JP2012074574A - Control system for processing apparatus and method for controlling processing apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a control system capable of improving manufacturing efficiency of a product to be processed in processing steps.SOLUTION: The control system 100 for the processing apparatus comprises: a prediction model for predicting a equipment performance (for example, polishing rate) of the processing apparatus such as a semiconductor wafer CMP apparatus according to a physical amount (for example, the accumulated use time) for indicating the state of the consumable part such as an abrasive pad and a dresser; and a meta prediction model for predicting parameters of the prediction model. A model creation simulator part 110 simulates and determines parameters of the meta prediction model and the prediction model for equipment performance by using processing history data accumulated in a processing history data storage part 140 and a random number conforming to predetermined statistical distribution, and sends the parameters to a control calculation part 130. The control calculation part 130 calculates a control amount of the processing apparatus 200 using a prediction model determined by received parameters and a current value of a physical amount for indicating the state of the consumable part.

Description

  The present invention relates to a control system and a control method for a processing apparatus that processes a processing target using consumable parts that affect processing performance.

  For example, in a polishing apparatus such as a semiconductor wafer CMP (Chemical Mechanical Polishing) apparatus, the performance is represented by a polishing rate which is a polishing amount per unit time. In many cases, the polishing rate is determined by the performance of a polishing pad for polishing a semiconductor wafer and a dresser for sharpening the polishing pad. The polishing pad and the dresser are consumable parts and wear with the time of use, so that the performance deteriorates. Therefore, when a predetermined amount of semiconductor wafer is to be polished, it is necessary to always know the polishing rate determined by the performance of the polishing pad and dresser.

  In Patent Document 1, a blanket wafer is subjected to test polishing to acquire a polishing rate (removal rate of a film to be polished) at that time, and the acquired polishing rate or a polishing rate predicted from the polishing rate is used. An example of a semiconductor wafer CMP apparatus for controlling the polishing amount (polishing time) is described. In such a semiconductor wafer CMP apparatus, the polishing rate can be grasped even when the performance of a polishing pad or a dresser which is a consumable part is exchanged, and therefore control suitable for the actual polishing rate is performed. Thus, the polishing accuracy is improved.

  Non-Patent Document 1 describes a method for determining and optimizing parameters of a statistical model from data using a Markov Chain Monte Carlo method (hereinafter abbreviated as MCMC method). Furthermore, it also describes that the device control model is treated as a statistical model when determining parameters of the device control model from data.

Japanese Patent No. 3859475

Christophe Andrieu, et al. 3 “An Introduction to MCMC for Machine Learning”, Kluwer Academic Publishers, Machine Learning, 50, 5-43, 2003

  In general, a semiconductor wafer CMP apparatus or the like cannot measure the thickness of a thin film to be polished at the same time while polishing. The actual value of the polishing rate obtained by the film thickness measurement can be obtained only after the film thickness is actually measured by the film thickness inspection apparatus after the polishing is completed. In addition, the film thickness measurement takes a considerable amount of time because it takes time and labor to transport and clean the target semiconductor wafer. Therefore, if the test polishing is performed and the film thickness is measured, the polishing process is delayed due to the waiting time. As a result, the production efficiency as a semiconductor wafer product is lowered.

  Accordingly, the present invention provides a processing apparatus control system and a processing apparatus capable of reducing a delay in a processing step (polishing step) due to test processing (test polishing) and improving production efficiency of a product to be processed (such as a semiconductor wafer). It is to provide a control method.

  The present invention is a processing device control system that predicts the processing performance of a processing device whose processing performance varies depending on the state of consumable parts, and controls the processing device, which is acquired from the processing device during processing by the processing device. A machining history data storage unit that stores machining history data, and a meta prediction model parameter that predicts a parameter of a prediction model that predicts the machining performance from a physical quantity representing the state of the consumable part is stored in the processing history data storage unit. A model creation simulator unit defined by a simulation using processing history data being performed and a random number according to a predetermined statistical distribution, and the meta prediction model having parameters defined by the model creation simulator unit Prediction model for predicting machining performance and an object representing the state of the consumable parts Based on the current value of the quantity, characterized in that it and a control arithmetic unit for calculating a control amount for the processing device.

  The processing apparatus control system of the present invention can create a prediction model that predicts the processing performance (for example, the polishing rate) of the processing apparatus from a physical quantity (for example, the cumulative usage time of the consumable part) that represents the state of the consumable part. Therefore, in order to predict the processing performance, a physical quantity (for example, a polishing rate) that directly represents the processing performance is not necessarily required. Therefore, immediately after the completion of the processing (polishing), the processing performance (for example, the polishing rate) of the processing apparatus can be predicted using the physical quantity (for example, the cumulative usage time of the consumable parts) indicating the state of the consumable part. Therefore, since the frequency of test processing can be reduced, process delay due to test processing and processing amount measurement associated therewith can be reduced. As a result, the production efficiency of the processed product is improved.

  ADVANTAGE OF THE INVENTION According to this invention, the processing apparatus control system and processing which can reduce the delay of the processing process (polishing process) accompanying test processing (test polishing), and can improve the production efficiency of processed products (semiconductor wafer etc.). A device control method can be provided.

The figure which showed the example of the structure of the functional block of the processing apparatus control system which concerns on the 1st Embodiment of this invention. The figure which showed the example of a structure of the computer system which implement | achieves the processing apparatus control system which concerns on the 1st Embodiment of this invention. The figure which showed the example of schematic structure of the semiconductor wafer CMP apparatus used as a representative example of a processing apparatus in embodiment of this invention. The figure which showed the example of the record structure of the process history data with respect to the semiconductor wafer CMP apparatus accumulate | stored in a process history data storage part. The figure which showed the example of transition chart of the polishing rate performance value when a semiconductor wafer is grind | polished with a semiconductor wafer CMP apparatus. Is a diagram showing an example of a predicted value transition chart of the polishing rate R _p in the case of the explanatory variables dresser cumulative use time, comparatively showing (a) the predicted value and actual value of the polishing rate R _p FIG. 4B is a diagram showing a predicted value error transition chart. Is a diagram showing an example of a predicted value transition chart predicted polishing rate R _p on the basis of the meta prediction model equation (9), (a) compares the predicted value and actual value of the polishing rate R _p The figure shown, (b) is the figure which showed transition of the predicted value error. The figure which showed the example of the processing flow of the model creation simulation process in the model creation simulator part of the processing apparatus control system which concerns on the 1st Embodiment of this invention. It is the figure which showed the example of a mode that the parameter sample series by a MCMC method converges, (a) showed the mode of the convergence about the case where a predetermined number of convergence intervals were included in addition to the convergence from the first time. FIG. 4B is a diagram showing a state of convergence in a predetermined number of convergence intervals. The figure which showed the example of the processing flow of the apparatus performance prediction and control amount calculation process in the control calculating part of the processing apparatus control system which concerns on the 1st Embodiment of this invention. The figure which showed the example of the alarm display screen displayed on the display apparatus of the computer for control. The figure which showed the example of the structure of the functional block of the processing apparatus control system which concerns on the 2nd Embodiment of this invention. The figure which showed the example of the processing flow of the model creation simulation process in the model creation simulator part of the processing apparatus control system which concerns on the 2nd Embodiment of this invention. It is the figure which showed a mode that the sample series of the learning gain (lambda) by MCMC method converges, (a) shows a mode that the convergence is carried out about the case where a predetermined number of convergence sections are included before it converges from the first time. FIG. 5B is a diagram showing a state of convergence in a predetermined number of convergence intervals. The figure which showed the example of the transition chart of control amount in the case of applying a polishing amount control simulation result to control.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In all the drawings for explaining the embodiments, the same constituent elements are given the same reference numerals, and the repeated explanation thereof is omitted.

<First Embodiment>
(1. Configuration of processing equipment control system)
FIG. 1 is a diagram showing an example of a functional block configuration of a machining apparatus control system according to the first embodiment of the present invention. As shown in FIG. 1, the machining apparatus control system 100 includes blocks such as a model creation simulator unit 110, a control calculation unit 130, and a machining history data storage unit 140.

  Here, the model creation simulator unit 110 includes therein a model creation trial unit 111, a stochastic parameter generation unit 115, a model accuracy convergence determination unit 116, a Markov chain sample value storage unit 121, an apparatus performance prediction model storage unit 122, and the like. The model creation trial unit 111 further includes a device performance prediction model meta prediction trial unit 112, a device performance prediction trial unit 113, and the like. In addition, the control calculation unit 130 includes blocks such as a device performance prediction model meta prediction unit 132, a device performance prediction unit 133, a control amount calculation unit 134, and an abnormality prediction unit 135 therein.

  The basic function of the processing apparatus control system 100 is to acquire various processing history data including an apparatus state in the processing apparatus 200 (for example, a semiconductor wafer CMP apparatus), and process according to the apparatus state and the processing history data. Various control amounts for controlling the apparatus 200 are output. Although this basic function is the same as that of a general control system, the unique functions of each block described above will be sequentially described in the following description of the embodiments.

  FIG. 2 is a diagram showing an example of the configuration of a computer system that realizes the machining apparatus control system 100. As shown in FIG. 2, a model management computer 31 provided in an operation center 300 that operates and manages an apparatus performance prediction model according to an embodiment of the present invention is connected to a plurality of remote locations via a communication network 500. The computer 400 for control installed in the site 400 is connected. A processing device 200 to be controlled is connected to the control computer 41 installed at each site 400.

