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Control of unconventional processes


J. Proc. Cont Vol. 6, N o 2/3, pp. 99-110, 1996

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Control of unconventional processes
Thomas F Edgar
Department of Chemical Engineering, University of Texas, Austin, TX 78712, USA
New modelling and control problems have arisen as chemical engineering has broadened its scope into areas such as materials processing and biotechnology. In addition, a move towards flexible manufacturing of specialty chemicals has generated more interest in batch operations, which is the normal manufacturing scheme in the new technology arenas. Advances in modelling, control and measurement techniques will be required to reach high levels of manufacturing productivity. This paper reviews some of the challenges faced in control of unconventional or nontraditional chemical processes. A number of vignettes exemplifying these challenges are presented in the areas of batch chemical processing, materials processing and microelectronics manufacturing. Keywords: materials processing; batch control; microelectronics manufacturing; model-based control; rapid thermal processing

The development of advanced manufacturing processes has become of great interest worldwide. Process modelling, control and measurement are critical technologies in making these manufacturing processes competitive in world markets. This paper focuses on the recent improvements in modelling, control and instrumentation for unconventional or non-traditional chemical processes, which are largely batch processes. Application areas that might be categorized as 'unconventional' include: ? ? ? ? ? ? ? ? ? ? specialty chemicals metals electronic materials ceramics polymers food and agricultural materials biochemicals multiphase materials/blends coatings composites

This clearly constitutes an extremely broad range of processes. Due to space limitations, only a few areas are highlighted in this paper. Special emphasis on one area of great potential, microelectronics processing, is given. During the next 20 years, all areas of manufacturing will see more emphasis on rapid delivery of smaller quantities of differentiated products ('time-based factories'). Plants will become smaller and located closer to customers, with increased usage of batch and semibatch configurations to shorten response times and reduce inventories. These plants will need to be more flexible (agile) in operation and must satisfy stringent

safety, health and environmental regulations. They will require a high degree of automation in order to reduce manpower costs and maximize productivity. The purview of chemical engineering technology in batch processing will be broad; unit operations will become more diverse, especially in plastics, ceramics, pulp and paper, and microelectronics, which will require development of new design principles. Traditional unit operations such as distillation may require some new emphases, e.g., packed columns with faster responses and batch stills. Batch processes exhibit more pronounced nonlinearities than their continuous counterparts and thus demand more attention in the process modelling and control areas. One example where a quantum change in processing philosophy is likely to occur is in the microelectronics industry. Presently the dominant technology for thin film deposition is the multiwafer low pressure chemical vapor deposition (CVD) system, which suffers from yield and process control problems. An emerging alternative (although not yet commercially viable) is single-wafer processing using rapid thermal CVD; by operating at higher temperatures it is possible to process larger wafers individually at a fraction of the time for the multi-wafer system. Many types of deposition reactors will be required, although it may be feasible to develop a flexible, multi-use reactor which could carry out novel processing techniques, e.g., silicon deposition, oxidation, and nitration performed sequentially in the same reactor. The success of this approach will hinge on developing fundamental mathematical models for process equipment, optimized design, new real-time sensors, and advanced process control strategies, all of which will require significant basic research efforts.

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Control o f unconventional processes: T. F. Edgar
empirical multivariable models such as artificial neural nets. By analysing extensive data sets from an operating plant, nonlinear input-output models can be developed automatically using available software, often surpassing in utility traditional models based on physical principles where there may be many unknown parameters. In fact, the US Environmental Protection Agency is permitting such an approach for predicting emissions of various chemical plants based on direct measurements of selected inputs and outputs. Quality sensors are another class of measurements that are needed for improved control in many applications. For example, real-time detection of cracks, inclusions, porosity, dislocations, or defects in metallurgical or electronic materials would be highly desirable during processing, instead of after processing is completed or products are shipped. The possible prediction of defects and out of specification products are strong incentives for real-time sensor development. However, models that can predict the formation and location of defects will reduce the stringent requirements imposed on the sensor. There is also now a greater emphasis on obtaining a basic understanding of various processes in order to obtain modelling tools that are predictive in nature, i.e., models that can be used for scale-up as well as influence design for controllability. With advances in control strategies such as nonlinear model predictive control' and the increased computational capability of new workstations, it is now realistic to control systems in real-time using distributed parameter physical models and nonlinear programming for model-based control:. Several examples where integration of sensors, models and control are critical to operating the process include heat treatment of materials and film forming.

There is also a need to develop a holistic approach to design and operation of the microelectronics 'factory of the future', including process synthesis, waste minimization, automation, and unit and products scheduling (tracking of individual wafers). Control issues in electronics materials processing are covered in detail later in this paper. Sensors and model-based control One of the common problems shared by many unconventional processes is the inability to measure the state variables of interest non-invasively and in real-time. This is also true in the relatively mature chemical industry, where frequently primary measurements are unavailable on-line, e.g., the composition of process streams. This has stimulated a fair amount of recent research on the development of new sensors, aided by the availability of modern microelectronics devices based on fibre and nonlinear optics and semiconductors. Process control strategies have historically relied on primary or secondary measurements as a direct part of the feedback loop, but this paradigm of control is unnecessarily restrictive. The concept of model-based control, which is also categorized in other fields as 'intelligent' control, utilizes an integrated view of the control strategy, incorporating a process model (and process understanding), multiple measurements (sensor fusion and data reconciliation), and an advanced control algorithm in one package. Figure 1 shows a general block diagram for model-based control. The concept of 'soft' sensors has received great interest recently, driven by the high cost of certain online measurements and a greater level of confidence in

