MSU LIBRARIES RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped beIow. 1{ 'm‘“’ __.- ‘_ ' DEVELOPMENT OF A MICROWAVE ION AND PLASMA SOURCE IMMERSED IN A MULTICUSP ELECTRON CYCLOTRON RESONANT MAGNETIC FIELD BY Mahmoud Dahimene A DISSERTATION Submitted to Michigan State University in partial fulfiIIment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of EIectricaI Engineering and System Science 1987 ABSTRACT DEVELOPMENT OF A MICROWAVE ION AND PLASMA SOURCE IMMERSED IN A MULTICUSP ELECTRON CYCLOTRON RESONANT MAGNETIC FIELD BY Mahmoud Dahimene This dissertation presents the experimental development and test of an electrodeless microwave (2.45 GHz) generated plasma and ion source in a discharge pressure range of 6x10-4 - 5x10.1 Torr and relatively low power (80 — 350 w CW). Also presented is a semi-empirical model applicable to low pressure microwave discharges with no static magnetic field. Initial experiments studied the properties of variable diffusion length (0.43 - 1.22 cm) disk shaped discharges generated and maintained in a cylindrical microwave resonant cavity applicator for argon and oxygen gases without static magnetic field. These discharges were characterized by measuring plasma densities and electron temperatures using a Langmuir double probe for different experimental conditions. The measured plasma densities and electron temperatures ranged from 8x101o to 5x1011 cm.3 and 2x104 to 8x104 0 K respectively. The ion temperature was less than 500 oK. Ion beams were extracted from these discharges using single and double grids. Argon ion beam currents densities were measured to be 3.0 mA/cm2 for the single grid and 5.8 mA/cm2 for the double grids with a maximum extraction voltage of 1.7 KV. This applicator was then retrofitted with magnets to study the effect of a multicusp static magnetic field. Using this concept, a new cylindrical microwave applicator was designed and tested. In this new applicator, seventeen pairs of samarium-cobalt magnets generated a multicusp static magnetic field surrounding the discharge chamber and produced an electron cyclotron resonant (ECR) surface (875 6) inside the discharge region. Experimental tests of this (ECR) applicator showed substantial improvements of the discharge and ion beam stability at 4 Torr. An argon ion beam current discharge pressures as low as 6x10- density of 6 mA/cm2 was obtained using the double grids at a discharge pressure of 1x10.3 Torr corresponding to an ion mass utilization of 34%. The model developed in this dissertation is based on the fluid equations and ambipolar diffusion theory. Despite its simplicity, it was found that the model is in good agreement with the experimental measurements. It is expected that the results of this investigation can be used to develop more efficient microwave ion and plasma sources. ACKNOWLEDGEMENTS The author is thankful for the guidance received from Dr. Jes Asmussen throughout this investigation. Additional thanks are given to Mr. Leonard Mahoney for his valuable contribution in the experimental research, to Mr. Ben Boyle for his help in the magnetic field mapping and to Mr. Jeff Hopwood for writing the Langmuir data processing computer program. Special thanks to Dr. Stanley Whitehair for his friendship, encouragement and help in completing this dissertation. This research was supported in part by grants from the National Science Foundation and Optics Electronics. iv TABLE OF CONTENTS LIST OF FIGURES ........................................ viii LIST OF TABLES................................ ..... ....xi CHAPTER I INTRODUCTION 1.1 INIRggggIIgg .................... . . ........ 1 1.2 ggsggggg. . ....... . ...................... 3 1.3 Ifl§§;§_9§g§glgy§§ ........ . ............... 4 1.4 THESIS OUTLINE .............................. 4 CHAPTER II REVIEW OF PLASMA AND ION SOURCES 2.1 INIRQQQQIIQN .............................. 6 2.2 gg_gLA§MA_ANQ_IQN_§ggggg§ ................... 7 2.2.1 AXIAL FIELD........ ................ 8 2.2.2 MULTIPOLE FIELD............. ...... .11 2. 2. 3 RADIAL FIELD ............ . .......... 13 2.3 BE_QI§QHAB§§§ .............................. 15 2.3.1 CAPACITIVELY COUPLED DISCHARGES. ..16 2.3.1. DESCRIPTION. ...........16 2.3.1.2 SELF BIAS ..... .. ... ..... 18 2.3.1.3 PLASMA PARAMETERS ........ 19 2.3.1.4 RF PLASMA RESONANCE ...... 21 2.3.1.5 EFFICIENCY.... ........... 22 2.3.2 INDUCTIVELY COUPLED DISCHARGES.....23 2.4 MIQBQWAVE_QI§QHAR§§§............. ..... ......26 2.4.1 THE PROPAGATION wAVE APPLICATORS...26 2. 