CN113189967B - Control performance diagnosis method for semiconductor process batch control system - Google Patents

Abstract

The invention provides a control performance diagnosis method of a semiconductor process batch control system, which comprises the following steps of firstly, estimating reference working condition white noise, a reference working condition disturbance model, reference working condition model residual error, actual working condition white noise, an actual working condition disturbance model and actual working condition model residual error according to closed loop data of historical normal working conditions and closed loop data of actual working conditions; secondly, acquiring four diagnostic monitoring quantities according to the reference working condition white noise and the model residual thereof, the actual working condition white noise and the model residual thereof, and acquiring the control performance monitoring quantity and the control upper limit/lower limit of the four diagnostic monitoring quantities according to the closed loop data of the historical normal working condition; and finally, evaluating the control performance of the batch control system according to the control performance monitoring quantity and the control upper limit/lower limit thereof. The method not only can correctly evaluate the control performance of the closed-loop system under the conventional operating condition of the semiconductor manufacturing process, but also can effectively diagnose the reason causing the performance reduction of the system, thereby reducing the maintenance cost of the system and improving the safety of the system.

Description

Control performance diagnosis method for semiconductor process batch control system

Technical Field

The invention belongs to the field of control performance evaluation and diagnosis of a process industrial control system, and particularly relates to a control performance diagnosis method of a semiconductor manufacturing process batch control system, which is used for evaluating the control performance of the semiconductor manufacturing process batch control system and diagnosing the reason of the degradation of the control performance.

Background

In recent years, with the adoption of a great market demand, abundant manpower resources and other advantages, the semiconductor industry in China has rapidly developed and has become the focus of attention of the global integrated circuit industry. The industrial level of semiconductors in China is still extremely disproportionate to the status of the big country in China. For example, high-tech enterprises in the middle customs area take up a large portion of the computer market in China, but the profit margin is only about 3%, whereas the pure profit margin of the central processor manufacturer intel continues for years is above 30%.

The semiconductor industry is primarily concerned with the industry of manufacturing semiconductor solid state devices and circuits, a process known as wafer fabrication. The production of wafers is a rather long and complex process involving hundreds of process steps, which cannot be performed perfectly at each time, and the occurrence of defects in any one process affects the final quality of the product. An Exponentially Weighted Moving Average (EWMA) batch-to-batch controller is an advanced controller commonly used in semiconductor manufacturing processes, and the controller adjusts manipulated variables of the next batch according to input and output data of historical batches, so that influences of process disturbances in forms of offset, drift and the like on product quality are reduced, and yield is improved. Wafer processing is often affected by internal and external uncertainties of the system, which can cause degradation of system control performance, reduction of energy, material utilization, and economic benefits, and even safety disasters. Therefore, it is important to research the performance monitoring and diagnosis technology of the EWMA batch control system in the semiconductor manufacturing process to improve the quality of the wafer product.

After the system is put into operation, the control quality of the EWMA batch controller is influenced by factors such as model mismatch, external disturbance change, controller adjustment and the like, and the system performance is reduced due to the factors. The product quality, operational safety, material energy consumption rate and economic performance of semiconductor manufacturing processes are closely related to the control performance of batch controllers. The loss of control performance from any one process can be quite dramatic, with losses of up to $ 5000 for 300 mm wafers.

Disclosure of Invention

The invention provides a control performance diagnosis method of a semiconductor manufacturing process batch control system, which aims to monitor the control performance of an EWMA batch controller and diagnose the reason of performance degradation, and solves the technical problem that the existing control performance monitoring method is difficult to determine the specific factors of control performance degradation.

The technical scheme of the invention is realized as follows:

a control performance diagnostic method for a semiconductor process batch control system comprises the following steps:

s1, obtaining N groups of input data and output data of historical normal working conditions of the EWMA batch control system in the semiconductor manufacturing process as sample data, dividing the sample data into S +1 windows, and calculating a white noise estimation value epsilon of the reference working condition by using the input data and the output data of the first window_rAnd reference working condition disturbance model estimation value

Obtaining process-disturbance combined model residual e (t), process data set

And output data set Y₁ ⁰And based on the process data set

Obtaining a matrix X of reference conditions₁From the output data set Y₁ ⁰Obtaining a matrix Y of reference conditions₁Constructing a Hankel matrix X_pAnd X_fAnd projection matrix J_q；

S2, constructing a process data set using the input data and the output data of the k' th window

And outputting the data set

From a process data set

Obtaining matrix X of actual working condition_k'From the output data set

Obtaining matrix Y of actual working conditions_k'Obtaining the control performance monitoring quantity of the EWMA batch-to-batch control system corresponding to the kth window by adopting a typical variable analysis method

Wherein k ═ 2,3, …, S + 1;

s3, according to the reference working condition disturbance model estimated value in the step S1

Obtaining reference working condition model residual error v from input data and output data of k' th window_r,k'(t) and model mismatch/perturbation dynamics joint monitoring volume

S4, obtaining the white noise estimation value epsilon of the practical working condition corresponding to the k 'th window by using the input data and the output data of the k' th window_h,k'(t) and actual condition disturbance model estimation value

And according to the actual working condition disturbance model estimated value

Obtaining the residual error v of the actual working condition model_h,k'(t)；

S5, according to the reference working condition white noise estimated value epsilon in the step S1_rAnd the white noise estimate of the actual condition ε in step S4_h,k'(t) calculating an interference characteristic monitoring quantity

According to the reference working condition model residual v in the step S3_r,k'(t) and the actual condition model residual v in step S4_h,k'(t) calculating the amount of monitoring of the disturbance model

According to the actual working condition white noise estimated value epsilon in the step S4_h,k'(t) and the actual condition model residual v_h,k'(t) obtaining a model mismatch monitoring quantity

S6, respectively obtaining the control upper limit UP of the control performance monitoring quantity by adopting a kernel density estimation method_CPIUpper control limit UP of combined monitoring quantity of model mismatch/disturbance dynamics_PDMIUpper limit UP of control of the monitored quantity of interference characteristics_DVILower limit of control LP of disturbance characteristic monitoring amount_DVILower control limit LP of disturbance model monitoring quantity_DMIAnd the upper control limit UP of the model mismatch monitoring quantity_PMI；

S7, collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line, and obtaining the control performance monitoring quantity eta of the current working condition_CPIAccording to the control upper limit UP in step S6_CPIJudging whether the control performance of the closed-loop system is reduced or not in real time;

s8, if the control performance monitoring quantity eta_CPIControl upper limit UP greater than control performance monitoring amount_CPIIf the performance of the EWMA batch control system is reduced, executing the step S9, otherwise, the EWMA batch control system has good performance;

s9, using the reference working condition disturbance model estimated value in the step S1

The N1 groups of input data and output data in the step S7 acquire the model mismatch/disturbance dynamic combined monitoring quantity eta of the current working condition_PDMI；

S10, if the model mismatching/disturbance dynamic joint monitoring quantity eta_PDMIControl upper limit UP larger than the model mismatch/disturbance dynamic joint monitoring amount in step S6_PDMIWhere the model mismatch or disturbance dynamics results in performance degradation of the EWMA batch-to-batch control system, step S11 is performed, otherwise, the controller parameter change results in the EWMA batchPerformance degradation of the inter-control system;

s11, calculating the disturbance characteristic monitoring quantity eta of the current working condition_DVIMonitoring quantity eta of disturbance model_DMIAnd model mismatch monitor η_PMI(ii) a Disturbance characteristic monitoring quantity eta when current working condition_DVIGreater than the upper control limit UP of the disturbance characteristic monitoring amount in step S6_DVIOr less than the lower control limit LP of the disturbance characteristic monitored quantity_DVIIn time, the performance of the EWMA batch control system is reduced due to the change of the interference characteristics; when the disturbance model monitors the quantity eta_DMILower control limit LP less than disturbance model monitoring amount_DMIMeanwhile, the performance of the EWMA batch control system is reduced due to the change of the disturbance model; when model mismatch monitor eta_PMIControl upper limit UP greater than model mismatch monitoring amount_PMIModel mismatch results in performance degradation of the EWMA batch-to-batch control system.

Matrix X of the reference condition₁And Y₁Respectively expressed as:

wherein u is_iRepresents the ith process input vector, i 1, …, m_u，m_uDenotes the number of input vectors, t denotes the sampling time, u ″_iRepresenting the i-th process input vector after normalization, i.e.

Means representing the ith process input vector, (σ)_u,r)_iRepresents the standard deviation of the ith process input vector; y is_jRepresents the jth process output vector, j ═ 1, …, m_y，m_yIndicates the number of output vectors, y ″)_jRepresenting the normalized jth process output vector, i.e.

Means for representing the jth process output vector, (σ)_y,r)_jRepresents the standard deviation of the jth process output vector; e.g. of the type_j(t) denotes the jth process-perturbation joint model residual vector, where e_j＝(e_j(t))，e_j(t)＝y_j(t)-(G_m(q^-1))_ju(t)，(G_m(q^-1))_jRepresenting the process model G used in the first window_m(q^-1) J-th line of (1), y_j(t) denotes the jth process output at the tth sampling instant, u (t) denotes the column vector formed by all process inputs at the tth sampling instant in the first window, e ″_jRepresents the normalized jth process-perturbation joint model residual vector,

represents the mean of the jth process-perturbation combined model residual, (σ)_e,r)_jRepresenting the standard deviation of the jth process-perturbation combined model residual error;

the projection matrix J_qComprises the following steps:

wherein, V_qRepresenting a matrix constructed from the first q columns of the unitary matrix V,

represents the Hankel matrix X_pThe covariance matrix of (2).

The process data set

And outputting the data set

Respectively expressed as:

wherein the content of the first and second substances,

procedure for representing the k' th windowThe vector is input to the computer system,

the process-perturbation joint model residual vector representing the kth window,

a process output vector representing the kth window;

matrix X of the actual working condition_k'And Y_k'Respectively expressed as:

wherein u is_i,k'The process input vector, u ", representing the k' th window_i，kRepresenting the process input vector of the normalized k' th window, i.e.

y_j,k'Represents the process output vector, y ″, of the k' th window_j,k'The process output vector representing the normalized k' th window, i.e.

e_j,k'Process-perturbation joint model residual vector representing the kth window, e_j,k'＝(e_j,k'(t))，e_j,k'(t)＝y_j,k'(t)-(G_m,k′(q^-1))_ju_k'(t)，y_j,k'(t) denotes the jth process output, u, at the tth sampling instant in the kth window_k'(t) represents the column vector formed by all process inputs at the tth sampling instant in the kth window, (G)_m,k′(q^-1))_jRepresenting the Process model G used by the EWMA batch-to-batch controller in the k' th window_m，k′(q^-1) Line j, e ″)_j,k'Representing the process-perturbation combined model residual of the normalized k' th window, i.e.

Obtaining control performance monitoring quantity of EWMA batch control system by adopting typical variable analysis method

Comprises the following steps:

wherein the content of the first and second substances,

represents the amount of control performance monitoring, J, of the EWMA batch-to-batch control system corresponding to the kth window_qRepresenting a projection matrix, p_k,k'Representation matrix X_p,k'The k-th column of (1).

The model mismatch/disturbance dynamic joint monitoring quantity

Comprises the following steps:

wherein the content of the first and second substances,

represents the model mismatch/disturbance dynamic joint monitoring quantity corresponding to the kth' window,

has a value range of (0, 1)]，ε_r(t) the white noise estimation value of the reference condition at the t-th sampling moment, v_r,k'(t) represents the reference condition model residual at the t-th sampling instant in the kth' window, | cov (ε_r(t)) | denotes ε_rDeterminant of covariance matrix of (t), | cov (v)_r,k'(t)) | denotes v_r,k'(t) determinant of covariance matrix;

the reference working condition model residual v_r,k'(t) is:

wherein v is_r,k'(t) represents the reference condition model residual error corresponding to the k' th window,

disturbance model estimation value representing reference working condition

Inverse of (y)_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window, u_k'(t) represents the process input vector at the t-th sampling instant in the k' -th window, G_m,k′(q^-1) Representing the process model used by the EWMA batch controller in the k' th window.

The actual working condition model residual error v_h,k'(t) is:

wherein v is_h,k'(t) represents the real model residual at the t-th sampling instant of the k' -th window,

actual condition disturbance model estimation value representing k' th window

Inverse of (y)_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window, u_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window, G_m,k′(q^-1) Representing the process model used by the EWMA batch controller in the k' th window.

Step S5 includes the steps of:

s5.1, calculating interference characteristic monitoring quantity

Wherein epsilon_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,k'(t) represents the white noise estimate for the actual condition at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotesε_h,k'Determinant of covariance matrix of (t), | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix;

s5.2, calculating the monitoring quantity of the disturbance model

Wherein the content of the first and second substances,

representing the monitored amount of the perturbation model for the k' th window,

has a value range of (0, 1)]If, if

Near or equal to 1, the perturbation model is unchanged, v_r,k'(t) represents the reference condition model residual at the t-th sampling instant in the k' -th window, v_h,k'(t) represents the actual condition model residual at the t-th sampling instant in the k' -th window, J (f (v)_r,k'(t)),g(v_h,k'(t))) represents v_h,k'(t) and v_r,k'(t) KL divergence, expressed as:

wherein, f (v)_r,k'(t)) represents v constructed using the nuclear density estimation method_r,k'(t) probability density function, f (v)_h,k'(t)) represents v obtained by the nuclear density estimation method_h,k'(t) probability density function, i ═ 1,2, …, N_f，N_fRepresenting the total number of independent identically distributed sample points resulting from the kernel density estimation;

s5.3, calculating model mismatch monitoring quantity

Wherein epsilon_h,k'(t) represents the white noise estimate of the actual condition at the t-th sampling instant in the k' -th window,v_h,k'(t) represents the real-world model residual at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (v)_h,k'(t)) | denotes v_h,k'(t) determinant of covariance matrix.

