Model-based adaptive process control: A CD-control exmple
07/01/1998
Model-based adaptive process control: A CD-control example
Emir G?rer, Tom Zhong, John Lewellen, Reese Reynolds, Silicon Valley Group, Track Division, San Jose, California
Equipment-based control of lithography CDs through the application of model-based adaptive process control (APC) of relative humidity (RH) and barometric pressure (BP) during resist spin shows the power of real-time process control. It seems to be the best alternative to more expensive, tighter control of equipment components and subsystems, which may not even be possible. The example presented here addresses some of the challenges of the 1997 National Technology Roadmap for Semiconductors (NTRS).
The 1997 NTRS identifies in situ process control as "a critical solution for the future factory." The set of potential solutions for advanced process and equipment control includes elements to achieve run-to-run and real-time process control (Fig. 1). The NTRS states, "real-time closed-loop control incorporating in situ sensors and model-based control algorithms ... will allow deterministic processing" that is directly related to IC performance.
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Figure 1. Envisioned solutions and time lines for real-time process control in the future of semiconductor manufacturing.
According to NTRS proposed solutions, deployment of such advanced process control will require a significant amount of research and development, particularly for direct feedback of wafer-state, multi-input multi-output control of process states, process modeling, and computational algorithms. It says, "Full factory-integrated process control will build on elements developed for equipment information management, in situ metrology, closed-loop product control, and process and equipment models for model-based control that are fully integrated into an advanced process control framework. These models and connectivity embedded in the framework will also provide the basis for a virtual factory and the ability to simulate process capability for implementation in the real factory."
Implementation of this new technology at the semiconductor equipment level is the first step in bringing it into the industry [1]. Model-based process control, which is discussed here, has the potential of increasing yield by keeping a process on target. It also reduces cost of ownership by reducing test wafer use. Model-based process control first requires detailed characterization of the associated chemistry and physics. Then, proper implementation requires linking this information to wafer and equipment models.
The basic premise of model-based process control is that on-the-wafer results and dominant process variables can be decoupled by means of APC methodologies. This is the basic premise that will allow a cost-effective new generation of equipment with improved overall equipment effectiveness and reduced cost of ownership. Early applications of APC involved real-time equipment monitoring, diagnosis, and fault detection. More sophisticated applications are expected to involve run-to-run model-based process control (MBPC) and real-time MBPC. To illustrate the power and potential of model-based APC methodology, we will show how CD control is achieved through sensory feedback of photoresist film-thickness profiles.
Fundamental physics to CD control
The physics of spin control provides valuable insight in developing empirical models for model-based APC methodologies. Theoretical calculations suggest that convective diffusion and evaporation are two strongly coupled mass transfer mechanisms that determine film-thickness uniformity profiles of spin-coated photoresist films [2]. Convective diffusion is the dominant thinning mechanism during the first few seconds of spin coating. Even though the evaporation mechanism starts two orders of magnitude smaller during the initial moments of dispense, its nonzero-and-constant value causes the viscosity of resist to increase dynamically, thus decreasing convective diffusion. Subsequently, evaporation becomes the dominant mechanism that eventually determines the final dry film-thickness profile. The resist-thinning rate due to evaporation starts to decrease eventually due to lowered diffusivity of the remaining solvents. In situ resist film thickness measured during spin coating of a 300-mm silicon wafer verifies this mechanistic explanation (Fig. 2).
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Figure 2. An in situ resist film-thickness profile that verifies the roles of convection and evaporation [3, 4].
Traditionally, this strong dependence of the spin-coating process on the evaporation mechanism has meant that resist-processing systems (i.e., "track systems") must be designed to control evaporation-related physical parameters tightly. Consider that on advanced track systems the RH sensitivity of a typical photoresist is 20-25 ?/%RH. For the future, semiconductor devices with linewidths of 0.13-0.18 ?m will require wafer-to-wafer mean resist-thickness control <20 ? due to limited depth of focus of 248-nm and 193-nm DUV exposure tools. (The swing curve, which represents CD variation as a function of resist film thickness, is more sensitive to resist film-thickness variations for 248-nm KrF and 193-nm ArF laser-based DUV exposure tools than lamp-based DUV and i-line exposure tools. This is due to the narrowband nature of single wavelength laser radiation.)
This suggests that the mean thickness (MT)-control budget will be entirely consumed by RH fluctuations of present-day environmental controllers. So far, the conventional approach to this type of problem has been to require tighter control specifications - in this case, RH control at least ?0.2 % or better, which is the limit of measurability with current sensor technology.
Tightening electrical and mechanical control specifications on any equipment contributes to the spiraling cost of processing wafers and may well limit the MT-control capability required by future generation devices, since mechanical tolerances on equipment will not alleviate required process variances. Our work has identified an alternate approach to achieve consistently more stringent process latitudes. Specifically, we have developed a model-based process control approach for improved CD control that would decouple the MT-control capability of a wafer track from evaporation-related physical parameters - RH and BP. This approach has already demonstrated improved resist film-thickness control without requiring tighter process variable (RH) control specifications.
