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Characterization and modeling of line width roughness (LWR)

Control of Line Width Roughness (LWR) is one of the biggest challenges of next generation lithographies. However, control necessitates accurate definition and characterization schemes. In this paper, a new definition of LWR is proposed with the benefit of being independent on the resist line length used in the measurement. The definition corresponds to the sigma value of LWR for infinite resist-line-length, but it can be measured using any finite line length. It is based on an appropriate combination of LWR and CD metrology. As the line length (gate width) decreases the LWR is being partitioned between the sigma of LWR for finite lengths and the CD variation. This partitioning is controlled by the correlation length and the roughness exponent. A protocol for LWR characterization is described using these three parameters. Furthermore, LWR modeling using methods for generating lines similar to the experimental ones is investigated. The aim is to control LWR deliberately for better input to device simulators and solving characterization problems. An algorithm based on the convolution method is shown to reproduce reliably the roughness characteristics of real lines. This algorithm needs as input a triplet of parameters similar to those defined above for LWR characterization.