  Here, the model management computer 31 includes an arithmetic processing device 32 and a storage device 33. The storage device 33 includes a Markov chain sample value storage unit 121, a device performance prediction model storage unit 122, a processing history. A data storage unit 140 and the like are provided. The control computer 41 includes an arithmetic processing device 42 and a storage device 43. The functions of the model creation simulator unit 110 shown in FIG. 1 are realized by the model management computer 31, and the functions of the control calculation unit 130 are realized by the control computer 41.

(2. Configuration of semiconductor wafer CMP apparatus)
FIG. 3 is a diagram showing an example of a schematic configuration of a semiconductor wafer CMP apparatus used as a representative example of the processing apparatus 200 in the embodiment of the present invention. As shown in FIG. 3, a semiconductor wafer CMP apparatus 200a includes a head 14 that holds and presses a semiconductor wafer 10 to be polished on its lower surface, a head rotation motor 15 that rotates the head 14, and a semiconductor wafer that is pressed by the head 14. 10, a polishing pad 11 that contacts the lower surface of the surface 10 and polishes the contact surface, a table 12 that holds the polishing pad 11 on its upper surface, a table rotation motor 13 that rotates the table 12, a dresser 16 that sharpens the polishing pad 11, A dresser rotation motor 17 that rotates the dresser 16, a dresser swing motor 18 that swings the dresser 16 in the radial direction of the polishing pad 11, a slurry supply unit 20 that supplies the slurry 19 to the upper surface of the polishing pad 11, and the like. The

  In the semiconductor wafer CMP apparatus 200a, the semiconductor wafer 10 is held by the head 14 and pressed against the upper surface of the polishing pad 11 with a predetermined pressure. On the other hand, a slurry 19 containing abrasive grains is supplied from the slurry supply unit 20 onto the polishing pad 11. When the head rotation motor 15 and the table rotation motor 13 rotate in this state, the contact surface of the semiconductor wafer 10 with the polishing pad 11 is polished. At this time, the polishing surface of the polishing pad 11 is worn with the progress of polishing. Therefore, when the dresser rotation motor 17 and the dresser swing motor 18 are rotated, the dresser 16 swings while rotating on the polishing pad 11, whereby the polishing surface of the polishing pad 11 is sharpened.

  The processing apparatus control system 100 controls, for example, the polishing time by the semiconductor wafer CMP apparatus 200a so that the thickness of the thin film formed on the semiconductor wafer 10 becomes a predetermined target value. In this case, the polishing time greatly depends on the sharpening state of the polishing pad 11 and the sharpening performance of the dresser 16. Therefore, the processing apparatus control system 100 acquires data as a clue to know the sharpening state of the polishing pad 11 and the sharpening performance of the dresser 16 from the semiconductor wafer CMP apparatus 200a as processing history data, and stores the processing history data. Stored in the unit 140.

FIG. 4 is a diagram showing an example of a record configuration of processing history data for the semiconductor wafer CMP apparatus 200a accumulated in the processing history data storage unit 140. As shown in FIG. 4, the processing history data record for the semiconductor wafer CMP apparatus 200a includes the polished wafer number, apparatus name, consumable part dresser use time, consumable part polishing pad use time, pre-polishing film thickness V ₁ , polishing It includes data such as post film thickness V ₂ , polishing time T _p , polishing rate R _p , installation environment temperature, and the like. Note that the processing history data of one record is acquired every time one semiconductor wafer 10 to be polished is polished.

(3. General prediction method of polishing rate)
First, here, in accordance with the basic concept of a general control system, when the semiconductor wafer 10 is polished by the semiconductor wafer CMP apparatus 200a, the polishing time for achieving the target film thickness is predicted, A method of setting will be described.

The control calculation unit 130 of the processing apparatus control system 100 firstly has a polishing amount dV (a difference between the film thickness V ₁ (measured value) before polishing of the semiconductor wafer 10 and the film thickness V ₂ (target value) after polishing. the polishing time T _p required to perform the polishing target value) only, calculated according to the following equation (1), sets the calculated polishing time T _p in the semiconductor wafer CMP device 200a.

According to equation (1), to calculate the polishing time T _p, it is necessary to determine the polishing rate R _p in advance. The polishing rate _Rp is a polishing amount per unit time, and is an amount representing the polishing performance of the semiconductor wafer CMP apparatus 200a. The polishing rate R _p can be calculated by the following equation (2).

According to equation (2) can be obtained by dividing the polishing amount dV in polishing time T _p. Therefore, here, using the measured value of the polishing amount dV in the previous polishing (n−1) and the set value of the polishing time T _p at that time, the previous (n−1) according to the following equation (3): The actual value of the polishing rate R _p is calculated, and the calculated actual value of the polishing rate R _p is set as the predicted value R _p (n) of the next (n) polishing rate. The previous (n-1) polishing here refers to the polishing of the semiconductor wafer 10 performed immediately before, and the next (n) polishing is to be performed next to the previous (n-1). The semiconductor wafer 10 is polished (hereinafter the same in this specification).

The measured values of the previous (n−1) film thicknesses V ₁ and V ₂ and the set value of the polishing time T _p in this equation (3) are obtained from the processing history data storage unit 140 and applied to the semiconductor wafer 10. The data of the film thickness V ₁ before polishing, the film thickness V ₂ after polishing, and the polishing time T _p included in the row of the polishing wafer number are read out.

In addition, in the notation of the expression (3), a so-called “hat” mark (“^”) is added above the symbol “R” of the predicted value R _p (n) of the next (n) polishing rate. However, this “hat” mark represents a predicted value, but is omitted in the text of the specification.

As described above, the control arithmetic unit 130 of the processing apparatus control system 100 may determine the predicted value of the polishing rate R _p of the next (n). Then, by substituting the target value of the predicted value and the polishing amount dV in the equation (1), it is possible to obtain a polishing time T _p to be set in the semiconductor wafer CMP device 200a.

In addition, when the polishing rate R _p calculated using the actual value of the previous (n−1) according to the formula (3) is used as the predicted value of the next (n) as it is, the inherent variation at the previous polishing Noise is directly reflected in the prediction error. Therefore, in order to reduce the influence of the fluctuation noise, a filter process is performed between the previous (n−1) actual value and the next (n) predicted value of the polishing rate R _p according to the equation (4). Just do it.

(4. Problems in general prediction methods)
However, the calculation method of the predicted value of the next (n) polishing rate R _p described above has a serious problem in practical use. That is, in order to calculate the equation (3), a measured value of the film thickness V _p (n−1) before polishing is necessary. However, in an actual semiconductor production line, the film thickness V before polishing is calculated. _Since it takes time to measure _p (n-1), the measured value of the film thickness V _p (n-1) before the polishing cannot be obtained until the next (n) polishing.

The measurement of the film thickness V _p (n−1) before polishing takes time because the film thickness measurement apparatus (not shown) is a separate apparatus from the semiconductor wafer CMP apparatus 200a. This is because when the film thickness is measured by the apparatus, in addition to the measurement time, it is necessary to clean and transport the target semiconductor wafer 10.

Of course, after the measurement value of the film thickness V _p (n−1) before polishing is acquired by the film thickness measuring device, the polishing rate R _p ( n) is predicted, and the next polishing (n) can be performed using the predicted polishing rate R _p (n). However, in such a case, the production efficiency of the semiconductor wafer 10 is greatly reduced due to the time delay associated with the film thickness measurement. Therefore, such a method is not taken in an actual production line.

Therefore, in such a case, instead of the polishing rate R _p (n) of the previous (n), for example, the polishing rate R _p (n− before L times) before the time delay associated with the film thickness measurement. L) can be used to take a measure that the predicted value of the next (n) polishing rate R _p (n) is used. In this case, the predicted value of the next (n) polishing rate R _p (n) can be obtained by Expression (5) obtained by expanding Expression (3).

Here, the actual value of L depends on various cases of the production line, but the approximate standard is about 5 to 10. Of course, also in this case, the influence of noise generated at the polishing rate R _p (n−L) before L times can be reduced by using an expression similar to Expression (4).

However, in the processing apparatus 200 such as the semiconductor wafer CMP apparatus 200a, the polishing pad 11 and the dresser 16 that are consumables are consumed with the usage time, and the performance is deteriorated. Therefore, the polishing pad 11 and the dresser 16 must be frequently replaced. When the polishing pad 11 and the dresser 16 are replaced, the performance is improved, so that the polishing rate _Rp is improved.

FIG. 5 is a diagram showing an example of a transition chart of a polishing rate actual value when the semiconductor wafer 10 is polished by the semiconductor wafer CMP apparatus 200a. In the polishing rate actual value transition chart 50 of FIG. 5, the horizontal axis represents the polishing order of numbers of the semiconductor wafer 10, the vertical axis represents the actual value of the polishing rate R _p. Also, the black square dots in the polishing rate actual value transition chart 50 represents the actual value of the polishing rate R _p obtained in the polishing of the semiconductor wafer 10 of each of the polishing order.

The polishing rate R _p differs greatly depending integrated circuit pattern to be formed on the material and the semiconductor wafer 10 to be polished of the membrane. Therefore, the polishing rate actual value transition chart 50 shown in FIG. 5, the actual value of the polishing rate R _p, are all actual values obtained from the semiconductor wafer 10 in the same integrated circuit products, the differences due to the integrated circuit pattern Consideration is given so that there is no impact.