Briefly, the model-based CD-control system uses two separate sensors to detect, at predetermined sampling rates, fluctuations in RH and BP inside a resist-coater process module. Sensor data is fed to a semi-empirical model that calculates a new drying spin speed (SS) in real time that is then implemented during the drying spin step following resist dispense. In essence, the system adapts to changes in RH and BP by correcting the nominal SS value to ensure that MT is under control all the time. This real-time process continues for every wafer in a closed-loop fashion.
Our work showed that both RH and BP affect resist-film MT in the same way. An increase in RH or BP, or both, reduces solvent evaporation. This causes convective diffusion to be more effective, thus yielding thinner films with increased RH and BP. The time constant for the rate of change of RH is typically much shorter than that of BP (see "The role of barometric pressure" on p. 206). Thus, our biggest challenge was to demonstrate process control using RH.
The role of barometric pressure
Today`s resist processing systems (i.e., "wafer tracks") do not have any control capabilities for barometric pressure (BP) change. But BP is another variable that can have a big impact on mean resist thickness and, subsequently, CD control. A typical resist has a 1.5-4.5 ?/mm-Hg sensitivity, depending on viscosity and casting solvent vapor pressure. This lack of appreciation of BP`s impact on MT control is possibly one of the major sources of long-term fluctuations of CD control.
BP variation can affect photoresist MT in the same way as RH - through the solvent evaporation mechanism. However, its impact takes place over a longer period. BP fluctuation of up to 30-40 mm-Hg is common in many locations around the world.
The figure shows actual measured BP fluctuations over a two-week period and the corresponding predicted MT variation for an empirical model
MT (?) = 13303 - 2.5 ? BP (mm-Hg)
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Actual measured BP fluctuations over a two-week period and the corresponding predicted MT variation for an empirical model.
The key here is that BP may take hours or days to fluctuate by an amount that can cause significant changes in MT. Actual implementation will have a single, combined model of BP and RH.
Our BP-based CD controller works under the same principle as our RH controller. As shown in the accompanying figure, actual BP fluctuations of about 38 mm-Hg can cause a mean-resist-thickness fluctuation of about 95 ?. This in turn corresponds to an improved CD-control potential of up to 16 nm using a BP sensor and an adaptive algorithm. This unique approach allows resist-film MT to be insensitive to BP fluctuations.
Development work
Details about our development effort show the rigor necessary to achieve model-based process control. To generate a statistical model, we began with a two-factorial design of experiment (DOE) using RH and drying SS as inputs and MT as output. The fifteen-wafer DOE gave us the resist MT of each wafer, the average RH during the coating period of each wafer, and the drying SS. (BP measurements revealed it varied less than 0.75 mm-Hg; therefore, it was not included in the RH model.) With this data and a statistical software package, we established a model of film MT as a function of SS and RH. It turns out that across the wafer, uniformity is independent of RH, BP, and drying SS, and therefore it was not taken as an output. This effectively reduces the problem to one dimension, simplifying the model needed to implement this new technology.
The model
MT (?) = 512.15 - 21.58 ? RH (%) + 529135.5/SS1/2
revealed that the functional dependence between the input and output variables reflected the physics of the spin-coating process. Dependence on drying SS is consistent with theoretical predictions, as well as experimental observations for a spin-coating process with convective diffusion and evaporation mechanisms. The functional dependence of MT on SS was taken from analytical solutions to fluid equations, and the linear dependence on RH is an approximation that agrees closely with experimental data [5] (Fig. 3). The negative slope is consistent with a decrease in RH, causing an increase in resist viscosity due to increased evaporation. This then limits the thinning of the resist film further via the convective diffusion mechanism, and yields thicker films.
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Figure 3. The model fit to experimental results (five different RH values for three drying spin speeds) revealed the goodness of fit is 0.999249.
We tested our model-based control process by comparing it to baseline results on a track system (SVG 90 SE) on which we purposely relaxed humidity control limits to 3% to increase the signal-to-noise ratio. The baseline system gave us a MT range of 59.2 ?. This variation was quantitatively explained by the measured ~3% average RH fluctuations on the track system (Figure 4). Note that the sensitivity of MT on RH is21.6 ?/% from the model. (During the experiment, BP pressure and air temperature variations were found to be less than 0.75 mm-Hg and 0.07?C.)
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Figure 4. Real-time RH measurements at the point of use showing induced RH fluctuations both within the wafer and wafer-to-wafer.
As explained above, the model-based CD-control approach measured time-averaged RH during dispense and drying steps and calculated the SS needed to control MT. The data presented in Fig. 5 clearly show the MT variation caused by RH fluctuations was reduced from 59.2 to 21.8 ? without any negative effect on across-the-wafer uniformity. This corresponds to a 6.5-nm CD-control improvement (see table) for this particular resist (SPR 508). The necessary adjustment to drying SS was in the range of 13 rpm around the nominal value of 2650 rpm.
