MFC design for semiconductor processing usingcomputational fluid dynamics
11/01/2007
EXECUTIVE OVERVIEW
Mass flow controller (MFC) designs must evolve to meet the need for ever more precise control of chemical and gas precursors used in semiconductor manufacturing. The flow-bypass thermal MFC technology that has been proven over decades of use can be extended to atomic-layer deposition (ALD) processes that ultimately specify chemicals in terms of moles/pulse instead of cubic-centimeters/min. Computational fluid dynamics (CFD) modeling can reduce hardware development time by cutting the number of iterations needed to handle nonlinearities in sensors and hysteresis in valves.
Fueled by Moore’s Law and the ever increasing competitiveness of the global IC market, UHP gas delivery systems for semiconductor manufacturing continue to evolve to provide higher reliability, faster response times, tighter accuracy specifications, and additional functionality. As microprocessor gate lengths shrink below 25nm and SRAM transistor densities approach a billion/cm2, gas delivery systems are pushed to ever higher performance expectations. New processes are challenging UHP gas delivery systems to provide very precise amounts of a broad range of materials with very high repeatability and reliability.
The basic measurement technique used in high accuracy MFCs-the thermal flow sensor in combination with a flow bypass (Fig. 1)-has remained constant throughout the history of the semiconductor industry. The fundamental principal is that the flow passing through the main body of an MFC is split off and diverted to a mass flow sensor. The flow sensor measures mass indirectly by measuring the heat transfer facilitated by the flow of gas between an upstream heater and a downstream temperature sensor.
ALD of metal, nitride, and high-k films all use high-speed gas pulsing strategies. These processes require gas delivery systems to provide ever increasing accuracy and faster response times. Thermal mass flow meters/controllers continue to lead the ultra-high purity industry as the gas measurement and metering instrument of choice. The fundamental measurement principle of the mass flow sensor provides the best known measure of the actual molar amount of gas delivered in a given recipe step.
 Figure 1. Cross-sectional schematic of a traditional thermal flow sensor and bypass architecture. |
To meet the needs of the ALD industry, MFC designs have been challenged to operate at much shorter and more frequent duty cycles. Advancing the knowledge at both the sensor and the valve requires a great deal of investment to determine the behaviors of different gases under varying operating conditions (pressures and temperatures).
MFC accuracy and response time
Accuracy and settling time continue to be the marquee performance parameters for cutting-edge MFCs. Improving these two parameters has the benefit of additionally improving ancillary performance parameters typically used to characterize MFCs. As an example, the quest for better accuracies has enabled a technology referred to as multi-gas/multi-range (MGMR). Propelled by enabling technologies such as digital control, these two performance parameters have improved over the years from typical single gas/single range accuracies around ±5% and settling times of ~10 sec (using older thermal valve technology) to accuracies as tight as ±0.5% and settling times as quick as 300 msec for MGMR MFCs.
MGMR MFCs allow a single device to be reconfigured by software to operate over a broad and continuous range of full scale flow values while flowing any of several hundred different gas species. Extending the operable range of an MFC has afforded tool OEMs and gas panel integrators the ability to reduce the number of gas sticks in a given gas panel. With wide-range MGMR MFCs, a single gas stick can deliver different ranges of a particular gas for different recipe steps.
Delivering high accuracy and fast response times for MGMR MFCs requires an understanding of exactly how the different subsystems behave under various operating conditions (gas species, pressures, temperatures, flow rates). Although several attempts have been made to build first principles models that can relate physical gas properties to thermal flow sensor readings, these efforts have not provided the level of accuracy demanded of contemporary MFCs. Figure 2 shows the flow readings of a typical thermal flow sensor for gasses. As can be seen, the sensor reading varies greatly from one gas to another.
Using computational fluid dynamics CAE tools
When developing empirical relationships between the gas dynamics of various gas species (often referred to as “live gas” studies), it is important to not only consider the effects observed at the sensor but to also understand the ratio of the flows split between the sensor tube and MFC bypass. This split flow varies across the full range of flow, different gas species, and various pressures and temperatures. The value of actual live gas studies for MFC design is that all of the combined non-linearities-from the sensor, bypass, electronics, etc.-can be accounted for by empirically derived coefficients.
