Closed-loop identification of wafer temperature dynamics in a rapid thermal process

Single wafer rapid thermal processing (RTP) can be used for various wafer fabrication steps such as annealing, oxidation and chemical vapor deposition. A key issue in RTP is accurate temperature control, i.e., the wafer temperatures should be rapidly increased while maintaining uniformity of the temperature profile. A closed-loop identification method that suppresses RTP drift effects and maintains a linear operating region during identification tests is proposed. A simple graphical identification method that can be implemented on a field controller for autotuning and a nonlinear least squares method have been investigated. Both methods are tested with RTP equipment based on a design developed by Texas Instruments.     

Design for control: Temperature uniformity in rapid thermal processor

It is well known that the design of the heating source imposes an inherent limitation on the performance of the rapid thermal processor (RTP). In this work, the similarities and differences between flat and angled reflectors are studied. Thediscontinuous characteristic of the angled reflector can be used to compensate for the edge heat loss of the thin wafer and, consequently, a better temperature uniformity can be achieved. A design procedure is proposed to place the lamp ring as well as the angle of the reflectors. For the control system design, the measurement selection criterion of Huang et al. is employed to find candidate measurement sets followed by a structured singular value criterion. Once the control structure is determined, multivariable temperature controllers are designed according to the internal model control (IMC) principle. From process insight, a fairly simple nonlinear compensation is also devised. Simulation results show that, while only half of the thermal budget is used, improved temperature uniformity can be obtained by using the proposed approach. This paper was presented at the 8th APCChE (Asia Pacific Confederation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

Iterative identification of temperature dynamics in single wafer rapid thermal processing

As the standard size of silicon wafers grows and performance specifications of integrated circuits become more demanding, a better control system to improve the processing time, uniformity and repeatability in rapid thermal processing (RTP) is needed. Identification and control are complicated because of nonlinearity, drift and the time-varying nature of the wafer dynamics. Various physical models for RTP are available. For control system design they can be approximated by diagonal nonlinear first order dynamics with multivariable static gains. However, these model structures of RTP have not been exploited for identification and control. Here, an identification method that iteratively updates the multivariable static gains is proposed. It simplifies the identification procedure and improves the accuracy of the identified model, especially the static gains, whose accurate identification is very important for better control.     

Combined run-to-run and LQG control of a 12-inch RTP equipment

A combined run-to-run (R2R) and LQG control method has been proposed for rapid thermal processing (RTP) equipment for run-wise improvement and real-time multivariable control of the temperature uniformity over the wafer surface. The standard LQG objective was modified to include a quadratic penalty term for input deviation from bias values which are updated by an R2R control law. The proposed method has been applied to commercial 12-inch rotating RTP equipment with four pyrometers and ten circular groups of tungsten-halogen lamps for measurements and manipulation of wafer temperatures. The performance of LQG control was evaluated under wafer rotation and found to show quite accurate tracking. For evaluation of the combined control technique, a wafer with seven thermocouples (TC’s) attached along the radial direction has been employed for the TC measurements to be used for R2R control, whereas the pyrometer measurements are fed back for real-time LQG control. It was observed that the temperature uniformity is improved as the run number increases.     

Multivariable Optimal Learning Control of Wafer Temperatures in a Commercial RTP Equipment

A multivariable optimal iterative learning control technique called BMPC (Batch Model Predictive Control) has been implemented and evaluated in a commercial RTP (Rapid Thermal Processing) system fabricating 200 mm silicon wafers. The wafer temperature was controlled at multiple points along the radial direction by manipulating multiple tungsten‐halogen lamp groups. The study has addressed the following two issues: feasibility of BMPC in a commercial RTP equipment and enhancement of temperature uniformity using redundant inputs. As a consequence, satisfactory tracking performance could be realized with BMPC with reduced efforts for design and implementation of the controller by the standardized identification and tuning procedure. Redundant inputs whose number is larger than that of the temperature measurements was attempted to relieve the directionality of the system. Experimental tests revealed that the approach can provide us with improved temperature uniformity as well as tracking performance.     

