PROCESSOR INCLUDING MODIFIED RADIAL BASIS FUNCTION (RBF) NEURAL NETWORK AND METHOD OF PROVIDING THE MODIFIED RBF NEURAL NETWORK

Provided is a method of providing a modified radial basis function (RFB) neural network. The method includes providing the modified RBF neural network configured to determine a breakdown of semiconductor equipment, wherein the modified RBF neural network assigns, to each of components of the measurement data, a standardization coefficient dependent on the components of the measurement data.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based on and claims priority under 35 U.S.C. § 119 to Korean Patent Application No. 10-2022-0055028, filed on May 3, 2022, in the Korean Intellectual Property Office, the disclosure of which is incorporated by reference herein in its entirety.

BACKGROUND

One or more embodiments relate to a processor including a modified radial basis function (RBF) neural network and a method of providing the modified RBF neural network.

2. Description of Related Art

A yield rate of a semiconductor device is directly related to manufacturing costs, therefore the yield rate is the most essential element in semiconductor device manufacturing. To improve the yield rate of a semiconductor device, it is highly important to monitor a state of semiconductor equipment in real time and predict a breakdown of the semiconductor equipment.

A breakdown of semiconductor equipment causes defects in a semiconductor device, and in certain cases, induces immense repair costs. To prevent these problems, a method and a system for predicting the breakdown of semiconductor equipment are required.

SUMMARY

One or more embodiments include a processor including a modified radial basis function (RBF) neural network and a method of providing the modified RBF neural network.

Objectives of the disclosure are not limited to those mentioned above, and other unmentioned objectives will be clearly understood by one of ordinary skill in the art from the descriptions below.

According to one or more embodiments, there is provided a method of providing a modified radial basis function (RBF) neural network. The method includes: providing an RBF neural network configured to determine, based on n-dimensional measurement data with respect to semiconductor equipment, a breakdown of the semiconductor equipment, wherein n is an integer; and based on the RBF neural network, providing a modified RBF neural network, wherein the modified RBF neural network assigns, to each of components of the measurement data, a standardization coefficient dependent on the components of the measurement data.

The standardization coefficient may be n-dimensional.

The standardization coefficient may be determined based on a standard deviation of a corresponding component of the measurement data.

The standardization coefficient may prevent an excessive increase or an excessive decrease of an effect of each of the components of the measurement data on a calculation of the RBF neural network.

When the semiconductor equipment has a breakdown, an RBF value calculated by the modified RBF neural network may be 1.

When the semiconductor equipment has a breakdown, an RBF value calculated by the modified RBF neural network may be 0.

The modified RBF neural network may be configured to determine, based on the following equation, a breakdown of the semiconductor equipment:

where Sjis a modified RBF value calculated based on the measurement data, wiselects an ithcomponent of the measurement data, a1 standardizes the ithcomponent of the measurement data, Zi,jis an ithcomponent of standard data indicating a normal state of the semiconductor equipment, and Xiis the ithcomponent of the measurement data.

wimay have a value of 0 or 1.

wimay have a value determined based on a correlation coefficient between components of the standard data.

According to one or more embodiments, a processor includes a modified radial basis function (RBF) neural network configured to determine, based on measurement data with respect to semiconductor equipment, a breakdown of the semiconductor equipment.

The modified RBF neural network is configured to determine, based on Equation 1 below, the breakdown of the semiconductor equipment:

where Sjis a modified RBF value calculated based on the measurement data, wiselects an ithcomponent of the measurement data, σistandardizes the ithcomponent of the measurement data, Zi,jis an ithcomponent of standard data indicating a normal state of the semiconductor equipment, and Xiis the ithcomponent of the measurement data.

wiis determined by Matrix C calculated based on the standard data and Equation 2 below:

wherein Matrix C is a correlation coefficient between components of the standard data.

When an ithcomponent of any one selected from among rows of Matrix C is less than or equal to a threshold value, wimay have a value of 0.

