# US 9,435,735 B1 · Optical parametric model optimization

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- Number: US 9,435,735 B1
- Document ID: US9435735B1
- Status: Granted
- Kind: B1
- Application number: 13/889,655
- Filed: 2013-05-08
- Granted: 2016-09-06
- Earliest claimed: 2012-05-08
- Assignees: KLA-Tencor Corporation
- Applicants: Thaddeus Gerard Dziura
- Inventors: Thaddeus Gerard Dziura
- Web page: https://patentgrep.com/patent/US9435735B1

## CPC

- G01N 21/4788: {Diffraction (for sizing particles G01N15/0205)}
- G03F 7/705: {Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions}
- G03F 7/70625: {Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness}
- G01B 2210/56: Measuring geometric parameters of semiconductor structures, e.g. profile, critical dimensions or trench depth
- G01N 21/47: Scattering, i.e. diffuse reflection (G01N21/25, G01N21/41 take precedence {G01N21/55 takes precedence})
- G01N 2021/213: {Spectrometric ellipsometry}
- 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)
- 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)
- G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS

## Abstract

Provided are scatterometry model optimizations for evaluating a diffracting structure. In one embodiment, a method includes identifying one or more parameters to test for inclusion in the model. The method includes computing a difference between modeled data generated with the one or more parameters and measured data. The one or more parameters are included in the model in response to a reduction in the difference between the modeled data and the measured data compared to previous modeled, and passing a statistical hypothesis test. In one embodiment, the one or more parameters pass the statistical hypothesis test in response to the probability of obtaining the reduction in the difference is less than a significance level. In one embodiment, the significance level is a function of an alpha wealth value. In one embodiment, the method includes ordering the plurality of parameters for testing according to one or more criteria.

## Claims

### Claim 1

A computer implemented method for evaluation of a diffracting structure, the method comprising:
performing measurements of the diffracting structure with a detector of an optical metrology system, including measuring optical reflectance of the diffracting structure;
identifying one or more parameters to test for inclusion in the model of the diffracting structure;
computing whether modeled optical reflectance data generated with the one or more parameters results in an improved fit to the measured optical reflectance data collected from the diffracting structure over previous modeled data generated without the one or more parameters;
computing a probability that the improved fit is due to chance;
determining the one or more parameters pass a statistical hypothesis test in response to the probability being less than a significance level dependent on whether one or more previously tested parameters passed the statistical hypothesis test;
storing to an electronic memory the one or more parameters as part of the model in response to the improved fit and passage of the statistical hypothesis test by the one or more parameters; and
determining a value of one or more parameters of the diffracting structure using the stored model.

### Claim 2 (depends on 1)

The method of claim 1, wherein determining a value of one or more parameters of the diffracting structure using the stored model includes:
performing a computation of at least one physical characteristic of the diffracting structure based on the measured optical reflectance data using the stored model.

### Claim 3 (depends on 2)

The method of claim 2, wherein computing the probability comprises:
computing an F-statistic based on a chi-square change of the modeled optical reflectance data obtained by including the one or more parameters, wherein the F-statistic is based on a ratio of the number of degrees of freedom in the model and a number of parameters in the model.

### Claim 4 (depends on 1)

The method of claim 1, further comprising:
setting an initial significance level;
setting an alpha wealth value to the initial significance level, wherein the statistical hypothesis testing terminates in response to the alpha wealth value decreasing to a threshold value;
decreasing the alpha wealth value by a first amount in response to the passage, by the one or more previously tested parameters, of the statistical hypothesis test;
increasing the alpha wealth value by a second amount in response to the passage, by the one or more previously tested parameters, of the statistical hypothesis test; and
modifying the significance level based on the increased or decreased alpha wealth value.

### Claim 5 (depends on 4)

The method of claim 4, wherein:
the first amount is given by a current significance level divided by one minus the current significance level;
the second amount is the initial significance level; and
the current significance level is set to the alpha wealth value multiplied by a current iteration number minus one, divided by one plus the current iteration number minus a most recent iteration in which a parameter failed the statistical hypothesis test.

### Claim 6 (depends on 1)

The method of claim 1, wherein the one or more parameters comprise a plurality of parameters, the method further comprising:
ordering the plurality of parameters for testing according to sensitivity, wherein high sensitivity parameters are to be tested prior to low sensitivity parameters; and
sequentially including and testing the plurality of parameters with the statistical hypothesis test.

### Claim 7 (depends on 1)

The method of claim 1, wherein the one or more parameters comprise a plurality of parameters, the method further comprising:
ordering the plurality of parameters for testing according to correlation, wherein low correlation parameters are to be tested prior to high correlation parameters; and
sequentially including and testing the plurality of parameters with the statistical hypothesis test.

### Claim 8 (depends on 1)

The method of claim 1, wherein the one or more parameters comprise a plurality of parameters, the method further comprising:
ordering the plurality of parameters for testing first according to sensitivity, wherein high sensitivity parameters are to be tested prior to low sensitivity parameters;
ordering the parameters having a same sensitivity according to correlation, wherein low correlation parameters are to be tested prior to high correlation parameters; and
sequentially including and testing the plurality of parameters with the statistical hypothesis test.

### Claim 9 (depends on 1)

The method of claim 1, wherein the one or more parameters comprise a plurality of parameters, the method further comprising:
ordering the plurality of parameters for testing according to precision, wherein high precision parameters are to be tested prior to low precision parameters; and
sequentially including and testing the plurality of parameters with the statistical hypothesis test.

