INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order.
University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9S16211
Laser diagnostics of atomic hydrogen and oxygen production in RF and microwave plasma discharges
Preppemau, Bryan Lee, Ph.D.
The Ohio State University, 1993
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 LASER DIAGNOSTICS OF ATOMIC HYDROGEN AND OXYGEN
PRODUCTION IN RF AND MICROWAVE PLASMA DISCHARGES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of the Ohio State University
By
Bryan Lee Preppemau, B.A., B.S.E.
ft ft ft * *
The Ohio State University
1993
Dissertation Committee: Approved by
T. Miller
E. Herbst Adviser T. Gustafson Chemical Physics Program ACKNOWLEDGMENTS
This dissertation reflects the culmination of many years of endeavor and I should express my appreciation to those who have contributed in many ways to enhance my own efforts while in Graduate School. In addition, I wish also to recognize the support and guidance of those I've have know professionally throughout the years and from my previous education. Therefore, I wish to sincerely thank all of those listed below as well as my parents and family and especially my wife, Mary Post, for their unending consideration and wisdom. The Ohio State University:
Dr. Terry Miller Dr. Vish Subramaniam Dr. Suliman Dregia Dr. Harris Kagan Dr. Richard Kass Dr. Terry Gustafson Dr. Jim Dunlop Dr. David Dolson Chris Carter Angelika Tserepi Tim Cerny Ken Pearce AT&T Bell Laboratories Dr. Richard Gottscho Advanced Plasma Group. Wright-Patterson Air Force Base:
Dr. Bish Ganguly Dr. Alan Garscadden Dr. Peter Bletzinger Dr. Charles Dejoseph Air Force Institute of Technology:
Dr. Eric Jumper Dr. William Bailey Dr. Max Stafford
Reed College:
Dr. Nick Wheeler Dr. David Griffiths Dr. Ken Davis VITA
April 18,1959 ...... Born - Aberdeen, Maryland
1981 ...... B.A., Physics, Reed College Portland, Oregon
1982-1987 ...... Officer, United States Air Force
1984 ...... B.S.E., Aeronautical Engineering Air Force Institute of Technology Wright-Patterson AFB, Ohio
1987-Present ...... Graduate Research Assistant Chemical Physics Program The Ohio State University
PUBLICATIONS
Absolute H-Atom Concentration Profiles in Continuous and Pulsed RF Discharges, A. Tserepi, J. Dunlop, B. Preppemau, and T. Miller, J. Appl. Phys., 72 (7), 2638, 1992.
The Effects of Surfaces on H-Atom Concentration in Pulsed and Continuous Discharges, A. Tserepi, J. Dunlop, B. Preppemau, and T. Miller, J. Vac. Sci. & Tech., 10 (4), 1188,1992.
Nucleation and Growth of Diamond on Silicon using Hot Filament CVD, J. Rebello, D.Straub, V. Subramaniam, E.. Tan, S. Dregia, B. Preppemau, and T. Miller, Mat. and Manuf. Processes, 6, 501,1991.
H-Atom Plasma Diagnostics: A Sensitive Probe of Temperature and Purity, J. Dunlop, A. Tserepi, B. Preppemau, T. Cerny, and T. Miller, Plasma Chem. and Plasma Process., 11 (4), 1991 hi Real-Time Monitoring of Low-Temperature Hydrogen Plasma Passivation of GaAs, R. Gottscho, B. Preppemau, S. Pearton, A. Emerson, and K. Giapis, J. Appl. Phys., 68 (2), 440,1990.
Enhanced Atomic Hydrogen Concentration Measurements in Radio Frequency Discharges, B. Preppemau and T. Miller, J. Vac. Sci. Technol. A, 8 (3), 1673, 1990.
Temporally Resolved Laser Diagnostic Measurements of Atomic Hydrogen Concentrations in RF Plasma Discharges, B. Preppemau, D. Dolson, R. Gottscho and T. Miller, Plasma Chem. and Plasma Process., 9 (2), 157, 1989.
Rydberg State Stark Spectroscopic Measurement of Electric-Field Profile in a Glow Discharge, B. Ganguly, J. Shoemaker, B. Preppemau, and A. Garscadden, J. Appl. Phys., 61 ( 8 ), 2778,1987.
Adaptations of a Wall-Catalytic Fluorine Recombination Model to Fluid- Dynamic Computations in an HF Laser Nozzle, E. Jumper, P. Wilkins, and B. Preppemau, J. AIAA, Apr 1987.
Laser-Based Diagnostics of Reactive Plasmas, B. Preppemau and T. Miller, (Plenum Press, New York, 1993).
FIELDS OF STUDY
Major Field: Chemical Physics TABLE OF CONTENTS Page ACKNOWLEDGMENTS...... ii VITA...... iii UST OF TABLES...... vi UST OF FIGURES...... vii CHAPTER I. INTRODUCTION TO LASER DIAGNOSTICS FOR PLASMA PROCESSING 1 A. Scientific and Technological Significance of Plasmas ...... 1 B. Technological Impact of CVD Diamond ...... 4 C. Overview of Plasma Diagnostic Techniques ...... 7 H. THE GEC REFERENCE CELL...... 12 m. DIAMOND CHEMICAL VAPOR DEPOSITION CHEMISTRY...... 21 IV. EXPERIMENTAL TECHNIQUES...... 34 A. Experiment Apparatus ...... 34 B. H-Atom and O-Atom Concentration Calibration Procedure ...... 44 C. Effects of Quenching Upon Concentration Measurements ...... 50 V. EXPERIMENTAL RESULTS FROM A GEC REFERENCE CELL...... 85 VI. EXPERIMENTAL RESULTS FROM AN ASTEX DIAMOND REACTOR...... 104 APPENDIX A: EXPERIMENTAL QUENCHING DATA...... 127 APPENDIX B: COMPUTER ACQUISITION AND ANALYSIS PROGRAMS...... 135 BIBLIOGRAPHY...... 174
v UST OF TABLES
Table Page
1. Comparison of Diamond and Silicon Electronic Properties ...... 5
2. Comparison of Measured and Calculated Fluorescence Lifetimes for Helium Quenching ...... 75
3. Comparison of Measured and Calculated Fluorescence Lifetimes for Argon Quenching ...... 79
4. Cross-Sections for Quenching of Hydrogen Atoms (n=3) ...... 82
5. Computed Maximum H-Atom Densities in GEC Reference Cell 92
vi UST OF FIGURES Figure Page 1. The GEC Reference Cell ...... 13
2. C-H-0 Phase Diagram. Unshaded area is nominal diamond growth region ...... 25
3. Experiment Layout Schematic for H-Atom TALIF ...... 36
4. Experiment Layout Schematic for O-Atom TAUF ...... 40
5. Representative H-Atom TAUF Signal Trace ...... 42
6 . Titration Assembly ...... 47
7. O-Atom TAUF Titration Curve. Data corresponds to a concentration of 5.98 x 1015 cm-3. Line is a linear regression extrapolation for determining the titration endpoint. X-intercept is 7.63 seem of NO2...... 49
8 . H-Atom TAUF by Photodissociation of C 2H2...... 52
9. Nonlinear Dependence of C 2H2 H-Atom TAUF Signal. Straight line represents a linear regression fit to the initial rise of the data 53
10. Inverse Quantum Yield Dependence on Pressure...... 55
11. Radiative Lifetime of n=3 State from Photodissociated C 2H2 H- Atom TAUF...... 58
12. Radiative Decay of n=3 Component Levels for 1 Torr Quenching by H2. Also shown is the Normalized Radiative Rate, R* ...... 63
13. Radiative Decay of n=3 Component Levels for 10 Torr Quenching by H2. Also shown is the Normalized Radiative Rate, R* ...... 64 14. Calculated Quenching Curves With and Without Nonradiative Deexcitation or L-State Mixing and the Total of Both Effects 65
15. Comparison of Calculated and Experimental H-Atom TAUF Quenching by Acetylene ...... 67
16. Measured Versus Calculated Photodissociated Acetylene H-Atom TAUF Signal ...... 69
17. Low-Pressure Detail of Figure 16. Straight line is from linear regression fit as shown in Figure 8 ...... 70
18. Measured versus Calculated H-Atom TAUF Lifetime from Photodissociation of C 2H2. Straight Line is from linear regression fit as shown in Figure 11 ...... 71
19. Comparison Fit of Quenching Model Calculations to Experimental Quenching of H-Atom TAUF by H 2 Gas...... 73
20. Expanded Horizontal Scale from Figure 19 ...... 74
21. Quenching of H-Atom TAUF by Helium. The upper curve is calculated based on data from Reference 87 ...... 76
22. H-Atom TAUF Quenching by Argon. Lower curve is calculated based on data from Reference 87 ...... 78
23. Quenching by Nitrogen. Lower calculated quenching curve is based on data from Reference 87 ...... 80
24. Quenching by Oxygen. Lower calculated quenching curve is based on data from Reference 87 ...... 81
25. GEC Reference Cell Geometric View Factor Correction. Origin is position of powered electrode ...... 87
26. TAUF H-Atom Signal Profiles in GEC Reference Cell for Different H2 Pressures. Power deposited in plasma is 30 Watts ...... 89
27. Quenching Corrected TAUF Signal Profiles From 26 ...... 90
28. H-Atom Balmer-a Emission Profiles in GEC Reference Cell as a Function of H 2 Pressure...... 93
viii 29. Interpolated 3-D Mesh Representation of H-Atom Balmer-a Emission Profiles ...... 94
30. Quenching Corrected H-Atom Baimer-ex Emission Profiles 97
31. Quenching Corrected Interpolated 3-D Mesh Representation of H-Atom Balmer-a Emission Profiles ...... 98
32. Plasma Current as a Function of H 2 Pressure in GEC Reference Cell...... 99
33. Total Plasma Voltage and DC Bias as a Function of H 2 Pressure in GEC Reference Cell...... 100
34. Comparison of Maximum H-Atom Density and the Product of Current and Pressure as a Function of Pressure...... 101
35. The ASTEX HPMM Microwave Diamond Growth Reactor 106
36. ASTEX Reactor Geometric View Factor Correction ...... 109
37. Raw Data for H-Atom TAUF Concentration Map in 0.7596 CH 4/H2 Methane-Based Diamond Growth Plasma. Xc=l, Xo=0, X h =0.996...... 112
38. Corrected Data for H-Atom TAUF Concentration Map in 0.7596 CH4/H2 Diamond Growth Plasma. Maximum H-Atom Density is 3.70 ± 0.18 x 10 17 per cm 3...... 113
39. Raw Data for H-Atom TAUF Concentration Map in Methane- Based Diamond Growth Plasma. Xc=0.451, X q =0.048, andXH=0.96 ...... 115
40. Corrected TAUF Data from Figure 39. Maximum H-atom density is 5.09 ± 0.93 x 10 17 per cm 3...... 116
41. Raw Data for H-Atom TAUF Concentration Map in Acetone-Based Diamond Growth Plasma. Xc=0.52, Xo=0.32, and XH=0.67 ...... 117
42. Corrected TAUF Data from Figure 41. Maximum H-Atom density is 2.77 ± 0.28 x 10 17 per cm 3...... 118
43. Repeat Corrected TAUF Scan for Conditions in Figure 41 ...... 119 44. Raw Data for O-Atom TAUF Concentration Map in Acetone-Based Microwave Plasma. Xc=0.41, X q =0.42, and XH=0.67 ...... 121
45. Corrected O-Atom TAUF Data from Figure 44. Maximum O-Atom Density is 1.2 ± 0.12 x 10 17 per cm 3...... 122
46. H-Atom TAUF and Stimulated Emission Pumping (SEP) Signals as a Function of H 2/O2 Mass Flow Ratio in Microwave Plasma. 123
47. O-Atom TAUF and Stimulated Emission Pumping (SEP) Signals as a Function of Acetone /0 2 Mass Flow Ratio in Microwave Plasma ...... 124
x CHAPTER I
INTRODUCTION TO LASER DIAGNOSTICS FOR PLASMA PROCESSING
A. Scientific and Technological Significance of Plasmas The final decade of the twentieth century is witness to a renewed impetus in our capability to manipulate chemically reactive environments to form novel materials in part based on detailed theoretical and computational calculations. As these predictions and models become more elaborate the constant need is to provide quantitative input data and experimental verification. The rapid advance of technologies derived from the inter-related fields of chemistry, physics, and materials science may give the impression that basic experimental inquiry is perhaps counter-productive or even unnecessary and that these achievements are solely driven by economic considerations. However, many areas of endeavor suffer from a lack of basic physical or chemical understanding and are not supported by a solidly established experimental database. The economic impetus to advance production techniques and volume is perhaps unfortunately overshadowing basic research considerations which always provide the initial stimulus for new technologies. A recent panel committee on plasma processing of materials formed under the Plasma Science Committee established by the National
1 2 Research Council agreed with this view and presented as one of their findings that
The demand for technology development is outstripping scientific understanding of many low-energy plasma processes. The central scientific problem underlying plasma processing concerns the interaction of low-energy collisional plasmas with solid surfaces. Understanding this problem requires knowledge and expertise drawn from plasma physics, atomic physics, condensed matter physics, chemistry, chemical engineering, electrical engineering, materials science, computer science, and computer engineering. In the absence of a coordinated approach, the diversity of the applications and of science tends to diffuse the focus of both .1 This course of events is suggested throughout recent work in low- temperature plasma processing of materials. The use of glow discharge plasmas to deposit materials or to modify surface structures through etching processes has been a developing area of technological expertise since the late 1960's. Now important advances are being made in the use of plasma etching techniques for producing novel devices such as quantum interference well surface-emitting lasers and materials such as light-emitting porous silicon 2 while, at the same time, there is poor understanding of the plasma-surface interface chemistry generated by reactive ion or neutral bombardment leading to selective anisotropic etching of the surface atomic components. Beside the etching process, surface modification by exposure to a glow discharge plasma is beginning to find use in the modification of composite materials and metal surfaces and for the critical surface passivation 3 of compound (GaAs) device interfaces for which no native oxide material exists as in the case of silicon. Here again there is incomplete knowledge of how the 3 plasma and its components affects the surface state in these applications. The purpose of this dissertation is to describe the experimental techniques and results for absolutely calibrated concentration measurements of atomic hydrogen and atomic oxygen. Both atomic hydrogen and oxygen are among the most important reactive species generated in plasma processing environments. Such absolutely calibrated measurements provide experimental reference data for a comparison between our theoretical understanding and computational modeling of plasma processing systems. In an effort to provide a secure experimental foundation and theoretical basis for understanding plasma processing techniques and systems such as those mentioned above, the plasma processing research community has in recent years advocated the development of standard reference plasma processing systems. Measurements in a reference plasma reactor would allow multiple plasma diagnostic techniques to characterize as completely as possible the internal operating environment of the reactor. By correlating measurements in several identical reference reactors at different institutions, a standardized concept of plasma reactor design and operation could be achieved. In turn, the standardization of diagnostic measurement techniques would provide reproducible input data and hence improve the ability of theory and computational programs to predict reactor operating parameters and to extrapolate the behavior of the standard reactor to either actual plasma processing production systems or to more innovative and developmental reactors. In 1988, at a workshop sponsored by the 4 Gaseous Electronics Conference (GEC), scientists and production engineers discussed the initial conceptual design of a standard reference cell reactor. The reactor came to be known as the GEC Reference Cell. Since the final design and manufacturing features were completed in 1989, ten of the GEC Reference Cells have been installed at 6 facilities around the U.S. This thesis presents the results of spatially-resolved absolute concentration measurements for atomic hydrogen and oxygen in two actual plasma processing systems. Atomic hydrogen concentration profiles were measured in one of the GEC Reference Cell reactors installed at Wright-Patterson Air Force Base, Ohio. Measurements were also made in a commercially built plasma reactor (ASTEX HPMM System) installed at The Ohio State University which is used for diamond thin film deposition from a microwave-excited CVD plasma. Measurements of atomic hydrogen and oxygen concentration profiles were obtained.
B. Technological Impact of CVD Diamond A recent area of vigorous development involves the deposition of high quality diamond thin films by enhanced chemical vapor deposition. Moderate pressure direct current (DC), radio frequency (RF), and microwave excited glow discharge plasmas are used (among other methods) to provide energetic dissociation and excitation to a hydrocarbon gas mixture. The combination plasma and neutral gas mixture can then be exposed to a variety of hot substrate materials to
nucleate and deposit a material consisting predominately of sp 3 bonded polycrystalline diamond. The technological impact of the advent of low- cost readily produced thin film diamond is enormous. Surface conforming thin film diamond can be made to coat machine tool and bearing surfaces taking advantage of diamond's inherent hardness. The excellent thermal conductivity of the diamond atomic structure has been utilized in the production of diamond heat sinks for use with high power or high density electronic circuitry. In it's own right, diamond has valuable electronic properties; several of which are shown in Table 1 in comparison with those for silicon .4
Table 1. Comparison of Diamond and Silicon Electronic Properties
Property Diamond Silicon Resistivity > 1012 f3-cm 105 f3-cm Breakdown Field 10 7 V / cm 103 V / cm Electron Mobility 2000 cm 2 / V*s 1450 cm2 / V*s Hole Mobility 2100 cm 2 / V*s 370 cm2 / V*s Saturation 2x l 05 m/s lx l 0 5 m /s Velocity Band Gap 5.50 eV 1.12 eV Transmutation Cross Section 3.2 mb 80 mb
With the advantages of low leakage current due to higher inherent resistivity and breakdown field, larger electron-hole mobilities which implies improved device operating speed, larger indirect band gap and radiation hardness, research into the use of diamond thin films is beginning to spawn a new generation of diamond-based semiconductor devices. 6 Along with the ambitious application of thin film diamond technology, there remains the central problem of an incomplete understanding of just how polycrystalline diamond is produced from a wide variety of chemical vapor deposition (CVD) environments such as thermally-activated hot filament reactors, oxy-acetylene flames, low pressure plasma assisted CVD and high pressure thermal arcs and even laser-assisted CVD. It is known that each of these systems is capable of producing polycrystalline diamond thin films under a variety of conditions with varying growth rates, crystalline texture, and resulting thermal and electronic film properties. But, several questions remain as to how these conditions and properties come about:
• Is there one key molecular radical gaseous precursor produced in diamond CVD systems which leads to surface deposition of diamond or are there many variants which lead to similar results? • What is the role of certain atomic species such as hydrogen, oxygen, or fluorine that are generated during the CVD process and are known to interact vigorously with the deposition surface? • Why do so many seemingly varied CVD environments provide remarkably similar diamond deposition characteristics? • What influence do the gaseous components of the CVD process have over the deposition surface crystal orientation and texture? • And, ultimately, can control of the diamond CVD process be achieved so as to step beyond polycrystalline or even homoepitaxial deposition to true heteroepitaxial diamond film growth at productive growth rates and uniformities. 7 Beyond these questions there are still unresolved issues concerning the adaptation of diamond's material and electronic properties for technological applications, but certainly progress in understanding the answers to the above fundamental research questions will provide a firm foothold for manipulating CVD diamond as an innovative material into the twenty-first century. For CVD diamond deposition, it appears that the highest quality diamond films (in terms of electronic and material properties) are produced via microwave plasma enhanced chemical vapor deposition. As far as application to the semiconductor processing, microwave or electron cyclotron resonance (ECR) plasma diamond deposition systems are probably the most readily adapted to current semiconductor production methods; indeed microwave-based systems are beginning to find uses in other areas of plasma processing of semiconductor materials such as reactive ion etching (RIE). However, the techniques discussed in this thesis may be extended to filament-assisted and flame deposited CVD diamond systems.
C. Overview of Plasma Diagnostic Techniques Critical to the development of our understanding of basic plasma chemistry systems is the parallel development of diagnostic techniques necessary to study these environments in situ. The current emphasis now is to develop diagnostics that can be applied towards the difficult task of discerning the variety and absolute quantity of plasma species. Because of the short-lived nature of many important species present in chemically reactive plasmas care must be taken to insure that diagnostic measurements accurately reflect their relative as well as absolute abundances and their relationship to the physical plasma parameters. Currently, plasma diagnostic measurements for plasma-induced species are derived from three basic approaches. External sampling techniques such as mass spectrometry or gas chromatography are capable of generating general survey information about the basic plasma constituents provided efforts are made to make measurements in as close proximity to the plasma volume as possible and to in turn reduce the effect of recombination mechanisms in the external analyzer which artificially perturb the analysis of the nascent population distributions for the species of interest. Wu et al have had good success in self- consistent analysis of reactant species which have been sampled by gas chromatograph probe at the boundary of a CVD diamond deposition hot- filament plasma .5 A second approach makes use of plasma emission spectrometry to detect the presence of certain radical species existing in the plasma. The major drawback of this technique is that it is capable of measuring only excited state radical distributions. Since these states are typically generated by electron impact excitation or dissociation, inferences must be made about the ground state populations for a particular radical. Often due to the low ( < 1 % ) fractional ionization and electron temperature found in electronic processing plasmas, excited state radical species concentrations are in turn a small percentage compared to the ground state concentrations. In addition, electron impact excitation and production cross sections are nonlinearly dependent upon electron translational energy making production pathways complicated functions of electron energy distributions. However, plasma emission spectroscopy can be used to partly determine the degree of dissociation of precursor molecules by determining what excited state fragments are present and to determine plasma physical parameters such as electric fields (Stark broadening) or translational or rotational gas temperatures by analyzing Doppler widths or resolved molecular rotational emission manifolds .6 The final set of experimental approaches utilize laser-based techniques. Such techniques currently offer the best procedures for making non-intrusive in situ measurements of plasma generated ground state radical concentrations as well as some plasma physical parameters. By using a single probe beam of light a reasonable degree of spatial resolution can be achieved in one or more dimensions compared to either mass spectrometry or optical emission measurements. Laser spectroscopic probe diagnostics can be further divided into two general classes. The first class of laser diagnostics consists of those techniques which make use of nonlinear absorption or multiphoton absorption and subsequent ionization to detect the sought after atomic, molecular, or radical species. Coherent anti-Stokes Raman spectroscopy (CARS) and resonantly-enhanced multiphoton ionization (REMPI) or laser optogalvanic spectroscopy (LOGS) are characteristic of this class of laser diagnostic. Both CARS and REMPI can provide an excellent means of detecting a large variety of plasma-generated ground state radicals ,7*8'9 either due to the efficient collection of ionization charge (REMPI and LOGS) or as in the case of CARS the emitted coherent beam of light is emitted in a single direction with small divergence and is easily collected 10 with near unit efficiency. However both techniques suffer from difficulties in calibration and it becomes problematic to place the species distribution on an absolute scale. Due to the highly nonlinear response of CARS calibration of these measurements rely on careful control of the incident beam intensities as well as their overlap in space and time. REMPI and LOGS in particular are difficult to calibrate due to interactions of the laser ionization electron with the surrounding plasma medium resulting in an undetermined electron multiplication factor. The second class of laser-based plasma diagnostics consists of laser absorption spectroscopy and laser-induced fluorescence (UF). While laser absorption spectroscopy may not provide a suitable dynamic range in signal sensitivity and laser-induced fluorescence, which is usually radiated isotropically, does not enable efficient signal collection, they are perhaps more manageable when one attempts to calibrate such measurements and often they can provide better signal to noise ratio than other techniques. Tunable infrared diode laser absorption spectroscopy has been used to measure absolute concentrations for a number reactive hydrocarbon radical species produced in methane-based deposition plasmas .10 Calibration of laser absorption measurements is achieved by using a detailed knowledge of the molecular spectroscopy for the radical of interest; including molecular band strengths, partition functions, spin degeneracy's, transition energies, and path length. Laser-induced fluorescence is beginning to be used to make absolutely calibrated radical species concentration profiles within low- temperature processing plasmas. Previously LIF has been used for 11 measurements on stable molecular species and metastables ,11 positive and negative ions ,12 and for plasma physical parameters such as the local electric field .13 By use of two-photon absorption from the ground state of an atom many light reactive atoms such as H, C, N, O, S, Cl, and F could conceivably be detected by UF measurements in situ in processing plasmas. In the course of research performed for this dissertation, two- photon allowed laser-induced fluorescence (or TAUF) diagnostics have been developed for calibrated concentration measurements for two of the most important ground state atomic species, atomic hydrogen and oxygen. This dissertation describes these measurements and their practical application. The remainder of the thesis is organized as follows: Chapter Two will briefly describe the development and design of the GEC Reference Cell, as well as the diagnostics performed to date on this system. Chapter Three will briefly review the historical development of diamond chemical vapor deposition and then describe what is currently known about the gas-phase plasma chemistry leading to diamond deposition. Chapter Four will describe the experimental techniques used to determine absolutely calibrated concentration spatial profiles for atomic hydrogen and atomic oxygen. Having discussed the experimental methods, Chapter Five will describe the results of experimental measurements in an actual GEC Reference Cell system. Finally, Chapter Six details the results of measurements of atomic hydrogen and oxygen concentrations in an ASTEX microwave diamond growth reactor. CHAPTER n
THE GEC REFERENCE CELL
The Gaseous Electronics Conference Reference Cell (known as the GECRC) concept was initially conceived in 1988. A workshop dealing with preliminary design proposals for a standard reference cell plasma processing reactor was held during the 41st Annual Gaseous Electronics Conference (GEC) at the University of Minnesota in Minneapolis in October 1988.14 The workshop attendees were asked to review several preliminary design proposals for the reference plasma system. Upon extended discussions a consensus was reached on developing a radio frequency (RF) excited parallel plate electrode plasma reference cell operating at 13.56 MHz. The following March of 1989, another workshop sponsored by SEMATECH was held in Austin, Texas .15 At this workshop a committee of representatives from the plasma processing community reviewed comments from forty other plasma processing researchers regarding the initial design proposal formulated at the previous conference. Upon review of these comments the committee then finalized the GECRC design and determined the need to have four of the reactor systems built by industrial suppliers to test the GECRC design. The basic configuration for the system is shown in Figure 1 in cross section.
