308
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING. VOL. 5 . NO. 4. NOVEMBER 1992
`
`Real-Time Statistical Process Control Using Tool
`Data
`
`Costas J. Spanos, Member, IEEE, Hai-Fang Guo, Alan Miller, and Joanne Levine-Parrill
`
`the last five years we have witnessed the
`Abstract-During
`widesprelld application of statistical process control in semi-
`conductor manufacturing. As the requirements for process
`control grow, however, traditional statistical process control
`applications fall short of their goal. This happens because mod-
`ern processes are more complex than they used to he. Further,
`because of the expanding use of the so called “cluster” tools,
`modern technologies are also less observable than before. Be-
`cause of these difficulties, we can no longer afford to wait until
`a malfunction can be detected on a traditional control chert.
`Fortunately, modern semiconductor manufacturing tools can
`communicate to the outside world a number of their internal
`parameters, such as throttle valve positions, chamber pres-
`sures, temperatures, etc. It is intuitively obvious that equip-
`ment malfunctions will manifest themselves first in the values
`of these internal parameters and much later on the wafer prop-
`erties. In this paper we describe a process monitoring scheme
`that takes advantage of such real-time information in order to
`generate malfunction alarms. This is accomplished with the ap-
`plication of time-series filtering and multivariate statistical
`process control. This scheme is capable of generating alarms
`on true real-time basis, while the wafer is still in the processing
`chamber. Several examples are presented with tool data col-
`lected from the SECSII port of single-wafer plasma etchers.
`
`I. INTRODUCTION
`S INTEGRATED CIRCUITS (ICs) become more
`
`A complex, the semiconductor manufacturing commu-
`
`nity is focusing its resources on achieving tight process
`control over the critical process steps. Many tools and
`techniques are being used toward this end. Statistical Pro-
`cess Control (SPC) is prominent among them, as it can
`help in the timely detection of costly process shifts.
`Historically, SPC has been used with process measure-
`ments in order to uncover equipment and process prob-
`lems. Such problems are manifested by significant deg-
`radation in equipment operation and product quality. To
`discover this degradation, critical process parameters are
`monitored using various types of control charts. The mea-
`surements consist mainly of in-line readings collected
`from wafers after the completion of the process step in
`question.
`Although this method is helpful in detecting process
`
`Manuscript received January 21, 1992; revised March 26, 1992.
`C. Spanos is with the Department of EECS, University of California at
`Berkeley, Berkeley, CA 94720.
`H:F. Gun was with the Department of EECS. University of California.
`She is presently with IBM Corporation, San Jose, CA
`A. Miller IS with Lam Research, Fremont, CA.
`J . Levine-Parrill is with IBM Corporation. East Fishkill, NY.
`IEEE Log Number 9202883.
`
`drifts, there is significant delay between the occurrence of
`a drift and the resulting control chart violation. As pro-
`duction volume increases, faster response to process drifts
`becomes necessary in order to assure high product quality
`and low cost. In addition, the proliferation of multi-cham-
`ber (cluster) tools, makes it even more difficult to collect
`the necessary in-line measurements. Under these circum-
`stances we must use other types of information for quality
`control purposes.
`Modem semiconductor manufacturing equipment can
`communicate internal sensor readings oyer standard
`RS232 ports using the SECSII protocol. This capability
`has been recognized as crucial for the diagnosis of equip-
`ment failures, and for the improvement of the overall
`product quality [I]. Unfortunately, in a high volume pro-
`duction facility the monitoring of multiple sensors results
`in an overload of information. Further, most of the pop-
`ular SPC strategies cannot be applied to real-time read-
`ings, since these readings usually show non-stationary ,
`auto-correlated and cross-correlated variation. A special
`type of SPC procedure is therefore needed to automate the
`processing of tool data.
`This paper describes the development and the applica-
`tion of a novel SPC method that uses the-series filters
`[2] and multivariate statistics [3] to analyze internal ma-
`chine parameters. These parameters are sampled several
`times per second, and the readings are filtered using a
`time-series model. The filtered readings are then com-
`bined into a single variable with well defined statistical
`properties [4]. This single statistical variable is calculated
`every few seconds, and is plotted against formally defined
`control limits. Real-time misproceshg alarms generated
`in this manner allow a controller to interrupt faulty runs
`and prevent any adverse effects on the equipment or the
`product. These alarms can be used for scheduling preven-
`tive maintenance. In the future, these alarms might also
`be used in conjunction with automated diagnosis routines
`t51.
