CN103376795A - Semiconductor process monitoring method based on integrated leaning modeling technology - Google Patents

Abstract

The invention discloses a semiconductor process monitoring method based on the integrated leaning modeling technology. According to the semiconductor process monitoring method, on the basis that the vector data description algorithm is allowed, the integrated leaning modeling technology is introduced, and monitoring performance in a semiconductor process is promoted due to the fact that results of different models allowing vector data description are integrated. In an integrated leaning modeling process, a very important part is selection of appropriate integration strategies. As for the semiconductor process monitoring method, the different models allowing vector data description are integrated by adopting the advanced Bayesian reasoning strategy, and the advantages of all the models are used effectively. Finally, the semiconductor process is monitored by building a global statistic. Compared with a monitoring method based on a single model, the semiconductor process monitoring method based on the integrated leaning modeling technology greatly promotes the modeling performance of the models allowing vector data description and effectively improves the monitoring effect in the semiconductor process.

Description

Semiconductor process monitoring method based on ensemble learning modeling technology

Technical Field

The invention belongs to the field of semiconductor industrial process monitoring, and particularly relates to a process monitoring method based on an ensemble learning modeling technology and support vector data description.

Background

Since the 21 st century, the monitoring problem of the semiconductor industrial process is more and more widely regarded by the industry and academia, because the semiconductor industrial process has extremely high requirements on the product quality, and how to effectively prevent the process from generating inferior and unqualified products is a problem which needs to be solved urgently. In addition, the semiconductor process is effectively monitored, and the obtained result can also guide the improvement of the production process and the production technology in turn. In addition to a method based on a mechanism model, most of the conventional semiconductor process monitoring methods adopt a multi-element statistical analysis method in a multi-directional form, such as a multi-directional principal component analysis Method (MPCA) and a multi-directional partial least squares Method (MPLS). In the case of a mechanism model which is difficult to obtain, a multivariate statistical analysis method based on data driving has become a mainstream method for monitoring a semiconductor process. However, the traditional multivariate statistical analysis method is often limited to gaussian data information of the process, and requires process variables to comply with linear relations, which is difficult to satisfy in the actual process. The support vector data description method is a new method introduced into the process monitoring field in recent years, and not only can effectively describe non-Gaussian information of data, but also can extract a non-linear relation between process variables. However, a single process monitoring model still does not meet the monitoring requirements of the semiconductor industry in many cases. With the continuous development and maturity of the ensemble learning modeling technology, if a plurality of effective process monitoring models can be established on the basis of the support vector data description method, the real-time monitoring effect of the semiconductor process can be improved, the robustness of the monitoring models can be greatly enhanced, and the semiconductor process automation implementation is facilitated.

Disclosure of Invention

The invention aims to provide a process monitoring method based on an ensemble learning modeling technology and support vector data description, aiming at the defects of the monitoring technology in the current semiconductor industry.

The purpose of the invention is realized by the following technical scheme:

collecting data of each normal working condition in the semiconductor process by using a distributed control system to form a three-dimensional training sample set for modeling: x is formed by R^I×J×KWherein I is the total number of batches, J is the number of variables, and K is the number of sampling data points of each batch. The data are stored in a history database respectively. Expanding the three-dimensional process data into an I multiplied by JK two-dimensional data matrix along the batch direction, preprocessing and normalizing the three-dimensional process data, namely, obtaining the mean value of each process variable as zero and the variance as 1, and obtaining a new data matrix set as

When following againArranging each data matrix in the direction of the intermediate point to obtain a new data matrix of

Randomly sampling in the sample direction aiming at the new two-dimensional data matrix to obtain a plurality of two-dimensional independent data matrices

Wherein B =1,2, …, B is the number of two-dimensional independent data matrix. And respectively establishing a support vector data description model aiming at each two-dimensional independent data matrix, and determining the sphere center position and the radius of the hypersphere in a high-dimensional characteristic space. And storing the modeling data and each model parameter into a historical database and a real-time database for later use.

New process data is collected, pre-processed and normalized. And respectively adopting different support vector data description models to monitor the model to obtain the monitoring result of a single model. And (3) integrating the results of the support vector data description models by a Bayesian inference method, calculating the fault probability value of the current data under a probability framework, and constructing new statistics to monitor the semiconductor process.

