# US 10,503,850 B2 · Generation of a map of a substrate using iterative calculations of non-measured attribute data

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- Number: US 10,503,850 B2
- Document ID: US10503850B2
- Status: Granted
- Kind: B2
- Application number: 15/484,436
- Filed: 2017-04-11
- Published: 2018-05-24
- Granted: 2019-12-10
- Earliest claimed: 2016-11-22
- Assignees: Tokyo Electron Limited
- Applicants: Tokyo Electron Limited
- Inventors: Daniel Morvay; Taejoon Han
- Web page: https://patentgrep.com/patent/US10503850B2

## CPC

- G06F 30/367: Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
- G03F 7/70: {Microphotolithographic exposure; Apparatus therefor (photo-masks G03F1/00)}
- G03F 7/70866: {of mask or workpiece}
- G03F 7/70875: {Temperature, e.g. temperature control of masks or workpieces via control of stage temperature}
- G06F 2111/10: Numerical modelling
- H10P 72/0602: {Temperature monitoring}
- H10P 72/0604: {Process monitoring, e.g. flow or thickness monitoring}
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- 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)
- H10P: GENERIC PROCESSES OR APPARATUS FOR THE MANUFACTURE OR TREATMENT OF DEVICES COVERED BY CLASS H10

## Abstract

Described herein are technologies to facilitate the generation and presentation of a map of an attribute of a substrate, such as a semiconductor wafer. Using the data of measured attribute (e.g., thickness, temperature, etc.) of a substrate, one or more of the described implementations generate data of non-measured (i.e., calculated) attributes to complete a map of the substrate using model parameters and a correlations model, such as a squared exponential Gaussian process model.

## Claims

### Claim 1

A method that facilitates generation of map of an attribute of a substrate, the method comprising:
obtaining measured attribute data of a substrate, the measured attribute data representing measured attributes of the substrate, and including measurements of locations outside a periphery of the substrate;
determining model parameters of a correlation model;
processing the measured attribute data to generate the correlation model;
iteratively calculating non-measured attribute data of the substrate, wherein the non-measured attribute data of the substrate represents attributes of the substrate that are calculated based on the correlation model and the model parameters, and includes calculations of locations outside the periphery of the substrate;
presenting a map of the substrate for viewing by a user, the map including the measured and non-measured attribute data.

### Claim 2 (depends on 1)

The method as recited in claim 1 further comprising determining calculation errors with each iteration of the iterative calculations, wherein the iterative calculations are performed until the calculation errors fall within a specified error range.

### Claim 3 (depends on 1)

The method as recited in claim 1 further comprising determining calculation errors with each iteration of the iterative calculations, wherein calculation errors are determined based on a comparison of subsequent iterative calculations.

### Claim 4 (depends on 1)

The method as recited in claim 1 further comprising determining calculation errors with each iteration of the iterative calculations, wherein the iterative calculations are performed until the calculation errors meet a specified error criterion.

### Claim 5 (depends on 1)

The method as recited in claim 1, wherein the correlation model is a squared exponential Gaussian process model.

### Claim 6 (depends on 1)

The method as recited in claim 1, wherein the presenting includes storing a map of the substrate in a memory of a computer system.

### Claim 7 (depends on 1)

The method as recited in claim 1, wherein the presenting includes storing a topographical map of the substrate in a memory of a computer system.

### Claim 8 (depends on 1)

The method as recited in claim 1, wherein the presenting includes displaying a map of the substrate on a visual display system.

### Claim 9 (depends on 1)

The method as recited in claim 1, wherein attributes represented by the measured and non-measured attribute data are selected from a group consisting of thickness of the substrate or a portion thereof, roughness of the substrate or a portion thereof, resistivity of the substrate or a portion thereof, temperature of the substrate or a portion thereof, and cross-section of the substrate or a portion thereof.

### Claim 10

One or more computer-readable media storing instructions thereon that, when executed by one or more processors, direct the one or more processors to perform operations that facilitate generation of map of an attribute of a substrate, the operations comprising:
obtaining measured attribute data of a substrate, the measured attribute data representing measured attributes of the substrate, and including measurements of locations outside a periphery of the substrate;
determining model parameters of a correlation model;
processing the measured attribute data to generate the correlation model;
iteratively calculating non-measured attribute data of the substrate, wherein the non-measured attribute data of the substrate represents attributes of the substrate that are calculated based on the correlation model and the model parameters, and includes calculations of locations outside the periphery of the substrate;
presenting a map of the substrate for viewing by a user, the map including the measured and non-measured attribute data.

### Claim 11 (depends on 10)

The one or more computer-readable media as recited in claim 10, wherein the operations further comprise determining calculation errors with each iteration of the iterative calculations, wherein the iterative calculations are performed until the calculation errors fall within specified error range.

### Claim 12 (depends on 10)

The one or more computer-readable media as recited in claim 10, wherein the operations further comprise determining calculation errors with each iteration of the iterative calculations, wherein calculation errors are determined based on a comparison of subsequent iterative calculations.

### Claim 13 (depends on 10)

The one or more computer-readable media as recited in claim 10, wherein the operations further comprise determining calculation errors with each iteration of the iterative calculations, wherein the iterative calculations are performed until the calculation errors meet a specified error criterion.

### Claim 14

A method that facilitates generation of map of an attribute of a substrate, the method comprising:
obtaining measured attribute data of a substrate, the measured attribute data representing measured attributes of the substrate, and including measurements of locations outside a periphery of the substrate;
determining model parameters of a correlation model, the correlation model being a squared exponential Gaussian process model;
processing the measured attribute data to generate the correlation model;
iteratively calculating non-measured attribute data of the substrate, wherein the non-measured attribute data of the substrate represents attributes of the substrate that are calculated based on the squared exponential Gaussian process model and the model parameters, and includes calculations of locations outside the periphery of the substrate;
determining calculation errors with each iteration of the iterative calculations, wherein the iterative calculations are performed until the calculation errors fall within specified error range;
presenting a map of the substrate for viewing by a user, the map including the measured and non-measured attribute data.

### Claim 15 (depends on 14)

The method as recited in claim 14, wherein calculation errors are determined based on a comparison of subsequent iterative calculations.

### Claim 16 (depends on 14)

The method as recited in claim 14, wherein the presenting includes storing a map of the substrate in a memory of a computer system.

### Claim 17 (depends on 14)

The method as recited in claim 14, wherein attributes represented by the measured and non-measured attribute data is selected from a group consisting of thickness of the substrate or a portion thereof, roughness of the substrate or a portion thereof, resistivity of the substrate or a portion thereof, temperature of the substrate or a portion thereof, and cross-section of the substrate or a portion thereof.