Identification and feedback control of rapid thermal processing systems

We consider the recursive identification and feedback control of the rapid thermal processing (RTP) system where the asymmetry of the convective heat transfer coefficient, caused by gas flow in the chamber, is taken into consideration. The success of RTP depends on the precise control of water temperature by adjusting the strength of the heating lamps to minimize dopant redistribution as well as wafer warpage. An efficient method of recursive identification and optimal feedback control is developed by separating the radiation field from the temperature field of the wafer and converting the heat conduction equation for the wafer temperature to a reduced-order model by means of the Karhunen-Loève Galerkin procedure.     

Nonlinear control of rapid thermal chemical vapor deposition under uncertainty

This article focuses on nonlinear control of a rapid thermal chemical vapor deposition (RTCV'D) process in the presence of significant model uncertainty and disturbances. Initially, a detailed mathematical model of the RTCVD process is presented consisting of a nonlinear parabolic partial differential equation (PDE) which describes the time evolution of the wafer temperature across the radius of the wafer, coupled with a set of nonlinear ordinary differential equations (ODEs), which describe the time evolution of the concentrations of the various species. Then, the synthesis of a nonlinearoutput feedback controller based on the RTCVD process model by following a control methodology for nonlinear parabolic PDE systems introduced in (Baker and Christofides, 1998) is discussed. The controller uses measurements of wafer temperature at four locations to manipulate the power of the top lamps in order to achieve uniform temperature, and thus, uniform deposition of the thin film on the wafer over the entire process cycle. The nonlinearoutput feedback controller is successfully implemented through computer simulations and is shown to attenuate significant model uncertainty end disturbances and to outperform a proportional integral (PI) control scheme.     

Carbon nanotube growth by rapid thermal processing

A new method for carbon nanotube (CNT) growth by rapid thermal processing (RTP) of amorphous carbon film is reported. This is a two-step method, involving an ion-beam sputtering process followed by an RTP treatment. Amorphous carbon film containing iron was first deposited by ion-beam sputtering. The as-deposited films were then annealed by RTP under an inert environment. High-density multi-wall carbon nanotubes with a length of 1 μm and a diameter of approximately 30 nm were observed on the surface of amorphous carbon film after RTP at 1200°C for 30 s in nitrogen (N₂). Detailed morphology and structure analyses of carbon nanotubes thus obtained using SEM and HR-TEM indicated that the number density and growth rate of the CNT were dependent on the process temperature and ambient gas. The use of RTP provides a straightforward, convenient and cost-effective method to grow carbon nanotubes with controllable length and density.     

基于相变储热技术的电池热管理系统研究进展

动力电池的最佳工作温度范围为20~50℃,因此热管理系统是其运行过程中不可分割的一部分。相变储热材料在发生相变时可以吸收或释放大量的热量并且温度基本保持不变,在电池热管理中得到广泛应用。本文综述了国内外基于相变储热技术的电池热管理系统的研究进展,主要介绍了基于相变材料的被动式热管理系统、主动式热管理系统以及主动式和被动相结合的耦合式热管理系统。综合来看,复合相变材料形状稳定性好、热导率高,可以有效地降低电池组的温度,提高电池组的温度均匀性。导电复合相变材料的电热转换特性还可用于低温下快速加热电池,实现加热-冷却一体化。然而在相变材料被动式热管理系统中,相变材料吸收的热量无法及时释放出去,热量的堆积会造成系统失效。将主动散热技术与相变材料耦合得到的耦合式热管理系统具有更好的控温性能、稳定性和安全性。此外,相变乳液以及相变微胶囊浆液具有比热容大、可相变等优点,替代水作为电池热管理系统的冷却介质可以获得更好的温度均匀性和更低的功耗。但相变乳液本身的稳定性差、过冷度大等问题亟需解决。总之,电池在高温和低温下都需要进行有效地温控,相变材料如何解决电池全温度段的热管理还值得进一步研究。     

Identification and control of an industrial steam-reforming plant

Reliable mathematical models for an industrial steam-gas reformer and a steam-boiler are simulated and used to study the dynamic behavior of the two coupled processes. Simulation results of the identified system are in good agreement with the nonlinear process operation. Three control loops are considered for multivariable control system design. These are Hydrogen product temperature and quality, and boiler water level. A new multivariable control structure is obtained, which manipulates steam-to-carbon (S/C) ratio for the control of coil outlet temperature (COT), the fuel gas rate to control hydrogen product quality (conversion) and the boiler feed water to control drum level. The selected structure is then tuned using the Biggest-Log modulus-Tuning (BLT) method. Results show a very satisfactory response of the temperature and quality loops with the BLT based controllers. It is also found that the boiler water level loop is partially decoupled from the other two loops and hence does not need to be detuned according to BLT criterion. The new multivariable control structure is compared with the conventional control utilising fuel gas rate to control COT. Closed-loop simulation results show a better performance for the multivariable structure under continuous operation.     

