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.
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.
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.
In this paper, we develop an image-gradient-based algorithm to simultaneously optimize various cost
functions for inverse mask design. The algorithm employs an iterative approach which evaluates the gradient
decent of the resist image, aerial image, and the aerial image contrast with a pre-assigned step length. Moreover,
an independent iteration step is inserted among iterations for binary mask conversion. We show that the
proposed algorithm allows fast convergence while achieving high aerial image contrast. The impacts of each
cost function on the pattern fidelity and convergence are also discussed.
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.