Making a trillion pixels dance

Abstract

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...

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

“…[6][7][8][9] Their approach operates on the mask that has been optimized by pixel-based OPC. 24,25 They place overlapping shots in such a way that the simulated mask image approximates the desired target mask. In contrast to conventional rule-based fracturing, model-based fracturing places shots based upon the models for both the mask writer and the photoresist.…”

Generalized inverse problem for partially coherent projection lithography

“…Thick mask effects are incorporated into the complex tau map by sampling the near field complex mask transmission obtained by a rigorous solution to Maxwell's equations or fast thick mask approximations. [20][21][22] The complex tau map is then used in the optimization step for evaluation of the image. In the second step, where we construct the mask from the complex tau map, the complex tau map is dithered into a set of mask primitives and the complex tau map is generated using thick mask models and compared to optimal complex tau map.…”

Pixelated phase mask as novel lithography RET

“…As a result, 100nm lateral pixel size on a mask (at 4X) was chosen as a compromise between considerations stated above. For pixels with 100nm side dimensions the accuracy of our proprietary EM modeling approximation that we had at the time, while sufficient up to the etch depth corresponding to and somewhat exceeding 180 o phase shift for standard AltPSM masks, degraded as much as 25% for pixels with etch depth significantly above that (See [2] for more details). This and the great benefit of using processing and metrology already in place in support of traditional AltPSM mask making at Intel led us to adopt an etch depth for phase shifted pixels to be the traditional 171.4 nm.…”

“…As described in a separate paper by two of the authors [2], none of the existing fast methods for modeling thick mask efforts was accurate enough to model our pixelated masks. Consequently, we enhanced one of the methods, the domain decomposition method, to take into account scattering effects arising from 1) the fact that the pixels, at mask dimension, are about half the size of the wavelength, 2) the rounding of the corners of the pixels, and 3) the sloping sidewall of the etched topography.…”

“…The details of the computational methods that were used to obtain the pixelated mask designs are described in reference [2]. The key elements of this method are the fast thick mask model described above, an optimization algorithm that finds the near optimal configuration of pixels out of the enormously large number of possible combinations, an objective function that helps drive the optimization, the ability to remove pixel configurations that present a problem in the mask making process, and machinery to handle full chip tapeout.…”