Step S6 includes the following steps:

s6.1, calculating the control upper limit UP of the control performance monitoring quantity_CPI：

Wherein, the first and the second end of the pipe are connected with each other,

the control performance monitoring quantity corresponding to the kth window is K ', K' is 2, 3.., S +1, h represents the kernel bandwidth, and K (·) represents the kernel density estimation with the kernel as a radial basis function;

s6.2, calculating the control upper limit UP of the model mismatch/disturbance dynamic combined monitoring quantity_PDMI：

Wherein the content of the first and second substances,

model mismatch/disturbance dynamic combined monitoring quantity corresponding to the kth' window;

s6.3, calculating the control upper limit UP of the interference characteristic monitoring quantity_DVIAnd a lower control limit LP_DVI：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the kth window;

s6.4, calculating a control lower limit LP of the monitoring quantity of the disturbance model_DMI：

Wherein the content of the first and second substances,

is the disturbance model monitoring quantity corresponding to the kth window;

s6.5, calculating the control upper limit UP of the model mismatch monitoring quantity_PMI：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the k' th window.

Step S7 includes the following steps:

s7.1, collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line as actual working condition sample data, and dividing the actual working condition sample data into S₁An online window, each window containing n groups of samples, wherein S₁＝N1-n+1；

S7.2, calculating the residual error of the online process-disturbance combined model: e.g. of the type_l(t)＝y_l(t)-G_m,l(q^-1)u_l(t) wherein e_l(t) represents the on-line process-perturbation joint model residual error at the tth sampling instant of the ith window, y_l(t) represents the process output vector at the tth sampling instant of the ith window, u_l(t) denotes the input vector at the tth sampling instant of the l-th window, t denotes the sampling instant, G_m,l(q^-1) Representing a Process model, q, used by an EWMA batch-to-batch controller in an on-line regime^-1Denotes a difference operator, where l is 1,2, …, S₁；

S7.3, acquiring a process input data set of the current working condition by using the process output vector, the process input vector and the process-disturbance combined model residual error which are acquired in real time

And output data set Y_l ⁰：

Wherein, the first and the second end of the pipe are connected with each other,

representing the on-line process input vector and,

representing the on-line process-perturbation joint model residual vector,

representing an online process output vector;

s7.4, constructing a matrix X_lAnd Y_l：

Wherein u is_i,lRepresents the process input vector, u ″, in the ith window of the online data_i,lThe process input vector representing the normalized l-th window, i.e.

y_j,lRepresents the process output vector, y ″, of the ith window of online data_j,lThe process output vector representing the normalized l-th window, i.e.

e_j,lProcess-perturbation joint model residual vector representing the ith window of online data, e_j,l＝(e_j,l(t))，e_j,l(t)＝y_j,l(t)-(G_m,l(q^-1))_ju_l(t)，(G_m,l(q^-1))_jProcess model G representing EWMA inter-batch controller usage in the ith window of online data_m，l(q^-1) J-th line of (1), y_j,l(t) denotes the jth process output at the tth sampling instant of the ith window of online data, u_l(t) represents online dataVector, e ″, formed by all process inputs at the tth sampling time of the ith window_j,lRepresenting the normalized process-perturbation joint model residual,

s7.5, constructing a Hankel matrix X_p,lAnd X_f,l：

Wherein p is_p+1,lRepresenting a history data vector at the p +1 th sampling instant in the ith window of line data, i.e. p_p+1,l＝[x_l(p)^T … x_l(1)^T y_l(p)^T … y_l(1)^T]^T，x_l(p) a representation matrix

P column of (2), x_l(1) Representation matrix

The p-th column of (2),

representation matrix X_lTranspose of (y)_l(p) represents a matrix Y_l ^TP column, y_l(1) Representation matrix Y_l ^TColumn 1, Y_l ^TRepresentation matrix Y_lTransposing; f. of_p+1,lThe vector of predicted data representing the p +1 th sampling instant in the l window of line data, i.e. f_p+1,l＝[y_l(p+1)^T y_l(p+2)^T … y_l(p+f-1)^T]^T，y_l(p +1) represents Y_l ^TP +1 column, y_l(p +2) represents Y_l ^TP +2 column, y_l(p + f-1) represents Y_l ^TP + f-1 column (b);

S7.6. obtaining control performance monitoring quantity eta of current working condition by using on-line data_CPI：

Wherein the content of the first and second substances,

indicating the control performance monitoring quantity, p, of the ith window of the on-line data_k,lRepresentation matrix X_p,lThe kth column vector of (1);

s7.7, control Upper Limit UP according to control Performance monitoring amount_CPIJudgment of

Whether or not less than UP_CPIIf, if

Less than UP_CPIThen the system performance is better, if eta_CPIlGreater than UP_CPIThe system performance is degraded.

Step S9 includes the following steps:

s9.1, obtaining a reference working condition model residual error by using online data:

wherein v is_r,l(t) represents the reference condition model residual error at the tth sampling time of the ith window of the online data,

representing the reference condition disturbance model estimate, y_l(t) an online data process output vector, u, at the tth sampling instant of the ith window_l(t) an online data process input vector at the tth sampling instant, G, for the ith window_m,l(q^-1) Representing a process model used by the EWMA batch controller in the ith window of the online data;

s9.2, input number acquired on lineComputing model mismatch/disturbance dynamic combined monitoring quantity eta according to output data_PDMI：

Wherein the content of the first and second substances,

has a value range of (0, 1)]，ε_r(t) represents the white noise estimate for the reference condition at the tth sampling instant, | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix, v_r,l(t) represents the on-line data reference case model residual at the tth sampling instant of the ith window, | cov (v)_r,l(t)) | denotes v_r,l(t) determinant of covariance matrix;

s9.3, combining control upper limit UP of model mismatch/disturbance dynamic joint monitoring quantity_PDMIThe factors for controlling the performance degradation are preliminarily diagnosed if the current working condition is met

Greater than UP_PDMIIf the model mismatch or the external disturbance dynamics is changed, the system performance is reduced due to the model mismatch or the external disturbance dynamics; if the current operating condition is

Less than UP_PDMIThen changes in the controller tuning parameters are a factor that causes degradation in system performance.

Step S11 includes the steps of:

s11.1, calculating interference characteristic monitoring quantity eta of online data_DVI：

Wherein the content of the first and second substances,

representing the interference characteristic monitoring amount of the online data corresponding to the l-th window,

for characterizing the change of the white noise variance, ε, in the actual operating conditions_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,l(t) represents the white noise estimation value of the actual working condition at the tth sampling moment of the ith window in the online monitoring stage, | cov (epsilon)_h,l(t)) | denotes ε_h,lDeterminant of covariance matrix of (t), | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix;

s11.2, calculating the actual working condition model residual error of the online data:

wherein v is_h,l(t) represents the model residual error of the online data actual condition corresponding to the ith window,

on-line data actual condition disturbance model estimation value y representing ith window_l(t) an online data process output vector, u, at the tth sampling instant of the ith window_l(t) an online data process input vector at the tth sampling instant, G, for the ith window_m,l(q^-1) Representing a process model used by the EWMA batch controller in the ith window of the online data;

s11.3, calculating disturbance model monitoring quantity eta of online data_DMI：

Wherein the content of the first and second substances,

representing the monitored quantity, v, of the disturbance model corresponding to the l-th window_r,l(t) represents the on-line data reference condition model residual at the tth sampling instant of the ith window, v_h,l(t) represents the on-line data real-time model residual error at the tth sampling time of the ith window, J (f (v)_r,l(t)),g(v_h,l(t))) represents v_h,l(t) and v_r,l(t) KL divergence;

s11.4, model for calculating online dataMismatch monitoring η_PMI：

Wherein the content of the first and second substances,

model mismatch monitoring quantity, epsilon, of the on-line data corresponding to the ith window of the on-line data_h,l(t) represents the white noise estimate of the actual condition at the tth sampling time of the ith window of the on-line data, v_h,l(t) represents the real model residual at the tth sampling instant of the l windows of online data, cov (ε_h,l(t)) represents ε_h,l(t) determinant of covariance matrix, cov (v)_h,l(t)) represents v_h,l(t) determinant of covariance matrix;

s11.5, combining the lower control limit LP of the interference characteristic monitoring quantity_DVIUpper limit UP of control of the monitored quantity of interference characteristics_DVIAnd a lower control limit LP of the monitoring quantity of the disturbance model_DMIAnd upper control limit UP of model mismatch monitoring quantity_PMIFurther diagnosing and identifying the factors causing the performance degradation of the EWMA batch-to-batch control system and a plurality of disturbance characteristic monitoring quantities

Greater than UP_DVIOr less than LP_DVIIf the white noise variance is changed, the performance of the EWMA batch control system is reduced; if the model monitoring quantity is disturbed

Less than LP_DMIIf so, the performance of the EWMA batch control system is reduced due to the change of the external disturbance model; monitoring quantity if model mismatching

Greater than UP_PMIThen the model mismatch causes the EWMA inter-batch control system performance to degrade.

Compared with the prior art, the invention has the following beneficial effects:

1) when monitoring the control performance of a semiconductor process batch control system, the control performance monitoring quantity constructed by adopting a typical variable analysis method is closely related to controller regulation, model mismatch and disturbance dynamics according to the relation between process output and process input and a process-disturbance combined model residual error; compared with other control performance evaluation indexes, the control performance monitoring quantity provided by the invention directly reflects the influence of controller regulation, model mismatch and disturbance dynamics on the control performance.

2) When the control performance of a semiconductor process batch control system is diagnosed, four diagnosis statistics are established, wherein the four diagnosis statistics are as follows: model mismatch/disturbance dynamic monitoring quantity, interference characteristic monitoring quantity, disturbance model monitoring quantity and model mismatch monitoring quantity; the model mismatch/disturbance dynamic monitoring quantity is not influenced by the adjusting parameters of the controller, the white noise variance change can be separated from other factors influencing the control performance by the disturbance characteristic monitoring quantity, the disturbance model change can be separated from other factors influencing the control performance by the disturbance model monitoring quantity, and the model mismatch monitoring quantity separates the model mismatch from other factors influencing the control performance.

3) The method can effectively monitor the control performance change condition of the system and can also effectively distinguish the influence of three factors of model mismatch, disturbance dynamics and controller adjusting parameters on the control performance, when the control performance is reduced, the closed-loop system needs to be shut down, and a system identification experiment is carried out on the closed-loop system to diagnose the reason of the reduction of the control performance of the system.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic diagram of a CMP process of the present invention;

FIG. 3 is a schematic diagram of the control performance monitoring index and each diagnostic index when the model is mismatched according to the present invention, wherein (a) is a monitoring graph of the monitoring quantity of the control performance, (b) is a monitoring graph of the monitoring quantity of the model mismatch/disturbance dynamics, (c) is a monitoring graph of the monitoring quantity of the disturbance characteristic, (d) is a monitoring graph of the monitoring quantity of the disturbance model, and (e) is a monitoring graph of the monitoring quantity of the model mismatch;

FIG. 4 is a schematic diagram of a control performance monitoring index and diagnostic indices when the white noise variance changes according to the present invention, wherein (a) is a monitoring graph of a control performance monitoring amount, (b) is a monitoring graph of a model mismatch/disturbance dynamics monitoring amount, (c) is a monitoring graph of an interference characteristic monitoring amount, (d) is a monitoring graph of a disturbance model monitoring amount, and (e) is a monitoring graph of a model mismatch monitoring amount;

FIG. 5 is a diagram of a control performance monitoring index and diagnostic indices when a controller parameter changes according to the present invention, wherein (a) is a monitoring graph of a control performance monitoring amount, (b) is a monitoring graph of a model mismatch/disturbance dynamics monitoring amount, (c) is a monitoring graph of a disturbance characteristic monitoring amount, (d) is a monitoring graph of a disturbance model monitoring amount, and (e) is a monitoring graph of a model mismatch monitoring amount;

FIG. 6 is a schematic diagram of the control performance monitoring index and each diagnostic index when the disturbance model is changed, wherein (a) is a monitoring graph of the control performance monitoring amount, (b) is a monitoring graph of the model mismatch/disturbance dynamics monitoring amount, (c) is a monitoring graph of the disturbance characteristic monitoring amount, (d) is a monitoring graph of the disturbance model monitoring amount, and (e) is a monitoring graph of the model mismatch monitoring amount, according to the present invention;

FIG. 7 is a schematic diagram of the control performance monitoring index and each diagnostic index when the model is mismatched and the white noise variance is changed, wherein (a) is a monitoring graph of the monitoring quantity of the control performance, (b) is a monitoring graph of the monitoring quantity of the model mismatch/disturbance dynamics, (c) is a monitoring graph of the monitoring quantity of the disturbance characteristic, (d) is a monitoring graph of the monitoring quantity of the disturbance model, and (e) is a monitoring graph of the monitoring quantity of the model mismatch;

fig. 8 is a schematic diagram of the control performance monitoring index and each diagnostic index when the model is mismatched and the disturbance model is changed according to the present invention, where (a) is a monitoring map of the control performance monitoring amount, (b) is a monitoring map of the model mismatch/disturbance dynamics monitoring amount, (c) is a monitoring map of the disturbance characteristic monitoring amount, (d) is a monitoring map of the disturbance model monitoring amount, and (e) is a monitoring map of the model mismatch monitoring amount.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.

As shown in fig. 1, an embodiment of the invention provides a method for diagnosing control performance of a semiconductor manufacturing lot-to-lot control system, which includes the following steps:

s1, obtaining N groups of input data and output data of historical normal working conditions of the EWMA batch control system in the semiconductor manufacturing process as sample data, dividing the sample data into S +1 windows, and calculating a white noise estimation value epsilon of the reference working condition by using the input data and the output data of the first window_rAnd reference working condition disturbance model estimation value

Acquisition processPerturbation joint model residual e (t), process data set

And output data set Y₁ ⁰Collecting the process data

Column i minus the process data set

Mean of all samples in column i divided by the process data set

Obtaining a matrix X of the reference working condition by the standard deviation of the sample of the ith column₁Will output data set Y₁ ⁰Is subtracted from the output data set Y₁ ⁰Is divided by the output data set Y after averaging all samples in column i₁ ⁰Obtaining a matrix Y of the reference working condition by the standard deviation of the sample of the ith column₁Construction of Hankel matrix X_pAnd X_fAnd projection matrix J_q。

Step S1 includes:

s1.1, acquiring N groups of input data and output data of historical normal working conditions in a semiconductor manufacturing process with an EWMA batch controller as sample data, dividing the sample data into S +1 windows, wherein each window comprises N groups of samples, and S is N-N. The calculation process of the window S is as follows: s ═ N/d ], where d is the window moving step length, [ · ] denotes rounding the data down, in this example, d ═ 1.

