Ahybrid approach combining experimental and simulation studies was used for model development. Several sets of experiments were conducted to investiga

Transcription

1 ABSTRACT Title of Dissertation: MODELING AND SIMULATION OF A TUNGSTEN CHEMICAL VAPOR DEPOSITION REACTOR Hsiao-Yung Chang, Doctor of Philosophy, 2000 Dissertation directed by: Assistant Professor Raymond A. Adomaitis Department of Chemical Engineering Chemical vapor deposition ècvdè processes are widely used in semiconductor device fabrication to deposit thin ælms of electronic materials. Physically based CVD modeling and simulation methods have been adopted for reactor design and process optimization applications to satisfy the increasingly strigent processing requirements. In this research, an ULVAC ERA-1000 selective tungsten chemical vapor deposition system located at the University of Maryland was studied where a temperature diæerence as large as 120 o C between the system wafer temperature reading and the thermocouple instrumented wafer measurement was found during the manual processing mode. The goal of this research was to develop a simpliæed, but accurate, three-dimensional transport model that is capable of describing the observed reactor behavior.

2 Ahybrid approach combining experimental and simulation studies was used for model development. Several sets of experiments were conducted to investigate the eæects of process parameters on wafer temperature. A three-dimensional gas æow and temperature model was developed and used to compute the energy transferred across the gasèwafer interface. System dependent heat transfer parameters were formulated as a nonlinear parameter estimation problem and identiæed using experimental measurements. Good agreement was found between the steady-state wafer temperature predictions and experimental data at various gas compositions, and the wafer temperature dynamics was successfully predicted using a temperature model considering the energy exchanges between the thermocouple, wafer, and showerhead.

3 MODELING AND SIMULATION OF A TUNGSTEN CHEMICAL VAPOR DEPOSITION REACTOR by Hsiao-Yung Chang Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulællment of the requirements for the degree of Doctor of Philosophy 2000 Advisory Committee: Assistant Professor Raymond A. Adomaitis, ChairmanèAdvisor Professor James W. Gentry Associate Professor Michael T. Harris Assistant Professor John N. Kidder, Jr. Associate Professor Evanghelos Zaæriou

4 cæ Copyright by Hsiao-Yung Chang 2000

5 Dedication To my parents and sisters ii

6 Acknowledgements Coming into the end of another phase in my life, it is only appropriate to think and acknowledge all the people who gave me the knowledge and support to pursue and complete another goal in my life. First of all, I would like to express my appreciation and gratitude to my advisor, Dr. Raymond A. Adomaitis. It has been my privilege to study under his direction and I thank him for providing me his invaluable and thoughtful guidance, encouragement, and expertise on every subject that arose. Iwould like to thank Drs. Gary W. Rubloæ and John N. Kidder, Jr. for their generous support on my experimental work and their advice and expertise on a variety of topics. I am grateful to all of my teachers. In particular, I would liketothank Dr. Evanghelos Zaæriou for his fascinating lectures, Drs. James W. iii

7 Gentry and Michael T. Harris for serving on my advisory committee and providing many valuable comments. I have been fortunate to work with many talented and interesting colleagues. Iwould like to thank Dr. Yi-hung Lin, Jiefei Huang, and Ashish Suresh Sabadra for their eæorts in MWRtools development and many useful discussions on the modeling and solution issues; Dr. Theodosia Gougousi, Laurent Henn-Lecordier, and Yiheng Xu for their technical support during the experimental work. Ihave been blessed to receive the constant love, support, understanding, and encouragement of my parents, sisters, and friends. This accomplishments is theirs to share with me. iv

8 Table of Contents List of Tables viii List of Figures x 1 Introduction 1 2 Chemical Vapor Deposition Reactor Mathematical Modeling Fundamentals of Chemical Vapor Deposition Processes : : : : : : Rapid Thermal Chemical Vapor Deposition : : : : : : : : Tungsten Chemical Vapor Deposition : : : : : : : : : : : : Tungsten Chemical Vapor Deposition Chemical Mechanisms Mathematical Modeling Overview of CVD Systems : : : : : : : : CVD Transport Modeling : : : : : : : : : : : : : : : : : : Literature Review : : : : : : : : : : : : : : : : : : : : : : : CVD Modeling Using Commercial CFD Software : : : : : General Modeling Assumptions : : : : : : : : : : : : : : : Gas Phase Transport Model : : : : : : : : : : : : : : : : : Wafer Thermal Dynamics Model : : : : : : : : : : : : : : ULVAC Selective Tungsten Chemical Vapor Deposition Cluster Tool : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 33 v

9 2.4 ULVAC W CVD Transport Model Formulation : : : : : : : : : : Gas Flow Field : : : : : : : : : : : : : : : : : : : : : : : : Gas Temperature Field : : : : : : : : : : : : : : : : : : : : Wafer Thermal Dynamics : : : : : : : : : : : : : : : : : : Showerhead Thermal Dynamics : : : : : : : : : : : : : : : Thermocouple Thermal Dynamics : : : : : : : : : : : : : : Gasous Reactants and Wafer Physical Properties : : : : : Dimensionless Equations : : : : : : : : : : : : : : : : : : : : : : : Gas Phase Flow and Energy Equations : : : : : : : : : : : Wafer and Showerhead Energy Balance Equations : : : : : 55 3 Experimental Studies Data Acquisition in the ULVAC ERA-1000 System : : : : : : : : Instrumented Thermocouple Wafer and Computer Boards LabVIEW Data Acquisition Interface : : : : : : : : : : : : Lamp Control Signal Correction : : : : : : : : : : : : : : : : : : : Inæuence of Gas Composition on Wafer Temperature : : : : : : : Wafer Thermal Dynamics : : : : : : : : : : : : : : : : : : : : : : Inæuence of the Chamber Pressure : : : : : : : : : : : : : Deposition Processing Window : : : : : : : : : : : : : : : Wafer Temperature Response of Single and Multiple Heating Cycles : : : : : : : : : : : : : : : : : : : : : : : : : : : 80 4 Numerical Solution Procedures Introduction to Method of Weighted Residuals : : : : : : : : : : : MWRtools : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 94 vi

10 4.3 Introduction to Nonlinear Least-Squares Parameter Estimation : : Nonlinear Least Squares Problem Formulation and the Newton Method : : : : : : : : : : : : : : : : : : : : : : : : The Gauss-Newton Method : : : : : : : : : : : : : : : : : Simulation Results Inæuence of Gas Composition on Steady-State Wafer Temperature Parameter Estimation : : : : : : : : : : : : : : : : : : : : Solution Procedure : : : : : : : : : : : : : : : : : : : : : : Model Validation and Discussion : : : : : : : : : : : : : : Wafer Thermal Dynamical Simulation : : : : : : : : : : : : : : : : Single Equation Wafer Temperature Model : : : : : : : : : The Three Equation Temperature Simulator : : : : : : : : Model Validation and Simulation Results : : : : : : : : : : Conclusions and Future Work Concluding Remarks : : : : : : : : : : : : : : : : : : : : : : : : : Suggested Future Work : : : : : : : : : : : : : : : : : : : : : : : : 134 Bibliography 136 vii

11 List of Tables 2.1 Important dimensionless groups and their typical range in low pressure CVD èlpcvdè reactors. : : : : : : : : : : : : : : : : : Summary of the dimensionless variables used in the transport model. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Deænitions and values of physical properties and dimensionless parameters evaluated at 1 atm, H 2 =N 2 =40=10sccm, T amb = 25, T w =304:3, T sh =150,and T f =60 o C. : : : : : : : : : : : : : : : Deænitions of dimensionless parameters used in wafer, showerhead, and thermocouple modeling equations. : : : : : : : : : : : Values of the lamp current and voltage and the lamp control signal. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Values of the ætting coeæcients c i in Equation è3.1è. : : : : : : : List of current MWRtools functions used for initialization, collocation methods, and solution reconstruction. : : : : : : : : : : : : List of the MWR functions especially designed for solving problems deæned in higher dimensions. : : : : : : : : : : : : : : : : : : List of classes in MWRtools and their corresponding methods. : : 98 viii

12 5.1 A list of model parameter values, their estimated values or range, and the ænal values obtained from the identiæcation procedure. : A list of identiæed model parameter values. : : : : : : : : : : : : 125 ix

13 List of Figures 1.1 Comparison of ULVAC CVD system adjusted wafer temperature and TC instrumented wafer measurements. : : : : : : : : : : : : Schematic illustration of modeling approach. : : : : : : : : : : : Top view schematic ULVAC cluster tool. : : : : : : : : : : : : : : Sketch of the Tungsten CVD reactor system. : : : : : : : : : : : ULVAC W CVD reactor operating and control structure. : : : : The default ULVAC look-up table correcting functions plotted as the ULVAC thermocouple measurements against the adjusted wafer temperature at ètopè 0.8 Torr and èbottomè 0.4 Torr total chamber pressure in pure H 2 or Ar gas. R1 and R2 represent the correcting function for reactors 1and2, respectively. : : : : : : : The default ULVAC look-up table correcting functions plotted as the ULVAC thermocouple measurements against the adjusted wafer temperature at ètopè 0.17 Torr and èbottomè 0.1 Torr total chamber pressure in pure H 2 or Ar gas. R1 and R2 represent the correcting function for reactors 1and2, respectively. : : : : : : : 39 x

14 2.7 The default ULVAC look-up table correcting functions plotted as the ULVAC thermocouple measurements against the adjusted wafer temperature at high vacuum condition 1.8æ10,6 Torr total chamber pressure in pure H 2 or Ar gas. R1 and R2 represent the correcting function for reactors 1and2, respectively. : : : : : : : Geometry of the heating lamp and wafer. : : : : : : : : : : : : : Radial variation of the lamp radiant heat æux at the wafer surface at full lamp power. : : : : : : : : : : : : : : : : : : : : : : : : : : ULVAC CVD reactor data acquisition system. : : : : : : : : : : The top and side views of the test wafer position with thermocouple positions marked. : : : : : : : : : : : : : : : : : : : : : : LabVIEW data acquisition interface window. : : : : : : : : : : : Relationship of the ULVAC wafer temperature ètopè and the steadystate lamp power control signal èbottomè at 0.2 Torr total chamber pressure and 100 sccm N 2. : : : : : : : : : : : : : : : : : : : Relationship of the lamp control signal and the true lamp power ècomputed by the product of lamp current and voltageè. : : : : : The temperature response of the wafer to reactant gas composition variations. : : : : : : : : : : : : : : : : : : : : : : : : : : : : The temperature response of the wafer to reactant gas æow rate and composition changes. : : : : : : : : : : : : : : : : : : : : : : The temperature trajectory of a slightly shifted wafer during a process cycle at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : 73 xi