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Control of unconventional processes: T. F. Edgar
When various materials undergo temperature cycles, fundamental understanding of the associated transport phenomena (energy, mass, momentum) and reaction kinetics is crucial for developing a quantitative relationship among manufacturing process variables and dependent variables such as mechanical and physical properties. This implies that principles of materials science and thermal science must be combined to predict properties based on microstructure. Processes where nucleation and growth control the time-temperature transformation are especially difficult to model. Knowledge of the internal temperature distribution is crucial to the success of many heat treatment, phase change, and crystal growth operations. The ability to map temperature with reasonable accuracy is limited by available technology and cost. The rate at which heat is added or removed is determined by a surface heat transfer coefficient, and the temperature distribution within a solid body can be predicted using well-known equations for heat conduction. A hybrid approach where heat transfer at the boundary is measured and then a model is used to predict temperature contours seems to be a practical approach. ]"he initial temperature of the solid (assuming it is uniform) could be estimated if a temperature measurement is available at some location using established methods for parameter estimation. Polymer-based composite materials are often cured in an autoclave. Under the effects of temperature, the polymer molecules grow into longer chains and crosslink. The speed of curing is a complex function of temperature, pressure, the thickness and shape of the part, heat transfer to and from the mould, and the thermal mass of the autoclave '. Most autoclaves are operated open-loop, with no feedback about the material state or the degree of cure. Monitoring the viscoelastic properties of the resin allows one to infer the state of the cure, which is related to the glass transition temperature. With appropriate sensors for viscosity, elastic modulus, and porosity, one can optimize the cure cycle (temperature and pressure) using mathematical models to minimize porosity and delaminations, to improve control of the resin compaction, and to ensure complete curing. Film forming is an important type of process used in the polymer film and paper sheets. The key problem faced in these applications is to control the film properties (usually thickness or 'gauge') as it is stretched, heated, dried, shrunk and possibly coated. A scanning sensor measures selected film properties before the film is rolled up on a drum as the final product. There are time delays in the process between the actuators (that control tile size of an opening) and the sensors, multiple actuators are installed across the width of the film (cross-direction) and the gauge sensor (usually a radiation emitter/detector) is a fairly noisy instrument that moves across the film width to give a thickness profile. Because the film is also moving in the machinedirection, data are obtained for a fairly small part of the film. This problem has been studied by Bergh and MacGregor*, Braatz et al. 5, and most recently by

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Rawlings ~. Most of these researchers have treated the process as a linear system with rather simple dynamics, although they differ on how to treat the moving sensor in the model equations. State estimation is required to treat the noisy data, and several of the manipulated variable constraints are active. A model predictive control strategy appears to be quite attractive for industrial application.

Batch process control
Here we discuss unconventional process control for several batch chemical unit processes, namely distillation, crystallization and bioprocessing.
Distillation

In many separation applications, batch distillation has distinct advantages over continuous fractionation. A single batch column can be used to yield many different products and variations in product specifications. Startup of a single batch column requires less expertise and labour than startup of a train of continuous columns. It is easier to tailor product specification on a batchto-batch basis. These advantages combine to offer a flexible, easily operated separation unit with low capital cost. The genera[ arrangement of a typical batch still and the important controlled and manipulated variables are shown in Figure 2. After charging the kettle and applying heat at the reboiler and cooling at the condenser, the column is allowed to reach either a certain overhead composition or a steady state. At this point distillate is withdrawn into a product receiver according to some policy. At discrete times the product receiver may be switched to make multiple products. At the end of the last product withdrawal, the column is shut down, the remaining bottoms residue and receiver holdup(s) are pumped to storage, and the column is readied for the next batch. When it is difficult or impossible to meet product specifications with one batch run, it is common to take a middle 'waste-cut'. which is recycled to the initial mix of the next batch. In normal operation there are purity constraints on products (including the residual amount left in the reboiler), duty constraints on pumps, heat exchangers, and other equipment, and operational constraints on liquid and vapour flow rates. Based upon discussions with industrial practitioners, the difficulties fi~ced with optimization and control of batch distillation can be classified as follows: ? ? ? ? accurate computer models that are computationally intensive poor agreement of simulation models with actual plant data time-varying process gains and time constants large open loop interactions

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Control of unconventional processes: T. E Edgar

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low process signal to noise ratio on-line sensors that are unavailable, unreliable or give delayed results state estimation that is difficult and computationally expensive very little experimental work on optimizing batch still operations.

