EP1444556A1 - Semiconductor run-to-run control system with state and model parameter estimation - Google Patents
Semiconductor run-to-run control system with state and model parameter estimationInfo
- Publication number
- EP1444556A1 EP1444556A1 EP02806777A EP02806777A EP1444556A1 EP 1444556 A1 EP1444556 A1 EP 1444556A1 EP 02806777 A EP02806777 A EP 02806777A EP 02806777 A EP02806777 A EP 02806777A EP 1444556 A1 EP1444556 A1 EP 1444556A1
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- 239000004065 semiconductor Substances 0.000 title claims description 16
- 238000000034 method Methods 0.000 claims abstract description 287
- 230000008569 process Effects 0.000 claims abstract description 209
- 238000005259 measurement Methods 0.000 claims abstract description 146
- 238000012545 processing Methods 0.000 claims abstract description 23
- 238000004519 manufacturing process Methods 0.000 claims description 11
- 238000005457 optimization Methods 0.000 claims description 9
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Classifications
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L22/00—Testing or measuring during manufacture or treatment; Reliability measurements, i.e. testing of parts without further processing to modify the parts as such; Structural arrangements therefor
- H01L22/20—Sequence of activities consisting of a plurality of measurements, corrections, marking or sorting steps
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B17/00—Systems involving the use of models or simulators of said systems
- G05B17/02—Systems involving the use of models or simulators of said systems electric
Definitions
- the present invention relates to the field of semiconductor processing and, more particularly, to run-to-run control in semiconductor processing.
- Run-to-run (R2R) control and fault detection (FDC) in semiconductor processing refers to the practice of updating equipment recipe settings based upon product measurements that occur after process completion.
- the practice applies in the semiconductor industry due to the inability to measure the product characteristics in situ.
- CMP chemical- mechanical-planarization
- pad rotational speeds, applied forces, and other parameters are measurable, but the film thickness, the actual product variable, is not.
- lithography the exposure power, exposure time and focus may be determined, but the actual overlay errors are not measured until after the development of the resist, a separate process occurring long after the lithographic exposure.
- the method for controlling a manufacturing process includes: processing materials using a process input and producing a process output, storing the process input in a database, the storing including using a timestamp, and storing at least one measurement of the process output in the database aligned with each process input using the timestamp.
- the method further includes iterating over the data in the database to estimate one or more coefficients for a model, and, if one or more measurements is missing, replacing the missing measurements based on a prediction from said model.
- the model is updated with said coefficient estimates.
- the method additionally includes iterating over the data from the database to estimate a process state, and, if one or more of the measurements is missing from the database, replacing the missing measurements for the database based on prediction from the model.
- the model is updated with said process state estimate.
- the replacement of missing measurements during parameter or state estimation can be accomplished implicitly or explicitly.
- a controller may receive the updated model and utilize the model to produce the next process input.
- the updated model may also be utilized to generate an estimate for a measurable process variable, wherein the estimate can be compared to an actual measurement to determine if the estimate is within confidence limits. If the estimate is not within- confidence limits, a fault is indicated.
- the method includes one or more modules coupled to the database, the one or more modules including at least a sorting module configured to sort measurements received asynchronously from the process according to the timestamp, the sorted measurements including later arriving measurements to allow the next process input to be based at least in part on an error calculated using later available measurements.
- the sorting module also sorts the data in the database for use during parameter estimation or state estimation. If actual measurements become available a time period after model coefficient estimation or process state estimation, for one or more measurements which was missing, the predicted measurements for the previously missing measurements are replaced with the actual measurements, and the actual measurements are stored in the database. In subsequent model coefficient estimation and process state estimation, the actual measurements are used in place of the predicted measurements.
- the time period during which one is waiting for the actual measurements to become available may be variable in the present invention.
- the state estimator filter and parameter estimator filter comprise separate receding-horizon filters that compute estimates using a constrained least-squares approach.
- the least-squares optimization requires the solution to a quadratic program.
- Figure 1 labeled "prior art”, illustrates an exemplary processing system of semiconductor wafers by a semiconductor tool.
- FIG. 2 is a block diagram of a control system in accordance with an embodiment of the present invention.
- Figure 3 is a timing diagram illustrating operation of a state/parameter estimator in accordance with an embodiment of the present invention.
- Figure 4 is- a flow diagram of a method in accordance with an embodiment of the present invention.
- Figure 5 illustrates a confidence region during fault detection in accordance with an embodiment of the present invention.
- the present invention provides a method and system for efficiently and accurately processing materials, for which processing measurements are collected asynchronously from material processing, such as in semiconductor processing. 'The present invention also provides a method for combined state and parameter estimation in a R2R control application.