`This method has been applied on a Lam Research Rain-
`bow single wafer plasma etcher, and on an Applied Ma-
`terials Precision 5000 cluster tool. The results show that
`the filtered statistical parameter has successfully re-
`sponded to several types of process faults, which were
`introduced in a controlled fashion. The faults included
`mismatched RF components, different loading factors, gas
`leaks, and miscalibrated equipment controls. It is note-
`worthy that none of these faults could have been easily
`detected by traditional wafer measurements.
`
`0894-6507/92$03,00 8 1992 IEEE
`
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`
`

`

`SPANOS el 01.: REAL-TIME STATISTICAL PROCESS CONTROL USING TOOL DATA
`
`309
`
`The rest of this paper is structured as follows: Section
`I1 presents a brief overview of traditional statistical pro-
`cess control. Section I11 describes the real-time, multi-
`variate SPC approach, which includes the time series-
`model and the calculation of Hotelling’s T 2 statistic. Ex-
`perimental results are presented in Section IV along with
`a brief description of the equipment and the data acqui-
`sition tools. Finally, Section V contains a summary and
`some suggestions for future extensions of this work.
`
`11. TRADITIONAL STATISTICAL PROCESS CONTROL
`The concept of statistical control of a production se-
`quence was introduced in 1924 by Walter A. Shewhart of
`the Bell Telephone Laboratories [6]. Today, SPC is
`understood as a collection of methods whose objective is
`to improve the quality of a process by reducing the vari-
`ability of its critical parameters.
`A process is said to be in statistical control when,
`“through the use of past experience, we cun predict, at
`least within limits, how the process may be expected to
`vary in the future” [7]. When a process is in statistical
`control, there is only natural variation or “background
`noise” because of mechanisms known as chance causes.
`Sometimes, however, a process can change due to assign-
`able causes, such as significant environmental changes,
`miscalibrations, variability of raw material, or human er-
`ror. Assignable causes make a process unpredictable and
`cause it to lose thg state of control as defined above. The
`main purpose of SPC is to detect the presence of an as-
`signable cause so that it can be corrected.
`From a statistical point of view, SPC casts the decision-
`making process as a formal hypothesis test. In this con-
`text, the null hypothesis (H,) states that the process under
`consideration is under statistical control, while the alter-
`native hypothesis (Ha) states that the process is out of sta-
`tistical contral. To test these hypotheses, a random sam-
`ple x is selected from the population of interest, and the
`suitable test statistic is calculated. Typically, we calculate
`the average of several readings of x , and the resulting sta-
`tistical score is tested against the limits listed in (1). The
`range of v?!pes that leads to the rejection of a hypothesis
`region or the rejection region. For
`is called the cr+al
`the Shewhart X chart, the upper and lower (UCL and
`LCL) limits used to validate Ha are given next:
`UCL = I” + Z&Ui
`LCL = p - Z&UF
`(1)
`where x is distributed according to the N ( p , U’) normal
`distribution, X is the arithmetic average calculated from n
`samples of x , and U? = U / & . Also, ZUl2 is the standard
`normal score which excludes the a / 2 portion off the high
`tail of the standard normal distribution. According to this
`equation, the probability of rejecting Ha by mistake, an
`occurrence known as a type I error, is equal to a. Alter-
`natively, accepting Ho by mistake is known as a type I1
`
`error. Thq distribution that illustrates the nature of the x
`
`chart is shoivn in Fig. 1.
`
`Fig. I . An x control chart and its hypothesis-testing nature
`A popular set of rules developed by Western Electric
`in the 1950s and known as the Western Electric Rules,
`provides additional ways to generate alarms [8].
`At this point, it is important to emphasize that the op-
`eration of the X chart is based on the model described by
`(1). This equation implies that all the “good” data must
`come from the same population, which must follow a nor-
`mal distribution around a fixed value. In other words, the
`data must be Identically, Independently and Normally
`Distributed. This is known as the IIND assumption and is
`summarized below:
`x l = p + a ,
`r = l , 2 ; - .