Intermediate and final specifications in batch operation impose much more stringent requirements on model accuracy and precision than are required for control of continuous distillation columns. In the continuous case, intermediate tankage often attenuates product deviations, allowing controllers to be tuned to minimize integral squared error. For batch runs, one must guarantee that a specific composition inequality specification is met at the end of the run. Optimization results often show high sensitivity of the profit objective to purity. This makes it costly to 'back off' the constraint. The determination of the optimal method of batch still operation has been investigated by many workers

using various models and an array of numerical techniques. Mujtaba 7 and Bosley8 have given reviews of work in the field. While citations in these references contain a wide array of interesting approaches, none rigorously analyse the problems of actually implementing optimization results, at least from a control standpoint. Further, sensitivity of modelling and optimization methods to different model structures, and to variation in specifications and model parameters, have been addressed only in an 'open-loop' sense. If optimal methods are to be used in practice, it is important to ensure reliable, robust implementation in the closed-loop. Almost all literature on batch distillation optimization is based upon simulation studies. Early optimization work centred on variational techniques as applied to simplified models of binary systems. Objective functions used included maximum distillate ~ and minimum time"'. Hansen and Jorgensen" found that multivariable control (reflux and boilup) yielded considerable improvement over using reflux flow only. Bosley8 has

Control of unconventional processes: 71.F. Edgar
found that in certain cases, the optimal policy is also sensitive to the ratio of initial charge to vapour boilup rate. For example, simulation runs for an ethanol-water column indicate that constant composition operation can be 40% more profitable than constant reflux ratio operation.
Crystallization

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Crystallization is an unconventional unit operation that can be used either in a batch or continuous mode. The quality of a crystalline product is usually specified in terms of the crystal size, shape and purity, although customer requirements may be stated in terms of related quantities such as ability to flow, dissolution rate, and aesthetic appeal. For photographic materials the CSD (crystal size distribution) is the principal consideration. If standards are not met, further processing by recrystallization or milling may be necessary. As indicated by Rawlings e t al. '2 population balance models provide a way to represent the distributed nature of the dispersed phase system. Batch crystallizer control requires a dynamic operational policy, which in the past has not been model-based. In addition, Rawlings e t al. pointed out that limitations on process measurements have confounded parameter estimation, leading to unreliable parameter estimates. In this application the interplay of the fundamental model, process measurements, parameter estimation, and control algorithm is significant. A general approach for model-based control of batch crystallizers has recently been proposed by Miller and Rawlings ~'. They found that the necessity for optimal control varied greatly depending upon the kinetics of growth and nucleation.
Ferrnen ration

The main process variables include fermentor temperature, dissolved oxygen, broth viscosity, biomass and substrate concentration, and pH. The controlled variables are temperature, pH and off-gas composition that can be measured with a sensor. The manipulated variables can include the feed and air flow rates, stirrer rpm and flow rate through the temperature control coil. The resulting control problem is multivariable and nonlinear in nature, and the models contain a number of parameters that may need to be estimated on-line. Most current models for fermentation reactors are fairly simplified and describe biomass and its activity as monolithic entities. A model should recognize the existence of different forms of biomass and that the culture consists of a population of materials all in different states of growth, differentiation and production (so-called structured-segregated models). Many of the control papers on fermentation control have used optimal control applied to fairly simple models; see the reviews by Wang and Stephanopoulos ~ and Omstead ~'. In general, there has been very little original development of control theory in the bioprocessing field. Fordyce et al. 1~ have reviewed the application of adaptive control and state estimation to fermentation processes.

Electronic materials processing
An integrated circuit consists of several layers of carefully patterned thin films, each chemically altered to achieve desired electrical characteristics. Although the design of integrated circuits is normally done by electrical engineers, these devices are manufactured through a series of physical and/or chemical batch unit operations similar to the way that specialty chemicals are made. From 30 to 300 such steps are typically required to construct a set of circuits on a single crystalline substrate called a wafer. The wafers are four to eight inches in diameter, 400 to 700 microns thick and serve as the substrate upon which microelectronic circuits (devices) are built. Circuits are constructed by depositing thin films (0.01 to 10 microns) of material of carefully controlled composition and then etching these films to exacting geometries (0.35 to 10 microns). Process control problems in microelectronics processing can be divided into four categories~': plant (fab) management, contamination control, materials handling and unit operations control. Much attention has been focused on coordinating the schedules of different unit operations, controlling the purity of the required reactants, and monitoring the transfer of wafers between machines. Relatively little effort has been devoted to improving the control of individual unit operations. The main unit operations are crystal growth, oxidation, chemical vapour deposition (CVD), physical vapour deposition (PVD), dopant diffusion, dopant ion implantation, photolithography and etcil. The primary focus of modelling and control studies has

Fermentation is a key unit operation in bioprocessing. The fermentor receives a variety of components through a feed stream, and a stirrer/baffle arrangement keeps the vessel well-mixed. An air or oxygen stream is sparged into the fermentor, and product is removed through an outflow stream. The temperature in the fermentor can be regulated by varying the flow rate of fluid through a cooling coil. There are three common modes of operation: batch, fed-batch (semibatch), and continuous. In the batch mode, the reactants are simply charged to the fermentor and stirred until the desired product yield is achieved. Fed-batch operation involves continuous feed of substrate to the fermentor, without product removal until the fermentation is finished. This mode is used to improve productivity when the microorganism is subject to growth limitation by substrate or product inhibition. During the continuous mode of operation, the reactor is fed a constant stream of substrate and a constant product stream is removed. This type of operation has strong economic advantages for high volume products because the reactor does not need to be taken off-line for emptying and refilling as with batch and fed-batch operation.