S1.2, regarding a first window in the S +1 windows acquired in the step S1.1 as a reference working condition, and respectively performing centralization processing on input data and output data of the first window:

wherein u' (t) represents the t-th sampling time after the centering processA process input vector at time u (t) representing the input vector at the t-th sampling instant of the first window,

mean vector, m, representing the input vectors at the t-th sampling instant of the first window_uRepresenting the number of input vectors, t representing the sampling instant, n representing the number of samples of the first window, y' (t) representing the process output vector at the t-th sampling instant after the centering process, y (t) representing the output vector at the t-th sampling instant of the first window,

mean vector, m, representing the output vector at the t-th sampling instant of the first window_yIndicating the number of output vectors.

S1.3, obtaining an estimated value of white noise of a reference working condition:

ε_r(t)＝y′_P(t){I-Y′_P(t)^T[Y′_P(t)Y′_P(t)^T]^-1Y′_P(t)}，

wherein epsilon_r(t) represents a reference condition white noise estimation value y 'at the t-th sampling time'_P(t)＝[y′(t)…y′(t-P+1)]Representing a data vector, Y ', constructed from the centralized process output vector Y ' (t) '_P(t)＝[y′_P(t-1)^T…y′_P(t-L)^T]^TIs represented by a data vector y'_P(t) a constructed data matrix, P representing the data window size of the estimated white noise, L representing the data matrix Y'_PThe number of row vectors of (T), T, represents the transpose operation.

S1.4, constructing an autoregressive moving average model of the process output data after centralization processing and with out-of-band source input:

wherein the content of the first and second substances,

denotes a delay factor phi₁，…，φ_ICoefficient, phi, representing the autoregressive part_I+1，…，φ_I+KCoefficient of exogenous input, phi_I+K+1，…，φ_I+K+JThe coefficient of the moving average is represented, I represents the maximum order of the autoregressive part, and K represents the maximum order of the exogenous input; j denotes the maximum order of the moving average.

S1.5, acquiring coefficient vectors and orders of an autoregressive moving average model with out-of-band source input according to an adaptive minimum absolute value contraction and operator selection method:

wherein the content of the first and second substances,

Y_W(t)＝[y′(t) … y′(t-W+1)]^T(ii) a W denotes the window size of the sampled data, Y_W(t) denotes a W × 1 dimensional data matrix, H_W(t) represents a W × (I + K + J) dimensional data matrix;

the method representing the adaptive minimum absolute value shrinkage and selection operator estimates the coefficient vector of the autoregressive moving average model, i.e.

Denotes the coefficients of the estimated autoregressive moving average model, phi denotes the coefficient vector of the actual but unknown autoregressive moving average type, phi ═ phi₁,…,φ_I+K+J]λ denotes an adjustable parameter controlling the penalty factor in the adaptive minimum absolute value shrinkage and selection operator method,

coefficient representing autoregressive moving average model_jCoefficient of phi_jThe weighting factor of (2).

S1.6, calculating a process-disturbance combined model residual error according to an input vector and an output vector of a first window:

e(t)＝y(t)-G_m(q^-1)u(t)，

wherein e (t) represents the process-perturbation joint model residual, G_m(_q ^-1) Representing the process model used by the EWMA batch controller in the first window, q^-1Representing a difference operator.

S1.7, acquiring a process data set of a reference working condition by utilizing a process input vector, a process output vector and a process-disturbance combined model residual error of a first window

And output data set Y₁ ⁰：

Wherein the content of the first and second substances,

which represents the input vector of the process,

representing the process-perturbation joint model residual vector,

representing the process output vector.

S1.8, calculating a mean vector and a standard deviation vector of process input vectors of a first window:

wherein the content of the first and second substances,

is the mean vector, σ, of the process input vectors at the t-th sampling instant of the first window_u,rA standard deviation vector of the process input vectors of the first window;

calculating a mean vector and a standard deviation vector of the output vector of the first window process:

wherein the content of the first and second substances,

is the mean vector, σ, of the process output vectors at the t-th sampling instant of the first window_y,rA standard deviation vector of the process output vector of the first window;

calculating a mean vector and a standard deviation vector of a first window process-disturbance combined model residual:

wherein the content of the first and second substances,

mean vector, σ, of the process-perturbation combined model residuals for the first window_e,rThe process-perturbation for the first window is the standard deviation vector of the joint model residual.

S1.9, constructing a matrix X₁And Y₁：

Wherein u is_iRepresents the ith process input vector, i 1, …, m_u，m_uDenotes the number of input vectors, t denotes the sampling time, u ″_iRepresenting the i-th process input vector after normalization, i.e.

Means representing the ith process input vector, (σ)_u,r)_iRepresents the standard deviation of the ith process input vector; y is_jRepresents the jth process output vector, j ═ 1, …, m_y，m_yIndicates the number of output vectors, y ″)_jRepresenting the normalized jth process output vector, i.e.

Means for representing the jth process output vector, (σ)_y,r)_jRepresents the standard deviation of the jth process output vector; e.g. of the type_j(t) denotes the jth process-perturbation joint model residual vector, where e_j＝(e_j(t))，e_j(t)＝y_j(t)-(G_m(q^-1))_ju(t)，(G_m(q^-1))_jRepresenting the process model G used in the first window_m(q^-1) J-th line of (1), y_j(t) denotes the jth process output at the tth sampling instant, u (t) denotes the column vector formed by all process inputs at the tth sampling instant in the first window, e ″_jRepresents the normalized jth process-perturbation joint model residual vector,

represents the mean of the jth process-perturbation combined model residual, (σ)_e,r)_jRepresents the standard deviation of the jth process-perturbation combined model residual.

S1.10, constructing Hankel matrix X_pAnd X_f：

Wherein m is m_u+2m_y，p_p+1Representing the historical data vector at the p +1 th sampling instant, i.e. p_p+1＝[x(p)^T … x(1)^T y(p)^T … y(1)^T]^TX (p) represents a matrix

P column of (2), x (1) represents a matrix

The number 1. sup. st column of (a),

representation matrix X₁Y (p) denotes a matrix Y₁ ^TY (1) denotes the matrix Y₁ ^TColumn 1, Y₁ ^TRepresentation matrix Y₁Transposing; f. of_p+1The vector of prediction data representing the p +1 th sampling instant, i.e. f_p+1＝[y(p+1)^T y(p+2)^T … y(p+f-1)^T]^TY (p +1) represents Y₁ ^TColumn p +1, Y (p +2) represents Y₁ ^TIn the p +2 th column, Y (p + f-1) represents Y₁ ^TM denotes the number of vectors of the history data vector and the prediction data vector constructed from n sets of observation data, and M is n-p-f + 1.

S1.11, calculating a unitary matrix V: h ═ U ∑ V^TWherein V represents a unitary matrix constructed when singular value decomposition is performed on the matrix H,

is represented by X_pAnd X_fThe constructed matrix Hankel matrix is used as a matrix,

represents the sample covariance of the historical data vector,

represents the sample covariance of the prediction data vector,

representing the cross covariance of the historical data vector and the predicted data vector.

S1.12, calculating a projection matrix J_q：

Wherein, V_qRepresenting a matrix constructed from the first q columns of the unitary matrix V,

represents the Hankel matrix X_pThe covariance matrix of (c).

S2, constructing a process data set using the input data and the output data of the k' th window

And outputting the data set

Collecting process data

Column i minus the process data set

Mean of all samples in column i divided by the process data set

Obtaining a matrix X of actual working conditions by the standard deviation of the sample of the ith column_k'Will output the data set

Column i minus the output data set

Is divided by the output data set after averaging all samples in column i

Obtaining a matrix Y of actual working conditions by the standard deviation of the sample of the ith column_k'Acquiring control performance monitoring quantity of an EWMA batch-to-batch control system by adopting a typical variable Analysis (CVA)

Where k' is 2,3, …, S + 1.

Step S2 includes:

s2.1, obtaining a process-disturbance combined model residual error of a k 'th window by using input data and output data of the k' th window: e.g. of the type_k'(t)＝y_k'(t)-G_m,k'(q^-1)u_k'(t) wherein e_k'(t) represents the process-perturbation joint model residual at the t-th sampling instant of the k' -th window, y_k'(t) denotes the kth' window process output vector at the tth sampling instant u_k'(t) represents the process input vector for the kth window at the tth sampling instant, G_m,k'(q^-1) Representing the process model used by the EWMA batch controller in the current operating regime.

S2.2, acquiring a process input data set under the current working condition according to the process input vector and the output vector of the kth window and the process-disturbance combined model residual error of the kth window

And outputting the data set

Wherein the content of the first and second substances,

the process input vector representing the kth window,

the process-perturbation joint model residual vector representing the kth window,

the process output vector representing the k' th window.

S2.3, constructing a matrix X_k'And Y_k'：

Wherein u is_i,k'The process input vector, u ", representing the k' th window_i,k'The process input vector representing the normalized k' th window, i.e.

y_j,k'Represents the process output vector, y ″, of the k' th window_j,k'The process output vector representing the normalized k' th window, i.e.

e_j,k'Process-perturbation joint model residual vector representing the kth window, e_j,k'＝(e_j,k'(t))，e_j,k'(t)＝y_j,k'(t)-(G_m,k′(q^-1))_ju_k'(t)，y_j,k'(t) denotes the jth process output, u, at the tth sampling instant in the kth window_k'(t) represents the column vector formed by all process inputs at the tth sampling instant in the kth window, (G)_m,k′(q^-1))_jRepresents G_m，k′(q^-1) Line j, e ″)_j,k'Representing the process-perturbation combined model residual of the normalized k' th window, i.e.

S2.4, constructing a Hankel matrix X_p,k'And X_f,k'：

Wherein p is_p+1kRepresenting the historical data vector at the p +1 th sampling instant in the k' th window, i.e. p_p+1,k'＝[x_k'(p)^T … x_k'(1)^T y_k'(p)^T … y_k'(1)^T]^T，x_k'(p) representation matrix

P column of (2), x_k'(1) Representation matrix

The number 1. sup. st column of (a),

representation matrix X_k'Transpose of (y)_k'(p) a representation matrix

P column, y_k'(1) Representation matrix

The number 1. sup. st column of (a),

representation matrix X_k'Transposing; f. of_p+1kDenotes the vector of prediction data at the p +1 th sampling instant in the k' th window, i.e. f_p+1,k'＝[y_(k')(p+1)^T y_(k')(p+2)^T … y_(k')(p+f-1)^T]^T，y_(k')(p +1) represents

P +1 column, y_(k')(p +2) represents

P +2 column, y_(k')(p + f-1) represents

Column p + f-1.

S2.5, obtaining control performance monitoring quantity of the EWMA batch control system by adopting a typical variable analysis method

Comprises the following steps:

wherein the content of the first and second substances,

represents the amount of control performance monitoring, J, of the EWMA batch-to-batch control system corresponding to the kth window_qRepresenting a projection matrix, p_k,k'Representation matrix X_p,k'The k-th column of (1).

S3, according to the reference working condition disturbance model estimated value in the step S1

Obtaining reference working condition model residual error v from input data and output data of k' th window_r,k'(t) and model mismatch/perturbation dynamics joint monitoring volume

Step S3 includes:

s3.1, disturbing the model estimated value according to the reference working condition

Obtaining reference working condition model residual error v from input data and output data of k' th window_r,k'(t)：

Wherein v is_r,k'(t) reference condition model residual error at the t-th sampling time of the k' -th window, y_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window, u_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window, G_m,k'(q^-1) A process model used by the EWMA batch controller in the k' th window is shown.

S3.2, according to the model residual error v of the reference working condition_r,k'(t) obtaining model mismatch/disturbance dynamic combined monitoring quantity by white noise estimated value of reference working condition

Wherein the content of the first and second substances,

represents the model mismatch/disturbance dynamic joint monitoring quantity corresponding to the k' th window,

has a value range of (0, 1)]，ε_r(t) the white noise estimation value of the reference condition at the t-th sampling moment, v_r,k'(t) represents the reference condition model residual at the t-th sampling instant in the kth' window, | cov (ε_r(t)) | denotes ε_rDeterminant of covariance matrix of (t), | cov (v)_r,k'(t)) | denotes v_r,k'(t) determinant of covariance matrix.

S4, obtaining the white noise estimation value epsilon of the practical working condition corresponding to the k 'th window by using the input data and the output data of the k' th window_h,k'(t) and actual condition disturbance model estimation value

And according to the actual working condition disturbance model estimated value

Obtaining the residual error v of the actual working condition model_h,k'(t)。

Step S4 includes:

s4.1, carrying out centralized processing on input data and output data of a k' th window:

wherein u'_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window after the centering process, u_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window that is not centered,

mean vector, y ' of process input vectors representing the t sample time instant of the k ' th window '_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window after the centering process, y_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window that is not centered,

the mean vector of the process output vectors at the t-th sampling instant of the k' -th window is represented.

S4.2, calculating an estimated value of white noise under an actual working condition: epsilon_h,k'(t)＝y′_P,k'(t){I-Y′_P,k'(t)^T[Y′_P,k'(t)Y′_P,k'(t)^T]^-1Y′_P,k'(t) }, in which ε_h,k'(t) represents an actual working condition white noise estimated value y 'of the acquired kth sampling moment of the kth window'_P,k'(t)＝[y′_k'(t) … y′_k'(t-P+1)]Represents the process output vector y ' using the centered k ' th window '_k'(t) constructed data vector, Y'_P,k'(t)＝[y′_P,k'(t-1)^T … y′_P,k'(t-L)^T]^TIs represented by a data vector y'_P,k'(t) the constructed data matrix.

S4.3, constructing an autoregressive moving average model of the out-of-band source input of the process output vector of the kth window:

wherein the content of the first and second substances,

which is indicative of the delay factor, is,

the coefficients of the auto-regressions are represented,

the coefficient representing the input of an external source,

coefficient representing moving average, I_k'Represents the maximum order of autoregressive, K_k'Represents the maximum order of exogenous input; j. the design is a square_k'Representing the maximum order of the moving average.