The invention has the beneficial effects that: the invention simultaneously introduces a support vector number description algorithm and an ensemble learning modeling technology, monitors a data model by modeling a plurality of semiconductor processes, and integrates online information of real-time data by using a Bayesian inference method. Compared with other existing semiconductor process monitoring methods, the method provided by the invention not only can effectively improve the monitoring effect of the semiconductor process, but also improves the robustness of the monitoring model to a great extent.

Drawings

FIG. 1 is a diagram illustrating the monitoring of a faulty batch by a single support vector data description method;

FIG. 2 shows the monitoring result of the method of the present invention on a faulty batch.

Detailed Description

Aiming at the monitoring problem of the semiconductor process, the invention firstly utilizes the distributed control system to collect the normal historical data of the process. And then expanding the three-dimensional process data into an I multiplied by JK two-dimensional data matrix along the batch direction, preprocessing and normalizing the data matrix, and rearranging each data matrix along the time point direction to obtain a new data matrix. And randomly sampling in the sample direction aiming at the new two-dimensional data matrix to obtain a plurality of two-dimensional independent data matrices, respectively establishing a support vector data description model aiming at each two-dimensional independent data matrix, and determining the sphere center position and the radius of the hypersphere in a high-dimensional characteristic space. And storing the modeling data and each model parameter into a historical database and a real-time database for later use. When monitoring new batch data, different support vector data description models are respectively adopted to monitor the new batch data, and the monitoring result of a single model is obtained. And (3) integrating the results of the support vector data description models by a Bayesian inference method, calculating the fault probability value of the current data under a probability framework, and constructing new statistics to monitor the semiconductor process.

The technical scheme adopted by the invention comprises the following main steps:

the first step is as follows: collecting data of normal working conditions in the semiconductor process by using a distributed control system to form a three-dimensional training sample set for modeling: x is formed by R^I×J×K. Wherein I is the total number of batches, J is the number of variables, and K is the number of sampling data points of each batch. Respectively storing the data into a historical database;

the second step is that: expanding the three-dimensional process data into an I multiplied by JK two-dimensional data matrix along the batch direction, preprocessing and normalizing the three-dimensional process data, namely, obtaining the mean value of each process variable as zero and the variance as 1, and obtaining a new data matrix as $\stackrel{\‾}{X}\∈R^{I\×\mathrm{JK}};$

Preprocessing the collected process data in a historical database, eliminating outlier points and obvious rough error data, and respectively normalizing the data of different variables in order to ensure that the scale of the process data does not influence the monitoring result, namely the mean value of each variable is zero and the variance is 1. In this way, the data of different process variables are under the same scale without affecting the subsequent monitoring effect.

The third step: rearranging each data matrix along the time point direction to obtain a new data matrix of $\stackrel{=}{X}\∈R^{\mathrm{KI}\×J};$

Conventional semiconductor process monitoring methods require prediction of unknown values when monitoring new lot data. To avoid this problem, we rearrange the data matrix. Therefore, the monitoring sample is changed from the original whole batch data into a single sampling data point, and the problem of prediction of unknown values of batches is well avoided.

The fourth step: randomly sampling in the sample direction aiming at the new two-dimensional data matrix to obtain a plurality of two-dimensional independent data matrices

Wherein B =1,2, …, B is the number of two-dimensional independent data matrix;

the fifth step: respectively establishing a support vector data description model aiming at each two-dimensional independent data matrix, and determining the sphere center position and the radius of the hypersphere in a high-dimensional characteristic space;

for each two-dimensional independently sampled data matrix

And establishing a support vector data description analysis model. First, the process data is projected into a high-dimensional feature space using a non-linear function, i.e.The support vector data description method builds a model by solving the following optimization propositions:

$\underset{R,a,\mathrm{\ξ}}{\min }{R}^2+C\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i$

s.t.||Φ(x_i)-a||²≤R²+ξ_i,ξ_i≥0i=1,2,…,n

r and a are respectively the radius and the center of a hyper-sphere in a high-dimensional characteristic space, phi (x) is a nonlinear projection function, C is a single-class support vector machine adjusting parameter, the single-class support vector machine can balance the volume of the hyper-sphere and the error fraction of a sample by selecting the parameter, and xi is a relaxation variable of each sample. In the actual solving process, the following dual proposition is usually adopted to solve the support vector data description model, namely

