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Minimizing Pilot Runs with Observable R2R Control For High-Mix Semiconductor Manufacturing

Jianping Zou, PhD, Adrianto Kumara, and Kwee Thiam Lim

INTRODUCTION

Pilot runs in semiconductor manufacturing are expensive. For a fab running 60,000 wafer starts per month, it could cost over $2.4 million per year for pilot runs, or $340,000 per year for each module. This does not include the cost associated with lost production while running non- product wafers and idle time spent waiting for metrology data.

One of the reasons for the large number of pilot runs is the widespread use of non-threaded run-to-run control technology in manufacturing. With this control technology, process data is grouped by a set of same-context values (e.g., equipment, recipe, product) into a “control thread.” Data in each thread is treated independently from other threads, and each thread has its own model parameters.

The initial model parameters can be determined by running online experiments or online pilot wafers, and these parameters can be estimated and updated from the data in the same thread afterwards. If the underlying process changes or a new thread is introduced to the production, pilot runs may be required to determine changes in the model’s parameters.

Typically, there are three situations in semiconductor manufacturing that necessitate the use of pilot runs to support a recalibration of a threaded run-to-run control system:

  1. After equipment/chamber preventive maintenance (PM): at least one pilot run in each active thread is required to determine equipment/ chamber condition changes before and after PM.
  2. Running new product: at least one pilot run is required on each equipment/chamber running the new product.
  3. Rerun of a low-running product: at least one pilot run is required on each equipment/chamber processing low-running product.

One way of reducing the costs of pilot runs is to decrease the number of required pilot runs by using more elective modeling and control techniques in run-to-run control. This article presents a non-threaded run-to-run control technique to help minimize pilot runs.

MODELING

The original concept of non-threaded run-to-run control was presented by Firth et al[1] around 2006. The idea is to reduce process variations introduced by context switches (such as changes in products) in threaded run-to-run control. In a non-threaded controller, it is assumed that process offset can be modelled as a summation of context offsets:

where k is the index of run, yk is controlled output, u is controlled input, and  is ith context offset. We further assume that each context i will have ni context values; therefore, the total number of context offsets will be (n1 x n2 x ... x nn ). If all context offsets can be estimated without bias, then the variations introduced by context switching will be reduced. We may take further advantage of a model (1.1) to support pilot run reduction. For example, since an equipment/chamber PM only impacts equipment offset, one pilot run may be performed after a PM to determine post-PM changes in equipment offset.

Many papers have been published previously to study more detailed properties of non-threaded controllers. However, these studies are limited in academia since it has been proven that true values of individual offsets in the system cannot be estimated because they are unobservable. Any step disturbances in the process (PM, introducing new products, etc.) will impact all estimated values of context offset. Therefore, the estimation may lead to drift in the relative tracking error, and production lots of a specific context may run off-target. This problem is of great concern in production when applying non-threaded control.[2]

In fact, there is no need to estimate each context offset in applications. In manufacturing, we are interested in what the summation of context offsets (thread offset) is for the next run, and we apply this thread offset in the recipe calculation of the next run. This observation largely reduces the problem and makes it possible to build an observable controller model to minimize pilot runs. One way to construct an observable model is to define model states to be a set of independent thread offsets that are linear combinations of context offsets.

Considering the controller model (1.1), let 

We further assume each context offset may have drifted by following a model (1.2) of integrated white noise

where  is white noise. The number of independent thread offsets is s = m – n + 1,[3] and they can be expressed as:

The observable controller model can be constructed as:

where xk is state vector consisting of (1.3), wk is white noise vector from (1.2), and A, B, Fk , and Ck are parameter matrices associated with context of run. Model (1.4) is a standard time-varying state space model, and can be analyzed/solved by existing linear system theories.[4] Under certain conditions, we can show that model (1.4) is observable and reconstructable.[4],[5]

PILOT RUN REDUCTION

We are now in a position to propose a solution for pilot run reduction.

  1. After equipment/chamber PM: In model (1.1), only the equipment offset will be changed after PM. One pilot run may be performed to estimate this step change. One way to perform this estimation is to decrease the weighting off the equipment offset while keeping all other weights high, and performing state estimation on pilot run only.
  2. Running new product: Running a new product in an existing manufacturing process will introduce a new independent thread offset. One pilot run is then required to estimate the initial value of the new independent thread offset, and the controller model (1.4) needs to be augmented with the new state.
  3. Rerun low-running product: From the controller model (1.1), low-running product does not change model states. If the current states are observable and reconstructable, no pilot run is required.

