IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING V O I X NO
`
`I FEBRlIARY I995
`
`17
`
`RTSPC: A Software Utility for
`Real-Time SPC and Tool Data Analysis
`
`Sherry F. Lee, Student Member, IEEE, Eric D. Boskin, Student Member, IEEE,
`Hao Cheng Liu, Eddie H. Wen, and Costas J. Spanos, Member, IEEE
`
`Abstract-Competition in the semiconductor industry is forcing
`manufacturers to continuously improve the capability of their
`equipment. The analysis of real-time sensor data from semi-
`conductor manufacturing equipment presents the opportunity to
`reduce the cost of ownership of the equipment. Previous work
`by the authors showed that time series filtering in combination
`with multivariate analysis techniques can be utilized to perform
`statistical process control, and thereby generate real-time alarms
`in the case of equipment malfunction. A more robust version
`of this fault detection algorithm is presented. The algorithm is
`implemented through RTSPC, a software utility which collects
`real-time sensor data from the equipment and generates real-
`time alarms. Examples of alarm generation using RTSPC on a
`plasma etcher are presented.
`
`I. INTRODUCTION
`0 COMPETE in today’s semiconductor industry, compa-
`
`T nies must continuously improve upon their manufacturing
`
`skills to maintain high product quality throughout the entire
`process. The ability to automatically perform early detection of
`equipment failures in a production line can lead to significant
`improvements in the overall capability and profitability of the
`process.
`Recently, there has been tremendous growth in the use of
`Statistical Process Control (SPC) to generate alarms when
`the variation occumng on the manufacturing line is unusually
`large. There are, however, limitations to the effectiveness of
`traditional SPC techniques when applied to modern semicon-
`ductor fabrication lines. First, the data ordinarily used for
`SPC is often collected long after misprocessing has occurred,
`causing additional scrap to be needlessly produced from the
`time of the initial malfunction until its detection. Much earlier
`detection of equipment malfunctions which cause yields loss
`will improve the capability and up time of critical process
`equipment. Second, much of the data available directly from
`equipment has statistical properties which violate the implicit
`assumptions used in traditional SPC. Therefore, new tech-
`niques are required to improve SPC on real-time data from
`semiconductor manufacturing equipment.
`In a previous publication, we have shown that the real-
`time data available from sensors in modern manufacturing
`
`Manuscript received May 18. 1994; revised August 9, 1994. This work
`has been supported by SRCISematech (93-MP700), The Stale of California
`MICRO Program, National Semiconductor, Texas Instruments, Digital Equip-
`ment Corporation, Lam Research Corporation, and IBM Corporation.
`S. F. Lee, E. D. Boskin, and C. J. Spanos are with the Department
`of Electrical Engineering and Computer Sciences, University of California.
`Berkeley, CA 94720 USA.
`H. C. Liu is with Societe Generale Securities Corporation, NY 10020 USA.
`E. H. Wen is with Morgan Stanely and Company. NY 10020 USA.
`IEEE Log Number 9407618.
`
`to detect malfunctions
`equipment can be used effectively
`within seconds after they occur [ I ] , [2]. The signals of interest,
`related to the electrical and mechanical signals within the
`equipment, are automatically collected while the equipment
`is processing. In this paper we present a method which has
`improved detection characteristics and is also suitable for
`equipment diagnosis.
`This improved algorithm is based on a decomposition of
`the signals and a different
`time series modeling scheme.
`Furthermore, the new algorithm has been implemented in
`RTSPC, a software package which includes automated model
`generation, data filtering, and a novel double T’ graphical
`control chart for the display of alarm conditions. RTSPC
`interfaces with a workcell controller and can serve as a
`platform for future real-time process control.
`In this paper, an overview of the improved algorithms for
`real-time SPC is given in Section 11. RTSPC, the software
`platform for implementing these algorithms is given in Section
`111, followed by an example of model generation and fault
`detection in Section IV.
`
`11. REAL-TIME STATISTICAL PROCESS CONTROL
`This section begins with an overview of the improved real-
`time SPC algorithm. Next, the real-time signals are described,
`followed by a description of the automatic time series model
`generator. Finally, the use of the Hotelling’s 7” to combine
`the multivariate signals into the double T 2 chart is discussed.