- an embodiment of a prior art control system shows a process input 106, which may be raw materials, partially processed materials, or other process inputs, such as semiconductor materials, that are processed on a process tool 104.
- Controller 102 is coupled to process tool 104 to provide one or more control input signals.
- Process tool 104 processes the materials of process input 106 and outputs process output 108.
- Control system 200 includes a process 210 for processing materials coupled to a controller 202.
- Controller 202 receives a process setpoint r 212 and outputs computed process inputs u 214.
- Process 210 receives an actual process input v 218 which includes the computed process input 214, as altered by an operator-induced input disturbance ⁇ u 216.
- Actual process input v 218 is further received by an input/output repository 208, which may be implemented as a database.
- Process 210 processes materials and outputs processed products requiring measurements.
- Process 210 delivers the products and the parameters of - the products.
- the output of the process tool 210 is measured.
- the measurements are shown as block 224 and include: (i) measurements that are done in situ; (ii) measurements done shortly after processing; and (iii) later accomplished measurements.
- Control system 200 operates on the measurements to add a disturbance d 222 via a transfer function, such as disturbance transfer function matrix 220.
- the process measurements are shown as process output ⁇ 226 and are further provided to input/output repository 208.
- measurements y 226 are generally collected asynchronously from actual material processing in process tool 210.
- the input measurement of such to process tool 210 may be shown as a dashed line.
- Input/output repository 208 provides data 228 to both a model 262 and to a state/parameter estimator 206.
- Input/output repository 208 can be implemented as a database that accumulates past inputs and measurements.
- Input/output repository 208 further includes a sorter for sorting the inputs and measurements according to a process timestamp and a receding horizon filter or an appropriate substitute filter that handles missing measurements. Sorter also sorts the data for use during either state estimation or parameter estimation.
- State/parameter estimator 206 receives data from model 262 as well and provides an updated model to controller 202. Controller 202, unlike controller 102, computes process inputs based on the updated model. The model is updated based on coefficient and process state estimates computed by state/parameter estimator 206.
- state/parameter estimator 206 employs more than one filter as estimators for different components of the model 262. State/parameter estimator 206 employs one filter for parameter estimation and another filter for state estimation.
- none, one, or a plurality of measurements on a product from past process runs may be performed by measurement tool 224.
- Coupled to input/output repository 208 are several modules 250-258.
- the modules include data storage module 250 that captures and stores actual process vectors and measured process output vectors from the input/output repository 208.
- Pairing module 252 pairs the process input and output vectors according to a process timestamp or a plurality of predicted process timestamps.
- Sorting module 254 sorts the input/output vector pairs according to the process timestamp(s). Sorting module 254 also sorts the data for use during either state estimation or parameter estimation.
- Compute module 256 computes a predicted process output or a plurality of process outputs using the process model, and estimation module 258 estimates a process state vector from process inputs, output predictions and actual output vectors.
- estimation module 258 estimates updated model coefficients from process outputs, the model output predictions and the actual output vectors. More particularly, data storage module 250 and pairing module 252 include routines to capture the actual process input v 218, attach a timestamp signifying the start of the process 210, store the input v 218 into a sorted list of process input/output pairs for maintenance in input/output repository 208, capture the product measurements y 226 and affiliate them with the corresponding process input v 218 in the stored list within the input/output repository 208.
- Input/output repository 208 may be implemented as a database for storing the coordinated input/output pairs for each unit of product.
- the unit of product may be implemented as a lot of wafers or individual wafers, depending on the granularity of control of a particular site and configuration parameters for the state/parameter estimator 206.
- the configuration parameters may include the horizon length, the expiration date for measurements and weight matrices. The expiration date of the measurements is a timestamp prior to which the system 200 ignores all process inputs and product measurements. Further configuration parameters are described below.
- Process model 262 can be characterized as follows:
- Equation (1) The explanation of the symbols appearing in Equation (1) appears in Table 1 below.
- Table 2 gives a description of the resulting disturbance model for various choices for ⁇ and w, which is a white noise process.
- the disturbance may be composed of several sub-vectors each containing information about the tool's, a durable's (e.g., reticle), or a product layer's additive contribution to the state model.
- the modifications to Equation (1) required to accommodate these separate contributions would be known to those skilled in the art.
- the matrices A, B, and G are usually known from process considerations.
- the coefficients in the matrix C are often indicative of different products' contributions to the process outcome as measured in the output variable, y.
- both unknown disturbances, embodied in the variable d, and unknown model coefficients in C may be present.