15 3.9 Comparison of the wafer temperature in the ærst æve minutes at diæerent gas composition and 0.5 Torr. Dash-dotted curve èfrom Figure 3.15è was found using H 2 èn 2 = 40è10 sccm and the solid curves èfrom Figure 3.6è correspond to 100 sccm H 2. : : : : : : : The ULVAC adjusted wafer temperature and the æve thermocouple measurements of the instrumented wafer during a process cycle at ètopè 0.17 Torr and èbottomè 0.5 Torr total chamber pressure in 2000 sccm H 2. : : : : : : : : : : : : : : : : : : : : : : : : : : : Comparison of wafer temperature at diæerent chamber pressure from Figure : : : : : : : : : : : : : : : : : : : : : : : : : : : Process recipe found by adjusting initial heating sequence at 0.2 Torr and N 2 = 100 sccm. : : : : : : : : : : : : : : : : : : : : : : Process recipe ètopè and corresponding lamp power signal èbottomè found by adjusting initial heating sequence at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : : : : : : : : : : : : : : : : : : The wafer temperature responses to ULVAC temperature setpoints 450 o C at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : The wafer temperature responses to ULVAC temperature setpoints 500 o C at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : The wafer temperature responses to ULVAC temperature setpoints 550 o C at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : ètopè The TC wafer temperature responses to three diæerenttemperature setpoints at 0.5 Torr and H 2 èn 2 = 40è10 sccm. èbottomè The temperature trajectories of each thermocouple at the beginning of the soak phase for the SP: 500 o C experiment. : : : 85 xii

16 3.18 TheTCwafer temperature responses during the ærst two minutes to three diæerent temperature setpoints ètopè and the corresponding lamp power signal èbottomè at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : The wafer temperature identiæcation trajectory ètopè and the long term temperature drift comparison èbottomè at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : : : : : : : : : : : : : : : : : : : : The wafer temperature responses to multiple heating cycles for model validation at 0.5 Torr and H 2 èn 2 = 40è10 sccm. : : : : : èaè Gas æow æeld and temperature contours where each contour represents 50 K temperature diæerence. èbè Waferègas heat transfer rate at centerline of the reactor chamber. Simulation performed at N 2 =100sccm and 500 mt orr. ècè Diæerence of heat æux across waferègas boundary between N 2 = 100 and 60 sccm, where æq = q N2 =100, q N2 =60. : : : : : : : : : : : : : : : : : : : : Wafer temperature from experimental data èsolid curves with circles at data pointsè and model prediction èdot-dash curves and squaresè. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Contributions of individual heat transfer mechanisms for èaè interior region, and èbè region outside the susceptor. : : : : : : : : Comparison of the wafer temperature between the experimental measurements T w;exp èfrom Figure 3.19è and the single equation nonlinear wafer temperature model predictions T w;1 ;T w;2 and T w;3 foramultiple heating cycles process. : : : : : : : : : : : : : : : : 120 xiii

17 5.5 The wafer temperature èthermocouplesè fast response to the lamp power variations during setpoint changes. Data are taken from Figure : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : The wafer temperature prediction from the identiæed model. Results are compared with experimental data shown in Figure The wafer temperature prediction from the identiæed model. Results are compared with experimental data shown in Figure The wafer temperature prediction from the identiæed model. Results are compared with experimental data shown in Figure The wafer temperature prediction from the identiæed model. Results are compared with experimental data shown in Figure The wafer temperature prediction from the identiæed model. Results are compared with experimental data shown in Figure The wafer temperature prediction from the identiæed model for processing window shown in Figure : : : : : : : : : : : : : 131 xiv

18 MODELING AND SIMULATION OF A TUNGSTEN CHEMICAL VAPOR DEPOSITION REACTOR Hsiao-Yung Chang August 1, 2000 This comment page is not part of the dissertation. Typeset by L A TEX using the dissertation style by Pablo A. Straub, University of Maryland. 0

19 Chapter 1 Introduction Chemical vapor deposition ècvdè is a technique extensively used in the semiconductor industry to form nonvolatile solid ælms on a substrate from chemical reactions fed by vapor phase reactants. Compared with other deposition techniques, CVD oæers good control of ælm structure and composition, high growth rates, excellent uniformity and conformality, and can deposit a wide variety of materials: doped and undoped silicon oxide, polysilicon, epitaxial silicon, silicide, silicon nitride, tungsten, titanium, copper, and aluminum when manufacturing silicon-based integrated circuits. Some III-V and II-VI compounds and more complex opto-electronic compounds can also be processed using CVD. These versatile processing properties and the wide selection of materials make the CVD techniques useful in many manufacturing steps in both the front-end devices and back-end interconnect processes. As the dimensions of the microelectronic devices decreases and the diameter of the wafers increase, to ensure the quality of the deposited ælms, e.g., the thickness, composition, and microstructure, be reproducible and uniform within wafer itself and from wafer to wafer in a processing batch is a critical manufacturing 1

20 requirement. To meet the more stringent requirements imposed by continually shrinking device sizes, physically based process modeling and simulation methods have been gradually adopted as both a design tool in the development of semiconductor manufacturing equipment ë1ë and a platform for process optimization of the existing systems using experimentally validated physical models ë2ë. The value of process modeling is especially underscored by its broad acceptance ë3, 4, 5, 6, 7, 8ë in CVD control systems design or improvement. Many research studies have focused on modeling the equipment and process transport phenomena in diæerent type of CVD systems, as those summarized in Kleijn ë9ë, Jensen et. al. ë10ë, and Badgwell et. al. ë11ë. Although some approaches, such as thermodynamic equilibrium ë12ë, particle transport modeling èptmè ë13ë, and the Monte Carlo èmcè simulations on trench step coverage ë14, 15ë, are employed for various simulation purposes, most of the modeling studies are based on the macroscopic transport phenomena in the diæerent types of the CVD reactors. In addition to studying the process parameters on reactor performance, chamber design, scale up, and process control applications, these ærst-principle CVD equipment models can also be used to help understand the process physics by providing the information on various transport and reaction mechanisms. With the help of the development of computational æuid dynamics ècfdè, these ærst-principle transport models are becoming more comprehensive and accurate. However, in order to reach the best predictive results, the computational eæciency is sacriæced by ænely discretizing the model equations with either æniteelement èfemè ë16ë, or ænite-volume èfvmè ë17ë, or ænite-diæerence èfdmè ë18ë methods. Because these discretization schemes use spatially localized basis func- 2

21 tions which determine the corresponding numerical values of the equations only at each separate local basis, obtaining acceptable resolution of simulation results requires a large number of basis functions which increases the total computing time. Motivation and Goals of this Research In this research, we focus on the ULVAC ERA-1000 selective tungsten chemical vapor deposition cluster tool that is located at the University of Maryland, College Park. This CVD system is designed for selectively depositing tungsten into the via or contact holes that connect the metal interconnection layers of the integrated circuits èicsè. The cluster tool has two production scale, cold-wall, horizontal single-wafer reactors in addition to the load-lock and buæer chambers and is capable to process 8inch wafers. A data acquisition system was built to collect the in-situ wafer temperature measured by an instrumented wafer and other process variables. Experimental results showed a temperature diæerence between the ULVAC system wafer temperature readings and the thermocouple wafer measurements as large as 150 o C during a process cycle in the IèO manual operation mode èsee Figure 1.1è. Instead of attempting to model the overall behavior of this system by considering all constituent physical mechanisms, the goal of this research was to develop a simpliæed but accurate, multi-dimensional transport model that is capable of describing the observed reactor behavior and can be used to improve the temperature control system. Toachieve quantitatively accurate predictions that can explain the true wafer 3

22 Temp reading from ULVAC Temp ( o C) Temp measured from TC wafer Time (min) Figure 1.1: Comparison of ULVAC CVD system adjusted wafer temperature and TC instrumented wafer measurements. temperature responses, a hybrid experimental-model simulation approach was used to explore heat transfer phenomena during the CVD process. Several sets of experiments were used to study the eæects of key process parameters such as wafer temperature setpoint and reactant gas compositions on wafer temperature response, and the modeling terms were adjusted accordingly to those experimental ændings. Both the steady-state and dynamic experiments were used to investigate the possible transport mechanisms because the gas phase eæects such as the thermal conductionèconvection at gasèwafer interface were relatively small when compared with the radiative energy transfer between the chamber components inside the reactor. Numerical simulations were then performed to test diæerent model structures 4

23 and the system dependent parameter values were estimated using the experimental data. If the identiæed parameter values did not satisfy the theoretical constraints or were found to diæer signiæcantly from the results reported in similar studies, modiæcations of the model were made and this experimental-model identiæcation based model development procedure was repeated. The weighted residual methods based on globally deæned trial functions were used to solve the three-dimensional gas æow and temperature æeld modeling equations. The MWRtools, a MATLAB based toolbox that collects the common numerical computing elements to form a one-to-one correspondence with the methods of weighted residual solution steps, was developed and implemented for both numerical simulation and parameter estimation. Scope and Contributions In summary, the scope and original contributions of this thesis research are listed as follows, 1. A systematic approach combining experimental and numerical simulation methods to build a chemical vapor reactor transport model was developed; 2. To facilitate the experimental studies, a data acquisition system was built to collect in-situ wafer temperature and other process information; 3. A method to estimate system dependent heat transfer parameters was established and the identiæed parameter values were validated with published data and transport model simulation results; 5

24 4. The most important energy transport mechanisms were identiæed through diæerent experimental designs and numerical simulations; 5. The method of weighted residuals based on global basis functions was applied to the CVD simulations as an alternative to FEM, FVM, and FDM methods. The simplicity of the global projection methods allowed researchers to focus on identifying the most important heat transfer modes; 6. A dynamic wafer temperature simulator was built that uses only the lamp power control signals to predict the wafer temperature trajectory. The simulator was tested on diæerent process recipes and showed good agreements with the experimental data. Organization of the dissertation This thesis is organized as follows. Chapter 2 The chemical vapor deposition mechanisms and the tungsten CVD kinetic model are introduced. The ULVAC CVD system as well as its operation procedure and control structure is also presented. The CVD modeling literature is reviewed and the formulation of the transport model developed in this research is addressed. Chapter 3 The data acquisition system built for the ULVAC CVD system is described and experimental results of the wafer temperature responses to diæerent process parameters are presented. Chapter 4 Mathematical preliminaries for solving the modeling equations and estimating the parameter values from experimental data are provided. A 6

25 brief review of the MWRtools is also given. Chapter 5 Simulation results of steady-state gas æow and temperature æelds are provided. Predictions of the wafer temperature response to diæerent gas compositions and wafer temperature dynamics are presented and compared with experimental results. Chapter 6 The thesis research contributions are concluded and the future research opportunities that can be built on this work are suggested. 7

26 Chapter 2 Chemical Vapor Deposition Reactor Mathematical Modeling This chapter addresses the problem of developing a high-ædelity, three-dimensional transport model for predicting the equipment process status of a commercial cold-wall, single-wafer CVD reactor used for depositing thin tungsten ælms on silicon wafer. This problem is studied as a joint project between Dr. Raymond A. Adomaitis of the Department of Chemical Engineering and Institute for Systems Research èisrè and Drs. Gary W. Rubloæ and John N. Kidder, Jr. of the Department of Materials and Nuclear Engineering and ISR, at the University of Maryland, College Park. The overall project objective is modeling and control applications of the ULVAC ERA-1000 selective tungsten CVD cluster tool. The fundamentals of chemical vapor deposition are introduced in Section 2.1 with special emphasis on the single-wafer rapid thermal CVD process. Tungsten CVD reaction kinetics and deposition rate expression are also presented. The overview of the general transport modeling of CVD systems is then given in Section 2.2 followed by the descriptions of the ULVAC tungsten CVD reactor in 8