State-of-the-art MFCs include pressure and temperature measurement capabilities. With this additional instrumentation, real-time corrections for influences of temperature and flow can be made in-situ. Although the models become very complex, today’s low-cost digital hardware allows support for accuracy models and control strategies that can very precisely map the behavior of a device calibrated using UHP N2 to the process gas in which it is ultimately put into service.
An approach that is showing great promise in being able to use historical live gas test data to predict the gas dynamics under new gas path geometries is that of CFD. Like other simulation software, CFD is not a panacea of high accuracy, bottoms-up prediction capability. Its application in the space of high precision, low flow, multiple-species gas dynamics modeling is limited to predicting the effects of minor geometry changes based on well correlated models. However, with the accumulation of large sets of live gas testing that have been gathered over the years, CFD has demonstrated good modeling results and has proven itself as a solid guide in the ongoing design iteration/optimization process.
 Figure 3. a) CFD model of pressure drop in a candidate bypass design based on an annular cross-section, and b) model of flow velocity in the same. |
High-end CFD tools are helping designers understand the very detailed nature of pressure drops (Fig. 3a) and velocities (Fig. 3b) in the bypass for various gas species and operating conditions. This is very important in understanding the range of localized flow regimes based on manufacturing tolerances. A critical design element of MFCs is to maintain Reynolds numbers well below the laminar-to-turbulent transition. CFD models help design engineers understand how the Reynolds number may change at various locations in the gas path given known manufacturing capabilities.
 Figure 4. CFD model of the temperature profile in a thermal flow sensor. |
These same sophisticated CFD toolsets are providing similar, heretofore unknown insight into the heat transfer dynamics at the thermal sensor (Fig. 4). With CFD, the relative impact of changes in sensor wire windings, variation in tube wall thickness and surface roughness while flowing different gasses is much easier to determine. Design optimizations can be arrived at much more quickly through simulation scripts, which iteratively determine the sensitivity to various parameters.
High-speed, pulsed-gas applications like ALD require fast acting valves as well as complex but efficient digital control strategies. CFD modeling provides valuable insight into the actual flow vs. sensor read-back relationship. The mature state of control theory combined with low-cost, high performance digital signal processing hardware allows for high-speed, sophisticated control strategies to be implemented.
The third element in achieving high-speed control is a thorough comprehension of the valve dynamics, which includes an understanding of how the flow vs. voltage relationship changes with different gasses, pressures, and temperatures. In addition to the flow dynamics modeled in CFD, valve actuators have hysteresis that must be mapped for different conditions. Using techniques such as the Preisach model [1] to account for this highly non-linear effect in the control strategy is one way to improve the response time dramatically. Compensating for hysteresis at this level of precision requires the inclusion of temperature and pressure sensors, which are now integrated in advanced MFCs to allow for automated compensation of these additional “process” factors.
Conclusion
The MFC is to the gas delivery system as the microprocessor is to the computer. New process demands such as ALD, combined with new technologies and design tools, are pushing the boundaries of MFC research. Cost reductions, increased reliability expectations, and new applications provide a steady source of motivations for improvements. The science of MFCs will continue to evolve to enable new process developments in the semiconductor industry and set the standards for MFC expectations in other industries.
Combining the advances of CFD modeling with empirical libraries of data, elevates the state of the art in MFCs to allow their use in what is being commonly referred to as a molar delivery system. In this approach, the MFC can deliver very precise amount of material according to a user-defined delivery profile.
Reference
1. Physica B, Condensed Matter. Proc. of the Third Int. Symposium on Hysteresis and Micromagnetic Modelling, 306, No. 1-4, Dec. 2001.
R. Mike McDonald received his electrical engineering degree from the U. of Utah. He is the director of flow engineering at Advanced Energy, where he has been employed since 2001. Advanced Energy, 1625 Sharp Point Drive, Fort Collins, CO 80525 United States; e-mail [email protected].