News Column

Patent Issued for Lithography Mask Functional Optimization and Spatial Frequency Analysis

May 6, 2014

By a News Reporter-Staff News Editor at Journal of Mathematics -- From Alexandria, Virginia, VerticalNews journalists report that a patent by the inventors Ungar, P. Jeffrey (Sunnyvale, CA); Torunoglu, Ilhami H. (Monte Sereno, CA), filed on November 27, 2012, was published online on April 22, 2014.

The patent's assignee for patent number 8707222 is Gauda, Inc. (Palo Alto, CA).

News editors obtained the following quote from the background information supplied by the inventors: "This invention relates to the field of electronic design automation, and in particular, the optimization of masks used for photolithographic printing of circuit designs, known in the field as optical proximity correction.

"Production-scale chip manufacturing uses photolithographic techniques to build up layers of materials on a wafer to create the transistors, wires, and so on, that realize a chip design. The sizes of the features to be printed on the wafer are approaching the limits set by the wavelength of the light, the optical projection system, and the behavior of the light sensitive materials used, among many other factors.

"Diffraction effects from the wavelength of the light source and the limits of the projection optics motivated the development of optical proximity correction (OPC) techniques to adjust the shapes on the mask to print more like the desired result on the wafer. For example, a square may have serifs added to its corners to compensate for excessive rounding of the corners of the printed feature, or the ends of a rectangle may have 'hammerheads' added to further ensure the printed feature reaches the desired line end.

"The first OPC methods were based on simple rules for modifying the shapes on the mask, but as the technology was pushed closer to optical resolution limits, model-based optimization, which adjusts the features on the mask to improve the calculated printed image, was developed. Two significant advantages of model-based OPC are the ability to account for proximity effects (warping a nearby feature will affect how a given feature prints) and to accommodate photoresist behavior.

"Sometimes, features are found to print with greater fidelity if extra features are added to the mask that are too small to print themselves, but nevertheless favorably affect the way nearby main features print, especially over a range of process conditions. Introduction of these so-called subresolution assist features (SRAFs) is still generally done according to preset rules. Typically they are inserted first and held fixed as OPC is applied to the main features on the mask.

"There are significant problems in applying these methods as the industry moves to ever smaller on-wafer dimensions. The rules used to insert SRAFs are becoming more complex and less reliable. The standard OPC methods do not have the flexibility needed to achieve the best results and require post-OPC verification and manual intervention.

"What is needed is a practical model-based method for mask design that can automatically determine a mask that both satisfies mask manufacturing and verification criteria, and produces the desired print on the wafer over a range of process conditions, such as exposure and focus variation. Such a method will generally result in a mask that warps existing layout geometry and adds or subtracts SRAFs from anywhere, including in ways that split or join the layout features."

As a supplement to the background information on this patent, VerticalNews correspondents also obtained the inventors' summary information for this patent: "Model-based OPC and more general 'inverse lithography' methods are both iterative optimization algorithms that adjust parameters defining the mask until the predicted print is within acceptable tolerances for a set or range of conditions. They differ chiefly in how the mask is represented, which is typically as simple geometry for OPC, and as pixels comprising an image of transmission values for 'inverse lithography'.

"Unless the mask representation automatically satisfies all desired mask constraints and characteristics, such as allowed transmission values or minimum feature size, the formula measuring a mask's suitability will introduce terms that add a cost related to the violation of these constraints. In field of 'inverse problems', introducing these terms is known as 'regularization', and is a means of selecting a solution from a potentially infinite set of solutions that fits the desired outcome equally or similarly well but also has other a priori desirable properties.

"This invention advantageously and most generally represents the mask as a function with an exact analytical form over the mask region. Furthermore, the present invention uses the physics of optical projection to design the solution based on a spatial frequency analysis. From a physics perspective, spatial frequencies above a cutoff determined by the optical system do not contribute to the projected image. Spatial frequencies below this cutoff affect the print (and the mask), while those above the cutoff only affect the mask.

"In some embodiments of the present invention, the mask function is expressed in a Fourier basis, which exposes perfectly the separation between the low frequencies that affect the print and the high frequencies that only adjust the mask. In other embodiments, different basis sets, such as wavelets, may be used that expose this frequency separation to a lesser degree.

"The present invention expresses the desirability of a given mask function as a functional (a mathematical form that is a function of a function over a defined region) that calculates the 'cost' with respect to the predicted printed image and possibly various a priori mask constraints. Since the present invention expresses the mask with an exact analytical form, the cost and its functional derivatives can be evaluated analytically and consistently, which enables the use of efficient cost minimization algorithms.

"In one embodiment, the invention first determines a band-limited continuous-tone mask function that is clamped through regularization to the minimum and maximum allowable mask values, and then proceeds to determine a mask quantized to the allowable values that is consistent with this mask through further regularization of the solution. The frequency cutoff used may be higher than the optical cutoff to accommodate clamping and quantization and may change as the optimization proceeds.

"The purpose of the clamping, which may be 'soft' in that small excursions outside the range are allowed, is both to accommodate the kind of mask being designed and to avoid unphysical values that would imply amplification. For both clamping and mask value quantization, regularization terms are incorporated into the cost functional in a manner familiar to one skilled in the art. Their effect and their specific form may be adjusted on any schedule during the course of the optimization.

"In an embodiment, the quantized optimal mask is decomposed into geometric shapes for further regularization to satisfy various geometric constraints. The shapes thus determined may appear as perturbed idealized mask shapes with extra features added or removed (SRAFs), or more generally as a pattern without a simple correspondence to the ideal target layout pattern.

"In an embodiment, the spatial locality of the optical projection process is used in addition to the frequency locality to enable the decomposition of a full mask into overlapping tiles in which the cost functional and functional derivatives may be evaluated in a manner consistent with handling the entire mask at once.

"In an embodiment, the invention is a method including: partitioning a layout mask into a plurality of regions, each region comprising geometric shapes; generating a two-dimensional pixel representation of a region; generating a analytical function (e.g., Fourier basis function) to represent the pixel representation of the region; performing a transformation on the analytical function to obtain a frequency space representation of the analytical function of the region; and based on the frequency space representation, removing low frequency components of the analytical function of the region.

"Other objects, features, and advantages of the present invention will become apparent upon consideration of the following detailed description and the accompanying drawings, in which like reference designations represent like features throughout the figures."

For additional information on this patent, see: Ungar, P. Jeffrey; Torunoglu, Ilhami H.. Lithography Mask Functional Optimization and Spatial Frequency Analysis. U.S. Patent Number 8707222, filed November 27, 2012, and published online on April 22, 2014. Patent URL:

Keywords for this news article include: Gauda Inc, Algorithms.

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Source: Journal of Mathematics

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