27 Section 2.3. The overall process equipment model for ULVAC system is detailed in Section 2.4, including the correlations used for computing the material thermal and transport properties. In Section 2.5, the dimensionless form of the modeling equations are developed. 2.1 Fundamentals of Chemical Vapor Deposition Processes In chemical deposition processes, thin ælms are formed on a substrate from the gas phase by chemical reactions. Vapor reactants are fed into the reactor chamber at a controlled composition and the reactions are initiated after receiving suæcient energy from thermal, plasma, or other energy sources. Because the involvement ofthechemical reactions, CVD processes are distinguished from other physical deposition methods such as sputtering, sublimation, and evaporation. From a chemical engineering point of view, a CVD process involves the combination of æuid transport phenomena and chemical reaction kinetic mechanisms, especially in the gas phase near the gasèwafer interface and on the wafer surface. The major transport and reaction sequences during a deposition process are summarized in the following steps, 1. Convective and diæusive transport of reactants, reactive intermediates, andèor byproducts from bulk gas phase to the gas boundary layer near the wafer surface; 2. Convective and diæusive transport bringing gas species from the gas phase boundary layer to the wafer surface; 3. Adsorption andèor chemisorption of those species on the wafer surface, often after some migration on the surface; 9

28 4. Heterogeneous surface reactions to form the desired thin ælms, primarily initiated by the high wafer temperature; 5. Desorption of the gas phase products; 6. Convective and diæusive transport of gaseous products from wafer surface to gas boundary layer and then from boundary layer to bulk gas phase. Due to the wide variety of deposited materials èconductors, insulators, and semiconductorsè and thin ælm requirements èconformality, planarization, and high growth rateè, many diæerenttypes of CVD reactors and processes have been developed. For example, the reactor operating pressure ranges from one atmosphere èapcvdè to ultra high vacuum conditions è10,9 Torrè in UHVèCVD; likewise, the deposition temperature measures from 250 o C for plasma enhanced deposition èpecvdè of silicon nitride passivation layers to 1100 o C for epitaxial silicon ælms ë19ë. Other issues, such as particle contamination and throughput requirements also change the reactor design from hot-wall to cold-wall, and batch to single wafer CVD reactors, respectively. However, as larger wafer size and the more stringent fabrication demands are continuously implemented to improve proæts and provide faster IC chips, the manufacturing technology shifts towards using single-wafer cluster tools that have the ability toreduce thermal budget. The single-wafer rapid thermal processing èrtpè technology is particularly suitable for those purposes and is increasingly accepted and used in the semiconductor manufacturing industry. The research presented in this thesis focuses on a commercial lamp-heating, single wafer chemical vapor deposition system which makes it similar to a rapid thermal CVD èrtcvdè reactor, thus it is useful to review the RTP processes. Additional information on the RTP pro- 10

29 cesses can be found in the next section; a general overview of the CVD processes can be found in Sherman ë20ë and Sivaram ë21ë Rapid Thermal Chemical Vapor Deposition A rapid thermal chemical vapor deposition reactor employing a single wafer technique èswtè generally uses a smaller deposition chamber designed to achieve a short residence time of the process gases. The SWT also introduces the possibility of sequential processing such as annealing, oxidation, and deposition in the same reactor, or in connected multiple processing chambers èa cluster toolè where the wafer can be transferred between chambers in a modest vacuum environment ë22ë. In order to compete with the throughput of conventional multi-wafer reactor systems, RTP systems use radiant lamp heating with reactor designs of stainless steel or aluminum chamber walls that reæect the optical radiation for wafer illumination and high heating rates. Combining the SWT technique and the cold-wall, low-pressure operating conditions, the contamination problem encountered in batch CVD processes are largely reduced in RTP reactors. Several equipment and process control issues are actively studied in RTCVD systems. A number of challenging aspects of these problems can be analyzed from a modeling point: for example, the cold wall process exhibits strong thermal gradients within the gas phase that can lead to signiæcant changes in æow patterns, mass transfer rates, and gas mixture physical properties. Moreover, due to the radiation heat transfer domination in RTP reactors, the wafer pattern and surface roughness can result in diæerent emissivities across the wafer and change the deposited ælm thickness signiæcantly ë23ë. The lack ofproven in-situ, real-time temperature and ælm thickness measurement technologies ë24ë makes 11

30 the wafer temperature control more complex and diæcult. Further details of these equipment and control issues can be found in Chapter 4 of Chang and Sze ë19ë and other references ë25, 26, 27, 28ë Tungsten Chemical Vapor Deposition The metalization, depositing and patterning of metal ælms, has become a critical aspect of semiconductor technology as larger chip size and higher packing density are used to manufacturing advanced integrated circuits èicsè. The interconnect metal layers provide long-distance electrical transport between the active areas of the chip and the communication with the outside world. The materials used in metalization èe.g., metals, contact diæusion barrierè thus should have low resistivity to permit high speed and limited power dissipation, good adherence to underlying materials such as silicon, non-reactive to the adjacent ælms or oxidizing ambient, and be stable enough that can withstand the following process steps of high-temperature treatments or chemically reactive environments. Tungsten, due to its favorable properties, is selected over the aluminum as the material to æll the contact holes, connecting the source or drain regions of transistors and interconnect layer, or via holes which connect multilevel interconnection layers. Tungsten has another major advantage over the other materials in the available deposition technique. Tungsten CVD uses a relative low process temperature so it will not degrade the previously formed device and provides good step coverage of the contact or via holes. The deposition rate of tungsten CVD is also fast enough to be economically feasible in industry. 12

31 2.1.3 Tungsten Chemical Vapor Deposition Chemical Mechanisms Deposition of tungsten ælms on silicon surface can be achieved either through hydrogen èh 2 è or silane èsih 4 è reduction of tungsten hexaæuoride èwf 6 è. By depositing a metal nucleation layer such as TiN on the entire wafer, tungsten can be blanket-deposited on the wafer and contact or via holes using a hydrogen reduction pathway at the temperature range o C ë19, 29ë. This process has the advantages of achieving high step coverage and good across-wafer conformality. Subsequent etch-back steps using chemical-mechanical polishing ècmpè or reactive ion eatching èrieè are required for planarization to ensure good interconnect metal ècu, Alè step coverage ë19ë. Tungsten can also been deposited selectively using the silane reduction of WF 6, where W is deposited on Si surface and not on SiO 2 insulator layer due to the reactivity diæerence at wafer temperature lower than 400 o C ë19ë. This deposition process does not require any metal liner such as TiN or TiW, or etch back steps for the plug processes ë29ë. However, the selectivity loss due to spurious nucleation and the following W growth on SiO 2 surface, as well as the diæculty to æll holes with diæerent depths within the wafer, are still major issues continuously under study ë19, 29ë. Currently, acombination of these two processes is used in industry for contact or via hole ælling. Silane is initially introduced without any æow of WF 6 to initiate the deposition of avery thin Si pre-nucleation layer, followed by a SiH 4 + WF 6 silane reduction nucleation process and then the high-rate H 2 + WF 6 hydrogen reduction deposition to æll via or contact holes. CMP steps are used afterward for global planarization ë19ë. An excellent review of the materials and processing parameters for the tungsten plug processes can be found in Ireland 13

32 ë30ë. Hydrogen Reduction of WF 6 In the hydrogen reduction reaction pathway currently used in the research in the ULVAC CVD system at the University of Maryland ë31ë, the wafer silicon surface provides the initial nucleation layer for the formation of W seed layer, 3Si +2WF 6,! 2W èsè+3sif 4 and 3Si + WF 6,! W èsè+3sif 2 2Si + WF 6 + H 2,! W èsè+3sihf 3 : This W seed layer provides the active sites for the H 2 reduction of the WF 6 through adsorption and removal of F-atom from the surface in the form of volatile HF product, W æ èsè+wf 6,! WF æ 6 + W èsè WF æ 6 +3H 2,! W èsè æ +6HF where æ denotes the activated surface sites. The hydrogen reduction process is usually performed at process conditions of o C and Torr total pressure ë32ë. In the chemical reaction kinetics rate-limited operation region, used in most industrial deposition processes due to the superior conformality produced under these conditions, the deposition rate shows square root dependence on H 2 partial pressure and zero-order dependence on WF 6 partial pressure ë29, 32ë. The empirical rate expression can be expressed as R H2 = k 0 P 0:5 H 2 P 0 WF 6 exp ç,ea ç RT è2.1è 14

33 where k 0 is the frequency coeæcient, P H2 and P WF6 are the partial pressure of each species, Ea is the activation energy and R is the gas constant. Kleijn et. al. ë17ë showed that the assumption of a zero order dependence on WF 6 partial pressure is still valid even when the WF 6 partial pressure is as low as 7.5æ10,3 Torr. The reported activation energy varies from 69 to 73 kjèmole in the temperature and pressure ranges of 270 to 470 o C and 0.2 to 10 Torr ë33, 34ë, respectively. Silane Reduction of WF 6 The silane reduction process ë19, 29, 35ë starts with silicon reduction step caused by WF 6, 2WF 6 +3Sièsè,! 2W èsè+3sif 4 : This reaction is self-limited in that it stops when the atomic silicon disappears from the wafer surface. Two competing kinetic mechanisms are found at common deposition conditions è150 to 300 o C and 40 to 50 Torrè: 2WF 6 +3SiH 4,! 2W èsè+3sif 4 +6H 2 WF 6 +2SiH 4,! W èsè+2sihf 3 +3H 2 : In the range of deposition temperatures of 145 to 395 o C, Ammerlaan ë32ë reports non-linear Arrhenius plots of the silane reduction process with the maximum rates observed near 300 o C. The author also ænds the kinetics are determined by the partial pressure ratio of silane and tungsten hexaæouride P SiH4 =P WF6 : æ For P SiH4 =P WF6 é 0:3, a ærst-order dependence in silane partial pressure P SiH4 and a small negative order dependence in tungsten hexaæouride par- 15

34 tial pressure P WF6 are found giving R SiH4 = k 1 P 1:06 SiH 4 P WF,0:16 6 P 0 H 2 exp ç,ea ç : RT æ For 0:5 ép SiH4 =P WF6 é 1, the dependence changes to almost second order in P SiH4 and minus ærst-order in P WF6, giving R SiH4 = k 2 P 1:80 SiH 4 P WF,0:94 6 P 0 H 2 exp ç,ea ç : RT Other researchers ë36, 37ë did not investigate the ratio of partial pressures and reported rate expression model with a ærst-order in the silane partial pressure P SiH4 and a zero or negative order in the tungsten hexaæouride partial pressure P WF6. However, measured activation energy values range between 8 and 50 kjèmole ë36, 37ë from diæerent reports. 2.2 Mathematical Modeling Overview of CVD Systems In this section, we will discuss the necessary modeling components and solution steps for developing a complete CVD equipment-process model, and will give a short survey of the published CVD equipment modeling studies. In the subsequent subsection, use of the currently available commercial computational æuid dynamic ècfdè software suitable for CVD modeling is discussed. An overview of the general transport equations of the gas phase and wafer for single wafer systems will be described in the following subsections. The other simulation components such as physical properties and a chamber heating model, will be discussed in Section 2.4. Further simpliæcations of the transport equations and the appropriate boundary conditions for the ULVAC W CVD reactor modeling are also addressed in Section