- controller 202 may consist of several types of controllers, including a model-predictive control (MPC) type controller, a direct model inverter type controller and simple proportional-integral controllers.
- MPC model-predictive control
- DRC direct model inverter
- simple proportional-integral controllers simple proportional-integral controllers
- Variable J is the objective function value
- vt> is the state error for lot z + 1 in the horizon
- v. is the error between the model predictions and measurements for lot i in the horizon
- Q t , R t are weighting matrices for lot / in the horizon
- x 0 is the initial condition of the state for the first lot, or wafer, in the horizon
- x is the state estimate for lot, or wafer
- y t is the measurement for lot, or wafer, in the horizon
- a l+l , B l+l , C, +1 are state-space matrices for lot + 1 in the horizon
- w mn , w max , f mm , F, max define constraints on the state error and state estimates.
- Equation (2) can be reformulated as follows:
- Equation (3) where w is of dimension (N + 1) • n s x 1 , u is of dimension (N + 1) • n u x 1 , y and Y are of dimension (N + 1) • n x 1 , matrix A is of dimension (N + 1) • n y x (N + 1) • n s , M B is of dimension (N + 1) • n y x (N + 1) • n u , M c is of dimension (N + 1) • n y x n s , Q is of dimension (N + 1) • n. x (N + 1) • n s , and R is of dimension (N + 1) • n y x (N + l)-n y .- The parameters in the constraint of Equation (3) are defined in (5) as:
- E m ⁇ n , E max are of dimension (N + 1) • n s x 1 , F m ,F A and E c are of dimension (N+ ⁇ ) -n_ x (N+l) -n s , and E s is of dimension (N + ⁇ - n ⁇ x ⁇ +l) - ⁇ .
- the missing measurements are replaced with the model predictions.
- This replacement can be accomplished explicitly by calculating the predicted measurement values from the model 262 and using them in place of the missing measurements.
- the replacement may also be accomplished, implicitly by zeroing the rows of M A and 7 in Equations (3) and (4) that correspond to the missing measurements. Either approach forces the elements of v in Equation (2) corresponding to the missing measurements to be 0.
- the state/parameter estimator 206 can store more past values than just the number in the estimate horizon, N. It stores all data up to and including the N-1 lots (or wafers) processed immediately prior to the lot (or wafer) with the oldest missing information. When a new measurement arrives, the state/parameter estimator 206 iterates over the sorted list of IO pairs stored in the input/output repository 208 in groups of N data points, dropping the oldest and adding the next point into the horizon of N points with each iteration. If a data point with a missing value appears in any group of the JV points, the state/parameter estimator 206 substitutes the model's 262 prediction for that point. It does not assume that the error for that point is zero. The state/parameter estimator 206 still estimates an error for that point during its solution of the QP.
- the input/output repository 208 substitutes the new measurement in the sorted list held in the database.
- the state/parameter estimator 206 uses the actual measurement instead of the model's 262 prediction for that point, and iterates over all the points from N points prior to the updated measurement to the current point, correcting prior estimates that were based upon use of the model's predictions.
- a time limit can be imposed, there is no requirement that the missing values become available within a set time period, and the time period during which the measurements become available can be variable.
- Fig. 3 a sequence progression of estimation intervals of a missing values state/parameter estimator is shown.
- the horizon used for configuring state/parameter estimator 206 includes a horizon, (N), of 3.
- N a horizon
- Fig. 3 illustrates four iterations 302, 304, 306 and 308, with each identified against a time index. Furthermore, each iteration illustrates an expiration limit 310, 312, 314 and 316.
- a measurement for an arbitrary lot or wafer, (j) is received.
- Data storage module 250 inserts a new measurement in the list maintained within the input/output repository 208 at the appropriate position.
- the appropriate position is determined in accordance with the receding horizon filter based upon the relevant process timestamp.
- Fig. 3 illustrates the new points as points 322, 324, 326 and 328.
- State/parameter estimator 206 retrieves the sorted list of input/output data from the input/output repository 208 and iterates over successive groups of N data points to arrive at a current estimate of the process state. In the example shown in Fig. 3, one of the values in the list is missing, as shown in iteration 302 by point 332.
- state/parameter estimator 206 can apply the model 262 prediction for that point.
- the model 262 prediction may be applied for point 334, except that the input repository 208 must continue to retain more than N-7 data points due to the missing value in the middle of the known data.
- the previously missing data is obtained.
- Data storage module 250 inserts the data 326 into the input/output repository 208 in the placeholder location for the missing data.
- State/parameter estimator 206 then iterates over the entire list again, this time using the actual data, not the model 262 prediction for the previously missing data point.