Multivariable process control - A survey

A survey is provided of the state of the art in multivariable process control. Recent literature is organized and tabulated by topic to provide material for further study. The survey encompasses both linear and nonlinear multivariable systems, on-line estimation, adaptive control, distributed systems, and recent developments in computer-aided control system design. These developments together with recent applications provide the basis for predictions of the future evolution of the field.     

Rapid thermal cycling with low thermal inertia tools

Solid freeform fabrication processes offer the manufacturing flexibility for tools with low thermal inertia and internal conformal channels for rapid thermal cycling in injection molding. This article analyzed each step of a rapid thermal cycling process and provided quantitative guidance for tooling design. The proposed design methodology was tested on a three‐dimensional (3D) printed benchmark tool with truss support. Rapid cooling test on the benchmark tool resulted in the mold time constant shorter than 2.3 s and the cavity temperature uniformity better than 3°C. Preliminary tests demonstrated the technical feasibility of using a solid freeform fabrication process to fabricate low thermal inertia tools for improved heat management in injection molding. POLYM. ENG. SCI., 2009. © 2008 Society of Plastics Engineers     

载人航天器环热控一体化仿真分析

采用系统建模及仿真方法搭建了一种典型载人航天器环热控一体化系统模型,分析了系统的性能。针对3人7天载人飞行工况开展了仿真分析,结果表明,经过合理设计,该系统可将舱内温湿度、压力、氧分压等参数控制在航天医学指标要求范围内。环热控系统仿真结果较好地预测了系统工作过程,显示了主要参数的变化情况,结果合理,验证了仿真方法、系统仿真模型的正确性。通过控制流体回路外回路旁通阀门开度,可准确控制外回路控温点温度,保证舱内温湿度在合理范围之内。此外,外回路控温点的设定会对环热控系统状态带来影响,通过合理设计外回路控温点,可保证舱内温湿度满足航天医学指标要求。     

Deposition uniformities on a wafer and in a trench for tungsten silicide LPCVD in a single-wafer reactor

A transient model of a single-wafer reactor in axisymmetric, stagnation point flow is used to study the effects of operating conditions on film thickness uniformity and composition uniformity across the wafer during low pressure chemical vapor deposition of tungsten silicide. Orthogonal collocation on finite elements is used to solve the transient model equations; continuity, momentum, energy and chemical species balances. A feature scale model for simultaneous Knudsen transport and heterogeneous reactions is used to predict film thickness in infinite trenches. Boundary conditions for the feature scale model are established using the reactor scale model. The use of a combined reactor scale and feature scale model is demonstrated to select deposition conditions which provide both good interwafer uniformity and good intrafeature uniformity. Film thickness and composition uniformity on a wafer are predicted using a model for a single-wafer reactor. Significant differences in step coverage predicted using partial pressures in the feed stream and partial pressures at the wafer surface were observed. Step coverage differences between the wafer center and the wafer edge were also significant under the operating conditions used in this study. Uniformities of interwafer and intrafeature step coverages inceased as either the wafer temperature or the partial pressure ratio of dichlorosilane to tungsten silicide in the feed was decreased.     

Adaptive Robust Generic Model Control of High‐Purity Internal Thermally Coupled Distillation Column

The internal thermally coupled distillation column (ITCDIC) is a frontier in energy‐saving distillation research. The process inside a high‐purity ITCDIC is of great nonlinear dynamics, which trouble the conventional control schemes. A multivariable adaptive robust generic model control (ARGMC) is presented to solve the difficulties, where an ARX model is derived and a recursive least squares estimation (RLSE) method is introduced. The benzene/toluene system is studied as an illustrative example. The results of ARGMC are compared with the robust generic model control (RGMC) and traditional PID control in detail. The performances in both servo control and regulatory control confirm the accuracy and validity of ARGMC for the high‐purity ITCDIC process.     