35 2.2.1 CVD Transport Modeling A general chemical vapor deposition simulation model has several building blocks as illustrated in Figure 2.1. Generally, the details of the reactor geometry and dimensions as well as processing conditions such as inlet gas æow rates, wafer temperature setpoints, chamber pressure, and heating lamp output eæciency are model input parameters. Simulator predictions such as the gas velocity and temperature proæles, across-wafer temperature contours, wafer temperature trajectory, chemical species concentration distribution, deposition rate, and deposited ælm uniformity are outputs of the model. Physical Properties Thermodynamic Properties eg., Cp, H,... Transport Properties eg., D, κ, µ,... Chemical Reaction Kinetics eg., SiH4 Si + 2H2 Chemical Vapor Deposition System Model Process Parameters Geometry, Temperature, Flow Rate,... Gas Phase Gas Flow, Gas Temperature, Compositions... Wafer Temperature, Surface Reaction,... Transport Equations Boundary Conditions Numerical discretization and solutions Miscellinous Heat Lamp, Reactor Walls,... Simulation Results Temperature and composition distributions Uniformity Deposition Rate Gas flow field... Figure 2.1: Schematic illustration of modeling approach. The core system model usually consists three submodels describing the transport phenomena in gas phase, wafer, and the other components in the reactor chamber. Conservation equation of mass, momentum, and energy ë38ë provide sets of coupled partial diæerential equations describing the interacting transport processes among the three submodels subject to appropriate boundary conditions. Physical properties including thermodynamic and transport properties 17

36 of the gases, wafer, and other chamber materials, as well as chemical reaction kinetics from either empirical experiments or computational chemistry predictions, are two supplementary blocks that interact with the governing equations providing parameter values for model computations. At the beginning of the simulation, a mesh generation program should be called to construct the computational domains from the true physical system domains. The governing equations of diæerent submodels are then discretized on the computation domains using aweighted residual projection method. The sets of equations must be solved simultaneously due to the interactive transfer mechanisms between submodels and the continuous boundary conditions across adjacent domains. The physical properties that strongly depend on the state variables should be updated simultaneously during the computation process Literature Review CVD reactor transport modeling began to receive broad attention in the early 1980s when researchers used the simulation results to study the transport mechanisms in the reactors and performed numerical experiments to evaluate diæerent reactor designs ë39, 40ë. Detailed CVD reactor models are developed by generalizing the transport equations to account for multiple dimensions, transient eæects, multiple mass and energy transport mechanisms, and chemical reactions. The relative importance between diæerent physical phenomena varies among different types of CVD reactors and processing modes. Middleman and Hochberg ë41ë give a comprehensive introduction of the CVD modeling for diæerent type of reactors from a chemical engineering viewpoint; Kleijn and Werner ë9, 42ë provide a general guideline for a CVD transport modeling procedure; Badgwell 18

37 et. al. ë11ë and Jensen et. al. ë10ë, as well as Kleijn ë9ë all give excellent reviews for the papers studying the CVD modeling problems. In this literature review section, the entire spectrum of CVD modeling research will not be covered; only the portion helpful in developing the modeling work for ULVAC system will be discussed. APCVD Reactor Modeling Most initial eæorts of CVD modeling focused on the atmosphere pressure deposition tools èapcvdè, which were mainly used for expitaxial deposition in horizontal rectangular chambers. Moæat and Jensen ë16, 40ë studied the transport models for horizontal, cold-wall GaAs metalorganic CVD èmocvdè and silicon epitaxial APCVD reactors. The models were based on steady-state mass, energy, and momentum balances in three dimensions, and was simpliæed by a2d boundary layer approximation for the case where secondary æow is not important. The ænite-element method was used to discretized the governing equations. The major conclusion of their work was that buoyancy driven transverse convection cells, due to the large temperature gradients near the cold chamber walls, signiæcantly altered the deposition process. The later papers by Jensen and coworkers èfotiadis et. al. ë43, 44ë, Jensen ë45ëè experimentally veriæed the gas æow and temperature æelds and the generation of recirculation cells using Raman scattering temperature measurement technology and smoke trace method. They also extended the three-dimensional, steady-state modeling approach toa vertical MOCVD reactor, and experimented with reactor design parameters to conclude that increasing the inlet gas æow rate, rotating the susceptor, reducing the pressure, and modifying the reactor shape can help to suppress the natural 19

38 convection æows. Similar simulation results of the natural convection eæects were also found by other researchers. Ingle and Mountziaris ë46ë developed a ænite element discretized two-dimensional æow and heat transfer model of a horizontal MOCVD reactor, and identiæed the operating conditions where the transverse buoyancydriven æow existed when H 2 or N 2 gas was used. Their predictions were in good agreement with the experimental values obtained from Chiu and Rosenberger ë47, 48ë. In another paper, Mountziaris et. al. ë49ë extended the modeling framework by adding reactant species mass balance equations and a detailed gas phase as well as surface reaction kinetic models to predict the GaAs deposition rate. Optimal operating conditions were found to maximize the thin ælm growth uniformity and precursor utilization. Holstein and Fitzjohn ë50ë studied the conditions for the formation of buoyancy driven secondary æows in the forms of transverse recirculation, longitudinal rolls, and traveling waves in a channel MOCVD reactor used for growing InP. They performed simulations on a Galerkin ænite element method solving twodimensional, steady-state model having the capability to predict the gas æow and temperature æelds as well as the ælm deposition rate. By changing the gravity in the modeling equations, they investigated the reactor performance in both horizontal and vertical orientations and categorized the operating conditions resulting in diæerent types of secondary æows in terms of the Rayleigh number èraè, Reynolds number èreè and Grashof number ègrè, and their ratios GrèRe and GrèRe 2. Evans and Greif ë51ë presented the transient solutions of the two-dimensional æow equations for a similar reactor geometry, showing the occurrence of transversal rolls leading to time-periodic, ësnaking" motion of the 20

39 gas that enhanced the heat transfer. In another paper, Evans and Greif ë52ë modeled the three-dimensional æow and temperature æelds of a vertical rotating disk CVD reactor. The coupled partial diæerential governing equations were solved with centralèupwind ænite diæerence method. They reported the formation of forced convection æows was determined by the value of a mixed dimensionless convection parameter GrèRe 3=2! where Re! = ç!d 2 =ç was the rotation Reynolds number with susceptor diameter D and rotation speed!. If the GrèRe 3=2! was smaller than 3, the æow æeld was dominated by the rotation-induced forced convection. When the GrèRe 3=2! value was larger than 3, strong natural convection æow induced recirculations were observed. A horizontal APCVD reactor with rotating disk was studied by Habuka and coworkers ë53, 54ë. The governing equations for gas velocity, temperature, and chemical species transport were solved with ænite-diæerence scheme in three dimensions. Unlike the vertical reactors with high rotating speed designed to have a simple gas stream and a rather homogeneous species distribution, they found an asymmetric and nonuniform gaseous reactant distribution proæle in the region above the wafer due to thermal diæusion and reactant consumption despite the wafer rotation induced gas circulation. However, good ælm thickness was observed in both simulation and experimental studies and was attributed to the averaging eæect of wafer rotation. LPCVD Reactor Modeling Horizontal low pressure CVD èlpcvdè reactors have been used to deposit polysilicon ælms, and the hot-wall multi-wafer reactor designs have demonstrated 21

40 homogeneous temperature distribution in the furnace tube. Jensen and Graves ë55ë used a one-dimensional description for the diæusive transport and deposition between the wafers, neglecting convective eæect and axial temperature gradients. This inter-wafer model was used with another one-dimensional model to describe the convection-diæusion phenomena for the annular region. Badgwell et. al. ë56ë performed a series of in-situ wafer temperature measurements that conærmed the radiant mechanisms were the most important heat transfer mode while the gas phase conduction and convection can be neglected in LPCVD operating conditions. In a paper published later ë57ë, they extended Jensen and Graves's work by adding the mass balance for the reactant gas phase and a radiation heat transfer model. This equipment model was solved by orthogonal collocation on ænite-element meshes and was used to optimize the processing recipe. Kuijlaars and coworkers ë58ë studied the multi-component diæusion phenomena in a LPCVD reactor similar to Jensen and Graves's. They used Fisk's law for binary diæusion in a bulk carrier gas to approximate the multi-component diæusion æuxes, and concluded that the Fick's law approximation should not be used in LPCVD modeling if the reactant and reaction-product species were not suæciently diluted or there was a large diæerence in the reactant molar mass. RTCVD Reactor Modeling Rapid Thermal chemical vapor deposition èrtcvdè has been used for various thermal processing applications including polysilicon, tungsten, and thin dielectric deposition as well as selective epitaxial growth. A large volume of literature can be found for RTCVD modeling due to the diæculties in temperature and uniformity control during the development of the RTP technology. 22

41 The ærst comprehensive modeling studies were those by Kleijn and coworkers ë17, 42, 59, 60, 61, 62ë and Werner and coworkers ë63, 64ë. Kleijn et. al. initially studied blanket tungsten deposition from WH 6 and H 2 in a cold-wall, single-wafer LPCVD reactor ë17ë. The two-dimensional axisymmetric model was solved by a ænite-volume method to predict the gas æow, heat transfer, species transport, and chemical reactions. Their results showed a transition from uniform, kinetically limited growth to nonuniform transport limited growth at decreasing WH 6 inlet concentrations. They also found that thermal diæusion in the reactor leads to large concentration gradients and a strong depletion of WH 6 at the waferègas interface. The same model later was used to study the eæect of micro-loading and macro-loading on growth rates in the selective tungsten growth from WH 6 and SiH 4 ë59ë. Werner and coworkers ë63ë use the PHOENICS computational æuid dynamics ècfdè software to solveatwo-dimensional mass and heat transfer model with a detailed surface reaction model for selective tungsten deposition. Their simulation results also showed that thermal diæusion was very important in such a cold-wall low-pressure systems and proposed two selectivity loss models that featured the formation of SiF y and WF x intermediates. Simulations were also used to study the reactor design for optimal selectivity. Pollard and coworkers ë65, 66ë developed a simultaneous reaction kinetics and steady-state transport model for tungsten deposition using WH 6 and H 2 in a LPCVD reactor. Their model included 8 gas phase reactions and 65 surface reaction steps and used statistical thermodynamics, transition state theory, and bond dissociation enthalpies to determine the reaction rate constants without ætting any parameters. Good agreements with experimental data were reported; they found the process was controlled by surface kinetics while the gas phase 23

42 reactions were unimportant. The major reaction pathways and the rate-limiting steps were also identiæed and used to develop the simpliæed rate expression. Kleijn and coworkers ë60, 61, 62ë later adopted Pollard's kinetic model in their two-dimensional transport phenomena simulations using a commercial CFD software PHOENICS-CVD to study the reaction intermediates and the optimization of selective processes. In a series studies, Jensen and coworkers ë10, 67, 68, 69, 23ë presented a systematic approach for simulating the rapid thermal processes. Their model was based on a axisymmetric RTCVD reactor and the wafer temperature trajectory was predicted. The major contribution of their work was the incorporation of the numerical computation methods for radiant heat transfer between lamps, substrates, reæectors, and system walls. The ænite element andèor the Monte Carlo èmcè methods were used to compute the view factors between radiation components exchanging radiant energy and the temperature dependent material radiative properties during the dynamic simulations. Quantum chemistry based computational chemistry models solved by Monte Carlo simulations were also included in the modeling framework to predict reaction kinetic parameters in an eæort to study processes without proven kinetic models. In the most recent paper ë23ë, a thin ælm optics model was included to predict the eæect of patterns on the wafer radiative properties; the resulting temperature distributions were used to predict the ælm stress and deformation. The University of Texas, Austin research group led by Edgar and Trachtenberg studied a polysilicon CVD reactor using a two-dimensional transport model discretized by a ænite-diæerence method ë8, 70, 71, 72ë. The main goal of their studies was to identify the dominant factors governing the heat transfer and æuid 24