Further, in FIG. 5, the dresser exchange point 50d represents the replacement time of the dresser 16 is a consumable part, in the example of FIG. 5, D ₁ to D a total of 4 times at each time point of _4, replaced with a dresser 16 new It has been expressed. The polishing pad exchange point 50p represents the replacement time of the polishing pad 11 is a consumable part, in the example of FIG. _5, a total of 9 times at each time point P 1, 1 _{to P 4, 2,} the polishing pad 11 is new It is shown that it was exchanged for something.

Further, as can be seen from FIG. 5, especially when the dresser 16 and the polishing pad 11 are replaced, the actual value of the polishing rate varies greatly. Therefore, when the actual value of the polishing rate R _p (n−L) before L times (n−L) is used as the predicted value of the polishing rate R _p (n) of the next (n) according to the equation (5). In this case, the error of the polishing time T _p (n) calculated from the predicted value also increases, and as a result, a large error also occurs in the film thickness to be polished.

  Therefore, in the semiconductor wafer 10 polished in this way, a large number of semiconductor wafers 10 that cannot achieve the target film thickness occur. In that case, the semiconductor wafer 10 that is overpolished must be discarded, and the semiconductor wafer 10 that is underpolished requires additional polishing. As a result, the production efficiency of the semiconductor wafer 10 is greatly reduced.

As described above, considering the problem that the production efficiency of the semiconductor wafer 10 is lowered, in particular, in the processing apparatus 200 in which a consumable part such as the semiconductor wafer CMP apparatus 200a determines the processing performance, L times before (n−L). It is actually difficult to predict the next (n) polishing rate R _p (n) using the actual value of the polishing rate R _p (n−L).

(5. Solution in the embodiment of the present invention)
As described above, a general method for predicting the polishing rate, that is, the polishing rate R _p (n−1), R _p (n in the previous (n−1) or L previous (n−L) polishing. The method of predicting the next (n) polishing rate R _p (n) using -L) has not been able to solve the problem of reduced production efficiency. Therefore, in this embodiment, the next (n) polishing rate R _p (n) is obtained using other manufacturing parameters (variables) that can be easily obtained by the previous (n−1) polishing. Present the method of prediction.

(5.1 Introduction of polishing rate prediction model)
In the processing apparatus control system 100 of the present embodiment, in order to solve the problem that the production efficiency is lowered, the apparatus performance prediction unit 133 of the control calculation unit 130 performs a polishing rate prediction model represented by the following equation (6). The polishing rate is predicted based on this.

Here, the variable x _k (n−1) is an explanatory variable representing the previous (n−1) state of the semiconductor wafer CMP apparatus 200a. When there is one explanatory variable, the equation (6) is a single regression equation. In the case of a plurality, a multiple regression equation is obtained. In this model, it is not necessary to select the previous (n−1) film thickness measurement value as the variable x _k (n−1), and the semiconductor wafer can be easily obtained immediately after the previous (n−1) polishing. Any variable may be used as long as it represents the state of the CMP apparatus 200a.

  That is, according to the equation (6), the apparatus performance of the processing apparatus 200 such as the polishing rate is not predicted from a physical quantity that represents the apparatus performance itself, but is to be predicted using “another physical quantity” that is highly correlated with the performance. Is. Here, the “other physical quantity” corresponds to the explanatory variable, and any physical quantity may be used as long as it can be easily obtained immediately after the machining process by the machining apparatus 200 is completed. If the “other physical quantity” is obtained immediately, the next (n) device performance can be predicted immediately.

In the present embodiment, the control calculation unit 130 can acquire the value of the variable immediately after the polishing of the semiconductor wafer 10 to be polished, accumulates the acquired value in the processing history data storage unit 140, and formula ( 6) can be calculated. Therefore, since the next (n) polishing rate R _p (n) is obtained immediately after the polishing is completed, it takes time to obtain the polishing rate R _p (n), so that the production efficiency of the semiconductor wafer 10 decreases. Problems in general prediction methods are solved.

In the case of the semiconductor wafer CMP apparatus 200a, usable explanatory variables (variable x _k ) are, for example, their accumulated usage time from the time of replacement of consumable parts such as the dresser 16 and the polishing pad 11, and the like. The cumulative number of semiconductor wafers to be polished from the time of replacement, the temperature of each part of the polishing pad 11, the torque of the table rotation motor 13, the pressure of each part of the head 14, etc. can be mentioned.

(5.2 Construction of prediction model by least squares method)
From among the candidates of the explanatory variable, any variable or, for either adopting a combination of any of the variables, processing history collected in the data storage unit 140, the polishing rate R _p actual value and explanatory variable candidates x _k of The coefficient _{ak of the} regression equation is statistically determined by the maximum likelihood method or the least square method using the actual value of the actual value, and can be determined by the contribution to the prediction accuracy of the explanatory variable obtained from the coefficient _ak . If there are a plurality of explanatory variables with the same contribution, it may be determined based on the collection cost of the values of the explanatory variables.

In the example of FIG. 5, the actual value of the polishing rate R _p (n) is before and after each time point D ₁ , D ₂ , D ₃ , D ₄ of the dresser replacement point 50d where the dresser 16 that is a consumable part is replaced. It changes greatly and decreases with the elapse of the cumulative use time after the dresser 16 is replaced. This means that the accumulated usage time after replacement of the dresser 16 has a high contribution as an explanatory variable of the polishing rate prediction model of the equation (6).

FIG. 6 is a diagram showing an example of a predicted value transition chart of the polishing rate R _p when the cumulative use time of the dresser is used as an explanatory variable. FIG. 6A compares the predicted value and the actual value of the polishing rate R _p. FIG. 8B is a diagram showing the predicted value error transition chart. Here, the prediction error represents a deviation of the actual value from the predicted value. Incidentally, in FIG. 6 (a), the gray circle dot represents the estimated value of the polishing rate R _p, white square dots represent actual values.

Referring to FIG. 6 (a), from the dresser cumulative use time, it can be seen predictable polishing rate R _p fairly good accuracy. However, referring to FIG. 6B, it can be seen that a prediction error offset to the plus side occurs in the A section 52a, and a prediction error offset to the minus side occurs in the C section 52c. In the B section 52b, a sharp inversion of the prediction error is observed.

In FIG. 6 (b), the offset of the prediction error in the A section 52a and section C 52c is exchanged _{D 1} of the dresser exchange point 50d, and dress performance of the dresser 16 used in the A section 52a, the dresser exchange point 50d exchanged with D _4, those caused by differences in the dress performance of the dresser 16 used in the C section 52c. This means that the prediction of the polishing rate R _p from the dresser cumulative usage time cannot prevent the occurrence of a prediction error offset due to the difference in dressing performance of the dresser 16.

In addition, although there is no dresser exchange point 50d in the B section 52b, a phenomenon occurs in which the prediction error suddenly reverses from the plus side to the minus side at the exchange points of P2 and _{3 at} the polishing pad exchange point 50p. . Such an inversion phenomenon of the prediction error does not occur except at the exchange point of P _{2 and 3} . In general, the initial dressing performance of the polishing pad 11 after replacement (aging performance of the polishing pad 11) varies depending on the accumulated usage time of the dresser 16. In the example of FIG. 6, the exchange points P _{2 and 3} at the polishing pad exchange point 50 p are examples in which the cumulative usage time of the dresser 16 is longer than the other exchange points. For this reason, even if the polishing pad 11 is replaced, sufficient initial dressing performance cannot be obtained, and the prediction error is inverted.

As described above, in the method of predicting the polishing rate R _p from the accumulated usage time of the dresser 16 based on the correlation between the accumulated usage time of the dresser 16 that is a consumable product acquired in advance and the polishing rate R _p , It is impossible to prevent a prediction error offset or a prediction error inversion (sudden shift) from occurring.

(5.3 Construction of meta prediction model)
(5.3.1 Model to prevent prediction error offset)
In this embodiment, in order to solve the problem that the offset of the prediction error occurs, the test polishing is performed every time the dresser 16 is replaced. Then, the apparatus performance prediction model meta prediction unit 132 of the control calculation unit 130 in the processing apparatus control system 100 (see FIG. 1), the actual value of the polishing rate obtained by the test polishing (hereinafter, the dresser 16 is replaced each time the dresser 16 is replaced). The test result is simply obtained), and the intercept a ₀ in the polishing rate prediction model is determined according to the following equation (7).

Further, when the coefficient a ₁ of the polishing rate prediction model changes every time the dresser 16 is replaced, the apparatus performance prediction model meta prediction unit 132 uses the test polishing result when the dresser 16 is replaced, and the equation (8 ) predicts the coefficients _{a 1} in accordance with.

As described above, in the equations (7) and (8), the intercept a ₀ and the coefficient a _{1 that} are parameters of the regression equation model for predicting the polishing rate R _p are expressed by the prediction models of other regression equations. The prediction model has a multiple structure. In the present specification, such a higher-level prediction model having a multiple configuration is referred to as a meta prediction model.