When an ithcomponent of any one selected from among rows of Matrix C is greater than or equal to a threshold value, wimay have a value of 1.

The threshold value may be in a range of about 0.5 to about 0.7.

σimay be a standard deviation of the ithcomponent of the measurement data.

According to one or more embodiments, a method of providing a modified radial basis function (RBF) neural network includes: providing an RBF neural network; and based on the RBF neural network, providing a modified RBF neural network.

The RBF neural network and the modified RBF neural network are configured to monitor semiconductor equipment.

The RBF neural network is configured to determine, based on Equation 1 below, a breakdown of the semiconductor equipment:

where Sj′ is an RBF value calculated based on measurement data of the semiconductor equipment, {right arrow over (ZJ)} is standard data indicating a normal state of the semiconductor equipment, {right arrow over (X)} is the measurement data, and σ is a standard deviation of the measurement data.

The modified RBF neural network is configured to determine, based on Equation 2 below, a breakdown of the semiconductor equipment:

where Sjis a modified RBF value calculated based on the measurement data, wiselects an ithcomponent of the measurement data, σistandardizes the ithcomponent of the measurement data, Zi,jis an ithcomponent of the standard data indicating the normal state of the semiconductor equipment, and Xiis the ithcomponent of the measurement data.

The providing of the RBF neural network may include: providing estimation values with respect to {right arrow over (ZJ)} and σ; and updating {right arrow over (ZJ)} and σ to improve accuracy of the RBF neural network.

The providing of the estimation values with respect to {right arrow over (ZJ)} and a may be unsupervised learning.

The updating of <<mth3>> and <<mth4>> may be supervised learning.

wimay be determined by Matrix C calculated based on the standard data and Equation 3 below:

wherein each of components of Matrix C is an absolute value of a correlation coefficient between components of the standard data.

When an ithcomponent of any one selected from among rows of Matrix C is less than or equal to a threshold value, wimay have a value of 0.

When the ithcomponent of any one selected from among the rows of Matrix C is greater than or equal to the threshold value, wimay have a value of 1.

The threshold value may be in a range of about 0.5 to about 0.7.

DETAILED DESCRIPTION

Hereinafter, embodiments are described in detail with reference to the accompanying drawings. For the same components on the drawings, the same reference numerals are used, and the same descriptions are not given.

FIG.1is a schematic diagram of a system10according to embodiments.

Referring toFIG.1, the system10may include a processor100and equipment200.

According to embodiments, the equipment200may perform a process of manufacturing a semiconductor device. The equipment200may be configured to perform, for example, any one of an oxidation process, a lithography process, an etch process, a thin-film process, a metallization process, an electric die sorting (EDS) process, and a packaging process.

The equipment200may include a plurality of measuring devices M1, M2, M3, M4, M5, M6, M7, and M8(hereinafter M1to M8). The plurality of measuring devices M1to M8may measure any one of a parameter and a condition of the equipment200. Unlike the illustration ofFIG.1, the equipment200may include n measuring devices, wherein n is a positive integer.

Here, the parameter may include a variable adjusted for process controlling, during an operation of the equipment200. Examples of the parameter may include power to drive the whole equipment200or portions of the equipment200. The condition may include a variable indicating a state of the equipment200. Examples of the condition may include a temperature, a pressure, etc. of the portions of the equipment200. Hereinafter, the parameter and the condition may be referred to as data.

The plurality of measuring devices M1to M8may measure different data from each other. The plurality of measuring devices M1to M8may measure the same types of data from different portions of the equipment200or different types of data from the same portions of the equipment200.

According to embodiments, the processor100may be configured to monitor the equipment200based on measurement values of the plurality of measuring devices M1to M8. According to embodiments, the processor100may be configured to determine a state of the equipment200based on the measurement values of the plurality of measuring devices M1to M8. According to embodiments, the processor100may be configured to determine whether the equipment200is normal or has a breakdown. According to embodiments, the processor100may predict an increased likelihood of a breakdown of the equipment200.

