Metrology system and method for determining a characteristic of one or more structures on a substrate

1. A metrology system for determining a characteristic of interest relating to at least one structure on a substrate, the metrology system comprising:

an illumination branch configured to direct illumination radiation at the substrate;

a detection branch configured to detect scattered radiation from the at least one structure on the substrate; and

a processor configured to:

computationally determine phase and amplitude information from an electric field of the scattered radiation;

model the effect of interaction between the illumination radiation and the at least one structure on the scattered radiation to obtain a modelled characteristic of the scattered radiation;

adjust phase and amplitude of the electric field so as to minimize the difference between the modelled characteristic of the scattered radiation and the detected characteristic of the scattered radiation; and

use prior knowledge of the at least one structure to optimize the phase and amplitude of the electric field,

wherein the processor is configured to use at least a part of the prior knowledge of the at least one structure as a regularization to or a constraint on the optimization of the phase and amplitude of the electric field.

2. The metrology system of claim 1 , wherein the scattered radiation is reflected, diffracted or refracted by the at least one structure as a result of illumination of the at least one structure with illumination radiation in a measurement acquisition.

3. The metrology system of claim 1 , wherein the processor is further configured to use the determined phase and amplitude to determine a characteristic of interest.

4. The metrology system of claim 1 , further comprising one or more optical elements in the detection branch between the at least one structure and a detection plane where the scattered radiation is detected, and the processor is configured to additionally model the effect of the one or more optical elements on the scattered radiation to obtain the modelled characteristic of the scattered radiation.

5. The metrology system of claim 1 , wherein the regularization and/or constraint comprises a total variation based regularization or constraint, and wherein the regularization and/or constraint comprises a vector total variation based regularization and/or constraint.

6. The metrology system of claim 1 , wherein the regularization or constraint imposes a coupling between different sets of values of the phase and amplitude information for the at least one structure, each set of values relating to a different illumination condition, and wherein the processor is operable to computationally determine the different sets of values of the phase and amplitude information simultaneously thereby suppressing coherent imaging artifacts.

7. The metrology system of claim 1 , wherein the processor is further configured to:

define a loss function that describes the difference between the modelled characteristic of the scattered radiation and the detected characteristic of the scattered radiation; and

minimize the loss function using at least a part of the prior knowledge of the at least one structure as a regularization or constraint on the minimization.

8. The metrology system of claim 1 , wherein the processor is configured to define a loss function that comprises a sum of a data fidelity function and a prior knowledge regularization function, the data fidelity function describing the difference between the modelled characteristic of the scattered radiation and the detected characteristic of the scattered radiation that is to be minimized and the prior knowledge regularization function being operable to perform the regularization or constrain the minimization, and wherein the processor is configured to define the minimization as a gradient method based minimization of the loss function or a Newton's method based minimization of the loss function.

9. The metrology system of claim 8 , wherein the processor is further configured to:

model variation in refractive index of the at least one structure against one or more of wavelength, polarization, or propagation direction to determine a dispersion model of structure; and

use the prior knowledge regularization function on input coefficients of the dispersion model.

10. The metrology system of claim 1 , wherein the processor is further configured to use complex numbers in the defining and performance of the optimization of the phase and amplitude of the electric field.

11. The metrology system of claim 1 , wherein the processor is further configured to computationally reimage the measurement acquisition of the at least one structure subsequent to a measurement.

12. The metrology system of claim 1 , further comprising one or more sensors for detecting characteristics of the scattered radiation subsequent to it having been reflected or scattered by the at least one structure, and wherein at least one of the one or more sensors is arranged in or near at least one of: an image plane of an optical system, a plane that is conjugate with the image plane of the optical system, a pupil plane of an optical system, and a plane that is conjugate with the pupil plane of the optical system, the far field of the at least one structure.

13. The metrology system of claim 12 , wherein the metrology apparatus is further configured to prevent a transmission of a zeroth diffraction order of the scattered radiation towards the one or more sensors.

14. A method of determining a characteristic of interest relating to at least one structure on a substrate, the method comprising:

computationally determining phase and amplitude information from an electric field of the scattered radiation;

model the effect of interaction between the illumination radiation and the at least one structure on the scattered radiation to obtain a modelled characteristic of the scattered radiation;

adjust phase and amplitude of the electric field so as to minimize the difference between the modelled characteristic of the scattered radiation and the detected characteristic of the scattered radiation; and

use prior knowledge of the at least one structure to optimize the phase and amplitude of the electric field, and use at least a part of the prior knowledge of the at least one structure as a regularization to or a constraint on the optimization of the phase and amplitude of the electric field.

15. The method of claim 14 , wherein the scattered radiation is reflected or scattered by the at least one structure as a result of illumination of the at least one structure with illumination radiation in a measurement acquisition.

16. The method of claim 14 , further comprising using the determined phase and amplitude to determine a characteristic of interest.

17. A non-transitory computer program product comprising machine-readable instructions for causing a processor to cause performance of the method of claim 16 .