# US 12,223,012 B2 · Machine learning variable selection and root cause discovery by cumulative prediction

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- Number: US 12,223,012 B2
- Document ID: US12223012B2
- Status: Granted
- Kind: B2
- Application number: 17/072,830
- Filed: 2020-10-16
- Published: 2021-04-22
- Granted: 2025-02-11
- Earliest claimed: 2019-10-16
- Assignees: PDF Solutions, Inc.
- Applicants: PDF Solutions, Inc.
- Inventors: Richard Burch; Qing Zhu; Jonathan Holt; Tomonori Honda
- Web page: https://patentgrep.com/patent/US12223012B2

## CPC

- G06F 18/2113: by ranking or filtering the set of features, e.g. using a measure of variance or of feature cross-correlation
- G03F 7/70483: {Information management; Active and passive control; Testing; Wafer monitoring, e.g. pattern monitoring}
- G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G06N 5/04: Inference or reasoning models
- G06N 20/00: Machine learning
- 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)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS

## Abstract

A sequence of models accumulates r-squared values for an increasing number of variables in order to quantify the importance of each variable to the prediction of a targeted yield or parametric response.

## Claims

### Claim 1

A computer-implemented method for predicting yield for semiconductor devices in a semiconductor process, wherein a plurality of process parameters are associated with the yield of semiconductor devices, comprising:
configuring and training a machine learning model to predict yield based on an input data set having a selected plurality of the process parameters;
selecting a first parameter of the plurality of process parameters for the input data set, providing the input data set to the machine learning model, predicting yield based on the input data set, and determining a first r-squared value for a first prediction by the machine learning model based on the input data set;
selecting a second parameter of the plurality of process parameters and adding the second parameter to the input data set, providing the input data set to the machine learning model, predicting yield based on the input data set, and determining a second r-squared value for a second prediction by the machine learning model based on the input data set;
repeating a step of selecting an additional parameter of the plurality of process parameters, adding the additional parameter to the input data set, providing the input data set to the machine learning model, predicting yield based on the input data set, and determining an additional r-squared value for another prediction by the machine learning model based on the input data set;
accumulating all determined r-squared values until the accumulation increases by less than a threshold value;
ranking the plurality of selected parameters on the basis of respective r-squared values; and
identifying as inputs to include or exclude from the machine learning model on the basis of the ranking of selected parameters.

### Claim 2

A computer-implemented method for predicting yield for semiconductor devices made in a semiconductor process, wherein a plurality of process variables are associated with yield, comprising:
providing a unique input data set to each of a plurality of processor-based models, each of the models programmed with instructions to predict yield based on a respective one of the unique input data sets;
wherein a first model of the plurality of models has a first input data set comprising a first variable of the plurality of process variables;
wherein a second model of the plurality of models has a second input data set comprising the first variable and a second variable of the plurality of process variables;
wherein successive additional models of the plurality of models have respective input data sets comprising the first variable, the second variable, and in succession, another variable added to the respective input data set:
wherein successive additional models each have a respective input data set consisting of the first variable, the second variable, and in succession, all variables that were added to the input data set of the immediately preceding model;
predicting yield using each of the plurality of models;
determining an r-squared value for each of a plurality of predictions made by respective ones of the plurality of models;
accumulating and ranking the respective r-squared values;
selecting ones of the plurality of process variables to include or exclude from a primary input data set based on the ranking of r-squared values; and
deploy a final model programmed with instructions to predict yield on the basis of the primary input data set.

### Claim 3

A computer-implemented method for predicting yield for semiconductor devices made in a semiconductor process, wherein a plurality of process variables are associated with yield, comprising:
predicting yield using:
a first machine-learning-based model programmed with instructions to predict yield based on an input of a first variable of the plurality of process variables;
a second machine-learning-based model programmed with instructions to predict yield based on an input of the first variable and a second variable of the plurality of process variables;
a plurality of successive additional machine-learning-based models as necessary, each successive additional model programmed with instructions to predict yield based on an input of the first variable, the second variable, and adding a single additional variable of the plurality of process variables with each successive model;
determining a respective r-squared value for each prediction made by the models;
ranking the respective r-squared values of the predictions;
selecting ones of the plurality of process variables to include or exclude from a primary input data set based on the ranking of respective r-squared values; and
deploying a production model into the semiconductor process, the production model programmed with instructions to predict yield on the basis of the primary input data set.

### Claim 4 (depends on 3)

The method of claim 3, further comprising:
using successive models to predict yield until all process variables have been provided as an input to a final one of the successive models.

### Claim 5 (depends on 3)

The method of claim 3, further comprising:
accumulating the respective r-squared values of the predictions; and
using successive models to predict yield until an accumulation of the respective r-squared values of the predictions exceeds a threshold value.

### Claim 6 (depends on 3)

The method of claim 3, further comprising:
accumulating the respective r-squared values of the predictions; and
using successive models to predict yield until an accumulation of the respective r-squared values of the predictions increases by less than a threshold value.