12 13
Cooing Wator Gas Feed Top Insulator
Metal Hold-down Ring Ground Shield Top Electrode O-RIng Seal Shower Head Top Flangt^
Main Viewing Ports Port tor High t. Vacuum Pump-oul
Bottom Flange Bottom Electrode Manifold for flowing gas f Ground Shield operation Bottom Electrode
Annular Pump-out \ Connection
Figure 1. The GEC Reference Cell 14 Since that time on the order of ten GECRC's have been installed and are operating at research organizations throughout the U.S. at institutions such as AT&T Bell Laboratories, IBM, National Institute of Standards and Testing (NIST), Sandia National Laboratories, the University of Michigan, the University of New Mexico, and Wright- Patterson Air Force Base. International interest in the standard reference cell concept has increased with researchers in France, Germany, and Taiwan planning to purchase the GECRC system. Japan is developing a separate reference cell design. The basic configuration of the GECRC as mentioned is shown in Figure 1. The cell is a UHV stainless steel chamber with a volume of approximately 12.9 liters, comparable in size to standard production plasma processing reactors. The 4 inch diameter water-cooled electrodes used are made of aluminum with an adjustable (optional) interelectrode spacing nominally set at 1 inch. Provisions were made in the design to allow for other electrode materials such as stainless steel. The electrodes are insulated from the rest of the assembly by either alumina or teflon insulators. Surrounding the electrode insulators are grounded guard rings or shields which serve to help confine the plasma discharge to a cylindrical region between the electrodes of diameter approximately equal to the electrode diameter as well as to reduce sputter etching of the insulator material. Vacuum pumping is accomplished through connection of the main chamber to a lower pump-out chamber. Slots in the flange interface between the two chambers serve to minimize angular variations in gas pumping speed around the main chamber volume. The chamber is 15 typically pumped with a 300 liter per second turbomolecular pumped backed on the foreline by a diaphragm roughing pump. The GECRC is designed to have a pump down base pressure of 10'? Torr and has low conductance because the pump-out manifold does restrict pumping speed. Typical gas flow rates are 10-100 standard cubic centimeters per minute (seem) and operating pressures range from 50 milhtorr to several Torr. Access to the main chamber is provided by eight in-plane viewports: two 8 -inch ports, two 6-inch ports orthogonal to the 8 -inch ports, and four 2.75-inch ports intermediate between the larger ports. Longitudinal optical access to the inter-electrode volume can be achieved through any of these ports while complete radial or lateral access can only be accomplished through the largest ports. The window material is nominally high-grade vacuum port glass or for the measurements discussed in this thesis two of the 2.75-inch viewports were made of Supersil-1 fused silica. The reactor chamber is typically filled with ultra-high purity research grade gases such as argon, helium, or hydrogen adjusted to specified flow rates by electronically controlled mass flow controllers. An electronically actuated throttle valve at the inlet to the turbomolecular pump provides pressure selection and stabilization. Either electrode of the GECRC can be grounded and the opposite excited by frequency/pulse generator and RF power amplifier configuration either with or without the use of an in-line matching network. Upon assembly and initial operation of five of the GECRC's, a program of electrical characterization was initiated. The electrical 16 characterization diagnostics were discussed at a conference session during the 42nd Annual GEC held at Palo Alto, California in October 1989.16 By the time of a separate workshop meeting hosted by SEMATECH of the GECRC design committee held in July 1990 at Dallas, Texas it had become apparent that electrical characterization and comparison between the few then operating GECRC's was not straightforward. This meeting established stringent procedures to make the required current and voltage measurements. The first public comparison of electrical data from six reference cells from five installations were presented at the 43rd Annual GEC held at the University of Illinois at Champaign-Urbana in October 1990.17 Initially, the electrical diagnostics were to be comprised of measurements of current and voltage waveforms for the amplitudes and phases of the first five harmonics (Fourier components) of the excitation frequency and the associated DC bias for specific applied peak-to peak voltages across the electrodes and at various pressures of argon. It quickly became apparent that a direct comparison of electrical measurements between plasma reactors was complicated by seemingly minor variations in the external circuitry associated with both the measuring probe instruments and the power electronics. Variations were to be expected between cells with differing electrode and insulator materials, but, remarkably, even minor variations in power amplifier output impedances at higher harmonics of the excitation frequency led to variations of as much as 20 percent in harmonic amplitudes and phases and as much as 40 percent variation in developed DC bias in the volume of the plasma. 17 For those experienced with RF parallel plate discharge operation, the complexity of these results was surprising and implied that the relatively simple assumptions describing the equivalent circuit for both the reactor chamber and the external circuitry had to be more carefully considered. Furthermore, the sensitivity of the electrical behavior of supposedly exactly similar reactor systems would force those modeling plasma processing reactors by the use of computers to rethink their assumptions regarding the influence of the external circuitry. The final effect of these measurements was to demonstrate that for commercial plasma etching systems, the choice of power supply equipment and networks, grounding, cabling, would strongly influence the reproducibility of system-to-system design and operation, impacting on the actual plasma voltage, current, and DC bias and hence in etching performance and the degree of anisotropy of etched profiles as well as potentially the etching chemistry at the plasma-surface interface. With the problems regarding electrical characterization and correlation having been clarified, researchers began to branch out into a variety of other diagnostic measurements on the GECRC. In 1990, the first reports on measurements of optical emission profiles from argon discharges in the GECRC appeared .18 The following year saw an enormous increase in the number and types of experiments being performed on the GECRC .19 These experiments fell into three categories. The first involved more refined electrical diagnostics, which were more precise impedance measurements over a wide frequency range leading to a detailed consistent description of the GECRC in terms of an improved equivalent circuit model. In addition, a low-pass filter circuit 18 was developed for the input power feed to the cell which eliminated the sensitivity of plasma operating conditions to the external circuitry .20 The second category of experiments were those performed to estimate plasma species' distributions and concentrations. Experiments have now encompassed measurements of electron densities, ne, in argon and helium discharges by microwave interferometry, helium metastable spatial density profiles by optical absorption, time-resolved optical emission studies, and ion kinetic energy distributions by quadrupole mass spectrometry. While practically none of these experimental results has yet appeared in publication, the intent to use the GECRC as an platform for reference diagnostic experiments is well established. A third category of experiments represents the first attempts to relate the reference capability of the GECRC to practical production etch processes by running CI 2 and C^/HBr etching discharges in a reference cell and observing the etching parameters and rates for the etching of silicon. The results demonstrated were consistent with etching rates and profiles from production systems. Soon after the initial development of the idea for a standard reference plasma system, researchers working in plasma modeling began to develop computer codes to simulate the GECRC. By 1991, results were presented at the GEC for a variety of computational approaches to modeling the reference cell. Along with the development of computer codes, a concerted effort has now been to compare the computational results with experimental measurements from the GECRC. Some debate has insued over whether or not the GECRC can be successfully modeled as a one-dimensional system. The computer codes used are currently 19 only capable of predicting some plasma parameters such as electron densities and energy distributions, voltage and current at the plasma, and electric fields internal to the plasma. Preliminary comparison of extrapolated emission profiles based on computational results and known excitation cross-sections with measured emission profiles seem to indicate that a one-dimensional modeling approach may be sufficient. Measured emission profiles show little radial variation across the diameter of the electrodes. Determining whether one-dimensional codes are reasonable is important because of the computational complexity and expense of higher-dimensional codes. Some researchers feel that while there is some scientific interest in measurements in a RF parallel plate electrode system such as the GECRC, the industrial uses of plasma processing are now focusing on the use of microwave-based electron cyclotron resonance (ECR) or Helicon 21 source plasmas and thus measurements on a parallel plate electrode configuration are beginning to be outmoded. The advantages, however, of using a system such as the GECRC are the generally simple design and the ability of researchers using the GECRC to correlate their measurements with the large amount of experience and literature that has been accumulated over the past several decades regarding the diagnostics and operation of parallel plate plasma processing reactors. A solid understanding and ability to predict, design, and control precisely a parallel plate reactor's environment as in the GECRC should provide a firm basis for extending the scientific (versus empirical) design of more innovative plasma processing systems. 20 Support for continued advances in diagnostic measurements and refinement in computational models for the GECRC is strong. In particular, those developing computer models are now being asked to incorporate excitation and production cross-sections and mechanisms for plasma species in addition to electrons such as ions and neutral species and to include the interactions of all plasma species with the electrode surfaces. The aim of computer modeling is to predict absolute concentration profiles of the most important plasma-generated species. At the same time, experimentalists are striving to develop diagnostic techniques to measure ion and neutral populations and distributions produced in the GECRC and to place these measurements on a absolutely calibrated scale rather than just a relative basis. Part of the work reported in this dissertation describes such absolutely calibrated measurements in a GECRC for concentration spatial profiles of neutral atomic hydrogen produced in the simple RF H 2 discharge. CHAPTER m
DIAMOND CHEMICAL VAPOR DEPOSITION CHEMISTRY
The deposition of diamond from a gaseous medium was first described in 1956 in a technical report discussing the 1952-3 work of William G. Eversole at Union Carbide Corporation .22 Eversole's low- pressure vapor deposition of diamond on diamond seed crystals predates the process for growing industrial grade diamonds at high pressure developed by General Electric Company in 1954 and is most certainly the first known instance of man-made diamond growth. Eversole patented the process in two U.S. patents in 1958.23 Parallel efforts at diamond synthesis also took place in Sweden (1953) and more notably in the U.S.S.R in 1956. The work in the Soviet Union was directed by B. Derjaguin whose work successfully culminated in the low-pressure deposition of diamond without the use of seed crystals. The work was of course published in Russian and was not known internationally until translated reviews began to appear in the late 1960's and early 1970's.24 Work on low-pressure diamond synthesis was continued through the 1970's by both the Russian researchers 25 and now American scientists. John Angus and his group as Case Western Reserve University improved upon methods of homoepitaxial vapor deposition of diamond onto natural diamond powder using various hydrocarbon gas mixtures and were the first to describe the critically important etching of
21 22 graphitic carbon by supersaturation of atomic hydrogen .26 Along with low-pressure synthesis, ion beam deposition of diamondlike carbon was first achieved in 1971.27 The early results with low-pressure diamond synthesis resulted in inhomogeneous films which grew at commercially impractical growth rates of less than 0.1 pm per hour, however this work provided the initial experimental motivation for the explosion of work on diamond CVD which began the early 1980's. Deposition of faceted polycrystalline diamond thin films without the use of seed crystals from hot filament and plasma-assisted CVD was conclusively demonstrated by researchers at the National Institute for Research in Inorganic Materials in Japan in 1982-83.28 The diamond grown by these processes were typified by the criteria later established for characterizing diamond growth: • The film can be characterized as having a definite crystalline morphology and texture observable by either optical or electron microscopy. • The deposition product has a clearly defined diamond crystalline structure identified by x-ray or electron diffractometry. • Using a Raman spectrometer, the film has a single first-order line centered at 1332 cm 1 shift. There has been much initial enthusiasm over CVD diamond because of the dramatic increase in diamond film growth rates; making the general CVD process for diamond applications at least conceptually possible. Work on CVD diamond continued throughout Japan with several hundred patents gained to date. Research on diamond CVD expanded internationally since 1982 as it became quickly apparent that 23 for a modest outlay in capital equipment anyone could produce CVD diamond. The original methods of hot filament-assisted and microwave plasma-assisted diamond CVD have been improved upon and additional techniques have also been developed. The approach of using ion beams for deposition has continued for either slow homoepitaxial growth on natural diamond or for preparing nucleation sites on substrate materials via ion bombardment .29 In 1988 journal papers appeared describing the use of atmospheric pressure oxy-acetylene torches for diamond deposition .30 The films grown in this manner have very high growth rates («100 fun/hr) and good crystalline quality, but are prone to nitrogen incorporation from ambient air entrainment and have poor uniformity and void defects. Extending the ideas of high temperature - high pressure deposition, several researchers have used thermal arcs (also known as plasma torches) to deposit diamond at very high growth rates on the order of 1 mm/hr .31 Homogeneous diamond growth has even been demonstrated directly from the gas phase and as a result of laser excitation of gas mixtures .32*33.34 Further reviews of diamond CVD technology can be found in several current journal articles .35-36-37-38 Since diamond growth from the vapor phase has been produced in a variety of CVD processes, several observations regarding the gas phase chemistry can be made which in turn generate some questions. First, an energetically activated gaseous medium is required to generate the necessary gas-phase diamond precursors. As of yet, merely the presence of a heated substrate in a simple gas flow of neutral low-temperature precursor gases is not sufficient to yield diamond growth; and there is no published data to suggest a high-temperature substrate can generate 24 diamond. The current evidence suggests that dissociation and/or activation of the precursor gases must be accomplished by either using the addition of electrical energy as in plasma-assisted CVD or the addition of thermal energy to the gas phase chemistry as in the cases of hot-filament-assisted or combustion-assisted CVD. Secondly, in reviewing the literature on reported methods of CVD diamond growth, one is struck by the wide variety of gas mixture compositions used to deposit diamond. Bachman et al have written an excellent review article tabulating most of the known diamond deposition gas mixtures as well as the corresponding deposition method .39 In addition, using the stated gas mixtures given by various researchers, they determined the atomic fractions of carbon, hydrogen, and oxygen atoms and then related the predominant precursor atomic fractions leading to diamond growth to a specific region in a ternary C-H- O phase diagram. A simplified presentation of the given in Reference 37 is shown in Figure 2. The axis scales of this diagram are fractions given by
*< = (C 70)' x'=j£cr X ° = WW) (1) where C, H, and O denote the atomic species concentrations. Thus, a gas mixture which gives diamond deposition from a microwave plasma such as 500 standard cubic centimeters per minute (seem) H 2, 50 seem CH4, and 20 seem O2 has atomic fractions Xc = 0.555, XH= 0.960, XQ = 0.032 which corresponds to datapoint #47 in the previous reference. Figure 2. C-H-0 Phase Diagram. Unshaded area is nominal diamond growth region 26 Beyond obviously needing a carbon-bearing precursor, it has been apparent for some time that a superabundance of atomic hydrogen, or oxygen, or even perhaps a halogen such as atomic fluorine must be present at the deposition gas-surface interface .40 Three reasons for this requirement can be advanced. First, it is known some atomic species react more readily with sp2-bonded or graphitic carbon than with diamond-bonded carbon and hence more rapidly etch away the non diamond carbon that has been deposited. Secondly, the presence of the non-carbon atomic species may promote the sp 3 bonding leading to diamond or may terminate the dangling carbon surface bonds in such a manner as to enable an advancing growth front. Finally, the non-carbon atomic species may play a role in the gas phase chemistry to help in the production of a suitable diamond deposition precursor species. We now review the previous work on measurements of gas phase species which are thought to be active in the chemistry of the diamond CVD process. To date the consensus among researchers working with diamond CVD is that one of the following radicals or molecules, CH 3,
CH4, C2H2, or C2H4 is probably the reactive precursor to diamond growth from the gas phase. Among these species, the methyl radical alone or a combination of methyl radicals and acetylene molecules seem to be the most likely candidates as derived from a variety of indirect observations and reaction kinetic calculations. Besides the need for a hydrocarbon precursor, it has long been know that a supersaturation of atomic hydrogen is required to achieve predominately sp3-bonded carbon deposition. The role of atomic oxygen is also thought to be important in that enhanced deposition rates and diamond film quality are observed 27 when oxygen is added to a CVD system either as O 2 or as part of a larger hydrocarbon complex. Some concentrations of gas-phase species in plasma CVD (also in filament-assisted CVD) can be ascertained by mass spectrometry, optical emission studies, resonantly-enhanced multiphoton ionization, and laser-induced fluorescence. All of these techniques have been applied to the study of the diamond CVD for either plasma-assisted or filament- assisted deposition. Emission studies of plasma-assisted diamond CVD from a methane-hydrogen gas mixture have shown increased emission from atomic hydrogen and radicals such as CH as one increases the applied excitation power, while CARS measurements of H 2 and CH4 concentrations show a corresponding depletion .41 These observations are indicative of a high degree of molecular dissociation. Optical emission can also show the presence of carbon monoxide, C 2 and OH radicals, and carbon atoms depending upon the gas mixture used. As such, even given the small amount of observed species which predominate in emission, experience with the kinetics of combustion chemistry suggests that there are many reactive pathways in diamond CVD plasmas which provide an involved reactive chemical environment made even more complex by the presence of ionic species. Modelers of the diamond CVD process use chemical kinetic computer codes to attempt to predict concentrations of possible diamond growth precursor species. However, several of these precursors
C2H2, C2H4, and CH3 do not emit in the plasmas and hence cannot be detected by optical emission measurements. Instead some researchers have used either infrared laser absorption, mass spectrometry, or REMPI 28 in an effort to detect them and assess their absolute or relative concentrations. Davies and Martineau have measured concentrations of
CH4, CH3, C2H2, C2H4, and C2H6 in methane CVD plasmas by using IR laser absorption.42 While their measurements were performed at lower pressures than typically used for diamond CVD form plasma (~ 1 Torr versus >10 Torr) they show that the concentration of methyl radicals depends linearly with increasing electron current in the plasma, decreases with pressure at constant current, and is enhanced by the addition of molecular hydrogen. Furthermore, enhanced diamond deposition rates were observed with increasing methyl radical concentration. The stable molecular species, CH4, C 2H2, C2H4, and C 2H6 have been shown to have concentrations which are roughly independent of plasma current or power. These results suggest the methyl radical is necessary for diamond CVD given the dependence on growth rates with increased methyl radical concentration. The CH3 radical and excited-state carbon atoms have also been detected using REMPI by Celii and Butler in a hot filament-assisted diamond CVD system.43 Under conditions of saturated electron collection, REMPI measurements for the methyl radical can be made linearly proportional to the concentration. The measurements are not on an absolutely calibrated basis, but do provide a linear response which can used to make relative measurements as a function of gas mixture ratios or distance from the filament. The relative CH3 concentration was found to be only slightly dependent on filament temperature, but strongly dependent on CH4/H2 feedstock ratio in the range from 0.5 to 296 CH4. The presence of excited state carbon atoms could not be 29
ascribed to the dissociation of the CH 3 or CH4. It was also postulated that the REMPI atomic carbon signal could be due to photolysis of aromatic carbon complexes by the probe laser as the signal did not vary in the same manner as the CH 3 response to operating conditions. These measurements have not yet been extended to plasma-assisted CVD systems. Gas chromatography or mass spectrometry can be used both with filament-assisted and plasma-assisted diamond CVD. Wu et al. results using a gas chromatograph show that for filament assisted CVD, CH 4 is converted into C 2H2 as the major stable molecular species, the interconversion rate increasing with filament temperature .44 Other hydrocarbons such as C 2H4 and C2H6 (reaction intermediates) were measured at nearly two orders of magnitude smaller concentrations than CH4 or C2H2. Recently Hsu at Sandia National Laboratory has adapted a molecular beam mass spectrometer to a microwave plasma-assisted diamond deposition system .45-46 This system is capable of determining mole fractions at the entrance to a quartz probe tip placed at the boundary of the plasma. The species measured were H, H2, CH3, CH 4, and
C2H2 for a methane-hydrogen gas mixture. Based on these measurements Hsu surmises that the neutral species relative abundances and concentrations are very similar to those found in filament-assisted thermal CVD below 196 CH 4 percentage and thus the CVD diamond deposition process is dictated primarily by neutral chemistry. The role then of the plasma is to produce greater amounts of atomic hydrogen by dissociation of H 2 than can be achieved by filament 30 decomposition and hence a greater supersaturation of H-atoms at the growth surface. Two other studies based upon isotopic enrichment of a hydrocarbon precursor by enriching with the 13C isotope merit
discussion. D'Evelyn et al. at Rice University performed 13CH4 - 12C2H2 isotopic competition experiments for diamond deposition to determine which precursor was most effective in promoting diamond growth .47 By studying the isotopic shift of the 1332 cm *1 Raman line of diamond, their results demonstrated that methane is ten times more effective as a CVD diamond growth precursor than acetylene and also by the efficient interconversion of CH 4 and CH3 reacting with H and H 2, the methyl radical is the indicated growth species. These conclusions were later reproduced by similar experiments using Raman shift analysis 48 The use of nuclear magnetic resonance (NMR) spectroscopy in conjunction with Raman isotopic shift studies has been performed to study the incorporation of ]H and 13C into filament-assisted CVD diamond films 49 In these experiments 13C was substituted either for the methyl radical carbon or for the carbonyl carbon in the acetone precursor for a 22% enrichment in either case. Careful analysis of the NMR resonance line shapes and line shifts enabled a determination of the concentrations of iH and 13C in the solid films. The overall enrichment of 13C in the diamond films was 2296 in accord with the gas phase enrichment. This agreement was shown to be true for either isotopic enrichment at the methyl radical or at the carbonyl radical comprising acetone. The isotopic shift of the 1332 cm *1 Raman line confirmed this observation. The incorporation of carbon from the carbon 31 attached to the oxygen in acetone has implications for the results presented in Chapter Six regarding measurements of atomic oxygen concentrations in a microwave plasma-assisted diamond CVD system. Plasma-assisted CVD diamond can be grown from a variety of gas mixtures, all of which provide some amount of atomic hydrogen and atomic oxygen. High growth rate CVD diamond growth was of course first demonstrated from gas mixtures of CH 4 and H 2 or C2H2 and H 2. Since then CVD diamond has been grown from mixtures such as CO-O 2-
H2,50 CH4-Ar-02,51 and H 2O with various alcohol's 52 to mention just a few. In many cases attempts have been made to describe the roles of atomic hydrogen and oxygen in producing CVD diamond. Comparison of film crystalline morphologies and other properties as a function of molecular hydrogen or oxygen content in the gas mixture is the most common means of inferring the effects of the atomic species. Along with film properties comparison, some investigators have use plasma emission or mass spectrometry to try to deduce the influences on gas phase chemistry. Initially attention was focused on the action of atomic hydrogen in
CVD plasmas .53 Next, additions of rare gases were seen to partially promote film quality and growth rates .54*55 Starting in 1987,56 the addition of oxygen was shown to have dramatic effect on the range of gas mixture ratios of hydrogen to hydrocarbon over which diamond could be grown as well as a general reduction in substrate deposition temperature. Over the past few years, several research groups have reported on the influence of atomic hydrogen and oxygen in their deposition processes, again, either by examining film properties or by 32 analyzing relative species concentrations measured as intensities taken from mass spectrometry .57-58.59.60.61-62 To summarize the current understanding of the roles of atomic hydrogen and oxygen in plasma-assisted diamond CVD, the following points can be made: • H atoms, primarily produced by electron impact dissociation in the plasma, readily diffuse to the growth substrate and act preferentially to etch sp2-bonded (graphitic) carbon at the growth surface.