$\underset{{\mathrm{\α}}_i}{\min }\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x_i,x_j)-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K(x_i,x_j)$

$s.t.0\≤{\mathrm{\α}}_i\≤C,\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i=1$

Wherein, K (x)_i,x_j)=Φ(x_i),Φ(x_j) Is a kernel function, usually chosen as a gaussian kernel, and α is the corresponding lagrange multiplier for each sample. The modeling result of the single-class support vector machine is as follows: most samples have corresponding alpha values of zero and only a small fraction of the key samples have corresponding alpha values of non-zero, and these samples are called support vectors. In high dimensional space, the center and radius of the hyper-sphere are determined as

$a_b=\underset{i=1}{\overset{{\mathrm{KI}}_b}{\mathrm{\Σ}}}{\mathrm{\α}}_i\mathrm{\Φ}\left({\stackrel{=}{x}}_i\right)$

$R_b=\sqrt{1-2\underset{i=1}{\overset{{\mathrm{KI}}_b}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K({\stackrel{=}{x}}_0,{\stackrel{=}{x}}_i)+\underset{i=1}{\overset{{\mathrm{KI}}_b}{\mathrm{\Σ}}}\underset{j=1}{\overset{{\mathrm{KI}}_b}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K({\stackrel{=}{x}}_i,{\stackrel{=}{x}}_j)}$

And a sixth step: storing the modeling data and each model parameter into a historical database and a real-time database for later use;

the seventh step: collecting new process data, and preprocessing and normalizing the new process data;

for newly acquired process data x_newFirst, each support vector data description model parameter is normalized by using the data description model parameter, namely

${\stackrel{=}{x}}_{\mathrm{new},b}=\frac{[x_{\mathrm{new}}-\mathrm{mean}\left({\stackrel{=}{x}}_b\right)]}{\mathrm{\σ}\left({\stackrel{=}{x}}_b\right)}$

Wherein B =1,2, …, B,

in order to model the mean of the data,

to model the standard deviation of the data, the new process data is normalized to the standard data with a mean of zero and a variance of 1 by the above equation.

Eighth step: monitoring the model by adopting different support vector data description models respectively to obtain a monitoring result of a single model;

projecting new data into a high-dimensional feature space by using a nonlinear function, calculating the distance between the new data and the spherical center of the hypersphere, and defining the following distance factors as monitoring statistics of the semiconductor process:

$D_{\mathrm{new},b}=d\left(\mathrm{\Φ}\left({\stackrel{=}{x}}_{\mathrm{new},b}\right)\right)=\left|\right|\mathrm{\Φ}\left({\stackrel{=}{x}}_{\mathrm{new},b}\right)-a_b\left|\right|$ $=\sqrt{1-2\underset{i=1}{\overset{\mathrm{KI}}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K({\stackrel{=}{x}}_{\mathrm{new},b},{\stackrel{=}{x}}_i)+\underset{i=1}{\overset{\mathrm{KI}}{\mathrm{\Σ}}}\underset{j=1}{\overset{\mathrm{KI}}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K({\stackrel{=}{x}}_i,{\stackrel{=}{x}}_j)\≤D_{\lim ,b}=R_b}$

wherein D is_lim,bFor the b-th monitoring statistic D_bIs equal to the radius of the corresponding hyper-sphere.

And the ninth step, integrating the results of the support vector data description models by a Bayesian inference method, calculating the fault probability value of the current data under a probability framework, and constructing new statistics to monitor the semiconductor process.

And after the monitoring results of the independent support vector data description models are obtained, different monitoring results are integrated by utilizing a Bayesian inference strategy to obtain a final global monitoring structure. First, the probability distribution of the current data under normal and fault conditions is defined separately, i.e.

$P_D^b\left(x_{\mathrm{new}}\right|N)=\exp \{-\frac{D_{\mathrm{new},b}}{D_{\lim ,b}}\}$

$P_D^b\left(x_{\mathrm{new}}\right|F)=\exp \{-\frac{D_{\lim ,b}}{D_{\mathrm{new},b}}\}$

The prior probability is respectively selected as the fault misclassification rate and the failure rate, namely

Where ν is the fault error rate. Based on a Bayesian inference method, the fault probability of the current year sample is calculated as follows:

$P_D^b\left(F\right|x_{\mathrm{new}})=\frac{P_D^b\left(x_{\mathrm{new}}\right|F)P_D^b\left(F\right)}{P_D^b\left(x_{\mathrm{new}}\right)}$