4. 2 RESONANT APPLICATORS ............... 29 2. 4. 3 ECR SOURCES ....................... 30 2 5 IQL§QQBQLEEBEQBEAU§§_§QQ£\IIQN§ ------------ 31 2 6 REVIEw 0F RF AND MICRowAVE ION SOURCES ...... 33 —-——_-—_----------——--_------—---~-—_— CHAPTER III DEVELOPMENT OF A SIMPLE MODEL 3.1INTRODUCTIONOOI.00.00....0.0.00.00000000000036 3.2 DERIVATION OF THE FLUID EQUATIONS... ........ 37 3.2.1 THE PARTICLES CONSERVATION EQUATIONOOOOOIOOOCOCOOC0......0.00.39 3.2.2 THE MOMENTUM TRANSFER EQUATION.....43 3.2.3 THE ENERGY CONSERVATION EQUATION...46 3.2.4 MAXWELL'S EQUATIONS................47 3 3 §IUELIEXIN§_A§§QUEIIQN§- ...... ..... ... ...... 47 3.3 1 ASSUMPTIONS ........................ 48 3.3.2 PRACTICAL SIMPLIFICATION OF THE BASIC EQUATIONS....................53 3.4 R§_PLA§§A_ggg§L.................... ......... 56 3 - 5 Ifl§_Afl§lEQEAB_QIEEQ§IQU_!QQ§L-EQB_A QXLINQRIQAL_§§9M§131 ........ ..... ......... 59 3 6 POSSIBLE IMPROVEMENT OF THIS MODEL ..... 71 CHAPTER IV EXPERIMENTAL SYSTEMS 4.1 INIRgggQIIQN. . ............. ....... ..... 75 4-2 Q§§QBIEIIQN-QE-IU§-MIQBQ!A¥§_IQN-§QUB§§§ 76 4.2.1 MICROWAVE PLASMA DISK ION SOURCE, APPLICATION I. . ..... ...... ....76 4.2.1.1 THE CAVITY APPLICATOR DESCRIPTION .............. 76 4.2.1.2 APPLICATOR OPERATION ..... 79 4.2.2 APPLICATOR I RETROFITTED WITH A MULTICUSP MAGNETIC FIELD.........85 4.2.3 MULTICUSP-MICROWAVE ION SOURCE ..... 91 4-3 OENEBAL_EIEEEIDENIAL_§1§IED........-...-.-..98 4.3.1 VACUUM AND GAS FLOW SYSTEMS ........ 98 4.3.2 MICROWAVE SYSTEM ................... 101 4.3.3 ELECTRON DENSITY AND TEMPERATURE MEASUREMENTS ..... .............. .103 4.3.4 EXTRACTION GRIDS............ .. .113 4.3.5 VOLTAGE EXTRACTION SYSTEM... ....... 120 4.3.6 FARADAY CUP ..... ...... ............. 126 vi CHAPTER V EXPERIMENTAL MEASUREMENTS 5.1 INTRODUCTION .............................. 130 5.2.1 EXPERIMENTAL DISCHARGE CONDITIONS..131 5.2.2 EXPERIMENTAL RESULTS OF ELECTRON DENSITY AND ELECTRON TEMPERATURE MEASUREMENTS..... ....... .....a.....132 5.2.3 ION BEAM EXTRACTION..... ........... 149 5.2.3.1 SINGLE GRID.... .......... 149 5.2.3.2 DOUBLE GRIDS.... ........ .154 5.2.3.3 OXYGEN ION BEAM EXTRACTION...... ....... ..158 5.3 APELIQAIQR_I_3§IRQEIIIED........... ......... 161 5.4 ECR APPLICATOR..................... ...... ...165 5.4.1 PRELIMINARY CALIBRATIONS...........165 5.4.2 ELECTRON DENSITY AND TEMPERATURE MEASUREMENTS ....... . ...... ........ 168 5.4.3 ION EXTRACTION....... .............. 168 CHAPTER VI COMPARISON OF THE EXPERIMENTAL RESULTS WITH THE THEORETICAL DISCHARGE MODEL 6.1 INIRQQUQIIQN. .......................... .177 6.2 M§A§g3§g_ggAN1;1Ig§. .... ...... .... . .177 6-3 IAIIIIAIIQI-9§-IIE_QI§EBIBIE_IIEIIBI9-IIII9 179 6.4 IQN_M9§ILIIX ................................ 188 6.5 ELEQIRQN_1§MPERAIUR§ ... .. ..... .......... 189 6.6 ION CURRENT AVAILABLE FOR BEAM EXTRACTION 192 CHAPTER VII SUMMARY AND CONCLUSIONS 7.1 INIRQQQQIIQN.................... ............ 196 7-2 IQDEABI§QI_§IIIEEI_IBE_IBBE§_AEEIIEAIQB§ I§§I§Q_IN_IUI§_IU§§I§ ....................... 197 7.3 QQUEABI§QN_QE_Ifl§-IflB§§_ABELIEAIQB§-ANQ QIBEB-BE_AID_IIIBQUIIE-IQI-§9939§§ .......... 200 7.4 ggNgLQSIgys. ..... . ..... . . ............. 202 7.5 FURTHER RESEARCH ............................ 203 APPENDIX A STATIC MAGNETIC FIELD MAPPING INTRODUCTION .................................... 205 -----~-—----~—-——----—-—— REFERENCES .............. . .............................. 209 vii LIST OF FIGURES Figure 2.1 DC Ion Source with Axial Magnetic Field ...... 9 Figure 2.2 DC Ion Source with Multipole Magnetic Field..12 Figure 2.3 DC Ion Source with Radial Magnetic Field ..... 14 Figure 2.4 Capacitively Coupled RF Plasma Source ........ 17 Figure 2.5 Inductively Coupled RF Plasma Source ......... 24 Figure 2.6 Surface Wave Microwave Applicator ............ 28 Figure 3.1 Discharge Geometry... ........................ 60 Figure 3.2 Superposition of the Electron Distribution and the Ionization Frequency ................. 65 Figure 3.3 Linear Approximation of the Ionization Cross Section ........ ... ..................... 55 Figure 4.1 Cross Section of Applicator I..... ........... 77 Figure 4.2 Cross Section of Cavity Mode ................. 82 Figure 4.3 Three Dimensional View of the Electromagnetic Cavity Resonant Fields for the TE21 Mode....83 Figure 4.4 Cross Section of Applicator I Retroiitted with Rare Earth Magnets... .............. ‘ ..... 88 Figure 4.5 Magnetic Field Lines in Applicator I Retrofitted. ................................. 