S4.4, acquiring coefficient vectors and orders of the autoregressive moving average model with out-of-band source input according to the adaptive minimum absolute value contraction and operator selection method:

wherein the content of the first and second substances,

W_k'which represents the window size of the sampled data,

represents W_k'A data matrix of x 1 dimensions is formed,

represents W_k'×(I_k'+K_k'+J_k') A dimensional data matrix;

the method representing the adaptive minimum absolute value shrinkage and selection operator estimates the coefficient vector of the autoregressive moving average model, i.e.

Coefficient, phi, representing the estimated autoregressive moving average model_k'A coefficient vector representing a real but unknown type of auto-regressive moving average,

j-th coefficient phi in coefficients representing autoregressive moving average model_j,k'The weighting factor of (2).

S4.5, obtaining an estimated value of the actual working condition disturbance model according to the autoregressive moving average model with out-of-band source input:

wherein the content of the first and second substances,

and representing the estimated value of the actual working condition disturbance model of the k' th window.

S4.6, calculating the residual error of the actual working condition model:

wherein v is_h,k'(t) represents the real model residual at the t-th sampling instant of the k' -th window,

actual condition disturbance model representing k' th windowEstimated value

Inverse of (y)_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window, u_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window, G_m,k′(q^-1) Representing the process model used by the EWMA batch controller in the k' th window.

S5, according to the reference working condition white noise estimated value epsilon in the step S1_rAnd the white noise estimate of the actual condition ε in step S4_h,k'(t) calculating an interference characteristic monitoring quantity

According to the reference working condition model residual v in the step S3_r,k'(t) and the actual condition model residual v in step S4_h,k'(t) calculating the amount of monitoring of the disturbance model

According to the actual working condition white noise estimated value epsilon in the step S4_h,k'(t) and actual condition model residual v_h,k'(t) obtaining a model mismatch monitoring quantity

Step S5 includes:

s5.1, calculating interference characteristic monitoring quantity

Wherein epsilon_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,k'(t) represents the actual condition white noise estimate at the t-th sampling time in the k' -th window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix.

S5.2, calculating the monitoring quantity of the disturbance model

Wherein the content of the first and second substances,

representing the monitored amount of the perturbation model for the k' th window,

has a value range of (0, 1)]If, if

Near or equal to 1, the perturbation model is unchanged, v_r,k'(t) represents the reference condition model residual at the t-th sampling instant in the k' -th window, v_h,k'(t) represents the actual condition model residual at the t-th sampling instant in the k' -th window, J (f (v)_r,k'(t)),g(v_h,k'(t))) represents v_h,k'(t) and v_r,k'(t) KL divergence, expressed as:

wherein, f (v)_r,k'(t)) represents v constructed using the nuclear density estimation method_r,k'(t) probability density function, f (v)_h,k'(t)) represents v obtained by the nuclear density estimation method_h,k'(t) probability density function, i ═ 1^,2,…,N_f，N_fRepresenting the total number of independent identically distributed sample points produced by the kernel density estimate.

S5.3, calculating model mismatch monitoring quantity

Wherein epsilon_h,k'(t) represents the white noise estimate of the actual condition at the t-th sampling instant in the k' -th window, v_h,k'(t) represents the real-world model residual at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (v)_h,k'(t)) | denotes v_h,k'(t) covariance matrixDeterminant (c).

S6, respectively obtaining the control upper limit UP of the control performance monitoring quantity by adopting a kernel density estimation method_CPIUpper control limit UP of combined monitoring quantity of model mismatch/disturbance dynamics_PDMIUpper limit UP of control of the monitored quantity of interference characteristics_DVILower limit of control LP of disturbance characteristic monitoring amount_DVILower control limit LP of disturbance model monitoring quantity_DMIAnd the upper control limit UP of the model mismatch monitoring quantity_PMI。

Step S6 includes:

s6.1, calculating the control upper limit UP of the control performance monitoring quantity_CPI：

Wherein the content of the first and second substances,

the control performance monitoring amount corresponding to the kth window is K ', K' is 2,3, …, S +1, h represents the kernel bandwidth, and K (·) represents the kernel density estimation with the kernel being a radial basis function.

S6.2, calculating the control upper limit UP of the model mismatch/disturbance dynamic combined monitoring quantity_PDMI：

Wherein the content of the first and second substances,

is the model mismatch/disturbance dynamic joint monitoring quantity corresponding to the k' th window.

S6.3, calculating the control upper limit UP of the interference characteristic monitoring quantity_DVIAnd a lower control limit LP_DVI：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the k' th window.

S6.4, calculating a control lower limit LP of the monitoring quantity of the disturbance model_DMI：

Wherein the content of the first and second substances,

is the perturbation model monitoring quantity corresponding to the kth' window.

S6.5, calculating the control upper limit UP of the model mismatch monitoring quantity_PMI：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the k' th window.

S7, collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line, and obtaining the control performance monitoring quantity eta of the current working condition_CPIAccording to the control upper limit UP in step S6_CPIAnd judging whether the control performance of the closed-loop system is reduced or not in real time.

Step S7 includes:

s7.1, collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line as actual working condition sample data, and dividing the actual working condition sample data into S₁An online window, each window containing n groups of samples, wherein S₁＝N1-n+1。

S7.2, calculating the residual error of the online process-disturbance combined model: e.g. of the type_l(^t)＝y_l(t)-G_m,l(q^-1)u_l(t) in which e_l(t) represents the on-line process-perturbation joint model residual error at the tth sampling instant of the ith window, y_l(t) represents the process output vector at the tth sampling instant of the l-th window, u_l(t) denotes the input vector at the tth sampling instant of the l-th window, t denotes the sampling instant, G_m,l(q^-1) Representing a Process model, q, used by an EWMA batch-to-batch controller in an on-line regime^-1Denotes a difference operator, where l is 1,2, …, S₁。

S7.3, acquiring a process input data set of the current working condition by using the process output vector, the process input vector and the process-disturbance combined model residual error which are acquired in real time

And output data set Y_l ⁰：

Wherein the content of the first and second substances,

representing the on-line process input vector and,

representing the on-line process-perturbation joint model residual vector,

representing an online process output vector.

S7.4, constructing a matrix X_lAnd Y_l：

Wherein u is_i,lRepresents the process input vector, u ″, in the ith window of the online data_i,lThe process input vector representing the normalized l-th window, i.e.

y_j,lRepresents the process output vector, y ″, of the ith window of online data_j,lThe process output vector representing the normalized l-th window, i.e.

e_j,lRepresenting the ith window of online dataProcess-perturbation joint model residual vector, e_j,l＝(e_j,l(t))，e_j,l(t)＝y_j,l(t)-(G_m,l(q^-1))_ju_l(t)，(G_m,l(q^-1))_jProcess model G representing EWMA inter-batch controller usage in the ith window of online data_m，l(q^-1) J-th line of (1), y_j,l(t) denotes the jth process output at the tth sampling instant of the ith window of online data, u_l(t) represents the vector formed by all process inputs at the tth sampling time of the ith window of online data, e ″_j,lRepresenting the normalized process-perturbation joint model residual,

s7.5, constructing a Hankel matrix X_p,lAnd X_f,l：

Wherein p is_p+1,lRepresenting a history data vector at the p +1 th sampling instant in the ith window of line data, i.e. p_p+1,l＝[x_l(p)^T … x_l(1)^T y_l(p)^T … y_l(1)^T]^T，x_l(p) a representation matrix

P column of (2), x_l(1) Representation matrix

The p-th column of (2),

representation matrix X_lTranspose of (y)_l(p) represents a matrix Y_l ^TP column, y_l(1) Representation matrix Y_l ^TColumn 1, Y_l ^TRepresentation matrix Y_lIs transferred to；f_p+1,lThe vector of predicted data representing the p +1 th sampling instant in the l window of line data, i.e. f_p+1,l＝[y_l(p+1)^T y_l(p+2)^T … y_l(p+f-1)^T]^T，y_l(p +1) represents Y_l ^TP +1 column, y_l(p +2) represents Y_l ^TP +2 column, y_l(p + f-1) represents Y_l ^TColumn p + f-1.

S7.6, acquiring control performance monitoring quantity eta of the current working condition by using online data_CPI：

Wherein the content of the first and second substances,

control performance monitor quantity, p, representing the current operating condition corresponding to the ith window_k,lRepresentation matrix X_p,lThe kth column vector of (1).

S7.7, control Upper Limit UP according to control Performance monitoring amount_CPIJudgment of

Whether or not less than UP_CPIIf, if

Less than UP_CPIThen the system performance is better, if

Greater than UP_CPIThe system performance is degraded.

S8, if the control performance monitoring quantity eta_CPIControl upper limit UP greater than control performance monitoring amount_CPIIf the performance of the EWMA batch control system is degraded, the step S9 is executed, otherwise, the performance of the EWMA batch control system is good.

S9, using the reference working condition disturbance model estimated value in the step S1

The N1 groups of input data and output data in the step S7 acquire the model mismatch/disturbance dynamic combined monitoring quantity eta of the current working condition_PDMI。

Step S9 includes:

s9.1, obtaining a reference working condition model residual error by using online data:

wherein v is_r,l(t) represents the reference condition model residual error at the tth sampling time of the ith window of the online data,

and representing the reference working condition disturbance model estimation value.

S9.2, calculating model mismatch/disturbance dynamic combined monitoring quantity eta_PDMI：

Wherein the content of the first and second substances,

has a value range of (0, 1)]，ε_r(t) represents the white noise estimate for the baseline condition, | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix, v_r,l(t) represents the reference condition model residual at the tth sampling instant, | cov (v)_r,l(t)) | denotes v_r,l(t) determinant of covariance matrix.

S9.3, combining control upper limit UP of model mismatch/disturbance dynamic joint monitoring quantity_PDMIThe factors for controlling the performance degradation are preliminarily diagnosed if the current working condition is met

Greater than UP_PDMIIf the model mismatch or the external disturbance dynamics is changed, the system performance is reduced due to the model mismatch or the external disturbance dynamics; if the current operating condition is

Less than UP_PDMIThen changes in the controller parameters are a factor that causes degradation in system performance.

S10, if the model mismatching/disturbance dynamic joint monitoring quantity eta_PDMIControl upper limit UP larger than the model mismatch/disturbance dynamic joint monitoring amount in step S6_PDMIIf the model mismatch or disturbance dynamics results in performance degradation of the EWMA batch control system, step S11 is executed, otherwise, the controller parameter change results in performance degradation of the EWMA batch control system.

S11, calculating the disturbance characteristic monitoring quantity eta of the current working condition_DVIDisturbance model monitoring quantity eta_DMIAnd model mismatch monitor η_PMI(ii) a Disturbance characteristic monitoring quantity eta when current working condition_DVIGreater than the upper control limit UP of the disturbance characteristic monitoring amount in step S6_DVIOr less than the lower control limit LP of the disturbance characteristic monitored quantity_DVIWhen the interference characteristic changes, the performance of the EWMA batch control system is reduced; when the disturbance model monitors the quantity eta_DMILower control limit LP less than disturbance model monitoring amount_DMIMeanwhile, the performance of the EWMA batch control system is reduced due to the change of the disturbance model; when model mismatch monitor eta_PMIControl upper limit UP greater than model mismatch monitoring amount_PMIModel mismatch results in performance degradation of the EWMA batch-to-batch control system.

Step S11 includes:

s11.1, calculating interference characteristic monitoring quantity eta of online data_DVI：

Wherein the content of the first and second substances,

representing the interference characteristic monitoring quantity of the on-line data corresponding to the ith window, representing the change of white noise variance in actual working condition_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,l(t) represents the white noise estimate for the actual condition at the tth sampling instant, | cov (ε_h,l(t)) | denotes ε_h,l(t) covariance matrix determinant, | cov (ε_r(t)) | denotes ε_r(t) Is determined by the covariance matrix determinant.

S11.2, calculating the actual working condition model residual error of the online data:

wherein v is_h,l(t) represents the model residual error of the online data actual condition corresponding to the ith window,

on-line data actual condition disturbance model estimation value y representing ith window_l(t) an online data process output vector, u, at the tth sampling instant of the ith window_l(t) an online data process input vector at the tth sampling instant, G, for the ith window_m,l(q^-1) Representing a process model used by the EWMA batch controller in the ith window of the online data;

s11.3, calculating disturbance model monitoring quantity eta of online data_DMI：

Wherein the content of the first and second substances,

representing the monitored quantity, v, of the disturbance model corresponding to the l-th window_r,l(t) represents the on-line data reference condition model residual at the tth sampling instant of the ith window, v_h,l(t) represents the on-line data real-time model residual error at the tth sampling time of the ith window, J (f (v)_r,l(t)),g(v_h,l(t))) represents v_h,l(t) and v_r,l(t) KL divergence.

S11.4, calculating model mismatch monitoring quantity eta of online data_PMI：

Wherein the content of the first and second substances,

model mismatch monitoring quantity, epsilon, of the on-line data corresponding to the ith window of the on-line data_h,l(t) represents the white noise estimate of the actual condition at the tth sampling time of the ith window of the on-line data, v_h,l(t) represents the model residual of the actual conditions at the t-th sampling instant of the l windows of online data, cov (ε_h,l(t)) represents ε_h,l(t) determinant of covariance matrix, cov (v)_h,l(t)) represents v_h,l(t) determinant of covariance matrix.

S11.5, combining the lower control limit LP of the interference characteristic monitoring quantity_DVIUpper limit UP of control of the monitored quantity of interference characteristics_DVILower control limit LP of disturbance model monitoring quantity_DMIAnd upper control limit UP of model mismatch monitoring quantity_PMIFurther diagnosing and identifying the factors causing the performance degradation of the EWMA batch-to-batch control system, and if the characteristic monitoring quantity is disturbed

Greater than UP_DVIOr less than LP_DVIIf so, the white noise variance changes to cause the performance of the EWMA batch-to-batch control system to be reduced; if the model monitoring quantity is disturbed

Less than LP_DMIIf so, the performance of the EWMA batch control system is reduced due to the change of the external disturbance model; monitoring quantity if model mismatch

Greater than UP_PMIThen the model mismatch causes the EWMA inter-batch control system performance to degrade.