43 æow using various levels of simpliæcation on the modeling equations. They found the gas-phase reactions can be neglected in predicting the polysilicon deposition rate ë71ë and developed an empirical rate expression for the conversion of silane to solid silicon from experimental data. Kailath led a Stanford research group that modeled the wafer temperature trajectory and uniformity in a polysilicon RTCVD reactor ë73, 74, 75, 76, 7, 77, 78, 79ë. Unlike Jensen's approach, they used an explicit method for computing the view factors in a simpliæed reactor geometry. However, their model did not consider the gas æow æeld and thermal diæusion, nor did include reactions that were induced by thewafer surface property variations, however, their model predictions were in good agreement with experimental wafer temperature data obtained in non-reacting gases. They also developed the semi-empirical heat transfer model by identifying several key parameters such as process time constant, view factors, and heat transfer coeæcient at the waferègas interface ë74, 7ë; a black-box linear model also was identiæed from process input-output data ë75ë. Their goal was to develop model-based control algorithms for lamp design and power control to achieve uniform heat æux across the wafer. Feature-Scale Modeling All of the above modeling studies considered equipment models that focused on the macroscopic transport phenomena of the systems. With decreasing feature dimensions in microelectronic devices, feature-scale models with the ability to predict the conformality is useful for determining optimal process conditions. Hasper and coworkers ë2, 80ë and Thiart and Hlavacek ë81ëdeveloped continuumlike diæusion-reaction models èdrmè based on simultaneous free molecular dif- 25

44 fusion and heterogeneous surface reactions. However, the DRM models needed simple and known kinetic models such as those developed by Pollard et. al. ë65, 66ë; the predictions only qualitatively agreed with the experimental observation ë82ë. An analytical model based on a hemispherical vapor source was reported by Yun and Rhee ë83ë. Their model computed the particle arriving angle and the re-emission eæect, thus largely reducing the computational resources required for the MC solution, but only qualitative comparison was made in their paper. Cale et. al. ë15, 14ë developed ballistic transport and reaction models èbtrmè to predict the step coverage in feature holes. Monte Carlo simulation methods were used to solve the direct and re-emitted deposition processes subject to feature geometrical eæects. The impact of the processing conditions on step coverage was explained in relation to reactive sticking coeæcient, the fraction of the total incident particles that stick on the surface. Quantitative agreement between prediction and experiment was reported when the deposition conditions are accurately known ë82ë. Multi-scale Modeling Cale and coworkers ë84ë and Jensen and coworkers ë85ë both reported integrated modeling approaches that combine the macroscopic æow and transport phenomena and feature-scale step coverage simulations. The multi-scale integration difæculties resulted from the length scale diæerences, from centimeters to microns. In both reports, ænite element solution procedures were used for macroscopic transport equations and MC methods were used to predict the feature conformality in BTRM models. To interface the computation between two scales, Cale 26

45 introduced an intermediate scale using local reænement on ænite element meshes in the vicinity of the features, and Jensen introduced an eæective reactivity function that determined the average number and nature of the molecules entering the substrate surface from macroscopic scale CVD Modeling Using Commercial CFD Software Commercially available computational æuid dynamics software packages provide powerful and æexible solution platforms of the multidimensional transport equations developed for the CVD models. To deal with the complex reactor geometries and the speciæc set of chemical reactions, these packages oæer ænite volume èfluent, PHOENICS-CVDè or ænite element methods, three dimensional grid generation functions and special material properties as well as chemical kinetics models for the CVD simulations. To set up problems and conduct simulations without detailed knowledge of æuid dynamics and computational techniques, these packages feature a user interface layer for the simulation inputèoutput purposes. This interface allows all the numerical computations to be processed in the background, however, there are drawbacks for such approach since it is often diæcult to use the CFD code in model reduction, control, or other specialized applications ë9, 86ë General Modeling Assumptions Kleijn indicated in ë9ë that there are several general assumptions can be made to simplify the complexity of the transport modeling problem and the solution computational eæort needed for typical chemical vapor deposition processes: 27

46 1. Gas mixtures usually can be treated as a continuum. This assumption is valid when the mean free path length èçè of the gas molecules is much smaller than the typical characteristic dimension of the reactor èlè, i.e., the Knudsen number Kn = ç=l é 0: At pressure and temperature conditions commonly used in CVD processes, the gas can be treated as ideal gas that satisæes the ideal gas law and Newton's law of viscosity. 3. The gas æow is in the laminar region. 4. The gas mixture is transparent to heat radiation. 5. The wafer is round èno chordè. 6. The wafer is relatively thin that there is no temperature gradient across the wafer thickness. A number of characteristic dimensionless groups, appearing in the transport equations by scaling all variables with reference values, are used to characterize the general features of CVD processes. Each dimensionless group can be interpreted as the ratio of the magnitudes of two physical mechanisms and can be used to estimate the importance of diæerent physical phenomena in a particular process, or to check the possible scale-up eæects. Typical values of the dimensionless groups as well as their physical interpretations are summarized in Table 2.1 ë9, 45, 87ë for low pressure chemical vapor deposition èlpcvdè processes. The deænitions and values of typical process in ULVAC W CVD will be given and further discussed in Section

47 Table 2.1: Important dimensionless groups and their typical range in low pressure CVD èlpcvdè reactors. Dimensionless Physical Value Groups Renolds èreè Grashof ègrè Prandtl èprè Rayleight èraè Peclet èthermalè èpe T è Peclet èmassè èpe M è Schmidt èscè Knudsen èknè Surface Damkohler èdaè Interpretation Interial forces Viscous forces Bouyancy forces Viscous forces Momentum diæusivity Thermal diæusivity Bouyancy forces Viscous forces Convective heat transfer Conductive heat transfer Convective mass transfer Conductive mass transfer Momentum diæusivity Species diæusivity Mean free path length Typical dimension Chemical reaction rate Diæusion rate 10, , , ,3-10,2 10, Gas Phase Transport Model Under the general assumptions listed in previous subsection, the gas æow in the CVD chamber is described by the equation of continuity and the momentum balance equations following the classic textbook by Bird et + ræèçvè + ræèçvvè,ræëçèrv +èrvè T è, 2 çèrævèië+rp + çg =0 3 è2.3è where T is gas temperature, ç is gas density, t is time, ç is gas viscosity, I is identity matrix, v is gas velocity, P is pressure, g is gravity. The ærst three 29

48 terms in the momentum balance equation è2.3è describe the transients in the æow, the inertial, and viscous forces, respectively. The last two terms account for the pressure and gravity forces. The æow equations are coupled to the energy balance p T + ræèçc p vt è,ræèçrt è,ræ, NX i=1 H i M i ræj i + NX KX i=1k=1 è RT NX i=1 D T i M i rèlnf i è! H i ç ik èr g k, R g,kè =0: è2.4è Here, C p is gas heat capacity, ç is gas thermal conductivity, R is the gas constant, D i, M i, f i, H i, and j i are the diæusion coeæcient, molecular weight, mole fraction, molar enthalpy, and diæusive mass æux with respect to the ith gas species, respectively. The kth gas phase reaction and its inverse reaction as well as the stoichiometric coeæcient corresponding to the ith component are denoted as Rk, g R g,k and ç ik. The ærst term in the energy equation shows the transient temperature variation; the second and third terms describe the convection and diæusion heat transfer in gas mixture. The heat transfer resulting from concentration gradient, known as Dufour eæect, and the heat æux generated by interdiæusion of chemical species are represented in the fourth and æfth terms, although they are not signiæcant in most CVD processes. The last term represents the heat generation or lost due to the gas phase reactions. Because the physical properties such asç, ç, C p, ç, andd i are not only functions of gas temperature and pressure, but also the functions of gas composition, the above equations thus are coupled with the species concentration equations. For the ith species, the conservation equation i =,r æ èçv! i è,ræj i + M i KX k=1 ç ik èr g k, R g,kè è2.5è 30

49 with mass average velocity v and diæusive massæux j i deæned as follows: v = NX i=1! i v i j i = ç! i èv i, vè where! i is the mass fraction and v i is the velocity vector of the ith species. In the above equation è2.5è, the ærst term represents the transient variation in species concentration; the second and third terms describe the convective and diæusive mass transport, and the last term accounts for the generationèlost of the gaseous species from gas phase reaction Wafer Thermal Dynamics Model The time evolution of the temperature distribution of the wafer is described by the energy èç wc pw T w è=ræèç w rt w è+ q top + q bot Z w è2.6è where T w is the temperature, C pw is the heat capacity, ç w is heat conductivity, and Z w is the thickness of the wafer. The ærst term in the right-hand side of the equation accounts for the conduction heat transfer and q top and q bot are heat æuxes coming in at the top and bottom of the corresponding components that 31

50 can be given as follows: q top ; q bot = q em + q ab + q conv + q cond + q rxn q X em =, F æ F A çètw 4, Tj 4 è j=wall;sh q ab = Quæ w q conv =,h g èt w, T g è q cond = X, h j èt w, T j è j=s;r NX KX q rxn =,Z w i=1k=1 H i ç ik èr k, R,k è where q em is radiative heat exchange from wafer to chamber wall T wall or showerhead T sh ; q ab is the radiative heat æux absorbed by wafer from heating lamps; q conv is convection and conduction heat transport between gas phase T g and wafer; q cond is conduction heat transfer from wafer to the susceptor T s or guard ring T r ; q rxn is the heat transport from wafer surface heterogeneous chemical reactions. The radiative heat æux is calculated by deæning the geometrical factor, or conæguration factor F A and emissivity factor F æ between two gray surfaces ë88, 89ë. The absorptivity and Boltzmann constant are represented as æ and ç, respectively. The other components in the reactor chamber such as quartz showerhead, can be modeled in a similar approach. Chamber walls are usually modeled by considering both heat transfer mechanisms inside the chamber and the cooling eæect provided outside the chamber by reactor cooling jackets. All modeling equations are subject to the system dependent boundary conditions. 32

51 2.3 ULVAC Selective Tungsten Chemical Vapor Deposition Cluster Tool Gas Exhaust PROCESS PUMPS PUMPS TMP TMP REACTOR BUFFER REACTOR LOAD UNLOAD Figure 2.2: Top view schematic ULVAC cluster tool. Our research focuses on the ULVAC ERA-1000 selective tungsten deposition cluster tool, consisting of two production-scale, cold-wall, single-wafer reactors joined by a buæer and a load-lock chamber for automatic loading and transfer of wafers. This CVD system is located at the Laboratory for Advanced Material Processing èlampè of the University of Maryland and an overhead view of the cluster tool is shown in Figure 2.2. Each reactor is water cooled to prevent deposition on the chamber walls and is equipped with two sets of pumps: a mechanical pump for maintaining gas æow during the processing and a turbo 33

