US-12619158-B2 - Metrology target simulation

US12619158B2US 12619158 B2US12619158 B2US 12619158B2US-12619158-B2

Abstract

A method of simulating an electromagnetic response of a metrology target comprising first and second gratings, wherein the second grating is below the first grating, the method comprising: receiving a model defining (i) the first grating as having a first number of grating lines within a pitch, each of the first number of grating lines separated by a first pitch; and (ii) the second grating as having a second number of grating lines within the pitch, each of the second number of grating lines separated by a second pitch; using the model and the first pitch to simulate properties of the first grating and generate a first scattering matrix; using the model and the second pitch to simulate properties of the second grating and generate a second scattering matrix; generating a scattering matrix defining properties of the metrology target by combining the first scattering matrix and the second scattering matrix.

Inventors

Markus Gerardus Martinus Maria Van Kraaij

Assignees

ASML NETHERLANDS B.V.

Dates

Publication Date: 20260505
Application Date: 20211208
Priority Date: 20201218

Claims (15)

1 . A computer implemented method of simulating an electromagnetic response of a metrology target having a multi-layer structure comprising a first grating and a second grating, wherein the second grating is below the first grating in the multi-layer structure, the method comprising: receiving a model representing the multi-layer structure, the model defining (i) the first grating as having a first predetermined number of grating lines within a pitch of the multi-layer structure, each of the first predetermined number of grating lines separated by a first pitch; and (ii) the second grating as having a second predetermined number of grating lines within the pitch of the multi-layer structure, each of the second predetermined number of grating lines separated by a second pitch; using the model and the first pitch to simulate the transmission and reflection properties of the first grating and generate a first scattering matrix associated with the first grating; using the model and the second pitch to simulate the transmission and reflection properties of the second grating and generate a second scattering matrix associated with the second grating; and generating a scattering matrix defining the scattering and reflection properties of the multi-layer structure by combining the first scattering matrix and the second scattering matrix.
2 . The computer implemented method of claim 1 , comprising: using the model and the first pitch to simulate the transmission and reflection properties of the first grating to generate a first block-diagonal matrix associated with the first grating; and reordering the first block-diagonal matrix to generate the first scattering matrix associated with the first grating.
3 . The computer implemented method of claim 2 , wherein the first block-diagonal matrix comprises scattering matrices each defining the transmission and reflection properties of the first grating in response to simulating light is incident on an upper surface of the first grating at a respective angle of incidence and is incident on a lower surface of the first grating at a respective angle.
4 . The computer implemented method of claim 2 , wherein the first block-diagonal matrix comprises the first predetermined number of scattering matrices.
5 . The computer implemented method of claim 1 , comprising: using the model and the second pitch to simulate the transmission and reflection properties of the second grating to generate a second block-diagonal matrix associated with the second grating; and reordering the second block-diagonal matrix to generate the second scattering matrix associated with the second grating.
6 . The computer implemented method of claim 5 , wherein the second block-diagonal matrix comprises scattering matrices each defining the transmission and reflection properties of the second grating in response to simulating light is incident on an upper surface of the second grating at a respective angle of incidence.
7 . The computer implemented method of claim 5 , wherein second block-diagonal matrix comprises the second predetermined number of scattering matrices.
8 . The computer implemented method of claim 1 , wherein the first scattering matrix comprises: (i) a first scattering matrix component defining the transmission properties of the first grating in response to simulating light is incident on an upper surface of the first grating, (ii) a second scattering matrix component defining the reflection properties of the first grating in response to simulating light is incident on an upper surface of the first grating, (iii) a third scattering matrix component defining the reflection properties of the first grating in response to simulating light is incident on a lower surface of the first grating, and (iv) a fourth scattering matrix component defining the transmission properties of the first grating in response to simulating light is incident on a lower surface of the first grating; wherein the second scattering matrix comprises: (v) a fifth scattering matrix component defining the transmission properties of the second grating in response to simulating light is incident on an upper surface of the second grating, and (vi) a sixth scattering matrix component defining the reflection properties of the first grating in response to simulating light is incident on an upper surface of the second grating.
9 . The computer implemented method of claim 8 , wherein combining the first scattering matrix and the second scattering matrix comprises performing a matrix inversion of a matrix obtained by subtracting the product of the third scattering matrix component and the sixth scattering matrix component from an identity matrix.
10 . The computer implemented method of claim 8 , wherein combining the first scattering matrix and the second scattering matrix comprises approximating a matrix inversion of a matrix obtained by subtracting the product of the third scattering matrix component and the sixth scattering matrix component from an identity matrix.
11 . The computer implemented method of claim 10 , wherein approximating the matrix inversion comprises using a geometric series.
12 . The computer implemented method of claim 10 , wherein approximating the matrix inversion comprises using an iterative solver.
13 . The computer implemented method of claim 1 , wherein the scattering matrix defining the scattering and reflection properties of the multi-layer structure is generated by the Redheffer product of the first scattering matrix and the second scattering matrix.
14 . The computer implemented method of claim 1 , further comprising determining one or more parameters associated with the electromagnetic response of the metrology target using the scattering matrix defining the transmission and reflection properties of the multi-layer structure.
15 . The computer implemented method of claim 1 , wherein the first predetermined number of grating lines is greater than the second predetermined number of grating lines such that the first pitch is less than the second pitch.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority of EP application 20215517.2 which was filed on Dec. 18, 2020 and which is incorporated herein in its entirety by reference. TECHNICAL FIELD The present invention relates to metrology target simulation. In particular, the present invention relates to a computer implemented method of simulating an electromagnetic response of a metrology target having a multi-layer structure. 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-k1 lithography 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, 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 k1 is an empirical resolution factor. In general, the smaller k1 the 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. Semiconductor-based devices may be produced by fabricating a series of layers on a substrate (e.g., a wafer), some or all of the layers including various structures. The relative position of these structures within a single layer and with respect to structures in other layers plays a key role in the performance of the devices. Overlay error relates to the misalignment between various structures. Overlay accuracy generally pertains to the determination of how accurately a first patterned layer aligns with respect to a second patterned layer disposed above or below it and to the determination of how accurately a first pattern aligns with respect to a second pattern disposed on the same layer. Overlay measurements are performed via metrology targets that are printed together with layers of the wafer. Images of the metrology targets are captured via an imaging tool and are analyzed to determine both X-overlay and Y-overlay measurements. Known techniques exist to simulate an electromagnetic response of a metrology target in software before fabricating them onto a substrate. This simulation enables a designer to determine one or more parameters associated with the electromagnetic response of the metrology target and make changes to the design of the metrology target to optimize the one or more parameters. SUMMARY Known techniques for simulating an electromagnetic response of a metrology target are typically applied to metrology targets comprising a multi-layer structure comprising an upper grating and a lower grating, wherein the grating lines of the upper grating and the lower grating have the same pitch. This involves rigorously simulating the electromagnetic response of the metrology target using Maxwell solvers, e.g. using Rigorous Coupled-Wave Analysis (RCWA), for various parameters of light incident on the metrology target and for different critical dimensions (CD) and pitches of the metrology target. The inventor has identified that when the grating lines of the upper grating and the lower grating are not equal, i.e. have different pitches,