Specific example 1

Chemical-mechanical planarization (CMP) is the planarization method of choice in the semiconductor industry today, as shown in figure 2. In 1989, Davari et al developed a CMP process for global planarization of interlevel dielectrics. In the early 90 s of the 20 th century, IBM successfully addressed the problem of slow dry etching of copper using the CMP process. In addition, CMP has been integrated with the dual-damascen process to simplify the fabrication steps of conductive lines between successive layers of a multi-layer integrated circuit. As wafer sizes increase to 300 mm or more, equipment and process designs improve to address these issues. In addition, as the fierce semiconductor market has an increasing demand for high performance products, the quality of semiconductor products is also increasingly important as manufacturers increase. This example uses a simulated CMP process. The discrete model of the CMP process is described as follows:

where θ is 0.65, and ∈ (t) ∈ N (0,100). According to the above formula, the process has a manipulated variable and a controlled variable, wherein the manipulated variable u (t) is the platen rotation speed and the controlled variable y (t) is the removal rate. The removal rate y (t) represents the average of the difference between the initial and final phosphosilicate glass thickness on the wafer. An EWMA inter-batch controller is used to control the removal rate during CMP. The EWMA batch controller consists of an EWMA filter and a minimum beat control rule, and is as follows:

wherein, a (t) represents the output of the EWMA filter, t represents the sampling time, lambda represents the adjusting parameter of the EWMA batch controller, b represents the coefficient of the process model in the EWMA batch controller, tau represents the set value of the controlled variable y (t), and u (t-1) represents the manipulated variable at the t-1 sampling time.

The control performance diagnosis method of the semiconductor process batch control system based on the model residual error provided by the invention is used for diagnosing the control performance of the CMP process, and comprises the following steps:

(1) the method comprises the steps of collecting 1000 groups of input data and output data of historical normal working conditions in a semiconductor manufacturing process of an EWMA batch controller as standard working condition sample data, and obtaining process input data and process output data after centralized processing.

The reference working condition sample data is divided into S +1 windows, and each window comprises 500 groups of samples, wherein S is 500. First, the mean value of the process input data is obtained, and the calculation formula is

Then, 500 sets of process input data after the centralization are obtained:

according to 500 sets of collected process output data, firstly, obtaining a mean value of process output, wherein a calculation formula is as follows:

then, 500 sets of process output data after centralization are obtained, and the calculation formula is as follows:

(2) acquiring an estimated value of white noise of a reference working condition;

firstly, outputting a data vector constructed by y' (t) according to the centralization processing process acquired in the step (1): y'_P(t)＝[y′(t) … y′(t-P+1)](ii) a Then, by vector y'_P(t) constructed data matrix: y'_P(t)＝[y′_P(t-1)^T … y′_P(t-L)^T]^TWhere P denotes the data window size of the estimated white noise. Obtaining an estimated value of the white noise of the reference working condition according to the following formula: epsilon_r(t)＝y′_P(t){I-Y′_P(t)^T[Y′_P(t)Y′_P(t)^T]^-1Y′_P(t)}。

(3) Obtaining a reference working condition disturbance model estimation value;

(3.1) obtaining an autoregressive moving average model of the out-of-band source input of the centralized process output according to the following formula:

wherein the content of the first and second substances,

denotes a delay factor, phi₁，…，φ_ICoefficient of autoregressive representation_I+1，…，φ_I+KCoefficient of exogenous input, phi_I+K+1，…，φ_I+K+JRepresenting the coefficient of the moving average, I representing the maximum order of autoregressive, and K representing the maximum order of exogenous input; j represents the maximum order of the moving average, y '(t) represents the process output after the centering process obtained in step (1), u' (t) represents the process input after the centering process obtained in step (1), ε_rAnd (t) representing the reference working condition white noise estimated value obtained in the step (2).

(3.2) according to the self-adaptive minimum absolute value contraction and operator selection method, obtaining the coefficient vector and the order of the autoregressive moving average model with out-of-band source input:

wherein the content of the first and second substances,

Y_W(t)＝[y′(t) … y′(t-W+1)]^T(ii) a W denotes the window size of the sampled data, Y_W(t) denotes a W × 1-dimensional data matrix, H_W(t) represents a W × (I + K + J) dimensional data matrix; y '(t) represents the process output after the centering process, u' (t) represents the process input after the centering process, ε_r(t) represents the acquired white noise estimate of the reference condition,

the method representing the adaptive minimum absolute value shrinkage and selection operator estimates the coefficient vector of the autoregressive moving average model, i.e.

Representing the coefficients of the estimated autoregressive moving average model, I representing the maximum order of the autoregressive portion, and K representing the maximum order of the exogenous input portion; j denotes the maximum order of the moving average part, phi denotes the coefficient vector of the actual but unknown autoregressive moving average type, phi ═ phi₁,…,φ_I+K+J]λ denotes an adjustable parameter controlling the penalty factor in the adaptive minimum absolute value shrinkage and selection operator method,

j-th coefficient phi in coefficients representing autoregressive moving average model_jThe weighting factor of (2).

(3.3) according to the autoregressive moving average model of the out-of-band source input estimated in the step (3.2), acquiring a reference working condition disturbance model estimated value according to the following formula:

wherein the content of the first and second substances,

coefficients representing the above estimated autoregressive portion and moving average portion, coefficients of an autoregressive moving average model,

and representing the reference working condition disturbance model estimation value.

(4) Obtaining process-disturbance combined model residual

Obtaining a process-perturbation combined model residual error of the first window according to the following formula: e (t) ═ y (t) — G_m(q^-1) u (t); wherein e (t) represents the process-perturbation combined model residual error, y (t) represents the process output at the t-th sampling moment, u (t) represents the process input at the t-th sampling moment, G_m(q^-1) Representing the process model used by the EWMA batch controller in the first window, q^-1A difference operator is represented.

(5) Construction of Hankel matrix X_pAnd X_f

(5.1) acquiring a process data set of the reference working condition according to the following formula by using the process output, the process input and the process-disturbance combined model residual error of the first window

And output data set Y₁ ⁰：

Wherein the content of the first and second substances,

representing the process input vector, m_uThe number of the input variables is represented,

representing the process-perturbation joint model residual vector,

representing the process output vector, m_yDenotes the number of output variables, m_y＝1。

(5.2) obtaining a process input mean vector and a standard deviation vector of the first window according to the following formula:

wherein the content of the first and second substances,

is the mean vector, σ, of the process inputs at the t-th sampling instant of the first window_u,rThe standard deviation vector of the process input, m, for the first window_uDenotes the number of input variables, m_u＝1，m_yDenotes the number of input variables, m_yT denotes the sampling time, n denotes the number of samples of the first window, n is 500, u₁(t) represents a first input variable,

denotes the m-th_uAn input variable; obtaining a mean vector and a standard deviation vector output by a first window process according to the following formula:

wherein the content of the first and second substances,

is the mean vector, σ, of the process outputs at the t-th sampling instant of the first window_y,rThe standard deviation vector of the process output of the first window, m_yDenotes the number of output variables, m_yN denotes the number of samples of the first window, n is 500, y₁(t) represents a first output variable,

denotes the m-th_yAn output variable; obtaining a mean vector and a standard deviation vector of a first window process-disturbance combined model residual error according to the following formula:

wherein the content of the first and second substances,

mean vector, σ, of the process-perturbation combined model residuals for the first window_e,rStandard deviation vector of process-perturbation combined model residual error of first window, m_yTo representNumber of output variables, m_y＝1，e₁(t) represents the first process-perturbation joint model residual,

denotes the m-th_yProcess-perturbation joint model residuals.

(5.3) constructing the matrix X according to the following equation₁And Y₁

Wherein u is_iRepresents the ith process input vector, i 1, …, m_u，u″_iRepresenting the i-th process input vector after normalization, i.e.

Means representing the ith process input vector, (σ)_u,r)_iRepresents the standard deviation of the ith process input vector; y is_jRepresents the jth process output vector, j ═ 1, …, m_y，y″_jRepresenting the normalized jth process output vector, i.e.

Means for representing the jth process output vector, (σ)_y,r)_jRepresents the standard deviation of the jth process output vector; e.g. of the type_j(t) denotes the j-th process-perturbation joint model residual vector, j is 1, …, m_y，e_j＝(e_j(t))，e_j(t)＝y_j(t)-(G_m(q^-1))_ju_j(t)，(G_m(q^-1))_jRepresentation process model G_m(q^-1) J-th line of (1), y_j(t) denotes the jth process output at the tth sampling instant u_j(t) denotes the process input at the tth sampling instant, e ″_jRepresents the normalized jth process-perturbation joint model residual vector,

represents the mean of the jth process-perturbation combined model residual, (σ)_e,r)_jRepresents the standard deviation of the jth process-perturbation combined model residual.

(5.4) construction of Hankel matrix X according to the following formula_pAnd X_f：

Wherein m is m_u+2m_y，p_p+1Representing the historical data vector at the p +1 th sampling instant, i.e. p_p+1＝[x(p)^T … x(1)^T y(p)^T … y(1)^T]^TX (p) represents a matrix

P column of (2), x (1) represents a matrix

The number 1. sup. st column of (a),

representation matrix X₁Y (p) denotes a matrix Y₁ ^TY (1) denotes the matrix Y₁ ^TColumn 1, Y₁ ^TRepresentation matrix Y₁Transposing; f. of_p+1The vector of prediction data representing the p +1 th sampling instant, i.e. f_p+1＝[y(p+1)^T y(p+2)^T … y(p+f-1)^T]^TY (p +1) represents Y₁ ^TColumn p +1, Y (p +2) represents Y₁ ^TIn the p +2 th column, Y (p + f-1) represents Y₁ ^TColumn p + f-1, M indicates the number of vectors of the history data vector and the prediction data vector constructed from n sets of observation data, M is n-p-f +1, n is 500, p is 10, f is 10, and M is 481.

(6) Obtaining a projection matrix J_q

(6.1) obtaining the unitary matrix V according to: h ═ U ∑ V^TWherein V represents the moment of alignmentA unitary matrix constructed when the matrix H is subjected to singular value decomposition,

is represented by X_pAnd X_fThe constructed matrix Hankel matrix is used as a matrix,

a sample covariance representing the vector of historical data,

represents the sample covariance of the prediction data vector,

representing the cross covariance of the historical data vector and the predicted data vector.

(6.2) obtaining the projection matrix J according to the following formula_q：

Wherein, V_qRepresenting a matrix constructed from the first q columns of the unitary matrix V,

represents the Hankel matrix X_pThe covariance matrix of (2).

(7) Obtaining process-perturbation joint model residuals for the kth window, k ═ 2,3, …, S +1

Acquiring a process-disturbance combined model residual error of the kth window by using the input and output data of the kth window acquired in the step (1): e.g. of a cylinder_k'(t)＝y_k'(t)-G_m,k'(q^-1)u_k'(t) wherein e_k'(t) represents the process-perturbation joint model residual at the tth sampling instant of the kth' window, y_k'(t) denotes the kth' window process output vector at the tth sampling instant u_k'(t) represents the process input vector for the kth window at the tth sampling instant, G_m,k'(q^-1) Representing the process model used by the EWMA batch controller in the current operating regime, and q-1 representing the difference operator.

(8) Construction of a Hankel matrix X according to the following formula_p,k'And X_f,k'

(8.1) acquiring a process input dataset according to

And outputting the data set

Wherein the content of the first and second substances,

process input vector, m, representing the kth window_uDenotes the number of input variables, m_u＝1，

The process-perturbation joint model residual vector representing the kth window,

process output vector, m, representing the kth window_yDenotes the number of output variables, m_y＝1。

(8.2) constructing matrix X_k'And Y_k'：

Wherein u is_i,k'The process input vector, u ", representing the k' th window_i,k'The process input vector representing the normalized k' th window, i.e.

y_j,k'Process output vector, y ', representing the kth ' window '_j′_,k'After representation standardizationThe process output vector of the kth' window of (1), i.e.

e_j,k'(t) Process-perturbation Joint model residual error, e, for the kth window_j,k'＝(e_j,k'(t))，e_j,k'(t)＝y_j,k'(t)-(G_m,k′(q^-1))_ju_k'(t)，y_j,k'(t) represents the jth process output at the tth sampling instant in the kth' window, u_k'(t) represents the column vector formed by all process inputs at the tth sampling instant in the kth window, (G)_m,k′(q^-1))_jRepresents G_m，k′(q^-1) Line j, e ″)_j,k'Representing the process-perturbation combined model residual of the normalized k' th window, i.e.

(8.3) construction of Hankel matrix X according to the following formula_p,k'And X_f,k'：

Wherein p is_p+1kRepresenting the historical data vector at the p +1 th sampling instant, i.e. p_p+1,k'＝[x_k'(p)^T … x_k'(1)^Ty_k'(p)^T … y_k'(1)^T]^T，x_k'(p) representation matrix

P column of (2), x_k'(1) Representation matrix

The number 1. sup. st column of (a),

representation matrix X_k'Transpose of (y)_k'(p) a representation matrix

P column, y_k'(1) Representation matrix

The number 1. sup. st column of (a),

representation matrix Y_k'Transposing; f. of_p+1,k'Representing the vector of predicted data at the p +1 th sampling instant in the k' th window, i.e. f_p+1,k'＝[y_(k')(p+1)^T y_(k')(p+2)^T … y_(k')(p+f-1)^T]^T，y_(k')(p +1) represents

P +1 column, y_(k')(p +2) represents

P +2 column, y_(k')(p + f-1) represents

Column p + f-1, M indicates the number of vectors of past and future data vectors constructed from n sets of observation data, M is n-p-f +1, n is 500, p is 10, f is 10, and M is 481.

(9) Obtaining a control performance monitoring index eta of an EWMA batch control system_CPIIndex (I)

Acquiring a control performance monitoring index eta of an EWMA batch control system according to the following formula_CPIIndexes are as follows:

wherein the content of the first and second substances,

represents the amount of control performance monitoring, J, of the EWMA batch-to-batch control system corresponding to the kth window_qRepresenting a projection matrix, p_k,k'Representation matrix X_p,k'The k-th column of (1).

(10) Obtaining a reference condition model residual error

Using formulas

Obtaining a reference condition model residual error of the kth sampling moment of the kth window, wherein,

representing the reference condition disturbance model estimated value y in the step (3.3)_k'(t) represents the process output vector of the kth window at the tth sampling instant u_k'(t) represents the process input vector for the kth window at the tth sampling instant, G_m,k'(q^-1) Representing the process model used by the EWMA batch controller in the k' th window.

