On the Utility of Run to Run Control in Semiconductor
`Manufacturing*
`
`John Musacchiot, Sundeep Rangant, Costas Spanost and Kameshwar Poollai
`
`t Dept. of EECS, Univ. of California, Berkeley, CA 94720
`tel: (510)642-7156, fax:(510)642-2739, email: musacchjClcory. eecs. berkeley. edu
`i Dept. of Mech. Eng., Univ. of California, Berkeley, CA 94720
`tel: (510)642-4642, fax:(510)643-5599, email: poollaCljagger .me. berkeley. edu
`
`Abstract- Run to Run (RTR) · control uses data from
`past proces.s runs to adjust settings for the nert run.
`By making better use of existing in-line metrology and
`actuation capabilities, RTR control offers the potential
`of reducing variability in manufacturing with minimal
`capital cost .. In this paper, we survey the types of equip(cid:173)
`ment model's that can be used for RTR control, compare
`existing RT'R control algorithms, and discuss issues af(cid:173)
`fecting the potential utility of RTR control.
`
`reasons, RTR control offers the promise of being rapidly
`integrated into existing fabrication lines and at modest
`capital cost.
`
`In this paper, we study process modeling, explore var(cid:173)
`ious control schemes, and discuss general implementa(cid:173)
`tion issues for RTR control as applied to semiconductor
`manufacturing processes.
`
`INTRODUCTION
`
`As integrated circuit producers are driven towards finer
`linewidths and feature sizes, there is a compelling need
`for precision manufacture.
`
`In the past, this need has been met by expending con(cid:173)
`siderable effort in the design of processes that are very
`stable, by isolating environmental effects, and by de(cid:173)
`signing equipment that is insensitive to process drift.
`Processes are then run with a fixed recipe over batches
`of several hundred wafers, and occasionally re-tuned by
`running test wafers.
`
`An alternative approach, and one that is receiving in(cid:173)
`creasing attention, is the use of feedback control tech(cid:173)
`niques to reduce product variability. Preliminary stud(cid:173)
`ies have shown that these techniques offer promise for
`precision manufacture with modest development and
`ownership cost. Various processes have been studied in
`this context;. See for example Rapid Thermal Process(cid:173)
`ing (RTP) [15], Reactive Ion Etching (RIE) [5], and litho(cid:173)
`graphic sequences [8]. For the next generation of IC
`technologies with 193 nm lithography, there is a grow(cid:173)
`ing consensus that feedback control will prove to be an
`enabling technology.
`
`Feedback control uses measurements during process(cid:173)
`ing to adjw;t process recipe settings to correct for pro(cid:173)
`cess drift. This requires a rudimentary process model,
`In Run-to-Run
`metrology, and actuation capability.
`(RTR) control, recipe settings are adjusted for a given
`wafer based! on metrology from previous wafers. This
`can use existing in-line metrology, does not require real(cid:173)
`time actuation, and is minimally intrusive. For these
`
`, Support<!d in part by the SRC, the State of California MICRO
`program, and by AMD, ATMEL, AMAT, LAM, SVG, Tl, and NSC.
`
`0-7803-3752-2 /97/$ 10
`©1997 IEEE
`
`MODELS
`
`RTR control strategies require a model of the pro(cid:173)
`cess and of the disturbances affecting the process. We
`should like to stress that these models need not be ex(cid:173)
`tremely accurate or detailed. Control strategies involve
`making modest adjustments to input settings to reduce
`process variability. Therefore, only the first-order sen(cid:173)
`sitivities of the process to input changes are required
`by the controller. Detailed, accurate models are very
`important for other problems including equipment and
`process design.
`
`A nominal process model / relates the process input u
`to the nominal process output y under idealized condi(cid:173)
`tions (no noise/disturbances) and can be written as
`Yk = /(0,., u,.)
`Here f is parameterized by the process parameters 0.
`The form of the model f is usually determined from a
`physical understanding of the process, and the parame(cid:173)
`ters 0 are obtained by fitting the model to experimental
`data. In many situations, the parameters 0 represent
`physical quantities (such as reaction rates or resist pa(cid:173)
`rameters) that are not directly measurable. At any rate,
`the parameters O may drift from one wafer to the next.
`We can model this drift as a random walk:
`
`81c+1 = 81c +w1c
`
`where k is the wafer index, and w1c is a random distur(cid:173)
`bance, which we will 1~efer to as the pammeter drift.
`
`We recognize that the nominal process output y 0 is ide(cid:173)
`alized, and we therefore write the measure process out(cid:173)
`put y as
`
`D-9
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`Applied Materials, Inc. Ex. 1016
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 1 of 4
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`