• In addition, H atoms may react with CH 4 in the gas phase to produce methyl radicals. • Not only will H atoms act as a surface etchant, but may help terminate carbon surface bonds. • O atoms may act in a similar manner to H atoms to etch non diamond surface complexes. • O atoms can react preferentially with certain hydrocarbons such
as C2H2, hence freeing up more atomic hydrogen to interact at the surface. • O atoms are not present in large concentrations compared to H atoms. This is because they easily react with hydrocarbons and are trapped, particularly when CO is formed. To date H atoms have only been detected and their concentrations measured in filament-assisted diamond CVD. H atom concentrations have been inferred from CARS detection of H 2 concentration and temperature measurements assuming translational and rotational temperature equilibrium between H and H 2 at a constant total 33 pressure .63 Two photon laser-induced fluorescence has been used to determine H atom concentrations near heated filaments in hydrocarbon-
H2 gas mixtures, though without the presence of a deposition substrate surface.64-65 Typical H atom concentrations are 1-3 x 10 14 cm'3. No in situ laser diagnostic measurements for H atoms or 0 atoms have as yet been performed in plasma-assisted diamond CVD systems. The importance of making absolutely calibrated concentration profile measurements of both H atoms, and when they occur, O atoms is readily apparent. Chapter 4 will describe the experimental techniques used for such measurements in a plasma and Chapter 6 will describe data measured during actual microwave plasma-assisted diamond CVD. CHAPTER IV
EXPERIMENTAL TECHNIQUES
A. Experiment Apparatus The use of the laser as a powerful spectroscopic tool has introduced the laser probe diagnostic to plasma discharge research as a means of making in situ, localized, and temporally precise measurements on a variety of chemical plasma parameters, including electric fields ,66 gas species temperatures and velocities 67 and concentrations .68 Important to all varieties of low temperature plasma discharge environments are the presence of atomic species usually generated via electron impact dissociation of larger parent molecules. The atomic species present in plasma discharges can be generated with considerable translational energies and have either excited state or ground state chemical activity relative to other species in the discharge or surfaces. The capability to measure relative populations or absolute concentrations of atoms in plasmas can provide information on one of the dominant active species in chemical plasmas. Laser-induced fluorescence (LIF) has been used to observe several atomic species important to plasma processing, including carbon ,69 chlorine ,70*71 fluorine ,72 hydrogen ,73 nitrogen ,74 oxygen ,75-76-77-78 and sulfur.79 Our research has focused on measuring ground state atomic hydrogen and atomic oxygen by two-photon absorption ILF (TALIF) in RF
34 35 discharges for both the spatial profile dependence and temporal behavior .80 Measurement of atomic ground state populations in discharges is important for two main reasons. First, as in the case of hydrogen, the use of hydrogen-bearing or hydrogenic plasmas are important for semiconductor processing applications such as amorphous
silicon deposition from silane (SiH 4) discharges, as previously mentioned for H 2 discharge passivation of GaAs, and for H 2/CH4 discharge etching of InP 81 and now for the production of novel materials such as diamond thin films by plasma-assisted chemical vapor deposition. Certainly, atomic hydrogen is known to be the dominant reactant species produced by these discharges, so that measuring H-atom production is useful for modeling and design control of these processes. Likewise, detection of ground state atomic oxygen is important for understanding a variety of oxygen-based discharges; such as O 2-CF4 discharge etching of silicon .82 Secondly, it is often the case that the TAUF or UF techniques for hydrogen and many other atoms require the use of a probe laser with a wavelength shorter than the tunable transmission cutoff of KDP at 217 nm .83 Although this makes the atomic detection technically more difficult, we have successfully demonstrated the TAUF technique for hydrogen using both Raman shifting in H 2 gas and sum-frequency generation (SFG) in a beta-barium borate crystal (BBO) to reach the 205 nm wavelength required.
1. Laser System Configuration A schematic of the general experimental scheme used for the TAUF H-atom detection is shown in Figure 3. The schematic layout shows a RF 36
FREQUENCY GENERATOR
DISCHARGE Nd:YAG 532 nm 615 nm DYE LASER KDP CRYSTAL GATE LASER MIXER
1Q-SWITCH TRIGGER -Q 6 1 5 n m fr- 1 RF POWER MATCHING AMPLIFIER NETWORK DICHROIC 307 nm MIRROR 6 - o - B - p ' POLARIZATION ROTATOR I ] BBO CRYSTAL
205 nm GATE ESII TO CELL POSTTION PELUN-BROCA TRANSLATION TIME DELAY SIGNAL GENERATOR PRISM STAGES
REACTOR CELL
IBM-AT X-Z STAGE DIGITIZER COMPUTER CONTROLLER
Figure 3. Experiment Layout Schematic for H-Atom TAUF 37 reactor cell power supply system, the 205 nm generating laser system, and the associated acquisition and control electronics. The laser light generation configuration will now be described and the acquisition electronics are discussed in the following section.
The TAUF transition for atomic hydrogen is from the ls 2S1/ 2 ground state to the 3d2D5/ 2,3/2 and 3s 2Si/ 2 excited states at 97492 cm'1. Both excited state levels are populated due to the energy level degeneracy in hydrogen for different angular momentum states and due to the two-photon absorption selection rule of Al = 0, ±2. The transition requires two 205.14 nm photons to excite the atomic ground state. The
TAUF transition has also been observed in deuterium at 97519 cm 1 in the course of this research. The excited state is weakly populated by the discharge impact kinetics due to a rapid (~15 nsec) radiative lifetime. Thus, the TAUF excitation can be expected to populate effectively the upper state provided sufficient photon density is available given the small two- photon absorption cross-section. TAUF measurements for H-atoms can be performed using a high pressure H2-filled Raman cell or by sum-frequency mixing (SFM) in a beta-barium borate (BBO) crystal. For our purposes the use of SFM with a BBO crystal is preferred since SFM generates far more 205 nm light. The light generation scheme depicted in 3 was used in all but our initial experiments. The probe laser is generated by pumping a Quanta-Ray PDL-2 dye laser with the second-harmonic 532 nm output of a Quanta- Ray DCR-2A Nd:YAG laser operating at 20 Hz. The dye laser operates with Exciton Sulfurhodamine 640 dye at 615 nm. The dye laser output is frequency doubled using a Quanta-Ray WEX KDP crystal providing an output of 7 mj/pulse at 307 nm and a residual 14 mj/pulse at 615 nm. Upon exiting the WEX system, the polarization of the 307 nm beam is rotated to coincide with the polarization of the 615 nm beam. Both beams are collimated with a 3:1 telescope and combined via a dichroic mirror. The collinear, collimated beams are input to the BBO crystal manually angle tuned to provide SFG at 205 nm. The input beams spot size diameter is 3 mm. The SFG output from the BBO crystal can be as high as 800 microjoules/pulse with careful alignment and overlap of the two input beams. The output pulse energy is carefully measured against a newly calibrated Molectron Model J3-05 Joulemeter. Using the BBO SFM technique gives over ten times the output of the H 2 Raman shift technique. The conversion efficiency of BBO at this wavelength has been quoted as high as 12% in the literature and the efficiency of our system was measured at 11% which is predominantly dictated by the input beam's profile quality and alignment. Upon leaving the BBO crystal the residual input pump beams are dispersed by a Pellin-Broca prism and beam dumped. The TAUF probe beam is tightly focused by a quartz lens through a Supersil 1 quartz window into the discharge reactor of interest. Detection of O-atoms by TAUF is accomplished by utilizing a two- photon transition from the 2p 3P2 ground state to the upper excited
3p3p 2>ii0 states upon absorption of two 226 nm photons. The fluorescence decay between the 3p3P states and the intermediate 3 3S} excited state is observed at 845 nm. The lowest energy (J”=2) fine structure component of the ground state is selected as the lower state 39 for the two-photon absorption process. The laser linewidth is sufficiently narrow to select only this component and also provides the greatest signal strength due to the inherent population of mainly this level. All of the upper excited state fine structure levels are populated by the transition. The generation of 226 nm photons is similar to the procedure used to generate 205 nm light; though for the wavelength required the use of a BBO crystal was unnecessary as KDP conversion was satisfactory. A schematic of the experimental layout for O-atom TAUF measurements is shown in Figure 4. Conversion of the dye laser system from one TALIF measurement to the other can be accomplished in one day, and most optical components can be left in place to facilitate a rapid conversion. The 226 nm light is generated by pumping a dye laser filled with a mixture of Rhodamine 590 and Rhodamine 610 laser dyes solvated in methanol using the 532 nm second harmonic output from a Nd:YAG laser. The dye fundamental output at 572 nm is upconverted to its second harmonic at 286 nm using a KDP doubling crystal and subsequently mixed with the residual 1.06 micron fundamental output of the Nd:YAG laser in a second KDP crystal. The residual beams were dispersed and discarded using a Pellin-Broca prism. The 226 nm laser probe beam was then passed into the reactor through a Supersil 1 quartz lens and window. Typical laser energy output at 226 nm is 500 microjoules per pulse at 20 Hertz. FREQUENCY GENERATOR
DISCHARGE Nd:YAG 532 nm DYE LASER 572 nm KDP CRYSTAL GATE LASER 1060 nm 1060 nm MKER 'Q-SWITCH TRIGGER J RF POWER MATCHING AMPLIFIER NETWORK Beam Dump
GATE 226 nm TO CELL POSITION PELUN-BROCA TRANSLATION TIME DELAY SIGNAL GENERATOR PRISM STAGES
REACTOR CELL
IBM-AT X-Z STAGE DIGITIZER COMPUTER CONTROLLER
Figure 4. Experiment Layout Schematic for 0-Atom TAUF 41 2. Signal Detection and Analysis Our initial refinement of both the H-atom and O-atom TAUF diagnostic was performed using a small glass discharge reactor that has a variable gap cylindrical planar electrode design with water-cooled stainless steel or aluminum electrodes. The discharge load power can be measured with a high voltage probe and a current loop detector with output acquired on a digital oscilloscope and multiplication averaged upon waveform transfer to the IBM-PC. The reactor cell is mounted on a stepper motor positioned X-Z translation stage which allows spatial profile measurements as the cell is translated relative to the fixed laser probe focal point, as viewed by the fluorescence collection optics.
The excited state fluorescence from the 3d2D5/2t3/2 and 3s2Sj/2 levels to the 2p 2p 3/2ii/2 at the Balmer alpha line (656.3 nm) transition is detected perpendicular to the primary discharge cell axis and the laser probe beam with focused collection optics. The TAUF passes through a 10 nm FWHM interference filter centered at 656 nm and focused on the photocathode of ITT Model 4123 gated photomultiplier tube (GPMT). Detection of H-atom TAUF is also easily achieved (provided the average DC current does not exceed the rating of the particular photomultiplier tube) by using continuous (CW) photomultipliers such as the RCA 1P28 or Thorn-EMI 9659 tubes. O-atom TAUF requires more red-sensitive tubes, in which case the Thorn-EMI 9659-QB or Hammatsu R928 tubes are satisfactory. The signal collected by either a GPMT or CW photomultiplier is fed directly to the input Tektronix DSA 601 Digital Signal Analyzer or other similar high-speed digital oscilloscope. The data acquisition, dye Figure 5. Representative H-Atom TAUF Signal Signal TAUF H-Atom Representative 5. Figure Trace H—Atom TAUF Signal, millivolts 20 10 25 15 30 35 5 1 2 3 4 5 6 7 B 0 100 00 BO 70 60 50 40 30 20 10 0 ie nanoseconds Time, M Vlae 0 V 700 PMT - Voltage HammatBU 02S
43 laser tuning, and experiment timing is controlled by a Stanford research System Digital Delay Generator in combination with an IBM-386 microcomputer. The experiment timing sequence allows for temporally- dependent measurements of H-atom TAUF over all relative phases of the RF discharge driving cycle. The use of a GPMT and a narrow-band interference filter in the collection optics allows detection of the TAUF response even in the presence of the bright plasma-induced emission (PIE). In working with the larger reactor systems it was found that even using a CW photomultiplier was sufficient provided the anode current of the tube was carefully monitored and did not exceed the maximum rating. A representative H-atom TAUF signal trace is shown in Figure 5. The TAUF resonance transition is shown for a typical set of discharge operating conditions. As shown, the TAUF signal has an excellent signal/noise ratio, which is typical of the TAUF signal over all phases of the RF cycle relative to the PIE. The full-width-half-maximum (FWHM) two- photon linewidth of the TAUF resonance is typically 3.5 ± 1 cm'1. The dye laser linewidth at 615 nm is approximately 0.6 cm 1, as measured independently by optogalvanic detection of neon and iron transitions in a hollow-cathode glow discharge lamp. Multiplying this by a factor of 6 (third harmonic of 615 nm times two photons) accounts for the FWHM linewidth of the TAUF transition. Note that the associated Doppler linewidth for the two-photon absorption in hydrogen at a neutral atom temperature of 300-500 Kelvin is <1.0 cm'1, which might be expected in the center of the discharge gap at zero degrees phase angle in the RF current cycle; thus, our TAUF 44 measurements do not have a sufficiently small laser probe linewidth to measure H-atoms with small translation energies without etalon narrowing of the dye laser fundamental output.
B. H-Atom and O-Atom Concentration Calibration Procedure. Having developed a laser diagnostic to detect H or O atoms, it would be useful to place the number of atoms detected on an absolutely calibrated scale and determine actual local concentrations of atoms directly in the plasma. By directing an external source of H or O atoms into a central position in the volume of a plasma reactor, the TAUF signal derived from this source can be made to simulate detection of plasma-generated atoms. The external source of atoms, usually generated via microwave discharge, provides a steady, reproducible, and controllable TAUF response. Simultaneously, small quantities of molecules known to efficiently react and combine with the atomic species can be added and a corresponding decrease in the TAUF signal intensity can be observed as the atoms are depleted. This reaction or titration technique can give a reliable means of determining the concentration of atomic species corresponding to a given amount of TAUF signal. Calibration of the fluorescence signal collected by the PMT-Filter combination was performed using in-situ titration of either the H-atoms or O-atoms by chemical reaction with NO 2.84 For H-atoms the titration reaction proceeds as
H + N 02 -* 0 H + N 0 (2) with a reaction rate constant of k 298 = 1.3 x 10'10 cm3 s_1 where the rate constant is given for room temperature (T=298K). There is also a secondary reaction of OH with H2 given by
H2+0H ->H 20 + H (3) with a reaction rate constant k2gg « 1.6 x 10-15 cm3 s 1. However, provided the ambient H2 concentration remains below 1 Torr (3.3 x 1016 cm-3) this reaction will not appreciably perturb the main reaction. For 0- atoms the titration reaction is
O + NO, -» O, +NO (4) with a reaction rate constant k2g8 = 9.5 x 1012 cm3 s 1. For both H and O atom reactions, sufficient mixing time must be allowed to insure that the reactions go to completion. To have a reaction go to 99% completion implies that the mixing time, t ^ , must be greater than 5 characteristic reaction times, t . In other words, we have that the percentage of complete reaction is
1 - e~t/T = 1 - The characteristic reaction time is the inverse of the reaction rate constant times the concentration of titrant. For example, in the case of the reaction in Equation 2, at the point of complete reaction (here called endpoint) a measured concentration of N02 is used to react completely 46 with an equal concentration of H-atoms. If the concentration of [NO 2] used is 1 x 1015 cm*3 then the required mixing time must be at least tmix >5t= 5(^298[^2]) * = 7.7 microseconds (6) In the titration assembly described below, the main gas flow rates are adjusted to reduce the slug flow gas velocity in the mixing zone and raise the mixing time to approximately 4 milliseconds satisfying the condition in Equation 6 even for the O-atom titration reaction, which has an order of magnitude lower rate constant. The titration assembly is shown in Figure 6. At the larger inlet a gas mixture of either H 2/Ar or O2 is passed through a microwave discharge produced by an air-cooled Evenson microwave discharge cavity which dissociates the molecular gas mixture. The presence of argon helps to induce complete dissociation. The discharge section is composed of quartz for both heat resistance and to minimize reactions of the microwave plasma with the walls. Further downstream, NO 2 is introduced through a glass coaxial tube which passes the gas to a perforated mixing zone approximately 2 cm in length and 2 cm in diameter. The inner tube is covered by a Teflon sleeve to reduce the amount of recombination of H-atoms on the tube surface. The assembly is placed through a 3/4" diameter (I.D.) Cajon O-Ring fitting welded to a 2-3/4" Conflat copper gasket sealed flange. The Conflat flange is mated to a port on a given reactor, and the length of the titration assembly N02 Dnlet Microwave Teflon Sleeve H2,0 2 /Ar MbdrjgZone Discharge Region Figure 6. Titration Assembly 48 allows the exit from the mixing zone to be placed at the center of the reactor and near the focal point of the probe laser. For a titration calibration measurement, a steady-state concentration of H or O-atoms is produced by the microwave cavity discharge source and NO 2 is introduced at known mass flow rates. The TAUF fluorescence is monitored and recorded manually as a function of addition of NO 2. A typical titration data curve for O-atom titration is shown in Figure 7. At the endpoint (minimum observable TAUF signal), the total pressure in the reactor is recorded. A straight line is least-squares fit to the first several titration data points and the exact NO 2 endpoint mass flow rate is extrapolated numerically. Combining this information, we can use the following equation, where at the endpoint (7) where [A ]0 is the concentration of H-atoms or O-atoms titrated, [NO 2J0 is the concentration of NO 2 used, F(N0 2 ) is the mass flow rate of NO 2 measured in standard cubic centimeters per minute (seem), SF is the total mass flow rates of all the gases used summed together, and P is the total pressure measured in Torr. The numerical coefficient is used to convert Torr into number density, per cm3. Titration curves can be taken for different initial atomic concentrations, PMT gain settings, and probe laser energy. The calibrations curves correlate an experimental TAUF signal with a known concentration. Typical uncertainties in the calibrations are 15% and the minimum detectable concentration is extrapolated to be 1012 cm*3. 400 P = 657 milliTorr 9 350 PMT Voltage = 800 V Laser Energy = 440 /jJoules/pulse 20 seem 0 . 300 S* 2 0 0 150 100 50 [0] = 6 xlO15 cm * 012345678B10 Mass Flow Rate of N0(l seem Figure 7. 0-Atom TAUF Titration Curve. Data corresponds to a concentration of 5.98 x 10 15 cm'3. Line is a linear regression extrapolation for determining the titration endpoint. X- intercept is 7.63 seem of NO 2. 