction-diffusion mechanisms. This source of noise is also called incident Photon Shot Noise, and it is a white-type of noise
2. Mask roughness, composed by absorber roughness (i.e. mask line edge roughness) and mask surface roughness which can form speckle patterns
3. Optical system and illumination which fix the minimum printable pitch, but also the maximum roughness frequency transmittable by the exposure tool
4. Photoresist, mainly split in three components:
a. Extinction coefficient k, which determine the minimum absorbed PSN which affects low-frequency roughness
b. Physical/chemical reaction-diffusion mechanisms such as electron blur and yield (for EUV lithography), and acid-quencher motion in the mid-high frequency range
c. Development dynamics, which can change correlation length accordingly to dissolution properties and development time, forming self-affine structures along the feature’s edges
5. Metrology, which affects the whole spectrum, and can lead to non-negligible roughness bias
In this work, we study how the correlation length ξ, and more in general the power spectral density curve, changes considering variations of process conditions for both experimental and simulated features. Controlled process perturbations are applied to all the elements composing the lithographic step: source, mask, optical system, and photoresists. Experiments are carried out at imec, simulations are run with PROLITH, and metrology is performed with Fractilia MetroLER.
The purpose of this study is to better understand which information can be extrapolated by a thorough roughness analysis in the frequency domain, and how these can be used to limit the variability and failure rates of the printed features.
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