Disclosed is a method of determining a process window within a process space comprising obtaining contour data relating to features to be provided to a substrate across a plurality of layers, for each of a plurality of process conditions associated with providing the features across said plurality of layers and failure mode data describing constraints on the contour data across the plurality of layers. The failure mode data is applied to the contour data to determine a failure count for each process condition; and the process window is determined by associating each process condition to its corresponding failure count. Also disclosed is a method of determining an actuation constrained subspace of the process window based on actuation constraints imposed by the plurality of actuators.

Provided is an extreme ultraviolet (EUV) mask manufacturing method of forming an optimum pattern on a wafer by efficiently reflecting a mask topography effect or a coupling effect between edges of a pattern and improving the accuracy of an EUV mask image. The EUV mask manufacturing method includes performing an optical proximity correction (OPC) method for obtaining EUV mask design data, transferring the EUV mask design data as mask tape-out (MTO) design data, preparing mask data based on the MTO design data, and completing an EUV mask by exposing an EUV mask substrate based on the mask data, wherein the performing of the OPC method applies a coupling filter to both a first case in which angles of an edge pair satisfy |θ1−θ2|=0, and a second case in which angles of an edge pair satisfy 0<|θ1−θ2|≤an angle tolerance.

A method, includes, in part, defining a continuous signal, defining a threshold value, calibrating the continuous signal and the threshold value from measurements made on edges of one or more patterns on a mask and corresponding edges of the patterns on a wafer, convolving the continuous signal with a kernel to form a corrected signal, and establishing, by a processor, a probability of forming an edge at a point along the corrected signal in accordance with a difference between the value of the corrected signal at the point and the calibrated threshold value. The kernel is calibrated using the same measurements made on the patterns' edges.

A method of forming a pattern of a semiconductor device includes: preparing a semiconductor substrate including a cell region and an outer region; applying a photoresist on the semiconductor substrate; irradiating extreme ultraviolet (EUV) light reflected from an EUV mask, onto the photoresist; forming a photoresist pattern in the cell region and the outer region; and etching the semiconductor substrate, using the photoresist pattern as an etch mask. The EUV mask includes: a plurality of main patterns in a first zone, of the EUV mask, corresponding to the cell region; and a first lane and a second lane in a second zone, of the EUV mask, corresponding to the outer region, wherein the first lane and the second lane surround the plurality of main patterns, wherein the first lane has a line-and-space pattern, and the second lane has a protruding pattern.

Feature images representing a layout geometry of a lithographic mask are received. Mask function (MF) contributions from individual feature images are calculated by convolving the feature image with a corresponding three-dimensional mask (M3D) filter. The M3D filters represent an electromagnetic scattering effect of that feature image. At least one M3D filter also accounts for effects arising from a fabrication process for the lithographic mask.

An optical proximity correction method includes: obtaining a test mask; obtaining wafer data under current photolithography conditions by the test mask; establishing an optical proximity correction model and a process variation band model by the wafer data; correcting a target pattern according to the optical proximity correction model and the process variation band model to obtain a first correction pattern and a second correction pattern respectively; calculating a difference value between a first simulation contour of the first correction pattern and a second simulation contour of the second correction pattern; and adjusting a correction mode for the target pattern according to the difference value.

In some aspects, an integrated model accounts for effects from both the mask fabrication process and the wafer lithography process. The aerial image incident on the wafer, the pattern printed on the wafer, and/or measures of the foregoing are estimated using an integrated three-dimensional mask (M3D) model, as follows. The shapes in the mask fabrication description are partitioned into feature images. Each feature image is convolved with a corresponding M3D filter. The M3D filter represents an electromagnetic scattering effect of that feature image in the wafer lithography process, and the feature image and/or M3D filter account for effects on the layout geometry from the mask fabrication process. This is done without estimating the mask pattern printed on the lithographic mask. The mask fabrication description is modified based on differences between the estimated lithography results and corresponding target results.

A mask layout is received. An interaction-free mask model is applied to the mask layout. An edge interaction model is applied to the mask layout. The edge interaction model describes an influence due to a plurality of combinations of two or more edges interacting with one another. A thin mask model is applied to the mask layout. A near field is determined based on the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model.

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 including: obtaining data based an optical proximity correction for a spatially shifted version of a training design pattern; and training a machine learning model configured to predict optical proximity corrections for design patterns using data regarding the training design pattern and the data based on the optical proximity correction for the spatially shifted version of the training design pattern.