Photoresist production using automated in-line viscosity control
07/01/2007
As the critical dimensions of semiconductor devices continue to get smaller, film thickness control in the photolithography process becomes increasingly important. Viscosity of photoresist is an important product parameter because it determines film thickness during spin coating. Producers of photoresist, therefore, have established manufacturing procedures that require fluid viscosity be measured several times during production to ensure product quality. Periodic samples are taken off-line to an analytical laboratory where viscosity is measured under controlled conditions. However, off-line measurements interrupt production, engage valuable human resources, and fail to provide adequate process feedback. An in-line measurement system would enhance repeatability and overall product quality.
Production process
Photoresist production flow proceeds as follows: To prepare an order, a vessel is selected and washed with solvent. Photoresist ingredients are brought together and are charged in the reactor. The mix is deliberately made thicker because it is easier to “thin” it by adding solvent, than it is to “thicken” it during production.
In the case of resist formulations for which photospeed is less dependent on viscosity, an initial sample is tested to first determine whether the batch meets requirements for photospeed. If the sample passes, the next sample is tested for viscosity using a bench-top viscometer to meet a film thickness specification. The resist batch is thinned according to a dilution model for the addition of solvents, and a sample is sent to the lab to verify the results.
The point at which the sample is taken, after solvents have been added, is arbitrary. There is no way to know when the process has stabilized without the ability to directly monitor it. Half a dozen samples may be necessary before the target viscosity is achieved in the reactor, with each testing consuming hours or even days. We have developed a viscosity feedback control system based on a unique in-line viscometer tool that allows for automating the production of photoresist. In the past, viscosity feedback control systems have been developed for process applications such as oil manufacturing [1], extrusion [2, 3], and dip coating [4]. However, these systems are not easily adaptable for the production of photoresist because they do not meet the industry’s high standard of cleanliness, repeatability, and robustness.
In contrast, the viscosity feedback control system described here uses a simple bearingless dynamic viscometer, a temperature sensor, and a flowmeter, all made of inert polymers (PFA, PTFE) to achieve tight process control. The choice of materials ensures no fluid contamination from incorporating the system, and implementation cost is reasonable. The resolution and repeatability performance of the in-line viscometer is sufficient to achieve highly accurate viscosity controls.
 Figure 1. Schematic diagram of the viscosity feedback control system. |
In this article, the system-level and subsystem-level designs of the developed viscosity feedback control system are discussed, including a blending plant to be controlled, an in-line viscometer, electric solenoid valves, and a nonlinear controller. Experimental results describe the performance characteristics of the viscosity feedback control system such as response speed, accuracy, stability, and steady-state error.
Viscosity feedback control system
The objective of the viscosity feedback control system is to automatically produce a fluid of a certain viscosity by mixing appropriate quantities of thin and thick constituents, starting from an initial viscosity value. Figure 1 shows the arrangement of the system in which fluid is circulated by a pump in a temperature-controlled loop.
Fluid temperature is measured by a PT-100 temperature sensor, which is located downstream of the pump. The Levitronix in-line viscometer [5] is used to measure viscosity continuously and in real-time. Two containers, with thin and thick materials, respectively, are positioned over the main holding tank. The system starts when a user inputs a target viscosity through the accompanying control software. The viscometer’s controller compares the target viscosity with that of the circulated fluid in real-time. Based on the resulting error (actual vs. target), a certain quantity of thin or thick material is dispensed into the main holding tank. Dispensing is accomplished by opening and closing the electronic valves of the containers. In doing so repeatedly, and based on proprietary control parameters, the viscosity of the circulated fluid reaches the target viscosity level, avoiding undershoots or overshoots.
