A positioning system to position a structure comprises an actuator and a control unit to control the actuator in response to a position setpoint received by the control unit. The actuator comprises a magnet assembly comprises a magnet configured to provide a magnetic flux, and a coil assembly, wherein the coil assembly and the magnet assembly are movable relative to each other, the coil assembly comprising a coil, an actuation of the coil by a drive current providing for a force between the magnet assembly and the coil assembly. The magnet assembly comprises a further electric conductor, the further electric conductor comprising a non-ferromagnetic electrically conductive material, wherein the further electric conductor is magnetically coupled to the coil of the coil assembly and forms a short circuit path for an inductive electrical current induced in the further electric conductor as a result of an actuator current in the coil.

The disclosure provides a method and to an apparatus for determining the heating state of a mirror in an optical system, in particular in a microlithographic projection exposure apparatus. A method for determining the heating state of an optical element includes: measuring values of a first temperature that the optical element has at a first position using a temperature sensor; and estimating a second temperature that the optical element has at a second position, which is located at a distance from the first position, on the basis of the measured values, wherein estimating the second temperature is accomplished while taking into account a temporal change in the previously measured values.

A method of determining a parameter of a pattern transfer process and device manufacturing methods are disclosed. In one arrangement, a method includes obtaining a detected representation of radiation redirected by a structure. The structure is a structure formed by applying a pattern processing to a pattern transferred to an earlier formed structure by a pattern transfer process. The pattern processing is such as to remove one or more selected regions in a horizontal plane of the earlier formed structure to form a pattern in the horizontal plane. The pattern is defined by a unit cell that is mirror symmetric with respect to an axis of mirror symmetry. An asymmetry in the detected representation is determined. The determined asymmetry in the detected representation is used to determine a parameter of the pattern transfer process.

An imprinting system according to an embodiment includes a first measuring device measuring an intensity of light reflected from an end of a shot area of a monitor substrate being an area on which imprinting has been performed, a dripping condition generating device generating a dripping condition of a resin-based mask material on the basis of the measured intensity of light, and an imprinting apparatus performing imprinting using the dripping condition. The imprinting apparatus includes a second measuring device measuring an intensity of light reflected from an end of a first shot area of a production substrate being an area on which imprinting has been performed, and a control unit adjusting arrangement of droplets of a resin-based mask material ejected on a second shot area of the production substrate being an area on which imprinting is to be performed on the basis of an intensity of light reflected from an end of the first shot area.

An exposure device has a cylindrical peripheral wall member. The peripheral wall member forms a processing space in which a substrate is storable and has an upper opening and a lower opening. Further, a light emitter is provided in an upper portion of the peripheral wall member to close the upper opening. A lower lid member that is provided to be movable in an up-and-down direction and configured to be capable of closing and opening the lower opening is provided below the peripheral wall member. The atmosphere in the processing space is replaced with an inert gas with the substrate stored in the processing space and the lower opening closed by the lower lid member. In this state, vacuum ultraviolet rays are emitted to the substrate from the light emitter, and the substrate is exposed.

An information processing apparatus for acquiring an inspection condition for performing an inspection on a pattern formed by a lithography apparatus that forms a pattern on a substrate with an original includes an acquisition unit configured to acquire a second inspection condition to be applied in a case where an inspection is performed on a second pattern by inputting third information indicating a state of the lithography apparatus acquired when the second pattern is formed to a model, wherein the model is acquired by machine learning with learning data including first information indicating a state of the lithography apparatus acquired when a first pattern is formed and second information indicating a first inspection condition applied when an inspection is performed on the first pattern.

A method of controlling a computer process for designing or verifying a photolithographic component includes building a source tree including nodes of the process, including dependency relationships among the nodes, defining, for some nodes, at least two different process conditions, expanding the source tree to form an expanded tree, including generating a separate node for each different defined process condition, and duplicating dependent nodes having an input relationship to each generated separate node, determining respective computing hardware requirements for processing the node, selecting computer hardware constraints based on capabilities of the host computing system, determining, based on the requirements and constraints and on dependency relations in the expanded tree, an execution sequence for the computer process, and performing the computer process on the computing system.

A body of a superstrate can be used to form an adaptive planarization layer over a substrate that has a non-uniform topography. A body of a superstrate can have bending characteristics that are well suited to achieve both conformal and planarization behavior. The body can have a surface and a thickness in a range of t.sub.1 to t.sub.2, t.sub.1=(Pd.sup.4/2Eh).sup.1/3; t.sub.2=(5Pd.sup.4/2Eh).sup.1/3; P is a pressure corresponding to a capillary force between the body and a planarization precursor material; d is a bending distance; E is Young's modulus for the body; and h is a step height difference between two adjacent regions of a substrate. In an embodiment, a thickness can be selected and used to determine the maximum out-of-plane displacement, w.sub.max, for conformal behavior is sufficient and that w.sub.max for planarization behavior is below a predetermined threshold.

A simulation apparatus has: a first processing part configured to obtain a value of a parameter in a first set relating to the forming of the pattern; a second processing part configured to obtain a value of a parameter in a second set that is at least partially same as the parameter in the first set and relating to the forming of the pattern; and an integration processing part configured to evaluate, based on the value of the parameter in the first set and the value of the parameter in the second set, a state of the pattern formed on the substrate and a forming condition when the pattern is formed, and to determine based on the result of the evaluation whether or not to make at least one of the first processing part and the second processing part recalculate the value of the parameter in the corresponding set.

The present invention provides a pattern forming apparatus including a detection optical system configured to obtain optical information of a mark provided on a substrate by detecting the mark, and a processing unit configured to perform a process of obtaining a position of the mark by using a template for obtaining the position of the mark by being applied to the optical information of the mark and a window which indicates a region for extracting an amount of characteristic indicating the position of the mark from a waveform signal obtained from the optical information, wherein the processing unit decides, based on the optical information of the mark obtained by the detection optical system, a parameter indicating at least one of a shape of the template and a shape of the window for each of a plurality of substrates.