# US 12,768,647 B2 · Flatness error resistant photomask measurement techniques

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- Number: US 12,768,647 B2
- Document ID: US12768647B2
- Status: Granted
- Kind: B2
- Application number: 18/945,782
- Filed: 2024-11-13
- Published: 2025-05-22
- Granted: 2026-10-20
- Earliest claimed: 2023-11-17
- Assignees: Corning Incorporated
- Applicants: Corning Incorporated
- Inventors: Thomas James Dunn; Steven James Van Kerkhove
- Web page: https://patentgrep.com/patent/US12768647B2

## CPC

- G01B 11/303: {using photoelectric detection means}
- G03F 7/70508: {Data handling in all parts of the microlithographic apparatus, e.g. handling pattern data for addressable masks or data transfer to or from different components within the exposure apparatus}
- G03F 7/70775: {Position control, e.g. interferometers or encoders for determining the stage position}
- G01B 5/0016: {due to weight (on machine tools B23Q11/001)}
- G05B 2219/37402: Flatness, roughness of surface
- H10P 74/203: {Structural properties, e.g. testing or measuring thicknesses, line widths, warpage, bond strengths or physical defects}
- G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G03F: PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR; (phototypographic composing devices B41B; photosensitive materials or processes for photographic purposes G03C; electrophotography, sensitive layers or processes therefor G03G)
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)
- H10P: GENERIC PROCESSES OR APPARATUS FOR THE MANUFACTURE OR TREATMENT OF DEVICES COVERED BY CLASS H10

## Abstract

A method of determining a flatness of a substrate, the method including measuring a first flatness measurement of the substrate at a first orientation relative to a vertical direction, measuring a second flatness measurement of the substrate at a second orientation relative to the vertical direction, measuring a third flatness measurement of the substrate at a third orientation relative to a vertical direction, and measuring a fourth flatness measurement of the substrate at a fourth orientation relative to a vertical direction, each of the first orientation, the second orientation, the third orientation, and the fourth orientation being at a different orientation relative to the vertical direction. The method further including generating a first set of differences, fitting the first set of differences to respective orthogonal polynomials, and generating a true flatness of the substrate.

## Claims

### Claim 1

A method of determining a flatness of a substrate, the method comprising:
measuring a first flatness measurement of the substrate at a first orientation relative to a vertical direction;
measuring a second flatness measurement of the substrate at a second orientation relative to the vertical direction;
measuring a third flatness measurement of the substrate at a third orientation relative to the vertical direction;
measuring a fourth flatness measurement of the substrate at a fourth orientation relative to the vertical direction, each of the first orientation, the second orientation, the third orientation, and the fourth orientation being at a different orientation relative to the vertical direction;
generating a first set of differences between one of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement and another of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement;
fitting the first set of differences to respective orthogonal polynomials and generating a fifth flatness measurement;
selecting a flatness measurement from the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement;
replacing orthogonal polynomial components associated with the selected flatness measurement with orthogonal polynomial components associated with the fifth flatness measurement; and
generating a true flatness of the substrate.

### Claim 2 (depends on 1)

The method of claim 1, wherein the orthogonal polynomials comprise Zernike polynomials.

### Claim 3 (depends on 2)

The method of claim 2, wherein the step of fitting the first set of differences to respective orthogonal polynomials comprises fitting the first set of differences to respective even Zernike polynomials.

### Claim 4 (depends on 1)

The method of claim 1, wherein the second orientation is 90 degrees relative to the first orientation, the third orientation is 90 degrees relative to the second orientation, and the fourth orientation is 90 degrees relative to the third orientation.

### Claim 5 (depends on 1)

The method of claim 1, wherein generating the first set of differences comprises subtracting one of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement with another of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement such that the subtracted flatness measurements are oriented 90 degrees relative to each other.

### Claim 6 (depends on 5)

The method of claim 5, further comprising generating a second set of differences between one of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement and another of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement.

