*Fewer send-ahead wafers. The ability to forecast optimum offset commands lessens the need for send-ahead wafers. (Dedicated routing, send-ahead wafers, and nonproduct wafers are all costly.)

*Increased stepper availability. Improved overlay and CD control reduces rework rates and the need for send-ahead and nonproduct wafers, increasing stepper availability.

*Accelerated design-rule programs. Reduced overlay and CD variation enables fabs to accelerate the introduction of smaller design rules.

R2R control offers well-documented benefits.^1–3 Nevertheless, it is not a panacea. In photolithography, it has limitations in the following areas:

*Calibration. A hallmark of feedback control is its ability to automatically compensate for short-term exposure-tool drifts. However, the full population of exposure tools must still be anchored regularly to a fixed reference using a traditional matching methodology. Failure to do so results in the decoupling of subgroups from the main group, leading to an increase in high-frequency noise entering the R2R controller and subsequently limiting the effectiveness of the control strategy.

*Performance. When there is a sudden and transient shift in process or tool state caused by a source outside the observable realm of the R2R controller, an overcompensation condition can arise, negatively affecting a small percentage of lots. However, when configured properly, feedback control minimizes overcompensation effects, improving average lot-to-lot performance. The positive performance of the great majority of lots far outweighs the poor performance of a very small number of lots.

*Rework rates. In most cases, R2R control results in reduced rework rates. However, if the rework rate is already quite low (less than 1%, for example), feedback control may not have a significant impact. Low rework rates may indicate that the production line is not fully using tool capability, using too many send-ahead or nonproduct monitor wafers, being controlled through the intense manual efforts of knowledgeable engineers, or experiencing a hidden yield issue where the metric used to determine the rework decision does not properly correlate to true overlay limited-yield criteria. Even when rework rates are low, R2R control is still beneficial because it corrects for future observed shifts and drifts without manual intervention.

*Zero errors. Feedback control calculates optimum job-offset commands for each exposure event so that systematic errors are driven close to zero. Most remaining errors can be attributed to noncorrectable residual sources (pattern placement errors on production wafers). Even under ideal conditions, processes and exposure tools are likely to generate noncorrectable residuals which are not correctable by any available combination of job-offset commands. Noncorrectable residual errors are caused by lens distortion, photomask pattern placement errors, metrology errors, random stage errors, boustrophedonic stage errors, wafer warping, or nonuniform expansion. In addition, the dynamic nature of the disturbances that cause overlay error results in a time delay between process, measurement, and control, causing high-frequency disturbances whose period is equivalent to the time delay being left uncompensated for.

How the R2R Controller Works

Feedback Optimizer. The feedback optimizer (FBO) is an application containing a set of automated algorithms to simulate the way the R2R controller handles feedback requests. FBO operates on a static data set that contains process stream information, exposure parameters, and modeled error parameters. Once the data set has been imported into the tool, the user can optimize filters, warning limits, and weighted moving average through a series of plots and menus, as illustrated in Figure 1. As shown in Figure 2, optimization decisions are simplified by reviewing FBO-estimated overlay improvement values. These values have proven to be quite accurate when compared with real-world control system data.

Figure 1: Screen capture showing run-to-run controller's feedback optimizer.

Working with a static data set to optimize the closed-loop R2R controller has several advantages:

*Reduced learning cycles. Filter and warning limits can be tried and tested off-line rather than during production. Improper selection of these limits can result either in false failures, which translates into unnecessary equipment downtime, or failure to detect real problems.

Figure 2: Screen capture showing estimated improvements in overlay control.

*Evolutionary operation. Experimenting with weighted moving average as a function of the time delay between the exposure event and the corresponding metrology measurement allows the R2R controller to be optimized for performance without suffering from time-delay sensitivities.

*Simplified configuration setup. Wildcarding and default settings simplify the configuration setup. By analyzing data off-line, the user can determine wildcarding rules that allow similar process streams to be combined and determine default settings that can be globally applied to many process streams.