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Control of unconventional processes: T. F. Edgar
Chemical vapour deposition

been on lithography, deposition and etching. In CVD, entering gases are activated thermally or by a glow discharge plasma to react and deposit a film on the wafer surface. In etching, reacting gases remove surface material which is not covered by a mask. By repetitive application of deposition and etch with lithography, devices can be constructed. In this paper we will focus only on deposition. A review of plasma etch and lithography modelling and control has been presented by Badgwell et al. TM. In industrial practice deposition and etch processes are often operated empirically, with relatively little understanding of the underlying physics and chemistry. As processing specifications become tighter and higher performance is demanded from the equipment, this lack of understanding becomes a significant problem. Currently, process control in microelectronics manufacturing consists mainly of PI (proportional, integral) controllers executing fixed process recipes without feedback of important process outputs. While statistical process control has been adopted in most wafer fabrication facilities, automatic process control has not been implemented on a large scale, due to the following reasons:
? In situ measurements of important process variables are rarely available. Process understanding is so poor that it is often difficult to determine which variables should be included in a control scheme. Post-process measurements are seldom used to automatically adjust process recipes. Product specifications are extremely tight, pushing the limits of measurement technology. Processing mistakes cannot be blended away; a processing error can destroy an entire batch of wafers with no hope of recovering the product through further processing. Equipment manufacturers are typically small companies without the resources required to develop advanced process control schemes.

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Only recently has there been much effort to develop fundamental mathematical models for processes such as plasma etching (PE) and CVD which would allow advanced process control and optimization strategies to be implemented. The lack of such analysis tools has prevented improved understanding of the complex mechanisms that are involved in solid state device processing, and has made the transition from one generation of equipment to the next (typically a time frame of about five years) costly and time-consuming. With experimentally-verified mathematical models for the key unit operations in solid state device processing, significant improvements in process control can be achieved, resulting in significant increases in yield and productivity. Furthermore, new equipment designs can be developed more rapidly and with greater confidence.

Chemical vapour deposition is the primary method used to deposit thin films for microelectronics manufacturing. Thin, highly uniform films of epitaxial silicon, polycrystalline silicon, amorphous silicon, silicon nitride, metals (such as tungsten), and some oxide films are deposited using this technique. CVD processes vary widely in their chemistry, reactor geometry and operating conditions. Most modelling efforts focus on the behavior of the reacting gas phase, with appropriate boundary conditions to bring in surface effects. Although the mean free path for the gas phase can be comparable to the spacing between wafers in a low pressure multiwafer furnace (about 0.5 cm), this is still small enough to allow for successful modelling with a continuum approach. Badgwell et al. ~8 have recently performed an extensive review of reactor-scale CVD models. CVD reactors can be categorized on the basis of their operating modes. Epitaxial (single crystal) films are typically deposited by running an atmospheric pressure CVD (APCVD) reactor in a mass transport limited mode, whereas polycrystalline and amorphous films are generally deposited by running a low pressure CVD (LPCVD) reactor in a surface reaction limited mode '7~. In a multiwafer LPCVD system (Figure 3), reactant gases flow at low pressure (typically < 2 tort) through a heated quartz tube to deposit on a stacked load of roughly 50 to 200 wafers. Multiwafer systems offer the tremendous economic advantage of processing a number of wafers simultaneously, which means that they will probably be used in microelectronics processing for some time to come. However, there are several problems inherent in multiwafer systems which limit their ultimate performance; these include variations in film properties from wafer to wafer, lower radial uniformity on a given wafer, and relatively long exposure of the wafer load to high temperatures. LPCVD reactors can be divided into cold-wall and hot-wall types. Hot-wall systems have the advantage of a more isothermal wafer environment, at the price of heating and cooling the wall and periodically cleaning the wall film deposits. Cold-wall systems can heat up and cool down more quickly, at the price of making wafer temperature control much more difficult. From a modelling point of view, cold-wall reactors exhibit strong thermal gradients within the gas phase, which can lead to significant changes in the flow patterns, mass transport effects, and physical properties. As a result, cold-wall reactor models often must include coupled mass, momentum, and energy balances, whereas hot-wall reactor models rarely include more than the mass balance. The two CVD processes most frequently analyzed are the epitaxial deposition of silicon in a horizontal APCVD reactor, and polysilicon deposition in a multiwafer LPCVD reactor. Silicon film processes are often studied because they are an important component of integrated circuit manufacturing. Most equipment models published to date assume steady-state operation

Control of unconventional processes: T. F. Edgar

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and are essentially mass balance models 2°, although some energy balance models have been developed for the multiwafer LPCVD furnaces :'. Response surface (empirical steady state) modelling has been commonly used in CVD applications (as well as in other unit operations) due to its ease of application and accuracy in fitting data. In this paper we focus mainly on instrumentation and control issues rather than mathematical modelling. Single wafer processing (SWP) technology has emerged recently as an attempt to overcome problems found in multiwafer designs. SWP systems must heat up and cool down quickly in order to compete economically with multiwat'er technology, and this has led to the development of rapid thermal processing (RTP). RTP systems load a single wafer into a cooled stainless

steel chamber where low pressure gases react on the radiatively heated wafer surface, which may be 400°C higher than the temperatures used in multi-wafer reactors (see Figure 4). Compared to a multiwafer design, the RTP system represents considerably less cost both in initial capital and in required wafer fabrication floor space. In addition, cold wall operation in the RTCVD system eliminates the particulate generation that occurs on the hot walls of the multiwafer system. The technical feasibility of completely replacing multiwafer systems with RTP technology was demonstrated several years ago:-'. The RTP system allows for non-steady state temperature programming (optimal control) in the deposition process. Single wafer processing also is advantageous from a process control point of view. Process measurements may be obtained from individual wafers

