Many modern thermal processing systems involve temperature control of heated plates, where the plate can be a single wafer, heated by an array of tungsten halogen lamps from one or both sides, or thicker carriers or susceptors on which one or more wafers are placed, heated by radiation from hot filaments. The plate's temperature is typically measured using pyrometers. These types of systems can be accurately described by a mathematical model of the physics. However, some of the system properties vary over time and/or from wafer-to-wafer and cannot be predicted in practice, although their range of values may be known. In many cases, the plate's temperature is controlled using a proportional-integral-derivative (PID) controller, which may not be able to meet the desired temperature tracking performance (e.g. settling time, overshoot, repeatability) over a broad range of operating conditions. In this paper, an alternative model-based control approach is discussed that can achieve good performance for a wide range of operating conditions. In our approach, the mathematical system model is directly incorporated into the feedback controller. Simulation studies show that this approach yields significantly better performance and exhibits a much smaller sensitivity to system properties variation than a gain-scheduled PID controller.

This work describes the application of model-based control system design techniques to rapid thermal processing (RTP). The work considers all aspects of the distributed temperature control problem from physics-based modeling to implementation of the real-time embedded controller. With its exceptionally stringent performance requirements (low non-uniformity of wafer temperature, high temperature ramp rates), RTP temperature control is a challenging distributed temperature control problem. Additionally, it is an important problem in the semiconductor industry because of the progressively smaller 'thermal budget' resulting from ever decreasing integrated circuit dimensions. Despite the emphasis on faster cold wall, single-wafer processing RTP chambers, the approach described here for solving distributed temperature control problems is equally applicable to slower distributed thermal systems such as, hot-wall batch-processing furnaces. For the physical model, finite volume techniques are used to develop high-fidelity heat transfer models that may be used for both control design and optimal chamber design. Model-order reduction techniques are employed to reduce these models to lower orders for control system design. In particular, principal orthogonal decomposition (POD) techniques have been used to derive low order models. Multivariable techniques such as LQG, H/sub 2// H/sub /spl infin// methods are employed for feedback control design. These methods have been successfully implemented on commercial RTP chambers.

A semiconductor wafer undergoes a wide range of processes before it is transformed from a bare silicon wafer to one populated with millions of transistor circuits. Such processes include physical or chemical vapor deposition, (PVD, CVD), chemical-mechanical planarization (CMP), plasma etch, rapid thermal processing (RTP), and photolithography. As feature sizes keep shrinking, process control plays an increasingly important role in each of these processes. We have found the model-based approach to be an effective means of designing commercial controllers for both semiconductor and advanced materials processing. It is our experience that the best models for control design borrow heavily from the physics of the process. The manner in which these models are used for a specific control application depends on the performance goals. In some cases (e.g., RTP), the closed-loop control depends entirely on having very good physical models of the system. For other processes, physical models have to be combined with empirical models or are entirely empirical. The resulting controller may be in-situ feedforward-feedback or run-to-run controller, or a combination thereof. The three case studies that are presented in this tutorial session (RTP, CMP, and PVD) are representative of the applications in this industry. Highlights of the session include physical modeling, model reduction and sensor selection, and feedback and run-to-run controller design.

The research described in this tutorial paper involves an effort for physical modeling and model-based sensing and control of CMP systems. A dynamic model of a rotational CMP process is developed, as well as simulation software. This dynamic model is used for feedback control design based on in-situ thickness measurements, as well as run-to-run control using in-line metrology. Simulation results of open-loop, feedback control, and combined feedback and run-to-run control are presented and compared. A multivariable LQ (linear quadratic) feedback controller was designed and showed improvement of within-wafer-nonuniformity (WFWNU) at the end of a run in simulation over existing open-loop control of a CMP process. It also showed the possibility of using feedback control as a means of end pointing the CMP process. Furthermore, a run-to-run (R2R) controller was designed and simulated. Additional improvement of WIWNU and tracking a desired average wafer thickness was obtained, showing the merits of a combined feedback / run-to-run control process.

Radio frequency (RF) diode sputtering is widely used for depositing giant magneto-resistive (GMR) thin films for multilayers, spin valves, and spin-dependent tunneling (SDT) devices used in data storage, computer memory, etc. However, the thin films thus produced often show unacceptably high variation in GMR properties from wafer to wafer. This paper describes a modeling and control effort that was undertaken for improving run-to-run repeatability. A multiscale input-output model was developed for the primary physical phenomena in the deposition process - gas flow, plasma discharge, sputtering, and atom transport. The model predicts the deposition rate, the energy distribution of sputtered atoms, and their sensitivity to deposition conditions such as power, working gas type, pressure, gas temperature, and electrode spacing. Simulations with this model were used to determine the process parameters to which the wafer properties have the maximum sensitivity. Experiments were performed to determine the relative importance of these parameters. Based on the results, a controller was designed to regulate the time-integrated target bias voltage. Implementation of the controller reduced wafer-to-wafer variation of GMR properties by over 50%. Additionally, application of control to SDT wafers led to improvement and optimization of the process.