52 molecular pump ètmpè that can bring down the pressure to as low as 10,7 Torr for reducing water vapor or other residual contaminants while idling. CVD Reactor Geometry Figure 2.3 depicts the individual reactor conæguration. Reactant gases are fed to the reactor from two sources: a gas mixture of silane, tungsten hexaæuoride, and argon or nitrogen èif usedè is injected through a two-dimensional nozzle array installed on one side wall, and hydrogen is pumped in through a transparent showerhead mounted in the top of the reactor chamber. Gases mix in the chamber and react at the surface of a wafer located at the chamber center. For convenience we use 4 inch diameter wafers, although the tool is capable of processing 8 inch wafers. The wafer is supported by a slowly rotating 4 inch diameter quartz susceptor to assure the azimuthal symmetry of the deposited ælm. An incoherent tungsten-halogen lamp ring above and outside the reactor chamber is used to heat the wafer to desired temperature through the transparent quartz showerhead window. Typical deposition runtimes last 5 minutes after operating temperature is reached. Process Operating Procedure The general operation procedure and control structure of the reactor is illustrated in Figure 2.4. An editable multi-step operating recipe, deæning the processing sequence including the choice of reactant gases, gas æow rates,chamber pressure, and wafer temperature setpoints, is setup ærst by touching the ULVAC system control screen prior to the processing. An integrated system controller receives the status signals from several sensors and adjusts the operating parameters 34

53 Heating Lamps H 2 WF 6 SiH 4 z 2Z (=0.092m) Showerhead Nozzle 2Y (=0.254m) 2X (=0.305m) y θ r x Outlet Wafer Susceptor Figure 2.3: Sketch of the Tungsten CVD reactor system. èpressure, temperature, reactant æow rates, and duration of each stepè preset by the recipe through the corresponding controllers. The equipment setting parameters such aswafer temperature PID controller parameters and wafer rotation speed can also be adjusted from hardware setting by the process engineers. However, in contrast to the recipe inputs, these equipment settings are usually not changed for each diæerent process recipes. Reactor Wafer Temperature Control System Because the system thermocouple is located outside the reactor chamber near the lamp ring, it receives most of the radiation energy from the lamp directly and measures the temperature in atmosphere pressure. The equipment manufacturer uses a predetermined look-up table, considering the eæects resulting from lower chamber pressure and diæerent gas æow rates, to predict the wafer temperature under the process conditions. Part of the look-up table wafer temperature ad- 35

54 Recipe Inputs Pressure Setpoint Pressure Controller Chamber Pressure Flow Rate Setpoints Choice of Gases Wafer Temp Setpoint Equipment Settings MFCs Look-up Table PID Control Process Gas Flow Rates ULVAC TC Measurement u(t) Lamp Systems Process Chamber Product PID Parameters Wafer Rotation Rotation Rate Figure 2.4: ULVAC W CVD reactor operating and control structure. justing functions at diæerent pressure ranges are plotted in Figures 2.5, 2.6, 2.7. This calibrated wafer temperature is then compared to the recipe setpoint and the PID controller adjusts the lamp power to bring wafer temperature to the desired value. However, because of the aging in the reactor lamps and the other changes of the equipment conditions, the look-up table deviates from current processing conditions and the adjusted wafer temperature value does not reæect the true wafer temperature as shown in the experimental results in the next chapter. The CVD reactor can also be operated in an inputèoutput èièoè mode. In the IèO mode, the set points must be changed manually while processing and the internal look-up table is inactive. As stated earlier, wafer temperature is set as recipe input. However, this single setting does not provide the capability to adjust the temperature distribution across the wafer surface. Although the wafer rotation can average out 36

55 the nonuniform heat æuxes received by wafer in the azimuthal direction, the single ring heat lamp does not provide suæcient freedom to control the temperature uniformity inwafer radial direction. Alternative heating methods such as heating susceptor plate are currently under investigation. 2.4 ULVAC W CVD Transport Model Formulation Two coordinate systems are used in two modeling domains corresponding to their physical geometries. For gas phase model, a simpliæed rectangular domain is adopted with its origin located at the left lower corner of the reactor chamber as shown in Figure 2.3. The streamwise, spanwise, and normal coordinates are labeled as x, y,andz, respectively. On the other hand, the cylindrical coordinate system is used for the wafer and showerhead, and the coordinate origin overlaps the center of rectangular domain at the chamber æoor. The radial and spinwise directions are deæned as r and ç, and the axial direction is the same as the z direction in gas rectangular domain. We assume the wafer shape is perfectly cylindrical and the wafer is pure silicon without the thin natural silicon oxide layer on the wafer surface. This allows us to use the physical properties of pure silicon for wafer Gas Flow Field Although feed gas can enter from both the showerhead and side slits, we will only consider the case where the gas æow æeld over the wafer is assumed to be dominated by the horizontal æow, generated by the feed gas entering through the side wall nozzle. This assumption is suitable in our simulated operating 37

56 ULVAC Temp measurement ( o C) H 2 (R1) H 2 (R2) Ar Adjusted Wafer Temp ( o C) 600 ULVAC Temp measurement ( o C) H 2 (R1) 250 H 2 (R2) Ar Adjusted Wafer Temp ( o C) Figure 2.5: The default ULVAC look-up table correcting functions plotted as the ULVAC thermocouple measurements against the adjusted wafer temperature at ètopè 0.8 Torr and èbottomè 0.4 Torr total chamber pressure in pure H 2 or Ar gas. R1 and R2 represent the correcting function for reactors 1 and 2, respectively. 38

57 550 ULVAC Temp measurement ( o C) H 2 (R1) H 2 (R2) Ar Adjusted Wafer Temp ( o C) 500 ULVAC Temp measurement ( o C) H 2 (R1) H 2 (R2) Ar Adjusted Wafer Temp ( o C) Figure 2.6: The default ULVAC look-up table correcting functions plotted as the ULVAC thermocouple measurements against the adjusted wafer temperature at ètopè 0.17 Torr and èbottomè 0.1 Torr total chamber pressure in pure H 2 or Ar gas. R1 and R2 represent the correcting function for reactors 1 and 2, respectively. 39

58 600 ULVAC Temp measurement ( o C) H 2 (R1) H 2 (R2) Adjusted Wafer Temp ( o C) Figure 2.7: The default ULVAC look-up table correcting functions plotted as the ULVAC thermocouple measurements against the adjusted wafer temperature at high vacuum condition 1.8æ10,6 Torr total chamber pressure in pure H 2 or Ar gas. R1 and R2 represent the correcting function for reactors 1 and 2, respectively. 40

59 condition in which H 2 is not used; it is also veriæed by our experimental and simulation results discussed later and is supported by the gas æow visualization tests performed by the system manufacturer èbtu-ulvac ë90ëè using a TiO 2 tracer which demonstrates that a rectangular pipe æow model maybe a suitable approximation for the reactant gas mixture in the neighborhood of the wafer. The fully developed, laminar velocity proæle is obtained by solving steady state Navier-Stokes and continuity equations. The transport and gas thermodynamic properties are assumed constant in the bulk phase and evaluated at the gas inlet temperature T amb. It is also assumed that the slow wafer rotation as well as buoyancy-induced secondary æows, such as longitudinal and transverse recirculation resulting from free thermal convection near the wafer surface and chamber walls, do not aæect the æow æeld. Because the Grashof number evaluated at the gas inlet is small ègr=1.32è in our simulation, transverse recirculations should not occur in this low-pressure system according to the criteria suggested by Ingle and Mountziaris ë46ë. Other studies, such as Holstein and Fitzjohn ë50ë and Jensen ë45ë, reveal that longitudinal recirculations occur in atmospheric pressure CVD systems at higher Rayleigh numbers èé 1780è than those representative of our system èra = 0:59è and so also should not occur. Therefore, the governing equations for the æow æeld component in the x direction are written æ æ = 0 vx vx æ dpæ è = æ2 dx æ 41

60 subject to the no-slip boundary conditions at y =0,2 ç Y and z = 0, 2 ç Z, v æ x =0 v æ x =0 at y æ =0; 2 çy at z æ =0; 2 ç Z where the superscript æ represents the dimensional quantities and 2 çy and 2 çz are the length of gas domain in y and z direction, respectively Gas Temperature Field Neglecting heat generated by viscous dissipation, interdiæusion, thermal diæusion, and the gas phase chemical reactions, the gas phase energy balance equation è2.4è æ çc p vx æ æ = k T æ æ2 T æ æ2! Tg æ æ 2 Gas inlet temperature is assumed equal to the water-cooled chamber wall temperature T wall ; a zero temperature gradient along the æow direction boundary condition is used at the gas outlet. Assuming uniform temperature distribution across the wafer and showerhead, the gas temperature is set equal to the wafer temperature T w inside the region of wafer radius R w at z = 0, and the showerhead temperature T sh inside the region of showerhead radius R sh at z = 2 çz. The remaining areas in the top and bottom domain boundaries are assumed at wall temperature. Overall, this gives the gas temperature boundary conditions: 42

61 T æ g = T amb at x æ æ æ =0 at x æ =2çX T æ g = T æ wall at y æ =0; 2 çy T æ g = T æ g = 8 é é: 8 é é: Wafer Thermal Dynamics T æ sh at z æ =2çY; èx æ, çxè 2 +èy æ, çy è 2 ér 2 sh T æ wall at z æ =2çY; R 2 sh é èx æ, çxè 2 +èy æ, çy è 2 T æ w at z æ =0; èx æ, çxè 2 +èy æ, çy è 2 ér 2 w T æ wall at z æ =0; R 2 w é èx æ, ç Xè 2 +èy æ, ç Y è 2 : The two-dimensional wafer thermal dynamics model can be written as follows, æ Zw ç ç C pw T w =æ Zw r 2 èç w T w è+q lamp + Q rad + Q top + Q bot è2.7è where the energy æuxes from the lamp heating, radiation loss, convectiveèconductive losses from wafer top, and conduction loss from wafer bottom are deæned as Q lamp = æ w èt w èq lp èrèuètè Q rad =, F A;topçèTw 4, Tshè 4 æ,1 w èt w è+æ,1 sh èt sh è, 1, F 4 A;botçèTw, Tf 4 è æ,1 w èt w è+æ,1 f èt f è, 1 Q top = ç g èt w;z=0 Q bot =,h eff èt w èèt w, T f è: è2.8è In the model, the subscripts w, sh, andf represent the state variables or physical properties corresponding to the wafer, showerhead, and chamber æoor, respectively. æ Zw is the wafer thickness, ç is the Boltzmann constant, and F A is the geometric factor that is equal to 1 for both wafer top and bottom surfaces ë88ë. 43

62 h eff is an eæective heat transfer coeæcient, Q lp is the incident lamp bank emissive power at the wafer surface, and uètè is dimensionless time-dependent lamp control signal recorded from the experiments. æ is the temperature-dependent total emissivity and the wafer absorptivity æ w is assumed equal to the emissivity of silicon ë91ë. The emissivity factor F æ deæned for parallel disk d 1 and d 2 is F æ = = æ 1 èt 1 èæ 2 èt 2 è æ 1 èt 1 è+æ 2 èt 2 è, æ 1 èt 1 èæ 2 èt 2 è 1 æ,1 1 èt 1 è+æ,1 2 èt 2 è, 1 : Calculation of Lamp Radiation Heat Flux Lamp Ring θa ra S l h l D Wafer h l S w ϕ θ r r - ra Figure 2.8: Geometry of the heating lamp and wafer. The lamp radiation absorbed by thewafer is a function of temperature dependent total wafer absorptivity æ w, adjustable input signal with the value between 0 and 1 from lamp power controller uètè, and the nominal lamp radiation Q lp èrè. The nominal radiative lamp heat æux at every point on wafer surface depends on both the distances between the lamp elements and the speciæc point and the incident angle at that point between radiation æux and wafer surface. Figure