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Control of unconventional processes: T. F. Edgar surface and the surface roughness can change as the film thickness increases. This in turn causes a timedependent change in the rate of heat transfer for constant lamp settings. In addition, temperature measurements (typically by pyrometry) will be in error. This suggests that a constant gain proportional controller using lamp voltage as the manipulated variable and temperature as the controlled variable could cause non-constant growth rates due to the nonlinear, timevarying process gain 2~. In fact, a proportional controller can become unstable in such circumstances. On the other hand, the RTP design discussed by Moslehi et al. 2"~ heats the wafer from the back-side, where there is no deposition. This permits the use of pyrometry to measure temperatures. In order to implement any real-time process control strategy, one needs on-line in situ sensors for monitoring of equipment, process, and wafer parameters 22. Table 1 shows various categories of needed in situ process measurements for a typical SWP reactor. Most of the significant equipment, process, and wafer performance variables are not normally monitored either in situ or in real-time. Critical performance variables that are directly related to fabrication yields and overall device performance include conductive layer sheet resistance, film thickness and uniformity, and equipment cleanliness 22. To meet current and future requirements, the development of certain critical in situ sensors is imperative to eliminate the need for many of the off-line pilot measurements and by enhancing the process and equipment reliability and yields. Wafer temperature is undoubtedly one of the most important process parameters that needs to be measured in real time. Severe uniformity and control issues make temperature measurement a major issue in RTP. Wafer temperature and uniformity during CVD processing directly impact film deposition rate and process uniformity. The generation of slip dislocations in the bulk material of the wafer during RTP applications furthermore requires that uniform temperatures be maintained during steady-state conditions as well as transient thermal cycles. Therefore, a reliable noninvasive real-time in situ temperature sensor is required. In addition, this sensor needs the capability to monitor several spatial locations on the wafer for control of temperature uniformity and thermal gradients. The equipment design of various RTP systems must recognize the interconnection between control and instrumentation. On-line temperature measurement has proven to be a major challenge for RTP 2', and the
Table 1
In situ sensors needed for RTP

immediately before and after processing. This greatly reduces the problem of misprocessing currently experienced with multiwafer systems and allows for the possibility to customize the process recipe for each individual wafer. Automatic handling of single wafers using cluster tools, where several reaction chambers are clustered around a main wafer handling system, will also avoid excessive manual handling, thus reducing clean room size and personnel cost. Implementation of single wafer RTP systems into microelectronics fabrication will require an improvement of the existing modelling and control technology for these systems. Rapid thermal processing has been used for various thermal processing applications 23. RTP applications include junction annealing, silicide formation, epitaxy, CVD, as well as rapid thermal oxidation (RTO) and nitridation (RTN) processes. RTCVD reactors have been used to perform polysilicon, tungsten and thin dielectric deposition as well as selective epitaxial growth. In fact, many advanced CMOS and BiCMOS devices simply could not be fabricated without the use of RTP in some capacity. Some of the process results obtained by using RTP are not obtainable using batch diffusion furnace. A major argument against SWP has been its lower processing throughput compared to that of multiwafer batch equipment. However, for many applications enhanced capabilities for integrated processing and improved manufacturing process control far outweigh the somewhat lower processing throughput. The semiconductor wafer in RTP systems is heated by infrared heat sources, usually tungsten-halogen or arc lamps. In these systems radiation is usually the dominant heat transfer mechanism. Temperature control, uniformity issues, and the introduction of slip dislocations have been the main barriers that have kept RTP from becoming a widely used production tool. Approximately five years ago, temperature reproducibilities of +_50°C from wafer-to-wafer and +_20°C across a given wafer were not uncommon. However, with the rapid changes in this technology, especially in equipment design and temperature instrumentation, RTP may become commercially feasible 2''25. The main factors affecting wafer temperature uniformity and process repeatability in RTP systems are the infrared heat source, the chamber design and the temperature control system, which includes a noninvasive real-time temperature sensing system. The infrared energy source and process chamber can be fabricated in various ways. Typically, a specific design is dictated by convenience in fabrication rather than process performance. Moslehi et al. :2 have developed advanced multi-zone lamp systems with overall cylindrical symmetry which have been demonstrated for uniform wafer processing and real-time process uniformity control for wafers up to 150 mm. It is crucial that temperature at the wafer surface be maintained uniform, since small variations in temperature can lead to large variations in reaction rates. An additional problem that arises for some RTP designs is that for silicon deposition the absorptivity of the

Equipment parameters ? ? ? ? ? ? ? shower head temperature background contamination quartz window temperature wall depositions energy source status wafer temperature process gas flow

Wafer parameters ? ? ? ? ? dielectric film thickness metal sheet resistance polycrystalline film grain size doping density thickness uniformity