NEURAL NETWORK-BASED PREDICTIVE CONTROL FOR MULTIVARIABLE PROCESSES

In this paper, the systematic derivations of setting up a nonlinear model predictive control based on the neural network are presented. This extends our previous work (Chen, 1998) into a multivariable system to explore the characteristics of the design. There are two stages for the development of nonlinear neural network predictive control: a neural network model and a control design. In the neural network model design, a parallel multiple-input, single-output neural network autoregressive with a model of exogenous inputs (NNARX) is proposed for multistep ahead predictions. In control design, the controller with extended control horizon is developed. The Levenberg-Marquardt algorithm is applied to training the NNARX model. Also, the sequential quadratic programming is used to search for the optimal manipulated inputs. The gradient of the objective function and constraints that require computation of Jacobian matrices are completely derived for optimization calculation. To demonstrate the control ability of MIMO cases, the proposed method is applied through two nonlinear simulation problems.     

Neural network-based predictive control for multivariable processes

In this paper, the systematic derivations of setting up a nonlinear model predictive control based on the neural network are presented. This extends our previous work (Chen, 1998) into a multivariable system to explore the characteristics of the design. There are two stages for the development of nonlinear neural network predictive control: a neural network model and a control design. In the neural network model design, a parallel multiple-input, single-output neural network autoregressive with a model of exogenous inputs (NNARX) is proposed for multistep ahead predictions. In control design, the controller with extended control horizon is developed. The Levenberg-Marquardt algorithm is applied to training the NNARX model. Also, the sequential quadratic programming is used to search for the optimal manipulated inputs. The gradient of the objective function and constraints that require computation of Jacobian matrices are completely derived for optimization calculation. To demonstrate the control ability of MIMO cases, the proposed method is applied through two nonlinear simulation problems.     

Conjugate thermal simulation for sheet extrusion die

The thermal effects on manifold temperature uniformity and output flow uniformity are important for polymer extrusion die design. Lin and Jaluria (Lin and Jaluria, Polym. Eng. Sci., 37, 1582 (1997)) has carried out a numerical study on conjugate heat transfer for extrusion polymer flow under the assumption that the die body surface is in uniform temperature or heat transfer coefficient. In this study, we have solved the non‐uniform body surface temperature as part of the simulation solutions based on heat flux boundary conditions (including radiation and convection heat transfer). The body temperature is computed in conjugated with the melt polymer flow with non‐linear viscous shear heating effect. The relative tough thermal conditions are set to test uniformity of the temperature distribution on the manifold wall. We also give the results of the heat transfer effect on the flow velocity distribution. POLYM. ENG. SCI., 54:682–694, 2014. © 2013 Society of Plastics Engineers     

Process control of profile extrusion using thermal method. Part II: Closed loop control

The analytical flow model developed in Part I was applied to the online control of profile extrusion. A rubberized polystyrene was extruded through a simple L-shaped profile die with one thin section and one thick section. Take-up speed was used to control the size of the extrudate, and die temperature was used to control the shape of the extrudate. Two different control algorithms, a dual single-loop feedback PI controller and a multivariable feedforward plus feedback control method (FFC), were carried out for set point changes of the extrudate shape and size, and load disturbances of screw speed. Results showed that the PI feedback controller was satisfactory for long-term set point changes but not for load changes. The FFC worked well for load disturbances lower than 10 cycles/min. Owing to the slow dynamic response of die temperature, the shape loop can only be controlled for long-term disturbances.     

高温甲醇燃料电池热管理系统设计

针对某型号高温甲醇燃料电池单电池模块,以实现精确控温、快速启动为目的进行了燃料电池热管理系统的设计、制造和测试。应用Matlab/Simulink平台开发了一种拟合简化方程的控制系统算法及其仿真计算平台,并对所设计的控制算法进行了仿真计算;同时对燃料电池内外传热介质循环回路及冷却系统换热器进行了重新设计与样件试制。完成了热管理系统单电池模块运行试验,将实测数据与仿真计算结果进行了对比分析。试验结果表明,所设计热管理系统成功将电池预热时间缩短了678s,稳定工况下冷却介质温度误差保持在±2℃以内,达到了预定的设计要求。样件试制及测试结果验证了热管理系统设计的可行性、准确性及实用性,为今后高温甲醇燃料电池热管理系统设计优化提供了理论和实际参考。