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In optical microlithography, the illumination source for critical complementary metal-oxide-semiconductor layers needs to be determined in the early stage of a technology node with very limited design information, leading to simple binary shapes. Recently, the availability of freeform sources permits us to increase pattern fidelity and relax mask complexities with minimal insertion risks to the current manufacturing flow. However, source optimization across many patterns is often treated as a design-of-experiments problem, which may not fully exploit the benefits of a freeform source. In this paper, a rigorous source-optimization algorithm is presented via linear superposition of optimal sources for pre-selected patterns. We show that analytical solutions are made possible by using Hopkins formulation and quadratic programming. The algorithm allows synthesized illumination to be linked with assorted pattern libraries, which has a direct impact on design rule studies for early planning and design automation for full wafer optimization.

In Abbe’s formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.

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.

For advanced CMOS processes, inverse lithography promises better patterning fidelity than conventional mask correction techniques due to a more complete exploration of the solution space. However, the success of inverse lithography relies highly on customized cost functions whose design and know-how have rarely been discussed. In this paper, we investigate the impacts of various objective functions and their superposition for inverse lithography patterning using a generic gradient descent approach. We investigate the most commonly used objective functions, which are the resist and aerial images, and also present a derivation for the aerial image contrast. We then discuss the resulting pattern fidelity and final mask characteristics for simple layouts with a single isolated contact and two nested contacts. We show that a cost function composed of a dominant resist-image component and a minor aerial-image or image-contrast component can achieve a good mask correction and contour targets when using inverse lithography patterning.

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.

The generation of subresolution assist features (SRAFs) using inverse-lithography techniques demands extensive computational resources which limits its deployment in advanced CMOS nodes. In this paper, we propose a wavefront-based pixel inversion algorithm to quickly obtain inverse masks with a high aerial image quality. Further assisted by a flexible pattern simplification technique, we present effective SRAF generation and placement based on the calculated inverse mask. The proposed approach can be easily inserted prior to a conventional mask correction flow for subsequent concurrent optimizations of both drawn patterns and SRAFs. The innovative pixel inversion and pattern simplification techniques allow quality mask corrections as produced by inverse lithography while maintaining the convenience of standardized/validated process flows currently used in the industry.