*Ability to test new functionalities. Advancements are continually being made in lithography R2R controllers. Simulating new functionalities in off-line mode allows the user to test the applicability of new functionalities for their specific process environment.

*Ability to determine active control. Improvement estimates are made for each correctable parameter. When a parameter exhibits a significant amount of high-frequency noise, the R2R controller may actually degrade performance. In such situations, it may be appropriate to disable active control until the root cause of the noise is isolated and corrected.

Overlay R2R Control. The first type of data collected by the control system is the actual vector (A), which represents the actual process conditions used at the exposure step.

As production wafers undergo the exposure step, some or all of them are measured using one or more metrology tools. The schematic diagram of an R2R control system in Figure 3 illustrates the point at which the measurement step takes place. Measurements, in the form of raw data, must be converted into a form that is useful for process control. The R2R controller performs that conversion by applying an analysis function to the raw data, resulting in the computation of an error vector (E). This vector describes the error in the input settings that were used to process the wafers that have just been measured. Error vector calculations are based on the settings of the process and tools that are being controlled. To ensure that only valid metrology events are considered for feedback, raw-data-quality filters (validation rules) are applied to the analysis. Examples of such filters may include the number of successfully measured raw data points > N and process events marked as ignored for feedback processing.

Figure 3: Schematic diagram of an R2R control system illustrating the points at which the measurement step takes place and the vectors are calculated.

In some cases, values contained in the error vector can exhibit a scaling or sign difference. This problem is corrected by using a variable-gain amplifier in the feedback loop. When the gain vector is applied, the error vector takes on the new form of E_g.

For a given exposure, the R2R controller collects the actual vector and error vector at different times. The actual vector generally arrives immediately following the completion of the exposure step, while the error vector is not available until the measurement function has been completed. Depending on when the metrology measurement occurs, the metrology time delay can be as short as 1 hour or longer than 24 hours. A process called store matching is used to link the two vectors together in the database.

Successful matching of the actual and error vectors ensures that the ideal vector can be computed. The ideal vector is the corrected vector that takes errors into account and determines the ideal command, which eliminates the errors caused by the sum of process, tool, and photomask variations. The ideal vector is the difference between the actual vector and the error vector (I = A – E). If it were possible to go back in time and use the error vector value to modify the job-offset command, wafer measurements would not reveal any systematic errors—the error vector would be zero and all errors remaining on the wafer would be noncorrectable residual ones. But because it is not possible to go back in time, the R2R controller uses a historical correlation method to apply past ideal vectors to current forecasting requests.

To compare events with similar characteristics, the controller uses a process-stream correlation method in which each lot at a particular process event belongs to a stream of lots that have experienced (or will experience) similar events. When ideal vectors are calculated, the correlation algorithm calculates a value for the command vector (C_FB) by considering the available history of the previously calculated ideal vectors. For example, by measuring wafers that have gone through the same stepper at different times, the user can determine how processing has changed over time.

Since fab operations present complex correlation challenges, the values of the error and command vectors by themselves cannot accurately forecast the correct value of the ideal vector. Therefore, a correlation algorithm that uses a history of vectors to calculate the command vector is needed. Manufacturing characteristics requiring multiple control loops governed by multiple correlation algorithms (not explicitly shown in Figure 3) include:

*Photomask offsets. Photomask-induced variations pose a special challenge to the feedback control loop because they are large and not as frequently observed as exposure-tool and process variations. For example, in high-part-count fabs, some photomasks are used only for one or two lots per month. Moreover, errors introduced by photomasks may vary from one exposure tool to another. Fortunately, photomask-induced errors are static and can be estimated once they are observed. Such errors are controlled by introducing an outer control loop that removes the photomask bias from the main control process.

*Setpoint bias. Setpoint bias controls the lithography process so that it regulates to a nonzero error value. A typical example is a known bias between a postdevelop measurement and a postetch measurement, where the postdevelop measurement can be controlled to a nonzero error in order to compensate for the known etch-process bias.