When compared to threaded run-to-run control, the new non-threaded control technique largely reduced number of pilot runs—especially after equipment/chamber PM.

EVALUATION AND RESULTS

To verify the proposed solution, Applied Materials worked with a foundry customer on a pilot project in poly etch using 4 tools with a total of 10 chambers. The project was run over an 8-month period. During the first 6 months the non-threaded controller was running in simulation mode; during the final 2 months it was running in production. Throughout the entire project period, 37 PMs were observed across all chambers. The goal of the evaluation was to reduce the number of pilot runs after chamber PM without any deterioration in run-time controller performance.

At the outset, the customer’s production was controlled by an in-house threaded run-to-run controller. The pilot run strategy on the customer’s current production was to run a pilot test for every product after PM. To simplify integration, Applied E3 was integrated into the customer’s in-house advanced process control (APC) system, as shown in figure 1. The APC system was able to control the Applied E3 to run in simulation or production mode. To avoid being too aggressive, E3 was configured to run one pilot test on each recipe after PM.

The evaluation was performed by comparing the distance between actual thread offset and estimated offset from the controller. The closer the estimated offset to actual offset, the better the performance of the controller.

Figure 2 shows the actual offset and estimated offsets from both the in-house APC and Applied E3 non-threaded controller in a specific control thread. It also shows estimated non-threaded state and PM time of the chamber. Every point of actual offset (i.e., every point on the green line) represents an offset from actual run in this specific thread (and thus these are the only places where the offset can be recalculated).

Figure 1. System integration for pilot run testing.

Figure 2. This chart depicts actual offset and estimated offset. Estimated state (black) shows step changes after all three PMs. TrueSeries = actual offset; E3 Series = estimated offset by E3; UApcSeries = estimated offset by in-house APC; E3Internal = estimated non-threaded state by E3.

Specifically, figure 2 shows that there is no run of this thread between the first and the second PM. Values of estimated non-threaded offset between these two PMs are the results of estimation through non-threaded controller model (1.4) with all the runs of other threads on this chamber. A step change of estimated non-thread state after PM is due to step change of tool offset after PM. Note that threaded control cannot perform this kind of estimation since there are no actual runs of this thread before and after PMs. It is clear that the estimated offset by the Applied E3 non-threaded controller tracked actual offset very well after PM.

Figure 3 shows results on all chambers. The number of pilot runs after PM potentially could be reduced by 80%. The tables in figure 3 also show that for those products without pilot runs, there is about a 20% chance that the first run after the PM may be off target and variations of these runs are slightly larger than that of current production.

A further analysis showed that unlike threaded run-to-run control, in which data in different threads are independent, in non-threaded control, all data are grouped together. Thus, with non-threaded control, performance in one thread may impact all other threads. To improve the results, the trim rate was recalibrated in a non-threaded R2R model and rerun in a simulation on TOOL_04, which had significantly lower- quality results than the fleet average without recalibration.

The results, shown in figure 4, indicate much better performance with roughly a 7% chance of off-target result. Specifically the pilot run reduction rate was kept about 77%, and both the mean and standard deviation of products without running a pilot was largely improved.

Figure 3. Results from all chambers without recalibration of trim rate.

Figure 4. Results of TOOL_04 after trim rate recalibration.

CONCLUSION

Applied Materials’ new run-to-run non-threaded control method has demonstrated that pilot runs for high-mix semiconductor manufacturing can potentially be reduced by 80% without undermining process performance.

For additional information, contact michael_d_armacost@amat.com

[1] S. K . Firth, W. J. Campbell, A . Toprac, and T. F. Edgar, “Just-in-Time Adaptive Disturbance Estimation for Run-to-Run Control of Semiconductor Processes,” IEEE Trans. Semicond. Manuf., vol. 19, no. 20, pp. 298–315, Aug. 2006.

[2] N. Patel, “Model Regulation for Hi-mix Control,” IEEE Trans. Semicond. Manuf., vol. 23, no. 2, pp. 151–158, May 2010.

[3] J. Wang, Q. P. He, and T. F. Edgar, “State Estimation in High-mix Semiconductor Manufacturing,” Journal of Process Control, vol. 19, no. 3, pp. 443–456, 2009.

[4] B. D. O. Anderson and J. B. Moore, “Detectablity and Stabilizability of Time-varying Discrete-time Linear System,” JIAM J Control and Optimization, vol. 19, no. 1, pp. 20–32, Jan. 1981.

[5] L. G. van Willigenburg and W. L. De Koning, “Linear Systems Theory Revisited,” Automatica, vol. 44, pp. 1686–1696, 2008.