Abstract: Methods and apparatuses for determining in-plane distortion (IPD) across a substrate having a plurality of patterned regions. A method includes obtaining intra-region data indicative of a local stress distribution across one of the plurality of patterned regions; determining, based on the intra-region data, inter-region data indicative of a global stress distribution across the substrate; and determining, based on the inter-region data, the IPD across the substrate.

Abstract: A method and control system for determining stress in a substrate. The method includes determining a measured position difference between a measured position of at least one first feature and a measured position of at least one second feature which have been applied on a substrate, and determining local stress in the substrate from the measured position difference.

Abstract: Methods and associated apparatus for reconstructing a free-form geometry of a substrate, the method including: positioning the substrate on a substrate holder configured to retain the substrate under a retaining force that deforms the substrate from its free-form geometry; measuring a height map of the deformed substrate; and reconstructing the free-form geometry of the deformed substrate based on an expected deformation of the substrate by the retaining force and the measured height map.

Abstract: Methods and apparatuses for determining in-plane distortion (IPD) across a substrate having a plurality of patterned regions. A method includes obtaining intra-region data indicative of a local stress distribution across one of the plurality of patterned regions; determining, based on the intra-region data, inter-region data indicative of a global stress distribution across the substrate; and determining, based on the inter-region data, the IPD across the substrate.

Abstract: Methods and associated apparatus for reconstructing a free-form geometry of a substrate, the method including: positioning the substrate on a substrate holder configured to retain the substrate under a retaining force that deforms the substrate from its free-form geometry; measuring a height map of the deformed substrate; and reconstructing the free-form geometry of the deformed substrate based on an expected deformation of the substrate by the retaining force and the measured height map.

Abstract: A method and control system for determining stress in a substrate. The method includes determining a measured position difference between a measured position of at least one first feature and a measured position of at least one second feature which have been applied on a substrate, and determining local stress in the substrate from the measured position difference.

Abstract: A lithographic process includes clamping a substrate onto a substrate support, measuring positions across the clamped substrate, and applying a pattern to the clamped substrate using the positions measured. A correction is applied to the positioning of the applied pattern in localized regions of the substrate, based on recognition of a warp-induced characteristic in the positions measured across the substrate. The correction may be generated by inferring one or more shape characteristics of the warped substrate using the measured positions and other information. Based on the one or more inferred shape characteristics, a clamping model is applied to simulate deformation of the warped substrate in response to clamping. A correction is calculated based on the simulated deformation.

Abstract: A lithographic process includes clamping a substrate onto a substrate support, measuring positions across the clamped substrate, and applying a pattern to the clamped substrate using the positions measured. A correction is applied to the positioning of the applied pattern in localized regions of the substrate, based on recognition of a warp-induced characteristic in the positions measured across the substrate. The correction may be generated by inferring one or more shape characteristics of the warped substrate using the measured positions and other information. Based on the one or more inferred shape characteristics, a clamping model is applied to simulate deformation of the warped substrate in response to clamping. A correction is calculated based on the simulated deformation.

Abstract: A method for determining a mechanical property of a layer applied to a substrate and associated control system for controlling a lithographic process. The method includes obtaining measured out-of-plane deformation of the substrate, the out-of-plane deformation including deformation normal to a substrate plane defined by, or parallel to, a substrate surface. The measured out-of-plane deformation is fitted to a second order polynomial in two coordinates associated with the substrate plane and the mechanical property (e.g. anisotropic Young's moduli) of the layer is determined based on characteristics of the fitted second order polynomial. The mechanical property of the layer can be used to calibrate an in-plane distortion model of the substrate for predicting in-plane distortion based on the measured out-of-plane deformation.