This paper investigates the application of model-based control design techniques to distributed temperature control systems. Multivariable controllers are an essential part of the-modern-day rapid thermal processing (RTP) systems. This paper considers all aspects of the control problem beginning with a physics-based model and concluding with implementation of the real-time embedded controller. The thermal system used as an example throughout the paper is a RTP chamber that is widely used in semiconductor wafer processing. With its exceptionally stringent performance requirements (low nonuniformity of wafer temperature, high temperature ramp rates), RTP temperature control is a challenging distributed temperature control problem. Additionally, it is an important-problem in the semiconductor industry because of the progressively smaller "thermal budget" resulting from ever decreasing. integrated circuit dimensions. Despite the emphasis in. this paper on faster cold wall single-wafer processing RTP chambers, the approach described here for solving distributed temperature control problems is equally applicable to slower distributed thermal systems such as, hot-wall batch-processing furnaces. For the physical model, finite volume techniques are used to develop high-fidelity heat transfer models that may be used for both control design and optimal chamber design. Model-order reduction techniques are employed to reduce these models to lower orders for control system design. In particular, principal orthogonal decomposition techniques have been used to derive low order models. Techniques such as linear quadratic Gaussian H-2/H-infinity methods are employed for feedback control design. While the methods are illustrated here using a generic RTP system, they have been. successfully implemented on commercial RTP chambers.

Radio frequency (RF) diode sputtering deposition is a widely used process for depositing GMR thin films for multilayers, spin valves, spin-dependent tunneling (SDT) devices, etc [1]. However, the thin films thus produced often show signification variation in GMR properties from wafer to wafer. As described in the earlier chapter, a multiscale model based on the primary physical phenomena gas flow, plasma discharge, sputtering and atom transport has been developed to explore the sputter deposition process. Simulations with this model were used to determine the process parameters to which the deposition characteristics have the maximum sensitivity. Experiments were performed to determine the relative importance of these parameters. Based on the results, a controller was designed to regulate the time-integrated target bias voltage. Implementation of the controller reduced wafer-to-wafer variation of GMR properties by over 50%. Additionally, application of control to SDT wafers also led to improvement and optimization of the process.

Radio frequency (RF) diode sputtering deposition is a widely used process for depositing thin films and multilayers [1-3]. The development, computational implementation, and integration of the appropriate physical models for RF diode sputtering, calibrated and refined using appropriate experimental results are believed to promise a reduction of the time consuming and costly trial-and-error approach used to design, operate, and control deposition systems used for the reliable fabrication of high-quality thin metal films. To meet these objectives, a multiscale model based on the primary physical phenomena gas flow, plasma discharge, sputtering and atom transport has been assembled to explore the RF diode deposition of thin metal films. The resulting multiscale input-output model is capable of predicting the thin-film deposition rate, the sputtered metal atoms’ energy and angular distribution, both upon emission at the target and just prior to deposition at the substrate, and their sensitivity to deposition conditions such as power, working gas type, pressure, gas temperature, and electrode spacing. The metal atom flux incident upon the substrate is then used as an input to atom assembly models to deduce surface morphology and film structure. The deduced performance measures of the RF diode deposition process, such as wafer-scale uniformity of the film thickness and surface roughness of the film, in turn, influence device characteristics that utilize these films, e.g. the saturation magnetic field, and magnetoresistance of giant magnetoresistive multilayer [1].

A methodology (based on the proper orthogonal decomposition and approximate inertial manifolds) is proposed for obtaining low order dynamic models of rapid thermal processing (RTP) systems. These nonlinear models are designed to retain the physical understanding of the RTP system dynamics and their dependence on critical parameters, making them an attractive choice for use in developing more advanced and intelligent controllers

General finite element models of single wafer systems that describe the dynamics of both solids and gas flow are usually unsuited for quick design iterations, because of computational complexity. In this paper a more efficient alternative is proposed. Solids can be modeled efficiently and with sufficient accuracy using a finite volume approach, and the gas flow can be modeled by finite element CFD software. The gas flow model can then be coupled to the solids model by iterating on the heat transfer coefficients at the interface.