*Feedforward bias. When the known quality of material entering the exposure tool produces a known bias in the optimal command settings, the command vector must be programmatically modified. For example, if the mean thickness of the nitride layer on a particular lot has been measured, a feedforward controller can create a bias rule to modify the commanded exposure dose to compensate for a thickness difference.

*When the known quality of material entering the exposure tool produces a known bias as a result of rework, the command vector can be programmatically modified so that it is similar to the feedforward bias.

The actual vector is equal to the command vector if no manual overrides are issued. However, if a command sent to a process tool by the R2R controller has been ignored or overridden, the wafers observed by the measurement step are affected by the actual offsets instead of the commanded offsets. Therefore, the definition of the ideal vector takes into account the possibility of ignored or overridden commands.

The Performance of the Automated Control System

Data Collection and Experimental Design. Manufacturing data from a high-part-count fab were collected over a five-month period from an exposure tool performing a single process. Data for the first two months represent material that was processed under a manually intensive feedback loop, where engineers were assigned to track and respond to shifts and drifts in overlay performance. The R2R controller's behavior was simulated using this data set and FBO to determine the controller's optimal configuration settings. Based on the summary results from FBO, the controller was activated. Data for the last three months represent actual overlay performance under active R2R control.

Because many of the product IDs listed in Figure 4 consisted of single product runs tailored to specific customers, it was not surprising that the quantity of wafers in process per product ID changed dramatically over the course of a few short months. Data for the first two months represent the number of manual-control exposure events, while data for the last three months represent R2R-control exposure events. All exposure events were performed on the same 5500/700 DUV step and scan exposure tool from ASML (Veldhoven, The Netherlands), and overlay registration was measured on a 5200XP system from KLA-Tencor (San Jose).

Figure 4: Chart showing the product mix at a single process level. Data for the first two months represent the number of manual-control exposure events, while data for the last three months represent R2R-control exposure events.

Performance with and without R2R control was characterized by comparing overlay results at the parameter level. The total improvement was determined by means of a model-based summation of each individual parameter. The accuracy of the FBO tool was characterized by comparing the estimated improvement with the actual improvement observed under R2R control.

Parameter Manual Control (nm) R2R Control (nm) Actual Improvement (nm) FBO-Predicted Improvement (nm) Translation X 11 11 0 1 Translation Y 8 4 4 5 Grid rotation 27 10 17 16 Grid orthogonality — — — — Grid scale X 14 15 –1 2 Grid scale Y 15 13 2 2 IFD symmetric rotation 4 3 1 0 IFD symmetric magnification 8 3 5 5 IFD asymmetric rotation 2 2 0 0 IFD asymmetric magnification 3 4 –1 1

Table I: Comparisons between tool running under manual and R2R control and between actual and FBO-predicted improvement.

Experimental Results. For all the product IDs listed in Figure 4, Table I summarizes the overlay performance achieved with manual versus R2R control for each correctable tool parameter. All values in the table have been normalized to nanometers. The individual column headings are: Parameter (individual step-and-scan overlay correctable-parameter names), Manual Control (average parameter performance over the 60-day period of manual process control), R2R Control (average parameter performance over the 90-day period of R2R process control), Actual Improvement (delta between performance with manual process control and performance with R2R control), and FBO-Predicted Improvement. Grid orthogonality was not activated under R2R control because a significant amount of high-frequency noise had a negative impact on the FBO-predicted performance of that parameter. For the other nine parameters, FBO accurately predicted overlay improvement to within 3 nm.

Total improvement can be realized more directly through a model-based summation of the individual terms. Several publications document the usefulness and formulation of this method.⁴ Total overlay improvement is listed in Table II.

Parameter TotalImprovement (nm) FBO-Predicted Improvement (nm) X 21 24 Y 28 28

Table II: Comparison between total and FBO-predicted improvement (based on model-based summation of individual parameters in Table I).