`
`A. Overview of RTSPC
`This section presents the real-time SPC algorithm. Much
`of the background information about time series has been
`previously presented in [2], and will not be repeated here.
`1 ) Buseline Modeling: The real-time SPC methodology uti-
`lizes time series models to analyze the real-time signals
`available from manufacturing equipment through the SECS-
`I1 (SEMI Equipment Communication Standard-11) interface.
`The objective is to use these automatically collected signals
`to establish the baseline behavior of a complex tool, and later
`detect deviations from this baseline. Before running RTSPC on
`production wafers, the following steps are taken to model the
`baseline condition of the process. The real-time signals from
`10 to 15 baseline wafers are first decomposed into long- and
`short-term components. In single wafer processing equipment,
`these components represent the wafer-to-wafer averages and
`the within-wafer signal trends, respectively. Each component
`
`08944507/95$04 00 GI 1995 IEEE
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 04:15:35 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1027
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 1 of 9
`
`

`

`18
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 8, NO. I , FEBRUARY 1995
`
`to transform the equipment signals to IIND signals. This is
`achieved by building time series models for each component
`of each signal. The time series models account for the expected
`patterns in the data. Once these patterns (whose presence does
`not indicate a malfunction) are filtered from the signal, SPC
`can be used to detect deviations in the filtered signals.
`The purpose of a time series model is to capture the
`dependencies among sequential readings of the same process
`variable. Dependencies within readings collected over time can
`be described by univariate time series models such as ARIMA
`( p , d , q ) models, where p is the auto-regressive order, d is
`the integration order, and q is the moving average order. The
`form of the equation for a nonstationary time series xt with
`autoregressive parameters & and moving average parameters
`O k is [4]
`
`P
`
`k=l
`
`9
`
`k=O
`
`o k a t - k
`
`(1)
`
`wt = - 1
`4kwt-k +
`where 80 = 1, the error at - N ( 0 , g 2 ) , and wt are the
`
`I Raw Dald
`
`I
`
`posiuon
`
`series
`Filter
`. I/ Term I/ Correlated
`Cmss
`Component
`
`I Correlated
`I
`I
`
`I
`I
`
`Filar
`
`Fig. 1. Real-time SPC data flow.
`
`is then modeled with a time series model. The resulting model
`forecasts the in-control behavior of the machine.
`2) Monitoring the Production Wafers: Once
`the baseline
`behavior has been established, production wafers can be run
`through the machine. As in the training case, the real-time
`signals from the production wafers are decomposed into the
`long- and short-term components. Each component is then
`filtered using the respective baseline time series model. The
`residuals (the difference between the actual and forecasted
`baseline values) for each component are then combined using
`the multivariate Hotelling’s T 2 statistic into a single score,
`which is graphically displayed in the resulting double T2
`control chart.
`If no equipment faults are detected, normal operation of
`the machine continues. When a malfunction is detected, the
`diagnostic routine is triggered, and an alarm is generated
`to alert the operator. Diagnosis currently uses the long-term
`residuals (the difference between the actual real-time signal
`averages for that wafer and the time series model predictions
`for the signal averages) as a signature of the specific equipment
`malfunction [3]. An overview of the real-time SPC data
`analysis flow is shown in Fig. 1.
`
`B. Real-Time Signals
`This section describes the properties of the real-time signals,
`followed by a discussion of the prefiltering and decomposition
`performed in the algorithm.
`1 ) Properties of Real-Time Signals: The data collected for
`fault detection are comprised of various electrical signals
`such as the radio frequency (RF) impedance and D.C. bias,
`and mechanical signals such as those signifying the coil and
`throttle positions. Since the data are collected sequentially at
`a typical sampling rate of 1 Hz, the signals are correlated in
`time, demonstrating time series behavior. Time series patterns
`are observed both within each wafer and across several wafers
`due to controller adjustments and equipment aging.