90 Figure 4.6 Cross Section of ECR Applicator .............. 92 Figure 4.7 Photograph of Assembled ECR Applicator ....... 93 Figure 4.8 Photograph of the ECR Applicator Disassembled ......... . ....................... 94 Figure 4.9 Radial Magnetic Field Lines in the ECR Applicator ................................... 96 Figure 4.10 Cross Sectional View Showing the Static Magnetic Field Lines in the ECR Applicator...97 Figure 4.11 Gas Flow and Vacuum Systems .................. 100 Figure 4.12 Microwave System ............................. 102 Figure 4.13 Langmuir Double Probe System ................. 104 Figure 4.14 Langmuir Probe and Electrical Circuit ........ 106 Figure 4.15 Typical Langmuir Probe Current-Voltage Characteristics..... ............. . ........... 109 Figure 4.16 Single Grid....... ........ . .................. 114 Figure 4.17 Double Grid Assembly ......................... 116 Figure 4.18 Plasma and Ion Sheath Near the Grids Apertures ............ . ....................... 117 viii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 5.19 Double Grids Dimensions and Potential ....... Electrical Circuit for Ion Beam Extraction......... Electron and Ion Currents Involved in Ion Beam Extraction ...................... Cross Sectional View Showing the Double Grid Assembly and the Shielding Metal screen.........OOOOOOOOOOIOO0.0.0....O0.00.0 Faraday Cup... Electron Density Versus Discharge Pressure.. Electron Temperature Versus Discharge Pressure for two Disk Sizes......... ........ Electron Density Versus Input Power for Three Disk Sizes.... Electron Temperature Versus Input Power for Three Disk Sizes........ Electron Density Versus Input Power Density for Three Disk Sizes. ............... Electron Temperature Versus Input Power Density for Three Disk Sizes ..... . .. ....... (a) Cross Sectional View of the Two Double Probes Positions .......... . . ....... (b) Top View Showing the Orientation of Both Probes Relative to the Coupling Antenna. . .......... Electron density Versus Discharge Pressure Electron Pressure Electron Pressure Electron Pressure Ion Beam Temperature Versus Discharge Density Versus Discharge Temperature Versus Discharge Current Versus Extraction Voltage for Different Powers ................ Ion Beam Current Versus Extraction Voltage With the 4.0 cm Disk ................ Versus Extraction Cavity Is Not Perfectly Ion Beam Current Voltage When the Tuned ....................................... Ion Beam Current Versus Extraction Voltage for Different Acceleration Voltages. Ion Beam Current Versus Extraction Voltage for Low Gas Flow Rates .............. Ion Beam Current Versus Extraction Voltage for Oxygen Gas ...................... Ion Beam Current Versus Extraction Voltage for Oxygen at Low Flow Rates ........ Ion Beam Current Versus Extraction Voltage for Oxygen with the 4.0 cm Disk ..... ix in Two Probes Locations. ........... for Two Probes Locations ........... for Oxygen Gas .......... . .......... for Oxygen Gas ..................... .118 .121 .123 .125 127 .135 136 137 138 140 141 142 .142 144 145 147 148 150 152 153 .156 .157 .159 .160 .162 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure FigUre Figure Figure 0303 500 030} 0501 Ion Extraction With Applicator I Retrofitted With Only 8 Magnets Surrounding the Discharge................................164 Ion Extraction With Applicator I Retrofitted With 17 Magnets.......... ....................166 Electron Density Versus Discharge Pressure For the ECR Applicator.............. ......... 169 Electron Temperature Versus Discharge Pressure For the ECR Applicator. ............. 170 Ion Extraction With the ECR Applicator Without Magnets....................... ....... 171 Ion Extraction With the ECR Applicator With All Magnets...................... ....... 174 Ion Beam Current Versus Gas Flow ............ .175 Ion Beam Current Versus Power................176 Calculated Electron-Neutral Effective Collision Frequency Versus Discharge Pressure ......... .... ..... .. .. .. ... ....... 182 Calculated Average Electric Field Versus Discharge Pressure Diffusion Length Product ..................................... 185 Calculated E/p A Versus p A .................. 186 Calculated Average Effective Electric Field........................................187 Calculated Ion Mobility. ...... ...... ...... ...190 Comparison Between Experimental Measurements and Theoretical Calculations of the Electron Temperature. ... .. ...............191 Comparison Between Experimental Measurements and Theoretical Calculations of Extracted Ion Beam Currents ............................ 