A computational technique to optimally design in-situ diffractive elements: Applications to projection lithography at the resist resolution limit

Abstract

Near-field interference lithography is a promising variant of multiple patterning in semiconductor device fabrication that can potentially extend lithographic resolution beyond the current materials-based restrictions on the Rayleigh resolution of projection systems. With H 2O as the immersion medium, non-evanescent propagation and optical design margins limit achievable pitch to approximately 0.53λ/nH 2O = 0.37λ. Non-evanescent images are constrained only by the comparatively large resist indices (typically 1.7) to a pitch resolution of 0.5/n resist (typically 0.29). Near-field patterning can potentially exploit evanescent waves and thus achieve higher spatial resolutions. Customized near-field images can be achieved through the modulation of an incoming wavefront by what is essentially an in-situ hologram that has been formed in an upper layer during an initial patterned exposure. Contrast Enhancement Layer (CEL) techniques and Talbot near-field interferometry can be considered special cases of this approach. Since the technique relies on near-field interference effects to produce the required pattern on the resist, the shape of the grating and the design of the film stack play a significant role on the outcome. As a result, it is necessary to resort to full diffraction computations to properly simulate and optimize this process. The next logical advance for this technology is to systematically design the hologram and the incident wave-front which is generated from a reduction mask. This task is naturally posed as an optimization problem, where the goal is to find the set of geometric and incident wavefront parameters that yields the closest fit to a desired pattern in the resist. As the pattern becomes more complex, the number of design parameters grows, and the computational problem becomes intractable (particularly in three-dimensions) without the use of advanced numerical techniques. To treat this problem effectively, specialized numerical methods have been developed. First, gradient-based optimization techniques are used to accelerate convergence to an optimal design. To compute derivatives of the parameters, an adjoint-based method was developed. Using the adjoint technique, only two electromagnetic problems need to be solved per iteration to evaluate the cost function and all the components of the gradient vector, independent of the number of parameters in the design. © 2009 SPIE.