`Time series signals are highly auto- and cross-correlated. In
`addition, the correlation structure and the mean value for a
`given signal may also vary with time, making the series non-
`stationary. Thus, the data are not identically, independently,
`normally distributed (IIND), and can not be used directly in
`a traditional control chart, e.g., a Shewhart chart. Since an
`underlying assumption of most conventional control charts
`is that the data is IIND, the first step in the algorithm is
`
`differenced data
`
`wt = Vdxt
`
`Vd is the dth order of differencing operator
`
`(2)
`
`(3)
`
`where
`
`and
`
`(4)
`
`v l x t = xt - xt-1,v2xt = v’xt - VlXt-1
`= xt - 2xt-1 + xt-2,. . . .
`The assumption behind the univariate analysis is that a sig-
`nificant portion of a parameter’s behavior can be explained
`by using past observations of the parameter. A more thorough
`explanation of time series models is given in [5]-[8].
`ARIMA (p, d, q ) models can be derived from the collected
`data when the process is under statistical control; in this way
`the models describe the baseline behavior of the process.
`Once developed, the models are used with current readings to
`forecast each new value. The difference between the forecasted
`value and the actual value is the forecasting error, or residual.
`When the equipment is in statistical control, the residuals are
`by definition IIND variables. As shown in [2], the residuals re-
`flect the equipment state and can be combined in a multivariate
`control chart to generate alarms.
`2) Pre-Filtering of Real-Time Data: RTSPC performs anal-
`ysis on the main etch step for each wafer. The signals collected
`during the main etch step are concatenated and filtered as
`described below. If necessary, the algorithm can be extended
`to include more than one etch step. The algorithm can also be
`extended to monitor the length of the etch step (as an additional
`“long-term” parameter of the wafer) and produce an alarm if
`the process step takes too long; for example, if an etch step
`did not endpoint correctly.
`Characteristics of the real-time signals caused by transient
`effects during processing must be accounted for before statisti-
`cal analysis. At the beginning of processing for each wafer, for
`example when RF power is applied, a small transient occurs
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 04:15:35 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1027
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 2 of 9
`
`

`

`LEE CI <I/.: RTSPC: A SOFTWARE UTILITY FOR KEA1.-TIME SPC AND TO01 DATA ANALYSIS
`
`19
`
`Dzlry
`
`Step k n g l h
`
`Grnupr
`
`iirnr
`
`Wafer I
`
`Fig. 2. Real-time signal filtering parameten
`
`which captures the short-term patterns during the processing
`of each wafer. Most importantly, the variation of the long-
`term component is much larger than that of the short-term
`component, illustrating the point that the short-term compo-
`nents are more sensitive to faster equipment fluctuations, while
`the long-term components reflect longer duration changes in
`overall equipment state. This decomposition of the signals into
`components with drastically different variances is the primary
`reason the false alarm rate has been decreased. After the
`I- Wdfer 2
`decomposition, both components are demeaned to simplify
`later calculations.
`Notice that the short-term component for each wafer in
`Fig. 3 roughly follows a downward trend. This trend, modeled
`by the integrative part of the ARIMA model, is captured for
`each wafer so that deviations from this trend will be detected.
`Deviations in each of the components reflect different changes
`in equipment state. For example, a shift in RF power that lasts
`the duration of the wafer each will be seen as a shift in the
`long-term signal. A short spike in RF power, however, will be
`exhibited in the short-term signals. As another example, a dirty
`film on the wafer is seen by the short-term signals but not by
`the long-term signal. Because the decomposition allows us to
`model two different types of faults, the resulting algorithm is
`more robust than the original method, gives significantly fewer
`false alarms, and generates residuals that are much more suited
`for diagnosis.
`
`while power is stabilizing. For SPC purposes, the analysis is
`delayed by a few seconds until the power has stabilized. The
`delay time is based on the stabilization time for a normally
`processed wafer. If the RF power, or any other monitored
`signal does not stabilize in the specified time, an alarm will be
`generated. To simplify the time series model building process,
`the same number of data points, or step length, is used for
`each wafer. Finally, to compensate for the noise in the signals,
`local averaging is performed within each wafer. The number
`of samples used in local averaging, or group size, is used
`to adjust the sensitivity of alarm generation. The delay, step
`length, and group size are illustrated in Fig. 2.