Control of unconventional processes: T. E Edgar
development of more accurate temperature measurement systems is still a critical research area. So far optical pyrometry has been the most widely used wafer temperature measurement technique in commercial R T P applications. The physical quantity that is measured by optical pyrometry is spectral radiosity, not temperature. The conversion of spectral radiosity measurements to temperature measurements is not a trivial task. The conversion requires knowledge of the spectral emissivity of the surface (which depends on surface roughness, surface temperature, the types of films on the surface and their thicknesses, and wafer doping characteristics). Because these parameters may not be quantified sufficiently, commercial R T P applications have employed pyrometer calibration techniques using Sensarray thermocouple wafers. However, there are two fundamental problems with this approach. First, in a typical semiconductor manufacturing facility, wafer-towafer variations are common. These variations include spectral emissivity variations, which introduce systematic bias errors in the optical pyrometer temperature measurement. The second problem has to do with the overlap between the narrow wavelength band operating regime of a typical pyrometer and the electromagnetic spectrum of the radiant heat sources. Interference of radiant heat source reflections must be taken into account when using pyrometers for temperature measurement in RTP systems. Closed-loop control of the 5 kW Zone 11 kW Zone 20 kW Zone 29 kW Zone

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radiant heat sources also signifies that the interference is not constant during a typical RTP process cycle. To overcome some of the problems of pyrometry, new temperature measurement techniques are being tested at Sematech and elsewhere, including ripple pyrometry (Accufiber), acoustic thermometry (Stanford University), and thin film thermocouples. These hold the potential of more accurate, multi-point measurements. Multi-point temperature control must be aligned with the number of manipulated variables in the system, i.e. it is feasible to control m temperature points on a wafer with m manipulated variables (e.g., lamp zones). Of course it is possible to have n controlled variables (temperatures) and m manipulated variables where rn < n or m > n. In the first case the n temperatures cannot be uniquely controlled to independent set points, whereas in the second case the controllers tend to react excessively and fight with each other due to multivariable interactions in the control system. The ways that lamp zones can be configured in an R T P system also vary, ranging from rectilinear lamp zones (rows) above and below the wafer (AG design) to the concentric rings of lamps in the T I - M M S T (now CVC) design (see Figure 5). This in turn can affect the control of the system, especially for multi-point temperature control. Aral et a l l and Breedijk et al. > have shown in studies of both the AG and TI-MMST reactors that the conditioning of the control system

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Control of unconventional processes: T. F. Edgar
nificant advantages, however, to operating the system in a dynamic fashion, e.g., to start the flow of reactants prior to reaching the final steady-state temperature. In fact, the best operating policy may be to operate the reactor cyclically, or in several distinct modes, as has been discussed by Cale e t al. 3° Even if it is desired to reach the steady-state temperature and profile prior to flowing the reactant gases, there is substantial room for improving the temperature control system so as to reach the steady-state conditions more quickly. The potential benefits of improved process control for this system are improved response time for changes between operating points, tighter control of desired steady-state operating conditions, reduced cycle time (increased throughput), and improved film uniformity. An optimal control system for the multiwafer LPCVD reactor would consist of two modules. The upper module would compute the optimal dynamic recipe for the run, using a dynamic model of the reactor in conjunction with an optimization algorithm. The optimal profile would be implemented by a real-time control module, which would use a multivariable controller and in s i t u measurements of important state variables to track the optimal recipe. Van Schravendijk and De Koning-'~ proposed a method to estimate and control wafer temperatures in a diffusion furnace directly. They developed a linearized energy balance model for radiative heat transfer within the furnace. They formulated a optimal multivariable control algorithm to minimize wafer temperature setpoint deviations and to minimize temperature variations from wafer to wafer. Roozeboom and Parekh ~2 have provided a good overview of RTP temperature control. They emphasize RTP system characteristics that are important for accurate and repeatable measurement and control of temperature. The radiant energy source, the chamber materials, and chamber/lamp design are some of the important factors that influence the controllability of RTP systems. Texas Instruments has been the first to design and implement a multi-zone axisymmetric illuminator (using concentric rings of lamps) compared to single-zone tungsten-halogen or arc lamps 2~. Norman ~ and Apte and Saraswat;' also showed the importance of using multiple independently-controlled zones for flexible radial flux control during transient and quasi-steady state operating modes. Chatterjee e t al. 26 performed step testing with instrumented wafers on a Rapro RTP system and found that both gain and time constants varied as much as 40% as power level was changed, suggesting the need for an adaptive control strategy. Bordeneuve e t al. 35 implemented adaptive process control for an RTP system. The same experimental system was used in both cases and consisted of a four-inch silicon or graphite wafer with one embedded thermocouple at the centre. This centre thermocouple was the only controlled variable of concern in these studies, which makes this system a single-input single-output (SISO) system. Ramp rates of over 100°C per second were obtained with overshoots