- input/output repository 208 trims the data list to only the N-l data points needed in anticipation of the N* value at the next iteration.
- input/output repository 208 trims the data list to only the N-l data points needed in anticipation of the N* value at the next iteration.
- the system 200 operates ' as it did for iteration /, because there are no missing data points in the list.
- Equation (6) provides the equations that the state/parameter estimator 206 uses to update the model coefficients of the matrix (J during parameter estimation.
- the parameter estimator filter is similar to the state estimator filter, except that the optimization uses data for the same product/layer from multiple process tools.
- sorting module 254 sorts the data in the input/output repository's 208 database for use by the parameter estimator filter.
- the parameter estimator filter relies on the data manager module to substitute the missing values into the data sequence when appropriate. In this way, parameter estimation benefits from the useful handling of missing and out-of-order data handling that the data manager module provides during state estimation.
- Block 402 provides for the initialization of the model coefficients, in model 262, and the disturbances, ⁇ u 216, to initial values.
- a recommended process input, u is computed using the current model 262.
- the output target, y, and the controller algorithm uu, cuo ⁇ wu, me u ⁇ cictiui uicii pi ⁇ viues ine acuiai input value, v u + ⁇ u, to the process.
- the material being manufactured is then processed in block 408, and the actual process output, y, is measured in block 410.
- state/parameter estimator 206 computes new coefficients for model 262 using the parameter estimation algorithm.
- Block 414 provides for model 262 to be updated with the new model coefficients computed in block 412.
- state/parameter estimator 206 computes a new disturbance estimate using the state estimation algorithm, and model 262 is updated with this new disturbance estimate.
- Block 418 involves the optional process of fault detection, described below.
- a new recommended process input, u is computed in block 404, the current model 262, as updated in blocks 414 and 416, is used to perform the computation.
- the parameter estimation and state estimation occur in separate steps. However, the order of these steps is immaterial.
- the state/parameter estimator 206 ensures that controller 202 always has access to the most up-to- date model. Furthermore, by substituting the predicted output of model 262 in the input/output (I/O) sequence when measurements have not been received, the estimator 206 makes the full use of all the information available to it, including the process model 262, without requiring the onerous restriction that processing wait until measurements are complete.
- a common prior art approach ignores the lot with the missing measurement, essentially assuming that the error for that lot is zero.
- Another prior art approach is to delay estimation until the time that the controller must supply a new input to the process. This prior art approach causes excessively slow controller calculations and does not address the missing values problem. It does reduce the number of missing values in the sequence, on average, because by waiting the controller allows more time to complete measurements in unmeasured lots or wafers.
- Fault detection applications require a bit of additional processing.
- the initial condition of the states following a maintenance event like wet cleans in plasma etchers, confuse the fault detection algorithm into identifying a fault when none really exists.
- the state/parameter estimator 206 compensates for these shifts by estimating the initial state from initial wafer processing in the same way as described above in the State Estimation section.
- the fault detection algorithms suffer from the same problem as R2R controllers based upon models built from blanket wafers, rather than product wafers.
- the (j , matrix provides the relationship between the blanket wafer model and the product wafer model for each product .
- the additional processing required for fault detection is that following state and parameter estimation, the model 262 residuals must be compared to the measured data. Since both parameter estimation and state estimation provide confidence estimates for their respective outputs, the system can compare the model residuals to the expected levels of variation and identify faults when the measured data fall outside the anticipated confidence intervals. Sufficient measurement data must be accumulated before fault detection becomes reliable. It is believed that measurement data of about two to three times the number of states being measured is sufficient to reliably determine if a fault is occurring. In an alternative embodiment, fault detection could begin when the confidence limits have been reduced to a predefined value.
- CI confidence interval
- step (2) Use the result from step (2) to calculate estimated covariance matrix of estimated parameter, P ⁇
- N(0,1) is the standard normal distribution with zero mean and variance one.
- a rejection of residual prediction error being white noise has in general, l,2,... ,n y (12) where ⁇ represents the significant level, and could be found from t-statistics table (for example, the value of 2.17 represents the level of significance of 3%). ._. _L calculation
- the estimated co-variance matrix of estimated parameter, P M is determined as follows:
- N(0,1) is the standard normal distribution with zero mean and ya ⁇ ance one.
- ⁇ N is the vector of estimated state disturbance
- n s is the number of states
- N is the estimation horizon.
- ⁇ represents the significant level, and could be found from t-statistics table (for example, the value of 2.17 represents the level of significance of 3%).