`a, - N ( 0 , u 2 ) .
`(2)
`The IIND assumption is essential for the simple control
`chart. Without it, the chart and its limits would not truly
`reflect the process. Unfortunately, real time data often vi-
`olate the IIND assumption. In the next chapter we focus
`on the statistical nature of such data.
`
`111. REAL-TIME STATISTICAL PROCESS CONTROL
`As the volume of production increases, instantaneous
`detection of process drifts becomes necessary. Most mod-
`em equipment have some automated data acquisition ca-
`pabilities. Unfortunately, traditional statistical process
`control methods cannot be applied directly on tool data,
`because most tool-generated data violate the IlND as-
`sumption. Indeed, in most cases, real-time data are non-
`stationary, and in addition they are auto-correlated and
`cross-correlated, even when they originate from a process
`that is under control.
`To accommodate this situation, a novel SPC scheme is
`developed and applied to several test processes. This
`scheme employs time-series [2] multivariate statistics [3].
`First, time-series models are needed to transform real-time
`sensor data into IIND signals; and a particular multivari-
`ate technique, known as the Hotelling’s T 2 statistic, is
`used to combine the IIND signals into a single, well be-
`haved statistical variable.
`This scheme is capable of generating alarms on true
`real-time basis, while the wafer is still in the processing
`chamber. In this way, we are able to detect misprocessing
`before it impacts the product. In this section we describe
`in some detail this real-time SPC scheme.
`‘The expression a, - N ( 0 , a2) means that the random variable a, is dis-
`tributed accordingly to a normal distribution with zero mean and a variance
`U 2 .
`
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`

`310
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 5, NO. 4. NOVEMBER 1992
`
`A. Time-Series Modeling
`Readings collected sequentially are rarely independent.
`It is this lack of independence, for example, that allows
`the forecasting of daily temperature lows and highs from
`recent readings and from historical records. Often, the
`statistical behavior of a time-varying parameter can be de-
`scribed by time-series model. The purpose of a time-se-
`ries model is to capture the dependencies among sequen-
`tial readings of a variable. Time-series models are often
`used to forecast the value of a future reading from the
`values of several past observations [9], [ll].
`The statistical behavior of data collected from most
`modem semiconductor manufacturing equipment can be
`modelled with the help of a time-series model. The fact
`that process readings are statistically related to past values
`can be intuitively understood: Consider, for example, that
`modem equipment use feedback control on critical pa-
`rameters, such as temperature or pressure. The sensors in
`the control loop record the deviation of the parameter from
`its target value, and, in the next instant, the controller
`tends to compensate the observed deviation. Thus, a read-
`ing higher than a target value is very likely to be followed
`by a low value and vice versa, leading to an apparent neg-
`ative autocorrelation between consecutive readings. Con-
`versely, at high sampling rates the monitored parameters
`are subject to “inertia,” leading to an apparent positive
`autocorrelation between consecutive readings. In general,
`dependencies among readings collected over time can be
`described by the following equation:
`
`where x is the signal and a is the IZND prediction error of
`the time series model. In this work, the main goal is to
`find suitable time-series models to filter real-time data
`used for statistical process control. The methods used to
`obtain the models are discussed next. Later we will see
`how the model can be applied within a practical real-time
`SPC technique. Next we give a very brief overview of
`time-series modeling. For an in-depth coverage, the reader
`should consult the extensive literature on the subject [2],
`[41, [91, [101, 1131, ~ 4 1 .
`
`B. Univariate Box-Jenkins Analysis
`In this application we use the univariate Box-Jenkins
`time-series analysis [2]. The assumption behind the uni-
`variate analysis is that the time-series behavior of one pa-
`rameter can be fully explained by using past observations
`of this parameter. A Box-Jenkins model is also called an
`ARIMA(p, d , q) model, and it consists of three linear
`components (or filters) as illustrated in Fig. 2. These
`components are the auto-regressive part of order p , the
`integration part of order d , and the moving-average part
`of order q [2].