194 Table Table Table Table LIST OF TABLES Comparison of Some RF and Microwave Ion Sources.......................... ....... 34 Applicator I Tuning Parameters. ............. 81 ECR Applicator Tuning Parameters. ........... 167 Comparison of the Three Ion Sources Tested in this Thesis........ ............... 198 xi CHAPTER I INTRODUCTION 1.1 INTRODUCTION This dissertation describes the experimental development and test of a low pressure microwave plasma source. The research, which was primarily experimental, developed special microwave applicators for the production of low pressure (<0.1 Torr) microwave discharges. Recent parallel research efforts have demonstrated or are investigating the potential of these low pressure microwave discharges in a number of applications. Some of these are 1.2.3.4 microwave ion sources for spacecraft propulsion and materials processing, low pressure, low temperature plasma 6 and assisted oxide growths, microwave plasma etching microwave plasma thin film deposition. Each of these applications makes use of a low pressure cylindrical microwave discharge which is operated either without or with an applied static magnetic field. Fundamental to the development of these applications is the experimental development of efficient low pressure microwave plasma applicators and the development of a theoretical knowledge of the low pressure microwave l discharges. This thesis concerns itself with these issues by first experimentally studying the microwave discharge behavior of three applicator configurations. Knowledge and understanding of the microwave discharge is obtained by measuring the electron density and electron temperature with double Langmuir probes over a wide range of experimental conditions. Ion beam extraction is also experimentally studied using two different grid sets. Finally a simple, approximate, theoretical, ambipolar diffusion model of the discharge is also developed to aid in the understanding of the experimental discharge behavior. Initial experiments studied the properties of a discharge generated in a cylindrical microwave resonant cavity without static magnetic field. The same microwave applicator is then retrofitted with small rare earth magnets to determine experimentally the effect of a multicusp magnetic field on the microwave generated discharge. Further experiments deal with the development and testing of a new cylindrical microwave applicator designed to operate either with or without a multicusp magnetic field. In this new applicator, rare earth magnets are located outside the cylindrical excitation volume occupied by the resonant electromagnetic fields. The location of these rare earth magnets produces a multicusp, electron cyclotron resonant (ECR) static magnetic field within the discharge zone which reduces the charged particle diffusion to the walls, and 3 facilitates operation at low discharge pressures by creating ECR zones. The theoretical model, which is based on the fluid equations for electron, ion and neutral gases makes a number of simplifying assumptions. These assumptions make an otherwise complicated problem solvable. It is not expected that this model will describe the experimental behavior in exact detail. However, under the simplifying assumptions, the model predicts the values of some discharge parameters _such as electron temperature, average effective electric field in the discharge and ion current available for extraction when the controllable parameters such as the gas type, the gas flow, the environmental pressure and the input microwave power are known. This thesis summarizes the experimental research and development that lead to a successful demonstration of a low pressure microwave ion source. Some of this work has 4.7 already been published in scientific publications and has been presented at international scientific conferencesa'9'1o. 1.2 RESEARCH The research described in this thesis was carried out by the author over a period of four years from 1983 to 1987 in Michigan State University under the direction of 4 Dr. Jes Asmussen. The work described in this thesis builds 3 on previous research carried out by J. Root , . 11 12 13 Dr. Freder1cks , Dr. Mallavarpu , Dr. Rogers and 14 Dr. Whitehair . 