63 shows the simpliæed geometry of the ULVAC system circular heating bulb ring and the wafer. Assuming there is a pair sample points S w èr,çè at the wafer surface and S l èr A ;ç A è on the lamp ring, the distance D from the wafer point S w to any lamp element S l can be calculated using the following equation, D = = q h 2 l +èrcos ç, r A cos ç A è 2 +èrsin ç, r A sin ç A è 2 q h 2 l + r 2 + ra 2, 2rr A cosèç, ç A è: The radiative heat æux at S l from the point heating source S w can be computed by sin ç Q max =èçd 2 è where Q max is the maximum total lamp power. Because the ULVAC uses circular heating ring, the radiant æux thus will be symmetric around the wafer center. Therefore, the nominal total radiant æux from lamp system at maximum power to the wafer surface at radius r is obtained by integrating the heat æux over the entire lamp ring, Q lp èrè = 1 Z 2ç sin ç Q max 2ç 0 4çD dç 2 A " h Z ç l = Q max è2çèè4çè,ç h h 2 l + r 2 + r 2 A, 2rr A cosèç, ç A è i,3=2 dça è è2.9è where sin ç = h l =D. The radial variation of the lamp radiant heatæuxat u =1 is plotted in Figure Showerhead Thermal Dynamics The transparent quartz showerhead at the top center of the reactor chamber is designed to pass the lamp radiation to wafer; however, it also absorbs part of the radiative energy directly from the tungsten halogen lamps and the radiation 45

64 1.755 x Heat Flux (J/m 2 s) Wafer Exposed Susceptor r (m) Figure 2.9: Radial variation of the lamp radiant heat æux at the wafer surface at full lamp power. emitted from wafer ë92, 93ë. To sustain the pressure diæerentialbetween the inner and outer surfaces, the quartz window also must be suæciently thick to handle the stress. The thick quartz window thus becomes a heat source because quartz is not a good thermal conductor and at the low pressure operating condition, the amount ofconvective cooling inside the chamber or provided by theh 2 æow is small ë92ë. To account for the radiant energy exchanges between the quartz showerhead and wafer, and also the showerhead and reactor walls to a lesser extent, a showerhead window energy balance equation similar to that of the wafer is formulated: æ Zsh ç ç C psh T sh = æ Zshç sh r 2 T sh + æ sh èt sh èq lp èrèuètè + F sh;wçètw 4, Tshè 4 æ,1 w èt wè+æ,1 sh èt shè, 1 + F 4 sh;fçètf, Tshè 4 æ,1 f èt wè+æ,1 sh èt fè, 1 +h sh èt sh èèt g;z=1, T sh è: è2.10è 46

65 2.4.5 Thermocouple Thermal Dynamics Although the commercially manufactured thermocouple instrumented wafer is designed to measure the wafer temperature, it is still recognized that the thermocouple temperature can be diæerent from the true wafer temperature ë94, 95ë. The heat losses through the wire, heat conduction in the wafer and the thermal contact resistance between the wafer and the thermocouple junction are some mechanisms that have been identiæed to account for the diæerence between true wafer temperature and the thermocouple reading ë94ë. In this research, we use a thermocouple temperature model similar to Vandenabeele and Renken ë4ë, M = æ TC Q lp uètè+h TC èt w, T TC è: è2.11è Gasous Reactants and Wafer Physical Properties In typical low pressure CVD processes, the dilute gas mixture assumption usually approximates the gas mixture properties satisfactorily ë9ë. However, the recipe for blanket tungsten deposition we studied on the ULVAC reactor uses a relatively small ratio of reactant gases èh 2 =W F 6 = 4è with large molecular weight diæerence èh 2 =W F 6 = 2è298è and no carrier gas. To accurately estimate the gas mixture properties, we employed a molecular kinetic theoretic model that was experimentally veriæed to have very high accuracy. On the other hand, the wafer temperature varies wildly during the process cycle, and its optical properties are strong functions of the temperature. Due to the dominant radiant transfer mechanism, represented by emissivity times fourth power of the wafer temperature, as well as other chamber components inside the reactor, a good emissivity model for the silicon wafer is critical to 47

66 accurately modeling the wafer dynamic temperature. Gas Mixture Physical Properties Two diæerent kinds of physical properties are used in the transport equations: thermodynamics properties and transport properties. For pure species, the thermodynamics properties such as heat capacity and enthalpy can be obtained either from original experimental data or from the computation of the polynomial interpolation functions ë38, 96ë. The mixture-average method ë96ë is used to ænd the corresponding thermodynamics properties of the gas mixture. While the pure species transport properties, e.g., viscosity and thermal conductivity, can be determined from the calculation of experimental data-based temperature functions if available, they also can be computed from the kinetic theory ë38, 96ë for the less common species. The Chapman-Enskog theory gives expressions for the transport coeæcients in terms of the potential energy of interaction between a pair of molecules, and the negative derivatives of the potential function with respect to the distance between molecules then represents the interactive forces. One reasonable accurate potential energy function is the Lennard-Jones potential function, ç LJ èrè = 4æëèç LJ =rè 12, èç LJ =rè 6 ë, where it shows weak attraction at larger separations èè r,6 è and strong repulsion at small separations èè r,12 è. Each species is characterized by a set of parameters of this potential function: the collision diameter ç LJ and the maximum energy of attraction between a pair of molecules æ LJ. The values of these two parameters for each species can be found experimentally or estimated from gas critical ècè 48

67 or liquid boiling èb,lè properties: æ LJ where ç is the Boltzmann constant. ç =0:77T c ç LJ =0:841 ~V c 1=3 æ LJ ç =1:15T b ç LJ =1:166 V ~ 1=3 b;l Deæning the dimensionless temperature variable æ ç = çt=æ LJ, the viscosity and thermal conductivity of pure species are then approximated as follows, p MT ç =2:6693 æ 10,5 çlj 2 æ ç ç = 8 é é: 5 R 2 M ç monatomic ç ç ^C p + 5 R 4 M ç polyatomic and the binary diæusion coeæcient can be obtained as D AB =1:8583 æ 10,3 r ç ç T 3 M,1 A + M B,1 Pç 2 AB;LJæ D;AB with æ D;AB = çt=æ AB;LJ, ç AB;LJ =èç A;LJ + ç B;LJ è=2 andæ AB;LJ = p æ A;LJ æ B;LJ. Here, R is gas constant and M is molecular weight. The dimensionless variables æ ç and æ D;AB can also be interpreted as the deviations from molecular rigid sphere behavior assumption. The mixture-average method ë96ë is still used to compute the mixture viscosity and thermal conductivity from the following equations: ç mix = ç mix = æ ij = 1 8 nx i=1 nx i=1 x i ç i Pnj=1 x i æ ij x i ç i Pnj=1 x i æ ij è 1+ M i M j!,1= è çi ç j! 1=2 ç Mj ç 3 1=2 5 M i 49

68 where x i is the i-th species molar fraction. One the other hand, the multicomponent formulation is adapted for computing the mixture diæusion coeæcients. This method gives better accuracy than mixture-average formula in multicomponent environments because the latter is only correct asymptotically in some special cases such as in a binary mixture, or in diæusion of trace amounts of species into a nearly pure species ë96ë. The multicomponent formulation of mixture diæusion coeæcient for species k is computed as P nj6=k x j M j D k;mix = where M is the mean molar mass. M P n j6=k x j =D jk If the mixture is exactly a pure species, x j = ^x j +^æ is used to avoid the numerical singularity, where ^x j is the actual molar fraction and ^æ is a small number less than 1 æ 10,12. Wafer è Showerhead è Chamber Wall Physical Properties The thermal radiative properties varies with wavelength and temperature. For example, the quartz showerhead is opaque to wavelengths greater than 4 çm and is transparent to shorter wavelengths. The radiant properties are more complicate for a wafer, where wafer emissivityalsovaries with surface roughness, wafer thickness, and doping ë97ë. The variation of emissivity beyond targeted wavelengths is one of the major problems for developing reliable in-situ, noncontact pyrometry wafer temperature measurement technique ë97, 91ë. In this research, we only consider the emissivity changes with respect to temperature and wavelength, and are interested in the wafer spectral emissivity æèçè which is deæned as the ratio of the radiation emitted by a wafer at agiven wavelength, angle of incidence, and plane of polarization to that emitted from 50

69 a black body under the same conditions. This spectral emissivity of an object under the same conditions should be identical to its absorptivity æèçè due to Kirchhoæ's law. Integrating the spectral emissivity over the chosen wavebands, weighted by the system's energy distribution, we can get the wafer or showerhead radiative properties as functions of corresponding temperatures. For typical CVD processes, the wavelength extremes of 0.4 and 25 çm include most of the emitted radiation ë97, 91ë. For example, the wafer emissivity is computed by æèt w è= R 25 0:4 æèç; T èw bbèç; T èdç R 25 0:4 æèç; T èdç where W bb is the spectrum of radiation emitted from a black body described by the Plank radiation function W bb èç; T è= c 1 ç 5 ç expè c 2 çt è, 1ç with constant c 1 = æ10 8 Wçm 4 m,2 and c 2 = æ10 4 çmk. The wafer absorptivity is assumed to be identical with its emissivity over the temperature range of interest ë98, 91ë, and the optical properties of the quartz showerhead and susceptor are interpolated from Dilhac et. al. ë99ë. A constant emissivity of 0.26 is used for the cooled, oxidized aluminum chamber wall and æoor. Temperature dependent heat capacities and thermal conductivities are used and are interpolated from the experimental data in ë100ë for silicon and ë101ë for quartz. 51

70 2.5 Dimensionless Equations The transport equations and boundary conditions can be made dimensionless by rescaling all the variables with the characteristic reference values. The resulting dimensionless groups in the governing equations will provide information regarding the relative importance of each tensor. The characteristic reference values and the dimensionless variables are summarized in Table 2.2. Table 2.2: Summary of the dimensionless variables used in the transport model. x = x æ =2 çx y = y æ =2 çy z = z æ =2Z ç r = r æ =R w t = t æ =ç v x = vx=é æ v é T g =ètg æ, T ambè=t amb T w = Tw=T æ amb T wall = Twall=T æ amb T sh = Tsh=T æ amb T f = Tf æ =T amb T TC = TTC=T æ amb Q lp = Q æ lp=q max In the table, T amb is the inlet gas temperature, évéis average gas entrance velocity, and 2 çx;2 çy, and 2 çz are the true dimensions of the gas domain Gas Phase Flow and Energy Equations Using the dimensionless variables deæned in Table 2.2, the fully developed, laminar velocity proæle is described by the continuity and steady-state Navier-Stokes 52