`
`Fig. 2. The three components of the ARIMA model
`
`(4)
`
`The general form of the ARIMA(p, d , q) model is
`given below:
`d(B)w, = O(B)a,,
`d(B) = 1 - d l B - d2B2 - . . . - dpBP
`- . . . e,Bq
`O(B) = 1 - e,B -
`where d z 0
`w, = Vdz,
`Difference Operator:
`vz, = z, - z,- , v2z, = V(Vz,) * . .
`Backward Shift Operator:
`Bz, = z , - ~ B2z, = z1-2 . . .
`where z, is the original reading collected at time t, w, is
`the respective differentiated signal, and a, is the IZND re-
`sidual. Below we explain the function of each of the three
`components of the ARIMA model.
`The first part of the ARIMA model is the integration
`component. This part is necessary because a condition for
`fitting the autoregressive and moving-average parts of the
`model, is that the signal must be stationary. This means
`that the mean, variance and autocorrelation functions of
`the time-series must be time invariant. The integration
`component of the ARIMA model is used to convert a non-
`stationary signal to a stationary one. Simple or higher-
`order differentiation can be used to achieve a time-invari-
`ant mean.’
`The second part of the ARIMA model is the autore-
`gressive (AR) part, which is needed in order to describe
`the dependency of the current observation on previous ob-
`servations. This is done through the autoregressive coef-
`ficients di.
`The third part of the ARIMA model is the moving-av-
`erage (MA) part, which describes the dependency of the
`current observation on previous forecasting errors (also
`known as random shocks), by means of the moving-av-
`erage coefficients O1.
`Occasionally, the original data show seasonal periodic
`patterns. These patterns can be modeled by creating
`ARIMA models for the seasonal variation as well as for
`the individual samples. The composite model is known as
`a Seasonal ARIMA model or SARIMA(p, d , q) x (P,
`D, Q)f, where p is the number of significant autocorrela-
`tions, d is the number of differentiations, q is the number
`of significant moving average terms within each season,
`
`2Taking the log or the square root of the data might be necessary in order
`to produce a constant variance.
`
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`
`

`

`SPANOS el a l . . REAL-TIME STATISTICAL PROCESS CONTROL USING TOOL DATA
`
`31 I
`
`and P, D , Q are the autocorrelations, differentiations and
`moving average terms, taken across seasons of duration s
`[14]. The complete SARIMA(p, d , q) X ( P , D , Q),
`model is expressed by (5):
`
`I#J(E)@(B~)W, = O(B)O(BS)al
`
`(6)
`
`w1 = V P ( V d Z , )
`A model can be obtained from the collected data when
`the process is under control; in this way the model de-
`scribes the “good” process. Once a model has been de-
`veloped, it can be used to forecast (or predict) each new
`value. The difference between the forecast value and the
`actual value is the forecasting error, or residual. The re-
`sidual is by definition, an IIND ~ a r i a b l e : ~
`a, = Z, - 2, - N(0, (r2)
`C. Creating Box-Jenkins Models
`To obtain a useful ARIMA model, Box and Jenkins
`proposed a three-step procedure [9]. This procedure is il-
`lustrated in Fig. 3. Two devices are used to select the
`ARIMA models: These are the discrete autocorrelation
`function (acf ) and the discrete partial autocorrelation
`function ( p a c f ) . The acfand the pacfare calculated from
`the properly differentiated signal and are compared with
`the theoretical acf and pacf patterns from known model
`structures.
`To further explain the acf we need to talk about the
`autocorrelation coefficient. The autocorrelation coeffi-
`cient describes the statistical dependence between two
`readings collected at different times. The auto-correlation
`coefficient takes values in the range from - 1 to + 1 . A
`zero value will be obtained when the observation of in-
`terest is independent from other observations, while a
`value of + 1 indicates complete synergistic dependence.
`The value of - 1 indicates complete antisynergistic de-
`pendence. The following equation defines the auto-cor-
`relation coefficient between all pairs of n readings that
`have been collected k observation time intervals apart from
`each other. The autocorrelation coefficient is calculated
`from n consecutive observations, by using the (n - k )
`pairs of observations separated by k observation intervals.