(11) Obtaining model mismatch/disturbance dynamic combined monitoring quantity

Using formulas

Obtaining the model mismatch/disturbance dynamic combined monitoring quantity, wherein,

represents the model mismatch/disturbance dynamic joint monitoring quantity corresponding to the k' th window,

has a value range of (0, 1)]，ε_r(t) white noise estimate for the reference condition at the tth sampling time, cov (ε_r(t)) represents ε_rCovariance of (t), cov (v)_r,k'(t)) represents v_r,k'(t) covariance.

(12) Centralizing the closed-loop input and output data of the k' th window

Input and output data in closed loop using the k' th windowThe closed loop input and process output are respectively centered as follows:

wherein u'_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window after the centering process, u_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window that is not centered,

mean vector, m, representing the process input at the t-th sampling instant of the k' -th window_uDenotes the number of input variables, m _u1, t denotes the t-th sampling time, n denotes the number of samples of the k '-th window, and n is 500, y'_k'(t) represents the process output vector, y, of the k' th window after centering_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window that is not centered,

mean vector, m, representing process output at the t-th sampling instant_yDenotes the number of output variables, m_y＝1。

(13) Obtaining the estimated value of white noise of actual working condition

First, y 'is output according to the centralized process obtained in step (12)'_k'(t) constructed data vector: y'_P,k'(t)＝[y′_k'(t) … y′_k'(t-P+1)](ii) a Then, by vector y'_P,k'(t) constructed data matrix: y'_P,k'(t)＝[y′_P,k'(t-1)^T … y′_P,k'(t-L)^T]^TWhere P denotes the data window size of the estimated white noise. According to the formula, an estimated value epsilon of white noise of the reference working condition is obtained_h,k'(t)＝y′_P,k'(t){I-Y′_P,k'(t)^T[Y′_P,k'(t)Y′_P,k'(t)^T]^-1Y′_P,k'(t)}。

(14) Obtaining an estimated value of a disturbance model of an actual working condition

(14.1) obtaining an autoregressive moving average model of the out-of-band source input for the process output of the kth window according to:

wherein the content of the first and second substances,

which is indicative of the delay factor, is,

the coefficients of the auto-regressions are represented,

the coefficient representing the input of an external source,

coefficient representing moving average, I_k'Represents the maximum order of autoregressive, K_k'Represents the maximum order of exogenous input; j. the design is a square_k'Represents the maximum order of the moving average;

(14.2) according to the self-adaptive minimum absolute value contraction and operator selection method, obtaining the coefficient vector and the order of the autoregressive moving average model input by the out-of-band source in the step (4.3):

wherein the content of the first and second substances,

W_k'which represents the window size of the sampled data,

represents W_k'A data matrix of x 1 dimensions is formed,

represents W_k'×(I_k'+K_k'+J_k') A dimensional data matrix;

the coefficient vector representing the adaptive minimum absolute value shrinkage and selection operator method for estimating the autoregressive moving average model, i.e.

Coefficient, phi, representing the estimated autoregressive moving average model_k'A coefficient vector representing an actual but unknown type of autoregressive moving average,

j-th coefficient phi in coefficients representing autoregressive moving average model_j,k'The weighting factor of (2).

(14.3) obtaining an estimated value of the actual working condition disturbance model according to the autoregressive moving average model of the out-of-band source input obtained in the step (13.2):

wherein the content of the first and second substances,

representing the coefficients of the auto-regressive part and the coefficients of the moving average part estimated in step (13.2),

and representing the estimation value of the actual condition disturbance model.

(15) Obtaining a model residual error of an actual working condition:

using formulas

Wherein the content of the first and second substances,

representing the actual condition disturbance model estimated value, G, obtained by the step (14.3)_m,k′(q^-1) Representing the process model used by the EWMA batch controller in the k' th window.

(16) Obtaining interference characteristic monitoring quantity eta_DVI

Using formulas

Obtaining interference characteristic monitoring quantity

Wherein epsilon_h,k'(t) represents the white noise estimate for the actual condition at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix.

(17) Obtaining a monitoring quantity eta of the disturbance model_DMI

Using formulas

Obtaining disturbance model monitoring quantity based on KL divergence

Has a value range of (0, 1)]If, if

Near or equal to 1, the perturbation model is unchanged, v_rk'(t) reference condition model residual, v, at the tth sampling time_h,k'(t) represents the actual condition model residual at the t-th sampling instant in the k' -th window, J (f (v)_r,k'(t)),g(v_h,k'(t))) represents v_h,k'(t) and v_r,k'(t) KL divergence, expressed as:

wherein, f (v)_r,k'(t)) represents v constructed using a kernel density estimation method_r,k'(t) probability density function, f (v)_h,k'(t)) represents v obtained by the nuclear density estimation method_h,k'(t) probability density function, i ═ 1,2, …, N_f，N_fRepresenting the total number of independent identically distributed sample points produced by the kernel density estimate.

(18) Obtaining model mismatch monitoring quantity eta_PMI

Using formulas

Obtaining model mismatch monitoring quantity

Wherein epsilon_h,k'(t) represents the white noise estimate of the actual condition at the t-th sampling instant in the k' -th window, v_h,k'(t) represents the real-world model residual at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (v)_h,k'(t)) | denotes v_h,k'(t) determinant of covariance matrix.

(19) Obtaining control limits of control performance monitoring quantity, model mismatch/disturbance dynamic monitoring quantity, interference characteristic monitoring quantity, disturbance model monitoring quantity and model mismatch monitoring quantity

(19.1) obtaining the control upper limit UP of the control performance monitoring amount according to the following formula_CPI：

Wherein the content of the first and second substances,

is the control performance monitoring amount corresponding to the kth window, K' is 2, 3.., S +1, h represents the kernel bandwidth, and K (·) represents the kernel density estimation with the kernel being a radial basis function.

(19.2) obtaining the control of the model mismatch/disturbance dynamic combined monitoring quantity according to the following formulaUpper limit UP_{P D M}：

Wherein the content of the first and second substances,

is the model mismatch/disturbance dynamic joint monitoring quantity corresponding to the k' th window.

(19.3) obtaining the control upper limit UP of the disturbance characteristic monitoring amount according to the following formula_{D V}And a lower control limit LP_{D V}：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the k' th window.

(19.4) obtaining the lower control limit LP of the disturbance model monitored quantity according to the following formula_{D M}：

Wherein the content of the first and second substances,

is the disturbance model monitoring quantity corresponding to the k' th window.

(19.5) obtaining the control upper limit UP of the model mismatch monitoring amount according to the following formula_PMI：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the k' th window.

(20) Construction of Hankel matrix X_p,lAnd X_f,l

(20.1) collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line as actual working condition sample data, and counting the actual working condition sample dataAccording to the division into S₁An online window, each window containing n groups of samples, wherein S₁＝N1-n+1。

(20.2) obtaining an online process-disturbance combined model residual according to the following formula:

e_l(t)＝y_l(t)-G_m,l(q^-1)u_l(t)，

wherein e is_l(t) represents the on-line process-perturbation joint model residual error at the tth sampling instant of the ith window, y_l(t) represents the process output vector at the tth sampling instant of the ith window, u_l(t) denotes the input vector at the tth sampling instant of the l-th window, t denotes the sampling instant, G_m(q^-1) Representing the Process model, q, used by the EWMA batch controller in the Current operating regime^-1Denotes the difference operator, l 1,2, …, S₁。

(20.3) acquiring a process input data set of the current working condition by using the process output vector, the process input vector and the process-disturbance combined model residual error which are acquired in real time

And output data set Y_l ⁰：

Wherein the content of the first and second substances,

representing an online process input vector, m_u＝1，

Representing the on-line process-perturbation joint model residual vector,

representing the on-line process output vector, m_y＝1。

(20.4) constructing matrix X according to_lAnd Y_l：

Wherein u is_i,lThe process input vector, u ", representing the ith window of online data_i,lThe process input vector representing the normalized l-th window, i.e.

y_j,lRepresents the process output vector, y ″, of the ith window of online data_j,lThe process output vector representing the normalized l-th window, i.e.

e_j,lProcess-perturbation joint model residual vector representing the ith window of online data, e_j,l＝(e_j,l(t))，e_j,l(t)＝y_j,l(t)-(G_m,l(q^-1))_ju_l(t)，(G_m,l(q^-1))_jProcess model G representing EWMA inter-batch controller usage in the ith window of online data_m，l(q^-1) J-th line of (1), y_j,l(t) denotes the jth process output at the tth sampling instant of the ith window of online data, u_l(t) represents the vector of all process inputs at the tth sampling instant of the ith window of online data, e'_j′_,lRepresenting the normalized process-perturbation joint model residual,

(20.5) construction of Hankel matrix X according to the following formula_p,lAnd X_f,l：

Wherein p is_p+1,lRepresenting the history of the p +1 th sampling instant in the ith window of online dataData vectors, i.e. p_p+1,l＝[x_l(p)^T … x_l(1)^T y_l(p)^T … y_l(1)^T]^T，x_l(p) a representation matrix

P column of (2), x_l(1) Representation matrix

The p-th column of (2),

representation matrix X_lTranspose of (a), y_l(p) represents a matrix Y_l ^TP column, y_l(1) Representation matrix Y_l ^TColumn 1, Y_l ^TRepresentation matrix Y_lTransposing; f. of_p+1,lThe vector of predicted data representing the p +1 th sampling instant in the l window of line data, i.e. f_p+1,l＝[y_l(p+1)^T y_l(p+2)^T … y_l(p+f-1)^T]^T，y_l(p +1) represents Y_l ^TP +1 column, y_l(p +2) represents Y_l ^TP +2 column, y_l(p + f-1) represents Y_l ^TColumn p + f-1, M indicates the number of vectors of past and future data vectors constructed from n sets of observation data, M is n-p-f +1, n is 500, p is 10, f is 10, and M is 481.

(21) Monitoring control performance of EWMA batch-to-batch control system

Obtaining the control performance monitoring quantity eta of the current working condition according to the following formula by utilizing the online data_CPI：

Wherein the content of the first and second substances,

control performance monitor quantity, p, representing the current operating condition corresponding to the ith window_k,lRepresentation matrix X_p,lThe kth column vector of (1).

According to the control upper limit UP of the control performance monitoring quantity obtained in the step (19.1)_CPIJudgment of

Whether or not less than UP_CPIIf, if

Less than UP_CPIThen the system performance is better, if

Greater than UP_CPIThe system performance is degraded.

(22) Preliminary diagnosis of factors that lead to degradation of system performance

(22.1) acquiring a reference working condition model residual error according to the following formula by using the online data:

wherein v is_r,l(t) represents the reference condition model residual error at the tth sampling time of the ith window of the online data,

and representing the reference working condition disturbance model estimation value.

(22.2) obtaining the model mismatch/disturbance dynamic combined monitoring quantity eta according to the following formula_PDMI：

Wherein the content of the first and second substances,

has a value range of (0, 1)]，v_r,l(t) represents the reference condition model residual at the tth sampling instant, | cov (v)_r,l(t)) | denotes v_r,l(t) determinant of covariance matrix.

(22.3) calculating model mismatch/disturbance dynamic combined monitoring quantity eta by using online acquired input data and output data_PDMIUpper control limit UP combined with model mismatch/disturbance dynamic joint monitoring quantity_PDMIThe factors for controlling the performance degradation are preliminarily diagnosed if the current working condition is met

Greater than UP_PDMIIf the model mismatch or the external disturbance dynamics is changed, the system performance is reduced due to the model mismatch or the external disturbance dynamics; if the current operating condition is

Less than UP_PDMIThen changes in the controller parameters are a factor that causes degradation in system performance.

(23) Further diagnosis of factors leading to system performance degradation

(23.1) acquiring an estimated value epsilon of white noise of the actual working condition according to the steps (13) to (15) by utilizing the online data_h,l(t) actual condition disturbance model estimation value

Actual condition model residual v_h,l(t)。

(23.2) obtaining the interference characteristic monitoring quantity eta of the on-line data according to the following formula_DVI：

Wherein the content of the first and second substances,

representing the interference characteristic monitoring quantity of the on-line data corresponding to the ith window, representing the change of white noise variance in actual working condition_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,l(t) represents the white noise estimate for the actual condition at the tth sampling instant, | cov (ε_h,l(t)) | denotes ε_h,l(t) covariance matrix determinant, | cov (ε_r(t)) | denotes ε_r(t) covariance matrix determinant.

(23.3) calculating the actual working condition model residual error of the online data:

wherein v is_h,l(t) represents the model residual error of the online data actual condition corresponding to the ith window,

on-line data actual condition disturbance model estimation value y representing ith window_l(t) an online data process output vector, u, at the tth sampling instant of the ith window_l(t) an online data process input vector at the tth sampling instant, G, for the ith window_m,l(q^-1) Represents the process model used by the EWMA batch controller in the ith window of the online data.

(23.4) obtaining the disturbance model monitoring quantity eta of the online data according to the following formula_DMI：

Wherein the content of the first and second substances,

representing the monitored quantity, v, of the disturbance model corresponding to the l-th window_r,l(t) reference condition model residual, v, at the tth sampling time_h,l(t) represents the actual condition model residual at the tth sampling instant, J (f (v)_r,l(t)),g(v_h,l(t))) represents v_h,l(t) and v_r,l(t) KL divergence.

(23.5) obtaining a model mismatch monitoring quantity eta of the on-line data according to the following formula_PMI：

Wherein, the first and the second end of the pipe are connected with each other,

model mismatch monitoring quantity, epsilon, representing the on-line data corresponding to the ith window_h,l(t) the white noise estimation value of the actual working condition at the t-th sampling moment obtained in the step (23.1), v_h,l(t) represents the actual condition model residual error, | cov (ε), of the t-th sampling time obtained in step (23.1)_h,l(t)) | denotes ε_h,l(t) determinant of covariance matrix, | cov (v)_h,l(t)) | denotes v_h,l(t) determinant of covariance matrix.

