Abstract: A method for determining a surface in a material is described. During this method, arrival times of a wavefront at a first depth in the material are calculated using an Eikonal equation. Note that the first depth is proximate to an outer surface of the material. Next, arrival times of the wavefront at a second depth in the material are calculated using the Eikonal equation and the calculated arrival times at the first depth. Then, the surface in the material is determined based on the calculated arrival times at the first depth, the calculated arrival times at the second depth, and a given time interval. Note that arrival times at a given depth in the material, which includes the first depth or the second depth, are calculated by directly determining a steady-state solution of the Eikonal equation.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: A method for determining a mask pattern to be used on a photo-mask in a photolithographic process is described. During the method, a target pattern that includes at least one continuous feature is provided. Then a mask pattern that includes a plurality of distinct types of regions corresponding to the distinct types of regions of the photo-mask is determined. Note that the mask pattern includes at least two separate features corresponding to at least the one continuous feature. Furthermore, at least the two separate features are separated by a spacing having a length and the spacing overlaps at least a portion of at least the one continuous feature.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by mask functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by mask functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic, manufacturability of photomasks. An accurate, slower merit function may be used to determine adjustment parameters for a faster, approximate merit function. The faster merit function may be used for iteration and adjusted based on the adjustment parameters.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.

Abstract: Contact hole patterns are disclosed having a plurality of peripheral regions formed around a target area in which a contact hole is to be formed. The peripheral regions visually resemble “lobes” or “leaves” extending outwards towards the periphery of the target area. The lobes may be disjoint or connected to each other. Present methods can be used to prepare masks for printing contact holes on wafers, as well as to prepare design patterns for laser-writers or direct-write lithography in order to print contact holes on masks or directly on wafers. The methods apply to both binary and phase-shift mask designs with varying illuminations.