50 C. Effects of Quenching Upon Concentration Measurements Another problem that figures predominantly in plasma concentration measurements above 200-300 millitorr is the quenching of the excited fluorescence state by collisions with the ambient background gas molecules. Molecular hydrogen, in particular, is known to be a very efficient fluorescence quenching molecule .85 Reference data in the form of collisional quenching cross-sections and collisional deexcitation rates are few and often in disagreement .86 Bittner et al have provided the most comprehensive collisional quenching cross sections to date in conjunction with their analysis of atomic hydrogen and oxygen measurements in low pressure flames .87 These effects have also been investigated by Goldschmidt in flames .88*89 Since collisional fluorescence quenching effects are noticeable even at a few Torr total pressure and are very pronounced at higher pressures, it is necessary to extend the previous work to much higher pressures. For this purpose photodissociation of either C 2H2 or NO2 by the TAUF laser probe beam is used to generate ground state H or O atoms respectively. The discussion here will focus on the quenching measurements for hydrogen atoms. Photodissociation of either acetylene or NO2 is also useful in determining a geometric view factor correction which accounts for the variation in solid angle collection efficiency as a function position of the laser probe beam in a reactor cell; this will be described in the following two chapters. The photodissociation of acetylene provides a convenient source of hydrogen atoms using the 205 nm TAUF laser probe beam. A previous study of photodissociation of acetylene was completed in the wavelength 51 region 201-216 nm .90 The photodissociation process at 205 nm was shown to produce solely ground state C 2H and H-atoms. The excited C2H2 predissociative state was also measured in this work to have a lifetime of 10-20 picoseconds, which implies that over the lifetime of this state the molecule can suffer practically no deexcitation collisions even up to ambient pressures of 100 Torr. Thus, collisional deexcitation of the predissociating acetylene can be neglected as a mechanism which could perturb these quenching measurements. One might expect, given the same concentration of C 2H2 and photon flux density, the photodissociation process should yield a H-atom concentration independent of the pressure or the identity of other gases present, provided the gas environment is optically thin to the probe laser. Our measurements in a static cell pressurized with acetylene have shown that the system will remain optically thin below ~5 Torr. For the other gases used here, the absorption at 205 nm can be determined from the literature or by experimental observation and none were shown to absorb at this wavelength. By having a fixed concentration of acetylene and by raising the ambient pressure by slowing adding a foreign gas, the variation in the fluorescence signal can be examined to test for optical opacity. An obvious first step would be to examine the effect of acetylene pressure on the fluorescence itself. The H-atom TAUF signal response as a function of acetylene pressure is shown in Figure 8 . The signal is produced as the total PMT current response across 50 Ohms integrated over a 100 nanosecond gate, giving units of nanovolt seconds. After an initial linear rise, the photodissociation-generated TAUF signal begins to Figure Figure C 2 H2. Acetylene Photodissociation TAUF Signal, nVs 0.0 0.5 2.0 2.5 1.0 3.0 3.5 4.0 1.5 4.5 5.0 8 0123456789 100123456789 11 . H-Atom TAUF by Photodissociation of of TAUFPhotodissociation .H-Atom by a 2 rsue Torr CaH2 Pressure, 5.0 d 4.0 3.5 d 30 a J 2.6 3o S *a 0.5 4 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 0.0 0.0 1.0 CjHjj Pressure, Torr Figure 9. Nonlinear Dependence of C 2H2 11- Atom TAUF Signal. Straight line represents a linear regression fit to the initial rise of the data. 54 saturate below 1 Torr ambient pressure. An expanded view for lower pressures of acetylene is shown in Figure 9. The straight line in this represents a line fit by linear regression over the initial linear rise in the TALIF signal. Clearly at pressures above 150 milliTorr, the TALEF signal response deviates strongly from a linear process which would depend solely on acetylene concentration. The quantum yield in this experiment can be defined as the ratio of the actual TAUF signal data to the value predicted by the straight line fit from the lower pressure data. A plot of the inverse of the quantum yield is shown in Figure 10. A linear regression fit straight line to the data is also shown and gives excellent agreement with the data. In this case, the inverse of the quantum yield follows a dependence know as the Stern-Volmer formula 91 where the quantum yield, Q, is given by where P is the pressure and C 0 is a constant. We can take the inverse of the Stern-Volmer formula and write (9) Therefore, a plot of the inverse of the quantum yield versus pressure of the quenching gas should, by the Stern-Volmer formula, yield a linear relationship. In the case of Figure 10 the constant found from the slope of the straight line is Co=3.053 Torr1. The constant CQ can next be related to a quenching rate constant for the foreign gas. 35 30 25 u 20 1 ors 0 1 2 3 4 5 6 7 8 9 10 11 CgHg Pressure, Torr Figure 10. Inverse Quantum Yield Dependence on Pressure. Since we can write (10) where [Nq ] is the concentration of quenching foreign gas, x is the radiative lifetime of the state being quenched , and kQ is the quenching rate constant. Equation 8 can be rewritten to give [We ] x (3.3x10X(,cm-'Torr ')Px~ (iMO^cnC'Torr-') r We can initially chose for x the statistical average natural lifetime of the n=3 excited state of atomic hydrogen which is 10.2 nanoseconds .92 Substituting this value into Equation 9 we find a rate constant of kQ = 9.07xl0'9 cm 3 s 1 for quenching of the H-atom fluorescence by acetylene. The product [Nq ] times kQ is the quenching collision frequency, Z q , which can be written as ze = [AreK = ,roiK]v (12) where v is the relative collision velocity of the hydrogen atom fragment (after photodissociation) to background gas molecules and c 2 q is a quenching cross-section. We can solve for o 2 q in terms of kQ giving 57 For the moment, let us consider a velocity, v, which is the maximum photodissociation-induced velocity the hydrogen atom can have after the photodissociation process, and calculate a quenching cross section. The photodissociation-induced velocity can be measured by analyzing the Doppler profile of the photodissociated acetylene H-atom TAUF transition .93 The velocity measured is 7123 m/s which corresponds to a temperature of 4100K. Using this velocity in Equation 11 gives a quenching cross-section for acetylene quenching of n=3 H-atoms of , kQ (9.07xl0-9cmV) o2 = _e = .L------L = 4,1x10 cw n \ 123x10cm/s) Besides affecting the overall TAUF signal strength as a function of pressure, the apparent radiative lifetime of the atom is also influenced. Figure 11 shows the lifetime dependence of the H-atom n=3 state as a function of background acetylene pressure. The lifetimes were determined by fitting a single exponential decay to digitized fluorescence waveforms detected with Thorn-EMI 9659-QB and acquired from the digital oscilloscope. Data were fit up to the 9096 level after the initial onset of the fluorescence signal. The contribution from the laser probe pulse temporal width is 5 nanoseconds and the minimum resolvable level for lifetime measurements is estimated to be 6 nanoseconds. From a linear regression fit, as shown in the figure, at very low pressures the radiative lifetime approaches 14 ± 1.5 nanoseconds. This value is larger than the statistical average lifetime of the n=3 state 58 16 14 io a it om i 10 03 dII 6 6 0 20 40 60 80 100 120 140 160 180 CjjHj, Pressure, milllTorr Figure 11. Radiative Lifetime of n=3 State from Photodissociated C 2H2 H-Atom TAUF. 59 mentioned earlier. The explanation for the observation are the three angular momentum states of the n=3 level are not equally populated. As described before, due to the selection rules for such a two-photon absorption transition only the L=0 and L=2 states and not the L=1 state are populated. In addition, the two-photon absorption cross-sections to the s and d state are different. The ratio of the d-state absorption cross- sections to that for the s-state is 7.56.94 Since the laser linewidth is wider than the energy separation between each L-state, this means that ~1296 of the n=3 population is contributed by the s-state and the remaining 8896 is contributed by the d-state. The natural radiative lifetime of the d-state is 15.6 nanoseconds and 159 nanoseconds for the s-state. Thus, most of the observed lifetime for the n=3 level in this experiment at low pressure is contributed by the d-state. It is also reasonable to expect that collisions could perturb the distribution in the angular momentum states after the initial population by the laser. This redistribution or mixing of the angular momentum state populations can have two effects. First, there would be variations in the contributions to the radiative lifetime of the Baimer-« fluorescence from each of the three states. And secondly, since the p-state could then be populated by mixing, not only does the fluorescence channel 3p-2s become available, but the 3p-ls fluorescence channel in the vacuum ultraviolet then allows for a loss of fluorescence from the Baimer-« transition. Therefore, collisional quenching of the excited state fluorescence can be thought of as having two mechanisms. The first would be an overall nonradiative (n level) deexcitation of the excited state atom. The 60 second mechanism would involve the mixing of angular momentum In state populations within an n-level. A simple model utilizing these mechanisms can be described by the following set of coupled decay rate equations which describe the time development of the n=3 angular momentum L-state populations after initial population by the laser probe: ^ L= -A,J 7 +Are( " - +*e) +3ATe*.(Ar.+JVJ) v "p / (15) where Ns, Np, and are the populations of the different s, p, and d angular momentum states, N q is the concentration of quenching molecules, and k ^ and kQ are rate constants associated collisional population mixing of the angular momentum L-states and nonradiative deexcitation of the entire n-level respectively. If we assume the mixing between different L-states have equal rate constants, then the integer coefficients account for the statistical weighting of the L-states degeneracy's by the number of mj sublevels. The right-hand side of each rate equation has two parts. The leftmost term is for population loss and the right term is for population gain. Loss occurs by natural fluorescence or by mixing to other angular momentum states or by nonradiative 61 dexcitation. and gain for a level occurs by mixing contribution from the other states. This set of coupled rate equations can be solved numerically by a Runge-Kutta differential equation routine written in Fortran .95 The initial conditions are given by the initial L-state distributions which are population by the laser. The time development of the L-state populations are shown for two different foreign gas pressures in Figures 12 and 13. The calculations are normalized with respect to the initial overall population of the n=3 energy level. Also displayed is a normalized radiative rate which is related to the time history of the total population of the n=3 level. A radiative rate from the n=3 level can be defined as R(,)=LN'(,)+L N r (/)+£*,(,) r - t p T‘ (16) where fs, fa, and fa are the branching ratios for fluorescence decay from each L-state of the n=3 level to lower n-levels. For the s and d states, each decay to a single lower state in the n=2 level. The p-state however, can decay not only to the 2s state, also to the Is level. The branching ratio, fa, can be calculated as the ratio of the transition probabilities for the transitions 3p-2s and 3p-ls 96 This gives a branching ratio for fa of 0.1183. The radiative rate in Equation 16 can be normalized to the initial radiative rate at time t=0. At time t=0, only the s and d states are populated and so the initial radiative rate, R0, is calculated as 62 882 = 5.73x17 O'5 _ - l s t .3 r d 1.59xl0_7s 1.56x10 * Thus, the normahzed radiative rate, R* can be given by 7510-4 R0 V(,. * ^1.59x10 W, s 5.4x10 s 1.56x10 a’j ^lgj Figure 13 shows at the higher pressure (10 Torr) the p-state has more contribution, while the s-state decay is unchanged and meanwhile normahzed radiative rate decays much more quickly. The exchange of In state populations can be checked in the numerical calculation output by artificially increasing the natural radiative lifetime for all three states to very large values (effectively turning off fluorescence) and by setting the rate constant Icq, for nonraditive deexcitation to zero. Calculated numbers for pressures above a few hundred milhtorr the populations of the L-states have equilibrated in the percentages: 11.1196 in the s-state, 33.3396 in the p-state, and 55.55% in the d-state. The ratio of these percentages is just 1:3:5; as expected by the statistical weighting given by the nij degeneracy's of each L-state. Since the contribution from the s- state population goes only from 11.8 % to 11.11%, one can again see that the principal exchange of L-state populations occurs between the p and d states. Trapezoidal integration of the normahzed radiative rate (Eq. 18) with respect to time gives the quantum yield of the Baimer-« fluorescence. The integration time is 100 nanoseconds which reflects the integration gate temporal width in the experiment. The numerical program used can repeat this process for different pressure of the quenching foreign gas. Figure 14 shows the resulting quenching curves, for given k ^ and kQ, both with and without the contribution of Levels for 1 Torr Quenching by H2. Also shown shown H2. Also by Quenching Torr 1 for Levels is the Normalized Radiative Rate, R*.Rate, Radiative Normalized the is Component n=3 of Decay Radiative 12. Figure Normalized n=3 Populations and Radiative Rate 0.1 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0 0.9 1.0 .B 0 ie nanoseconds Time, 10 20 25 30 is the Normalized Radiative Rate, R*.Rate, Radiative Normalized the is H by Quenching 10Torr for Levels Figure 13. Radiative Decay of n=3 Component Component n=3 of Decay Radiative 13. Figure Normalized n=3 Populations and Radiative Rate 0.1 0.3 0.5 0.7 0.9 0.0 0.2 0.4 0.6 0.8 1.0 . 05 . 15 . 25 . 35 . 45 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 ie nanoseconds Time, 2 . Also shown shown .Also Figure 14. Calculated Quenching Curves With With Curves Quenching Calculated 14. Figure n Wtot ordaie exiain r In or Effects.of Both Total the and Mixing Deexcitation state Nonradiative Without and Quantum Yield 0.S 0.0 0.1 0.2 0.0 0.4 0.7 0 1.0 .B 2 6 1 1 1 1 1 20 18 16 14 12 10 B 6 4 2 0 Sum o -tt Mixing L-State No o ordaie Deexcitation Nonradiative No Pressure, Torr .0 1 c /■ cm 10 z 1.90 66 mixing and or collisional deexcitation. As one can see from the figure, nonradiative deexcitation is the dominant contribution to the quenching process. However, by adding to the calculation the effect of L-state mixing, the variation of the angular momentum state populations also provides some discernible effect. A further extension to the numerical program is to include the described computational model as a subroutine in a nonlinear-least- squares fitting program. Quenching data taken in the laboratory is used as input to the program which then fits the model and the corresponding mixing and deexcitation rate constants to the data. Rate constants were converted to cross-sections by using Equation 13. Figure 15 shows a comparison of the fitting program results and experimental data for the "self-quenching" effect by C 2H2 itself on the H-atom TALIF quantum yield. The best fit to the data required only a single nonradiative deexcitation cross-section and no mixing cross-section. The deexcitation cross-section, ctq, was calculated to be 8.87±0.2 7 x 10 *15 cm2. If both mixing, 0^ , and deexcitation, oq, cross-sections were used the values calculated were 8.03±4.12 x 10 ‘15 cm2 and 0.42±2.22 x 10 ' 15 cm2 respectively. The error in the calculated mixing cross-section would imply this value was not statistically significant and could not be adequately determined. For some of the gases discussed later, it was found that for those with larger nonradiative deexcitation cross-sections, a determination of the mixing cross-section often gave larger uncertainties in the calculated values. It is probable that for gases which are more 1.0 0.0 0.0 0.7 sII 0.5 I 0.4 or 0.3 0.2 0.1 0.0 0 1 2 3 4 5 6 7 8 0 10 11 CaHg Pressure, Torr Figure 15. Comparison of Calculated and Experimental H-Atom TAUF Quenching by Acetylene. 68 effective nonradiative quenchers (acetylene having the largest deexcitation cross-section measured to date), a determination of the mixing cross-section is more uncertain because of the dominance of the nonradiative mechanism. It will be shown later that for gases which are not as effective in nonradiative deexcitation, particularly helium, the effect of a mixing cross-section is readily apparent. Using the single calculated deexcitation cross-section, a TAUF signal response can be predicted as a function of acetylene pressure. Figure 16 shows a comparison between the original data from Figure 8 and the predicted signal. Over a large range of pressure the agreement between the calculated signal and the data is excellent, Only above ~3 Torr does the calculated curve predict a slightly larger signal than is observed. One explanation is that the model does not take into account the onset of optical opaqueness near 5 Torr of acetylene as was previously mentioned. As our use of acetylene as a photodissociated source of H-atoms is accomplished at 100 milliTorr, this discrepancy can likely be ignored. Figure 17 further demonstrates the agreement between the calculated result and the data in the low pressure region. The measured n=3 lifetime data can be compared to the model calculation as shown in Figure 18. Displayed is the original measurement data, a linear regression fit to the lifetime data (as before in Figure 11), and calculated lifetimes derived by fitting a single exponential decay to the normalized radiative rate, R*; in the same manner as the original measurements were determined. The calculated lifetimes he weh within the error bars of the measurements with a slight curvature as a function of pressure as compared to the linear regression line. The extrapolated 69 5.0 r- *2 4.5 - I 4.0 - no d 30 ' H I 80I ! 101 CL. I 3 io I *> i 0.5 0.0 0 1 2 3 4 5 6 7 8 0 10 11 CjHj, Pressure, Torr Figure 16. Measured Versus Calculated Photodissociated Acetylene H-Atom TALIF Signal. 70 s.o 4.0 3.5 fl 3.0 % A 2.6 I 2,0 &I 15 3 i-o « 0.5 I 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 O.B 0.9 i.O CjHj Pressure, Torr Figure 17. Low-Pressure Detail of Figure 16. Straight line is from linear regression fit as shown in Figure 8 . 16 14 ie i>a 12 10 3 nII 0 B 6 0 20 40 60 80 100 120 140 160 160 CgHj Pressure, milliTorr Figure 18. Measured versus Calculated H-Atom TAUF Lifetime from Photodissociation of C 2H2. Straight Line is from linear regression fit as shown in Figure 11. 72 natural lifetime at zero pressure is 15.6 nanoseconds in good agreement with the natural lifetime of the n=3 d-state. Quenching data can be taken using other gases and the computer program used to calculate quenching curves and rate constants or cross- sections. However, given the partial pressure of acetylene present, Equation 15 must be modified to account for the "self-quenching" by acetylene. Addition of a constant term to Equations 15 is straightforward since there is a constant 130 milliTorr partial pressure of acetylene with a fixed quenching cross-section. As shown in Equations 19 the constant term is only added to the loss term of the right-hand-side of each individual equation: - + M 8* - + *») + * 42*10V 1+V -.K + *«) V Ts J dN t ^ jl = -Nb - + ^e(6 ^ + ^ ) + 3.42xl075-' +3NQk^(Ns+Nd) dt pvtp dN]d _ = -N a - + +*c) + 3.42*107r ' +5Nak^(N.+N„) dt K*d (19) Figures 19 and 20 show a comparison of experimental quenching data for quenching by molecular hydrogen with the calculated quenching curve. Two sets of experimental data were combined to comprise the figures. As shown in Figure 20 with an expanded horizontal scale the agreement of the calculated quenching curve with the data is very good. 73 0.65 0.60 0.55 0.50 0.45 | 0.40 ^ 0.35 I 0.30 9 0.25 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 50 60 70 80 90 100 HB Pressure, Torr Figure 19. Comparison Fit of Quenching Model Calculations to Experimental Quenching of 11- Atom TAIJF by H 2 Gas. 74 0.6S 0.60 0.55 0.50 0.45 2 1 0.40 0.35 0.30 0.25 or 0.20 0.15 0.10 0.05 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Hg Pressure, Torr Figure 20. Expanded Horizontal Scale from Figure 19. 75 Figure 21 shows the results for quenching of H*atom TAUF by helium. Shown are the averaged experimental data and the corresponding calculated quenching curves. The upper curve in the is the calculated quenching curve using only nonradiative quenching and the cross-section reported by Bittner et al for quenching by helium .97 The experimental data differs significantly from this calculated curve suggesting their lower pressure (up to 7 Torr) data was not sufficient to determine the appropriate cross-section value. Calculation of the mixing and dexcitation cross-sections fitted to the helium data show the calculated deexcitation cross-section to be a factor of 24 smaller than the corresponding mixing cross-section. The dominance of the mixing cross-section would suggest a large change in effective radiative lifetime of the n=3 energy level due to mixing. Table 2 shows measured effective lifetimes as a function of helium pressure. Also shown are lifetimes calculated using the cross-section reported by Bittner and lifetimes calculated by our two cross-section model. Table 2. Comparison of Measured and Calculated Fluourescence Lifetimes for Helium Quenching He Pressure, 0 . 0 1.5 3.0 4.5 6.0 7.5 Torr t (measured) 12.7 ns 12.1 ns 11.8 ns 11.7 ns 11.7 ns 11.3 ns x (Bittner) 11.3 ns 11.1 ns 10.9 ns 10.7 ns 10.5 ns 10.3 ns x (New Model) 11.3 ns 6.8 ns 6.5 ns 6.3 ns 6.2 ns 6.1 ns 76 0.65 r 0.60 0.55 0.50 0.45 | 0.40 0.35 I 0.30 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 50 60 70 60 00 100 He Pressure, Torr Figure 21. Quenching of H-Atom TALIF by Helium. The upper curve is calculated based on data from Reference 87. 77 As can be seen from the table there is actually very little change in radiative lifetime over the given range of helium pressure. While by using Bittner's cross-section for helium quenching the agreement is within about one nansecond, for the current calculations there is nearly a factor of two in difference. One explanation for the discrepancy is that presence of acetylene has interfered with the mixing of L-states by helium. As mentioned before, around pressures of 100-200 milUTorr of foreign quenching gas L-state mixing has nearly reached statistical equilibrium. Though a cross-section for mixing by C 2H2 could not be reliably determined here, it is very likely that acetylene is also very effective in promoting L-state mixing. Thus, given a partial pressure of acetylene of 100 milUTorr used in these experiments, there may be already nearly complete mixing of the L-state populations so that the addition of helium does not discernibly contribute to this effect. The small lifetime variations would make the determination of quenching cross-sections based on lifetime measurements very difficult. This is the method used by Bittner et al in their measurements using the same photomultipher tube as for the present measurements. Their quenching cross-section is a factor of three smaUer than the present colhsional deexcitation cross-section measurement. The difficulty of not observing significant lifetime variation during heUum quenching while at the same time the overall quenching behavior is reproduced by the current model suggests the exact mechanism for colhsional mixing by helium could stiU remain unclear. By selecting another rare gas like argon, which is larger and heavier than helium, there should be an increase in the quenching effect and the 78 0.65 r 0.60 0.66 0.50 0.45 g 0.35 1 0.30 or 0.26 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 50 60 70 60 00 100 Ar Preaaure, Torr Figure 22. H-Atom TALIF Quenching by Argon. Lower curve is calculated based on data from Reference 87. 