### Claim 10 (depends on 1)

The method of claim 1, further comprising:
repeating the statistical hypothesis test for additional parameters until a stopping condition is reached, wherein the stopping condition comprises reaching a number of consecutively excluded parameters.

### Claim 11 (depends on 10)

The method of claim 10, further comprising:
ordering the plurality of parameters for testing according to sensitivity;
wherein the number of consecutively excluded parameters that result in the stopping condition being reached is three or greater.

### Claim 12

A machine-readable storage medium having instructions stored thereon which, when executed by a data processing system, cause the data processing system to perform a method of optimizing a model for evaluation of a diffracting structure, the method comprising:
performing measurements of the diffracting structure with a detector of an optical metrology system, including measuring optical reflectance of the diffracting structure;
identifying one or more parameters to test for inclusion in the model of the diffracting structure;
computing whether modeled optical reflectance data generated with the one or more parameters results in an improved fit to the measured optical reflectance data collected from the diffracting structure over previous modeled data generated without the one or more parameters;
computing a probability that the improved fit is due to chance;
determining the one or more parameters pass a statistical hypothesis test in response to the probability being less than a significance level dependent on whether one or more previously tested parameters passed the statistical hypothesis test;
storing to an electronic memory the one or more parameters as part of the model in response to the improved fit and passage of the statistical hypothesis test by the one or more parameters; and
determining a value of one or more parameters of the diffracting structure based on the stored model.

### Claim 13 (depends on 12)

The machine-readable storage medium of claim 12 having instructions stored thereon which, when executed by a data processing system, cause the data processing system to perform the method further comprising:
setting an initial significance level;
setting an alpha wealth value to the initial significance level, wherein the statistical hypothesis testing terminates in response to the alpha wealth value decreasing to a threshold value;
decreasing the alpha wealth value by a first amount in response to the passage, by the one or more previously tested parameters, of the statistical hypothesis test;
increasing the alpha wealth value by a second amount in response to the passage, by the one or more previously tested parameters, of the statistical hypothesis test; and
modifying the significance level based on the increased or decreased alpha wealth value.

### Claim 14 (depends on 12)

The machine-readable storage medium of claim 12 having instructions stored thereon which, when executed by a data processing system, cause the data processing system to perform the method further comprising:
ordering the plurality of parameters for testing according to sensitivity, wherein high sensitivity parameters are to be tested prior to low sensitivity parameters; and
sequentially including and testing the plurality of parameters with the statistical hypothesis test.

### Claim 15 (depends on 12)

The machine-readable storage medium of claim 12, further comprising:
repeating the statistical hypothesis test for additional parameters until a stopping condition is reached, wherein the stopping condition comprises reaching a number of consecutively excluded parameters.

### Claim 16

An optical measurement system comprising:
a scatterometry tool including a detector for performing optical measurements of a diffracting structure disposed on a sample, performing optical measurements including the scatterometry tool to generate optical reflectance measurement data for the diffracting structure;
first logic for receiving the optical reflectance measurement data for the diffracting structure;
an electronic memory to store a model for evaluation of the diffracting structure;
a processor to:
optimize the model for evaluation of the diffracting structure according to a method comprising:
identifying one or more parameters to test for inclusion in the model;
computing whether modeled optical reflectance data generated with the one or more parameters results in an improved fit to the optical reflectance measurement data over previous modeled data generated without the one or more parameters;
computing a probability that the improved fit is due to chance;
determining the one or more parameters pass a statistical hypothesis test in response to the probability being less than a significance level dependent on whether one or more previously tested parameters passed the statistical hypothesis test;
storing to the electronic memory the one or more parameters as part of the model in response to the improved fit and passage of the statistical hypothesis test by the one or more parameters; and
determining a value of one or more parameters of the diffracting structure using the stored model.

### Claim 17 (depends on 16)

The optical measurement system of claim 16, wherein determining a value of one or more parameters of the diffracting structure using the stored model includes:
performing a computation of at least one physical characteristic of the diffracting structure based on the measured optical reflectance data using the stored model.

### Claim 18 (depends on 16)

The optical measurement system of claim 16, the optical measurement system further comprising:
a display to display the modeled optical reflectance data; and
second logic to output the modeled optical reflectance data to the display.

### Claim 19 (depends on 16)

The optical measurement system of claim 16, the processor to optimize the model for evaluation of the diffracting structure according to the method further comprising:
setting an initial significance level;
setting an alpha wealth value to the initial significance level, wherein the statistical hypothesis testing terminates in response to the alpha wealth value decreasing to a threshold value;
decreasing the alpha wealth value by a first amount in response to the passage, by the one or more previously tested parameters, of the statistical hypothesis test;
increasing the alpha wealth value by a second amount in response to the passage, by the one or more previously tested parameters, of the statistical hypothesis test; and
modifying the significance level based on the increased or decreased alpha wealth value.

### Claim 20 (depends on 16)

The optical measurement system of claim 16, the processor to optimize the model for evaluation of the diffracting structure according to the method further comprising:
ordering the plurality of parameters for testing according to sensitivity, wherein high sensitivity parameters are to be tested prior to low sensitivity parameters; and
sequentially including and testing the plurality of parameters with the statistical hypothesis test.

### Claim 21 (depends on 12)

The machine-readable storage medium of claim 12, wherein determining a value of one or more parameters of the diffracting structure using the stored model includes:
performing a computation of at least one physical characteristic of the diffracting structure based on the measured optical reflectance data using the stored model.