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Figure 5. Compared to baseline results without RH control, process-modeled control of SS derived from real-time RH measurement produced a dramatic improvement in resist thickness control.
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Conclusion
We have shown that by measuring RH dynamically, a resist-processing system can optimize SS in real time during the resist-drying step, so MT stays under control for all values of RH. We obtained thickness-control capability of 21.8 ? for an RH fluctuation of ?1.5%, demonstrating a 6.5-nm CD-control improvement potential using an existing RH sensor and an adaptive software algorithm. The heart of this process control scheme is a statistical model that establishes a semi-empirical relationship between RH and SS, and mean resist thickness. This is only the beginning. Further improvements in algorithm designs, which include periodically upgraded models by means of filters, such as exponentially weighted moving averages, have been shown to extend control capabilities of APC technologies to satisfy future industry requirements [6, 7].
Conventionally, control capability of 21.8 ? would require RH control tighter than ?0.5%. Thus, we were able to increase the RH process latitude of MT by a factor of three without requiring tighter RH control. In a similar way, model-based APC approaches will allow us to continue improving MT-control capability without requiring BP control. Accordingly, for production of next-generation devices, APC methodologies similar to the example in this article have the capability of improving process latitudes in a cost-effective way.
The focused scope of this work for just resist processing has a larger message. Our model-based methodology for improving CD control through control of resist-film MT clearly addresses the 1997 NTRS identification of in situ process control as "a critical solution for the future factory." The model-based CD-control scheme presented is cost-effective compared to more expensive system-based control approaches that may not even be possible.
We believe real, cost-effective solutions to maintain the industry`s infamous productivity curve lie in developing intelligent technology concepts that take advantage of a fundamental understanding of process mechanisms by decoupling "on the wafer results" from "first-order process parameters." This work is one of the many APC applications that the SVG Track Division has been rigorously developing for equipment-level implementation.
Acknowledgment
The authors thank Rich Savage for his insight and his belief in equipment-level APC implementations, and John Salois for his support of the equipment used in this study.
References
1. Patent pending.
2. D.E. Bornside, "Spin Coating," PhD Thesis, University of Minnesota, 1988.
3. R. Savage, E. G?rer, "Implementations of APC in Lithography: Can We Really Improve CDControl?" SEMATECH Advanced Process & Equipment Control Program, AEC/APC Workshop VIII Proceedings, p. 234, 1996.
4. B. Lorifice, D. Chen, B. Mullen, E. G?rer, R. Savage, R. Reynolds, "Minimizing Resist Usage During Spin Coating," 1997 SVG Technology Symposium on Advanced Photolithography and Photoprocess Technologies, p. 105, 1997.
5. A.G. Emsile, F.T. Bonner, L.G. Peck, "Flow of a Viscous Liquid on a Rotating Disk," J. Appl. Phys., Vol. 29, p. 858, 1958.
6. J. Stefani et al., "Model-based Run-to-Run Process Control of Metal Sputter Deposition," SEMATECH Advanced Process & Equipment Control Program, AEC/APC Workshop IX Proceedings, p.354, 1997.
7. T.H. Smith, D. Boning, "An Artificial Neural Network EWMA Controller for Semiconductor Processes," J. of Vacuum Science and Tech. A, Vol. 15, No. 3, p. 1377, 1997.
EMIR G?RER received BS and MS degrees in physics from METU of Ankara, Turkey, and MS and PhD degrees in physics from Lehigh University in Pennsylvania. Prior to joining Silicon Valley Group (SVG), he worked on spectroscopic investigation of transition metal and semiconductor surfaces and their interactions with adsorbate molecules, and point defects in silicon. G?rer is manager of the 300-mm process module and advanced technology development team in the Track Division of SVG, 541 E. Trimble Rd., San Jose, CA 95131; ph 408/432-6890, fax 408/325-6781, e-mail [email protected].
TOM ZHONG received his BS degree from Kunming Institute of Technology, China, his MS degree from California Polytechnic State University, San Luis Obispo, and his PhD from the University of Arizona (U of A), all in materials science and engineering. Prior to joining SVG, he was a research specialist for the Optical Science Center at U of A. Zhong is a senior staff process engineer in the Track Division of SVG.
JOHN LEWELLEN received his BS degree in chemical engineering from the University of Missouri. He has 15 years of experience in optical lithography with Synertek, Perkin-Elmer, and SVG. Lewellen is a principal technologist in the Track Division of SVG.
REESE REYNOLDS received his MS degree in organic chemistry from Arizona State University, Tempe. He has more than 20 years of industry experience at Motorola, National Semiconductor, AMD, and Varian Thin Film Systems; at the latter he was director of process technology. He has multiple patents and numerous publications in the fields of photolithography, etch, thin film, and diffusion. Reynolds is VP of engineering and technology in the Track Division of SVG.