As described above, according to the equation (7) or the equation (8), the intercept a ₀ and the coefficient a ₁ in the regression equation model for predicting the polishing rate R _p are performed each time the dresser 16 is replaced. It will be updated according to the test polishing result. This means that individual dress performance differences of the dresser 16 are corrected. Thus, generation of an offset of the prediction error in prediction value of the polishing rate R _p can be prevented.

(5.3.2 Model that prevents reversal of prediction error (sudden shift))
Next, think about how to solve the problems inversion (sudden shift) occurs in the prediction error in the prediction value of the polishing rate R _p. One solution is to use the equations (7) and (8) as in the case of replacing the dresser 16. That is, the test polishing is performed even when the polishing pad 11 is replaced, and the result of the test polishing is applied to the equation (7) to determine the intercept a ₀ of the polishing rate prediction model. The coefficient a ₁ may be predicted by applying the result of test polishing to Equation (8).

  However, in such a case, the number of test polishing increases. In the case of test polishing, when the actual value of the polishing rate obtained by the polishing is used in the next polishing, as described above, only the time for measuring the film thickness of the target semiconductor wafer 10 with the film thickness measuring device is used. However, it takes time to clean or transport the semiconductor wafer 10, and the production efficiency is reduced. Therefore, in the present embodiment, a method that does not need to increase the number of test polishing is adopted.

  That is, in this embodiment, every time the dresser 16 or the polishing pad 11 that is a consumable part is replaced, the apparatus performance prediction model meta prediction unit 132 sets the polishing rate prediction model based on the meta prediction model of Expression (9). Update. Each time the semiconductor wafer 10 is polished, the apparatus performance prediction unit 133 predicts the polishing rate using the prediction model.

That is, when the dresser 16 is replaced, the apparatus performance prediction model meta prediction unit 132 updates the polishing rate prediction model according to the equation (7) or the equation (8). On the other hand, when the polishing pad 11 is replaced independently, the apparatus performance prediction model meta prediction unit 132 uses the accumulated usage time of the dresser at the time of replacement of the polishing pad as an explanatory variable of the meta prediction model. Intercept a ₀ and coefficient a ₁ are predicted and updated.

  By using the meta prediction model as described above, when the dresser cumulative usage time at the time of polishing pad replacement is short, that is, when the dressing performance of the dresser 16 is high, the replaced polishing pad 11 has a high polishing rate. On the other hand, if the accumulated use time of the dresser at the time of replacing the polishing pad is long, that is, if the dressing performance of the dresser 16 is low, the polishing pad 11 is only initialized to a low polishing rate state. It has become possible to faithfully predict phenomena such as not being aged.

(5.3.3 Prediction model intercept learning)
Furthermore, in order to improve the accuracy of the polishing rate prediction model, the apparatus performance prediction unit 133 may learn the polishing rate prediction model every time polishing is performed, as shown in Expression (10). As described above, since the film thickness measurement involves a time delay, it is difficult to always obtain the previous actual polishing rate value.

Therefore, here, the apparatus performance predicting unit 133 feeds back the difference between the polishing rate actual value and the predicted value of any previous L times (n−L), and multiplies it by a predetermined learning gain λ to generate a prediction model. learning sections of a _0, it may be configured to update. This learning gain λ corresponds to the feedback control gain of the actual polishing rate value. The learning model may be configured to learn and update not only the prediction model intercept a ₀ but also the prediction model coefficient a ₁ .

なお、式（１０）中の左向きの矢印（←）は、左辺で計算された値を右辺に代入することを意味する。

Note that a leftward arrow (←) in equation (10) means that the value calculated on the left side is substituted into the right side.

(5.4 Effects of the meta prediction model)
FIG. 7 is a diagram illustrating an example of a predicted value transition chart in which the polishing rate R _p is predicted based on the meta prediction model of Expression (9), and (a) is a predicted value and actual value of the polishing rate R _p. The figure which compared and showed, (b) is the figure which showed transition of the predicted value error. Incidentally, in FIG. 7 (a), the gray circle dot represents the estimated value of the polishing rate R _p, white square dots represent actual values.

  In the meta prediction model of Expression (9), every time the dresser 16 or the polishing pad 11 that is a consumable part is replaced, the intercept and coefficient of the regression prediction model are predicted and updated. Moreover, when the dresser 16 is updated, test polishing is performed, and the polishing result is substituted into the meta prediction model of Expression (9), and the polishing rate prediction model is updated.

Therefore, in the meta prediction model of Equation (9), as shown in FIG. 7B, the offset of the prediction error that occurred in the A section 52a and the C section 52c in the case of FIG. 6B occurs. Not. In addition, the inversion (abrupt shift) of the prediction error in the B section 52b does not occur. Thus, the meta prediction model, by which is adapted to predict the intercept and coefficients of a regression model to predict the polishing rate R _p, it is possible to prevent inversion (sudden shift) of the offset and the prediction error of the prediction error The accuracy of prediction can be improved.

(5.5 Issues existing in the meta prediction model)
In the meta prediction model based on the equation (9) shown above, two meta prediction models are prepared in order to predict the two parameters of the intercept a ₀ and the coefficient a ₁ of the prediction model of the polishing rate R _p . Therefore, in order to use the meta prediction model, two parameters of an intercept and a coefficient are necessary for each of the two meta prediction models, and it is necessary to determine a total of four parameters in advance.

  These meta-prediction model parameters are parameters of the regression model and should be defined statistically, but a large amount of test polishing cannot be performed to determine the parameters. If it does so, the production efficiency of the semiconductor wafer 10 will be reduced. Accordingly, these parameters need to be promptly determined from the smallest possible amount of machining history data accumulated in the machining history data storage unit 140.

  The parameters of these meta prediction models can be statistically determined by applying a maximum likelihood method, a least square method, or the like. However, in the case of the semiconductor wafer CMP apparatus 200a, the meta prediction model is expressed by different prediction formulas when the dresser 16 is replaced and when the polishing pad 11 is replaced separately. Must be determined individually. Therefore, a small amount of processing history data accumulated in the processing history data storage unit 140 is further divided into a small amount of data according to the conditions in each case, and the parameters of the meta prediction model are used for the small amount of data. To be determined statistically. In that case, when a parameter is statistically determined using the small amount of data, how to ensure the accuracy of the parameter becomes a problem.

(6. Processing in the model creation simulator)
Therefore, in order to solve this problem, the present embodiment does not adopt a method of determining the parameters of the meta prediction model from a small amount of processing history data, and evaluates the probability distribution of the parameters of the meta prediction model by simulation, A method of determining the parameter value from the average value or the mode value is adopted.

  In order to realize such a method for determining the parameters of the meta prediction model, the machining apparatus control system 100 (see FIG. 1) in the present embodiment is provided with a model creation simulator unit 110, and further, the model creation is performed. Inside the simulator unit 110, a model creation trial unit 111, a stochastic parameter generation unit 115, and a model accuracy convergence determination unit 116 are provided.

In the model creation simulator unit 110, the stochastic parameter generation unit 115 probabilistically generates parameter candidates for the four meta-prediction models in Expression (9), and the generated parameter candidates are used as the model creation trial unit 111. Send to. Furthermore, the model creating trying unit 111, based on the candidate of the parameters of the meta prediction model, a predicted value of the polishing rate R _p and Simulation, obtains the prediction error. The model accuracy convergence determination unit 116 performs statistical convergence determination of the prediction error obtained by the simulation evaluation. The processes in the stochastic parameter generation unit 115, the model creation trial unit 111, and the model accuracy convergence determination unit 116 are repeated until the convergence is determined in the convergence determination.

  In more detail, the model creation trial unit 111 includes a device performance prediction model meta prediction trial unit 112 and a device performance prediction trial unit 113. The apparatus performance prediction model meta-prediction trial unit 112 uses the four meta-prediction model parameter candidates received from the probabilistic parameter generation unit 115 to construct a meta-prediction model candidate of Expression (9). Then, the consumable component accumulated use time data in a predetermined continuous wafer polishing section from the processing history data storage unit 140 (in this embodiment, the consumable component dresser use time and the consumable component polishing pad use time in the processing history data of FIG. 4). , And sequentially update the polishing rate prediction model candidates according to the consumable part replacement derived therefrom, and transmit it to the apparatus performance prediction trial unit 113.

Similarly, the apparatus performance prediction trial unit 113 acquires consumable component accumulated use time data of a predetermined continuous wafer polishing section from the processing history data storage unit 140, and sequentially receives the acquired consumable component accumulated use time data. By substituting it into the candidate for the rate prediction model, the polishing rate R _p that is the device performance of the semiconductor wafer CMP apparatus 200a is predicted.

  Furthermore, the apparatus performance prediction trial unit 113 acquires the polishing rate actual value (polishing rate Rp in the data table of FIG. 4) of a predetermined continuous wafer polishing section from the processing history data storage unit 140 and compares it with the predicted polishing rate value. Then, the deviation is calculated, and the variance is transmitted as a prediction error to the model accuracy convergence determination unit 116.

  Subsequently, the model accuracy convergence determination unit 116 determines whether or not the prediction error data for the parameter candidate data of the series of meta prediction models has converged to a predetermined probability sample distribution (for example, a normal distribution), and determines the convergence interval. Determine. Details of the convergence determination will be described separately with reference to the drawings.

  The model creation simulator unit 110 calculates an average value or mode value from the simulation data of the convergence interval of each parameter candidate of the meta prediction model, determines the calculated value as a parameter value, and transmits it to the control calculation unit 130.