`Expressed as a function of the integer k , the estimated acf
`is given by (7):
`
`Dinerentiate and
`use acland cfto seled
`candidate AKMA model
`Estimate the parameters
`01 the model seleded
`at step 1
`
`Check the adequacy
`of the model
`
`Fig. 3. The 3-step procedure for ARIMA modeling
`
`complished by fitting the following regression equation:
`z t + k = 6 k l Z r C k - l + 6 k Z Z r + k - 2
`+ 6 k 3 Z r i k - 3 f ’ . ’ + 6 k k Z r + U r + I
`(8)
`where this equation is fitted on the signal multiple times,
`with increasing value of k starting from k = 1. The pacf
`is the series 6, I , 622r . . . , qhkk which is usually displayed
`as a discrete function of k .
`Both the acf and the pacf are needed in order to infer
`the structure of the best fitting ARIMA model. The infer-
`ence of the best model structure is usually done by trial
`and error, using the acf and pacf of the original signal and
`its residuals for guidance [9]. After the structure of the
`model is inferred and its coefficients extracted, the acf and
`the pacf of the residuals are used to check the adequacy
`of the selected model. The process terminates when a sat-
`isfactory model is obtained. This interactive sequence is
`illustrated in Fig. 3. Attempts to automate this procedure
`have also been reported in the literature [IO].
`
`D. Hotelling’s T 2 Statistic
`A piece of equipment will, in general, be monitored
`through a number of sensor signals. Using the appropriate
`time-series model, each signal is filtered down to its IIND
`residual. Assuming that the time-series models have been
`properly built and that the machine is under control, each
`of these residuals will be an IIND random number.
`This means that one could use a simple Shewhart con-
`trol chart to monitor each residual. However, since the
`signals are originating from the same physical process,
`their residuals will probably be statistically correlated and
`using them in separate control charts can be misleading.
`In fact, it can be shown that as the number of correlated
`variables increases, the probability of generating false
`alarms from a control procedure that uses a large number
`of separate charts grows significantly [6]. This is because
`treating correlated signals separately leads to the under-
`estimation of the probability of generating false alarms
`and the probability of not detecting a malfunction. Fur-
`ther, the information content of multiple, concurrent real-
`time control charts will undoubtedly overwhelm the hu-
`man operator.
`The function of Hotelling’s T2 statistic is to combine
`several cross-correlated variables into a single statistical
`
`n - k
`
`rk =
`
`r = 1
`
`( z i - 7) ( z r + k - 7)
`n
`
`c (z, - z)2
`
`k = 1 , 2 , . . .
`
`(7)
`
`I = I
`The partial autocorrelation function ( p a c f ) also gives
`a measure of dependence across pairs of readings, only
`now this dependence is given after the dependence of the
`intervening readings has been accounted for. This is ac-
`
`3The hat ( . ) signifies a value predicted by the model
`
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`

`312
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL 5 , NO 4. NOVEMBER 1992
`
`score. This number is simply the square of the maximum
`possible univariate student-t score computed from any lin-
`ear combination of the various outcome measures [3]. This
`score is calculated from the p correlated residuals as fol-
`i o ~ ~ : ~
`T2 = n(H - O)TS-l(ii - 0)
`where group mean H T = [a, . . . ii,]
`nominal value of residuals OT = [0 . . . 01
`r
`. . * . . . . . .
`
`variance-covariance matrix S =
`
`I
`
`1
`
`I
`
`is related to the cumulative F distribution at level a:
`
`which, assuming that the number of measurements is high,
`can be approximated by a simple chi-square distribution
`with p degrees of freedom:
`
`Of course, the way the T2 score has been defined here
`makes it the optimum statistic for controlling "unstruc-
`tured" mean shifts, i.e., shifts that might happen in any
`direction within the p-dimensional space. This property is
`very useful in the context of our application, since shifts
`can indeed happen in any direction. When, however, par-
`ticular, known directions are more susceptible to a shift,
`better statistics (such as the principal components [7] or
`the Z-scores [SI) might be utilized. In addition, although
`this property is not being investigated in this paper, the
`T 2 statistic can be extended to guard against a shift in the
`variance of the monitored parameter [7].
