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Source optimization (SO) becomes increasingly important to resolution enhancement in sub-32 nm lithography nodes because the dense pattern configurations significantly limit the capability of mask correction. A key step in SO is the image formation by Abbe's method, which is a linear operation of integrating all source points' images incoherently to form aerial images. However, the aerial images are usually converted to resist images through the nonlinear sigmoid function. Such operation loses the merit of linearity in optimization and leads to slow convergence and time-consuming calculation. In this paper we propose a threshold-based linear resist model to replace the sigmoid model in SO. The effectiveness of our proposed model can be clearly seen from mathematical analysis. We also compare results based on linear and sigmoid models. Highly similar optimal sources are obtained, but the linear model has a significant advantage over the sigmoid in terms of convergence rate and simulation time. Furthermore, the process variations characterized by exposure-defocus (E-D) windows are still in similar trends for optimal sources based on two different resist models.

Inverse lithography which generates model-based patterns theoretically has superior patterning fidelity comparing to conventional rule-based technique. Cost functions are the determinant of performance inverse lithography that is also an optimization problem. However, the design and know-how of cost functions have rarely been discussed. In this paper, we investigate the impacts of various cost functions and their superposition for inverse lithography patterning exploiting a steepest descent algorithm. We research the most generally used objective functions, which are the resist and aerial images, and also deliver a derivation for the aerial image contrast. We then discuss the pattern fidelity and final mask characteristics for simple layouts with a single isolated contact and two nested contacts. Moreover, the convergences which are expressed by edge-placement error (EPE) and contrast versus iteration numbers rapidly attain to steady sate in most hybrid cost functions. All in all, we conclude that a cost function composed of a dominant resist-image component and a minor aerial-image or image-contrast component can carry out a good mask correction and contour targets when using inverse lithography patterning.

As lithography still pushing toward to low-k1 region, resolution enhancement techniques (RETs) including source optimization (SO) and mask optimization (MO) are expected to overcome the fundamentally physics in optics. Recently inverse lithography (IL) is widely studied for source and mask optimization (SMO) to enhance the resolution for over diffraction limit integrate circuit (IC) patterns. In this paper, we propose a gradient based SMO algorithm where the SO and MO are two sequential steps due to their different image formation mechanism. Moreover, we employ three cost functions including aerial and resist image and the image contrast which is proposed in our previous work. We show that IL patterns produced by SMO have better pattern fidelity and image contrast than MO only patterns.

Convergence speed and local minimum issue have been the major issues for inverse lithography. In this paper, we propose an inverse algorithm that employs an iterative gradient-descent method to improve convergence and reduce the Edge Placement Error (EPE). The algorithm employs a constrained gradient-based optimization to attain the fast converging speed, while a cross-weighting technique is introduced to overcome the local minimum trapping.

We propose an inversion calculation method based on a simple "pixel-flipping" approach. The simple method features innovative wavefront-expansion and wavefront-based damping techniques in order to obtain accentuated corrections near the drawn pattern. The method is first employed to be a stand-alone optical proximity correction solution that directly calculates the corrected masks with acceptable contours and image contrast. In addition, a model-based pre-OPC flow, where the initial sizing of drawn patterns and surrounding sub-resolution assist features (SRAF) are simultaneously generated in a single iteration using this inversion calculation is also proposed to minimize technology-transition risks and costs. A mask simplification technique based on the central moments is introduced in order to snap the corrections into 45 degree and axis-aligned line segments. This approach allows achieving optimized corrections while minimizing the impact to the existing and validated correction flow.

The conventional segment-based OPC approach has been applied successfully for many CMOS generations and is currently favored. However, Inverse lithography technology (ILT) is a promising candidate for next-generation optical proximity correction (OPC). Still, there are issues that need to be thoroughly addressed and further optimized. In this work, we propose a model-based pre-OPC flow where the sizing of drawn patterns and placement of surrounding sub-resolution assist features (SRAF) are simultaneously generated in a single iteration using an ILT method. The complex patterns can then be simplified for a conventional OPC solution.