1.3 THESIS OBJECTIVES The objectives of this thesis are divided into three parts. The first was to develop and test a microwave plasma applicator which was able to generate a stable discharge and was able to allow ion beam extraction at very low pressures and gas flow rates. The second objective was to experimentally characterize a low pressure microwave plasma and ion source by measuring electron density and electron temperature over a wide range of discharge conditions. The third objective was to generate a simple theory that would predict the macroscopic properties of a disk shaped microwave plasma. These properties include the ion current available for extraction from the discharge. 1.4 THESIS OUTLINE This dissertation is organized as follows. Chapter II presents a background and review of the basic concepts of different plasma and ion sources. A brief review of the 4 Dr. Jes Asmussen. The work described in this thesis builds on previous research carried out by J. Roota, Dr. Fredericks“, Dr. Mallavarpu12. Dr. Rogers‘3 and 14 Dr. Whitehair . 1.3 THESIS OBJECTIVES The objectives of this thesis are divided into three parts. The first was to develop and test a microwave plasma applicator which was able to generate a stable discharge and was able to allow ion beam extraction at very low pressures and gas flow rates. The second objective was to experimentally characterize a low pressure microwave plasma and ion source by measuring electron density and electron temperature over a wide range of discharge conditions. The third objective was to generate a simple theory that would predict the macroscopic properties of a disk shaped microwave plasma. These properties include the ion current available for extraction from the discharge. 1.4 THESIS OUTLINE This dissertation is organized as follows. Chapter II presents a background and review of the basic concepts of different plasma and ion sources. A brief review of the 5 performance of some operating RF and microwave ion sources is presented. Chapter III presents a simple model derived from the fluid equations applicable to a microwave plasma without static magnetic field. The fluid equations are separated into AC and DC parts. The AC part is used to calculate expressions for the plasma electric conductivity (or equivalent complex dielectric constant), the power absorbed by the discharge and the average effective electric field in the discharge. The DC part. along with the ambipolar diffusion assumption, provides expressions for the ion density distribution in the discharge, the electron temperature versus discharge pressure and discharge chamber dimensions, and finally the total ion current available for extraction. Chapter IV describes the basic experimental setup and methods used to conduct the experiments and measure data. Chapter V presents the measured plasma density and ion beam currents obtained with three different microwave applicators. Chapter VI correlates the measured data to the predictions of the model developed in Chapter III and Chapter VII presents a summary of the experimental results and recommendations for further research. CHAPTER II REVIEW OF PLASMA AND ION SOURCES 2.1 INTRODUCTION The basic concepts of many different plasma and ion sources are reviewed in this chapter. The primary emphasis of this review concerns low pressure ion sources and their associated discharge configurations. Section 2.2 contains a classification of DC plasma and ion sources according to their static magnetic field pattern. Section 2.3 reviews the concepts of two kinds of RF plasma sources. These sources are based on two different methods by which the RF electrical power is transferred to the discharge. These are the capacitively coupled discharges and the inductively coupled discharges. The first type of discharge is described in more detail since these discharges are more often operated at lower gas pressures. In Section 2.4 a brief overview of different microwave plasma applicators is presented. A more complete description of a resonant microwave applicator will be presented in the following chapters. Finally the last Section 2.6 reviews and compares the performances of some RF and microwave ion sources. This 7 comparison is based on figures of merit described in Section 2.5. 