 Figure 2. Block diagram of the viscosity feedback control system. |
Figure 2 shows the block diagram of the viscosity feedback control system depicted in Fig. 1. Parameters ηt(t), η(t), and e(t) represent target viscosity of the circulated fluid, current viscosity of the circulated fluid measured by the in-line viscometer, and error between ηt(t) and η(t) accordingly. The volume rate of a dispensed fluid is denoted as v(t), which is the control input to a plant (dispensing/blending system). The system’s output, the viscosity of the circulated fluid, is denoted as η(t). If the dispensed volume is very small compared to that of the main tank, the transfer function (Gp(s)) of the plant can be considered a linear system described as follows:
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where α is a constant determined by such parameters as the volume of the circulated fluid, the viscosities of thick and thin dispensing materials, etc. The closed loop transfer function (Gclosed(s)) for the viscosity feedback control system is obtained as
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and its error transfer function (Ge(s)) is
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If a proportional controller (Gc(s) = Kp) is employed for simplicity, then Ge(s) is obtained as
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For a unit step input of the target viscosity, the final value theorem [6] gives the steady-state error as follows:
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A simple proportional controller enables perfect reference tracking for a step target viscosity input without external disturbances. There should be no undershooting or overshooting the target range with the proportional controller for a step target viscosity input because the loop transfer function, Gc(s)·Gp(s) has an integrator. An integrator controller should be added to achieve perfect tracking for a step target input under a second order external disturbance (such as the evaporation of the circulated fluid over time). In this case, the controller should be carefully designed to prevent and reduce any undesirable overshoots or undershoots.
The feedback controller of the developed viscosity control system is designed to improve response speed and stability and to achieve “soft landing,” a real-world process requirement.
Specifically, the design of the feedback control system includes a dead-band filter, a “P” controller, two gain adjustments, and a limiter. The dead-band filter avoids constantly hunting for small viscosity errors, within specified error bounds, whereas the first gain adjustment, depending on the magnitude of errors, improves response speed and achieves the desired “soft landing.” The second gain adjustment is intended to automatically compensate for plant gain variations, which depend on many parameters including target viscosity level, dispensing fluid levels, viscosities of thick and thin dispensing materials, etc. The function of the limiter is to limit control input in case the resolution of the dispensing volume is not high enough, which helps avoid the undesirable overshoots or undershoots of the system.
In practice, the magnitude of the control input determines the “open time” of the dispensing valve relative to the period (inverse of sampling time) in a pulse width modulation fashion. The sign of the control input corresponds to the choice of the valves. The resolution of the dispensed volume rate is determined by the size of the orifice of the electrical valve, the level of the thin or thick dispensing material, and their corresponding viscosities. The sampling time should be longer than the “time-to-blend” requirement, which in practice represents the desired time for viscosity stabilization.
The “time-to-blend” parameter is a delay element that may deteriorate a phase margin and limit the bandwidth of the overall closed feedback control system. A stirrer helps shorten the time-to-blend and improves response speed. The bandwidth of the in-line viscometer should be at least 3-4× faster than the bandwidth of the closed-loop control system. The resolution of the in-line viscometer and the dispensing system should be high compared to the maximum allowable viscosity errors specified in an actual application.
Experimental results
The resolution of the in-line viscometer was calculated to determine the control parameters of the system. By adding small amounts of a high viscosity fluid to a fluid of ~2.767 centipoise (cP) every minute for a period of 5 min., we were able to discern a change of 0.005cP. It was calculated that the viscometer had a resolution of 0.2% of reading, and repeatability (3σ) of 1% of reading. The viscometer’s repeatability could be further improved, up to 0.2% of reading, if the environment were well controlled.
 Figure 3. a) Time response of viscosity for the developed viscosity feedback control system; b) detailed view of a). |
Figure 3 shows empirical viscosity response data for the developed viscosity feedback control system. The data show that the control system was able to automatically alter the fluid’s initial viscosity of 4.586cP and bring it close to a target viscosity of 2.0 ±0.007cP within 43 min and without undershoots.
