# US 12,766,667 B2 · Polishing state analysis prediction program, storage device, cathodeluminescence device, and polishing state analysis prediction method

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 12,766,667 B2
- Document ID: US12766667B2
- Status: Granted
- Kind: B2
- Application number: 18/044,862
- Filed: 2021-09-15
- Published: 2024-07-04
- Granted: 2026-10-20
- Earliest claimed: 2020-09-15
- Assignees: National University Corporation Nagaoka University of Technology; Sanoh Industrial Co., Ltd.
- Applicants: National University Corporation Nagaoka University of Technology; Sanoh Industrial Co., Ltd.
- Inventors: Hideo Aida; Natsuko Omiya
- Web page: https://patentgrep.com/patent/US12766667B2

## CPC

- B24B 49/04: involving measurement of the workpiece at the place of grinding during grinding operation
- B24B 37/005: Control means for lapping machines or devices
- B24B 49/12: involving optical means
- G01N 23/2254: Measuring cathodoluminescence
- G01N 2223/611: patterned objects; electronic devices
- G01N 2223/6116: semiconductor wafer
- B24B: MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING (grinding of gear teeth B23F, of screw-threads B23G1/36; by electro-erosion B23H; abrasive or related blasting B24C; tools for grinding, buffing or sharpening B24D; polishing compositions C09G1/00; abrasives C09K3/14; electrolytic etching or polishing C25F3/00; grinding arrangements for use on assembled railway tracks E01B31/17); DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

Provided are a polishing state analysis prediction program, a storage, a cathodeluminescence device, and a polishing state analysis prediction method. The polishing state analysis prediction program to predict a future polishing state of a polishing-target substrate to be polished based on a cathodeluminescence image of the polishing-target substrate, the image being obtained by a cathodeluminescence method, the program, when executed by a computer, causing the computer to perform: calculating average light emission intensity data or average luminance data from the cathodeluminescence image of each predetermined time after start of polishing the substrate; and plotting the average light emission intensity data or the average luminance data, and deriving a formula representing a fitting curve resulted from the plotting by using a predetermined function.

## Claims

### Claim 1

A non-transitory computer-readable storage medium storing therein programming instructions for a polishing state analysis prediction program to predict a future polishing state of a polishing-target substrate to be polished, the instructions, when executed by a computer, causing the computer to perform the steps of:
detecting cathodeluminescence light emitted from the substrate;
obtaining, based on the cathodeluminescence light emitted from the substrate, a cathodeluminescence image of each predetermined time after a start of polishing;
calculating average light emission intensity data or average luminance data from each cathodeluminescence image;
plotting the average light emission intensity data or the average luminance data, and deriving a formula representing a fitting curve resulted from the plotting by using a predetermined function; and
calculating a polishing rate based on the formula of the fitting curve.

### Claim 2 (depends on 1)

The non-transitory computer-readable storage medium according to claim 1, wherein the predetermined function is a logistic function.

### Claim 3 (depends on 1)

The non-transitory computer-readable storage medium according to claim 1, wherein the predetermined function is represented by formula (1) or formula (2) below:
I
⁡
(
t
)
=
H
1
+
e
-
2
⁢
a
⁡
(
t
-
T
)
(
1
)
L
⁡
(
t
)
=
G
1
+
e
-
2
⁢
a
⁡
(
t
-
T
)
(
2
)
wherein the formulas (1) and (2), I(t) is light emission intensity of CL light at a time t in the polishing, H is an upper limit value of the formula (1), L(t) is luminance at a time t in the polishing, G is an upper limit value of the formula (2), and T and a are constants obtained when deriving each formula of the fitting curve.

### Claim 4

A non-transitory computer-readable storage medium storing therein programming instructions for a polishing state analysis prediction program to predict final polishing time of a polishing-target substrate to be polished, the instructions, when executed by a computer, causing the computer to perform the steps of:
detecting cathodeluminescence light emitted from the substrate;
obtaining, based on the cathodeluminescence light emitted from the substrate, a cathodeluminescence image of each predetermined time after a start of polishing;
calculating a black line density from each cathodeluminescence image;
plotting each calculated black line density and extracting a plot of a polishing time range in which the black line density decreases from 106 cm−2 to 104 cm−2;
fitting a plot of a polishing time range in which the black line density decreases from 106 cm−2 to 104 cm−2 by using a linear function; and
calculating, as the final polishing time, a time which is taken for the black line density in the formula to reach a threshold of less than 104 cm−2.