According to embodiments, the processor100may include a modified radial basis function (RBF) neural network. According to embodiments, the processor100may calculate a modified RBF value based on the measurement values of the plurality of measuring devices M1to M8. The modified RBF value may indicate a degree of similarity (or a distance) between a state of the equipment200and a normal state (or a breakdown state) of the equipment200.

Hereinafter, an example of the processor configured to calculate the modified RBF value indicating a distance between measured data of the equipment200and standard data corresponding to a normal state of the equipment200is described. Based on the description herein, one of ordinary skill in the art may easily achieve an example of the processor configured to calculate the modified RBF value indicating a distance between measured data of the equipment200and standard data corresponding to a breakdown state of the equipment200.

According to embodiments, the processor100may be configured to determine the modified RBF value according to Equation 1 below.

In Equation 1, Sjis a modified RBF value calculated based on jthdata. Zi,jindicates pieces of standard data, and Xiindicates pieces of measurement data.

i is an ordinal number for identifying a dimension of data and has an integer value of 1 to n. As shown in this example, when eight measuring devices M1to M8are used, n is 8. A value of i of the data measured by the measuring device M1may be 1, and a value of i of the data measured by the measuring device M2may be 2.

σimay standardize an ithcomponent of the measurement data. σimay be a standardization coefficient of the ithcomponent of the measurement data. σimay prevent some of the measuring devices M1to M8from being excessively dominant with excessive deviations, compared with measurement values of the other measuring devices M1to M8. According to cases, σimay assign a high weight to a component of the measurement data, the component being critical for sensing a breakdown of the equipment200.

wiis a selection function of the ithcomponent of the measurement data. In an RBF neural network, wimay select components of the data sensitive for a breakdown of the equipment200from among components of the data. wimay have a value of 0 or 1. When the measurement data Xihas a low degree of sensitivity with respect to a breakdown, wimay be 0. When the measurement data Xihas a high degree of sensitivity with respect to a breakdown, wimay be 1.

The processor100may be trained to classify the measurement data Xiof the equipment200into a breakdown state and a normal state. The processor100may be configured to determine, based on a distance between the measurement data Xiand the standard data whether the measurement data X is data of the equipment200in the breakdown state or data of the equipment200in the normal state.

When the distance between the measurement data X and the standard data Zi,jis sufficiently small, the RBF value Sjaccording to the jthdata may be approximated to 0. In this case, the processor100may determine that the equipment200is in the normal state.

When the distance between the measurement data Xiand the standard data Zi,jis sufficiently large, the RBF value Sjaccording to the jthdata may be approximated to 1. In this case, the processor100may determine that the equipment200has a breakdown.

According to embodiments, the processor100may predict the likelihood of the breakdown of the equipment200, based on a trend of Sjin a series of the measurement data. According to embodiments, the processor100may predict the likelihood of the breakdown of the equipment200, based on a change of the value of the Sjtoward 1 in the series of measurement data. According to embodiments, when the value of Sjexceeds a threshold value (for example, 0.7) in specific measurement data, the processor100may determine that the equipment200is highly likely to have a breakdown.

The processor100may include a computing device, such as a workstation computer, a desktop computer, a laptop computer, a tablet computer, etc. The processor100may include a simple controller, a complex processor, such as a microprocessor, a central processing unit (CPU), a graphics processing unit (GPU), etc., a processor including software, dedicated hardware, or firmware. The processor100may be realized, for example, by a general-purpose computer or application-specific hardware, such as digital signal process (DSP), a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), etc.

According to some embodiments, the operations of the processor100may be implemented by commands stored on a machine-readable medium readable and executable by one or more processors. Here, the machine-readable medium may include an arbitrary mechanism to store and/or transmit information in a form readable by a machine (for example, a computing device). For example, the machine-readable medium may include read-only memory (ROM), random-access memory (RAM), a magnetic disk storage medium, an optical storage medium, flash memory devices, and an optical, acoustic, or other type radio wave signal (for example, a carrier wave, infrared, or digital signal) and other arbitrary signals.