79 cross-sections. Figure 22 shows quenching data and calculated quenching curves for quenching by argon. Again, the lower calculated quenching curve is based on data published by Bittner et al in Reference 87. Lifetime variation was observed in the case of argon quenching as shown in Table 3 in for the same range of pressure as for the helium measurements. The measured fluorescence lifetimes varied from 12 nanoseconds down to 3 nanoseconds at higher pressures. Table 3. Comparison of Measured and Calculated Fluorescence Lifetimes for Argon Quenching Ar Pressure, 0.0 1.5 3.0 4.5 6.0 7.5 Torr x (measured) 12.3 ns 8.0 ns 5.7 ns 4.4 ns 3.0 ns 3.2 ns x (Bittner) 11.3 ns 5.9 ns 4.0 ns 3.0 ns 2.4 ns 2.0 ns x (New Model) 11.3 ns 6.1 ns 4.8 ns 4.1 ns 3.5 ns 3.1 ns Now in the case of argon quenching we have better agreement in comparing the calculated versus measured radiative lifetimes; with the results calculated by use of the previously measure cross-section now being significantly lower. In both cases for helium and argon quenching the lifetime data has been corrected for a 5 nanosecond laser/instrumental contribution. Thus, it would appear for gases such as argon and other molecular gases that the radiative lifetime of the n =3 level would rapidly drop to levels where variations in the lifetime would be unresolvable from instrumental contributions. 80 0.85 0.60 0.66 0.50 0.46 ■0 0.40 |H£ fj 0.35 I 0.30 0.25 or1 0.20 0.16 0.10 \ 0.05 - o.oo L 4 - U 10 20 30 40 SO 60 70 60 00 100 N_ Pressure, Torr Figure 23. Quenching by Nitrogen. Lower calculated quenching curve is based on data from Reference 87. from Reference 87. Reference from Figure 24. Quenching by Oxygen. Lower Lower Oxygen. by Quenching 24. Figure calculated quenching curve is based on data data on based is curve quenching calculated Quantum meld 0.00 O.OS 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.46 0.50 0.56 0.60 .6 r 0.66 1 2 3 4 5 6 7 6 0 100 00 60 70 60 50 40 30 20 10 0 8 riue Torr Preiaure, 08 82 Table 4. Cross-Sections for Quenching of Hydrogen Atoms (n=3). Present Bittner et al Quenching Gas Measurements Measurements (x 10’15 cm2) (x 1 0 '15 cm2) o -2q = 0.10 ±0.004 He ct2q = 9.23 ± 0.16 h 2 o -2q = 4 . 3 3 ± 0.01 ct2 q ■ 10.9 ± 0.43 n 2 ^m ix = 0.25 ± 0.08 EXPERIMENTAL RESULTS FROM A GEC REFERENCE CELL In 1990 a GEC Reference Cell was assembled from commercially supplied components at the Advanced Plasma Research Group, Wright- Patterson Air Force Base (WPAFB), Ohio. After the initial stages of assembly and equipment checkout, a series of electrical characterization experiments based on discharges through Argon and Helium were performed. These measurements were made in conjunction with electrical measurements being made at other facilities around the United States equipped with the GEC Reference Cell. In the Summer of 1992, the first ground-state atomic species density measurements performed in a GEC Reference Cell were accomplished in the WPAFB GECRC. The techniques for H-atom detection discussed in the previous chapter were used to derive the results which are presented here. Generation of the TAUF probe beam for H-atom detection was accomplished in the manner described in Chapter 4. The hydrogen atom TAUF probe beam was introduced into the reactor cell through a Supersil 1 Quartz 2.75" diameter viewport, parallel to the 4" diameter aluminum electrode surfaces. The probe beam exited the cell through an identical viewport. Translation of the laser probe beam relative to the 25 millimeter interelectrode gap was accomplished by using a computer- controlled AeroTech stepper motor translation stage to which was 85 86 attached a quartz prism periscope. Minimum step resolution was 10 microns, but typically step sizes down to 200 microns were all that were required to achieve reliable H-atom concentration profiles. The collection optics assembly consisted of two plano-convex lenses between which a narrow band (10 nm FWHM) filter centered at 656 nm was placed. The assembly was focused on the center of the reactor cell through one of the 6" diameter glass viewports. No translation of the collection optics synchronous with the laser probe beam was required or attempted. The output of the collections optics was loosely focused on the photocathode of a Hammatsu R928 photomultiplier. The output of the photomultiplier anode was preamplified and then fed to either a digital oscilloscope or to a Princeton Applied Research Boxcar Integrator and then the integrated output was digitized in a digital multimeter connected to a Hewlett-Packard personal computer through an IEEE-488 bus cable. TAUF signal acquisition was controlled by computer as a function of stepper motor-controlled laser probe position. The signal could be normalized to variations in the laser energy, by monitoring the energy with a Molectron J3-01 Joulemeter detector whose output was again digitized by a digital multimeter. The normalization with respect to laser probe energy was calculated as the square of the variation since two photons are required for the TAUF transition. Calibration of the TAUF response in the GECRC was performed using the same titration assembly described in Chapter 4. The assembly was mounted on one of the 2.75 inch Conflat flanges and extended into the middle of the reactor volume. Concentration calibrations were performed over a range of laser intensities and PMT voltage settings. 87 3.0 Raw Data, and Polynomial Fit | 2.5 d $ 2.0 u £ u l.S I 0 $0) Normalized Fit to Raw Data 1 & 0.0 0 2 4 8 B 10 12 14 16 IB 20 22 24 Interelectrode Position, mm Figure 25. GEC Reference Cell Geometric View Factor Correction. Origin is position of powered electrode. 88 To correction for variations in solid angle collection efficiency as a function of laser probe beam position between the electrodes, the reactor cell is filled with acetylene to 1 Torr and the photodissociated TAUF signal is recorded with the discharge off as a function of laser probe beam position. Figure 25 shows the raw correction data, a linear regression curve fit to the data, and final form where the regression curve fit values have been normalized to unity. The periodic variation in the data and regression fit resulted from the combination of fixed collection optics and interference with the focused photocathode spot by the dynode grid structure of the side-viewing photomultiplier. The correction factor was truncated close to the electrodes to avoid a unduly large corrections due to the occultation of the laser probe beam by the electrode surfaces. H-atom TAUF concentration profiles were collected for variations of discharge conditions due to RF power and reactor pressure. Over the range of parameters investigated the most dramatic changes were seem as a function of discharge pressure. Figure 26 shows TAUF profile data collected for pressures ranging from 0.3 to 5 Torr for a total deposited discharge power of 30 Watts. The driven electrode is at the origin. The data was acquired every 200 microns and averaged for 50 laser shots at 10 Hertz. The data has also been corrected by the data from Figure 25 by dividing geometric view factor into the raw data. The median values for the profiles start at low values for low pressures and then reach an apparent maximum at approximately 1 Torr and then declining again at higher pressures. The slope of the data would appear to be roughly flat except at the higher pressures where a distinct slope is observable. 0 4 B 12 16 20 24 28 Interelectrode Poeition, mm Figure 26. TAUF H-Atom Signal Profiles in GEC Reference Cell for Different H 2 Pressures. Power deposited in plasma is 30 Watts. 90 16 a oi 14 3 Torr 12 10 5 Torr 'O B 1 Torr g t 6 u0 4 0.5 Torr 1o ri» 2 0.3 Torr or 0 4 B 12 16 20 24 2B Interelectrode Position, mm Figure 27. Quenching Corrected TALIF Signal Profiles From 26. 91 These H-atom concentration profiles were corrected for the influence of quenching on the TAIIF quantum yield by dividing the profile at a given pressure by the associated quantum yield calculated from the model presented in Chapter 4. The quenching corrected profiles are shown in Figure 27. Now it becomes apparent that the slope of the data is much more dramatic at higher pressures as well as there is a shift in the maximum concentration to 3 Torr instead of 1 Torr. These observations can be correlated with emission measurements as described below. Based on in-situ titration calibration of the TAUF signal from the GECRC, the TALIF signals observed can be used to calculate absolute hydrogen atom concentrations generated in the Reference Cell plasma. Table 5 shows the maximum H-atom densities as a function of pressure both before and after correction for the influence of fluorescence quenching. Also shown is the percentage dissociation fraction calculated as the ratio of the corrected maximum H-atom density over the particular total pressure of H 2 in the reactor. The maximum between 1-3 Torr in the concentration profiles corresponds over fifty percent dissociation of the H 2 gas. To the eye, the visible emission from the H 2 plasma in the GECRC is asymmetric with a much stronger visible negative glow region after the cathode sheath near the driven electrode. This asymmetry correlates with the variation in TAUF concentration profiles as a function of pressure. Balmer-« emission from the n=3 level was profiled as a function of H 2 pressure in the reactor at the same RF power level. A 100 micron slit was placed in front of the combination of interference filter Table 5. Computed Maximum H-Atom Densities in GEC Reference Cell Integrated H-Atom Density Corrected Dissociation H2 Pressure Signal Fluorescence H-Atom Fraction (x 1 0 16 cm-3) Quantum Yield Density (Torr) (Volts) (x 1 0 16 cm’3) (%) 0.3 0.70 0.110 0.39 0.28 28 0.5 1.00 0.155 0.28 0.55 33 1.0 1.75 0.271 0.16 1.69 51 3.0 1.60 0.262 0.06 4.37 44 5.0 0.75 0.116 0.04 2.90 18 CDN3 Figure 28. H-Atom Balmer-a Emission Profiles in in Profiles Emission H-Atom Balmer-a 28. Figure GE C Reference Cell as a Function of of H Function GECa Cell as Reference H—Atom. n=3 Emission Signal, (a.u.) 0.0 0.5 2.0 2.5 1.0 1.5 3.0 0 neeetoe oiin mm Poeition, Interelectrode 15 5 . Torr 0.7 . Torr 1.5 . Torr 0.3 Torr 7 Torr 10 2 20 Pressure. 25 B aimer-a Emission Profiles. Emission B aimer-a Figure 29. Interpolated 3-D Mesh Representation of H-Atom H-Atom of 3-DRepresentation Mesh Interpolated 29. Figure Emission Intensity (a.u.) Ixxictolc® r ““ “ - 0 0 * * O P * d tro 94 95 and photomultiplier used for the TAUF measurements and the assembly mounted on a computer-controlled stepper motor translation stage. The emission profiles as a function of position and reactor pressure are shown in Figures 28 and 29. Figure 28 shows two-dimensional plots of the emission profiles, while Figure 29 shows a three-dimensional interpolated mesh representation of the profiles presented in the previous figure. Both Figures 28 and 29 show a general asymmetric behavior, sloping down from the driven electrode. The slopes of the profiles are more pronounced in the emission profiles as compared to the TAUF concentration profiles shown earlier. This can be expected since electron-impact dissociative excitation of H 2 which generates excited state H-atoms mainly occurs in or near the electrode sheaths where the electrons can gain sufficient energy by acceleration through the sheath potential drop. Given the short radiative lifetime of the n=3 state the electron impact-produced atoms do not diffuse uniformly through the interelectrode gap before they radiate. Ground-state H-atoms, on the other hand, do not readily recombine in the gas phase and they diffuse throughout the bulk plasma; generally recombining only on the walls or electrodes .98 This makes for a more uniform profile of ground-state H- atoms as detected by the TAUF diagnostic. At lower pressures two peaks are seen in the emission profiles near the driven electrode. The one further out into the plasma is due to the contribution from electron impact dissociation discussed above. The peak which is more proximal the electrode surface is thought to be caused by H+ and H 2+ ions colliding with the electrode surface and 96 generating fast H-atoms. The fast H-atoms are then backscattered and collide with H 2 in the cathode sheath. The collisions have sufficient translational energy to dissociatively excite the H 2 molecules leaving excited state H-atoms which emit. Similar observations have been made in the case of low pressure direct current (DC) hydrogen discharges." Electrons should not play a role since electrons leaving the cathode have to cross the cathode sheath region before they generally have sufficient energy to cause this type of process. As the pressure increases the sheath regions contract and the two peaks observed at lower pressures coalesce into one and there appears to be a maximum in the emission profiles near 1 Torr. Again, as in the case of the TAUF concentration profiles, these emission profiles can be corrected for the influence of collisional quenching on the fluorescence quantum yield. Figures 30 and 31 are the emission profiles from Figures 28 and 29 corrected as a function of pressure for variations in quantum yield. In both figures the asymmetry in emission profiles is very pronounced at the higher pressures. This behavior correlates well with the behavior of the TAUF profiles shown in Figure 27. Overall there is increased production of ground-state and excited-state hydrogen nearer the driven electrode for the higher pressure discharges. Another set of observations which help to validate both the TAUF and emission profile data are electrical characterization measurements for plasma current and voltage. Figure 32 show the measured total current through the plasma as a function of pressure. The effects of external impedance were carefully evaluated using an equivalent circuit 97 18 16 0« 4 1.5 Torr * 14 ’a 1 12 8 10 3 Torr •X■ B 0.7 Torr M II 6 d 7 Torr a 4 I w 2 0.3 Torr 0 0 5 20 Interelectrode Position, mm Figure 30. Quenching Corrected H-Atom Baimer-« Emission Profiles. 7 8 pres««*e* 'torT Figure 31. Quenching Corrected Interpolated 3-D Mesh Representation of H-Atom Baimer-ex Emission Profiles. 99 1.0 0.9 0.B 0.7 0.6 0.5 « 0.4 0.3 0.2 - 0.1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Preiaure, Torr Figure 32. Plasma Current as a Function of H 2 Pressure in GEC Reference Cell. 100 700 650 600 Total Plaama Voltage 550 500 450 400 o 350 > 300 250 200 150 100 Plasma DC Bias 50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Pressure, Torr Figure 33. Total Plasma Voltage and DC Bias as a Function of H 2 Pressure in GEC Reference Cell. 12 12 11 10 9 B 7 6 S 4 3 2 1 0 0 0 1 2 3 4 6 6 Hg Preaiure, Torr Figure 34. Comparison of Maximum H-Atom Density and the Product of Current and Pressure as a Function of Pressure. 102 model of the GEC Reference Cell and deconvoluted from the plasma current data .100 A maximum in the plasma current is observed at approximately 3 Torr pressure of H 2. This maximum coincides with the observed maximum in plasma emission and ground-state H-atom concentration as measured by the TAUF diagnostic. The shows a reproducible local maximum in the plasma current about 0.75 Torr which may correlate with a maximum production of fast H-atoms near the driven electrode as observed from the plasma emission measurements. However, the mechanism for enhancing electron production and hence the current by electron avalanche multiplication in this region is not readily apparent. Measurements of the total plasma voltage and plasma DC voltage bias are shown in Figure 33. Over a range of several Torr the total voltage drop across the plasma is roughly constant near 600 Volts. The plasma DC bias exhibits more variation ; ranging from 50 to 200 Volts. The large plasma DC bias again demonstrates that the hydrogen plasma is very asymmetric since such a large bias of approximately 20 percent on average would induce the plasma to behave partially in a DC discharge-like manner .101 The source of the bias and overall asymmetry of the discharge in the GECRC is due to the effect of unequal electrode areas between the top driven electrode and the bottom electrode .102 The bottom electrode effectively has a larger surface area due to the presence of the grounded guard ring and other reactor surfaces. An interesting comparison may be made between the pressure dependence of the maximum H-atom density as measured by TAUF and the pressure dependence of the product, I x P, plasma current times 103 pressure. The comparison is shown graphically in Figure 34. For pressures below about 2 Torr the H-atom density follows the increase of the I x P parameter; indicating the production of H-atoms is roughly linearly proportional to the product of current and pressure in the lower pressure regime. Above 2 Torr, the H-atom density reaches a maximum and then decreases; diverging from the product of I x P. As seen from Figure 32 the current has also saturated in this pressure region suggesting the source of H-atoms due to electron impact dissociation has diminished; possibly due to electron cooling by collision. The plasma current and voltage measurements reported here are the first observed for the GEC Reference Cell and a H 2 plasma and in a system which is of industrial scale. At this point the H 2 plasma is in principle the most understandable system that currently exists, measurement of ground state atomic concentrations along with dissociation fraction has determined the majority of the neutral species within the discharge. Practically all important plasma species densities can now be measured or inferred from developed experimental techniques; including electron densities by microwave interferometry, H and H 2 concentrations by TAUF, and detection of H* ions by laser photodetachment measurements. The H 2+ and H 3+ ion densities and production regimes remain to be investigated. However, given the nearly complete list of measured plasma species as well as other plasma parameters such as current and voltage characteristics it may now be possible to develop a complete and self-consistent model of the simple hydrogen glow discharge. CHAPTER VI EXPERIMENTAL RESULTS FROM AN ASTEX DIAMOND GROWTH REACTOR Starting in January 1992, a high-power microwave plasma diamond deposition reactor system was constructed at the Ohio State University Laser Spectroscopy Facility. Most of the component parts comprise the ASTEX HPMM Microwave Plasma Source. Figure 35 shows a basic schematic drawing of the HPMM system. The main microwave radiation source is a 1.5 kiloWatt magnetron power generator. The microwaves are propagated through rectangular waveguides and coupled to the cylindrical plasma chamber through a TEqi to TMqi mode symmetric coupler. The microwave radiation is then passed through a quartz vacuum window into the reactor volume. Tuning elements are also provided to effectively match the forward microwave power deposition and minimize reflected power back to the magnetron power head. At the bottom of the reactor chamber is the gas pumping manifold and the heater substage assembly. The system is pumped by a 18 liter per second chemically resistive Krytox oil roughing pump. A base pressure of 1 miUiTorr can be reached with this pump. In addition, the entire chamber can be pumped by a compound turbomolecular pump down to 10 ‘7 Torr to help remove water vapor and other outgassing products. 104 105 The heater sub stage assembly consists of a water-cooled radio frequency antenna coil powered by 3.5 kilowatt RF power generator. The RF antenna radiation is absorbed in a graphite susceptor heating element. The RF radiation then heats the graphite to temperatures approaching 1000 degrees Celsius. The heating stage is 5 inches in diameter and can accommodate up to a 4 inch diameter diamond growth substrate; typically a 3 inch diameter semiconductor-grade silicon wafer. The entire heating stage can be positioned vertically inside the plasma chamber by means of an adjustable motor drive. By using the motor drive positioning of the heated wafer substrate allows for some control of exposure of the substrate to the plasma. The ASTEX HPMM system is capable of generating a microwave- sustained plasma from about 10 to 100 Torr. Gases are added to the chamber through a gas dispersion ring on the vacuum side of the quartz plasma window. Gas mixtures are controlled by calibrated electronic mass flow controllers and the chamber pressure is monitored by a 100 Torr range capacitance manometer (Baratron). The pressure in the chamber is controlled to less than one percent fluctuation via a electronically-controlled throttle valve assembly in a feedback loop with the pressure readout of the capacitance manometer. For the experiments described here the operating conditions for from the plasma were maintained at constant values and only the gas mixtures were varied to optimize the diamond deposition process. The microwave power deposited to the chamber was 1200 Watts with practically no reflected power measured. The heater assembly was positioned at the midpoint of the chamber as measured by an electronic 106 — 36.5------" Directional 3 Stub Coupler T u n e r ^ n Symmetric S u ftA Circulator / Plasma I I tDummy Coupler I 'L oadl f l . ity=wD=i3— Ujmjiutr II Power Head ■^-Magnet#! Rapid-load_ I t © =111. Heater level Door ---- ► 'Optional 2nd Magnet ^ Tabletop level ‘ 8 in o.d. 58, .5" Conflat flange tt ‘Pumping and instrumentation ports .Motor Drive 45" min. L I ‘for height above floor adjustment 29" Heater Matching Network Figure 35. The ASTEX HPMM Microwave Diamond Growth Reactor 107 position monitor on the motor drive assembly. The heater stage temperature was maintained at 830±1 °C as monitored by a thermocouple placed on the back side of the graphite susceptor block which was in a feedback loop with the heater stage RF power generator. The chamber pressure was kept constant at 40 Torr and a maximum gas load of 600 standard cubic centimeters per minute (seem) was passed into the reactor. Under these conditions a plasma ball of approximately 4 inches in diameter forms in the middle of the chamber. Diamond is deposited directly under the plasma bah. Diamond deposition was confirmed by use of surface Raman laser spectroscopy and by scanning electron microscopy (SEM). However, in what follows no descriptive analysis of the materials deposited will be given, partly because this research is still ongoing and also because the focus here is on the gas phase laser diagnostics and chemistry. The diamond deposition gas mixtures used will be described in further detail later in the text. Due to the physical dimensions of the diamond deposition system, the TAUF laser probe beam was introduced into the reactor chamber by means of a quartz prism periscope to accommodate the height of the apparatus. Two stepper motor-controlled translation stages positioned the laser probe beam relative to one of the 2.75" Conflat Supersil 1 quartz viewports. One translation stage controls the vertical position and the other the horizontal position with respect to the window. Close to the viewport where the laser probe enters, a second set of two stepper motor-controlled translation stages was placed to control the positioning of the final quartz focusing lens to focus the TAUF probe in the central vertical plane of the reactor chamber. Both sets of translation stages 108 were under computer control and synchronously stepped in unison to translate the laser probe beam across the quartz viewport in two dimensions. The TALIF fluorescence was collected at right-angle to the direction of the laser probe by a combination of narrow-band interference filter and focusing lenses as describe previously. The collected fluorescence was detected using either Thorn-EMI 9659 or Hammatsu R928 photomultiplier tubes. As for the measurements in the GEC Reference Cell, is necessary to correct for variations in the fluorescence collection efficiency as a function of laser probe beam position. In this instance, however, the geometric view factor correction was obtained in two dimensions instead of one as for the case of the GECRC profiles. Figure 36 shows the raw data for the view factor correction measured by filling the reactor with 1 Torr of acetylene (no plasma) and profiling the photodissociation- induced TALIF signal. One hundred percent reflects the largest signal recorded. As shown in the figure, the circular outline of the quartz viewport can be seen as well as the top of the heater stage and wafer substrate which limits the circular region near the bottom of the outline. The TALIF signal is strongest to the right of the which reflects the fact that as the laser probe beam rasters horizontally is then closer to the side with the collection lenses and photomultiplier. There is an asymmetry about the horizontal centerline of the which results from vignetting due of the collection lens assembly and tilt adjustment of the collection optics to better view the plasma ball which forms in the reactor. 