### Claim 5

A cathodeluminescence device configured to predict a future polishing state of a polishing-target substrate to be polished, the device comprising:
an electron beam irradiation device configured to emit an electron beam onto the substrate;
a cathodeluminescence photodetector configured to detect cathodeluminescence light emitted from the substrate; and
a calculation device comprising a central processing unit and a computer-readable storage medium storing programming instructions that, when executed by the central processing unit, cause the central processing unit to:
obtain, based on the cathodeluminescence light emitted from the substrate and detected by the cathodeluminescence photodetector, a cathodeluminescence of each predetermined time after a start of polishing;
calculate an average light emission intensity data or average luminance data of each cathodeluminescence image; and
plot the average light emission intensity data or the average luminance data, and derive a formula of a fitting curve resulted from the plotting by using a predetermined function; and
calculate a polishing rate based on the formula of the fitting curve.

### Claim 6

A cathodeluminescence device configured to predict a final polishing time of a polishing-target substrate to be polished, the device comprising:
an electron beam irradiation device configured to emit an electron beam onto the substrate;
a cathodeluminescence photodetector configured to detect cathodeluminescence light emitted from the substrate; and
a calculation device comprising a central processing unit and a computer-readable storage medium storing programming instructions that, when executed by the central processing unit, cause the central processing unit to:
obtain, based on the cathodeluminescence light emitted from the substrate and detected by the cathodeluminescence photodetector, a cathodeluminescence image of each predetermined time after a start of polishing;
calculate a black line density from each cathodeluminescence image obtained;
plot each black line density calculated and extract a plot of a polishing time range in which a black line density decreases from 106 cm−2 to 104 cm−2;
perform a linear function fitting in the plot, and derive a formula representing a fitting linear line; and
calculate, as final polishing time, a time which is taken for a black line density in the formula to reach a threshold of less than 104 cm−2.

### Claim 7

A computer-implemented polishing state analysis prediction method to predict a future polishing state of a polishing-target substrate to be polished, the polishing state analysis prediction method comprising:
emitting an electron beam onto the substrate;
detecting cathodeluminescence light emitted from the substrate;
obtaining, based on the cathodeluminescence light emitted from the substrate, a cathodeluminescence image of each predetermined time after a start of polishing;
calculating average light emission intensity data or average luminance data of each cathodeluminescence image;
plotting the average light emission intensity data or the average luminance data, and deriving a formula representing a fitting curve resulted from the plotting by using a predetermined function; and
calculating a polishing rate based on the formula of the fitting curve.

### Claim 8

A computer-implemented polishing state analysis predicting method to predict final polishing time of a polishing-target substrate to be polished, the polishing state analysis prediction method comprising:
emitting an electron beam onto the substrate;
detecting cathodeluminescence light emitted from the substrate;
obtaining, based on the cathodeluminescence light emitted from the substrate, a cathodeluminescence image of each predetermined time after a start of polishing;
calculating a black line density from each cathodeluminescence image;
plotting each calculated black line density to derive a formula representing a fitting linear line;
fitting a plot of a polishing time range in which a black line density decreases from 106 cm−2 to 104 cm−2 by using a linear function; and
calculating, as final polishing time, a time which is taken for the black line density in the formula to reach a threshold of less than 104 cm−2.

### Claim 9 (depends on 5)

The cathodeluminescence device according to claim 5, wherein the predetermined function is a logistic function.

### Claim 10 (depends on 5)

The cathodeluminescence device according to claim 5, wherein the predetermined function is represented by formula (1) or formula (2) below:
I
⁡
(
t
)
=
H
1
+
e
-
2
⁢
a
⁡
(
t
-
T
)
(
1
)
L
⁡
(
t
)
=
G
1
+
e
-
2
⁢
a
⁡
(
t
-
T
)
(
2
)
where in the formulas (1) and (2), I(t) is light emission intensity of CL light at a time t in the polishing, H is an upper limit value of the formula (1), L(t) is luminance at a time t in the polishing, G is an upper limit value of the formula (2), and T and a are constants obtained when deriving each formula of the fitting curve.