(7. Application of MCMC method)
By the way, when the generation of parameter candidates for the meta prediction model in the stochastic parameter generation unit 115 is performed randomly by a simple Monte Carlo simulation method, it takes a long time for the probability sample distribution of the prediction error to converge. Or the problem of not converging arises. Therefore, in the present embodiment, a series of processes for generating parameter candidates (sample sampling) for meta prediction models, updating candidate polishing rate prediction models, and evaluating convergence of prediction error probability sample distribution in the model creation simulator unit 110, Apply MCMC method to hierarchical base model.

  If the MCMC method for the hierarchical base model is applied to a series of processes in the model creation simulator unit 110, the parameter posterior probability distribution can be obtained from the product of the likelihood derived from the actual value of the prediction error and the parameter prior probability distribution, Further, since the parameter candidates of the meta prediction model can be generated (by sample sampling) based on the posterior probability distribution, there is an effect that the convergence of the prediction error probability sample distribution is accelerated.

  FIG. 8 is a diagram illustrating an example of a processing flow of model creation simulation processing in the model creation simulator unit 110. As shown in FIG. 8, the model creation simulation process includes a parameter initial value setting process by Markov chain (step S10), a model prediction trial process (step S11), a prediction error variance calculation, and a posterior distribution update process (step S12). , Markov chain convergence determination processing (step S13), extraction processing of sample values in the convergence interval from the Markov chain (step S14), parameter determination processing from the distribution of sample values in the convergence interval (step S15), model of the control operation unit The update process (step S16) is included.

  The model prediction trial process (step S11) includes a device data section initialization process (step S11a), a device data read process (step S11b), and a device performance prediction model meta prediction trial process (step S11c) for a model creation trial. The apparatus performance prediction trial process (step S11d) from the apparatus performance prediction model, the apparatus performance prediction error calculation process (step S11e), and the apparatus data end process (step S11f) are configured.

Hereinafter, the details of the MCMC method and the model creation simulation process to which the MCMC method is applied will be described with reference to FIG. First, as a preliminary preparation, as shown in the following equation (11), a polishing rate prediction error ε, which is a deviation between the actual value and the predicted value of the polishing rate, is a normal distribution having an average value of zero and a variance of σ ² . Let N be a random variable according to N. Note that “˜” in the formula indicates that the random variable (polishing rate prediction error ε) on the left side follows the statistical distribution (normal distribution N) on the right side.

  Further, the hierarchical base model shown in the equation (12) is set with the four parameters of the meta prediction model and the dispersion parameter of the normal distribution N followed by the polishing rate prediction error ε of the equation (11) as a random variable θ. .

  As shown in the equation (12), the function π (left side) which is a posterior probability density function of the random variable θ based on the actual value of the polishing rate is the polishing rate prediction error data when the random variable θ is given. Is expressed by a product of a function f that is a likelihood function of and a function π (right side) that is a prior probability density function of a random variable θ.

  Of the prior probability density functions of the random variable θ, the prior probability density functions of the four parameters of the meta prediction model are represented by a normal distribution N shown in Expression (13).

  If there is prior knowledge, the average value and variance value of these normal distributions N are set based on that knowledge. In this embodiment, since it is not assumed that there is prior knowledge, a wide distribution having an average value of zero and a variance value of 10,000 is set as the normal distribution N. However, in the absence of prior knowledge, the statistical value such as the average value or the variance value has a small sensitivity to the result, and therefore it is not necessary to set these statistical values exactly to these values.

Further, among the prior probability density functions of the random variable θ, the prior probability density function of the variance σ ² of the normal distribution N followed by the polishing rate prediction error ε of the formula (11) is expressed by the following formula (14). , Represented by an inverse gamma distribution IG.

If there is prior knowledge, the two parameters n ₀ and S ₀ of the inverse gamma distribution IG are set based on that knowledge. In this embodiment, since it is not assumed that there is prior knowledge, a wide distribution having a parameter n ₀ of 0.002 and S ₀ of 1 is set as the inverse gamma distribution IG. If there is no prior knowledge, the sensitivity to the result of the parameter is small, so it is not necessary to set the two parameters exactly to these values.

  Next, a processing flow of model creation simulation processing by the MCMC method will be described with reference to FIG. First, the model creation simulator unit 110 sets the initial value of the variance of the normal distribution N that the four parameters of the meta prediction model included in the random variable θ and the polishing rate prediction error ε of Equation (11) follow ( Parameter initial value setting process: Step S10). Since the sensitivity to the results of these initial values is not high, it may be set by sampling appropriately from the preset distributions of Equation (13) and Equation (14).

  Next, the model creation simulator unit 110 repeatedly executes the processing of step S11a to step S11f that sequentially calculates the sample values according to the Markov chain and according to the posterior distribution of the equation (12) (model prediction trial processing: step S11). ).

  In the model prediction trial process (step S11), the apparatus performance prediction model meta prediction trial unit 112 transmits the random variable θ (four parameters of the meta prediction model and variance of the polishing rate prediction error) transmitted from the stochastic parameter generation unit 115. The current value of (parameter) is received, the meta prediction model of Expression (9) is constructed using the four parameters of the received meta prediction model, and a device data section for a model creation trial is set (device data section) Setting process: Step S11a).

  Next, the device performance prediction model meta prediction trial unit 112 sequentially reads the consumable component accumulated usage time data of the set device data section from the machining history data storage unit 140 (device data reading process: step S11b). Then, meta-prediction of the polishing rate prediction model is tried according to the replacement results of consumable parts derived from the read data, and the obtained polishing rate prediction model is transmitted to the device performance prediction trial unit 113 (device performance prediction). Model meta prediction trial process: Step S11c).

  Further, the apparatus performance prediction trial unit 113 sequentially acquires the consumable component accumulated usage time data of the continuous wafer polishing section in the apparatus data section set in step S11a from the processing history data storage section 140, and receives the previously received polishing. Substituting into the rate prediction model, trial of prediction of the polishing rate as the apparatus performance is tried (polishing rate prediction trial process: step S11d). And the apparatus performance prediction trial part 113 acquires the polishing rate performance value of the continuous wafer polishing area set previously from the processing history data storage part 140, and calculates a prediction error compared with the polishing rate prediction value ( Device performance prediction error calculation processing: Step S11e).

  Next, the apparatus performance prediction trial part 113 determines whether the apparatus data section which should perform model prediction trial calculation was complete | finished about the apparatus data area set by step S11a (step S11f). As a result of the determination, if the device data section to be subjected to the model prediction trial calculation has not ended (No in step S11f), the process returns to the previous and the processing after the device data reading process (step S11b) is repeatedly executed. To do.

  On the other hand, when the device data section to be subjected to the model prediction trial calculation is completed (Yes in step S11f), the device performance prediction trial unit 113 calculates the variance of the prediction error sequence obtained by the processing so far, The prediction error variance, the current value of the random variable θ, and, if necessary, the consumable component accumulated usage time data are input to the equation (12), and the posterior distribution of the random variable θ is updated (prediction error variance calculation and posterior Distribution update processing: Step S12).

Next, the model accuracy convergence determination unit 116 converges a chain set of sample values from the posterior distribution of the polishing rate prediction error variance σ ² included in the sample values of the random variable θ into the inverse gamma distribution IG, and It is determined whether or not a predetermined number of Markov chain samples has been calculated after the convergence determination (Markov chain convergence condition determination processing: step S13).

  When the convergence condition is not satisfied (No in step S13a), the probabilistic parameter generation unit 115 thereafter performs the parameters of the meta prediction model included in the random variable θ and One of the variance parameters of the polishing rate prediction error is selected in order according to the Markov chain, and the sample value is newly generated from the posterior distribution of Equation (12) in which the parameter was updated last time, and the updated parameter And the remaining parameter values same as those of the previous time are transmitted to the model creation trial unit 111 (step S17).

  Subsequent to step S17, the processing shifts from the stochastic parameter generation unit 115 to the processing of the model creation trial unit 111, and the processing after step S11a is repeatedly executed.

  On the other hand, when the convergence condition in step S13 is satisfied (Yes in step S13a), the model accuracy convergence determination unit 116 ends the repeated calculation processing so far, determines the convergence section, and determines the probability. A sample series of the variable θ is cut out (convergence interval sample series cut-out process: step S14).

  FIG. 9 is a diagram showing an example of how the parameter sample series converges by the MCMC method (repetitive processing up to step S13 in FIG. 8). FIG. 9A shows a predetermined number of times in addition to convergence from the first time. The figure which showed the mode of the convergence about the case where a convergence area was included, (b) is the figure which showed the mode that it converged in the convergence area of the predetermined number of times.

In FIG. 9A, the left chart 55a shows how the reciprocal sample series of the variance parameter σ ² converges, and the right chart 55b shows a sample of the parameter β ₀ that is one of the parameters of the meta prediction model. It shows how the sequence converges. Here, it is determined that convergence has been confirmed, for example, the number of repetitions from 2,000 to 5,000 is referred to as a convergence section 56.

  In FIG. 9B, the left chart 57a is a parameter sample series obtained by cutting out the convergence section 56 from the left chart 55a in FIG. 9A, and the right chart 57b is the frequency distribution. The average value 58 is calculated from the parameter sample series in the convergence section 56. Further, as can be seen from the right chart 57b, the parameter sample series in the convergence section 56 forms a normal distribution.

