Generalized inverse problem for partially coherent projection lithography

Davids, Paul; Bollepalli, Srinivas B.

doi:10.1117/12.772040

Cited by 16 publications

(8 citation statements)

References 9 publications

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“…A Pixelated Phase Mask exhibits properties of a mask with variable phase and transmission thus it is uniquely suitable to support advancements in Inverse Lithography due to its ability to provide the highest number of quantization terms needed to reduce general ILT solutions to practice [4,5]. Yet it is remains to be seen if it will find significant use in the manufacturing environment as both ILT and PPM technologies are complex, relatively immature and might be at the limits of their usefulness in support of single exposure patterning for 22nm node for logic products.…”

Section: Pixelated Phase Mask and Iltmentioning

confidence: 99%

Pixelated phase mask as novel lithography RET

Borodovsky

Cheng

Schenker

et al. 2008

Optical Microlithography XXI

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Novel RET-Pixelated Phase Mask (PPM) is proposed as a novel Resolution Enhancement Technique (RET). PPM is made of pixels of various phases with lateral dimensions significantly smaller than the illuminating radiation wavelength. Such PPM with a singular choice of pixel dimensions acts as a mask with variable phase and transmission due to radiation scattering and attenuation on pixel features with the effective intensity and phase modulated by the pixel layout. Key properties of the pixelated phase masks, the steps for their practical realization, and the benefits to random logic products discussed. Wafer patterning performance and comparative functional yield results obtained for a 65nm node microprocessor patterned with PPM, as well as current PPM limitations are also presented.

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Section: Pixelated Phase Mask and Iltmentioning

confidence: 99%

Pixelated phase mask as novel lithography RET

Borodovsky

Cheng

Schenker

et al. 2008

Optical Microlithography XXI

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“…The first step is to parameterize the estimated mask signal or the solution space . There are multiple ways of representing the mask function including level-set functions [6], pixel map [5,8], tau-map [14], and frequency orders [12,13]. The next step is to define the forward imaging model.…”

Section: The Solutionmentioning

confidence: 99%

Model-based assist feature placement: an inverse imaging approach

Poonawala¹,

Painter²,

Mayhew³

2008

Photomask Technology 2008

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The continuing reduction in feature dimensions and tightening of process constraints have led to an increasing demand for model-based approaches, which can efficiently explore the AF solution space, and achieve AF configurations not easily accessible via rules. In this work, we approach the AF placement problem as an inverse imaging problem. We discuss the generation of an inverse mask field and its use in determining the assist feature location. The results are compared with the single iteration intensity-field based AF placement with regard to symmetry, speed, memory, convergence, and accuracy. Several results with different pitches and illumination conditions are presented to demonstrate the robustness and adaptability of the inverse mask AF placement.

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“…To address those difficulties, we chose a mixture of stochastic and direct descent algorithms to find an arrangement that meets the lithographic requirements. A subset of our methods are described in a separate paper [6].…”

Section: Pixelation and Initial Conditionsmentioning

confidence: 99%

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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Generalized inverse problem for partially coherent projection lithography

Cited by 16 publications

References 9 publications

Pixelated phase mask as novel lithography RET

Pixelated phase mask as novel lithography RET

Model-based assist feature placement: an inverse imaging approach

Making a trillion pixels dance

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