(whether it has three, four, or five lamp zones) is usually poor, leading to potentially unsatisfactory control of several temperature points on the wafer. The design of the gas distribution system also influences the choice of sensors. In the TI-MMST system, the wafer is mounted over the showerhead, which minimizes interference between the showerhead and the lamps, and wafer deposition is carried out on the bottom of the wafer. Temperature measurement is performed on the top side of the wafer but unfortunately this is in the same area where the lamps are located, a major obstacle to accurate temperature measurement. Alternatively, if adequate gas distribution can be carried out without a showerhead, then the in s i t u sensors can be located underneath the wafer, and deposition and heating can be performed on the top of the wafer. Limited process control studies have been conducted on deposition processes to date. Sachs e t al. 29 have presented a supervisory control structure for a general fab unit operation, using the multiwafer LPCVD reactor as the process example. Their control scheme consists of a three-level cascade structure similar to supervisory control schemes used in refineries. The uppermost control module, denoted as the flexible recipe generator, determines an initial process recipe which will give good results in the presence of process fluctuations. The second level of control is a sequential optimization module called the Run-By-Run Controller (RBR). This module uses feedback information from post-process measurements to make small adjustments to the process recipe, using the recipe computed by the flexible recipe generator as an initial guess. This approach is similar to online optimization schemes such as Evolutionary Operation (EVOP), which originated in the 1960s in the chemical industry. The third and most basic level of control described by Sachs e t al. is a real-time control module which must execute the recipe computed by the RBR module. In current lab unit operations, this level of control is dominated by single loop PID algorithms. Significant improvements should be possible, however, by designing a control system for the full multivariable unit operation. Badgwell e t al. 2'' computed optimal process recipes for a hot-wall multiwafer LPCVD reactor, using a model which considers both mass and energy transport effects. The objective for this study was to maximize the reactor throughput (number of good wafers per hour), subject to maximum constraints on across-wafer film thickness variations. Badgwell e t al. found that the optimal process recipe called for the heater end-zones to be some 120°C hotter than the middle zone so as to even out wafer-to-wafer temperature variations. The optimal recipe provided an increase in throughput of 25% over a nominal recipe used at Sematech. Dynamic control of thin film deposition in a multiwafer LPCVD reactor appears promising. The most common mode of operation involves reaching a desired steady-state temperature and pressure as quickly as possible, at which time the reactant flows are switched on for the desired deposition time. There may be sig-

Control of unconventional processes: T. F. Edgar
of less than 5°C. Practical drawbacks of these studies are that the wafer diameter was only four inches and that spatial uniformity was not considered. Norman and Boyd~ and Schaper e t al. ~ have used a low-order nonlinear model in the design of a multivariable feedforward/feedback control strategy. The strategy employed the model in an openqoop optimal computation based on the desired trajectory. Linear multivariable feedback combined with gain-scheduling was used to compensate for modelling errors and disturbances. The experimental work was performed using a four-inch silicon wafer with three radial embedded thermocouples. A controlled ramp was achieved from 20°C to 900°C at a rate of 45°C per second. The wafer edge to center temperature difference was less than 15°C during the ramp up and less than I°C at the steady-state temperature of 900°C. Ella ~ has reported the successful application of optimal multivariable control to the Applied Materials RTP chamber for both annealing and oxidation. The AM-RTP has 12 independently actuated groups of lamps and has eight temperature measurements (the specific type of sensor is not reported) across the width of the chamber. The wafer is rotated to allow more uniform heating. The number of manipulated variables was reduced to eight so that the number of inputs and outputs were equal. A simple-discrete time model was developed (first order) based on input-output testing using pseudo-random binary sequences (PRBS) over several temperature ranges. The specifications on the controller included: (a) a uniform temperature profile in the chamber with less than + 2.5°C error band during ramps (b) steady state error of less than 1.5°C peak and 0.5°C average (c) less than 5°C overshoot at the end of the ramp with a fast settling time. A robust controller design using MATRIX-X was relatively straightforward, with some additional logic needed to prevent reset windup and lamp voltage saturation. For a 200 mm wafer, Elia reported that six temperatures were successfully controlled from 750°C to 1050°C with a 50°C/s ramp rate. Slower (25°C/s) ramp rates were used for 125 mm and 150 mm wafers. Breedijk e t al. '~ reported an enhanced nonlinear model predictive control scheme using successive model linearization and QDMC for the TI-MMST reactor, which gives improved control over linear model-based schemes developed previously. They obtained a simplified distributed parameter model for the energy equation in the semiconductor wafer. After collocating the model to a set of four ode's, they were able to fit this model to different lamp configurations and chamber geometries through parameter estimation of configuration factors. Hence the model structure can probably be generalized to other RTP systems. In developing the multivariable control system for the four-zone reactor (see F i g u r e 5), Breedijk e t al. recognized the ill-condi-

109

tioned nature of the 4 x 4 control system as seen in the condition number of the gain matrix. Instead of controlling the four temperatures directly, they proposed controlling the average and standard deviation of the four temperatures using the QDMC algorithm for model predictive control. Transformation of the output equation resulted in a 4 × 2 reduced system. A plot of normalized gain matrix norms for the 4 × 2 and 4 x 4 systems suggested that the transformed system was less nonlinear than the original system. In addition, a plot of gain matrix condition numbers indicated that the transformed system was much better conditioned (by a factor of over 100), and therefore easier to control than the original system. At each sampling period the transformed control model was linearized analytically, discretized, and converted to a multivariable dynamic matrix representation. Model-predicted outputs of the transformed system and the optimal control were calculated using QDMC. A new quadratic programming (QP) problem was solved at each sampling period, and the first element of every manipulated variable of the newly computed Au was implemented. Feedback was incorporated by additive output disturbance estimation that is kept constant over the prediction horizon. Experimental comparison of closed-loop performance of this method with gain-scheduled IMC ~4 shows that the QDMC approach was superior.