109 Figure 36. ASTEX Reactor Geometric View Factor Correction 110 Measurements at each stepped position was averaged for 32 shots of the pulsed laser. The position resolution used here is 1 mm in both dimensions. Finer stepped resolution could be obtained down to 100 microns, but the time required to make such detailed measurements became several hours over which the laser energy was apt to fluctuate significantly. The position resolution used in the measurements described here represent the best compromise between resolution and laser stability. The raw data shown in Figure 36 is normalized to a range of zero to one hundred percent in TAUF response. To correct the actual TAUF data acquired from different diamond growth plasma, the data at each point was divided by the percent factor given at the corresponding point in the view factor correction profile. The corrected data in turn is normalized to a 100 percent scale. The maximum concentration of H or O-atoms for a specific is presented in the caption. All data shown in the following figures was collected using over a period of 11 days after initial measurement of the view factor correction. This was done to insure that any systematic or inadvertent change to the optical alignment of the laser system was minimized. All the measurements were accomplished using a Thorn-EMI 9659 photomultiplier operating at either 500 or 600 volts. The low voltage used was necessary to reduce the average anode current below the maximum rating for this photomultiplier. Laser pulse energy was stabilized at 225 microjoules per pulse as measured by a Molectron Joulemeter. The data presented here has the background contribution from plasma-induced emission and thermal radiation of the heater stage subtracted. I l l Figures 37 and 38 show uncorrected and corrected TAUF concentration profile maps for a methane-based diamond growth gas mixture consisting of 0.7596 CH 4 in H 2 (500 seem) or in terms of atomic fractions Xq=1, Xq=0, and XH=0.996. This corresponds to a position in the lower left vertex of the C-H-0 phase diagram shown in Figure 2. This gas mixture is a standard mixture used for depositing diamond in hot filament and plasma-assisted diamond CVD systems. The maximum 11- atom density is calibrated at 3.37 ± 0.16 x 10 15 per cm3. However, at a pressure of 40 Torr in the reactor chamber, the fluorescence is strongly quenched. Since the gas mixture is nearly 100 percent hydrogen, we can use the results from Chapter 4 for quenching by H 2. This corrects the calibrated concentration by a factor of 110 to a maximum of 3.70 ± 0.18 x 10 17 per cm3. Thus, approximately 11.2 Torr out of 40 Torr total H 2 pressure or - 28 percent is hydrogen atoms. In Figure 37 most of the uncorrected TAUF signal comes from the upper region of the 2-D profile. Upon correction the TAUF signal response is much more uniform over the volume sampled in the reactor. Variations in H-atom density are on the order of 1596. The correction of the raw TAUF data is even effective to within ~1 mm of the heater/wafer surface. At 40 Torr concentration gradients into the wafer are expected to occur over a length of a millimeter or less. Figures 39 and 40 are uncorrected and corrected TAUF profiles for a diamond growth mixture were oxygen has been added. For this experiment Xc=0.451, Xo=0.048, and XH=0.96. This mixture corresponds to a position further towards the C-0 line in the phase diagram and is denoted point #48 in Reference 39. The maximum H-atom density 112 Figure 37. Raw Data for H-Atom TAUF Concentration Map in 0.75% CH4/H 2 Methane-Based Diamond Growth Plasma. Xc=l, Xo=0, X h ®0.996. 113 Figure 38. Corrected Data for H-Atom TAUF Concentration Map in 0.7596 CH4/H 2 Diamond Growth Plasma. Maximum H-Atom Density is 3.70 ± 0.18 xlO 17 per cm3. 114 measured for this data after correcting for quenching by H 2 is 5.09 ± 0.93 x 10 17 per cm 3 or approximately 3996 dissociation H 2 gas. This concentration is a factor of ~1.4 larger than the previous mixture. A comparison between Figures 37 and 39 shows the second mixture to give a stronger overall TAUF signal, though the corrected data shows the 11- atom density to be as uniform as before. Beside growing diamond from more standard gas mixture of methane, hydrogen, and oxygen, experiments were also performed using acetone as the hydrocarbon source. Figure 41 shows uncorrected TAUF data for a diamond growth gas mixture of acetone vapor and oxygen. The conditions for diamond growth (9.76 seem acetone and 8.65 seem 0 2) give Xc=0.52, X q =0.32, X h =0.67 which is roughly in the middle of the C-H-0 phase diagram and duplicates point # 23 for diamond growth from acetone which was also performed by the authors of Reference 39. Figure 42 is the view factor corrected data from Figure 41. Figure 43 is a second corrected repeat scan taken a few hours later under the same operating conditions. Both figures show profiles which are different than Figures 38 and 40. In this instance there are two interesting features present in these corrected profiles. First, there appears to be a region corresponding roughly with the center of the plasma ball where there is approximately 30 percent depletion of H-atoms. Next, further away from the central plasma location there is a layer of larger H-atom density near the heated wafer surface. For these profiles the H-atom TAUF signal is a factor of two larger than the previous plasmas investigated. If we assume that the mayor quencher in this plasma is 0 2 at a partial pressure of 19 Torr, the quenching correction factor is 25.8. Therefore, the TAUF signal 115 Figure 39. Raw Data for H-Atom TAUF Concentration Map in Methane-Based Diamond Growth Plasma. Xc=0.451, X q =0.048, and X h =0.96. 116 Figure 40. Corrected TAUF Data from Figure 39. Maximum H-Atom density is 5.09 ± 0.93 xlO 17 per cm3. 117 Figure 41. Raw Data for H-Atom TAUF Concentration Map in Acetone-Based Diamond Growth Plasma. Xc=0.52, X q =0.32, and X h =0.67. 118 Figure 42. CoiTected TAUF Data from Figure 41. Maximum H Atom Density is 2.77 ± 0.28 xlO 17 per cm3. 119 Figure 43. Repeat Corrected TAUF Scan for Conditions in Figure 41. 120 corresponds to a maximum H-atom concentration of 2.77±0.28 x 10 17 per cm 3 or approximately 8.4 Torr of hydrogen atoms. This concentration is remarkable in that all of the hydrogen atoms must come solely from the dissociation of acetone by the plasma. Oxygen atom TAUF was also used to investigate the acetone-oxygen diamond growth plasma. However, no oxygen atoms could be detected in the plasma for the acetone-oxygen mixture ratio used to grow diamond. O-atoms could be detected at lower percentage of acetone in the plasma; under conditions which did not lead to diamond deposition. Figures 44 and 45 show uncorrected and corrected O-atom TAUF profile measurements for a acetone-oxygen-based (5.55 seem acetone and 9.18 seem O2) plasma where Xc=0.41, Xq=0.42, and XH=0.67 which is in the oxygen-rich no-growth region just below the main diamond growth region in the C-H-0 phase diagram given in Figure 2. The O-atom TAUF signal uncorrected for quenching corresponds to a concentration of 1.19 x 10 15 per cm3. The initial partial pressure of oxygen in this plasma is approximately 25 Torr. Based on preliminary O-atom TAUF quenching data for quenching by 0 2, the measured maximum O-atom TAUF signal can be corrected by a factor of 98 giving a maxim um density of 1.2 ± 0.12 x 1017 per cm3. Two experimental results which may shed some light on the reason for the lack of measurable O-atom TAUF under oxygen-acetone diamond growth conditions are shown in Figures 46 and 47. In both cases O-atom TAUF was monitored as a function of gas mixture ratio. In addition, stimulated emission pumping (SEP) can also be observed from the O- atom TAUF diagnostic in the direction of the laser probe beam .103 121 Figure 44. Raw Data for 0-Atom TALIF Concentration Map in Acetone-Based Microwave Plasma. Xc=0.41, X q =0.42, and X h =0.67. 122 Figure 45. Corrected O-Atom TAUF Data from Figure 44, Maximum O-Atom Density is 1.2 ± 0.12 x 10 17 per cm3. Emission Pumping (SEP) Signals as a Function Function a (SEP) as Signals Pumping Emission Figure 46. H-Atom TAUF and Stimulated Stimulated and TAUF H-Atom 46. Figure of of H Signal, millivolts 2 30 30 30 40 10 10 30 /O 0 0 . 03 . 00 . 10 . 31 . 37 3.0 3.7 3.4 3.1 1.0 1.0 1.3 0.0 0.0 0.3 0.0 2 Mass Flow Ratio in MassMicrowaveFlow Plasma. in Ratio TAUF n lw Ratio Flow an M SEP 124 40 SEP o TAUF 0.0 0.2 0.4 0.6 0.6 1.0 1.2 1.4 1.6 Mm Flow Ratio Figure 47. O-Atom TAUF and Stimulated Emission Pumping (SEP) Signals as a Function of Acetone /0 2 Mass Flow Ratio in Microwave Plasma. 125 A thin glass slide which blocks the transmission of the 226 nm probe light with low UV fluorescence is placed after the exit quartz viewport and the highly directional SEP fluorescence continues to pass on through a narrow-band 845 nm interference filter and is subsequently detected by a Hammatsu R928 photomultiplier. Thus, both the TAUF and SEP signals can be monitored simultaneously. Figure 46 shows the response of O-atom TAUF and SEP as a function of H2 to 0 2 mixture ratio in a microwave plasma at constant 40 Torr pressure. Both the TAUF and SEP signals are appreciable over a large range of mixture ratios up to nearly 3 to 1 H 2 to 0 2. Both signals have somewhat of a similar behavior in that there is a relatively gentle decline in the signals at higher mixture ratios. The fact that TAUF signal response follows the same functional behavior as the SEP signal especially at higher mixture ratios indicates the TAUF signal is not significantly perturbed by the presence of SEP emission. The curves in Figure 47 both demonstrate a drastically different behavior as one increases the acetone to oxygen mixture ratio. At a ratio of 0.4 there is a sharp drop in both TAUF and SEP signals. The data in Figures 44 and 45 was acquired at a mixture ratio of 0.6 where some signal from both diagnostics is still observable. In the case of diamond growth the mixture ratio is around 1.2 where the signals have declined into the background. The qualitative difference between the results from the mixture ratio measurements and also from comparing H-atom versus O-atom TAUF measurements in the acetone-oxygen diamond growth plasma was also confirmed by plasma emission measurements. In this case a 126 Photometrix CCD camera monitored the plasma emission through the narrowband interference filters used to detect H-atom (656nm) or 0- atom (845 nm) TAUF. In the case of hydrogen atoms emission was clearly seen by the CCD camera and was localized to the boundary of the plasma ball seen visibly with the eye. This would suggest that the H-atom emission was generated by electron-impact excitation from electrons generated in the plasma. For oxygen atoms no emission was detected by the CCD camera system. Careful adjustments in exposure and contrast were used to enhance the possibility of detection of the emission, but no observable emission was found. This measurement coupled with the results of TAUF measurement for O-atoms suggests that no free atomic oxygen was present at levels which could be discerned. The fact that atomic oxygen could not be detected either by TAUF or plasma emission measurements in the case of the acetone/ 0 2 -based diamond deposition plasma is also in accord with the mass spectrometry measurements discussed in Chapter 3. In those measurements no atomic oxygen and O 2 were detected in the gases flowing out of the reactor. The hypothesis is that oxygen reacts with carbon or some hydrocarbon and is very effectively trapped in these plasma. The effect of excess carbon removal by oxygen capture would seem to enhance the preferred type of carbon or hydrocarbon form required for higher quality diamond growth at the surface. Calibrated UF measurements for carbon monoxide in the plasma may help to clarify this mechanism by determining concentrations of CO and hence the amount of removal of free oxygen. APPENDIX A EXPERIMENTAL QUENCHING DATA 127 C2H2 Quenching 0.412 0.4299 Input Data File to MNV.EXE 0.449 0.40934 63 1 2 0.49 0.3952 3.2D-15 0.513 0.37791 5.0D-16 0.555 0.36539 0 1 0.702 0.32235 0.005 0.94566 0.762 0.30172 0.0068 0.93698 0.818 0.2875 0.0101 0.92984 0.881 0.27296 0.0151 0.93597 0.93 0.26593 0.0211 0.94015 1.016 0.24888 0.0275 0.94101 1.063 0.23884 0.0302 0.95083 1.11 0.22957 0.0354 0.95388 1.22 0.21219 0.0408 0.91758 1.44 0.18538 0.0463 0.91452 1.71 0.1607 0.0503 0.89036 1.91 0.14701 0.0536 0.87137 2.42 0.11848 0.0655 0.79074 2.94 0.099231 0.1025 0.67337 3.93 0.075431 0.1115 0.62685 4.93 0.061199 0.115 0.6486 6.92 0.043962 0.1207 0.65265 7.06 0.042354 0.1255 0.63883 10.49 0.028565 0.1335 0.63663 .00000D+00 0.141 0.63905 .00000D+00 0.153 0.64203 .50000D-15 0.161 0.6312 .00000D+00 0.171 0.62208 .OOOOOD+OO 0.182 0.60602 •00000D+00 0.192 0.60102 .00000D+00 0.203 0.58936 .00000D+00 0.211 0.57425 63 0.225 0.5543 1 0.234 0.53484 2 0.243 0.58095 0 0.251 0.5721 1 0.28 0.5366 1 0.291 0.53913 1 0.303 0.50985 0.32 0.502 0.336 0.47486 0.357 0.46146 0.386 0.44027 H2 Quenching #1 40.042 0.00925 Input Data File to MNV.EXE 44.962 0.0091859 47 1 2 49.982 0.010166 ID-14 59.982 0.0073714 ID-15 69.962 0.0054026 0 0.99167 80.062 0.0048758 0.099 0.77143 89.972 0.0043895 0.2 0.59945 99.952 0.0018099 0.302 0.47949 .00000D+00 0.403 0.41812 .00000D+00 0.498 0.36601 .50000D-15 0.602 0.32589 .00000D+00 0.702 0.29211 .OOOOOD+OO 0.798 0.26374 .OOOOOD+OO 0.9 0.23727 .OOOOOD+OO 0.998 0.22777 .OOOOOD+OO 1.098 0.2152 47 1.198 0.20206 1 1.3 0.19116 2 1.398 0.18167 0 1.497 0.1709 1 1.598 0.16676 1 1.695 0.15763 1 1.796 0.14914 10 I.898 0.14475 2.9 0.10369 3.901 0.080543 4.903 0.065131 5.901 0.056449 6.911 0.048937 7.906 0.04346 8.904 0.039449 9.893 0.03634 II.922 0.02777 13.942 0.025264 15.932 0.023518 17.922 0.020071 19.972 0.018564 21.972 0.017433 23.912 0.017037 25.952 0.013664 27.972 0.013461 29.912 0.013135 34.992 0.011906 130 H2 Quenching #2 90.161 0.0093256 Input Data File to MNV.EXE 99.861 0.0083197 41 1 2 .00000D+00 ID-15 .OOOOOD+OO ID-15 .50000D-15 0 1.00000 .OOOOOD+OO 0.061 0.90293 .OOOOOD+OO 0.152 0.66890 .OOOOOD+OO 0.295 0.50748 .OOOOOD+OO 0.378 0.44055 .OOOOOD+OO 0.47 0.38718 41 0.587 0.33998 1 0.686 0.31209 2 0.788 0.28677 0 0.883 0.28023 1 1.081 0.20602 1 1.271 0.18586 1 1.47 0.17181 10 1.679 0.15865 1.889 0.14572 2.883 0.10982 3.875 0.086545 4.891 0.083156 5.908 0.069675 6.881 0.061892 7.896 0.057406 8.906 0.045459 9.899 0.040152 11.931 0.036884 14.011 0.035791 15.991 0.030620 17.911 0.028248 19.951 0.026769 22.001 0.029038 24.061 0.028081 26.061 0.027725 28.111 0.028389 30.151 0.020875 34.961 0.019125 40.011 0.019208 50.061 0.014412 60.081 0.013075 70.311 0.011217 79.961 0.012358 He Quenching 13.877 0.4207 Input Data File to MNV.EXE 15.867 0.4149 59 1 2 17.892 0.3824 ID-15 19.887 0.3781 ID-15 24.371 0.3345 0 1 27.895 0.2877 0.0665 0.8524 30.876 0.2936 0.1645 0.7857 34.376 0.2782 0.277 0.7258 39.862 0.258 0.37 0.7063 44.885 0.243 0.469 0.68 49.872 0.2332 0.571 0.6595 54.862 0.2249 0.663 0.6503 59.871 0.2155 0.765 0.647 64.967 0.2046 0.868 0.635 69.872 0.1991 1.071 0.637 74.887 0.192 1.273 0.6346 79.962 0.1892 1.477 0.6206 84.867 0.1847 1.671 0.6295 94.842 0.1754 1.868 0.6144 99.871 0.1712 2.071 0.6239 .OOOOOD+OO 2.266 0.6495 .OOOOOD+OO 2.493 0.6105 .50000D-15 2.689 0.6255 .OOOOOD+OO 2.871 0.5975 .OOOOOD+OO 3.057 0.6317 .OOOOOD+OO 3.268 0.6245 .OOOOOD+OO 3.462 0.6179 .OOOOOD+OO 3.695 0.6089 59 3.92 0.5852 1 4.378 0.5986 2 4.408 0.5774 0 4.906 0.5774 1 5.46 0.5331 1 5.884 0.5311 1 6.385 0.5565 10 6.883 0.5005 7.375 0.4853 7.847 0.4796 8.415 0.4725 8.876 0.4915 9.543 0.4804 9.851 0.4874 11.872 0.4529 At Quenching .OOOOOD+OO Input Data File to MNV.EXE .OOOOOD+OO 33 1 2 33 1.74D-15 1 0.61D-15 2 0 1 0 0.081 0.911 1 0.449 0.829 1 0.5563 0.704 1 0.658 0.649 10 0.757 0.679 1.813 0.537 2.8 0.474 3.861 0.394 4.854 0.364 5.854 0.321 6.822 0.293 7.88 0.279 8.842 0.253 9.83 0.248 11.834 0.209 13.87 0.182 15.85 0.165 17.88 0.151 35.29 0.108 39.79 0.087 44.78 0.075 49.81 0.063 54.8 0.0556 59.8 0.049 64.8 0.045 69.8 0.041 74.8 0.038 79.8 0.037 84.8 0.036 89.8 0.035 94.8 0.035 98.8 0.035 .OOOOOD+OO .OOOOOD+OO .50000D-15 .OOOOOD+OO .OOOOOD+OO .OOOOOD+OO N2 Quenching 51.16 0.0133 Input Data File to MNV.EXE 54.92 0.0123 50 1 2 59.87 0.132 ID-15 64.89 0.0123 ID-15 69.87 0.0118 0 1 74.86 0.0084 0.067 0.9655 79.91 0.0117 0.163 0.8191 84.95 0.0105 0.27 0.7534 89.97 0.0071 0.372 0.651 94.91 0.0081 0.464 0.626 99.93 0.0091 0.572 0.511 .OOOOOD+OO 0.675 0.477 .OOOOOD+OO 0.765 0.45 • 50000D-15 0.869 0.426 .OOOOOD+OO 1.064 0.303 .OOOOOD+OO 1.404 0.31 .OOOOOD+OO 1.871 0.262 .OOOOOD+OO 2.29 0.227 .OOOOOD+OO 2.874 0.194 50 3.462 0.17 1 3.904 0.154 2 4.378 0.142 0 4.863 0.134 1 5.376 0.125 1 5.89 0.112 1 6.37 0.106 10 6.868 0.101 7.378 0.0931 8.365 0.092 8.847 0.0815 9.35 0.0785 9.907 0.0714 11.89 0.0588 13.88 0.0504 15.89 0.044 17.9 0.0378 19.9 0.0332 23.89 0.0269 27.96 0.0248 35.36 0.0229 39.86 0.0188 44.86 0.0165 49.65 0.0147 O2 Quenching 12.259 0.09421 Input Data File to MNV.EXE 12.884 0.090805 69 1 2 13.374 0.090318 ID-15 13.934 0.091534 ID-15 14.193 0.074485 0 1 14.404 0.087935 0.065 0.93744 14.904 0.084828 0.116 0.84923 15.364 0.079662 0.163 0.84055 15.864 0.082924 0.288 0.83058 16.063 0.063491 0.369 0.62031 18.013 0.058779 0.511 0.64715 19.873 0.050727 0.60838 0.46106 21.913 0.047639 0.85173 0.3946 23.923 0.043123 1.1165 0.30033 25.903 0.041226 1.3739 0.31304 27.913 0.038773 1.6152. 0.24165 29.903 0.039314 I.8534 0.26448 34.943 0.035683 2.1145 0.20758 39.543 0.029752 2.3394 0.2309 44.953 0.026752 2.618 0.18677 49.573 0.023596 2.8529 0.21412 54.913 0.021992 3.1155 0.17217 59.893 0.021323 3.3871 0.18561 65.563 0.029744 3.6188 0.15578 70.03 0.027606 3.8831 0.17565 79.863 0.021453 4.1165 0.14793 84.943 0.02036 4.3759 0.16687 89.923 0.019881 4.6178 0.13875 94.903 0.016059 4.8452 0.1688 99.933 0.01591 5.3945 0.15439 .00000D+00 5.8885 0.14622 .00000D+00 6.3718 0.14069 .50000D-15 6.8678 0.1341 .00000D+00 7.3778 0.13233 .OOOOOD+OO 7.8665 0.12633 .OOOOOD+OO 8.3705 0.1225 .OOOOOD+OO 8.9065 0.11771 .OOOOOD+OO 9.3768 0.11822 69 9.8952 0.11345 1 10.374 0.10463 2 10.88 0.10434 0 II.404 0.10027 1 11.884 0.102 10 APPENDIX B COMPUTER ACQUISITION AND ANALYSIS PROGRAMS 135 136 £******************************************************************** C Program: DIAMSCAN.FOR C C This program allows collection of data for spatial C profiling in the ASTEX microwave reactor. This program C does not control the PDL dye laser, but allows collection of C data as a function of the cell position as controled C by the stepping motor controller. The laser must first C be tuned to the peak of a transition of interest and C the peak intensity will be recorded versus position. C On the fly geometric viewing correction is an option. C This program contains many of the subroutines C previously written for PDLTEK4.FOR by Tim Cerny. C C 3-26-91 Geli Tserepi (Early Position Scanning of RF Cell) C 4-10-92 Bryan Preppernau (Inital 1-D Scan Version) C 7-25-92 Bryan Preppernau ^******************************************************************** $ storage:2 INCLUDE 'FGRAPH.FF INCLUDE 'FGRAPH.FD' C********** DECLARE AND DIMENSION VARIABLES ***************** C DEFINE VARIABLES USED FOR DATA DOUBLE PRECISION XPOSmON(5000),YPOSITION(5000) REAL SIGNALDATA(5000) COMMON/DATAVARS/XPOSmON.YPOSmON.SIGNALDATA C SPATIAL SCAN LOOP VARIABLES INTEGER*2 IXSTART.IXFINISH.IYSTART.IYFINISH.STEPSIZE INTEGER* 2 XDATAPOINTS.YDATAPOINTS.TOTALPOINTS INTEGER* 2 ISDIREC ,XMT,YINIT REAL XSTART.XHNISH.YSTART.YFINISH.MMSTEP CHARACTER*30 MESSAGE CHARACTER* 1 RESP CHARACTER*3 SDIREC1.SDIREC2 CHARACTER*4 DATE LOGICAL BECHOOFF,BRS232INIT,BDSASET COMMON/SSCANVARS/XSTART,XHNISH,YSTART,YFINISHISTEPSIZE, + XD ATAPOINTS, YD ATAPOINTS.MMSTEP, SDIREC1 .SDIREC 2, + IXSTART.IXFINISH.ISDIREC.IYSTART.IYFINISH C FILE NAME VARIABLES INTEGER*2 SRUNNUM, SHOTS COMMON/SFILEVARS/SRUNNUM,DATE C DEFINE VARIABLES USED IN COMMON BLOCK IBGLOBAL INTEGER RD(15),WRT(15),TEKBD,CNT £************* ATT AT SCAN LOOP ******************************* C INITIALIZE PROGRAMM VARIABLES BDSASET=. FALSE. BECHOOFF=.FALSE. BRS232INIT=.FALSE. IF (.NOT.BRS2 3 2INIT) THEN CALL RS232INTT0 UNITIALIZE COM1 & PORT BUFFER BRS2 3 2INTr=.TRUE. END IF C INITIALIZE SPATIAL SCAN VARIABLES IXHNISH=630 IXSTART=0 IYHNISH=630 IYSTART=0 STEPSIZE=315 SRUNNUM=1 SDIREC 1=' r SDffiEC2=' IM' ISDIREC=2 CALL DSAINTT(TEKBD)! MTIALIZE IEEE BUS GOTO 4 C DISPLAY AND CHANGE SPATIAL SCAN PARAMETERS 3 CALL CLEARSCREEN($GCLEARSCREEN) WRTTE(MOl) 138 101 FORMAT(/////T2 0,'WOULD YOU LIKE TO TAKE ANOTHER SPATIAL SCAN?'