This paper is the second of two papers describing the Virtual Concurrent Design Tool (VCDT), a GUI-based software that facilitates integrated design of a RTP chamber and the associated temperature control system, and describes the thermal modeling method. The VCDT is implemented within the framework of Integrated Systems' MATRTX(X) product family which includes graphical modeling, simulation, and control design software. The VCDT allows one to perform rapid, get accurate, dynamic heat transfer simulations suitable for model-based feedback control design. This tool models two-dimensional (axisymmetric) geometries using either the Control Volume-Finite Element Method, or a purely Finite Element Method for triangular meshes. The radiative exchange factors are calculated using a Monte-Carlo method. The simulations yield transient temperature profiles for wafer, window, guard-ring, etc., during the process cycle.

Processes described by partial differential equations (PPEs) such as thermal models of RTP reactors are frequently discretized into a high-order lumped model for the purpose of simulation. The advantage of using a lumped model lies in the fact that it corresponds with a system of ordinary differential equations (ODEs). The high order of the lumped model can still be prohibitive for practical applications such as control design which makes model reduction necessary. We have applied the "method of snapshots" (also called: Proper Orthogonal Decomposition method) for the model reduction of a generic RTP simulation model. The snapshot method is based on principal component analysis and projection of the ODEs on a lower-dimensional space of basis functions. We describe how this method applies to the RTP model and demonstrate how the model order can be reduced by a factor 4 without essential loss of accuracy over a wide operating range.

The proper orthogonal decomposition, also called snapshot method, is a nonlinear model order reduction method where reduction of the size of the state space is achieved using a singular value decomposition of a matrix of snapshots of the state vector. This method has been shown to work well for a simple lumped physical model of a rapid thermal processing chamber. Although a substantial reduction of the number of states is achieved, some numerical computations still need to be performed in the high-dimensional state which is computationally expensive. In this paper we demonstrate how this can be avoided using aggregation of terms, resulting in a significant model simulation speed improvement.

Rapid thermal processing (RTP) is becoming increasingly more important in semiconductor wafer fabrication. A nonlinear physical model for a generic RTP system is described. This generic RTP system is representative of the state-of-the-art RTP systems. A low-order nonlinear model is developed. A model-based LQG controller is designed for the low-order model which successfully controls the full-order nonlinear simulation model.

A radiation source with high output in both the visible and infrared spectral ranges has been developed, and its operating parameters are described. The hot element, a carbon composite board, is simple to fabricate as well as to operate. The source has been compared to both a tungsten strip lamp and a Nernst glower. For applications where both the visible and infrared ranges are of interest, this source allows for simplified experimental design.

Fly ash particles, which are predominantly spherical and glassy, are produced by melting of the mineral inclusions in the coal during combustion. Particle diameters can range from sub-micrometer (micron or {mu}m) to greater than 100 {mu}m. The size distribution of fly ash is needed to determine its role in the radiation transfer process in pulverized coal combustors. The Coulter Multisizer is an useful instrument for sizing powders with a broad size distribution. A single Multisizer orifice can size particles only within a specific size range limited at the lower end to a few percent of orifice diameter by sensitivity and at the upper end by increasing non-linearity of the signal-volume relation. A scheme for combining data obtained using orifices of different diameters is described. The manufacturers state that the smallest particle which can be sized accurately is nominally 2% of the diameter of the orifice. However, it was found that the data for particles less than 4% of the orifice diameter were not reliable. In order to use the smaller orifices, the larger particles have to be removed from the sample. A wet-sieving apparatus, designed for accurate separation of the particles by size, is described. A log-normal distribution function, truncated outside the measurement limits, fits the size distribution data well. Size parameters for fly ashes of six representative US coals are presented.

Spectrally resolved data for the real part, n(λ) of the complex refractive index, n̂ = n +ik, of bromoform (tribromomethane, CHBr3) at room temperature (298 K) in the wavelength range 1–13 μm are presented. The measurements were made using the near-normal reflectance technique. The accuracy of the method was confirmed by comparing measured values of n(λ) of water with available data in the literature. For bromoform, n(λ) is found to decrease gradually from 1.58 to 1.51 over this wavelength range, except in the region of anomalous dispersion near absorption bands at 3.3 and 8.7 μm. A complete infrared window for extinction measurements on suspended particulates can be obtained using CCl4 in the spectral range 1–6 μm, CHBr3 in the ranges 6.0–7.4 μm and 11–13 μm, and CS2 in the range 7.4–11.0 μm. The data for n(λ) of CCl4 in the range 1–9 μm, and those for CS2 in the range 7.4–11.0 μm, obtained from reflectance measurements, compare favorably with data available in the literature.

Run-to-run control using static linear models is examined. Conditions are presented for stability, (statistical) performance, and robustness using the standard control theory. A simulation example shows the usefulness of the method applied to a rapid thermal oxidation process