`Another potential problem might arise from the fact that
`the TZ statistic is not geared towards identifying a shift in
`the variance-covariance matrix and, in fact, will confound
`such a shift with a shift in the mean vector. Because of
`this the S matrix has to be re-calculated every time a new
`time-series model is calculated.
`Other multivariate control methods are, of course,
`available. Most, however, suffer from the significant dis-
`advantage of requiring the monitoring of multiple control
`charts. Such methods might prove advantageous for ana-
`lyzing an alarm for diagnostic purposes and will most
`probably be the subject of future work by the authors. For
`routine monitoring applications, however, the simplicity
`of having to maintain a single control chart makes the T 2
`statistic a very attractive proposition.
`
`E. Implementation of the Real-Time SPC Scheme
`In summary, the real-time SPC scheme takes multiple
`sensor data that are auto-correlated and cross-correlated,
`and then feeds them into individual time-series filters that
`produce multiple, cross-correlated IIND residuals. Ho-
`telling's T 2 equations combine the cross-correlated resid-
`uals into a single real-time alarm signal. This sequence is
`illustrated in Fig. 4.
`This alarm signal can be used either as a passive SPC
`alarm, or it can initiate a diagnostic procedure [5]. A soft-
`ware package has been developed to implement this real-
`time SPC scheme. It includes four modules: data manip-
`ulation, ARIMA filtering, Hotelling's T 2 calculation, and
`alarm generation. These operations were initially imple-
`mented in the commercial statistical packages SAS" [ 161
`and RS/l" [17]. Recently, we have completed indepen-
`dent implementations for Unix and DOS environments.
`Coupled with a SECS11 server, either of these implemen-
`tations is capable of actual real-time operation. The most
`recent implementation imports ARIMA models that are
`
`L
`
`(9)
`where, in order to further ascertain that the entries in this
`formula are normally distributed, it is customary to use
`averages calculated over small, consecutive groups of size
`n for each residual. Some discussion is necessary con-
`cerning the estimation of the variance-covariance matrix
`S. First, the diagonal elements in S are calculated as the
`average s value for each of the m groups of size n:
`
`(10)
`The off-diagonal terms are estimators of the covari-
`ances and are calculated as follows:
`
`k = 1 , 2 , . . . , m
`j = l , 2 ; . . , p
`h = 1 , 2 , *
` , p
`(11)
`*
`*
`Finally, the actual elements of the variance-covariance
`matrix S are calculated by averaging over the m groups
`the values found in (IO) and (11):
`
`j # h .
`
`.
`
`m
`
`
`
`The T 2 score is sensitive to a shift in the mean value of
`one or more of the variables. This score can be used in a
`one-sided control chart, whose limit is set according to
`the number of variables, the sample size and the accept-
`able false alarm rate. The control limit of the T 2 statistic
`
`'In this paper we employ bold-faced symbols to represent non-scalar
`quantities such as arrays and matrices. All arrays are columns, unless used
`with the superscript
`which symbolizes transposition.
`
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`Applied Materials, Inc. Ex. 1025
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`
`

`

`SPANOS er a / ’ REAL-TIME STATISTICAL PROCESS CONTROL USING TOOL DATA
`
`313
`
`TABLE I
`REAL-TIME SIGNALS COLLECTED FROM THE LAM RAINBOW 4400
`
`Number
`
`1
`2
`3
`4
`5
`
`Name
`
`Position of the RF tune vane
`Position of the RF load coil
`Amount of RF phase error
`Plasma Impedance between electrodes
`Peak-to-peak voltage across the electrodes
`
`Cross-correlated
`Fig. 4. Summary of the real-time SPC scheme
`
`..........................................................
`
`Set-up Procedure
`
`user sets SARIMA i
`models interactively 1
`
`....
`
`timate the means and the variance-covariance matrix of
`the residuals for the T 2 calculation.
`Although 25 parameters could be monitored from the
`LAM Rainbow etcher, using all of them into the scheme
`Plasma
`SARIMA
`Etcher
`proved to be unnecessary, since only a few carried useful
`models
`U I r---...---.--..---.......-....-.-.-.-...k
`..............................................