`

`where e is the measurement noise, and z is an offset
`drift. Note that, unlike the parameter drift, offset drift
`simply adds to the output and does not affect input
`sensitivites.
`
`RTR CONTROL METHODS
`
`RTR control methods fall broadly into two distinct
`classes: offset drift cancellation and pammeter adaptive
`control approaches.
`
`Offset Drift Cancellation Approaches
`
`Here process variation is assumed to be entirely in the
`offset term (i.e. the parameter drift is absent). Conse(cid:173)
`quently, the input sensitivities are assumed to be con(cid:173)
`stant and known. The idea is to estimate the current
`offset Zk based on past wafer data, and to select the
`input settings to compensate for the estimated offset.
`
`Exponentially-Weighted Moving Average (EWMA)
`
`This is one of the most intuitive methods [3]. Gradual
`Mode EWMA assumes a nominal process model of form
`Yk = Auk + Zk + ek
`It is assumed that the sensitivity matrix A is fixed and
`that the process variation is entirely accounted for by
`z,.. An estimate i,. for the drift is computed recursively
`as
`
`i,. = (1 - w)i1<-1 + w(Yk-1 - Au,._1)
`The choice of w is usually ad-hoc, with higher values
`resulting in more aggressive control. See [4] for a treat(cid:173)
`ment of this subject.
`
`Having obtained an estimate of the drift, the input set(cid:173)
`
`ting u,. is chosen as the smallest adjustment necessary
`to meet the target T by canceling the estimated drift:
`
`T= Au,.+ i,..
`
`As a compliment to Gradual Mode EWMA, Sachs, et.
`al., develop a Rapid Mode EWMA Controller [3]. This
`uses Bayesian decision theory to decide whether or not
`the plant parameters have changed abruptly, and to
`then take aggressive corrective action.
`
`The attractiveness of the EWMA scheme lies in its sim(cid:173)
`plicity. The principal difficulties are weight selection
`and implementation on processes -with multiple sen(cid:173)
`sors. EWMA control methods have been successfully
`deployed on applications such as CMP [7].
`
`Robust Drift Cancellation
`
`This is a novel RTR control approach that like EWMA,
`assumes a process model of the form
`Yi<= Au,.+ Zk + e,..
`In robust drift cancellation, the drift is estimated as a
`weighted average of residuals on a finite window of past
`
`D-10
`
`data. The advantages of robust drift cancellation are
`that the weights are explicitly computed from a long
`history of past process data. Also, an a priori estimate
`of the benefit of RTR control can be determined based
`on worst-case assumptions of the offset drift statistics.
`
`Suppose we have m lots of process data for lots of L
`wafers. The design proceeds as follows:
`
`1. Select a window size n, n < < L
`
`2. For each of the m lots, compute the residual signal
`d1o = y,e - Au,e. We will assume some modeling has
`been performed to estimate the sensitivity matrix A.
`Note that d,. includes both the measurement noise and
`process drift. Compute the correlations
`
`Re= average (d,.d,._t)
`
`The values Re may vary from lot to lot.
`
`3. Find a matrix K, such that for all lots,
`
`Rn-1 l Rn-2
`
`Ro
`R1
`:
`
`K>R=
`
`[
`
`Rn-1 R...-2
`The matrix K is a measure of the worst case covariance
`of the residual.
`
`Ro
`
`4. Find a row matrix C, such that for all lots,
`
`where
`
`L = [ R1
`Rn ]
`The matrix C is a measure of the worst-case autocor(cid:173)
`relation in the measured residuals.
`
`5. Use any RTR control u satisfying
`
`If there is no parameter drift, and if the process
`6.
`data is representative, then this RTR control scheme
`will reduce the output variance (per wafer) by
`
`Obserre that if there iB t:1ubt:1tantial measurement noise,
`then L will approximately be zero and the RTR control
`will disconnect. The advantage of this scheme, is that it
`robust to statistical assumptions on the offset drift z,..
`This is at the expense of using less aggressive control.
`
`Parameter Adaptive Stmtegies
`
`In this situation, we assume that the observed process
`drift is due to both parameter and offset drift. The
`strategy is to "tune" or update the process parameters
`0 as data becomes available. The input settings are
`
`Applied Materials, Inc. Ex. 1016
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 2 of 4
`
`

