Metrics to assess fracture quality for variable shaped beam lithography

2014

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.

Section: Model Based Fracturingmentioning

confidence: 99%

“…Currently, geometric rules are used to decompose the masks 1, 2 resulting in a fast fracture time but also a prohibitively large number of shots resulting in long write times. 4 This increased write time is a major concern for the semiconductor industry.…”

Section: Introductionmentioning

confidence: 99%

Shot overlap model-based fracturing for edge-based OPC layouts

2014

“…In addition, the heuristics described in next section is applied to simultaneously reduce the trapezoid count and the total external sliver length. Thus, requirements (2) and (3) are the foci of our algorithm. Requirements (5) and (6) and mask patterns with 45-degree slant edges are part of our future work.…”

Section: Fracturing Problem Formulationmentioning

confidence: 99%

A cost-driven fracture heuristics to minimize external sliver length

2011

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%.

“…For example, in Fig. 6, the subsection of the polygon embedded with sub-rectangle [(2,3), (5,5)] is shaded. This representation allows us to enumerate all possible sub-rectangles for a given rectilinear polygon.…”

Section: Representation Of Rectilinear Polygonsmentioning

confidence: 99%

“…Bloecker et al have evaluated many metrics to quantify fracturing quality [5]. The authors proposed and demonstrated that shoreline or external sliver length is a suitable metric for evaluating fracturing quality as it closely correlates with manufacturability while being fast to evaluate.…”

Section: Introductionmentioning

confidence: 99%

A recursive cost-based approach to fracturing

2011

In microlithography, mask patterns are first fractured into trapezoids and then fabricated with a variable shaped beam writing 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 parameter 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 have raised new challenges to control the trapezoid number 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 utilizes a natural recurrence while the second one utilizes a more complex recurrence. Under Cartesian convexity conditions, the second algorithm is shown to provide optimal solutions; however, it has a drastically increased runtime as compared with the natural recurrence. Our simulations demonstrate the natural recurrence algorithm to produce significantly less sliver length than a commercially available fracturing tool by up to 60% in terms of external sliver length without increasing the polygon count.