Method and apparatus for calculating electromagnetic scattering properties of finite periodic structures

Patent metadata

Field	Value
Publication number	US-10948409-B2
Application number	US-201715644072-A
Country	US
Kind code	B2
Filing date	Jul 7, 2017
Priority date	Jul 7, 2016
Publication date	Mar 16, 2021
Grant date	Mar 16, 2021

Abstract

A method of determining electromagnetic scattering properties of a finite periodic structure has the steps: 1002 : Calculating a single-cell contrast current density, within a unit-cell supporting domain of a single one of a finite collection of unit cells. 1004 : Calculating a scattered electric field outside the finite collection of unit cells, by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density. 1006 : The Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells. The Green's function integrated with the determined single-cell contrast current density is obtained for observation points above the supporting domain with respect to a substrate underlying the finite periodic structure. 1008 : Determining an electromagnetic scattering property, for example a diffraction pattern, of the finite periodic structure using the calculated scattered electric field.

First claim

The invention claimed is:

1. A method, for implementation in a lithography or metrology process, of determining electromagnetic scattering properties of a finite periodic structure on a target portion of a semiconductor substrate, the finite periodic structure comprising a finite collection of unit cells periodically distributed across the finite periodic structure and defining its supporting domain, wherein each unit cell comprises at least one contrasting object defining a unit-cell supporting domain, the method comprising:
determining a single-cell contrast current density within a unit-cell supporting domain of a single unit cell of the finite collection of unit cells of the finite periodic structure on the target portion of the semiconductor substrate;
determining a scattered electric field outside the finite collection of unit cells, arising from the finite periodic structure by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density, wherein the Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells;
determining an electromagnetic scattering property of the finite periodic structure using the scattered electric field;
storing the determined electromagnetic scattering property for subsequent adjustment of a parameter of the lithography or metrology process for the semiconductor substrate or another semiconductor substrate; and
transmitting the determined electromagnetic scattering property to a lithographic apparatus or a metrology tool in order to adjust the parameter and improve accuracy of the lithographic apparatus or the metrology tool.

2. The method of claim 1 , wherein the determining a single-cell contrast current density is performed by solving an integral equation, over the single unit cell's supporting domain, for the unknown single-cell contrast current density with a kernel being a Green's function obtained for observation points inside a supporting domain of a periodic structure comprising a plurality of the unit cells.

3. The method of claim 2 , wherein the plurality of the unit cells is the finite collection of unit cells and the kernel Green's function is obtained by summation across the finite collection of unit cells.

4. The method of claim 2 , wherein the plurality of the unit cells is an infinite collection of the unit cells and the kernel Green's function is obtained by summation across the infinite collection of unit cells.

5. The method of claim 1 , wherein in the determining a scattered electric field, the Green's function that is integrated with the determined single-cell contrast current density is obtained for observation points above the supporting domain with respect to a semiconductor substrate underlying the finite periodic structure.

6. The method of claim 1 , wherein the electromagnetic scattering property comprises a diffraction pattern.

7. A method, for implementation in a lithography or metrology process, of reconstructing an approximate structure of a finite periodic structure on a target portion of a semiconductor substrate from a detected electromagnetic scattering property arising from illumination of the finite periodic structure by radiation, the method comprising:
estimating at least one structural parameter of the finite periodic structure on the target portion of the semiconductor substrate;
determining at least one model electromagnetic scattering property from the at least one structural parameter, the determining comprising:
determining a single-cell contrast current density within a unit-cell supporting domain of a single unit cell of the finite collection of unit cells;
determining a scattered electric field outside the finite collection of unit cells, arising from the finite periodic structure by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density, wherein the Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells; and
determining an electromagnetic scattering property of the finite periodic structure using the scattered electric field;

comparing the detected electromagnetic scattering property to the at least one model electromagnetic scattering property;
determining an approximate structure of the finite periodic structure based on the result of the comparison;
storing the determined electromagnetic scattering property for subsequent adjustment of parameter of the lithography or metrology process for the semiconductor substrate or another semiconductor substrate; and
transmitting the determined electromagnetic scattering property to a lithographic apparatus or a metrology tool in order to adjust the parameter and improve accuracy of the lithographic apparatus or the metrology tool.

8. The method according to claim 7 , further comprising:
arranging a plurality of the model electromagnetic scattering properties in a library; and
the comparing comprises matching the detected electromagnetic scattering property to contents of the library.

9. An inspection apparatus of a lithographic apparatus or a metrology tool, the inspection apparatus comprising:
an illumination system configured to illuminate a finite periodic structure on a target portion of a semiconductor substrate with radiation;
a detection system configured to detect an electromagnetic scattering property arising from the illumination of the finite periodic structure on the target portion of the semiconductor substrate; and
a processor configured to:
estimate at least one structural parameter based on the detection;
determine at least one model electromagnetic scattering property from the at least one structural parameter, the determining comprising:
determining a single-cell contrast current density within a unit-cell supporting domain of a single unit cell of a finite collection of unit cells;
determining a scattered electric field outside the finite collection of unit cells, arising from the finite periodic structure by integrating, over the single unit cell's supporting domain, a Green's function with the determined single-cell contrast current density, wherein the Green's function is obtained for observation points outside the finite collection of unit cells by summation across the finite collection of unit cells; and
determining an electromagnetic scattering property of the finite periodic structure using the scattered electric field;

compare the detected electromagnetic scattering property to the at least one model electromagnetic scattering property;
determine an approximate structure of the finite periodic structure based on the result of the comparison;
store the determined electromagnetic scattering property for subsequent adjustment of a parameter of a lithography or metrology process for the semiconductor substrate or another semiconductor substrate; and
transmit the determined electromagnetic scattering property to the lithographic apparatus or the metrology tool in order to adjust the parameter and improve accuracy of the lithographic apparatus or the metrology tool.

10. A computer program product containing one or more sequences of machine-readable instructions for determining electromagnetic scattering properties of a finite periodic structure on a target portion of a semiconductor substrate, the instructions being adapted to cause one or more processors in a lithographic apparatus or a metrology tool to perform operations comprising:
determining a single-cell contrast current density within a unit-cell sup

Assignees

• Asml Netherlands Bv

Inventors

• Setija Irwan Dani
• Van Den Berg Petrus Maria

Classifications

• G03F7/705 Primary

  Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions · CPC title

• G03F7/70625

  Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness · CPC title

• G01N2201/12

  Circuits of general importance; Signal processing · CPC title

• G01N21/4788 Primary

  Diffraction (for sizing particles G01N15/0205) · CPC title