  Referring to the processing flow in FIG. 8 again, the model creation simulator unit 110 calculates the average value based on the sample series of the convergence interval 56 of each parameter included in the random variable θ and determines the parameter value (parameter determination Process: Step S15). Thereafter, the model creation simulator unit 110 transmits the average value of each of the four parameters of the meta prediction model (for example, reference numeral 58 in FIG. 9B) to the device performance prediction model meta prediction unit 132 of the control calculation unit 130. Then, the prediction model in the control calculation unit 130 is updated (prediction model update process: step S16).

  The content of the model creation simulation process based on the MCMC method executed by the model creation simulator unit 110 has been described with reference to FIG. 8. Details of the actual calculation include, for example, the Metropolis Hastings algorithm, Gibbs Sampler algorithm, Slice Sampler It is executed based on an algorithm or the like (see Non-Patent Document 1, etc.).

  The model creation simulation process described above is stored in the storage device 33 as a program of the model management computer 31 installed in the operation center 300 shown in FIG. Executed. Further, when the program is executed, data in the Markov chain sample value storage unit 121, the apparatus performance prediction model storage unit 122, and the machining history data storage unit 140 are appropriately read and written.

(8. Processing in the control calculation unit)
FIG. 10 is a diagram illustrating an example of a processing flow of apparatus performance prediction and control amount calculation processing in the control calculation unit 130 of the processing apparatus control system 100. As illustrated in FIG. 10, the device performance prediction model meta prediction unit 132 of the control calculation unit 130 first receives the four parameter values of the meta prediction model transmitted from the model creation simulator unit 110, and receives the received parameter values. Thus, the meta prediction model is updated (step S20), that is, the meta prediction model for predicting the intercept a ₀ and the coefficient a ₁ in the polishing rate prediction model of Expression (9) is updated.

  Next, the apparatus performance prediction model meta prediction unit 132 acquires the previous value of the usage time of the consumable parts (the dresser 16 and the polishing pad 11) from the processing history data storage unit 140 in synchronization with the arrival of the semiconductor wafer 10 to be polished. (Step S21), and the replacement of the consumable parts (the dresser 16 and the polishing pad 11) is detected (Step S22). In order to detect the replacement of the consumable parts, it is only necessary to subtract the previous value from the previous value of the use time of the consumable parts (dresser 16 and polishing pad 11) in the machining history data and detect whether the sign is reversed. .

  If the replacement of the dresser 16 is detected by detecting the consumable part (Yes in step S23), the apparatus performance prediction model meta prediction unit 132 acquires the test polishing result and uses the test polishing result. That is, the polishing rate prediction model is updated by substituting the test polishing result into the meta prediction model at the time of dresser replacement of the equation (9) (step S23a).

  If the replacement of the dresser 16 is not detected (No in step S23) and the replacement of the polishing pad 11 is detected (Yes in step S24), the apparatus performance prediction model meta prediction unit 132 uses the dresser usage time. That is, the polishing rate prediction model is updated by substituting the dresser usage time into the meta prediction model at the time of polishing pad replacement of Equation (9) (step S24a).

On the other hand, if neither the replacement of the dresser 16 nor the replacement of the polishing pad 11 is detected (No in step S24), the apparatus performance prediction model meta prediction unit 132 records the polishing rate obtained from the processing history data storage unit 140. A value is acquired, and an intercept a ₀ of the polishing rate prediction model is learned based on the equation (10) (step S25). At this time, it may be learned together coefficient a ₁ of the polishing rate prediction model.

  The apparatus performance prediction model meta prediction unit 132 sends the polishing rate prediction model updated or learned by the processing so far to the apparatus performance prediction unit 133. Then, the apparatus performance predicting unit 133 that has received the transmission uses the previous value of the dresser usage time, that is, substitutes the previous value of the dresser usage time into the polishing rate prediction model of Equation (9). (Step S26), and the predicted polishing rate is sent to the control amount calculation unit 134 and the abnormality prediction unit 135.

  Subsequently, the abnormality predicting unit 135 determines whether or not the polishing rate is abnormal by comparing the predicted polishing rate with a predetermined threshold. If the polishing rate is abnormal (Yes in step S27), An alarm is transmitted to the processing apparatus 200 (semiconductor wafer CMP apparatus 200a) (step S27a).

  On the other hand, if the polishing rate is not abnormal (No in step S27), the control amount calculation unit 134 calculates the polishing time based on the equation (1), and uses the polishing time obtained by the calculation as the processing device 200 ( Then, the semiconductor wafer CMP apparatus 200a) is transmitted to the semiconductor wafer CMP apparatus 200a) (step S28), and polishing is instructed for the transmitted polishing time.

  When the control arithmetic unit 130 detects the arrival of the next semiconductor wafer 10 to be polished based on the notification from the processing apparatus 200 (semiconductor wafer CMP apparatus 200a) (Yes in step S29), the process proceeds to step S21. The process from step S21 is repeated and executed. When a predetermined number of actual data is newly accumulated in the machining history data storage unit 140, the iterative process after step S21 is temporarily suspended, and the model creation simulator unit 110 causes the meta prediction model to be updated. You may make it update four parameter values.

  As described above, the apparatus performance prediction and control amount calculation processing in the control calculation unit 130 described with reference to FIG. 10 is stored in the storage device 43 as a program of the control computer 41 installed at the site 400 (see FIG. 2). The program is executed by the arithmetic processing unit 42.

  In this case, the control computer 41 uses the processing apparatus 200 (semiconductor wafer CMP apparatus 200a) to calculate the polishing rate calculation result predicted based on the parameter value of the meta prediction model acquired from the model management computer 31 via the communication network 500. Processing history data (consumed part use time, film thickness before and after polishing, etc.) obtained by polishing by the processing apparatus 200 is acquired, stored in its own storage device 43 and used. Further, the control computer 41 transmits a copy of the accumulated machining history data to the model management computer 31. Therefore, the control computer 41 and the model management computer 31 have the machining history data storage unit 140 in a substantially mirror state.

  FIG. 11 is a diagram showing an example of an alarm display screen displayed on the display device of the control computer 41. The alarm may be issued and displayed on the processing apparatus 200 (semiconductor wafer CMP apparatus 200a) side, but if an alarm display screen as shown in FIG. Convenient. Even when no alarm has occurred, it is convenient for the maintenance staff to display a similar display screen at the timing when maintenance staff performs maintenance such as replacement of consumable parts.

  As shown in FIG. 11, the alarm display screen 80 includes a notification content display field 81, and in the notification content display field 81, for example, “the polishing rate predicted value lower limit lower limit” is reported. The contents are displayed. The alarm display screen 80 also includes a status display column 82 for the current consumable parts. The status display column 82 displays the dresser replacement date and time, the accumulated usage time thereof, the polishing pad replacement date and time and the cumulative usage time thereof, and the like. Is done.

  The alarm display screen 80 also includes a polishing rate prediction result display field 83. The polishing rate prediction result display field 83 includes a predicted polishing rate when the polishing pad is replaced alone and a polishing rate when the dresser and the polishing pad are simultaneously replaced. In addition to displaying predicted values, prediction buttons 83a and 83b for instructing execution of the polishing rate prediction simulation are displayed. Further, a predicted polishing rate / actual value transition chart 84 is displayed on the alarm display screen 80, and includes a predicted value 84a of the polishing rate, a lower limit 84b that is a lower limit threshold, and the like. Is displayed.

  Note that such an alarm display screen 80 is displayed when step S27a of the processing flow shown in FIG. 10 is executed, for example, when the predicted polishing rate when the polishing pad is replaced alone exceeds the lower limit. Is done. At this time, the display column of the predicted polishing rate at the time of simultaneous replacement of the dresser and the polishing pad is blank. Here, if the maintenance staff at the site 400 presses the “prediction” button at the time of simultaneous dresser / polishing pad replacement, a polishing rate prediction simulation is executed, and the predicted result is predicted polishing at the time of simultaneous dresser / polishing pad replacement. Displayed as a rate.

  As a result, the maintenance personnel make an appropriate selection of maintenance work, such as whether to perform additional test polishing after exchanging the polishing pad alone, or to perform simultaneous dresser / polishing pad replacement. Will be able to.

(9. Effects of the present embodiment)
In the present embodiment, the device state (for example, the polishing rate) of the processing device 200 is not a measurement value of a physical quantity that directly represents the device performance, but a device state that is more easily acquired that correlates with the device performance. Can be performed by using a physical quantity (for example, cumulative usage time of the dresser 16 and the polishing pad 11). As a result, for example, a predicted value of the polishing rate can be obtained without measuring the film thickness of the semiconductor wafer 10 using a film thickness inspection apparatus. Therefore, the processing apparatus 200 (semiconductor wafer) can be obtained using the predicted value. It is possible to control the operating condition (polishing time) that compensates for the performance variation of the CMP apparatus 200a). Therefore, the delay time for film thickness measurement for predicting the polishing rate is eliminated, so that the production efficiency of the semiconductor wafer 10 and the like can be improved.