`information. The criterion for selecting the relevant sen-
`sor readings was that the parameter must have some phys-
`ical significance, in addition to being suitable for time-
`series modeling. This meant that after applying a reason-
`ably simple SARIMA model to the parameter, the result-
`ing residuals should be IIND. The five parameters that
`were finally selected are shown in Table I.
`The statistical behavior of these readings conveys a
`comprehensive picture of the etching conditions. Other
`readings of apparent significance, such as the RF power,
`the chamber pressure, or the gas flows, were not used.
`Since these parameters were actively controlled by the
`machine according to externally set targets, their readings
`were insensitive to internal machine changes.
`The real-time data from the baseline wafers are plotted
`in Fig. 6. These plots show only the first 60 readings col-
`lected during the first minute of the RF cycle for each of
`the four baseline wafers. The frequency of data acquisi-
`tion is about 1 Hz. It is obvious from these plots that the
`readings are not stationary and that they have strong “sea-
`sonal” patterns, where each new wafer constitutes a
`‘‘season. ”
`The SARIMA(0, 1, 1) x ( 1 , 1, 0)60 model, listed in
`(15), was selected and fitted for all parameted with the
`help of the SAS/ETS’” statistical package:
`a, = (zr - z t - 1 ) - (zr-m - zr-61) - 41
`x [(Zi-fXl - z - 6 1 ) - (Zr-120 - Zr-121)l + e l a r - l
`
`: ............................................................................................
`Produdion Run
`Fig. 5. The implementation of the Real-Time SPC System.
`
`<
`
`generated interactively using the SAS /ETS’” (Economet-
`ric Time Series) module. The monitoring program then
`performs the real-time alarm generation function auto-
`matically. This sequence is illustrated in Fig. 5.
`
`IV. APPLICATION EXAMPLES
`To date, the real-time SPC scheme has been success-
`fully applied on a Lam Research Rainbow 4400 plasma
`etcher, and on Applied Materials Precision 5000 cluster
`tool. These applications are described next.
`
`A. The Lam Research Experiments
`In these experiments, a number of 6” patterned poly-
`silicon wafers were etched using a C12-based polysilicon
`etch recipe [18] on a Lam Research Rainbow 4400 single-
`wafer etcher. Through the SECS11 protocol link a remote
`host communicated directly to the Rainbow in order to
`acquire real-time analog data, using the Lam Station
`package provided by Brookside Software [ 191. Using this
`package, up to 32 separate parameters can be sampled si-
`multaneously with rates of up to 3 Hz. For this experi-
`ment, we monitored signals from the RF network because
`we found that they are very responsive to small process
`changes [20]. Two experiments are described next.
`
`B. The First LAM Rainbow Experiment
`The initial objective was to select the proper parameters
`from all of the available sensor readings, and also to find
`the proper time-series models for these parameters. To
`this end the machine was calibrated to a stable operating
`point by processing over 100 wafers. Four polysilicon
`wafers that were processed afterwards gave us the base-
`line data-set. The baseline data-set was used to select and
`characterize the appropriate time-series models, and to es-
`
`This model was applied to all five monitored parame-
`ters, with different values fitted for the coefficients 41 and
`el for each parameter. The ZIND residuals for the five ob-
`served parameters are plotted in Fig. 7. Note that (11)
`cannot be used to generate residuals for readings 1 to 121,
`since the data from the first two baseline wafers, as well
`as the first reading of the third wafer, are lost due to dif-
`ferencing. The plots in Fig. 7 show the residuals for the
`baseline data points 122 to 240.
`
`‘Naturally, the fact that the same SARIMA structure was applicable to
`all five signals in this example is just a coincidence. In general, different
`signals require different SARIMA structures.
`
`Authorized licensed use limited to: LEHIGH UNIVERSITY. Downloaded on July 12,2021 at 02:05:12 UTC from IEEE Xplore. Restrictions apply.
`
`Applied Materials, Inc. Ex. 1025
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 6 of 11
`
`

`

`314
`
`IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 5. NO. 4, NOVEMBER 1992
`
`Orieinal RF Tune Vane
`
`Onginal RF Load Coil
`
`I --
`
`I
`
`1
`
`I
`
`I
`
`Original RF Plasma Impedance
`I
`I,
`1 II
`1111
`
`1
`
`