`3 ) Signal Decomposition of Real-Time Datu: As
`mentioned in the Section Properties (f Red-Erne Signals,
`time-series models of baseline equipment sensor data are
`used to filter the nonstationary and autocorrelated patterns in
`the data. The algorithm presented in 121 builds one seasonal
`ARIMA (SARIMA) model for each sensor variable.’ A major
`disadvantage of this algorithm is that false alarms often
`occur at the start of a wafer. While these false alarms can
`be anticipated and ignored, the new algorithm solves this
`problem more formally.
`First, SARIMA models are not appropriate to model the
`real-time data, because as described in the Section Pre-
`Filtering of Real-Time Data, the pre-filtered wafer signals
`from the main etch step are concatenated together. This
`concatenation means the data do not form a natural continuous
`stream. One assumption behind the SARIMA model is that
`the variance and the mean of the filtered residuals is the
`same regardless of the season. Since the discontinuity violates
`this assumption, the idea of seasons is eliminated in the new
`algorithm.
`The most significant change in the algorithm is the de-
`composition of the real-time signals from each sensor into
`long-term and short-term components before modeling. This
`decomposition is necessary because each component describes
`a different behavior of the process. An example of signal
`decomposition of the impedance signal for several wafers is
`shown in Fig. 3. The long-term component, comprised of the
`average value of the signal for each wafer, models the overall
`trend across a number of wafers. On the other hand, the smaller
`deviations within each wafer create the short-term component,
`
`‘Time series exhibiting periodic variation are \aid to have seasons, and can
`be modeled with SARIMA models.
`
`C. Automatic Time Series Model Generation
`Automatic time series model generation, a key module in the
`new RTSPC software package, makes the difficult and usually
`tedious process of generating models transparent to the user.
`In this section, the automatic time series model generation
`algorithm is described.
`1 ) Automatic Model Generation; Time series models are
`typically generated interactively using sophisticated statistical
`analysis tools. The process can be time consuming and tedious,
`requiring specialized skills to choose statistically significant
`models. Because models are built for each component of
`each signal for every recipe, the model generation process
`can be labor intensive and time consuming. The automatic
`model generator developed makes this difficult modeling step
`transparent to the user of RTSPC, thus making the software
`practical for the factory floor. It is also very fast, typically
`taking less than one minute on a modem workstation to
`generate a complete set of models.
`Automatic model generation is achieved through several
`stages. First, if the series is nonstationary, the data is differ-
`enced until stationarity is achieved. Next, both the order and
`values for the autoregressive coefficients are found. Finally,
`the moving average order is calculated, and an optimizer is
`used to solve for the moving average coefficients. These steps
`are outlined below.
`To determine whether the series is stationary and requires
`differencing, the autocorrelation function is calculated. If the
`first few absolute student4 values of the autocorrelation func-
`tion drop slowly, differencing is required [5]. This procedure
`is repeated until the series becomes stationary.
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 04:15:35 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1027
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 3 of 9
`
`

`

`20
`
`r
`
`I
`
`8
`8
`
`H
`D
`
`-400
`8
`
`=
`
`
`
`Original Data
`
`I:
`-50 i- I
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 8, NO. 1, FEBRUARY 1995
`
`n
`
`I
`
`0
`
`WK)
`
`m
`
`m
`
`Fig. 3. Real-time signal decomposition.
`
`Next, the modified Yule-Walker equations are used to
`determine both the order and the value of the autoregressive
`coefficients. As adapted from [9], the modified Yule-Walker
`equations are derived starting from the ARMA model. In the
`following expressions it is assumed that wt is a real, causal
`stationary time series that can be modeled with the form shown
`in (1) and the autocorrelation of the white noise error at is
`defined as Raa(k) = a 2 S k .
`Multiplying both sides of (1) by
`expectation, we obtain
`
`and taking the
`
`where
`
`R,,(m)
`
`E(atw-,).