Firmware, software, routines, instructions, etc. for performing the operations described with reference to the processor100or performing arbitrary processes to be described hereinafter may be configured. For example, the processor100may be realized by a deep learning model trained to provide an RBF neural network according to Equation 1. For example, the processor100may be realized by a deep learning model configured to calculate the RBF value described with reference to Equation 1.

However, this is only for convenience of explanation, and the operations of the processor100described above may also be implemented by a computing processor, a processor, a controller, or other devices executing firmware, software, routines, instructions, etc.

FIG.2is a flowchart of a method of obtaining a model, according to embodiments.

Referring toFIGS.1and2, in P10, an RBF neural network may be provided by using the processor100.

The RBF neural network may be in compliance with Equation 2 below.

While each of Zi,jand X is a scalar value in Equation 1, each of {right arrow over (ZJ)} and {right arrow over (X)} may be an n-dimensional row vector including n components in Equation 2. σ may be a standard deviation of {right arrow over (X)}.

In an RBF, {right arrow over (ZJ)} may indicate a central tendency of normal data, and a may indicate a width of the normal data. In P10, first, for {right arrow over (ZJ)} and σ, the central tendency of the normal data and an estimation value with respect to a standard deviation may be used, respectively.

The processor100may update {right arrow over (ZJ)} and σ to improve the accuracy of prediction of the RBF neural network of Equation 2. Thus, {right arrow over (ZJ)} and σ may be determined. The operation of providing the estimation values of {right arrow over (ZJ)} and σ may be unsupervised learning, and the operation of updating {right arrow over (ZJ)} and σ may be supervised learning.

Next, in P20, a modified RBF neural network may be provided based on the RBF neural network by using the processor100. The providing of the modified RBF neural network may include calculating wi, σi, and standard data Zi,j.

wimay be determined from a correlation coefficient of the standard data Zi,j, but is not limited thereto. In more detail, wimay be determined according to Equation 3 below.

Matrix C is a correlation matrix and may indicate a correlation coefficient between components of standard data. In more detail, each component of Matrix C may indicate an absolute value of the correlation coefficient between the components of the standard data. For example, a component (4,3) of Matrix C may be the correlation coefficient between a fourth component of the standard data and a third component of the standard data. As another example, a component (3,4) of Matrix C may be the correlation coefficient between the third component of the standard data and the fourth component of the standard data.

In Matrix C, a diagonal component is autocorrelational, and thus, is identically 1. Also, from a definition of Matrix C, it is obvious that Matrix C is a symmetric matrix (that is, symmetrical with respect to the diagonal component). For example, a value of the component (3,4) of Matrix C may be substantially the same as a value of the component (4,3) of Matrix C.

According to an embodiment, determining wimay include selecting any one of rows of Matrix C and comparing an ithcomponent of the selected row of Matrix C with a threshold value. Here, the threshold value may be in a range of 0.5 to 0.7. The selecting of the row from Matrix C may be based on calculation of each component of the row. For example, a row of Matrix C having the maximum sum of components may be used in the determining of wi.

For example, when a kth row of Matrix C is selected, wimay be determined according to Equation 4 below.

According to another embodiment, the determining of wimay include calculating an average of each column of Matrix C to calculate an n-dimensional row vector composed of the average of each column and comparing an ithcomponent of the calculated n-dimensional row vector with a threshold value. Here, the threshold value may be in a range of 0.5 to 0.7.

An example of a1 may include a historical standard deviation of measurement data Xi. Here, the historical standard deviation of the measurement data Ximay be a standard deviation of a set of the measurement data Xiupdated during a predetermined time period. Another example of σimay include a calculation result based on the historical standard deviation of the measurement data Xi.

Unlike the case of an RBF according to the related art, σimay have a different value for each component Xiof data. Accordingly, an excessive decrease or an excessive increase of the contribution of the component Xiof data selected (that is, corresponding to withat is non-zero) in the modified RBF, to the modified RBF, may be prevented.