Determining Return on Investment. Because it reduces rework, decreases the need for send-ahead wafers, increases stepper availability, and accelerates design-rule programs, R2R control can lower fab costs. Improvements in any one of those areas can quickly cover the cost of implementing R2R control and increase fab profitability.⁵

The data from this study were used to estimate the cost savings realized by a medium-sized fab as a result of rework reduction. The rework rate from the experimental data set is displayed in the cumulative probability plot shown in Figure 5, where each data point represents the cumulative probability of overlay performance. With manual control, the observed rework rate was 8%, while with R2R control, this highly visible metric fell to 2%.

Figure 5: Cumulative probability plot of rework rate characterization, where each data point represents the cumulative probability of overlay performance. The rework rate was 8% with manual control and 2% with R2R control.

Since production flow conditions and, consequently, the level of rework across all process levels varies, it is necessary to project R2R-control cost savings as a function of rework rate using both optimistic and conservative assumptions. The optimistic estimate assumes that the observed reduction in rework will be the same for all process levels and equivalent to the reduction illustrated in Figure 5. The conservative estimate assumes that the observed rework reduction will vary across all process levels but that the average reduction of all process levels will be 3%. Both estimates were based on the same number of wafer starts per year, the same number of photolithography steps and corresponding overlay measurements, and the same single-wafer cost of ownership incurred by performing resist strip, coat, and exposure steps. As summarized in Table III, the optimistic and conservative estimates of annual cost savings achieved by implementing R2R control were $2.9 million and $1.5 million, respectively.

Assumption Optimistic Estimate Conservative Estimate Number of wafer starts per year 240,000 240,000 Number of photolithography steps with overlay measurement per wafer 12 12 Total number of photolithography steps per year 2,880,000 2,880,000 Rework reduction rate 6% 3% Actual rework reduction 172,800 86,400 Total savings from rework reduction $2,937,600 $1,468,800

Table III: Optimistic and conservative estimates of rework reduction resulting from implementation of R2R control.

Conclusion

The performance of a single exposure tool at a single process level was reviewed to quantify the effects of implementing R2R control. Overlay improvement was determined by comparing a 60-day period of manual process control with a 90-day period of R2R process control. Improvement resulting from R2R control was compared with FBO-estimated improvement. Finally, overlay improvement and a corresponding reduction in rework were used to project a return on investment for the project. From this work, several conclusions can be drawn: R2R improvement is significant, FPO estimates are accurate, rework can be reduced significantly, and implementing the system has a high return on investment.

References

1. JL Sturtevant et al., "Implementation of a Closed-Loop CD and Overlay Controller for sub-0.25-µm Patterning," in Proceedings of SPIE, Metrology, Inspection, and Process Control for Microlithography XII, vol. 3332 (Bellingham, WA: SPIE, 1998), 461–470.

2. R Reuel, "Run to Run Overlay Control Using APC Feedback," in Proceedings of AEC/APC Symposium XIII (Austin, TX: International Sematech, 2001), 1295–1306.

3. D Crow and EL Joubert, "Application of Feedforward Reticle: Offset for Overlay APC in a High-Part-Count Fab," in Proceedings of SPIE, Metrology, Inspection, and Process Control for Microlithography XVI, vol. 4689 (Bellingham, WA: SPIE, 2002), 1151–1161.

4. D Crow et al., "A Comprehensive Analysis of Statistical and Model-Based Overlay Lot Disposition Methods," in Proceedings of SPIE, Metrology, Inspection, and Process Control for Microlithography XV, vol. 4344 (Bellingham, WA: SPIE, 2001), 127–138.

5. J Baliga, "Advanced Process Control: Soon to Be a Must," Semiconductor International (July 1999), 76.

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David Crow is manager of advanced applications for New Vision Systems (Cambridge, MA), where he oversees R&D for product enhancements and provides process expertise to the company's new business development activities. Previously, he was a photolithography technology development engineer and an etch technology development engineer at Cypress Semiconductor. Crow has published many articles, holds one patent, and has multiple patents pending. He received a BS in chemical engineering from the University of Minnesota, Minneapolis. (Crow can be reached at 617/551-2200 or dcrow@nvs.com.)