(23.6) disturbance feature monitoring amount calculated using on-line data

Disturbance model monitoring quantity

Amount of model mismatch monitoring

Lower control limit LP combined with disturbance characteristic monitoring quantity_DVIUpper limit UP of control of the monitored quantity of interference characteristics_DVILower control limit LP of disturbance model monitoring quantity_DMIAnd upper control limit UP of model mismatch monitoring quantity_PMIFurther diagnosing and identifying the factors causing the performance degradation of the EWMA batch-to-batch control system, and if the characteristic monitoring quantity is disturbed

Greater than UP_DVIOr less than LP_DVIIf so, the white noise variance changes to cause the performance of the EWMA batch-to-batch control system to be reduced; if the model monitoring quantity is disturbed

Less than LP_DMIIf so, the performance of the EWMA batch control system is reduced due to the change of the external disturbance model; monitoring quantity if model mismatching

Greater than UP_PMIThen the model mismatch causes the EWMA inter-batch control system performance to degrade.

In the reference operating mode, the control parameter of the controller is λ ═ 0.35, and the object model used in the controller: g_m(q^-1)＝159.3q^-1I.e., b is 159.3, the variance of white noise is

The present simulation will consider six scenarios shown in table 1:

TABLE 1 parameter settings

When a model mismatch occurs, fig. 3 shows the trend of the change in the control performance index and each diagnostic index. As can be seen from FIG. 3(a), the control performance indicator η_CPIExceeding the upper control limit from the 481-th sampling instant indicates a decrease in system performance, and therefore further diagnosis of the cause of system performance degradation is required. As can be seen from FIG. 4(b), η is after the 481-th sampling timing_PDMIBeyond its upper control limit UP_PDMIModel mismatch or perturbation dynamics changes are accounted for. By observing fig. 3(c) - (e), starting from the 481 th sampling timing, the interference characteristic monitoring amount η_DVIAnd the monitored quantity eta of the disturbance model_DMIAre all kept within a control interval, i.e. LP_DVI＜η_DVI＜UP_DVIAnd η _DMI1, but the model mismatch monitor η_PMIBeyond its control limit, i.e. η_PMI＞UP_PMIThis shows that neither the disturbance signature (or white noise variance) nor the disturbance model of the EWMA batch-to-batch control system has changed, but the process model of the batch-to-batch control system does not match the actual process and results in a degradation of system performance. Therefore, the method of the present invention effectively evaluates system performance and identifies model mismatch from factors that control performance degradation.

Fig. 4 shows the variation tendency of the control performance index and each diagnostic index when the white noise variance of the external disturbance changes. As can be seen from FIG. 4(a), the control performance indicator η_CPIExceeding the upper control limit from the 481-th sampling instant indicates a decrease in system performance, and therefore further diagnosis of the cause of system performance degradation is required. As can be seen from FIG. 4(b), η is after the 481-th sampling timing_PDMIBeyond its upper control limit UP_PDMIModel mismatch or perturbation dynamics changes are accounted for. By observing FIGS. 4(c) - (e), the sample was taken from the 481 stThe model mismatch monitoring quantity eta begins at the sample time_PMIAnd the monitored quantity eta of the disturbance model_DMIAre all kept within a control region, i.e. η_PMI＜UP_PMIAnd η _DMI1, but the interference characteristic monitoring quantity eta_DVIBeyond its control line, i.e. eta_DVI＜LP_DVIThis indicates that the process model and the actual process matching and disturbance model of the EWMA batch control system have not changed, but the disturbance signature (or white noise variance) has changed and resulted in a degradation of system performance. Thus, the method of the present invention effectively evaluates system performance and identifies changes in the interference signature (or white noise variance) from factors that control performance degradation.

Fig. 5 shows the trend of the control performance index and each diagnostic index when the controller parameter changes. As can be seen from FIG. 5(a), the control performance indicator η_CPIExceeding the upper control limit from the 481-th sampling instant indicates a decrease in system performance, and therefore further diagnosis of the cause of system performance degradation is required. As can be seen from FIG. 5(b), eta is obtained after the 481-th sampling timing_PDMIWithin its control limits, i.e. eta_PDMI＜UP_PDMIAccounting for the controller parameter changes and resulting in a degradation of system performance. By observing fig. 5(c) - (e), the model mismatch monitor amount η starts from the 481 th sampling time instant_PMIInterference characteristic monitoring quantity eta_DVIDisturbance model monitoring quantity eta_DMIAre all kept within a control region, i.e. η_PMI＜UP_PMI、LP_DVI＜η_DVI＜UP_DVIAnd η_DMIThis indicates that the process model of the EWMA batch-to-batch control system matches the actual process, and neither the disturbance signature (or white noise variance) nor the disturbance model has changed. Thus, the method of the present invention effectively evaluates system performance and identifies changes in controller parameters from factors that control performance degradation.

Fig. 6 shows the trend of the change in the control performance index and each diagnostic index when the disturbance model is changed. As can be seen from FIG. 6(a), the control Performance index η_CPIThe upper limit of the control is exceeded from the 481-th sampling moment, which indicates that the system performance is reduced, so that the system performance needs to be reducedThe cause of change is further diagnosed. As can be seen from FIG. 6(b), η is after the 481-th sampling timing_PDMIBeyond its upper control limit UP_PDMIModel mismatch or perturbation dynamics changes are accounted for. By observing fig. 6(c) - (e), the model mismatch monitor amount η starts from the 481 th sampling time instant_PMIAnd interference characteristic monitoring quantity eta_DVIAre all kept within a control region, i.e. η_PMI＜UP_PMIAnd LP_DVI＜η_DVI＜UP_DVIHowever, the disturbance model monitoring quantity eta_DMIBeyond its control line, i.e. eta_DMI＜LP_DMIThis indicates that the process model and the actual process matching and disturbance characteristics (or white noise variance) of the EWMA batch-to-batch control system have not changed, but the disturbance model has changed and resulted in a degradation of system performance. Thus, the method of the present invention effectively evaluates system performance and identifies changes in the disturbance model from factors that control performance degradation.

Fig. 7 shows the trend of the change in the control performance index and each diagnostic index when the model mismatch and the white noise variance change occur simultaneously. As can be seen from FIG. 7(a), the control performance index η_CPIExceeding the upper control limit from the 481-th sampling instant indicates a decrease in system performance, and therefore further diagnosis of the cause of system performance degradation is required. As can be seen from FIG. 7(b), η is after the 481-th sampling timing_PDMIBeyond its upper control limit UP_PDMIModel mismatch or perturbation dynamics changes are accounted for. By observing fig. 7(c) - (e), starting from the 481 th sampling timing, the interference characteristic monitoring amount η_DVIAnd model mismatch monitor η_PMIAre all changed, i.e. eta_DVI＜LP_DVIAnd η_PMI＞UP_PMIHowever, the disturbance model monitoring quantity eta_DMIStill within its control limits, i.e. eta_DMIThis indicates that the disturbance model of the EWMA batch-to-batch control system has not changed, but the process model and the actual process do not match and the disturbance signature (or white noise variance) has changed, and both cause degradation in system performance. Therefore, the method of the invention effectively evaluates the system performance and factors that change the interference characteristics and model mismatch degrade from control performanceIs identified.

When the models are mismatched and the disturbance model is changed, fig. 8 shows the variation tendency of the control performance index and each diagnostic index. As can be seen from FIG. 8(a), the control performance index η_CPIExceeding the upper control limit from the 481-th sampling instant indicates a decrease in system performance, and therefore further diagnosis of the cause of system performance degradation is required. As can be seen from FIG. 8(b), η is after the 481-th sampling timing_PDMIBeyond its upper control limit UP_PDMIModel mismatch or perturbation dynamics changes are accounted for. By observing fig. 8(c) - (e), starting from the 481 th sampling timing, the interference characteristic monitoring amount η_DVIAnd the monitored quantity eta of the disturbance model_DMIAre all changed, i.e. eta_DVI＜LP_DVIAnd η_DMI＜LP_DMIBut the amount of model mismatch monitoring η_PMIStill within its control limits, i.e. eta_PMI＜UP_PMIThis shows that the process model of the EWMA batch-to-batch control system matches the actual process, but both the disturbance signature (or white noise variance) and the disturbance model change, and both result in a degradation of the system performance. Thus, the method of the present invention effectively evaluates system performance and identifies changes in the disturbance signature and disturbance model from factors that control performance degradation.

Through the analysis of 1-6, 6 kinds of fault conditions of actual working conditions, the control performance diagnosis method of the semiconductor manufacturing process batch control system based on model residual errors can be used for accurately diagnosing the factors of system performance degradation.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A control performance diagnosis method of a semiconductor process batch control system is characterized by comprising the following steps:

s1, obtaining N groups of input of historical normal working conditions of EWMA batch control system in semiconductor manufacturing processTaking data and output data as sample data, dividing the sample data into S +1 windows, and calculating a white noise estimation value epsilon of a reference working condition by using the input data and the output data of the first window_rAnd reference working condition disturbance model estimation value

Obtaining process-disturbance combined model residual e (t), process data set

And output data set Y₁ ⁰And based on the process data set

Obtaining a matrix X of reference conditions₁From the output data set Y₁ ⁰Obtaining a matrix Y of reference conditions₁Construction of Hankel matrix X_pAnd X_fAnd projection matrix J_q；

S2, constructing a process data set by using the input data and the output data of the k' th window

And outputting the data set

From a process data set

Obtaining matrix X of actual working condition_k'From the output data set

Obtaining matrix Y of actual working conditions_k'Adopting a typical variable analysis method to obtain the control performance monitoring quantity of the EWMA batch control system corresponding to the kth window

Wherein k ═ 2,3, …, S + 1;

s3, according to the reference working condition disturbance model estimated value in the step S1

Obtaining reference working condition model residual error v from input data and output data of k' th window_r,k'(t) and model mismatch/perturbation dynamics joint monitoring volume

S4, obtaining the white noise estimation value epsilon of the practical working condition corresponding to the k 'th window by using the input data and the output data of the k' th window_h,k'(t) and actual condition disturbance model estimation value

And according to the actual working condition disturbance model estimated value

Obtaining the residual error v of the actual working condition model_h,k'(t)；

S5, according to the reference working condition white noise estimated value epsilon in the step S1_rAnd the white noise estimate of the actual condition ε in step S4_h,k'(t) calculating an interference characteristic monitoring quantity

According to the reference working condition model residual v in the step S3_r,k'(t) and the actual condition model residual v in step S4_h,k'(t) calculating the amount of monitoring of the disturbance model

According to the actual working condition white noise estimated value epsilon in the step S4_h,k'(t) and the actual condition model residual v_h,k'(t) obtaining a model mismatch monitoring quantity

S6, respectively obtaining the control upper limit UP of the control performance monitoring quantity by adopting a kernel density estimation method_CPIUpper control limit UP of combined monitoring quantity of model mismatch/disturbance dynamics_PDMIUpper limit UP of control of the monitored quantity of interference characteristics_DVILower limit of control LP of disturbance characteristic monitoring amount_DVILower control limit LP of disturbance model monitoring quantity_DMIAnd the upper control limit UP of the model mismatch monitoring quantity_PMI；

S7, collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line, and obtaining the control performance monitoring quantity eta of the current working condition_CPIAccording to the control upper limit UP in step S6_CPIJudging whether the control performance of the closed-loop system is reduced or not in real time;

s8, if the control performance monitoring quantity eta_CPIControl upper limit UP greater than control performance monitoring amount_CPIIf the performance of the EWMA batch control system is reduced, executing the step S9, otherwise, the EWMA batch control system has good performance;

s9, using the reference working condition disturbance model estimated value in the step S1

The N1 groups of input data and output data in the step S7 acquire the model mismatch/disturbance dynamic combined monitoring quantity eta of the current working condition_PDMI；

S10, if the model mismatching/disturbance dynamic joint monitoring quantity eta_PDMIControl upper limit UP larger than the model mismatch/disturbance dynamic joint monitoring amount in step S6_PDMIIf the performance of the EWMA batch control system is reduced due to model mismatch or disturbance dynamics, executing the step S11, otherwise, the performance of the EWMA batch control system is reduced due to the change of the controller parameters;

s11, calculating the interference characteristic monitoring quantity eta of the current working condition_DVIMonitoring quantity eta of disturbance model_DMIAnd model mismatch monitor η_PMI(ii) a Interference characteristic monitoring quantity eta of current working condition_DVIGreater than the amount of monitoring of the disturbance characteristic in step S6Upper control limit UP of_DVIOr less than the lower control limit LP of the disturbance characteristic monitored quantity_DVIWhen the interference characteristic changes, the performance of the EWMA batch control system is reduced; when the disturbance model monitors the quantity eta_DMILower control limit LP less than disturbance model monitoring amount_DMIMeanwhile, the performance of the EWMA batch control system is reduced due to the change of the disturbance model; when model mismatch monitor eta_PMIControl upper limit UP greater than model mismatch monitoring amount_PMIModel mismatch results in performance degradation of the EWMA batch-to-batch control system.

2. The method of claim 1, wherein the matrix X of baseline operating conditions is a matrix of run-to-run control systems₁And Y₁Respectively expressed as:

wherein u is_iRepresents the ith process input vector, i 1, …, m_u，m_uDenotes the number of input vectors, t denotes the sampling time, u ″_iRepresenting the i-th process input vector after normalization, i.e.

Means representing the ith process input vector, (σ)_u,r)_iRepresents the standard deviation of the ith process input vector; y is_jRepresents the jth process output vector, j ═ 1, …, m_y，m_yIndicates the number of output vectors, y ″)_jRepresenting the normalized jth process output vector, i.e.

Means for representing the jth process output vector, (σ)_y,r)_jRepresents the standard deviation of the jth process output vector; e.g. of the type_j(t) denotes the jth process-perturbation joint model residual vector, where e_j＝(e_j(t))，e_j(t)＝y_j(t)-(G_m(q^-1))_ju(t)，(G_m(q^-1))_jRepresenting the process model G used in the first window_m(q^-1) J-th line of (1), y_j(t) denotes the jth process output at the tth sampling instant, u (t) denotes the column vector formed by all process inputs at the tth sampling instant in the first window, e ″_jRepresents the normalized jth process-perturbation joint model residual vector,

represents the mean of the jth process-perturbation combined model residual, (σ)_e,r)_jRepresenting the standard deviation of the jth process-perturbation combined model residual error;

the projection matrix J_qComprises the following steps:

wherein, V_qRepresenting a matrix constructed from the first q columns of the unitary matrix V,

represent the Hankel matrix X_pThe covariance matrix of (2).

