Pixelated phase mask as novel lithography RET

Borodovsky, Yan; Cheng, Wen‐Hao; Schenker, Richard E.; Singh, Vivek K.

doi:10.1117/12.772116

Cited by 23 publications

(13 citation statements)

References 6 publications

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“…In particular, the use of sub-resolution assist features and pixelated phase masks requires thick mask scattering and polarization effects to be accurately modeled for acceptable lithographic patterning. 18,19 Recently, several papers proposed methods to capture these effects in a fast and efficient way. 20,21 The forward and inverse lithography problem formulation outlined in this paper must be extended to take into account thick mask effects.…”

Section: Discussionmentioning

confidence: 99%

Generalized inverse problem for partially coherent projection lithography

Davids

Bollepalli

2008

Optical Microlithography XXI

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In this paper, we will outline general mathematical techniques applied to the solution of the inverse problem for partially coherent lithographic imaging. The forward imaging problem is reviewed and its solution is discussed within the framework of 2D sampling and matrix coherence theory. The intensity distribution on the wafer is shown to be a bilinear functional in the sampled mask transmission values, and represents a continuous sparse set of variables for optimization. We review various iterative techniques to optimize the sampled mask transmission, called a tau-map. From the optimal tau-map, a procedure is required to construct a pixelated mask representation with restricted transmission values. This mask representation is not unique since the problem is ill-posed, and leads to multiple mask solutions for a single optimal tau-map. Various procedures based on spectral techniques and principle component analysis to quantize the mask are reviewed.

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Section: Discussionmentioning

confidence: 99%

Generalized inverse problem for partially coherent projection lithography

Davids

Bollepalli

2008

Optical Microlithography XXI

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“…It was also shown that this technology can be used to eke out significantly more performance from steppers of a given generation. Figures 17 and 18 briefly describe this; this is also described in detail elsewhere [7]. Fig.…”

Section: Silicon Validationmentioning

confidence: 97%

Making a trillion pixels dance

Singh

Toh

et al. 2008

Optical Microlithography XXI

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In June 2007, Intel announced a new pixelated mask technology. This technology was created to address the problem caused by the growing gap between the lithography wavelength and the feature sizes patterned with it. As this gap has increased, the quality of the image has deteriorated. About a decade ago, Optical Proximity Correction (OPC) was introduced to bridge this gap, but as this gap continued to increase, one could not rely on the same basic set of techniques to maintain image quality. The computational lithography group at Intel sought to alleviate this problem by experimenting with additional degrees of freedom within the mask. This paper describes the resulting pixelated mask technology, and some of the computational methods used to create it. The first key element of this technology is a thick mask model. We realized very early in the development that, unlike traditional OPC methods, the pixelated mask would require a very accurate thick mask model. Whereas in the traditional methods, one can use the relatively coarse approximations such as the boundary layer method, use of such techniques resulted not just in incorrect sizing of parts of the pattern, but in whole features missing. We built on top of previously published domain decomposition methods, and incorporated limitations of the mask manufacturing process, to create an accurate thick mask model. Several additional computational techniques were invoked to substantially increase the speed of this method to a point that it was feasible for full chip tapeout. A second key element of the computational scheme was the comprehension of mask manufacturability, including the vital issue of the number of colors in the mask. While it is obvious that use of three or more colors will give the best image, one has to be practical about projecting mask manufacturing capabilities for such a complex mask. To circumvent this serious issue, we eventually settled on a two color mask -comprising plain glass and etched glass. In addition, there were several smaller manufacturability concerns, for example a "1X1" glass pillar (an isolated 0 phase pixel) were susceptible to collapse under the stress of mask processing, and therefore these had to be constrained out of the final configuration. A third key element was defining the objective function. We experimented with a large number of choices and eventually settled on a form that allows us to trade-off fidelity and contrast. A fourth key element was the optimization algorithm. The number of possible configurations for a trillion pixels present on our final product mask is greater than the number of total elementary particles in the known universe, so finding the proverbial needle in this haystack was difficult to say the least. We chose a mixture of stochastic and direct descent algorithms to find an arrangement that meets the demands. While we have not proved we are close to the absolute global minimum, we conducted several experiments to suggest this is the case. A fifth key element, and a large one at that, was scalin...

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“…Moreover, technologies such as "pixilated-phase masks" [5] and the need for "computational scaling" [6] further fuel the need for increasing computing resources for advanced process nodes. The introduction of server farms and hardware accelerated OPC has eased the computational challenge, but the growing cost and complexity of OPC is still paramount.…”

Section: Growing Complexity Associated With Scaling In Low K 1 Regimementioning

confidence: 99%

OPC simplification and mask cost reduction using regular design fabrics

Jhaveri

Stobert²,

Liebmann³

et al. 2009

SPIE Proceedings

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Cost and complexity associated with OPC and masks are rapidly increasing to the point that they could limit technology scaling in the future. This paper focuses on demonstrating the advantages of regular design fabrics for OPC simplification to enable scaling and minimize costs for technologies currently in volume production. The application of such a simplified OPC flow results in much smaller mask data volumes due to significantly fewer edges compared to the conventional designs and OPC flows. Moreover, the proposed approach enables reduced mask write times, hence lower mask costs.We compare OPC performance and complexity on standard cell designs to that of layouts on a regular design fabric. We first demonstrate advantages and limitations within an industrial model-based OPC solution. Then, a simplified rulebased OPC solution is discussed for the Metal 1 layer. This simplified OPC solution demonstrates a 70X run time improvement and an order of magnitude reduction in both the output edge count per unit shape and shot count per unit shape while maintaining the printabalility advantages of regular design fabrics. The simplified OPC also demonstrates a 50% reduction in mask-write time. Finally, the benefit of regular design fabrics for OPC simplification and mask cost reduction at a 32nm node is discussed.

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Pixelated phase mask as novel lithography RET

Cited by 23 publications

References 6 publications

Generalized inverse problem for partially coherent projection lithography

Generalized inverse problem for partially coherent projection lithography

Making a trillion pixels dance

OPC simplification and mask cost reduction using regular design fabrics

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