`

`adjusted based on the tuned nominal model and the
`target output value T.
`
`Kalman Filter Methods
`
`Here, Kalman filtering is used to recursively estimate
`process parameters B,.. This requires a linear nominal
`process model and knowledge of the measurement noise
`covariance a.nd of the offset drift covariance. These co(cid:173)
`variances can be estimated from pa.st data.
`
`The equations involved in Kalman filter RTR control
`methods are somewhat involved: the reader is referred
`to [1] for details. In [1], these methods were applied
`to the resist coat process to reduce variability in re(cid:173)
`sist thickne:~s and photoactive compound concentration.
`Kalman Filter based control techniques have been suc(cid:173)
`cessfully applied to other processes, such as Reactive
`Ion Etching; [5].
`
`The shortcoming of Kalman filter methods for RTR
`control in particular, and parameter adaptive control
`methods in general, is as follows. If there are too many
`process parameters 0,., estimating them requires a lot
`of data. By the time we have enough data to estimate
`the process parameters, they may have drifted consid(cid:173)
`erably. As a result, the nominal process model is poor
`and RTR control based on this model can increase pro(cid:173)
`cess variance. These problems are illustrated in (1].
`
`Statistical Response Surface Approach
`
`In this approach the behavior of the nominal process
`is described by linear regression models. During the
`operation of the process, a model-based SPC criterion
`is used to detect discrepancies between the models and
`the actual observations. This criterion can be tuned to
`detect slow, consistent process changes ( multivariate,
`model-based CUSUM or EWMA charts can be used
`for this). Once a slow, consistent change has been de(cid:173)
`tected, the most recent points are used to update the
`response surface models using step-wise, principal com(cid:173)
`ponent regression, and the updated models are then
`used for estimating the new operational recipe. This
`technique has been used for feedforward, as well as feed(cid:173)
`back control [ 8]. An additional statistical criterion can
`be used to detect abrupt discontinuities in process be(cid:173)
`havior (T2 charts are suitable for this). This can play
`the role of traditional SQC, where human intervention,
`or a knowledge based diagnostic system is needed to
`correct problems [9].
`
`ISSUES
`
`W'hen should RTR Control be deployed?
`
`In semiconductor manufacturing, much effort is made
`to eliminate sources of variance from manufacturing
`processes. A natural objection to RTR control is that
`tweaking process settings between runs adds an unnec(cid:173)
`essary source of variability. This would only increase
`
`the variability in ex-situ wafer characteristics. This ob(cid:173)
`jection is indeed true when the process drift is statisti(cid:173)
`cally white. However, when the process drift is colored,
`RTR control can reduce process variance. This is be(cid:173)
`cause the drift can be "learned" from pa.st wa.f er data.
`
`In deciding whether to use RTR control, it is therefore
`important to check if the process drift is colored. The
`utility of RTR control increases with greater correlation
`in the measured drift sequence.
`
`Another common concern is that a RTR control strat(cid:173)
`egy might be too sensitive to measurement noise. Then
`process setting decisions a.re made on the basis of spuri(cid:173)
`ous data. Measurement noise can indeed be a problem
`for a RTR controller, but there are ways to mitigate
`its affects. For example, Kalman Filtering methods ex(cid:173)
`plicitly use a model of the measurement noise. A larger
`measurement noise variance used in the design equa(cid:173)
`tions will lead to less aggressive RTR control.
`
`Large measurement n()ise variances can also be incorpo(cid:173)
`rated into an EWMA design, by decreasing the weight
`w.
`
`Offset Drift Cancellation vs. Parameter Adaptation
`
`It is possible to determine whether or not a process
`has significant parameter drift by computing cross(cid:173)
`correlations between the measured drift d,. and the in(cid:173)
`put settings u,. on a large lot of wafers.
`If there is
`little correlation, we can be confident that the offset
`drift dominates. In this case, we should employ drift
`cancellation based RTR control.
`
`Offset drift cancellation is a far simpler control strategy
`in comparison to para.meter adaptation. In addition to
`the benefits of a simpler implementation, the simpler
`control design offers improved roboustness. This is at
`the expense of possibly reduced performance. Neverthe(cid:173)
`less, we believe that offset drift cancellation should be
`the default choice. Parameter adaptive control methods
`should be investigated when there is significant param(cid:173)
`eter drift.
`
`Making a choice between the various available methods
`for RTR control is a difficult problem. We feel that
`this is a process dependent issue, and one that should
`be made on the basis of experiment. It is possible to
`investigate optimality conditions for various methods,
`and this can assist the choice of method.
`
`Optimality
`
`If a drift process does indeed have some modest corre(cid:173)
`lation between successive outputs, and/or the measure(cid:173)
`ment noise is significant, then it is important that the
`RTR controller be carefully optimized.
`
`When the drift obeys a time series stochastic model, it
`can be shown that the Kalman Filter is optimal. Be(cid:173)
`cause of its limited complexity, EWMA methods are
`
`D-11
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`Applied Materials, Inc. Ex. 1016
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 3 of 4
`
`

`

`[9] C. Spanos, S. Leang, S. Lee, "A control and di(cid:173)
`agnosis scheme for semiconductor manufacturing,"
`American Control Conference, San Francisco, CA,
`vol. 3., pp. 3008--12, June 1993.
`
`[10] J. Musacchio, M.S. thesis, Univ. of California,
`Berkeley, in preparation, 1997.
`
`optimal for a smaller class of problems. Conditions for
`the optimality of EWMA can be derived, and more(cid:173)
`over, optimal choice of the weight w can be computed
`based on the variances of the measurement noise and
`the offset process drift [10].
`
`Stability
`
`The formal analysis of stability in the context of RTR
`control is difficult, particularly for parameter adaptive
`control methods. For simple EWMA schemes, stability
`has been studied in the context of process assumptions
`[3).
`
`In practice, however, the stability of RTR control is pro(cid:173)
`tected by means of hard limits on inputs, and by limit(cid:173)
`ing permissible input changes. In addition, techniques
`such as ~process input SPC" can apply statistical cri(cid:173)
`teria such as the Western Electric Rules to controlled
`process da:ta to closely monitor the behavior of both the
`controller and the the process.
`
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`
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`
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`D-12
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`Applied Materials, Inc. Ex. 1016
`Applied v. Ocean, IPR Patent No. 6,836,691
`Page 4 of 4
`
`