A method and apparatus for optical metrology is disclosed. There is disclosed, for example, a method involving a radiation intensity distribution for a target measured using an optical component at a gap from the target, the method including calculating a correction factor for the variation of radiation intensity of the radiation intensity distribution as a function of variation of the distance of the gap.

A lithographic apparatus includes an alignment sensor including a self-referencing interferometer for reading the position of an alignment target comprising a periodic structure. An illumination optical system for focusing radiation into a spot on said structure. An asymmetry detection optical system receives a share of positive and negative orders of radiation diffracted by the periodic structure, and forms first and second images of said spot on first and second detectors respectively, wherein said negative order radiation is used to form the first image and said positive order radiation is used to form the second image. A processor for processing together signals from said first and second detectors representing intensities of said positive and negative orders to produce a measurement of asymmetry in the periodic structure. The asymmetry measurement can be used to improve accuracy of the position read by the alignment sensor.

A method of position control of an optical component relative to a surface is disclosed. The method may include: obtaining a first signal by a first position measurement process; controlling relative movement between the optical component and the surface for a first range of motion using the first signal; obtaining a second signal by a second position measurement process different than the first position measurement process; and controlling relative movement between the optical component and the surface for a second range of motion using the second signal, the second range of motion being nearer the surface than the first range of motion.

A method of calculating electromagnetic scattering properties of a structure, the structure including materials of differing properties and the structure being periodic in at least one lateral direction and extending in a vertical direction, comprises: numerically solving a volume integral equation for electromagnetic scattering for a plurality of modes in the at least one lateral direction, by performing, for each respective mode, integration (1350) of a pseudo-spectral polynomial (Chebyshev) expansion in the vertical direction multiplied by a ID Green's function using the same sample points in the orthogonal direction for all of the plurality of modes. The integration is performed by solving a regularized linear system of equations between first (1116) and second (1120) discrete transformation steps to compute (1118) values of a regularized Chebyshev expansion coefficient vector (γ). Electromagnetic scattering properties of the structure are calculated using the results of the numerical solution.

In a dark-field metrology method using a small target, a characteristic of an image of the target, obtained using a single diffraction order, is determined by fitting a combination fit function to the measured image. The combination fit function includes terms selected to represent aspects of the physical sensor and the target. Some coefficients of the combination fit function are determined based on parameters of the measurement process and/or target. In an embodiment the combination fit function includes jinc functions representing the point spread function of a pupil stop in the imaging system.

There is disclosed a method of measuring a process parameter for a manufacturing process involving lithography. In a disclosed arrangement the method comprises performing first and second measurements of overlay error in a region on a substrate, and obtaining a measure of the process parameter based on the first and second measurements of overlay error. The first measurement of overlay error is designed to be more sensitive to a perturbation in the process parameter than the second measurement of overlay error by a known amount.

A method of controlling a manufacturing process, the method including the steps of a) providing a testing area with a periodic structure, where the periodic structure includes a series of sets of patterned features, b) illuminating the periodic structure with a light, thereby producing a non-zero order diffraction signal, c) collecting the diffraction signal to produce a test signature, d) matching the test signature with a reference signature, where the reference signature was previously produced by performing steps a), b), and c) with respect to a reference structure that is at least similar to the periodic structure, and e) controlling a manufacturing process using a control setting set associated with the matching reference signature.

The present invention provides a determination method of determining a first prediction formula for predicting a fluctuation in optical characteristics of a projection optical system while a substrate is exposed on a first exposure condition, the method comprising obtaining a correlation coefficient between the first exposure condition and a second exposure condition corresponding to a second prediction formula for predicting the fluctuation in the optical characteristics, determining, when the correlation coefficient falls within an allowable range, the first prediction formula based on the second prediction formula without actually measuring the fluctuation in the optical characteristics, and determining, when the correlation coefficient falls outside the allowable range, the first prediction formula based on a result of actually measuring the fluctuation in the optical characteristics.

Disclosed is a method of monitoring a lithographic process parameter, such as focus and/or dose, of a lithographic process. The method comprises acquiring a first and a second target measurement using respectively a first measurement configuration and a second measurement configuration, and determining the lithographic process parameter from a first metric derived from said first target measurement and said second target measurement. The first metric may be difference. Also disclosed are corresponding measurement and lithographic apparatuses, a computer program and a method of manufacturing devices.

A sensor for use in lithographic apparatus of an immersion type and which, in use, comes into contact with the immersion liquid is arranged so that the thermal resistance of a first heat path from a transducer of the sensor to a temperature conditioning device is less than the thermal resistance of a second heat flow path from the transducer to the immersion liquid. Thus, heat flow is preferentially towards the temperature conditioning device and not the immersion liquid so that temperature-induced disturbance in the immersion liquid is reduced or minimized.