71 2 v = v x 2 = æ v : The dimensionless pressure drop term æ v = 2P çy 2 =èç é v é çxè can only be determined after the æow æeld equations are solved. Thus, deæning the æow velocityèpressure drop ratio as ^v x = v x =æ v, the momentum balance equation can be written 2^v 2 + æ 2^v x =1 è2.12è subject to no-slip boundary conditions v x =0aty =0; 1 and z =0; 1. The dimensionless gas temperature can be described by the steady-state conservation of energy equation g v 2 æ gt T g = LT g 2 è2.13è After chosing the gas inlet temperature equal to the water-cooled chamber wall temperature, the gas temperature boundary conditions are simpliæed to T g = 0 at x = 0 at x =1; T g = 0 at y =0; 1; T g = T g = 8 é é: 8 é é: C g;t èt æ shè at z =1; èx, 0:5è 2 + R 2 xyèy, 0:5è 2 ç R 2 t ; 0 at z =1; èx, 0:5è 2 + R 2 xyèy, 0:5è 2 ér 2 t ; C g;b èt æ wè at z =0; èx, 0:5è 2 + R 2 xyèy, 0:5è 2 ç R 2 b; C g;f at z =0; èx, 0:5è 2 + R 2 xyèy, 0:5è 2 ér 2 b: è2.14è 53

72 Representative process operating conditions correspond to a feed volumetric æow rate of 50 sccm, a feed gas temperature of 298K and mixture ratio of WF 6 =H 2 equal to 1è4 sccm, chamber pressure of 0.5 torr, and a uniform wafer temperature set point at500 o C. The value of dimensionless parameters are given in Table 2.3. Table 2.3: Deænitions and values of physical properties and dimensionless parameters evaluated at 1 atm, H 2 =N 2 = 40=10sccm, T amb = 25, T w = 304:3, T sh = 150, and T f =60 o C. Physical Value Dimensionless Value Properties Parameters ç g æ10,4 kgèm 3 æ v = çy 2 = çz ç g Jèèm K sè æ v =2PY ç 2 =èç g évéxè ç C pg Jèèkg Kè æ gt = ç g =èç g C pg è ç g æ10,5 kg èèm sè æ gt = æ gt è2 évé çxè ç w 2300 kgèm 3 æ gt = æ gt çx=è2 évé çy 2 è ç w Jèèm Ksè æ gt = æ gt çx=è2 évé çz 2 è C pw Jèèkg Kè C g;t = T sh =T amb æ w 0.28 C g;b = T w =T amb ç qtz e3 kgèm 3 C g;f = T f =T amb ç qtz C pqtz Jèèm K sè Jèèkg Kè æ qtz

73 2.5.2 Wafer and Showerhead Energy Balance Equations By normalizing the temperature dependent physical properties with respect to the set of reference values, the dimensionless parameters are grouped and represent the relative importance of each transport mechanisms at those reference conditions. The resulting dimensionless wafer energy balance equation is shown as follows, C = C w;cd è wèt w èt w + C w;lp ëæ w èt w èq lp +C w;top h Fæ;top F A;top ç T 4 sh, T 4 wçi + Cw;bot h Fæ;bot F A;bot ç T 4 f, T 4 w çi +C w;g ëh g èt w èèt g +1, T w èë + C w;f ëh w;f èt w èèt w, T f èë è2.15è where the new wafer heat capacity is deæned by C C pw = ~ p æ and ~C p ~C æ w = Tw æ p æ w + Cp æ w : w Similarly, the dimensionless susceptor heat capacity C psh is deæned as C C psh = ~ p æ and ~C p ~C æ sh = Tsh æ p æ sh sh + C æ p sh and the dimensionless conservation of energy equations for susceptor and thermocouple are C = C sh;cd è shèt sh èt h ç +C sh;w Fæ;sh,w F A;sh,w T 4 w, Tsh 4 h ç çi +C sh;f Fæ;sh,f F A;sh,f T 4 f, Tsh 4 + C sh;lp ëæ sh èt sh èq lp uètèë çi +C sh;g ëh sh èt sh èèt g +1, T sh èë è2.16è C = C T C;lp ëæ TC Q lp uètèë + C T C;cd ëh TC èt w, T TC èë : è2.17è 55

74 The dimensionless variables in equations è2.15è, è2.16è, and è2.17è are deæned in Table2.4. Table 2.4: Deænitions of dimensionless parameters used in wafer, showerhead, and thermocouple modeling equations. C w;z = ç=èæ zw ç w ~C pw;ref T amb è a C w;cd = C w;z èæ z;w ç w;ref T amb è=æ 2 r w C w;lp = C w;z Q max C w;top ;C w;bot = C w;z çtamb 4 C w;g = C w;z h g;ref T amb C w;f = C w;z h f;ref T amb C sh;z = ç=èæ zsh ç sh ~C psh;ref T amb è a a C TC;z = ç=m TC T amb C sh;lp = C sh;z Q max C sh;w ;C sh;f = C sh;z çtamb 4 C sh;g = C sh;z h sh;ref T amb C T C;lp = C TC;z Q max C T C;lp = C TC;z h TC;ref T amb a Dimensional parameters èm 2 s=jè. 56

75 Chapter 3 Experimental Studies In this chapter we address the problem of setting up a data acquisition system for the ULVAC tungsten CVD reactor and present experimentally measured wafer temperature data used for equipment transport model development and validation. As stated in Section 2.3, the current ULVAC CVD reactor does not have an in-situ wafer temperature measurement apparatus and relies on the internal look-up table to compute the process condition-adjusted wafer temperature. Thus, the thermocouple instrumented wafer placed in the reactor chamber will provide valuable information regarding the true wafer temperature during the processes. By carefully designing the processing conditions and recipes, the experimental results can be used to examine the basic assumptions of the mathematical models and distinguish the most important heat transfer eæects from the others. The conduction and convection energy transfer at the gasèwafer interface is studied in this research by changing the gas composition and total æow rate, while other system dependent parameters, such aswafer thermal time constant, are estimated from the wafer temperature transient response. 57

76 Detailed descriptions of the thermocouple wafer and the data acquisition system hardware and software are presented in Section 3.1. Signal conditioning and integration issues are also discussed. The nonlinear behavior between the lamp power control signal and the power actually supplied to the lamp ælaments are investigated using the steady-state experiments discussed in Section 3.2. In the following section, the inæuence of the gas composition on wafer temperature is demonstrated and diæerent heat transfer mechanisms are examined. Results of the wafer temperature dynamics including the chamber pressure eæects, recipes for achieving near constant deposition temperature, and parameter identiæcation experiments are given in Section Data Acquisition in the ULVAC ERA-1000 System The data acquisition system built in this research was used to record a variety of signals including the instrumented wafer temperature from æve attached thermocouples, the ULVAC system wafer temperature, the lamp power controller signal, and the gas æow rates. Among these collected variables, only the TC wafer measurements were recorded directly from the measurement sensors and the remaining signals were collected by intercepting the inputs or outputs from the corresponding ULVAC system controllers. The general structure of the data acquisition system was demonstrated in Figure 3.1, and the ULVAC control scheme is shown in Figure 2.4. There were three main components of this data acquisition system, namely the measurement apparatus èthe TC test waferè, the signal processing hardware èfor example, the computer boardsè, and the computer software user interface. 58

77 u(t) Computer Lamp ULVAC TC Temp LabView TC Wafer Pressure, Flow rates ULVAC System Controller Data Acquisition board C L Figure 3.1: ULVAC CVD reactor data acquisition system. Several integration issues between those main components had to be resolved to achieve high signal resolutions and ready-for-analyze data æles: æ Compared to the signals such as lamp power controller output taken from the ULVAC system in the range of 0 to 10 V, the thermocouple signals from TC wafer were very small, measuring only between 10,4 and 5æ10,2 V. Therefore, the length of the connection cable between the extension board and the thermocouple wafer was restricted and the thermocouple signal had to be ampliæed as early as possible to obtain better signal-to-noise ratio before environmental noise was picked up by the connection cables. The connection cables were shielded with aluminum tape and the data acquisition board was housed in a metal box to reduce the environmental noise corruption. Because the signals taken from the ULVAC system were already close to the safety limitations of the computer boards, they could not be further ampliæed and were separately collected and processed in the second bank of signal terminals on the extension board. The TC measurements were collected and ampliæed with a high ampliæcation ratio 59

78 in the other bank. æ In contrast to the single-ended voltage signals that were intercepted from the ULVAC system, the signal from the instrumented wafer measurement was of the æoating diæerential type and the low and ground terminals of the corresponding channels on the extension board had to be closed with mounds of solder to provide a proper ground for the measurement. We used the same procedure to close out capacitors between the high and low terminals to add on-board signal ælters for better thermocouple signal conditioning. æ A special data acquisition board having the capability to receive both æoating diæerential and single ended signals was required to connect with the extension board. This particular acquisition board provided special treatment of the æoating diæerential signals to increase the signal to noise ratio. æ Due to the setting of another data acquisition system on which the new system was built, we were only be able to record the adjusted ULVAC wafer temperature and did not have the access to the original ULVAC thermocouple measurements. A more detailed descriptions of the instrumented thermocouple wafer and computer boards, and the LabVIEW software user interface are given in the following two subsections. 60

79 3.1.1 Instrumented Thermocouple Wafer and Computer Boards A SensArray 1530 thermocouple ètcè wafer was used to measure the true wafer temperature, and the system was operated in IèO mode to enable manual loadingèunloading of the instrumented wafer. There are æve thermocouples, labeled as shown in Figure 3.2, attached to the top surface of this instrumented TC wafer. We note that the instrumented wafer is designed to measure the wafer temperature - as opposed to wafer surface or thermocouple temperature - by bonding the thermocouple leads in an undercut wafer area in a symmetric pattern ë102, 95ë. A æ 1.0 o C or better measurement variation between these thermocouples has been reported ë102, 95ë. The wafer rotation was turned oæ during the experiments to protect the leads of the test wafer. Instrumented Wafer Susceptor X cm 2.7cm X 0.6cm X 2 X 1 N flow 2 Wafer z w,f R TC5 TC4 TC1-3 z w Susceptor 2.2cm X Chamber floor Figure 3.2: The top and side views of the test wafer position with thermocouple positions marked. The temperature data collected from the instrumented wafer was sent to a personal computer-based data acquisition system that included a LabVIEW software interface and two computer boards: a CIO-DAS801 data acquisition board ë103ë and a CIO-EXP32 extension board ë104ë. Each thermocouple was 61

80 connected to a channel on the expansion board, where a low pass ælter with bandwidth 7Hzwas implemented between the high and low ends and a 100 kæ resistor was installed between low and ground to provide ground reference. The temperature signals were then ampliæed 300-fold before being sent to the data acquisition board. An on-board semiconductor sensor provides the adjustable cold junction compensation ècjcè function that subsequently is used as a reference to the measured thermocouple signals in the LabVIEW program. Additional processing variables of ULVAC CVD system, such as the system thermocouple temperature measured near the lamp, lamp power control signal, chamber pressure, and gas feed rates, are collected during the processing cycle. The default sampling rate was 20 Hz LabVIEW Data Acquisition Interface The LabVIEW is a graphical programming language developed by National Instruments, Inc. ë105ë for a broad range of applications including data acquisition and analysis, process monitoring and control, and factory automation and personnel instrumentation. We built our data acquisition computer interface by prototyping the existing modules such as hardware drivers in the forms of dynamic link library èdllè in the LabVIEW. Figures 3.3 showed the LabVIEW graphical user interface èguiè developed in this research for collecting instrumented wafer temperature and other system parameters. There were three main construction blocks in this interface program. To receive the signals from extension and data acquisition boards, we used the code interfaces, which were part of the DLL library supplied by acquisition board vendor Computer Boards, for temperature measurements of each thermocouple 62

81 Figure 3.3: LabVIEW data acquisition interface window. 63