CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase entry of PCT patent application No. PCT/EP2019/058231, which was filed Apr. 2, 2019, which is based upon and claims the benefit of priority of European patent application No. 18172621.7 which was filed on May 16, 2018 and which is incorporated herein in its entirety by reference.

FIELD

The present invention relates to methods for estimating parameters on a surface for lithographic processes.

BACKGROUND

A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern (also often referred to as “design layout” or “design”) at a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer).

To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which can be formed on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm and 13.5 nm. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within the range 4-20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

Low-k1lithography may be used to process features with dimensions smaller than the classical resolution limit of a lithographic apparatus. In such process, the resolution formula may be expressed as CD=k1×λ/NA, where λ is the wavelength of radiation employed, NA is the numerical aperture of the projection optics in the lithographic apparatus, CD is the “critical dimension” (generally the smallest feature size printed, but in this case half-pitch) and k1is an empirical resolution factor. In general, the smaller k1the more difficult it becomes to reproduce the pattern on the substrate that resembles the shape and dimensions planned by a circuit designer in order to achieve particular electrical functionality and performance. To overcome these difficulties, sophisticated fine-tuning steps may be applied to the lithographic projection apparatus and/or design layout. These include, for example, but not limited to, optimization of NA, customized illumination schemes, use of phase shifting patterning devices, various optimization of the design layout such as optical proximity correction (OPC, sometimes also referred to as “optical and process correction”) in the design layout, or other methods generally defined as “resolution enhancement techniques” (RET). Alternatively, tight control loops for controlling a stability of the lithographic apparatus may be used to improve reproduction of the pattern at low k1.

Another fine-tuning step which may be taken is to take into account the topology of the surface of the substrate to be lithographically patterned. This can be done by obtaining values of a parameter of the substrate, for example through measurements, and using these values to determine a fit of the parameter across whole or part of the substrate. The parameter fit can then be used, for example, to optimize lithographic process settings by taking the parameter topology across the substrate into account.

SUMMARY

According to the invention in an aspect, there is provided a method for estimating a parameter across a region on a substrate, the region being divided into a plurality of sub-regions, the method comprising: obtaining values of the parameter for at least two sub-regions out of said plurality of sub-regions; and estimating the parameter for a position on the region by evaluation of a function having said values of the parameter as input values, wherein the function: a) comprises piecewise defined base functions, wherein a single base function is defined across a sub-region; and b) is continuous between one or more adjacent sub-regions of the at least two sub-regions comprised within the region.

In exemplary arrangements, the parameter may comprise focus, overlay and/or dose.

Optionally, the plurality of sub-regions of the region form a rectangular grid. A rectangular grid allows the sub-regions to match directions of features which may have been patterned on the substrate. For parameters like focus and overlay, deviations and parameter features are often expressed in an x or y direction and are therefore captured better or more easily with a rectangular grid. In an alternative configuration the sub-regions can be radial sections or slices, to more accurately capture parameter features with radial dependency and features, for example dose.

Optionally, one or more of the plurality of sub-regions is substantially coincident with one or more dies or fields on the substrate.

Optionally, at least one value of the parameter is obtained per sub-region.

Optionally, at least for one sub-region no value of the parameter is obtained.

Optionally, at least for one sub-region the function is not evaluated.

Optionally, the function comprises symmetrical base functions.

Optionally, the function forms part of a spline function.

Optionally, the function is composed out of one or more non-uniform rational basis splines (NURBS). NURBS capture roll-off at an edge of a substrate while also capturing high-quality parameter estimations, achieve continuity, have adjustable sub-region size and may be described in radial and rectangular sub-regions.

Optionally, the method further comprises determining a number of measurements of the parameter associated with the region, and determining an order of the function based on the number of measurements.

Optionally, estimating the parameter across region comprises: determining a plurality of provisional estimations of the parameter based on different orders of the function; and selecting one of the provisional estimations to be the estimation of the parameter based on a performance indicator of the provisional estimations.

Optionally, the performance indicator is based on minimum and/or maximum values of the provisional estimations.

Optionally, selecting one of the provisional estimations comprises rejecting any provisional estimation having a magnitude of the minimum and/or maximum values that exceeds a magnitude of minimum and/or maximum values of the one or more measurements, and accepting any remaining provisional estimations.

Optionally, selecting one of the provisional estimations further comprises selecting one of the accepted provisional estimations based on a difference between the one or more measurements of the parameter and a value of the accepted provisional estimations at a position of the one or more measurements.

Optionally, the method further comprises selecting the provisional estimation for which the magnitude of the difference is smallest.

Optionally, the provisional estimations comprise polynomials of different orders.

Optionally, determining the plurality of provisional estimations comprises: determining a first plurality of polynomials of different orders in a first direction; determining a second plurality of polynomials of different orders in a second direction transverse to the first direction; and combining different ones of the first and second polynomials to form the plurality of provisional estimations.

According to an aspect of the invention, there is provided a computer program comprising instructions which, when executed on at least one processor, cause the at least one processor to control an apparatus to carry out a method according to any disclosed herein.

According to an aspect of the invention, there is provided an apparatus for estimating a parameter across a region on a substrate, the region being divided into a plurality of sub-regions, the apparatus comprising a processor configured to execute computer program code to undertake the method of: obtaining values of the parameter for at least two sub-regions out of said plurality of sub-regions; and estimating the parameter for a position on the region by evaluation of a function having said values of the parameter as input values, characterized in that the function is continuous between one or more adjacent sub-regions of the at least two sub-regions comprised within the region for any number of input values and any required accuracy of the estimate.

According to an aspect of the invention, there is provided a metrology system for estimating a parameter across a region on a substrate and comprising the apparatus above and/or described herein.

According to an aspect of the invention, there is provided a lithographic system comprising the metrology system above and/or described herein.

According to an aspect of the invention, there is provided a lithographic cell system comprising the lithographic system above and/or described herein.