Conclusions
Unconventional processes occur in a wide range of manufacturing applications of interest to chemical engineers and include specialty chemicals manufacture and advanced materials processing. The batch nonlinear nature of these processes, coupled with the lack of realtime sensors for many performance variables, present serious difficulties in the design of process control strategies. Model-based control offers a framework so that an integrated analysis of sensor, model and control algorithm can be performed and maximize the closedloop performance. Future technological changes in areas such as electronic materials will cause effective process control to become even more critical to successful process operations.

References
1 Patwardhan, A. A., Rawlings. J. B. and Edgar, T. V. ('hem Engr. Comm. 1990, 87, 123 2 Wright, G. T. and Edgar T, I-. Comp. Chem. Engr. 1993, 18, 83 3 Lee, W. I ,Loos. A. C. and Springer. G S. C~)mp M a u ' r 1982, 16, 510 4 Bergh. L G. and MacGregor. J. F Cml J Chcm Engr 1987.65, 148 5 Braatz, R. D., Tyler, M. L., Morari. M . Prankh, F R. and Sartor, L A1ChEJ. 1992, 38, 1329 6 Rawlings. J. B. and Chien, I-L. AIChE J. 1995, submitted 7 Mujtaba, I. M. 'Optimal Operational Policies in Batch Distillation' Ph.D. thesis, University of London. 1989 8 Bosley. J R. 'Experimental Investigation of Batch Distillation

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Control of unconventional processes: T. F. Edgar
Modeling Techniques for Use in Control and Optimization', Ph.D. thesis, University of Texas, Austin 1994 Converse, A. O. and Gross, G. D. Ind. Eng. Chem. Fundam. 1963, 2, 217 Robinson, E. R. Chem. Eng. Sci. 1969, 24, 1661 Hansen, T. T. and Jorgensen, S. B. Chem. Eng. J. 1986, 33, 151 Rawlings, J. B., Miller, S. M. and Witkowski, W. R. IEC Research, 1993 Miller, S. M. and Rawlings, J. B. AIChEJ. 1994, 40;8, 1312 Wang, W. S. and Stephanopoulos, G. CRC Crit. Rev. Biotechnol. 1985, 2, 1 Omstead, D. R. (Ed.) 'Computer Control of Fermentation Processes' CRC Press, Boca Raton, FL, 1990 Fordyce, A. P., Rawlings, J. B. and Edgar, T. F. in 'Computer Control of Fermentation Processes', D. R. Omstead (Ed.) CRC Press, Boca Raton, FL, 1990, 165 Lee, H. H. 'Fundamentals of Microelectronics Processing', McGraw-Hill, New York, NY 1990 Badgwell, Y. A. et al. Comput. Chem. Engr. 1995, 19:(1), 1 Sze, S. M. 'VLSI Technology' McGraw-Hill, New York, NY, 1988 Badgwell, T. A., Edgar, T. F., Tracbtenberg, I. and Elliott, J. K. AIChEJ. 1992, 38, 926 Badgwell, T. A., Edgar, T. F. and Trachtenberg, I. J. Electrochem. Soc. 1994, 141, 161 Moslehi, M., Chapman, R., Wong, M., Paranjpe, A., Najur, H., Kuehne, J., Yeakley, R. and Davis, C. IEEE Trans. Electron. Dev. 1992, 39, 4 Singh, R. and Moslehi, M. M. (Eds.) 'Rapid Thermal and Related Processing Technique', SPIE, 1991, 1393 24 Roozeboom, F. In 'Rapid Thermal Processing, Science and Technology' R. B. Fair, Ed. Chapter 9, Academic Press, New York, 1992 25 Lojek, B. RTP'93 Conf., R. B. Fair and B. Lojek (Eds.), Scottsdale, AZ, 1993, 2 26 Chatterjee, S., Trachtenberg, I. and Edgar, T. F. Proc. RTP Conf., R. B. Fair and B. Lojek (Eds.), Scottsdale, AZ, 1993, 386 27 Aral, G. et al. Proc. RTP Conf., 1994, 288 28 Breedijk, T., Edgar, T. F. and Trachtenberg, I. Proc. RTP Conf. 1994, 267 29 Sachs, E., Guo, R., Ha, S. and Hu, A. IEEE Trans. Semicon. Manuf 1991, 4, 134 30 Cale, T. S., Jain, M. K. and Raupp, G. B. J. Electrochem. Soc. 1990, 137, 1526 31 van Schravendijk, B. J. and De Koning, W. L. ,L Appl. Phys. 1987, 61, 1620 32 Roozeboom, F. and Parekh, N. a~ Vac. Sci. Technol. B. 1990, 8, 1249 33 Norman, S. A. and Boyd, S. P. Proc. Amer. Cont. Conf. 1992, 811 34 Schaper, C., Moslehi, M., Saraswat, K. and Kailath, T. IEEE Trans. Semicond. Manuf 1994, 7 (2), 202 34 Apte, P. P. and Saraswat, K. C. IEEE Trans. Semicond. Manuf 1992, 5, 3 35 Bordeneuve Guibe, J., Dilhac, J. M. and Dahnou, B. J. Proc. Cont. 1992, 2, 3 36 Elia, C. F. Proc. Amer. Cont. Conf., 1994, 907 37 Breedijk, T., Edgar, T. F. and Trachtenberg, I. Proc. RTP Conf. 1994, 267

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