3. According toThe method of claim 2, wherein the process data set is a control performance diagnostic of a semiconductor process batch-to-batch control system

And outputting the data set

Respectively expressed as:

wherein the content of the first and second substances,

the process input vector representing the kth window,

the process-perturbation joint model residual vector representing the kth window,

a process output vector representing the kth window;

matrix X of the actual working condition_k'And Y_k'Respectively expressed as:

wherein u is_i,k'The process input vector, u ", representing the k' th window_i,k'The process input vector representing the normalized k' th window, i.e.

y_j,k'Represents the process output vector, y ″, of the k' th window_j,k'The process output vector representing the normalized k' th window, i.e.

e_j,k'Process-perturbation joint model residual vector representing the kth window, e_j,k'＝(e_j,k'(t))，e_j,k'(t)＝y_j,k'(t)-(G_m,k′(q^-1))_ju_k'(t)，y_j,k'(t) denotes the jth process output, u, at the tth sampling instant in the kth window_k'(t) represents the column vector formed by all process inputs at the tth sampling instant in the kth window, (G)_m,k′(q^-1))_jRepresenting the Process model G used by the EWMA batch controller in the kth' Window_m，k′(q^-1) Line j, e ″)_j,k'Representing the process-perturbation combined model residual of the normalized k' th window, i.e.

Obtaining control performance monitoring quantity of EWMA batch control system by adopting typical variable analysis method

Comprises the following steps:

wherein the content of the first and second substances,

represents the amount of control performance monitoring, J, of the EWMA batch-to-batch control system corresponding to the kth window_qRepresenting a projection matrix, p_k,k'Representation matrix X_p,k'The k-th column of (1).

4. The method as claimed in claim 1 or 3, wherein the model mismatch/disturbance dynamics joint monitoring is

Comprises the following steps:

wherein the content of the first and second substances,

represents the model mismatch/disturbance dynamic joint monitoring quantity corresponding to the k' th window,

has a value range of (0, 1)]，ε_r(t) the white noise estimation value of the reference condition at the t-th sampling moment, v_r,k'(t) represents the reference condition model residual at the t-th sampling instant in the kth' window, | cov (ε_r(t)) | denotes ε_rDeterminant of covariance matrix of (t), | cov (v)_r,k'(t)) | denotes v_r,k'(t) determinant of covariance matrix;

the reference working condition model residual v_r,k'(t) is:

wherein v is_r,k'(t) represents the reference condition model residual error corresponding to the k' th window,

disturbance model estimation value representing reference working condition

Inverse of (y)_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window, u_k'(t) represents the process input vector at the t-th sampling instant in the k' -th window, G_m,k′(q^-1) A process model used by the EWMA batch controller in the k' th window is shown.

5. The method of claim 4, wherein the operating condition model residual error v is a real-time model residual error_h,k'(t) is:

wherein v is_h,k'(t) represents the real model residual at the t-th sampling instant of the k' -th window,

actual condition disturbance model estimation value representing k' th window

Inverse of (y)_k'(t) represents the process output vector at the t-th sampling instant of the k' -th window, u_k'(t) represents the process input vector at the t-th sampling instant of the k' -th window, G_m,k′(q^-1) Representing the process model used by the EWMA batch controller in the k' th window.

6. The method of claim 5, wherein the step S5 includes the steps of:

s5.1, calculating interference characteristic monitoring quantity

Wherein epsilon_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,k'(t) represents the white noise estimate for the actual condition at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix;

s5.2, calculating the monitoring quantity of the disturbance model

Wherein the content of the first and second substances,

representing the monitored amount of the perturbation model for the k' th window,

has a value range of (0, 1)]If, if

Near or equal to 1, the perturbation model is unchanged, v_r,k'(t) represents the reference condition model residual at the t-th sampling instant in the k' -th window, v_h,k'(t) represents the actual condition model residual at the t-th sampling instant in the k' -th window, J (f (v)_r,k'(t)),g(v_h,k'(t))) represents v_h,k'(t) and v_r,k'(t)The KL divergence of (1) is expressed as:

wherein, f (v)_r,k'(t)) represents v constructed using the nuclear density estimation method_r,k'(t) probability density function, f (v)_h,k'(t)) represents v obtained by the nuclear density estimation method_h,k'(t) probability density function, i ═ 1,2, …, N_f，N_fRepresenting the total number of independent identically distributed sample points generated by the kernel density estimation;

s5.3, calculating model mismatch monitoring quantity

Wherein epsilon_h,k'(t) represents the white noise estimate of the actual condition at the t-th sampling instant in the k' -th window, v_h,k'(t) represents the real-world model residual at the t-th sampling instant in the kth' window, | cov (ε_h,k'(t)) | denotes ε_h,k'Determinant of covariance matrix of (t), | cov (v)_h,k'(t)) | denotes v_h,k'(t) determinant of covariance matrix.

7. The method of claim 1 or 5, wherein the step S6 includes the steps of:

s6.1, calculating the control upper limit UP of the control performance monitoring quantity_CPI：

Wherein the content of the first and second substances,

the control performance monitoring quantity corresponding to the kth window is K ', K' is 2, 3.., S +1, h represents the kernel bandwidth, and K (·) represents the kernel density estimation with the kernel as a radial basis function;

s6.2, calculating the control upper limit UP of the model mismatch/disturbance dynamic combined monitoring quantity_PDMI：

Wherein the content of the first and second substances,

model mismatch/disturbance dynamic combined monitoring quantity corresponding to the kth' window;

s6.3, calculating the control upper limit UP of the interference characteristic monitoring quantity_DVIAnd a lower control limit LP_DVI：

Wherein the content of the first and second substances,

is the interference characteristic monitoring quantity corresponding to the kth window;

s6.4, calculating a control lower limit LP of the monitoring quantity of the disturbance model_DMI：

Wherein the content of the first and second substances,

is the disturbance model monitoring quantity corresponding to the kth window;

s6.5, calculating the control upper limit of the model mismatch monitoring quantityUP_PMI：

Wherein, the first and the second end of the pipe are connected with each other,

is the model mismatch monitoring quantity corresponding to the k' th window.

8. The method of claim 2 or 3, wherein the step S7 includes the steps of:

s7.1, collecting N1 groups of input data and output data of the EWMA batch control system of the semiconductor process on line as actual working condition sample data, and dividing the actual working condition sample data into S₁An online window, each window containing n groups of samples, wherein S₁＝N1-n+1；

S7.2, calculating the residual error of the online process-disturbance combined model:

e_l(t)＝y_l(t)-G_m,l(q^-1)u_l(t)，

wherein e is_l(t) represents the on-line process-perturbation joint model residual error at the tth sampling instant of the ith window, y_l(t) represents the process output vector at the tth sampling instant of the ith window, u_l(t) denotes the input vector at the tth sampling instant of the l-th window, t denotes the sampling instant, G_m,l(q^-1) Representing a Process model, q, used by an EWMA batch-to-batch controller in an on-line regime^-1Denotes a difference operator, where l is 1,2, …, S₁；

S7.3, acquiring a process input data set of the current working condition by using the process output vector, the process input vector and the process-disturbance combined model residual error which are acquired in real time

And output data set Y_l ⁰：

Wherein, the first and the second end of the pipe are connected with each other,

representing the on-line process input vector and,

representing the on-line process-perturbation joint model residual vector,

representing an online process output vector;

s7.4, constructing a matrix X_lAnd Y_l：

Wherein u is_i,lRepresents the process input vector, u ″, in the ith window of the online data_i,lThe process input vector representing the normalized l-th window, i.e.

y_j,lRepresents the process output vector, y ″, of the ith window of online data_j,lThe process output vector representing the normalized l-th window, i.e.

e_j,lProcess-perturbation joint model residual vector representing the ith window of online data, e_j,l＝(e_j,l(t))，e_j,l(t)＝y_j,l(t)-(G_m,l(q^-1))_ju_l(t)，(G_m,l(q^-1))_jProcess model G representing use of EWMA batch-to-batch controller in first window of online data_m，l(q^-1) J-th line of (1), y_j,l(t) denotes the jth process output at the tth sampling instant of the ith window of online data, u_l(t) represents the vector formed by all process inputs at the tth sampling time of the ith window of online data, e ″_j,lRepresenting the normalized process-perturbation joint model residual,

s7.5, constructing a Hankel matrix X_p,lAnd X_f,l：

Wherein p is_p+1,lRepresenting a history data vector at the p +1 th sampling instant in the ith window of line data, i.e. p_p+1,l＝[x_l(p)^T…x_l(1)^T y_l(p)^T…y_l(1)^T]^T，x_l(p) a representation matrix

P column of (2), x_l(1) Representation matrix

The number 1. sup. st column of (a),

representation matrix X_lTranspose of (y)_l(p) represents a matrix Y_l ^TP column, y_l(1) Representation matrix Y_l ^TColumn 1, Y_l ^TRepresentation matrix Y_lTransposing; f. of_p+1,lThe vector of predicted data representing the p +1 th sampling instant in the l window of line data, i.e. f_p+1,l＝[y_l(p+1)^T y_l(p+2)^T…y_l(p+f-1)^T]^T，y_l(p +1) represents Y_l ^TP +1 column, y_l(p +2) represents Y_l ^TP +2 column, y_l(p + f-1) represents Y_l ^TP + f-1 column (b);

s7.6, acquiring control performance monitoring quantity eta of the current working condition by using online data_CPI：

Wherein the content of the first and second substances,

indicating the control performance monitoring quantity, p, of the ith window of the on-line data_k,lRepresentation matrix X_p,lThe kth column vector of (1);

s7.7, control Upper Limit UP according to control Performance monitoring amount_CPIJudgment of

Whether or not less than UP_CPIIf, if

Less than UP_CPIThen the system performance is better, if

Greater than UP_CPIThe system performance is degraded.

9. The method of claim 5, wherein the step S9 includes the steps of:

s9.1, obtaining a reference working condition model residual error by using online data:

wherein v is_r,l(t) represents the reference condition model residual error at the tth sampling time of the ith window of the online data,

representing the reference condition disturbance model estimate, y_l(t) an online data process output vector, u, at the tth sampling instant of the ith window_l(t) an online data process input vector at the tth sampling instant, G, for the ith window_m,l(q^-1) Representing a process model used by the EWMA batch controller in the ith window of the online data;

s9.2, calculating model mismatching/disturbance dynamic combined monitoring quantity eta by utilizing online collected input data and output data_PDMI：

Wherein the content of the first and second substances,

has a value range of (0, 1)]，ε_r(t) represents the white noise estimate for the reference condition at the tth sampling instant, | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix, v_r,l(t) denotes the th of the l-th windowOn-line data reference behavior model residual for t sampling instants, | cov (v)_r,l(t)) | denotes v_r,l(t) determinant of covariance matrix;

s9.3, combining control upper limit UP of model mismatch/disturbance dynamic joint monitoring quantity_PDMIThe factors for controlling the performance degradation are preliminarily diagnosed if the current working condition is met

Greater than UP_PDMIIf the model mismatch or the external disturbance dynamics is changed, the system performance is reduced due to the model mismatch or the external disturbance dynamics; if the current operating condition is

Less than UP_PDMIThen changes in the controller tuning parameters are a factor that causes degradation in system performance.

10. The method of claim 8, wherein the step S11 includes the steps of:

s11.1, calculating interference characteristic monitoring quantity eta of online data_DVI：

Wherein the content of the first and second substances,

representing the interference characteristic monitoring quantity of the online data corresponding to the ith window,

for characterizing the change of the white noise variance, ε, in the actual operating conditions_r(t) represents the white noise estimation value of the reference condition at the t-th sampling moment, epsilon_h,l(t) represents the white noise estimation value of the actual working condition at the tth sampling moment of the ith window in the online monitoring stage, | cov (epsilon)_h,l(t)) | denotes ε_h,lDeterminant of covariance matrix of (t), | cov (ε_r(t)) | denotes ε_r(t) determinant of covariance matrix;

s11.2, calculating the actual working condition model residual error of the online data:

wherein v is_h,l(t) represents the model residual error of the online data actual condition corresponding to the ith window,

on-line data actual condition disturbance model estimation value y representing ith window_l(t) an online data process output vector, u, at the tth sampling instant of the ith window_l(t) an online data process input vector at the tth sampling instant, G, for the ith window_m,l(q^-1) Representing a process model used by the EWMA batch controller in the ith window of the online data;

s11.3, calculating disturbance model monitoring quantity eta of online data_DMI：

Wherein the content of the first and second substances,

representing the monitored quantity, v, of the disturbance model corresponding to the l-th window_r,l(t) represents the on-line data reference condition model residual at the tth sampling instant of the ith window, v_h,l(t) represents the on-line data real-time model residual error at the tth sampling time of the ith window, J (f (v)_r,l(t)),g(v_h,l(t))) represents v_h,l(t) and v_r,l(t) a KL divergence;

s11.4, calculating model mismatch monitoring quantity eta of online data_PMI：

Wherein the content of the first and second substances,

model mismatch monitoring quantity, epsilon, of the on-line data corresponding to the ith window of the on-line data_h,l(t) represents the white noise estimate of the actual condition at the tth sampling time of the ith window of the on-line data, v_h,l(t) represents the real model residual at the tth sampling instant of the l windows of online data, cov (ε_h,l(t)) represents ε_h,l(t) determinant of covariance matrix, cov (v)_h,l(t)) represents v_h,l(t) determinant of covariance matrix;

s11.5, combining the lower control limit LP of the interference characteristic monitoring quantity_DVIUpper limit UP of control of the monitored quantity of interference characteristics_DVILower control limit LP of disturbance model monitoring quantity_DMIAnd upper control limit UP of model mismatch monitoring quantity_PMIFurther diagnosing and identifying the factors causing the performance degradation of the EWMA batch-to-batch control system and a plurality of disturbance characteristic monitoring quantities

Greater than UP_DVIOr less than LP_DVIIf so, the white noise variance changes to cause the performance of the EWMA batch-to-batch control system to be reduced; if the model monitoring quantity is disturbed

Less than LP_DMIIf so, the performance of the EWMA batch control system is reduced due to the change of the external disturbance model; monitoring quantity if model mismatching

Greater than UP_PMIThen the model mismatch causes the EWMA inter-batch control system performance to degrade.

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