`
`(6)
`
`Since the error is white noise and is uncorrelated with future
`values of wt, it follows that RaTl,(m) = 0 for m > 0.
`Therefore, in (5), we set Raw(Z - k) = 0 for 1 > q and
`obtain an explicit set of equations used directly to solve for
`both the autoregressive order and coefficients. To accomplish
`this an initial value is chosen for q. The only requirement at
`this stage is to choose a value equal to or greater than the
`actual number of moving average terms in the final model.
`Since the actual value of q is not known at this stage, it is safe
`
`to choose a fairly large initial value for q at this point
`
`(7)
`For the case of I = q + 1, q + 2 , . . . , p + p , (7) can be
`rewritten in matrix form. This system is known as the modified
`Yule-Walker equations [see (8), shown at the bottom of the
`page]. As shown in (8), the modified Yule-Walker equations
`relate the ARIMA parameters to the autocorrelation function
`of the series, regardless of the MA behavior of the process,
`as long as q in (8) is chosen to be equal or larger than the
`actual q of the process. When the dimension of the matrix
`exceeds the number of autoregressive coefficients the matrix
`becomes singular and its determinant is zero. Therefore, one
`method often used to choose the autoregressive order of the
`model is to assume a large number for q so that (8) holds.
`Then starting with a small number for p , p is increased until
`the determinant equals zero, or is sufficiently small. Once the
`autoregressive order has been found, the coefficients can be
`calculated by solving (8) [9]. This method, however, is not
`robust in the presence of noise because it is difficult to choose
`a cut-off point for the determinant, so an alternative method
`was chosen.
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 04:15:35 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1027
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 4 of 9
`
`

`

`LEE er ul.: RTSPC: A SOFTWARE UTILITY FOR REALTIME SPC AND TOOL DATA ANALYSIS
`
`21
`
`Factory CIM i-)
`
`\
`
`RT S K
`
`DB
`
`Fig. 4. RTSPC software system environment.
`
`currdwafer: 0
`
`CurrentModek kehe..mdc
`
`Delay: 7
`
`StepLength: I5
`
`criticalstep: 5
`GrrmpSize:l 1 2 A 3 4 5 6 7 8 9 1 0
`
`Modelloded.
`I Wew Baseline I
`I
`I
`SianaJs
`
`Helo
`
`Model
`
`Start
`
`Quit
`
`Fig. 5. RTSPC main window
`
`Equation (7) is used directly to obtain both the autoregres-
`sive order the coefficients. For a large initial guess for (1 (which
`must be greater than or equal to the actual value of q), a linear
`regression model using (7) is fitted to the time series data.
`To determine the order of the model, the significance of the
`coefficients is calculated using the student-f test. The least
`significant coefficients are eliminated one at a time until all
`of the coefficients are statistically significant. This method has
`been found to be both robust and computationally efficient.
`for each of the long- and short-term components for every
`Once the autoregressive order and coefficients are deter-
`monitored real-time signal. Because some of the signals are
`mined, the moving average order can easily be calculated
`cross-correlated, using individual SPC charts will show an
`from (7) using the proper autoregressive coefficients. This
`+
`exaggerated false alarm rate [ 101. Instead, the residuals for
`entails finding the largest integer k for which II'~,,,,,(/)
`each component are combined into a multivariate statistical
`E:=, ~~k.R,,:,,,(l-k) # 0. The moving average coefficients are
`score using Hotelling's T 2 statistic, which takes into account
`then solved using a nonlinear optimizer. The algorithm used
`the correlation among the variables used in SPC. More detail
`for optimization is the Han-Powell variable metric algorithm,
`on Hotelling's T 2 statistic in the context of this application
`which is fairly efficient for a small number of parameters
`can be found in [2].
`(under 10) and can easily handle both equality as well as
`The resulting Hotelling's T' scores for each component are
`inequality constraints.