 Figure 4. Time response of viscosity for the developed viscosity feedback control system for a small step input at a high viscosity level. |
Figure 4 shows the performance of the system at a high viscosity level. From an initial viscosity of 38.0cP, the system was able to change the fluid’s viscosity to its predetermined target of 35.2cP ±0.176cP within ~15 min without undershoots. This challenging dilution example was successfully carried out using JSR Micro’s KrF photoresist and solvent products. Figure 4 also illustrates how the performance of the system is independent of material type as long as set-up is consistent.
 Figure 5. Time response of viscosity for the developed viscosity feedback control system for an impulse disturbance. |
Figure 5 depicts the system’s rejection of a disturbance, such as an abrupt or accidental addition of thick material in the main tank, in order to maintain a target viscosity of 3.56cP ±0.02cP. The error band is designed to avoid constantly hunting for negligible viscosity errors. The reference tracking accuracy of the developed system is better than the error bands shown here and is as good as ±0.3% of a target viscosity independent of viscosity level.
Future system improvements
Fluid temperature control can be eliminated by adopting a mathematical model describing the relationship between viscosity and temperature of various combination ratios for the thick and thin dispensing materials mixture. The use of dual solenoid valves (small orifice valve for fine control and large orifice valve for coarse control) per container may improve response speed without deterioration of control accuracy. Additional improvements of the system’s performance can be realized by performing fine adjustments on the controller gain. Feedback information of levels of the thick and thin dispensing tanks and the main tank may be used to adjust a controller gain and to further improve its control performance. Stability and robustness of the viscosity feedback control system under significant time delay elements such as mixing time should be further analyzed, and its controller should be designed accordingly. More detailed mathematical modeling of all parameters for the plant in consideration, and appropriate simulation, should be developed to further understand nonlinear characteristics of the system. Advanced controllers, such as time-delay control or a model reference adaptive control, can be used to improve system performance.
Conclusion
Using a simple, bearingless, dynamic viscometer made of inert polymers makes it possible to implement an automatic viscosity feedback control system for the production of high purity materials such as photoresist. We have shown that the performance of the system can meet and exceed the requirements of photoresist production. Producers of semiconductor chemicals now have an automated viscosity feedback control system that they can deploy to improve productivity, repeatability, and overall product quality.
Acknowledgment
Portions of this work were presented at the 2007 SPIE Advanced Lithography Conference, paper number: 6519-148, San Jose, CA, United States.
References
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- S.-H. Chiu, S.-H. Pong, “In-line Viscosity Control in an Extrusion Process with a Fuzzy Gain-scheduled PID Controller,” Journal of Applied Polymer Science, 74(3), 541-555, 1999.
- A. Kumar, S.A. Eker, P.K. Houpt, “A model based approach for estimation and control for polymer compounding,” Proc. of 2003 IEEE Conference on Control Applications, Vol. 1, 729-735, 2003.
- D.E. Curtiss, J. Leigh, F. Quan, “Photoresist Recirculation and Viscosity Control for Dip-coating Applications,” US Patent 6,740,163, 2004.
- www.levitronix.com
- K. Ogata, Modern Control Engineering, 2nd Ed., Prentice-Hall International, Inc., NJ, 1990.
Woo Sok Chang received his PhD in electrical engineering and computer science from MIT and is the director of technology at Levitronix, 45 First Ave., Waltham, MA 02451, United States; ph 781/466-6567, e-mail [email protected].
Christos Monovoukas received his MS degree from Columbia U. and his MBA from Harvard Business School. He is a GM at Levitronix.
Michael Tanaka received his BS degree in chemical engineering from the U. of California at Berkeley and is a senior production engineer at JSR Micro, Sunnyvale, CA; e-mail [email protected].
Norbert Fronczak received his MS degree in chemical engineering from Iowa State U. and is a production manager at JSR Micro.
Mark Ignatowicz received his BS degree in chemical engineering from Northwestern U. and is plant manager at JSR Micro.