A lithographic apparatus includes an illumination system to produce a beam of radiation, a support to support a patterning device to impart a pattern on the beam, a projection system to project the patterned beam onto a substrate, and a metrology system that includes a radiation source to generate radiation, an optical element to direct the radiation toward a target, a detector to receive a first and second radiation scattered by the target and produce a first and second measurement respectively based on the received first and second radiation, and a controller. The controller determines a correction for the first measurement, an error between the correction for the first measurement and the first measurement, and a correction for the second measurement based on the correction for the first measurement, the second measurement, and the error. The lithographic apparatus uses the correction to adjust a position of a substrate.

A method for generating a sampling scheme for a device manufacturing process, the method including: obtaining a measurement data time series of a plurality of processed substrates; transforming the measurement data time series to obtain frequency domain data; determining, using the frequency domain data, a temporal sampling scheme; determining an error offset introduced by the temporal sampling scheme on the basis of measurements on substrates performed according to the temporal sampling scheme; and determining an improved temporal sampling scheme to compensate the error offset.

Methods and apparatus for determining an intensity profile of a radiation beam. The method comprises providing a diffraction structure, causing a relative movement of the diffraction structure relative to the radiation beam from a first position, wherein the radiation beam does not irradiate the diffraction structure to a second position, wherein the radiation beam irradiates the diffraction structure, measuring, with a radiation detector, diffracted radiation signals produced from a diffraction of the radiation beam by the diffraction structure as the diffraction structure transitions from the first position to the second position or vice versa, and determining an intensity profile of the radiation beam based on the measured diffracted radiation signals.

A double-sided digital lithography or exposure system and method are provided. The system includes a first optical engine 110 for exposing a front side of a substrate 910, a second optical engine 120 for exposing the back side of the substrate 910, a control system 710 for generating a first exposure pattern and a second exposure pattern aligned on the front and back surfaces of the substrate 910 based on the position information of the first optical engine 110 and the second optical engine 120, and controlling the first optical engine 110 and the second optical engine 120 to expose the front and back surfaces of the substrate 910 with the first exposure pattern and the second exposure pattern.

One or more images of a device feature are acquired using an imaging tool. A geometrical shape is defined encompassing the relevant pixels of each image, where the geometrical shape is represented in terms of one or more parameters. A cost function is defined whose variables comprise the one or more parameters of the geometrical shape. For each image, numerical optimization is applied to obtain optimal values of the one or more parameters for which the cost function is minimized. The optimal values of the one or more parameters are reported as metrology data pertaining to the device feature.

A lithographic apparatus includes an illumination system to produce a beam of radiation, a support to support a patterning device to impart a pattern on the beam, a projection system to project the patterned beam onto a substrate, and a metrology system that includes a radiation source to generate radiation, an optical element to direct the radiation toward a target, a detector to receive a first and second radiation scattered by the target and produce a first and second measurement respectively based on the received first and second radiation, and a controller. The controller determines a correction for the first measurement, an error between the correction for the first measurement and the first measurement, and a correction for the second measurement based on the correction for the first measurement, the second measurement, and the error. The lithographic apparatus uses the correction to adjust a position of a substrate.

A method is performed for scheduling a calibration relating to an optical device in a light source. The method can be performed by a calibration system including a calibration apparatus and a prediction controller. The method includes: receiving a property associated with the optical device while the optical device is being calibrated; calculating a current degradation metric based at least on the optical device property, the degradation metric modeling behavior of the optical device; estimating when a degradation of the optical device would exceed a threshold based on the current degradation metric; and scheduling a calibration of the optical device based at least in part on the estimate of optical device degradation.

Method and apparatus for adapting a distribution model of a machine learning fabric. The distribution model is for mitigating the effect of concept drift, and is configured to provide an output as input to a functional model of the machine learning fabric. The functional model is for performing a machine learning task. The method may include obtaining a first data point, and providing the first data point as input to one or more distribution monitoring components of the distribution model. The one or more distribution monitoring components have been trained on a plurality of further data points. A metric representing a correspondence between the first data point and the plurality of further data points is determined, by at least one of the one or more distribution monitoring components. Based on the error metric, the output of the distribution model is adapted.

A method for accelerating calibration of a fabrication process model, the method including performing one or more iterations of: defining one or more fabrication process model terms; receiving predetermined information related to the one or more fabrication process model terms; generating a fabrication process model based on the predetermined information, the fabrication process model configured to generate one or more predictions related to a metrology gauge; determining whether a prediction related to a dimension of a gauge is within a predetermined threshold of the gauge as measured on a post-fabrication process substrate; and responsive to the prediction not breaching the predetermined threshold, optimizing the one or more fabrication process terms such that the prediction related to the dimension of the gauge is within the predetermined threshold of the gauge as measured on the post-fabrication process substrate.

A method of determining a parameter of a lithographic apparatus, wherein the method includes providing first height variation data of a first substrate, providing first performance data of a first substrate, and determining a model based on the first height variation data and the first performance data. The method further includes obtaining second height variation data of a second substrate, inputting the second height variation data to the model, and determining second performance data of the second substrate by running the model. Based on the second performance data, the method determines a parameter of the apparatus.