### Claim 7 (depends on 6)

The method of claim 6, wherein generating the second set of differences comprises subtracting one of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement with another of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement such that the subtracted flatness measurements are oriented 180degrees relative to each other.

### Claim 8 (depends on 6)

The method of claim 6, wherein the orthogonal polynomials comprise Zernike polynomials, and the method further comprising fitting the second set of differences to respective odd Zernike polynomials to generate the fifth flatness measurement.

### Claim 9 (depends on 1)

The method of claim 1, further comprising:
replacing the orthogonal polynomial components associated with the selected flatness measurement with the fifth flatness measurement to generate a sixth flatness measurement; and
subtracting the selected flatness measurement with the sixth flatness measurement to generate a seventh flatness measurement.

### Claim 10 (depends on 9)

The method of claim 9, wherein the orthogonal polynomials comprise Zernike polynomials, and the method further comprising:
extracting a Zernike astigmatism factor associated with gravitational force from the seventh flatness measurement;
generating a Zernike power factor associated with gravitational force by multiplying the Zernike astigmatism factor by a scale factor; and
subtracting the Zernike power factor from the sixth flatness measurement to generate the true flatness of the substrate.

### Claim 11 (depends on 1)

The method of claim 1, further comprising:
selecting a second flatness measurement from the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement; and
replacing orthogonal polynomial components associated with the selected second flatness measurement with orthogonal polynomial components associated with the fifth flatness measurement.

### Claim 12 (depends on 1)

The method of claim 1, wherein generating the first set of differences comprises subtracting the first flatness measurement from the second flatness measurement, subtracting the second flatness measurement from the third flatness measurement, subtracting the third flatness measurement from the fourth flatness measurement, and subtracting the fourth flatness measurement from the first flatness measurement.

### Claim 13 (depends on 1)

The method of claim 1, wherein generating the first set of differences comprises subtracting the first flatness measurement from the second flatness measurement, subtracting the second flatness measurement from the third flatness measurement, subtracting the third flatness measurement from the fourth flatness measurement, and subtracting the fourth flatness measurement from the first flatness measurement, and
the method further comprising generating a second set of differences by subtracting the first flatness measurement from the third flatness measurement and subtracting the second flatness measurement from the fourth flatness measurement.

### Claim 14 (depends on 1)

The method of claim 1, further comprising rotating the substrate to each of the first orientation, the second orientation, the third orientation, and the fourth orientation by removing the substrate from a support and reattaching the substrate to the support.

### Claim 15

An apparatus, comprising:
a support configured to maintain a substrate at one or more orientations using one or more support members;
an interferometer configured to:
measure a first flatness measurement of the substrate at a first orientation relative to a vertical direction;
measure a second flatness measurement of the substrate at a second orientation relative to the vertical direction;
measure a third flatness measurement of the substrate at a third orientation relative to the vertical direction; and
measure a fourth flatness measurement of the substrate at a fourth orientation relative to the vertical direction, each of the first orientation, the second orientation, the third orientation, and the fourth orientation being at a different orientation relative to the vertical direction; and
a controller configured to:
generate a first set of differences between one of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement and another of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement;
fit the first set of differences to respective orthogonal polynomials and generate a fifth flatness measurement;
select a flatness measurement from the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement;
replace orthogonal polynomial components associated with the selected flatness measurement with orthogonal polynomial components associated with the fifth flatness measurement; and
generate a true flatness of the substrate.

### Claim 16 (depends on 15)

The apparatus of claim 15, wherein the substrate is a photomask.

### Claim 17 (depends on 15)

The apparatus of claim 15, wherein the one or more support members comprise a support member positioned along a top surface of the substrate and a support member positioned along a bottom surface of the substrate.

### Claim 18 (depends on 15)

The apparatus of claim 15, wherein the one or more support members are each a cantilever member extending from a base.

### Claim 19 (depends on 15)

The apparatus of claim 15, further comprising a reference surface and one or more optical elements.

### Claim 20 (depends on 19)

The apparatus of claim 19, wherein the reference surface is a Fizeau surface.