Optical proximity correction (OPC) is a resolution enhancement technique extensively used in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the layout is divided into small pixels, which are then iteratively modified until the simulated print image on the wafer matches the desired pattern. However, the increasing complexity and size of modern integrated circuits make PBOPC techniques quite computationally intensive. This paper focuses on developing a practical and efficient PBOPC algorithm based on a nonparametric kernel regression, a well-known technique in machine learning. Specifically, we estimate the OPC patterns based on the geometric characteristics of the original layout corresponding to the same region and a series of training examples. Experimental results on metal layers show that our proposed approach significantly improves the speed of a current professional PBOPC software by a factor of 2 to 3, and may further reduce the mask complexity.
The semiconductor manufacturing industry has been continuously shrinking the critical dimension of integrated circuits. An important step in manufacturing integrated circuits is transforming the photomasks into constituent shots, a process referred to as fracturing. A major problem with fracturing is the explosion of shots which leads to long mask write times and costly masks. In this paper, we develop fracturing algorithms that are tailored towards curvilinear layouts, such as those optimized by pixel based OPC. Our proposed fracturing algorithms generate the location, size, and dosage of shots given the mask layout and mask manufacturing parameters. We propose two classes of algorithms that both allow for shot overlap. The first manhattanizes a curvilinear mask and applies our previously developed rectilinear fracturing algorithm upon the resulting rectilinear mask. The second one directly generates the shots by matching the boundary of the input polygon with a dictionary of possible shot corners that are associated with a shot dosage. This is followed by the same rectilinear fracturing algorithm to refine the shot edges. An important feature of all our algorithms is that they can readily trade off between mask error and shot count by adjusting input parameters. Compared to a commercially available non- overlapping shot software package, our algorithm results in up to a 50% reduction in shot count with comparable mask error.
In this paper, we develop a novel fracturing algorithm with shot overlap that is tailored towards rectilinear
masks, such as those generated via edge based OPC software. Our proposed fracturing algorithm generates
both the location and dosage of shots given the mask layout and mask making parameters. In the first step we
heuristically cover the mask polygon with overlapping shots. Next, we incorporate the forward scattering and
resist model in a least squares problem to compute the best dosage for all shots. Finally, we update the locations
of the shot edges by computing the edge placement error between our simulated contour and the desired contour.
One unique feature of our algorithm is that it can readily trade off between edge placement error and shot
count by adjusting two input parameters. Compared to a commercially available non-overlapping shot software
package, for a 400μm×400μm micron SRAM unit with about 1 million polygons, our algorithm results in a 23%
reduction in shot count, while increasing the weighted average EPE from 0.7 to 1 nanometers.
Traditionally, Variable Shape Electron Beam (VSEB) mask writing tools generate pixel-based optical proximity
correction (OPC) or inverse lithography technology (ILT) masks by first simplifying them into a rectilinear
polygon, and then partitioning the rectilinear polygon into shots. However, as these masks are complex and
curvilinear, this approach results in an explosion of shot count and mask write time, and a loss of optimality of
the OPC solution. In this work we propose an alternative fracturing approach to minimize mask write time in
which the shot location, size, and dose are determined using the mask fabrication model. In doing so we allow
shots to overlap in order to reduce the shot count while maintaining mask and wafer quality. Our approach is
based on overcomplete signal expansion algorithms which have traditionally been used for sparse representation
and compression of images and videos. Our simulation results on a 45nm random logic and contact hole circuit
show shot count reduction by as much as 50%.
In optical lithography, mask pattern is first fractured into basic trapezoids, and then fabricated by the variable
shaped beam mask writing machine. Ideally, mask fracture tools aim at both suppressing the trapezoid count
to speed up the write time, and minimizing the external sliver length to improve CD uniformity. However, the
increasing transistor density, smaller feature sizes, and the aggressive use of resolution enhancement techniques
pose new challenges to write time and CD uniformity. In this paper, we propose a fracture heuristics to improve
the sliver performance of current commercially available fracturing tools. In the proposed approach, the mask
layout is first decomposed into elemental rectangles by the rays emitted from each concave corner. Then, a rectangle
combination technique is applied to search and eliminate the external slivers from the polygon boundaries
by moving them to the center. This approach guarantees that the resulting trapezoid count approaches the
theoretical lower bound. Compared to a current commercially available fracturing tools, our proposed approach
effectively reduces the external sliver length by 8% to 13%.
In microlithography, mask patterns are first fractured into trapezoids and then written with a variable shaped
beam machine. The efficiency and quality of the writing process is determined by the trapezoid count and
external slivers. Slivers are trapezoids with width less than a threshold determined by the mask-writing tool.
External slivers are slivers whose length is along the boundary of the polygon. External slivers have a large
impact on critical dimension (CD) variability and should be avoided. The shrinking CD, increasing polygon
density, and increasing use of resolution enhancement techniques create new challenges to control the trapezoid
count and external sliver length. In this paper, we propose a recursive cost-based algorithm for fracturing which
takes into account external sliver length as well as trapezoid count. We start by defining the notion of Cartesian
convexity for rectilinear polygons. We then generate a grid-based sampling as a representation for fracturing.
From these two ideas we develop two recursive algorithms, the first one utilizing a natural recurrence and the
second one a more complex recurrence. Under Cartesian convexity conditions, the second algorithm is shown to
be optimal, but with a significantly longer runtime than the first one. Our simulations demonstrate the natural
recurrence algorithm to result in up to 60% lower external sliver length than a commercially available fracturing
tool without increasing the polygon count.