$P_D^b\left(x_{\mathrm{new}}\right)=P_D^b\left(x_{\mathrm{new}}\right|N)P_D^b\left(N\right)+P_D^b\left(x_{\mathrm{new}}\right|F)P_D^b\left(F\right)$

where B =1,2, …, B, 'F' and 'N' represent fault and normal operating conditions, respectively. Finally, by averaging the monitoring results of each independent support vector data description model, the overall monitoring result is obtained as follows

$P_D\left(F\right|x_{\mathrm{new}})=\frac{1}{B}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{P}_D^b\left(F\right|x_{\mathrm{new}})$

Wherein,

namely, the new global monitoring statistic is obtained, and the monitoring statistic limit is v.

The effectiveness of the present invention is illustrated below in connection with a specific semiconductor process example. The data for this process was from Texas instruments, USA, with a total of 40 normal data and 20 fault data. The source of the fault is mainly caused by the variation of the respective power and pressure, and a total of 17 process variables were selected for monitoring the process, as shown in table 1. In addition, the sampling time point of each batch was 85. The following detailed description of the steps of the present invention is provided in conjunction with the specific process:

1. collecting normal working condition data in the process, preprocessing the data, normalizing, rearranging and sampling

Carrying out data preprocessing on 60 batches of collected effective process data samples to eliminate process fieldsA value point and a coarse error point. Then 32 batches of data among 40 batches of normal data are selected to form a modeling data matrix. The data matrix is expanded into a two-dimensional data matrix according to the batch direction and is normalized to obtain

Then, the two-dimensional data matrix is rearranged along the sampling time direction to obtain a new data matrix ofRandomly sampling in the sample direction for a new two-dimensional data matrix, wherein the sampling number is 16 batches of data volume, and obtaining 10 two-dimensional independent data matrices

Wherein b =1,2, …,10 two-dimensional independent data matrix number.

2. Respectively aiming at each two-dimensional independent data matrix, establishing a support vector data description model, and determining the sphere center position and the radius size of the hypersphere in a high-dimensional characteristic space

For each new two-dimensional data matrix respectively

b =1,2, …,10, establishing a support vector data description analysis model, and determining the position of the sphere center and the size of the radius of the hypersphere in a high-dimensional space. The error rate was controlled to be around 1% when the parameters were chosen, so that the resulting monitoring statistics represent a 99% confidence limit.

3. Acquiring current monitoring data information, and preprocessing and normalizing the current monitoring data information

To test the effectiveness of the new method, the data of the normal and failed batches were tested separately. And randomly selecting data of a certain normal batch, and processing the data by utilizing the normalization parameters under various working conditions. And selecting a typical fault for testing, and performing normalization processing on the typical fault.

4. On-line process monitoring

Firstly, the process data of normal batches are monitored, and the monitoring results obtained by the new method and the single support vector data modeling method are shown in table 2. As can be seen from the table, the new method and the single support vector data modeling method can well monitor the batch, and the false alarm rate of the fault is within an acceptable range, which indicates that the new method does not lose the monitoring effect under the normal working condition. Then, the monitoring effect of the new method and the single support vector data modeling method is shown in fig. 1 and fig. 2. It can be obviously seen that the monitoring performance of the method is superior to that of a single support vector data modeling method (the fault detection rate is high).

Table 1: description of the monitored variables

Serial number	Variables of	Serial number	Variables of
				1	BCl3Flow rate	10	RF power
2	Cl2Flow rate	11	RF impedance
				3	RF bottom power	12	TCP tuning
4	A detection of endpoints	13	TCP phase error
				5	Helium pressure	14	TCP impedance
6	Room pressure	15	TCP top power
				7	RF tuning	16	TCP load
8	RF load	17	Vat valve
				9	Phase error

Table 2: false alarm rate of monitoring method on normal batch

Monitoring method	Failure false alarm rate of normal batch
		Single support vector data description method	0.019
Multi-support vector data description model based on ensemble learning modeling	0.020

The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are within the spirit of the invention and the scope of the appended claims.

Claims (4)

1. A semiconductor process monitoring method based on support vector data description and integrated learning modeling technology is characterized by comprising the following steps:

(1) collecting data of each normal working condition in the semiconductor process by using a distributed control system to form a three-dimensional training sample set for modeling: x is formed by R^I×J×KWherein I is the total number of batches, J is the number of variables, and K is the number of sampling data points of each batch. The data are stored in a history database respectively.

