A first set of critical dimension (CD) measurements of resist patterns created by a lithography process and a second set of CD measurements of water patterns created by an etch process may be obtained. A forward etch model and an inverse etch model may be calibrated together by reducing (1) a first prediction error between the second set of CD measurements and a first set of simulated CDs predicted by the forward etch model based on the resist patterns, a second prediction error between the first set of CD measurements and a second set of simulated CDs predicted by the inverse etch model based on the wafer patterns, and a matching error between the forward etch model and the inverse etch model.

A method for obtaining exposure data may be provided. MTO (Mask Tape Out) design data for a mask pattern may be received. A mask data preparation operation with respect to the MTO design data may be performed to obtain exposure data. Two-dimensional contours of a plurality of types of test patterns in an exposure mask may be extracted through simulation using a mask process model. First critical dimensions may be measured at measurement points of the contour of each of the plurality of types of test patterns by using a metrology algorithm. The first critical dimensions may be averaged to obtain a first average critical dimension for each of the plurality of types of test patterns. Second critical dimensions in consideration of dispersion in each of the plurality of types of test patterns may be measured using an inverse function of a standard normal distribution, and the second critical dimensions may be averaged to obtain a second average critical dimension for each of the plurality of types of test patterns. A mean to target (MTT) value may be calculated as a difference between the second average critical dimension and a target critical dimension for each of the plurality of types of test patterns. Differences between ones of the MTT values may be calculated. When one or more of the differences between the ones of the MTT values may is outside of a tolerance threshold, the exposure data may be corrected.

A method for obtaining exposure data may be provided. MTO (Mask Tape Out) design data for a mask pattern may be received. A mask data preparation operation with respect to the MTO design data may be performed to obtain exposure data. Two-dimensional contours of a plurality of types of test patterns in an exposure mask may be extracted through simulation using a mask process model. First critical dimensions may be measured at measurement points of the contour of each of the plurality of types of test patterns by using a metrology algorithm. The first critical dimensions may be averaged to obtain a first average critical dimension for each of the plurality of types of test patterns. Second critical dimensions in consideration of dispersion in each of the plurality of types of test patterns may be measured using an inverse function of a standard normal distribution, and the second critical dimensions may be averaged to obtain a second average critical dimension for each of the plurality of types of test patterns. A mean to target (MTT) value may be calculated as a difference between the second average critical dimension and a target critical dimension for each of the plurality of types of test patterns. Differences between ones of the MTT values may be calculated. When one or more of the differences between the ones of the MTT values may is outside of a tolerance threshold, the exposure data may be corrected.

A system, methods, and a non-transitory computer-readable medium for digital lithography to reduce mura in substrate sections. The boundary lines of the digital lithography need to be invisible. In one example, a system includes a processing unit configured to print a virtual mask file provided by a controller. The controller is configured to receive data and convert the data into a virtual mask file having an exposure pattern for a lithographic process. The exposure pattern includes a plurality of first sections, and second sections. Each first section forms a boundary with each second section along a first column of image projection systems of the processing unit. The controller patterns the substrate. The exposure pattern includes a first section pattern of each first section that crosses the eye to eye boundary with the second section making the boundary invisible.

A system, methods, and a non-transitory computer-readable medium for digital lithography to reduce mura in substrate sections. The boundary lines of the digital lithography need to be invisible. In one example, a system includes a processing unit configured to print a virtual mask file provided by a controller. The controller is configured to receive data and convert the data into a virtual mask file having an exposure pattern for a lithographic process. The exposure pattern includes a plurality of first sections, and second sections. Each first section forms a boundary with each second section along a first column of image projection systems of the processing unit. The controller patterns the substrate. The exposure pattern includes a first section pattern of each first section that crosses the eye to eye boundary with the second section making the boundary invisible.

In a method of manufacturing a photo mask used in a semiconductor manufacturing process, a mask pattern layout in which a plurality of patterns are arranged is acquired. The plurality of patterns are converted into a graph having nodes and links. It is determined whether the nodes are colorable by N colors without causing adjacent nodes connected by a link to be colored by a same color, where N is an integer equal to or more than 3. When it is determined that the nodes are colorable by N colors, the nodes are colored with the N colors. The plurality of patterns are classified into N groups based on the N colored nodes. The N groups are assigned to N photo masks. N data sets for the N photo masks are output.

In a method of manufacturing a photo mask used in a semiconductor manufacturing process, a mask pattern layout in which a plurality of patterns are arranged is acquired. The plurality of patterns are converted into a graph having nodes and links. It is determined whether the nodes are colorable by N colors without causing adjacent nodes connected by a link to be colored by a same color, where N is an integer equal to or more than 3. When it is determined that the nodes are colorable by N colors, the nodes are colored with the N colors. The plurality of patterns are classified into N groups based on the N colored nodes. The N groups are assigned to N photo masks. N data sets for the N photo masks are output.

Computer implemented methods and computer program products have instructions for generating transfer functions that relate segments on lithography photomasks to features produced by photolithography and etching using such segments. Such methods may be characterized by the following elements: (a) receiving after development inspection metrology results produced from one or more first test substrates on which resist was applied and patterned using a set of design layout segments; (b) receiving after etch inspection metrology results produced from one or more second test substrates which were etched after resist was applied and patterned using said set of design layout segments; and (c) generating the transfer function using the set of design layout segments together with corresponding after development inspection metrology results and corresponding after etch inspection metrology results.

Computer implemented methods and computer program products have instructions for generating transfer functions that relate segments on lithography photomasks to features produced by photolithography and etching using such segments. Such methods may be characterized by the following elements: (a) receiving after development inspection metrology results produced from one or more first test substrates on which resist was applied and patterned using a set of design layout segments; (b) receiving after etch inspection metrology results produced from one or more second test substrates which were etched after resist was applied and patterned using said set of design layout segments; and (c) generating the transfer function using the set of design layout segments together with corresponding after development inspection metrology results and corresponding after etch inspection metrology results.

Systems and methods for performing local Critical Dimension Uniformity (CDU) modeling in a virtual fabrication environment are discussed. More particularly, local CD variance is replicated in the virtual fabrication environment in order to produce a CDU mask that can be used during a virtual fabrication sequence to produce more accurate results reflecting the CD variance of features that occurs in a pattern for a semiconductor device being physically fabricated.