Methods include inputting an array of pixels, where each pixel in the array of pixels has a pixel dose. The array of pixels represents dosage on a surface to be exposed with a plurality of patterns, each pattern of the plurality of patterns having an edge. A target bias is input. An edge of a pattern in the plurality of patterns is identified. For each pixel which is in a neighborhood of the identified edge, a calculated pixel dose is calculated such that the identified edge is relocated by the target bias. The array of pixels with the calculated pixel doses is output. Systems for performing the methods are also disclosed.

Methods include inputting an array of pixels, where each pixel in the array of pixels has a pixel dose. The array of pixels represents dosage on a surface to be exposed with a plurality of patterns, each pattern of the plurality of patterns having an edge. A target bias is input. An edge of a pattern in the plurality of patterns is identified. For each pixel which is in a neighborhood of the identified edge, a calculated pixel dose is calculated such that the identified edge is relocated by the target bias. The array of pixels with the calculated pixel doses is output. Systems for performing the methods are also disclosed.

An exposure apparatus includes a projection optical system configured to project a pattern of a mask onto a substrate, a substrate stage configured to hold and move the substrate, and a controller configured to control exposure of the substrate held by the substrate stage, wherein the controller obtains an amount of deviation of an image of the pattern projected onto the substrate with respect to the pattern of the mask based on telecentricity information, which is information on telecentricity for respective image heights of the projection optical system, and height information, which is information on the height of a surface of the substrate, and corrects deviation of the image based on the obtained amount of deviation to expose the substrate.

A method of manufacturing a semiconductor structure includes providing a substrate and a photoresist over the substrate; placing a mask over the photoresist; exposing the photoresist to a predetermined electromagnetic radiation through the mask; and removing at least a portion of the photoresist exposed to the predetermined electromagnetic radiation. The mask includes a first portion configured to totally allow the predetermined electromagnetic radiation passing through, a second portion configured to partially allow the predetermined electromagnetic radiation passing through, and a third portion configured to block the predetermined electromagnetic radiation, the second portion is disposed between the first portion and the third portion.

A method includes measuring a topography of a semiconductor wafer. A distortion function is generated based on the measured topography. Measured alignment data associated with the semiconductor wafer is adjusted using the distortion function. At least one correction factor for an exposure tool is generated based on the adjusted alignment data. The exposure tool is configured based on the at least one correction factor.

Methods include inputting an array of pixels, where each pixel in the array of pixels has a pixel dose. The array of pixels represents dosage on a surface to be exposed with a plurality of patterns, each pattern of the plurality of patterns having an edge. A target bias is input. An edge of a pattern in the plurality of patterns is identified. For each pixel which is in a neighborhood of the identified edge, a calculated pixel dose is calculated such that the identified edge is relocated by the target bias. The array of pixels with the calculated pixel doses is output. Systems for performing the methods are also disclosed.

Methods include inputting an array of pixels, where each pixel in the array of pixels has a pixel dose. The array of pixels represents dosage on a surface to be exposed with a plurality of patterns, each pattern of the plurality of patterns having an edge. A target bias is input. An edge of a pattern in the plurality of patterns is identified. For each pixel which is in a neighborhood of the identified edge, a calculated pixel dose is calculated such that the identified edge is relocated by the target bias. The array of pixels with the calculated pixel doses is output. Systems for performing the methods are also disclosed.

A method for forming a mask pattern is provided, comprising forming a negative photoresist on a substrate; in an environment without oxygen, to performing a first exposure on the negative photoresist by use of a first ordinary mask plate, so that a fully-cured portion of the negative photoresist is exposed to light and a semi-cured portion and a removed portion of the negative photoresist are not exposed to light; in an environment with oxygen, performing a second exposure on the negative photoresist by use of a second ordinary mask plate, so that the semi-cured portion of the negative photoresist is exposed to light and the removed portion of the negative photoresist not exposed to light; removing the uncured negative photoresist and forming the mask pattern.

A photolithography model used in an optical proximity correction process modifies an image output intensity of a point disposed along a two dimensional plane and having coordinates (x,y) in accordance with a gradient of a convolution of a mask value at the point and a sampling pattern function selected at the point. The sampling pattern function includes, in part, a first subset of sampling patterns and a second subset of sampling patterns. The first subset of sampling patterns includes first and second nodes. The second subset of sampling patterns include first and second antinodes. The gradient of the convolution of the mask value and the first and second nodes of the first subset are scaled by a first coefficient. The gradient of the convolution of the mask value and the first and second antinodes of the second subset are scaled by a second coefficient.

A method of correcting an optical image formed by an optical system, the method including obtaining a map indicative of a polarization dependent property of the optical system across a pupil plane of the optical system for each spatial position in an image plane of the optical system, combining the map indicative of the polarization dependent property of the optical system with a radiation map of the intensity and polarization of an input radiation beam to form an image map, and using the image map to correct an optical image formed by directing the input radiation beam through the optical system.