(2) Developing three-dimensional process data along batch directionIs an I multiplied by JK two-dimensional data matrix which is preprocessed and normalized, namely, the mean value of each process variable is zero, the variance is 1, and a new data matrix is obtained

(3) Rearranging each data matrix along the time point direction to obtain a new data matrix of

(4) Randomly sampling in the sample direction aiming at the new two-dimensional data matrix to obtain a plurality of two-dimensional independent data matrices

Wherein B =1,2, …, B is the number of two-dimensional independent data matrix.

(5) And respectively establishing a support vector data description model aiming at each two-dimensional independent data matrix, and determining the sphere center position and the radius of the hypersphere in a high-dimensional characteristic space.

(6) And storing the modeling data and each model parameter into a historical database and a real-time database for later use.

(7) New process data is collected, pre-processed and normalized.

(8) And respectively adopting different support vector data description models to monitor the model to obtain the monitoring result of a single model.

(9) And (3) integrating the results of the support vector data description models by a Bayesian inference method, calculating the fault probability value of the current data under a probability framework, and constructing new statistics to monitor the semiconductor process.

2. The method for monitoring the semiconductor process based on the support vector data description and the ensemble learning modeling technique according to claim 1, wherein the step (5) is specifically as follows: independent number of samples for each two-dimensionalAccording to the matrix

And establishing a support vector data description analysis model. First, the process data is projected into a high-dimensional feature space using a non-linear function, i.e.

The support vector data description method builds a model by solving the following optimization propositions:

s.t.||Φ(x_i)-a||²≤R²+ξ_i,ξ_i≥0i=1,2,…,n

r and a are respectively the radius and the center of a hyper-sphere in a high-dimensional characteristic space, phi (x) is a nonlinear projection function, C is a single-class support vector machine adjusting parameter, the single-class support vector machine can balance the volume of the hyper-sphere and the error fraction of a sample by selecting the parameter, and xi is a relaxation variable of each sample. In the actual solving process, the following dual proposition is usually adopted to solve the support vector data description model, namely

Wherein, K (x)_i,x_j)=Φ(x_i),Φ(x_j) Is a kernel function, usually chosen as a gaussian kernel, and α is the corresponding lagrange multiplier for each sample. The modeling result of the single-class support vector machine is as follows: most samples have zero alpha values and only a small fraction of key samples have non-zero alpha values, and these samples are calledIs a support vector. In high dimensional space, the center and radius of the hyper-sphere are determined as

。

3. The method for monitoring the semiconductor process based on the support vector data description and the ensemble learning modeling technique according to claim 1, wherein the steps (7) and (8) are specifically as follows: for newly acquired process data, each support vector data description model parameter is firstly utilized to carry out normalization processing, namely

Wherein B =1,2, …, B,

in order to model the mean of the data,

to model the standard deviation of the data, the new process data is normalized to the standard data with a mean of zero and a variance of 1 by the above equation. Then, the new data is projected into the high-dimensional feature space also by using a nonlinear function, and the distance between the new data and the spherical center of the hyper-sphere is calculated, and the following distance factors are defined as monitoring statistics of the semiconductor process:

wherein D is_lim,bFor the b-th monitoring statistic D_bIs equal to the radius of the corresponding hyper-sphere.

4. The method for monitoring a semiconductor process based on support vector data description and ensemble learning modeling technique according to claim 1, wherein the step (9) is specifically: and after the monitoring results of the independent support vector data description models are obtained, different monitoring results are integrated by utilizing a Bayesian inference strategy to obtain a final global monitoring structure. First, the probability distribution of the current data under normal and fault conditions is defined separately, i.e.

The prior probability is respectively selected as the fault misclassification rate and the failure rate, namely

Where ν is the fault error rate. Based on a Bayesian inference method, the fault probability of the current year sample is calculated as follows:

where B =1,2, …, B, 'F' and 'N' represent fault and normal operating conditions, respectively. Finally, by averaging the monitoring results of each independent support vector data description model, the overall monitoring result is obtained as follows

Wherein, P_D(F|x_new) Namely, the new global monitoring statistic is obtained, and the monitoring statistic limit is v.

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