`plotted in a one-sided SPC chart. Data points corresponding
`2) Applying the Short-Term and Long-Term Time Series
`to run-time faults have residuals which cause the Hotelling's
`Models: Usually, at least 10 to 15 baseline wafers are
`7''
`statistic to be significantly different from zero. One set
`required for accurate baseline models. For each of the short-
`of scores, obtained from the short-term components, detects
`term components, the autocorrelation is calculated between
`faults during the process time of each of the wafers, while the
`adjacent points in each wafer, and then averaged across the
`second set of scores, obtained from the long-term components,
`wafers. The autocorrelations between adjacent wafers of the
`detects faults by looking at violations in trends across several
`short-term components are ignored, which differs from the pre-
`wafers.
`viously published algorithm [ 2 ] . The average autocorrelations
`across each wafer are then used in the modified Yule-Walker
`equations to build the models. The time series models of
`the long-term components are built from the average signal
`value sampled during the time it takes to process one wafer.
`The resulting time series model generation follows the steps
`outlined in the previous section.
`If a new point is 3-sigma from the baseline forecasted point
`during the monitoring of production runs, an alarm is generated
`and the algorithm replaces the "bad' or faulty point with the
`forecasted point. Thus, consecutive faulty points are detected
`and the models retain their baseline behavior. This method is
`used for both the long- and short-term components.
`
`111. RTSPC: THE SOFI-WARE UTILITY
`RTSPC is a software application which interfaces with a
`workcell controller to perform statistical analysis on the real-
`time sensor data collected from the equipment. An overview of
`the RTSPC software system environment is shown in Fig. 4.
`RTSPC communicates with the workcell controller, which
`collects the real-time signals from the equipment over the
`SECS communication port. In the current implementation, the
`controller accumulates the real-time data from the processing
`of each wafer and then sends a file to RTSPC for analysis.
`This analysis is typically completed a few seconds after the
`wafer leaves the chamber.'
`RTSPC is written for UNIX workstations in a combination
`of the C and Tcl/Tk programming languages. Tcl/Tk is used for
`the graphical interface, while C is used for the data analysis.
`'In the current version of the RTSPC software, a true real-time implemen-
`tation is only inhibited by data collection logistics.
`
`D. Multivariate Analysis: Double T' Chart
`In production, new observations are compared to the base-
`line time series model forecasts, creating lIND residuals that
`can be used in control charts. One set of residuals is generated
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 04:15:35 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1027
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 5 of 9
`
`

`

`22
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING. VOL. 8, NO. I , FEBRUARY 1995
`
`M y :
`
`0
`stq, Length:
`
`0
`5
`mw.4 step:
`
`0
`
`10
`
`3
`
`-U
`7
`
`5
`
`A
`15
`m
`15
`A
`5
`
`6
`
`I
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`9
`
`I
`
`12
`
`15
`
`Fig. 6. Model building window.
`
`This section gives a brief look at the software structure,
`the graphical user interface, and the specific capabilities of
`RTSPC.
`
`A. The Main Window
`The main window of RTSPC is shown in Fig. 5. The
`window displays the current wafer number and the model
`set currently selected from the model library. This model
`set contains both the long- and short-term component time
`series models for a particular process and piece of equipment.
`The window also displays the delay, step length, critical step
`and group size. As explained in the Section Pre-Filtering
`Of Real-Time Data, delay is the number of samples ignored
`while the signals become stable, step length is the number of
`samples used per wafer in the time series models, and group
`size is the number of points averaged within each wafer to
`compensate for noise in the system. Critical step specifies the
`code number used by the data collection software to select the
`active processing step from the continuous stream of real-time
`data.
`The routines available from the main menu include on-line
`help, access to the model library with the model button, and
`the ability to select specific real-time signals with the signals
`button. View baseline allows the user to view the double
`T 2 , raw signals, and residuals of the baseline wafers used
`
`to create the model. Start initiates the monitoring program,
`which accepts additional files from the equipment containing
`the real-time signals of wafers being processed. Upon receipt
`of a new data file, the analysis program is initiated and the
`results are graphically displayed.