  Further, in this embodiment, when replacing some consumable parts (polishing pad 11) among a plurality of consumable parts (for example, the dresser 16 and the polishing pad 11), the apparatus performance (polishing rate) is changed by the replacement. How much the prediction model fluctuates is predicted using the state (cumulative usage time) of other consumable parts (dresser 16). Therefore, during maintenance, even if all consumable parts (dresser 16 and polishing pad 11) are not replaced, but only a part of them are replaced, the performance of the apparatus (polishing rate) is continuously maintained. Since the prediction can be made with high accuracy, the life of the consumable parts can be extended according to the life of each consumable part.

  Further, in the present embodiment, even when there is little accumulation of actual data of replacement of consumable parts and apparatus performance fluctuations accompanying the replacement, parameters (intercepts and coefficients) of the prediction model of apparatus performance (polishing rate) are regarded as random variables, and prediction is performed. By repeating generation of model parameter candidate sample values and device performance prediction or device control simulation by application to a small amount of data, the distribution of predicted model parameters is determined. Then, by using the average value or mode value of the distribution determined in this way as the optimal prediction model parameter, it is possible to create a highly accurate prediction model even when there is little accumulation of actual data.

  Furthermore, in the present embodiment, MCMC for the hierarchical base model is performed in a series of steps including generation of sample values of prediction model parameter candidates, update of apparatus performance (polishing rate) prediction model candidates, and evaluation of convergence of probability sample distribution of prediction errors. The law is applied. By applying this MCMC method, the parameter posterior probability distribution is obtained from the product of the likelihood derived from the actual value of the prediction error and the parameter prior probability distribution, and the prediction model parameter candidate sample is generated using the posterior probability distribution. Thus, the distribution of the prediction model parameters can be determined efficiently.

<Second Embodiment>
FIG. 12 is a diagram illustrating an example of a functional block configuration of a machining apparatus control system according to the second embodiment of the present invention. As shown in FIG. 12, the machining apparatus control system 100A includes blocks such as a model creation simulator unit 110A, a control calculation unit 130, and a machining history data storage unit 140. Hereinafter, the same components as those in the processing apparatus control system 100 of the first embodiment shown in FIG. 1 are denoted by the same reference numerals, and the description thereof is omitted.

  In the present embodiment, the model creation simulator unit 110A includes a control simulator 214 and a control performance convergence determination unit 224, and differs from the model creation simulator unit 110 in the first embodiment in that the apparatus performance (polishing rate) prediction model is different. In addition to evaluation and creation, it is possible to evaluate and create a device control (polishing amount control) model.

  FIG. 13 is a diagram illustrating an example of a process flow of a model creation simulation process in the model creation simulator unit 110A. The process flow shown in FIG. 13 is different from the process flow of the model creation simulation process in the first embodiment (see FIG. 8) in that the model prediction creation process (step S11A) is a control simulation process based on the predicted apparatus performance value. (Step S11g) and a control error calculation process (Step S11h). The other processes are the same as those in the first embodiment, and the same step numbers as those in FIG. 8 are given.

  In the present embodiment, learning of Expression (10) is performed on the dispersion parameter of the normal distribution N followed by the four parameters of the meta prediction model described above and the polishing rate prediction error of Expression (11) as the random variable θ in the MCMC method. A gain (feedback control gain) λ is added to set a hierarchical base model as shown in Expression (15) (not shown in FIG. 13 for the preparatory steps).

  The prior probability density function of the learning gain λ added to the random variable θ is assumed to be a uniform distribution U shown in Expression (16). The uniform distribution U takes an integer value of the reciprocal probability of the interval width (= 99-1 + 1 = 99) whose upper and lower limits are integer values, and the learning gain (feedback control gain) λ is 0.01 times the value ( 0.01 to 0.99).

  As in the case of the first embodiment, the model creation simulator unit 110A executes step S10 and step S11a, and then sequentially performs sample value calculation from the posterior distribution of Expression (15) according to the Markov chain. The loop processing from step S11b to step S11f is repeated.

However, the control simulator 214 performs a control simulation based on the predicted value of the apparatus performance (polishing rate) following the trial of predicting the polishing rate by the apparatus performance prediction trial process (step S11d) (step S11g). Specifically, delay learning (feedback control) is performed based on the actual polishing rate value of the polishing rate prediction model intercept a ₀ in equation (10).

  Further, as shown in the following equation (17), the control simulator 214 divides the polishing amount requirement value by the polishing rate prediction value to predict the polishing time. Then, a polishing amount simulation value is obtained by multiplying the estimated polishing time value by the actual polishing rate value. Then, the polishing amount simulation value is transmitted to the control performance convergence determination unit 224.

  The control performance convergence determination unit 224 obtains the actual polishing amount value of the continuous wafer polishing section set in step S11a from the processing history data storage unit 140, and compares it with the polishing amount simulation value to calculate a control error ( Step S11h). Subsequently, it is determined whether or not the sequential control simulation calculation based on the device data of the section is completed (step S11f).

  When the sequential control simulation calculation based on the device data in the section is completed (Yes in step S11f), the control performance convergence determination unit 224 calculates the variance of the obtained control error sequence, and the control error sequence And the current value of the random variable θ including the learning gain λ, and if necessary, the consumable component accumulated usage time data are substituted into the equation (15), and the posterior distribution of the random variable θ is updated (step S12). ).

  Next, the control performance convergence determination unit 224 converges the chain set of sample values from the posterior distribution of the variance of the control error included in the sample value of the random variable θ into a normal distribution, and after the determination of convergence, It is determined whether or not the number of Markov chain samples has been calculated (step S13). When the convergence condition is not satisfied (No in step S13a), the probabilistic parameter generation unit 115 thereafter performs the parameter of the meta prediction model included in the random variable θ every time this step is passed, One of the dispersion parameter of the polishing rate prediction error and the learning gain (feedback control gain) λ is sequentially selected according to the Markov chain, and the sample value is newly determined from the posterior distribution of the equation (12) in which the parameter was updated last time. The updated parameter values and the remaining parameter values that are the same as the previous parameter are transmitted to the model creation trial unit 111A (step S17).

  On the other hand, when the convergence condition in step S13 is satisfied (Yes in step S13a), the control performance convergence determination unit 224 ends the repeated calculation processing so far, determines the convergence section, and determines the probability. A sample series of the variable θ is cut out (step S14).

  FIG. 14 is a diagram showing how the sample sequence of the learning gain λ converges by the MCMC method (repetitive processing up to step S13 in FIG. 13). FIG. 14A shows a predetermined number of times in addition to the convergence from the first time. (B) is the figure which showed a mode that it converges in the predetermined number of times of the convergence area.

  In FIG. 14A, the left chart 70a shows how the sample series of the learning gain λ converges, and the right chart 70b shows the frequency distribution. As shown in FIG. 14A, for example, if the convergence interval 56 is set to 20000 or more iterations, the sample series of the learning gain λ converges to an exponent family distribution such as an inverse beta distribution. Further, in the section before the convergence section 56, the parameter of the polishing rate prediction model has not converged to an accurate value, so an attempt is made to increase the learning gain value. On the other hand, in the convergence section 56, it can be seen that since the accurate model has been made, the convergence is made to a small learning gain value.

  In FIG. 14B, the left chart 71a is a sample series of the learning gain λ obtained by cutting out the convergence section 56 from the left chart 70a in FIG. 14A, and the right chart 71b shows the frequency. Distribution. The mode value 72 is calculated from the parameter sample series in the convergence section 56, and the optimum value of the learning gain (feedback control gain) λ is determined.

  FIG. 15 is a diagram illustrating an example of a transition chart of the control amount when the polishing amount control simulation result is applied to the control. In FIG. 15, gray round dots represent simulation values of control amounts (polishing amounts), and white square dots represent actual values. From this figure, as an effect of the polishing amount control simulation in which the parameters and learning gain (feedback control gain) of the polishing rate prediction model described above are determined by the MCMC method, the simulation value is compared with the actual value before the simulation is applied. Then, it can be seen that the variation in the polishing amount is greatly reduced.

  As described above, according to the second embodiment, by including the learning gain (feedback control gain) λ in the random variable θ, simultaneously with the four parameters of the meta prediction model for predicting the polishing rate prediction model by the MCMC method, As for the learning gain (feedback control gain) λ, a value capable of reducing the control error can be obtained.

<Third Embodiment>
In the present embodiment, not only data of one processing apparatus 200 (for example, a polishing apparatus such as a semiconductor wafer CMP apparatus 200a) but also data of a plurality of processing apparatuses 200 are mixed. An example of the machining apparatus control system 100 capable of creating a unified prediction model in a form including a difference will be described. In addition, this embodiment is implemented with the form which expanded 1st Embodiment or 2nd Embodiment.

  When mixing data from a plurality of processing apparatuses 200, Expression (18) is used instead of Expression (9) described above. Here, description of the part having the same function as that of the already described formula (9) is omitted. As shown in the following equation (18), an offset for each apparatus is added to each of two meta prediction models for predicting the intercept and coefficient of the polishing rate prediction model.

  Further, similarly to the previously described equation (12) or equation (15), in the following equation (19), the offset for each of the two processing devices 200 is added to the random variable θ by the number of devices, The prior probability density function is set to a normal distribution N shown in Expression (20). When there is prior knowledge, the average parameter and the dispersion parameter of the normal distribution N are set based on the knowledge. In this embodiment, since it is not assumed that there is prior knowledge, a wide distribution having an average value of zero and a variance value of 10,000 is set as the normal distribution N. However, in the absence of prior knowledge, the statistical value such as the average value or the variance value has a small sensitivity to the result, and therefore it is not necessary to set these statistical values exactly to these values.