/ / + T20/ENTER Y TO CONTINUE OR N TO QUIT \ ) CALL INKEY(RESP) SELECT CASE(RESP) CASE (Y, Y) GOTO 2 CASE DEFAULT GOTO 1000 END SELECT C MANUALLY MOVE THE CELL INTO POSITION 4 CALL CLEARSCREEN($GCLEARSCREEN) 99 WRTTE(M02) 102 FORMAT(/////T20,'DATE (MMDD) ?') READ(*,'(A4)',ERR=99)DATE 2 CALL CLEARSCREEN($GCLEARSCREEN) CALL PREPCELLO 1 CALL SSCANPARDISO CALL SSCANINIT(BECHOOFF) C INITIALIZE SPATIAL SCAN DATA AQUISITION CALL DATAJNIT(TEKBD) IF (.NOT.BDSASET) THEN CALL CLEARSCREEN( $ GCLEARSCREEN) CALL STRACESEL(RD,WRT,TEKBD,CNT) BDSASET=.TRUE. END IF CALL CLEARSCREEN(S GCLEARSCREEN) 50WRTTE(M00) 100 FORMAT(////T20,'HOW MANY SHOTS TO AVERAGE ?') READ (V(I3)\ERR=50)SHOTS CALL DSAAVEG(SHOTS,TEKBD,WRTfCNT) C ACQUIRE DATA CALL CLEARSCREEN($ GCLEARSCREEN) C MOVE STEPPER MOTORS INTO POSITION UNDER COMPUTER CONTROL 139 XDMTT=MM2INDEX(XSTART) YINTT=MM2INDEX(YSTART) CALL INTTMOVER(SDIREC 1, SDIREC 2 .XINTT, YINIT) K=0 DO J=0,YDATAPOINTS DO I=0,XDATAPOINTS MESSAGE='DIG RUN' CALL S1R2GPIB(MESSAGE,WRT,CNT) CALL IBWRT (TEKBD, WRT, CNT) CALL STOPCHECK (WRT,RD,TEKBD,CNT) !MAKE SURE DIGITIZER IS OFF CALL COLLECTDATA(K,TEKBD,WRT,RD,CNT) XPOSITION(K)=XSTART+I*MMSTEP EFCSDIRECl.EQ.' I-') THEN XPOSmON(K)=XFINISHT*MMSTEP END IF YPOSmON(K)=YSTART+J*MMSTEP WRITE(*,300) XPOSmON(K),YPOSmON(K),SIGNALDATA(K) C MOVE MOTORS AND UPDATE COUNTERS, EXCEPT ON FINAL PASS IF(I.NE.XDATAPOINTS) CALL SIDEMOVER(SDIRECl,STEPSIZE) K=K+1 TOTALPOINTS=K END DO mSDIRECLEa’ I-') THEN SDIREC 1=' r ELSEIF(SDIREC 1 .EQ.' I') THEN SDIREC 1=' I-' END IF IF(J.NE.YDATAPOINTS) CALL VERTMOVER(SDIREC 2 .STEPSIZE) END DO message='COND TYP: CONTI' 140 call str2gpib (message, wrt, cnt) call ibwrt (tekbd,wrt,cnt) message='AVG OFF' call str2gpib (message, wrt, cnt) call ibwrt (tekbd,wrt,cnt) CALL ZEROMOVER0 C STORE DATA CALL CLEARSCREEN( $ GCLEARSCREEN) 450 WRrTE(*,501) 501 FORMAT(//////T2 5'END OF SPATIAL SCAN. OPTIONS:'//Tl5, + 'l) SAVE DATA YT15, + ’2) CONTTNUE'/Tl 5, 'SELECTION?^ 600 CALL INKEY(RESP) SELECT CASE(RESP) CASE DEFAULT GOTO 600 CASE (’2') GOTO 2 CASE ('1') CALL FILENAMEO WRITE(2,299) TOTALPOINTS 299 FORMAT (14) DO 11=0,TOTALPOINTS-1 WR1TE(2,300) XPOSmON(Il),YPOSmON(Il),SIGNALDATA(Il) 300 FORMAT (3F10.3) END DO CLOSE(UNrr=2,STATUS='KEEP') SRUNNUM=SRUNNUM+1 GOTO 3 END SELECT 1000 CALL OFFINT STOP END C************* prepare cell for a spatial scan ***************** subroutine prepcell () 141 C Definitions needed to use clearscreen in a subroutine integer *2 $gclearscreen parameter(Sgclearscreen= 0) external clearscreen character*! resp call clearscreen (Sgclearscreen) 200 write (*, 100) 100 format (///////T 10,'Please move the cell manually into position.'/ + T10, 'Touch any key when ready. '\) call inkey (resp) return end C****** Display and change parameters for spatial scan ************* subroutine sscanpardisO C Definitions needed to use clearscreen in a subroutine integer*2 Sgclearscreen parameter(Sgclearscreen= 0) external clearscreen C Spatial file name construction variables integer *2 srunnum common /sfilevars/ srunnum,date real xstart,xfinish,ystartfyfinish,mmstep integer *2 stepsize,xdatapoints,ydatapoints integer *2 ixfinish,iyfinish,mm 2indexlisdireclixstartliystart character*3 sdirecl,sdirec2 character*4 date COMMON/SSCANVARSASTART,XHNISH,YSTART,YFINISH,STEPSIZE, + XDATAPOINTS,YDATAPOINTS,MMSTEP,SDIREC 1.SDIREC2, + IXSTART.IXFINISH.ISDIREC.IYSTART.IYFINISH character*! resp, cr parameter (cr=char(13)) character*30 spatdirtxt(2) data spatdirtxt / 'Left to right','Right to left'/ xfinish=50 yfinish=50 mmstep=l 1 0 0 xdatapoints=(xfinish-xstart)/mmstep ydatapoints=(yfinish-ystart)/mmstep call clearscreen($gclearscreen) write (*, 200) spatdirtxt(isdirec),xstart,xfinish,ystart,yfinish, + mmstep.srunnum 200 format (/////T20,'Spatial Grating Scan Parameters'//T10, + ’a) Scan Direction: '.A30/T10, + Id) X-Position Start: '.F9.3,' mm'/TIO, + ’c) X-Position Stop: '.F9.3,' mm '/T10, + ’d) Y-Position Start: \F9.3,' mm'/TIO, + 'e) Y-Position Stop: ',F9.3,' mm '/T10, + 'f) Spatial step size: \F9.4,' mm (min.step=.0032mm)'/T10, + 'g) Spatial scan rim number: '.I2//T7, +'ENTER when ready'/T9) 300 call inkey (resp) select case(resp) case default goto 300 case ('a','A') call sdirecsetO case Cb'.'B') 305 write (*,310) 310 format (//T10,'Please input the X - starting position in mm: '\) read (*,'(F8.0)',err=305) xstart if (xstart.lt. 0.) xstart=-xstart ixstart=mm 2index(xstart) case ('c','C') 315 write (*,320) 320 format (//T10,'Please input the X - stopping position in mm: '\) read (*,'(F8.0)',err=315) xfinish if (xfinish.lt. 0.) xfinish=-xfinish ixfinish=mm 2index(xfinish) case ('d'.'D') 321 write (*,322) 322 format (//T10,'Please input the Y - starting position in mm: '\) 143 read (V(F8.0)',err=321) ystart if (ystart.lt.O.) ystart=-ystart iystart=mm2 index(ystart) case ('e'/E') 323 write (*,324) 324 format (//T10,'Please input the Y - stopping position in mm: \) read (*,'(F8.0)',err=323) yfinish if (yfinish.lt.O.) yfinish=-yfinish iyfinish=mm 2index(yfinish) case (T.'F) 325 write (*,330) 330 format (//T10,'Please input the spatial step size in mm: ’\) read (*,'(F8.0)',err=325) mmstep if (mmstep.lt.O) mmstep=-mmstep stepsize=mm 2index(mmstep) case Cg’.’G’) 335 write (*,340) 340 format (//T10,'Please input the new spatial scan number:'\) read (*,'(I2)',err=335) srunnum case (cr) return end select goto 100 end £*************** Qjjgogg spatial scan direction ********************* subroutine sdirecset () C Definitions needed to use clearscreen in a subroutine integer *2 Sgclearscreen parameter($gclearscreen= 0) external clearscreen real xstart,xfinish,ystart,yfinish,mmstep integer *2 stepsize,xdatapoints,ydatapoints integer *2 ixstart,ixfinish,isdirec,iystartIiyfinish character*3 sdirecl,sdirec 2 COMMON/SSCANVARS/XSTART,XFINISH,YSTART,YFINISH,STEPSIZE, + XD ATAPOINTS, YD ATAPOINTS,MMSTEP, SDIREC 1, SDIREC 2, + IXSTART,KFINISH,ISDIREC,IYSTART,IYFINISH character*! resp call clearscreen($gclearscreen) write (*, 100) 100 form at(//////T2 5'Spatial scan direction options7/T15, + ’1) Scan from left to right.'/T15, + *2) Scan from right to left.'//Tl 5,'Selection?'\) 200 call inkey (resp) isdirec=ichar(resp)-48 select case (isdirec) case default goto 200 case (1) sdirecl=' I-' case (2) sdirecl=' I' end select return end ^*********************** Construct file nainp *********************** subroutine filename() C Filename construction variables integer *2 srunnum character* 17 pathname character*4 date character*3 sttus character* 12 file com m on /sfilevars/srunnum,date integer *2 tens character *2 chsrunnum character* 1 resp C Convert the run number into a string tens=srunnum/l 0 chsrunnum=char(tens+48)//char((srunnum-10*tens)+48) file='HSy/date//chsrunnum//,.DAT pathname='DATA/7/file sttus='NEW' 50 open (unit=2, file=pathname, status=sttus, err=400) return c Error saving data 400 write (*,500) 500 format(//' There is an I/O error saving the data.'/ + ’ Most likely, the file name is already in use.’/ + ' Would you like to overwrite? (Y/N) '\) call inkey (resp) select case (resp) case (T,V) sttus=,OLD’ goto 50 case default call sscanpardisO end select return end C********* Select signal and calibration signals on DSA 601 ********* subroutine stracesel (rd, wrt, tekbd, cnt) C Define variables associated with gpib functions integer rd(15),wrt(15),tekbd,cnt character*30 message character*30 labtrace integer *2 i character* 1 resp write (*, 100) 100 format (///////T5,'Please make sure the signal channer/T5, + 'is selected. Touch any key when ready. ’\) call inkey (resp) C Query for the selected trace message='SEL?' call str2gpib (message, wrt, cnt) call ibwrt (tekbd,wrt,cnt) call ibrd (tekbd,rd,30) call gpib 2str (message, rd, cnt) 146 C Find the trace number i=l do while (.not.((ichar(message(i:i)).ge.48).and. + (ichar(message(i:i)).lt.56))) i=i+l end do C Construct command and label trace labtrace=’LAB TRA7/message(i:i)//’:”SIGNAL"' call str2gpib (labtrace, wrt, cnt) call ibwrt (tekbd, wrt, cnt) return end C******** Initialize spatial grating scan variables ******************* subroutine sscaninit (bechooff) character*32 message logical bechooff C Enable communication (E) and zero position counter (Z) if (bechooff) then message='EZ' else message='EZT' !Toggle echo off on first time bechooff=.true. end if call strout (message) return end C**************** sen(i averaging information to DSA *************** subroutine dsaaveg (shots,tekbd,wrt,cnt) integer *2 shots C Define variables used in common block ibglobal integer wrt(15) integer tekbd,cnt character* 30 message character*4 inttochar message='AVG ON;NAVG 7/inttochar(shots)//';COND TYP:AVG’ call str2gpib (message, wrt, cnt) call ibwrt (tekbd,wrt, cnt) return end C********* Convert a string to an ASCII integer array *************** subroutine str 2gpib (message, wrt, cnt) C Define variables associated with gpib functions integer wrt(15),cnt,odd,i character*30 message cnt=len_trim(message) odd=mod(cnt, 2) i=l do while (i.le.cnt/ 2) wrt(i)=ichar(message(2*i-l:2*i-l)) !Set low byte wrt(i)=wrt(i) + ichar(message(2*i:2*i))*256 !Set high byte i=i+l end do if (odd.eq.l) wrt(i)=ichar(message(cnt:cnt)) return end check and wait until DSA digitizer is off ************ subroutine stopcheck (wrt,rd,tekbd,cnt) C Define variables associated with gpib functions integer rd(15),wrt( 15), tekbd, cnt character*30 tekresponse,message tekresponse='' do while (index(tekresponse,’STOP,).eq.O) 148 message='DIG?' call str2gpib (message, wrt, cnt) call ibwrt (tekbd, wrt, cnt) call ibrd (tekbd, rd, 30) call gpib2str (tekresponse, rd, 14) end do return end C*********** initialize tfff. bus and initialize bus variables ********** subroutine dsainit (tekbd) C Define variables associated with gpib functions integer tekbd,v,reos C gpib status, error and count variables character* 1 resp C Locate various devices on the GPIB bus tekbd=ibfind('DSA601') if (tekbd.lt. 0) then write (*, 100) 100 format (//T5'An error occurred opening the DSA 601.7 + T5'Press CTRL+ALT+DELETE to terminate program.’\) call inkey (resp) return end if C Set read statements to terminate when an EOI is encountered reos=1024 call ibeos (tekbd,reos) C Set write statements to terminate with an EOI v=l call ibeot (tekbd, v) return 149 end C************ Rea(i and convert signal/cal from DSA *************** subroutine collectdata (k,tekbd,wrt,rd,cnt) C Define local variables integer k real areacon C Define variables associated with gpib functions integer rd( 15 ),wrt( 15),tekbd,cnt character* 30 tekresponse,message C Define variables used for data double precision xposition(5000),yposition(5000) real signaldata (5000) common/datavars/xposition,yposition,signaldata message='YTMNS_AREA?' call str2gpib (message, wrt, cnt) call ibwrt (tekbd, wrt, cnt) call ibrd (tekbd,rd,30) call gpib2str (tekresponse, rd, 24) signaldata(k)=areacon(tekresponse) return end C********** Convert an ASCII integer array to a string ************** subroutine gpib 2str (message,rd,cnt) integer i, hbyte, lbyte C Define varibles associated with gpib functions integer rd(15),cnt character*30 message C gpib status, error and count variables odd=mod(cnt, 2) m essaged' i=l do while (i.le.cnt/ 2) lbyte=iand(rd(i),2 5 5) hbyte=rd(i)/256 message( 2 *i- 1:2 *i -1 )=char(lbyte) message(2*i: 2*i)=char(hbyte) i=i+l end do if (odd.eq.l) message(cnt:cnt)=char(iand(rd(i),255)) return end j’**************** Send a string out to Coml *********************** subroutine strout (message) character* 3 2 message character*33 tmessage integer *2 port / 0/, sndsta C tmessage(l:32)=message tmessage(33:33)=char(13) call sndstr (tmessage, port, sndsta) return end q S t r ill^ fr fllTl C O U ll subroutine strin (message) character*32 message character* 1 bytin, cr integer *2 ier, il, avail integer*4 i2, maxwait /100000/ cr=char(13) bytin=' ' message^ ' ier=l C Creat buffer to store input store to buffer Creat C C Set Coml up for appropriate parameters appropriate for up Coml Set C n n n £******************* R.S232********************* the port initialize 10 format (' There was an error receiving a a byte.'/ receiving error an was (' There format 10 + rtstat, ier) rtstat, + + worcLlength /7/, comm_port /0/, rtstat, ier rtstat, /0/, comm_port /7/, worcLlength + + ' The error code is: ’,14) is: code error The ' + integer call stbaud (baucLrate, parity, stop.bit, worcLlength, comm_port, comm_port, worcLlength, stop.bit, parity, (baucLrate, stbaud call return return (*, write end select end message*'' subroutine rs232init () rs232init subroutine end do end i2=l l il+ il= message(il:il)='' (ichar(bytin).lt.32) if message(il:il)=bytin i i2=l case default default case select case (ier) case select l l il= case ( case ier) (bytin, fchchr call do end (avail) bfstat call ((avail.ne.l).and.(i while do avail do while (bytin.ne.cr) while do 2 =i 2 =0 +l +l 1 ) adrt= 1200 baud_rate=4 parity* parity* ompr= COM1 comm_port=0 *2 10 baucLrate /4/, parity / parity /4/, baucLrate ) ier )ier 2 even even 2 . 1 t.maxwait)) 2 /, stop.bit / stop.bit /, 2 /, 151 152 call comon return end C********** Move Side Translation Stage Stepper Motors *********** subroutine sidemover(sdirecl,stepsize) integer *2 stepsize character*3 sdirecl character*4 xstepsize,inttochar character*32 message integer i C Find leading blanks in converted step size xstepsize=inttochar(stepsize) i=l do while (xstepsize(i:i).eq.'') i=i+l end do C Step translation stage message=’C'//sdirecl//xstepsize(i:)//', R' call strout (message) return end C********** Move Vertical Translation Stage Stepper Motors ******** subroutine vertmover(sdirec 2,stepsize) integer *2 stepsize character* 3 sdirec2 character*4 ystepsize.inttochar character*32 message integer j C Find leading blanks in converted step size ystepsize=inttochar(stepsize) j- 1 do while (ystepsize(j:j).eq.'') H + l end do C Step translation stage message='C7/sdirec2//ystepsize(j:)//', R' call strout (message) return end C***************** initialize Stepper Motor Positions **************** subroutine initmover(sdireclfsdirec 2,xinitIyinit) integer *2 xinit.yinit character*3 sdirecl,sdirec2 character*4 xjump,yjump,inttochar character*32 message integer ij C Find leading blanks in converted step size xjump=inttochar(xinit) i=l do while (xjump(i:i).eq.'') i=i+l end do yjump=inttochar(yinit) j=l do while (yjump(j:j).eq.'') j=j+l end do C Step translation stage message='C,//sdirecl//xjump(i:)//' 7/sdirec2//yjump(j:)//', R' call strout (message) return end C**************** Return Stepper Motors to Zero Position *********** subroutine zeromoverO character*9 zmessage zmessage='CIMO 10 R' call strout (zmessage) return end C*************** Return Stepper Motor #2 to Zero Position ********* subroutine zeromover 2() character*? zmessage zmessage='CIM0, R’ call strout (zmessage) return end £******************** initialize data arrays ************************* subroutine datainitO C Define variables used for data double precision xposition(5000),yposition(5000) real signaldata(5000) common /datavars/ xposition.yposition.signaldata integer *2 i do i=l,5000 xposition(i) = 0.D0 yposition(i) = 0.D0 signaldata(i)= 0. end do return end £******************************************************************** C C PDLFUN2.FOR c CODE FOR FUNCTIONS c To accompany PDLTEK2.FOR and PDLSUB2.FOR c £******************************************************************** C********** find the first character in a string ***************** integer* 1 function findfirstchar (string) character *10 string integer* 1 i i=l do while (string(i:i).eq.'') i=i+l end do findfirstchar=i return end C***** CONVERT F10.2 FORMAT TO CHARACTER STRING *********** CHARACTER* 10 FUNCTION RTOCHAR(Y) REAL X, Y, XI INTEGER* 2 XTEMP CHARACTER* 1 C(10) INTEGER* 11, II, FLAG X=Y !Switch to a working variable not transferred X1=X-AINT(X) '.Avoid rounding errors-save decimal portion C Check for negative value IF (X .LT. 0.) THEN RTOCHAR=' .00' RETURN END IF FLAG=0 !Flag to signal first significant figure C Convert the figures to the left of the decimal DO 1=1,7 11=7-1 XTEMP=INT(X/10.**I1) !Pick off leading figure 156 C(I)=CHAR(48+XTEMP) ! Convert to a character IF((XTEMP.EQ.O).AND.(FLAG.EQ.O)) C(I)='' !Use blanks if flag off IF(XTEMP.NE.O) FLAG=1 !Flag on when 1st figure non-zero X=X-REAL(XTEMP)*(10.**I1) ISubtract off converted figure END DO C Convert the figures to the right of the decimal DO 1=1,2 XTEMP=INT(X1*(10.**I)+.01) !Pick off leading figure C(8+I)=CHAR(48+XTEMP) 'Convert to a character X1=X1-REAL(XTEMP)/(10.**I) ISubtract off converted figure END DO C Construct entire string RTOCHAR=C(1)//C(2)//C(3)//C(4)//C(5)//C(6)//C(7)//'.V/C(9)//C(10) RETURN END q ************* Convert 4 digit integer to character ***************** character*4 function inttochar(y) integer *2 x,xtemp,y character* 1 c(4) integer* 1 i,il x=y do i-1,4 il=4-i xtemp=x/( 10**il) c(i)=char(48+xtemp) x=x-xtemp*( 10**il) end do inttochar=c(l)//c(2)//c(3)//c(4) return end C********* Convert DSA area measure string to a real ************** real function areacon (tekresponse) character*30 tekresponse character* 1 csign integer mpy, i, imark, il, xmpy, xponent double precision temparea, power, confactor /-5.0D-11/ 157 C Initialize variables areacon=0. temparea=O.DO xmpy=l xponent=0 i=l do while (tekresponse(i:i).ne.Y) '.Find Y for a reference i=i+l end do i=i+ll IMovetosign csign=tekresponse(i:i) select case (csign) case (V) mpy=+l case mpy=-l case default areacon=-l. IReturn a negative value if a read error occurs return end select C Find the decimal point imark=i+l do while (tekresponse(imark:imark).ne.7) imark=imark+l end do C Convert portion to the left of the decimal point do il=i+l,imark-l power= 1 .D1 **(imark-il-1) temparea=temparea+dfloat(ichar(tekresponse(il:il))-48)*power end do i=imark+l !Move to the right side of the dec pt imark=i C Find the E position do while (tekresponse(imark:imark).ne.,E') imark=imark+l end do C Convert the right hand side of the decimal point do il=i,imark-l power=l.Dl**(i-il-l) temparea=temparea+dfloat(ichar(tekresponse(il:il))-48)*power end do C Round to 5 dec places temparea=dble(int4((temparea* 1 .D 5)+. 5))/l.D 5 158 i=imark+l !Move to the right side of the E imark=i C Find the comma position do while (tekresponse(imark:imark).ne.7) imark=imark+l end do csign=tekresponse(i:i) select case (csign) case(V) i=i+l !xmpy ok, but increment marker case('-') i=i+l ! change xmpy and increment marker xmpy=-l end select C Determine the exponent value do il=i,imark-l xponent=xponent+(ichar(tekresponse(il:il))*48)*(10**(imark-il-l)) end do xponent=xmpy*xponent !Put in sign C Combine results; confactor puts value in familiar integrator units ar eacon=mpy *float((tempar ea* 1 .D1 * *xponent)/confactor) C Check TEK acquire error if (tekresponse(imark+l:imark+2).ne.'EQ') areacon=-l return end C********* Function to get date and convert to a string ************* character*8 function condate () integer*2 imonth, iday, iyear, il, i2 character*4 cmonth, cday, cyear, inttochar C Get current date call getdat(iyear, imonth, iday) C Convert integer format to character*4 variables cmonth=inttochar(imonth) cday=inttochar(iday) cyear=inttochar(iyear) C Remove leading zeroes in the day and month il=3 if (cmonth(3:3).eq.'0') il=4 12=3 if (cday(3:3).eq.'0') i2=4 C Construct string and return 159 condate=cmonth(il :)//'-'//cday(i2 :)//'-'//cyear( 3:) return end C************* convert millimeters to index units ****************** integer* 2 function mm2index (mm) real m m mm2index=int2(. 5+mm/(3.175E-3)) return end convert index units to millimeters ***************** real function index2mm (indx) integer*2 indx index2mm=float(indx)* 3.17 5E-3 return end 160 £************************************************************************* C PROGRAM TO CONVERT ACQUIRED DSA TEK WAVEFORMS CFROMIBIC.COM C Bryan L. Preppernau, Hydrogen Plasma Group 10-19-92 C Tim Cerny contributed Binary String Conversion Algorithms q ************************************************************************ $ storage: 2 INTEGER TEKBD, V,REOS REAL XINCR.YMULT.YZERO REAL XINCR1.YMULT1.YZER01 CHARACTER* 20 FILE TEKBD=IBFIND('DSA601') REOS=1024 CALL IBEOS(TEKBD,REOS) V=1 CALL 1BE0T(TEKBD,V) CALL CLS CALL WAVEFORMDATA(TEKBD,XINCRtYMULT,YZERO) XINCR1=XINCR YMULT1 = YMULT YZERO1 = YZERO WRITE (*,50) 50 FORMAT (T5,'Please input a filename (include path): ’\) READ (*,'(A20)') FILE CALL D ATASAVE(XIN CR1 .YMULT1, YZERO 1 .FILE) STOP END q**************** OUTPUT WAVEFORM TO DISK ******************** SUBROUTINE DATASAVE(XINCR1, YMULT 1, YZERO 1,FILE) INTEGER*2 NEWCURVE(1029),CURVE(1029),I1,I2 REAL XINCR1.YMULT1.YZER01,CHI,TIME CHARACTER* 20 FILE OPEN (UNIT=3, FILE='CDAT',FORM='BINARY',STATUS='OLD') OPEN (UNrr=2, HLE=HLE, STATUS='UNKNOWN') TIME=0. DO 1=1,1029 READ(3) CURVE(I) END DO DO 1=5,1029 11 =IAND(CURVE(I), 16#FF00) I2=IAND(CURVE(I+1), 16#00FF) NEWCURVE(I-4)=Il/2 56+12*2 56 END DO DO 1=1,1024 CHl=YZERO 1+YMULT1 *NEWCURVE(I) WRITE (2/(2E20.5)') TIME,CHI TIME=TIME+XINCR 1 END DO CLOSE (2) RETURN END *************** COLLECT KEY WAVEFORM QUANTITIES ************ SUBROUTINE WAVEFORMDATA(TEKBD,XINCR,YMULT,YZERO) INTEGER WRT(15),RD(300),TEKBD,CNT REAL XINCR,YMULT, YZERO CHARACTER*300 PREAMBLE CHARACTER*30 MESSAGE MESSAGE='OUT TRA1' CALL STR2GPIB(MESSAGE,WRT,CNT) CALL IBWRT(TEKBD,WRT,CNT) MESSAGE='WFM?' CALL STR2GPffi(MESSAGE,WRT,CNT) CALL IBWRT(TEKBD,WRT,CNT) CALL IBRD(TEKBD,RD,600) CALL GPIB2STR(PREAMBLE,RD,600) Convert ascii to real 162 CALL MAKEREAL(PREAMBLE,XINCRf YMULT, YZERO) RETURN END C************* MAKE ASCn TO REAL CONVERSION******************* SUBROUTINE MAKEREAL (PREAMBLE,XINCR, YMULT,YZERO) CHARACTER*300 PREAMBLE REAL XINCR,YMULT,YZERO OPEN (UNrr=l,STATUS='SCRATCH') C Find XINCR value I=INDEX(PREAMBLE,'XINCR') 11=0 DO WHILE (PREAMBLE(I+I1+6:I+I1+6).NE.',') 11= 11+1 END DO WRITE(1,'(A15)') PREAMBLE(I+6:I+Il+5) C Find YMULT value I=INDEX(PREAMBLE,'YMULT') 11=0 DO WHILE (PREAMBLE(I+I1+6:I+I1+6).NE.V) 11= 11+1 END DO WRITE(1,'(A15)') PREAMBLE(I+6:I+Il+5) C Find YZERO value I=INDEX(PREAMBLE,’YZERO') 11=0 DO WHILE (PREAMBLE(I+I1+6:I+I1+6).NE.',') 11= 11+1 END DO WRITE(1,’(A15)’) PREAMBLE(I+6:I+Il+5) REWIND 1 READ(1,10) XtNCR,YMULT,YZERO 10 FORMAT(E15.0) CLOSE (UNIT=1) RETURN END C************ convert a string to an ASCII integer array ************* subroutine str2gpib (message, wrt, cnt) C Define variables associated with gpib functions integer wrt(15),cnt,odd,i character* 30 message cnt=len_trim(message) odd=mod(cnt,2) i=l do while (i.le.cnt/2) wrt(i)=ichar(message(2*i-l:2*i-l)) !Set low byte wrt(i)=wrt(i) + ichar(message(2 *i: 2 *i))*2 56 ! Set high byte i=i+l end do if (odd.eq.l) wrt(i)=ichar(message(cnt:cnt)) return end C************* convert an ASCII integer array to a string ************ subroutine gpib2str (message,rd,cnt) integer i, hbyte, lbyte C Define varibles associated with gpib functions integer rd(15),cnt character*30 message C gpib status, error and count variables odd=mod(cnt,2) message^ ' i=l do while (i.le.cnt/2) lbyte=iand(rd(i),2 5 5) hbyte=rd(i)/256 mes sage(2 *i-1:2 *i-1 )=char(lby te) message(2 *i: 2 *i)=char(hbyte) i=i+l end do if (odd.eq.l) message(cnt:cnt)=char(iand(rd(i),255)) return end 164 PROGRAM N3DECAY DOUBLE PRECISION XP(5000),YP(3,5000),YSTART(3),DXSAV DOUBLE PRECISION Xl,X2,Hl,HMINIEPSIP,PV,VELtRADRATE(5000) DOUBLE PRECISION INTRO,INTRP,aYPOP(3) COMMON /PATH/ KMAX.KOUNT.DXSAV.XP.YP CHARACTER*20 FILE WRITE (*,20) 20 FORMAT (T5,'Please input a filename (include path): ’\) READ (*,'(A20)') FILE OPEN (UNIT=2, FILE=FILE, STATUS='UNKNOWN') DO K=l,6 VEL=9.027D+5 X1=0 X2=lD-7 NVAR=3 YSTART(1)=0.118 YSTART(2)=0.0 YSTART(3)=0.882 YPOP(l)=YSTART(l) YPOP(2)=YSTART(2) YPOP(3)=YSTART(3) H1=5D-10 HMIN=0 DXSAV=(X2-X1)/1000 KMAX=5000 EPS=lD-6 P=(K-1)*1.5 PV=P*3.29D+16*VEL CALL 0DEINT(YSTART,NVAR,X1,X2,EPS,H1IHMIN,N0K,NBAD,PV) DO 1=1,4999 XP(I)=XP(I)/lD-09 RADRATE(I)=((YP(l,I)/1.59D-7)+(YP(2,I)*0.1183/5.4D-9) 165 + +(YP( 3,1)/l. 5 6D-8))/((YPOP( 1 )/l. 5 9D- 7) + +(YPOP(2)*0.1183/5.4D-9)+(YPOP(3)/1.56D-8)) END DO DO 1=1 4999 IF(XP(I).LE.100)THEN C WRITE(2I,(2XIF12.6,2XtF12.8I2XtF12.8>2X,F12.8,2X,F12.8)') C + XP(I),YP( 1 ,D,YP(2,1),YP(3,I)IRADRATE(I) WR1TE(2,,(2X,F12.6,2X,F12.8),)XP(I),RADRATE(I) END IF END DO INTRP=0 DO 1=1 4999 IF (XP(I+1).LE.100) THEN INTRP=INTRP+(XP(I+1 )-XP(I))*(RADRATE(I+1) + +0.5 *(RADRATE(D-RADRATE(I+1))) END IF END DO IF (P.EQ.0) THEN INTR0=INTRP END IF Q=(INTRP/INTR0) WRITE(*I,(2X,F10.5,2X,F10.6)')P,Q WRrrE(2l,(2X,F10.5t2X,F10.6)')P,Q END DO CLOSE(2) END SUBROUTINE DERIVS(Y,DYDX,PV) DOUBLE PRECISION Y(3),DYDX(3),PV,PA,PAV DOUBLE PRECISION TS.TP.TD DOUBLE PRECISION Q,QA,MIX,MXA TS=1.59D-7 166 TP=5.4D-9 TD=1.56D-8 PA=0.1 PAV=PA*2.97D+22 0=0.035D-15 QA=8.85D-15 MK=0 MXA=0 D YDX( 1 )=-Y( 1 )* (1 /TS+PV*(8 *MIX+Q)+PAV* QA+PAV* 8 *MXA) + +PV*MIX*(Y(2)+Y(3))+PAV*MXA*(Y(2)+Y(3)) DYDX(2)=-Y(2)*(1/TP+PV*(6*MIX+Q)+PAV*QA+PAV*6*MXA) + +3*PV*MIX*(Y(1)+Y(3))+3*PAV*MXA*(Y(1)+Y(3)) DYDX(3)=-Y(3)*(1AD+PV*(4*MIX+Q)+PAV*QA+PAV*4*MXA) + +5*PV*MK*(Y(1)+Y(2))+5*PAV*MXA*(Y(1)+Y(2)) RETURN END SUBROUTINE ODEINT(YSTART,NVARlXllX2IEPS,Hl>HMIN>NOKINBAD,PV) PARAMETER (MAXSTP=10000,NMAX= 10,TWO=2.0,ZERO=0.0,TINY= 1 .E- 30) DOUBLE PRECISION YSTART(NVAR),YSCAL(NMAX),Y(NMAX),DYDX(NMAX) DOUBLE PRECISION X,Xl,X2,EPS,HtHlIHMIN,XSAV,HDID,HNEXTlPV DOUBLE PRECISION DXSAV,XP(5000),YP(3,5000) COMMON /PATH/ KMAX,KOUNT,DXSAVfXPfYP DO J=l,5000 XP(J)=1.01D-07 YP(1J)=0 YP(2,J)=0 YP(3,J)=0 END DO X=X1 H=SIGN(H1,X2-X1) NOK=0 NBAD=0 KOUNT=0 167 DO 11 I=1,NVAR Y(I)=YSTART(I) 11 CONTINUE XSAV=X-DXSAV*TWO DO 16 NSTP=1,MAXSTP CALL DERIVS(YIDYDX,PV) DO 12 I=1,NVAR YSCAL(I)=ABS(Y(I))+ABS(H*DYDX(I))+TINY 12 CONTINUE IF(KMAX.GT.O)THEN IF(ABS(X-XSAV).GT.ABS(DXSAV)) THEN EF(KOUNT.LT.KMAX-l)THEN KOUNT=KOUNT +1 XP(KOUNT)=X DO 13 I=1,NVAR YP(I,KOUNT)=Y (I) 13 CONTINUE XSAV=X ENDIF ENDIF ENDIF IF((X+H-X2)*(X+H-X1 ).GT.ZERO) H=X2-X CALLRKQC(Y iDYDX iNVAR,X,H,EPS,YSCAL iHDID,HNEXT,PV) IF(HDID.ECl.H)THEN NOK=NOK+l ELSE NBAD=NBAD+1 ENDIF IF((X-X2)*(X2-X1).GE.ZER0)THEN DO 14 I=1,NVAR YSTART(I)=Y(I) 14 CONTINUE IF(KMAX.NE. 0)THEN KOUNT=KOUNT +1 XP(KOUNT)=X DO 15 I=1,NVAR YP(I,KOUNT)=Y(I) 15 CONTINUE ENDIF RETURN ENDIF IF(ABS(HNEXT).LT.HMIN) PAUSE ’Stepsize smaller than m inim um .' H=HNEXT 16 CONTINUE 168 C PAUSE ’Too many steps.’ RETURN END SUBROUTINE RKQC(Y,DYDXIN,X,HTRYIEPS,YSCALIHDIDIHNEXT,PV) PARAMETER (NMAX=10,FCOR=.0666666667,ONE=1.( + SAFETY=0.9,ERRCON=6.E-4) DOUBLE PRECISION Y(N),DYDX(N),YSCAL(N) DOUBLE PRECISION YTEMP(NMAX),YSAV(NMAX),DYSAV(NMAX) DOUBLE PRECISION X,XSAV,H»HHIHTRY,EPS,HDIDtHNEXT,ERRMAX,PV PGROW=-0.20 PSHRNK=-0.25 XSAV=X DO 11 I=1,N YSAV(I)=Y(I) DYSAV(I)=DYDX(I) 11 CONTINUE H=HTRY 1 HH=0.5*H CALL RK4(YSAV,DYSAVIN,XSAVIHH,YTEMP,PV) X—xSAV+HH CALL DERIVS(YTEMP,DYDX,PV) CAUL RK4(YTEMP,DYDX,N,X,HH,Y,PV) X=XSAV+H IF(X.EQ.XSAV)PAUSE 'Stepsize not significant in RKQC.' CALL RK4(YSAV,DYSAVIN,XSAV,H,YTEMP,PV) ERRMAX=0. DO 12 1=1 ,N YTEMP(I)=Y(I)-YTEMP(I) ERRMAX=MAX(ERRMAX,ABS(YTEMP(I)/YSCAL(I))) 12 CONTINUE ERRMAX=ERRMAX/EPS IF(ERRMAX.GT.ONE) THEN H=SAFETY*H*(ERRMAX**PSHRNK) GOTO 1 ELSE HDID=H IF(ERRMAX.GT.ERRCON)THEN HNEXT=SAFETY*H*(ERRMAX**PGROW) ELSE HNEXT=4.*H ENDIF ENDIF 169 DO 13 1=1 ,N Y(I)=Y(I)+YTEMP(I)*FCOR 13 CONTINUE RETURN END SUBROUTINE RK4(YIDYDX,NIX,H,YOUT,PV) PARAMETER (NMAX=10) DOUBLE PRECISION Y(N),DYDX(N),YOUT(N), + YT(NMAX),DYT(NMAX),DYM(NMAX) iX,H,PV,HH iH6(XH HH=H*0.5 H6=H/6. XH=X+HH DO 111=1,N YT(I)=Y(I)+HH*DYDX(I) 11 CONTINUE CALL DERIVS(YT,DYT,PV) DO 12 1=1 ,N YT(I)=Y(I)+HH*DYT(I) 12 CONTINUE CALL DERIVS(YT,DYM,PV) DO 13 1=1 ,N YT(I)=Y(I)+H*DYM(I) DYM(I)=DYT(I)+DYM(I) 13 CONTINUE CALL DERIVS(YTtDYT,PV) DO 141=1,N YOUT(I)=Y(I)+H6*(DYDX(I)+DYT(I)+2.*DYM(I)) 14 CONTINUE RETURN END PROGRAM MNV IMPUCIT REAL*8(A-H,0-Z) CHARACTER* 20 FUN DIMENSION X(3 50,1),Y(3 50),RRR(3 50),IB(20),NAR(8),ARR(8) COMMON/BLK1/B(20),P(20),RE,N,M,K 311 FORMAT(4F10.2,F12.6) 400 WR^E(V(A\),), SOURCE FILE:' READ(*,,(A20),)FUN OPEN(llFILE=FLIN)STATUS='OLD'lACCESS='SEQUENTlAL') READ(1,*)N,MIK WRnE(Y(A\)')' # OF LINES WRrrE(*,*)N WRnE(V(A\)')' # OFASSIGNMENTS = ' WRTTE(V)M WRrrE(V(A\)')'# OF PARAMETERS WRITE(V)K READ(1,*)(B(I),I=1,K) DO 410 J=1,N READ( 1,*)(X0,I),I= 1,M),Y(J) 410 CONTINUE READ( 1 ,*)( ARR(I),I= 1,8) READ(1,*)(NAR(I),I=1,8) IF (NAR(4).LT.l) GOTO 415 READ( 1 ,*)(IB(I),I= 1 ,NAR(4)) 415 CLOSE( 1, STATUS='KEEP') DO 4201=1,K 420 WRITE(*,430)1,B(I) 430 F0RMAT(1X,,B(,,I2,,)=',D12.6) 450 WRITE(*,451)NAR(4) 451 FORMAT(lX,' No. parameters held constant = ',15) IF (NAR(4).NE.O) WR1TE{*,452)(IB(I),I=1,NAR(4)) 452 FORMAT(IX,' They are ’,816) CALL NLLSQ(Y,X,B,RRR,NAR,ARR,IB,FMT) STOP END Use Subroutine Model in Conjuction with NLLSQV.FOR 171 SUBROUTINE MODEL (F,Y,XIRRR,I,JP) IMPLICIT REAL*8(A-H,0-Z) COMMON/Bm/B(20),P(20),RE,N,M,K DIMENSION Y(3 50),RRR(3 50),X(3 50,1) DOUBLE PRECISION XP(5000),YP(3,5000),YSTART(3),DXSAV DOUBLE PRECISION X1,X2,H1,HMIN,EPSIPPIPVIVEL,RADRATE(5000) DOUBLE PRECISION INTRO,INTRP,SQ,PQ,DQISP,SD1DP,YPOP(3) COMMON /PATH/ KMAX,KOUNT,DXSAVIXP,YP VEL=9.03D+5 SQ=B(1) PQ=SQ DQ=SQ SP=B(2) SD=SP DP=SP X1=0 X2=lD-7 NVAR=3 YSTART(1)=0.118 YSTART(2)=0.0 YSTART(3)=0.882 YPOP(l)=YSTART( 1) YPOP(2)-YSTART(2) YPOP(3)=YSTART(3) H1=5D-10 HMIN=0 DXSAV=(X2 -XI )/l 000 KMAX=5000 EPS=lD-7 PP=X(I,1) WRTIE(*t*) PP PV=PP*3.29D+16*VEL CALL ODEINT(YSTART,NVAR,XllX2,EPS,Hl.HMIN.NOK.NBAD, + pv.sapaDasp.sD, dp ) DO 11=1,2000 XP(Il)=XP(Il)/lD-09 RADRATE(11 )=((YP( 1,11 )/l. 5 9D-7)+(YP(2,11 )*0.118 3/5.4D-9) + +(YP(3,Il)/1.56D-8))/((YPOP(l)/1.59D-7) + +(YPOP(2)*O.H83/5.4D-9)+(YPOP(3)/X.56D-8)) END DO INTRP=0 n n T1 - 1 4QQQ IF (XP(I1+1).LE.100) THEN INTRP=INTRP+(XP(I1+1 )-XP(Il ))*(RADRATE(11+1) + +0.5*(RADRATE(U)-RADRATE(I1+1))) ENDIF END DO IF (PP.EQ.0) THEN INTRO=INTRP ENDIF F=INTRP/INTRO RE=Y(I)-F JP=3 RETURN END SUBROUTINE DERIVS(Y,DYDXtPVlSQ,PQlDQ,SP,SDfDP) DOUBLE PRECISION Y(3),DYDX(3),PVIPA,PAV DOUBLE PRECISION TS.TP.TD DOUBLE PRECISION SaPCiDaSP.SD.DP.QA TS=1.59D-7 TP=5.4D-9 TD=1.56D-8 PA=0.13 PAV=PA* 2.9 7D+2 2 QA=8.87D-15 DYDX( 1 )=Y( 1 )*(- 1/TS-PV*( 3 *SP+ 5 *SD+SQ)- PAV*QA)+PV*(SP*Y(2)+SD*Y(3)) DYDX(2)=Y( 2)*(- 1/TP-PV*(SP+ 5 *DP+PQ)- PAV*QA)+3*PV*(SP*Y(1)+DP*Y(3)) 173 DYDX(3)=Y(3)*(-1/TD-PV*(SD+3*DP+DQ)- PAV*QA)+5*PV*(SD*Y(1)+DP*Y(2)) RETURN END From This Point Onward Subroutine Model is the same as N3DECAY.FOR BIBLIOGRAPHY 1. Plasma Processing of Materials: Scientific Opportunities and Technological Challenges. Plasma Science Committee, National Research Council (Washington, D.C.: National Academy Press, 1991). 2. Semiconductor International 15 (9), 12,1992. 3. R. Gottscho, B.. Preppernau, S.Pearton, A.Emerson, and K. Giapis, Real- Time Monitoring of Low-Temperature Hydrogen Plasma Passivation of GaAs. Journal of Applied Physics 68 (2), 440,1990 4. Semiconductors: Group IV Elements and HI-V Compounds, ed. O. Madelung, Data in Science and Technology Series (Berlin: Springer-Verlag, 1991). 5. C. Wu, M. Tamor, T. Potter, and E. Kaiser, A Study of Gas Chemistry During Hot-Filament Vanor Deposition of Diamond Films Using Methane/Hvdrogen and Acetylene/Hydrogen Gas Mixtures. Journal of Applied Physics 68 (9), 4825,1990. 6. F. Tochikubo, T. Makabe, S. Kakuta, and A. Suzuki, Study of the Structure of Radio Frequency Glow Discharges in CH^ and Ho bv Spatiotemnoral Optical Emission Spectroscopy. Journal of Applied Physics 71 (5), 2143,1992. 7. R. Fantoni, M. Giorgi, A. Moliterni, W. Berden, V. Lazic, 0. Martini, and F. Mattiot, On-Line Gas-Phase Optical Diagnostics in Plasma CVD Deposition of Carbon Films. Journal of Material Research 7 (5), 1204, 1992. 8 . K. Chen, M. Chuang, C. Penney, and W. Banholzer, Temperature and Concentration Distribution of Ho and H Atoms in Hot-Filament Chemical- Vapor Deposition of Diamond. Journal of Applied Physics 71 (3), 1485, 1992. 174 175 9. F. Celii and J. Butler, Direct Monitoring of CH 3 In a Filament-Assisted Diamond Chemical Vanor Deposition Reactor. Journal of Applied Physics 71 (6), 2877, 1992. 10. P. Davies and P. Martineau, Infrared laser Diagnostics in Methane fhemiral-Vapor-Deposition Plasmas. Journal of Applied Physics 71 (12), 6125,1992. 11. P. Hargis and K. Greenberg, Laser-Induced-Fluorescence Detection of SO and SO? in SFc/Oo Plasma Etching Discharges. Journal of Applied Physics 68 (2), 505,1990. See also P. Hargis and K. Greenberg, Dissociation and Product Formation in NFo Radio-Freauencv Glow Discharges. Journal of Applied Physics 67 ( 6), 2767,1990. 12. C. Gaebe, T. Hayes, and R. Gottscho, Effect of Photodetachment on a Radio-Freauencv Discharge Through BCI 3. Physical Review A 35 (7), 2995, 1987. 13. B. Ganguly, J. Shoemaker, B. Preppernau, and A. Garscadden, Rvdberg State Stark Spectroscopic Measurements of Electric Field Profile in a Glow Discharge. Journal of Applied Physics 61, 2778,1987. 14. Program and Abstracts. 41st Annual Gaseous Electronics Conference. 18-21 October, 1988, Minneapolis, Minnesota. 15. G.E.C. RF Reference Cell Newsletter, ed. J.R. Roberts, 3 (1) April 1991. 16. Program and Abstracts. 42st Annual Gaseous Electronics Conference. 17-20 October, 1989, Palo Alto, California. 17. Abstracts E-25 and E-26, Program and Abstracts. 43st Annual Gaseous Electronics Conference. 16-19 October, 1990, Champaign-Urbana, Illinois. 18. P. Hargis and K. Greenberg, Abstract R-27, Program and Abstracts. 43st Annual Gaseous Electronics Conference. 16-19 October, 1990, Champaign-Urbana, Illinois. 19. Abstracts DB-1 through DB-26, Program and Abstracts. 44st Annual Gaseous Electronics Conference. 22-25 October, 1991, Albuquerque, New Mexico. 176 20. P. Miller, H. Anderson, and M. Splichal, Electrical Isolation of Radio- Freauencv Plasma Discharges. Journal of Applied Physics 71 (3) 1171, 1992. See also M. Sobelewski, Electrical Characterization of Radio- Freauencv Discharges in the Gaseous Electronics Reference Cell. Journal of Vacuum Science and Technology A 10 (6), 3550,1992. 21. P. Loewenhardt, B. Blackwell, R. Boswell, G. Conway, and S. Hamberger, Plasma Production in a Toroidal Heliac bv Helicon Waves. Physical Review Letters 67 (20), 2792,1991. 22. J. Angus and C. Hayman, Low-Pressure. Metastable Growth of Diamond and "Diamondlike" Phases. Science 241, 913, 1988. 23. W. Eversole, U.S. Patent No. 3030187 (23 July 1958) and No. 3030188 (17 April 1958). 24 B.. Derjaguin, D. Fedossev, V.. Lukyanovich, B. Spitsyn, V. Ryabov, and A. Lavrentyev, Journal of Crystal Growth 2, 380,1968. 25. B. Derjaguin and D. Fedossev, Growth of Diamond and Graphite from the Gas Phase. (Moscow: Jzd. Nauka, 1977) and B. Spitsyn, L. Bouliv, and B. Derjaguin, Journal of Crystal Growth 52, 219,1981. 26. J. Angus, H. Will, and W. Stanko, Journal of Applied Physics 39, 2915, 1968 and D. Poferl, N. Gardner, and J. Angus, Journal of Applied Physics 44, 1418, 1973. 27. S. Aisenberg and R. Chabot, Journal of Applied Physics 42, 2953, 1971. 28. S. Matsumoto, Y. Sato, M. Kamo, and N. Setaka, Vanor Deposition of Diamond Particles from Methane. Japanese Journal of Applied Physics 21, (4) 183,1982. M. Kamo, Y. Sato, S. Matsumoto, and N. Setaka, Diamond Synthesis from Gas Phase in Microwave Plasma. Journal of Crystal Growth 62, 624,1983. 29. T. Ong, F. Xiong, and R. Chang, Mechanism for Diamond Nucleation and Growth on Single Crystal Conner Surfaces Implanted with Carbon. Applied Physics Letters 60 (17), 2083,1992. 177 30. G. Janssen, W. Van Enckevort, J. Schaminee, W. Vollenberg, L. Giling, and M. Seal, Rapid Single Crystalline Diamond Growth bv Acetvlene- Oxveen Flame Deposition. Journal of Crystal Growth 104, 752,1990. 31. Y. Mitsuda, T. Yoshida, and K. Akashi, Development of a New Microwave Plasma Torch and its Application to Diamond Synthesis. Review of Scientific Instruments 60 (2), 249,1989. 32. M. Frenklach, R. Kematick, D. Huang, W. Howard, K. Spear, A. Phelps, and R. Koba, Homogeneous Nucleation of Diamond Powder in the Gas Phase. Journal of Applied Physics 66 (91) 395,1989. 33.P. Buerki and S. Leutwyler, Homogeneous Nucleation of Daimnnd Powder bv COo-Laser-Driven Gas-Phase Reactions. Journal of Applied Physics 69 ( 6), 3739, 1991. 34. J. Rebello, D. Straub, and V. Subramaniam, Diamond Growth from a CO/CH4 Mixture bv Laser Excitation of CO: Laser Excited Chemical Vapor Deposition. Journal of Applied Physics 72 (3), 1133,1992. 35. C. Deshpandey and R. Bunshah, Diamond and Diamondlike Films: Deposition Processes and Properties. Journal of Vacuum Science and Technology A 7 (3), 2291, 1989. 36. W. Yarbrough and R. Messier, Current Issues and Problems in the Chemical Vapor Deposition of Diamond. Science 247, 688,1990 37. F Celii and J. Butler, Diamond Chemical Vapor Deposition. Annual Reviews of Physical Chemistry 42, 643,1991. 38. M. Geis and J. Angus, Diamond Film Semiconductors. Scientific American, Page 84, October 1992. 39. P. Bachmann, D. Leers, and H. Lydtin, Towards a General Concept of Diamond Chemical Vapor Deposition. Diamond and Related Materials 1, 1,1991. 40. M. Kadono, T. Inoue, A. Miyanaga, and S. Yamazaki, Diamond Deposition From CF 4-H2 Mixed Gas bv Microwave Plasma. Applied Physics Letters 61 (7), 772,1992. 178 41. See Reference 7. 42. See Reference 10. 43. See Reference 9. 44. See Reference 5. 45. W. Hsu, Gas-Phase Kinetics During Microwwave Plasma-Assisted Diamond Deposition: Is the Hydrocarbon Product Distribution Dictated bv Neutral-Neutral Interactions?. Journal of Applied Physics 72 (7), 3102, 1992. 46. W Hsu and D. Tung, Application of Molecular Beam Mass Spectroscopy to Chemical Vapor Deposition Studies. Review of Scientific Instruments. 63 (9) 4138, 1992. 47. M. D'Evelyn, C. Chu, R. Hange, and J. Margrave, Mechanism of Diamond Growth bv Chemical Vapor Deposition: Carbon-13 Studies. Journal of Applied Physics 71 (3), 1528,1992. 48. C. Johnson, W. Weimer, and F. Cerio, Efficiency of Methane and Acetylene in Forming Diamond bv Microwave Plasma Assisted Chemical Vapor Deposition. Journal for Materials Research 7 ( 6), 1427,1992. 49. K. McNamara and K. Gleason, Selectively 13C-Enriched Diamond Films Studied bv Nuclear Magnetic Resonance. Journal of Applied Physics 71 (6), 2884, 1992. 50. Y. Muranaka, H. Yamashita, and H. Miyadera, Characterization of Diamond Films Synthesizd in the Microwave Plasmas of CO/Hg and CO/Og/Hg Systems at Low Temperatures (403-1023 K). Journal of Applied Physics 69 (12), 8145,1991. 51. P. Joeris, C. Benndorf, and S. Bohr, Diamond Deposition in an Arcon- Methane-Oxveen Plasma. Journal of Applied Physics 71 (9), 4638,1992. 52. R. Rudder, G. Hudson, J. Posthill, R. Thomas, R. Hendry, D. Malta, T. Humphreys, and R. Nemanich, Chemical Vapor Deposition of Diamond Films From Water Vapor RF-Plasma Discharges. Applied physics Letters 60 (3), 329, 1992. 179 53. 0. Matsumoto and T. Katagiri, Effect of Dilution Gases in Methane on the Deposition of Diamond-I.ike Carbon in a Microwave Discharge II: Effect of Hydrogen. Thin Solid Films 146, 283,1987. 54. O. Matsumoto, H. Toshima, and Y. Kanzaki, Effect of Dilution Gases in Methane on the Deposition of Diamond-Like Carbon in a Microwave Discharge. Thin Solid Films 128, 341,1986. 55. W. Zhu, A. Inspektor, A. Badzian, T. McKenna, and R. Messier, Effects of Noble Gases on Diamond Deposition From Methane-Hvdrogen Microwave Plasmas. Journal of Applied Physics 68 (4), 1489,1990. 56. Y. Hirose and Y. Terasawa, Japanese Journal of Applied Physics, 25, L519,1986. 57. J. Mucha, D. Flamm, and D. Ibbotson, On the Role of Oxygen and Hydrogen in Diamond-Forming Discharges. Journal of Applied Physics 65 (9), 3448, 1989. 58. S. Harris and A. Weiner, Effects of Oxygen on Diamond Growth. Applied Physics Letters 55 (21), 2179,1989. 59. Y. Liou, R. Weimer, D. Knight, and R. Messier, Effect of Oxygen in Diamond Deposition at Low Substrate Temperatures. Applied Physics Letters 56 (5), 437,1990. 60. Y. Liou, A. Inspektor, R. Weimer, D. Knight, R. Messier, The Effect of Oxygen in Diamond Deposition bv Microwave Plasma Enhanced rhemical Vanor Deposition. Journal for Materials Research 5 (11), 2305,1990. 61. K. Takeuchi and T. Yoshida, The Effect of Oxygen on Diamond Synthesis in a Microwave Plasma let. Journal of Applied Physics 71 ( 6), 2636, 1992. 62. J. Chang and T. Mantei, Effects of Oxygen and Pressure on Diamond Synthesis in a Magnetoactive Microwave Discharge. Journal of Applied Physics 71 ( 6), 2918,1992. 63. See Reference 8 . 64. U. Meier, K. Kohse-Hoinghaus, L. Schafer, and C.-P. Klages, Two- Photon Excited UF Determination of H-Atom Concentrations Near a 180 Filament in a Low Pressure Ht Fnvironmpnt. Applied Optics 29 (33), 4993,1990. 65. L. Schafer, C.-P. Klages, U. Meier, and K. Kohse-Hoinghaus, Atomic Hydrogen Concentration Profiles at Filaments Used for C h e m i c a l Vapor Deposition of Diamond. Applied Physics Letters 58 ( 6), 571,1991. 66. See Reference 13. 67. G. Herzberg, Molecular Spectra and Molecular Structure. Vol. 1 Snectra of Diatomic Molecules. (Van Nostrand, New York, 1950). 68 . B.Smith, J. Womack, N. Omenetto, and J. Winefordner, Applied Spectroscopy 43, 873,1989. 69. P.Das, G. Ondrey, N. van Veen, and R. Bersohn, Two Photon Laser Induced Fluorescence of Carbon Atoms. Journal of Chemical Physics 79 (2), 724,1983. 70. G. Selwyn, L. Baston, and H. Sawin, Applied Physics Letters 51, 898, 1987. See also K. Ono, T. Oomori, M. Tuda, and K. Namba, Measurements of the Cl Atom Concentrations in Radio-Freauencv and Microwave Plasmas bv Two-Photon Laser-Induced Fluorescence: Relation to the F.tching of Si. Journal of Vacuum Science and Technology A 10 (4) Part 1, 1071,1992. 71. M. Heaven, T. Miller, R. Freeman, J. White, and J. Bokor, Two-Photon Absorption. Laser-Induced Fluorescence Detection of Cl Atoms. Chemical Physics Letters 8 6 , 458.1982. 72. S. Hansen, G. Luckman, G. Nieman, and S. Colson, Formation and Decay of Metastable Fluorine Atoms in Pulsed Fluorocarbon/Oxvgen Discharges Monitored bv Laser-Induced Fluorescence. Applied Physics Letters, 56, 719,1990 73. J. Bokor, R. Freeman, J. White, and R. Stortz, Two-Photon Excitation of the n=3 Level in H and D Atoms. Physical Review A 24, 612,1981. 74. W. Bischel, B. Perry, and D. Crosley, Two-Photon Laser-Induced Fluorescence in Oxygen and Nitrogen Atoms. Chemical Physics Letters 82, 85, 1981. 181 75. L. DiMauro, R. Gottscho, and T. Miller, Two-Photon Laser-Induced Fluorescence Monitoring of O Atoms in a Plasma Etching Environment. Journal of Applied Physics 56 2007,1984. 76. M. Alden, A. Edner, P. Grafstrom, and S. Svanberg, Two-Photon Excitation of Atomic Oxygen in a Flame. Optics Communications 42, 244, 1982. 77. R. Walkup, K. Saenger, G. Selwyn, Plasma Synthesis and Etching of Electronic Materials. Proceedings of the Materials Research Society 38, 69, 1985. 78. G. Selwyn, Spatially Resolved Detection of O Atoms in Etching Plasmas bv Two-Photon Laser-Induced Fluorescence. Journal of Applied Physics 60 ( 8 ), 2771,1986. 79. P. Brewer, N. Van Neen, and R. Bersohn, Two-Photon Induced Fluorescence and Resonance-Enhanced Ionization of Sulfur Atoms. Chemical Physics Letters 91 (2), 126,1982. 80. B. Preppernau, D. Dolson, R. Gottscho, and T. Miller, Temporally Resolved Laser Diagnostic Measurements of Atomic Hydrogen Concentrations in RF Plasma Discharges. Plasma Processing and Plasma Chemistry 9 (2), 157,1989. 81. D. Lecrosnier, L. Henry, A. LeCorre, and C. Vaudray, Electronics Letters 23,1254,1987. 82. R. Walkup, K. Saenger, G. Selwyn, Studies of A tom ic Oxygen in O2+CF4 RF Discharges bv Two-Photon Laser-Induced Fluoresence and O p tical Emission Spectroscopy. Journal of Chemical Physics 8 4 (5), 2668, 1986. 83. T. Miller, Optical Emission and Laser-Induced Fluorescence Diagnostics in Reactive Plasmas. Journal of Vacuum Science and Technology A 4, 1768, 1986. 84. Reactive Gas Phase Intermediates: Generation and Monitoring. Ed. D. Setser, (Academic Press, New York, 1979). 85. A. Mitchell and M. Zemansky, Resonance Radiation and Excited Atoms. (Cambridge University Press, New York, 1961). 182 86 . A. Catherinot, B. Dubreuil, and M. Gand, Quenching nf Atomic States in a Low-Pressure Hydrogen Glow Discharge. Physical Review A 18 (3), 1097,1978. 87. J. Bittner, K. Kohse-Hoinghaus, U. Meier, and Th. Just, Quenching nf Two-Photon-Excited H(3s. 3d) and Q(3n 3P2 i p) Atoms Bv Rare Gases and Small Molecules. Chemical Physics Letters 1^3 ( 6), 571,1988. 88 . M. Alden, U. Westblom, and J. Goldsmith, Two-Photon-Excited Stimulated Emission from Atomic Oxygen in Flames and Cold Gases. Optics Letters 14 ( 6), 305,1989. 89. J. Goldsmith, Two-Photon-Excited Stimulated Emission from Atomic Hvdroeen in Flames. Journal of the Optical Society of America B 6 (11), 1979,1989. 89. D. Baldwin, M. Buntine, and D. Chandler, Photodissociation of Acetylene: Determination of DQn(HCC-H) bv Photofragment Imaging. Journal of Chemical Physics 93 (9), 6578,1990. 91. See Reference 85. 92. E. Condon and G. Shortley, The Theory nf Atomic Spectra. (Cambridge University Press, New York, 1979). 93. J. Dunlop, A. Tserepi, B. Preppernau, T. Cerny, and T. Miller, H-Atom Plasma Diagnostics: A Sensitive Probe of Temperature and Puritv. Plasma Chemistry and Plasma Processing 11 (4), ,1991 94. J. Tung, A. Tang, G. Salamo, and F. Chan, Two-Photon Absorption of Atomic Hydrogen From Two Light Beams. Journal of the Optical Society of America B 3 (6), 837,1986. 95. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes: The Art of Scientific Computing. (Cambridge University Press, New York 1986). 96. See Reference 92. 97. See Reference 87. 183 98. A. Tserepi, J. Dunlop, B. Preppernau, and T. Miller, The Effects of Surfaces on H-Atom Concentration in Pulsed and Continuous Discharges. Journal of Vacuum Science and Technology, A 10 (4), 1188,1992. See also A. Tserepi, J. Dunlop, B. Preppernau, and T. Miller, Absolute H-Atom Concentration Profiles in Continuous and Pulsed RF Discharges. Journal of Applied Physics 72 (7), 2638,1992. 99. P. Petrovic, B. Jelenkovic, and A. Phelps, Excitation Bv and Surface Reflection of Fast Hydrogen Atoms in Low-Pressure Hydrogen Discharges. Physical Review Letters 68 (3), 325,1992. 100. See Reference 20. 101. A. Von Engel, Electric Plasmas: Their Nature and Uses. (Taylor and Francis Limited, New York, 1983). 102. B. Chapman, Glow Discharge Processes: Sputtering and Plasma Etching. (John Wiley & Sons, New York, 1980). 103. See Reference 88.