`
`B. The Model Building Window
`The panel displaying the model building window is shown
`in Fig. 6. The signals available for automatic model building
`are listed on the left, and the files which can be used to
`generate the model are listed on the right. Each file contains
`the data from the processing of a single wafer. In general, the
`number of baseline wafers included in model generation must
`be greater than the number of signals being modeled. Since
`a "clean" baseline is needed, model building is an iterative
`process. Using the view baseline command from the main
`menu, the user can see if all the wafers used in model building
`actually were in control with respect to the new model. If
`not, those wafers should be deleted from the baseline, and the
`model r e b ~ i l t . ~
`The buttons on the model window either start the model
`generation process, or allow the user to load an existing model
`
`'In the future, the software will have the ability to add good production
`wafers to the baseline. This will make the models more robust, especially if
`more weight is given to the data from the more recent wafers.
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 04:15:35 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1027
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 6 of 9
`
`

`

`LEE PI NI.: RTSPC: A SOFTWARE UTILITY FOR REAL-TIME SPC AND TOOL DATA ANALYSIS
`
`set. Pressing the load button brings up another window listing
`the available model sets in the library.
`
`C. The Double T’ Control Chart
`The graphical display of the double ‘I”’ chart in Fig. 8 shows
`the control chart for the real-time SPC example discussed in
`Section IV. In the double T’ control chart, the long- and short-
`term component control charts are scaled along the y axis in
`order to share the same control limit. The control chart is
`one-sided because the Hotelling’s T 2 produces only positive
`numbers. The data are plotted consecutively along the .r axis
`of the control chart as wafers are processed in the equipment.
`The vertical bars represent the score associated with the long-
`term components, and the continuous line represents the score
`associated with the short-term components of the signals.
`A malfunction during processing is signalled when either
`the long- or short-term component score exceeds the control
`limit. In the example shown in Fig. 8, three wafers caused a
`long-term component wafer alarm. The causes of the alarms
`are explained in Section IV.
`
`20.12
`
`16.096
`
`DouCle-T^Z
`
`Double-TA2
`
`I?:.
`
`7 . Baseline double T’ chart
`
`20.12
`
`16.096
`
`12.012
`
`8.048
`
`4.024
`
`IV. REAL-TIME SPC EXAMPLE
`To demonstrate the capability of RTSPC, several experi-
`ments were conducted in the Berkeley Microfabrication Lab-
`oratory. The equipment chosen for the experiment was the
`Lam Rainbow 4400 Plasma Etcher, a single wafer processing
`tool. The real-time equipment data was collected from the
`etcher using Brookside Software’s Lam Station software [ I 11.
`Lam Station runs on a PC connected to the SECS port of the
`Rainbow. The PC is NFS (Network File Server) mounted onto
`a UNIX workstation, allowing for very simple data transfer
`from the equipment controller to the UNIX data analysis
`platform.
`
`A. Baseline Processing and Model Genercitiori
`To use RTSPC on a specific process, a set of baseline wafers
`must first be processed to build the time series models needed
`for data filtering. During the processing of these wafers, it
`is essential that the machine be operating in statistical process
`control. In this example 1 1 baseline wafers were first processed
`on the Rainbow using the given recipe. The real-time data from
`five signals (RF impedance, RF phase, endpoint, coil, and tune
`vane position) were selected to generate a model set using the
`automatic model generation routine.
`The results of the baseline model generation are shown in
`Fig. 7, which displays the double ?’? chart for the data used to
`generate the model. Note that the long-term signal is never out
`of control, although the short-term signals show some points
`close to the control limit. If the baseline contains alarms, the
`user may choose to eliminate the wafers showing alarms and
`rebuild the model. The user may also view the signals and
`residuals resulting from the baseline model.
`
`B. Real-Time SPC During Processing
`Once the time series models for the baseline of this process
`are created, the RTSPC software generates real-time alarms
`
`‘‘‘0
`
`1
`
`2
`
`3
`
`4 5
`
`6
`
`7
`
`8
`
`3 10 11 12 13 1 4 1 5 16 17 18
`
`Fi:.
`
`X. Graphical display of production douhle T’ control chart.
`
`in the case of misprocessed wafers. To demonstrate the alarm
`generation capability of RTSPC, an additional 15 wafers were
`processed with the