  The model creation simulator units 110 and 110A (see FIGS. 1 and 12) apply the MCMC method to a data set in which data of a plurality of processing apparatuses 200 are mixed, and based on the prior distribution of Expression (20), A sample value from the posterior distribution of Expression (19) is generated, and an average value or mode value of the random variable θ including the offset for each processing device 200 corresponding to the number of devices is obtained. The control calculation unit 130 assigns this value to the meta prediction model of Expression (18), calculates the polishing time based on the prediction of the polishing rate for each processing apparatus 200, and controls the polishing amount.

As described above, according to the present embodiment, by introducing the offset parameter for each processing apparatus 200 into the meta prediction model for predicting the polishing rate prediction model, the meta data is obtained from the data set in which the data of the plurality of processing apparatuses 200 are mixed. A predictive model can be created. Therefore, even when the number of actual data per processing apparatus 200 is small, it is possible to predict the polishing rate R _p by using the data of other processing apparatuses 200.

(Modification of the embodiment: mixed flow of multiple products)
In addition, if offsets are set for a plurality of types of semiconductor wafers 10 to be polished in the same manner instead of the plurality of processing apparatuses 200, data when polishing is performed by mixing a plurality of types of semiconductor wafers 10. A meta prediction model can be created from the set, and even when the number of actual data per type of the semiconductor wafer 10 to be polished is small, the polishing rate can be obtained by utilizing the data of other types of semiconductor wafers 10. it is possible to make predictions of R _p. Furthermore, it is possible to simultaneously process the mixing of the data sets of the plurality of processing apparatuses 200 and the mixing of the data sets of the mixed flow products.

<Generalization>
In the embodiment described above, the previous dresser usage time x ₁ (n−1) is adopted as an explanatory variable for predicting the polishing rate R _p of Equation (9), and the intercept a ₀ and coefficient a _{1 of the} prediction model are adopted. As an explanatory variable of the meta prediction model for predicting the dressing, the test polishing result is adopted at the time of dresser replacement, and the dresser usage time x ₁ (P _{i, j} −1) immediately before the time point P _{i, j} immediately before the replacement is adopted at the time of pad replacement. did. However, the present invention is not limited to this, and appropriate explanatory variables vary depending on the configuration of the processing apparatus 200 and the processing (polishing) process procedure (polishing process conditions).

  For example, as a consumable part, in addition to the dresser 16 and the polishing pad 11, a semiconductor wafer (adsorbed rubber film) of the head 14 that holds the semiconductor wafer 10, and an outer periphery of the semiconductor wafer 10 and simultaneously polishing the semiconductor wafer Retainer rings that prevent over-polishing of the outer peripheral portion 10, edge sag, peeling, and the like are candidates.

  Further, in addition to the consumable component usage time, physical quantities that change according to the consumption progress of the consumable component, for example, the temperature of the polishing pad 11, the temperature of the semiconductor wafer 10, the temperature of the dresser 16, the table driving torque, the head driving torque, and the dresser driving torque. Alternatively, a cumulative value after replacement of the consumable part squared of these physical quantities may be used as the explanatory variable. Moreover, the apparatus performance prediction method of the present invention can be applied not only to replacement of consumable parts but also to all physical quantities handled in maintenance that changes the state of the processing apparatus 200.

Which variable or combination of variables is adopted as the explanatory variable from among the explanatory variable candidates, for example, the actual value of the polishing rate R _p accumulated in the machining history data storage unit 140 and the explanatory variable candidate. By statistically determining the coefficient a _{k of the} regression equation from the actual value of x _{k by} the maximum likelihood method or the least square method, and evaluating the degree of contribution to the prediction accuracy of the explanatory variable obtained from the coefficient a _k I can decide. In addition, when there are a plurality of explanatory variables having the same contribution degree, it may be determined from the collection cost of the explanatory variable values.

  Furthermore, in the embodiment described above, the semiconductor wafer CMP apparatus 200a has been described as the processing apparatus 200 to be controlled, but the processing apparatus 200 is not limited to the semiconductor wafer CMP apparatus 200a. If the processing apparatus 200 to be controlled is one that polishes or grinds other products or materials, the prediction of the polishing rate as the apparatus performance becomes an issue, and the control performance is the same as in the embodiment described above. Can be improved. In addition to a polishing apparatus, if the processing apparatus is affected by deterioration of a plurality of consumable parts, the apparatus performance can be accurately predicted by applying the present invention, and the control performance can be improved. Can do.

DESCRIPTION OF SYMBOLS 10 Semiconductor wafer 11 Polishing pad 12 Table 13 Table rotation motor 14 Head 15 Head rotation motor 16 Dresser 17 Dresser rotation motor 18 Dresser swing motor 19 Slurry 20 Slurry supply part 31 Model management computer 32 Arithmetic processing device 33 Storage device 41 Control Computer 42 Arithmetic processing device 43 Storage device 100, 100A Processing device control system 110, 110A Model creation simulator unit 111, 111A Model creation trial unit 112 Device performance prediction model meta prediction trial unit 113 Device performance prediction trial unit 115 Probabilistic parameter generation unit 116 Model Accuracy Convergence Determination Unit 121 Markov Chain Sample Value Storage Unit 122 Device Performance Prediction Model Storage Unit 130 Control Operation Unit 132 Device Performance Prediction Model Meta Prediction Unit 133 Device Performance Prediction Unit 134 Control amount calculation unit 135 Anomaly prediction unit 140 Processing history data storage unit 200 Processing device 200a Semiconductor wafer CMP device 214 Control simulator 224 Control performance convergence determination unit 300 Operation center 400 Site 500 Communication network

Claims (14)

A processing device control system that predicts the processing performance of a processing device whose processing performance varies depending on the state of consumable parts, and controls the processing device,
A machining history data storage unit that accumulates machining history data acquired from the machining device during machining by the machining device;
Machining history data stored in the machining history data storage unit are parameters of a meta prediction model that predicts parameters of a prediction model that predicts the machining performance from a physical quantity that represents the state of the machining device including the state of the consumable part. And a model creation simulator unit determined by simulation using random numbers according to a predetermined statistical distribution determined in advance,
Control of the processing device based on a prediction model for predicting the machining performance determined by a meta prediction model having parameters determined by the model creation simulator unit, and a current value of a physical quantity representing a state of the consumable part A control calculation unit for calculating the quantity;
A processing apparatus control system characterized by comprising: The processing apparatus control system according to claim 1, wherein the prediction model for predicting the machining performance is a regression model having a physical quantity representing the state of the consumable part as an explanatory variable. The meta prediction model for predicting a parameter of a prediction model for predicting the machining performance is a regression model having a physical quantity representing a state of the consumable part at the time of replacement of the consumable part as an explanatory variable. The processing apparatus control system described. The processing apparatus control system according to claim 1, wherein the meta prediction model that predicts a parameter of a prediction model that predicts the machining performance includes a model that predicts a learning gain. The processing apparatus control system according to claim 1, wherein the physical quantity representing the state of the consumable part is an accumulated usage time since the replacement of the consumable part. The model creation simulator unit
The processing apparatus control system according to claim 1, wherein when executing the simulation, a random number according to the statistical distribution is generated by a Markov chain Monte Carlo method. The control calculation unit is
When a control amount outside a predetermined threshold range is calculated by calculating a control amount for the processing device, it is determined that the control amount is abnormal, and an alarm is notified to the processing device. The processing apparatus control system according to claim 1. A processing device control method for predicting the processing performance of a processing device whose processing performance varies depending on the state of consumable parts, and controlling the processing device by a computer,
The calculator is
A processing history data storage unit that stores processing history data acquired from the processing device during processing by the processing device,
Machining history data stored in the machining history data storage unit are parameters of a meta prediction model that predicts parameters of a prediction model that predicts the machining performance from a physical quantity that represents the state of the machining device including the state of the consumable part. And a model creation simulation step determined by simulation using a random number according to a predetermined statistical distribution determined in advance,
Control of the processing device based on a prediction model for predicting the machining performance determined by the meta prediction model having parameters determined by the model creation simulation step, and a current value of a physical quantity representing the state of the consumable part A control amount calculation step for calculating the amount;
The processing apparatus control method characterized by performing this. The processing apparatus control method according to claim 8, wherein the prediction model for predicting the machining performance is a regression model having a physical quantity representing the state of the consumable part as an explanatory variable. The meta prediction model for predicting a parameter of a prediction model for predicting the machining performance is a regression model having a physical quantity representing the state of the consumable part at the time of replacement of the consumable part as an explanatory variable. The processing apparatus control method as described. The processing apparatus control method according to claim 8, wherein the meta prediction model that predicts a parameter of a prediction model that predicts the machining performance includes a model that predicts a learning gain. The processing apparatus control method according to claim 8, wherein the physical quantity representing the state of the consumable part is an accumulated usage time since the replacement of the consumable part. The calculator is
The processing apparatus control method according to claim 8, wherein when executing the model creation simulation step, a random number according to the statistical distribution is generated by a Markov chain Monte Carlo method. The calculator is
When a control amount outside a predetermined threshold range is calculated by calculating a control amount for the processing device, it is determined that the control amount is abnormal, and an alarm is notified to the processing device. The processing apparatus control method according to claim 8.

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