- PCA Principle Component Analysis
- a threshold (from a confidence interval, e.g., 95%) defines a hyper-elliptical confidence region 502. Any residuals outside this region 502 will be considered to be a fault.
- An example of a fault is identified by reference numeral 504.
- control system may set to alarm or shut down the tool.
- program storage media and signal bearing media include recordable type media such as floppy disks, CD-ROM, and magnetic tape transmission type media such as digital and analog communications links, as well as other media storage and distribution systems.
- the present invention may be implemented as those skilled in the art will recognize, in whole or in part, in standard Integrated Circuits, Application Specific Integrated Circuits (ASICs), as a computer program running on a general-purpose machine having appropriate hardware, such as one or more computers, as firmware, or as virtually any combination thereof and that designing the circuitry and/or writing the code for the software or firmware would be well within the skill of one of ordinary skill in the art, in view of this disclosure.
- ASICs Application Specific Integrated Circuits
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Application Number | Priority Date | Filing Date | Title |
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US10/046,359 US6725098B2 (en) | 2001-10-23 | 2001-10-23 | Semiconductor run-to-run control system with missing and out-of-order measurement handling |
US46359 | 2001-10-23 | ||
US10/171,758 US6748280B1 (en) | 2001-10-23 | 2002-06-14 | Semiconductor run-to-run control system with state and model parameter estimation |
US171758 | 2002-06-14 | ||
PCT/US2002/033853 WO2003096130A1 (en) | 2001-10-23 | 2002-10-23 | Semiconductor run-to-run control system with state and model parameter estimation |
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EP1444556A4 EP1444556A4 (en) | 2006-06-07 |
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CN (1) | CN100354776C (en) |
AU (1) | AU2002367635A1 (en) |
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CN109932908B (en) * | 2019-03-20 | 2022-03-01 | 杭州电子科技大学 | Multi-directional principal component analysis process monitoring method based on alarm reliability fusion |
CN111611536B (en) * | 2020-05-19 | 2023-04-07 | 浙江中控技术股份有限公司 | Data processing method, data processing device, storage medium and electronic equipment |
CN113536983B (en) * | 2021-06-29 | 2023-12-12 | 辽宁工业大学 | Petroleum pipeline stealing positioning method based on P-RLS adaptive filtering time delay estimation |
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WO2000079355A1 (en) * | 1999-06-22 | 2000-12-28 | Brooks Automation, Inc. | Run-to-run controller for use in microelectronic fabrication |
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US6002839A (en) * | 1992-11-24 | 1999-12-14 | Pavilion Technologies | Predictive network with graphically determined preprocess transforms |
US5448684A (en) * | 1993-11-12 | 1995-09-05 | Motorola, Inc. | Neural network, neuron, and method for recognizing a missing input valve |
DE69813040T2 (en) * | 1998-08-17 | 2003-10-16 | Aspen Technology, Inc. | METHOD AND DEVICE FOR SENSOR CONFIRMATION |
US6542782B1 (en) * | 1998-12-31 | 2003-04-01 | Z. Joseph Lu | Systems for generating and using a lookup table with process facility control systems and models of the same, and methods of operating such systems |
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2002
- 2002-10-23 AU AU2002367635A patent/AU2002367635A1/en not_active Abandoned
- 2002-10-23 WO PCT/US2002/033853 patent/WO2003096130A1/en not_active Application Discontinuation
- 2002-10-23 EP EP02806777A patent/EP1444556A4/en not_active Withdrawn
- 2002-10-23 CN CNB02823393XA patent/CN100354776C/en not_active Expired - Fee Related
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
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US5710700A (en) * | 1995-12-18 | 1998-01-20 | International Business Machines Corporation | Optimizing functional operation in manufacturing control |
US5859964A (en) * | 1996-10-25 | 1999-01-12 | Advanced Micro Devices, Inc. | System and method for performing real time data acquisition, process modeling and fault detection of wafer fabrication processes |
US5926690A (en) * | 1997-05-28 | 1999-07-20 | Advanced Micro Devices, Inc. | Run-to-run control process for controlling critical dimensions |
WO2000079355A1 (en) * | 1999-06-22 | 2000-12-28 | Brooks Automation, Inc. | Run-to-run controller for use in microelectronic fabrication |
Non-Patent Citations (1)
Title |
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See also references of WO03096130A1 * |
Also Published As
Publication number | Publication date |
---|---|
CN100354776C (en) | 2007-12-12 |
CN1592873A (en) | 2005-03-09 |
AU2002367635A1 (en) | 2003-11-11 |
EP1444556A4 (en) | 2006-06-07 |
WO2003096130A1 (en) | 2003-11-20 |
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