Abstract: The invention is directed to a process for the anaerobic purification of waste water using a sludge bed system, which process comprises feeding waste water, and optionally recycle water, to the lower part of an upflow reactor, containing mainly granular biomass thus producing biogas in the treatment passing the resulting gas/liquid/solid mixture upward and separating the gas and solid from the liquid in a three phase separator and thereby generating an anaerobic effluent that is withdrawn from the top of the separator, the improvement comprising separating the solids from the liquid in a separator, wherein, above the separation of the gas from the liquid phase, tilted plates, tubes or other tilted internals are installed in the three phase separator body to increase the effective settling surface, to an upflow reactor suitable for this process as well as to a three phase separator.

Abstract: The invention is directed to a process for the anaerobic purification of waste water using a sludge bed system, which process comprises feeding waste water, and optionally recycle water, to the lower part of an upflow reactor, containing mainly granular biomass thus producing biogas in the treatment passing the resulting gas/liquid/solid mixture upward and separating the gas and solid from the liquid in a three phase separator and thereby generating an anaerobic effluent that is withdrawn from the top of the separator, the improvement comprising separating the solids from the liquid in a separator, wherein, above the separation of the gas from the liquid phase, tilted plates, tubes or other tilted internals are installed in the three phase separator body to increase the effective settling surface, to an upflow reactor suitable for this process as well as to a three phase separator.

Abstract: An apparatus for determining the paramagnetic characteristics of substances such as oxygen includes a cuvette rotating in a magnetic field. The cuvette includes measuring chambers and reference chambers and an alternating voltage is induced in the measuring field coils by the rotation of the cuvette along the magnetic field. A base signal disturbing the measuring signal is also generated. This base signal is caused primarily by changes in the thickness of the material in the reference chambers and the measuring chambers and/or by material thickness changes of the cuvette. To eliminate this base signal, the cuvette includes a magnetic compensating device. This device is mounted at such a position that it generates a compensating magnetic field during its rotation through the magnetic field. This compensating field generates a compensating voltage which has the same amplitude as the base signal but has a signal waveform which is opposite in phase to the base signal.

Abstract: The invention is directed to a method of operating a laser diode in a measuring system for spectroscopically measuring the concentration of a gaseous component in a gas sample. This method is improved in that the mode jumps of the laser diode are easily recognized when adjusting the temperature-current operating point of the laser diode. An optical filter is placed in the beam path for adjusting the temperature-current operating point of the laser diode and, by changing the temperature T and the operating current I of the laser diode while simultaneously receiving the output signal supplied by an evaluation unit, the spectral positions of the mode jumps of the laser diode are determined which are included in the absorption lines of the gas sample. Thereafter, the temperature-current operating point is adjusted so that the distance of this operating point to the positions of the mode jumps is not less than a fixed spacing.

Abstract: The invention is directed to an apparatus for determining the proportion of substances having paramagnetic characteristics, such as oxygen, in a mixture of substances. The apparatus has a housing and the mixture of substances is passed along an arrangement of four magnetic field sources by a rotatable cuvette arrangement mounted in the housing. The apparatus is improved in that the effect of external disturbing influences on the penetration of the cuvette by the magnetic field is reduced and so that the measuring characteristics are independent of the position of the plurality of magnetic field generating units. For this purpose, the arrangement of the magnetic field sources is simply disposed at one side of the housing lying opposite to the rotating surface of the cuvette arrangement facing toward the drive shaft. The arrangement of magnetic field sources includes a carrier plate on which the magnetic field sources are accommodated and carry respective measuring field coils.

Abstract: The invention is directed to a sensor for making capacitive measurements of the pressure in gases and contains two measuring electrodes conjointly defining a capacitor and arranged in spaced relationship to each other. This sensor is improved such that a pressure measurement is possible without deformable parts. Long-term drift free measurements can be carried out with even the smallest electrode spacing being realized so that miniature sensors can be provided. The intermediate space between the electrodes is accessible to the gas to be investigated and has electrically insulating spacers between the electrodes. The spacers determine the spacing between the electrodes and maintains the electrode spacing during the measurement.