2.2 DC PLASMA AND ION SOURCES. The classification of some plasma and ion sources as DC is mainly due to the existence of other sources in which the discharge is activated with an electromagnetic field, such as RF or microwave. DC ion sources are presently used in a variety of research and production applications. The basic principle shared by all direct-current sources is fairly simple, it involves the ionization of a low pressure gas, or a mixture of gases. from electron bombardment. The electrons responsible for the impact ionization, usually called primary electrons, are emitted from a heated filament. This filament is biased negatively with respect to the discharge chamber walls. which have, usually a cylindrical geometry. The potential between the filament, or cathode and the walls is used to accelerate the primary electrons, until they reach the required ionizing energies. These ion sources are usually operated at low gas pressures, where the mean free path for electron impact ionization is larger than the chamber dimensions. To prevent the rapid escape of these electrons to the anode, a static magnetic field is applied to the discharge chamber. Since there are many possible ways to apply this magnetic field, DC ion sources can be classified according to their magnetic field configuration. An extensive review of electrostatic sources is found in Reference‘s. A few of the most important broad beam ion source configurations are discussed below. 2.2.1 AXIAL FIELD. The conventional axial field discharge chamber is probably the simplest one to describe. It was first 16 in 1961. A cross sectional View of designed by M. Kaufman this type of ion source is shown in Figure 2.1. The discharge chamber is almost always cylindrical. The cathode is located near the axis and the anode forms the cylindrical boundary to the discharge region. The magnetic field is oriented approximately parallel to the cylinder axis. The primary electrons emitted from the cathode have energies corresponding approximately to the discharge potential difference, which is also the potential between the cathode and the anode. The discharge is found to have two groups of electrons. The primary electron group with higher energy, and the thermally randomized group with a lower energy. The magnetic field in the discharge chamber is made strong enough to make the electrons follow a helical trajectory centered around the axis of the cylinder. The effect of this field is to lengthen the trajectory of the electrons, allowing them to collide with the neutral particles before Cos Feed '11 ' "1 Anode i i Cathode B Fleld \ \ 4 ~V L. Screen grld . cacatz EJCDI: carat: r, f IIJEDIIJCZHZJCZHIJCJEZJC31 J Acceleration grld Ion beam Figure 2.1 DC Ion Source with Axial Magnetic Field 10 reaching the anode. Usually the gas is fed from one end of the cylinder, and the ions are collected or extracted from the other end. Typically, the magnetic field strength at the downstream and is 60% to 80% of that at the upstream end. The cathode position is not critical, except that it should be near the axis and downstream of the magnetic field maximum. The theoretical minimum magnetic field for containment of primary electrons in an axial field chamber. corresponds to a value that would make the electron cyclotron radius smaller than the chamber radius by approximately a factor of two. For efficient operation, a magnetic field strength about 50% higher is desirable. Higher fields than that increase the minimum gas pressure or the discharge voltage. Because of their heavy mass, the ions move nearly equally in all directions. This tendency results in a discharge loss 15 per beam ion (in eV/ion) of roughly 50 Ap/Aex where Ap is the outside area of the primary electron region defined as the volume where the primary electrons do not suffer collisions. In many cases this region can be approximated by the whole discharge chamber volume. Aex is the projected open area of the ion extraction system. A similar equation can be given for the minimum gas pressure required within the discharge chamber for efficient Operation17. This density, in neutrals/m3, is roughly 17 1.4x10 A V P/ P 11 where Vp is the primary electron region volume. Both of these equations are for Argon gas, and have about a factor of 2 incertainty due to various designs. Axial field discharge chambers are widely used in applications requiring small beam diameters, up to 10 cm. In larger diameters. this design has beam uniformity problems. For a typical axial field chamber with a length equal to its diameter and a 58% open screen extraction grid, the discharge loss is about 300-800 eV/ion. The minimum operating pressure is in the 10"4 Torr range. 2.2.2 MULTIPOLE FIELD. The multipole magnetic field configuration is a more recent development in discharge chambers‘a. An example of such an ion source is shown in Figure 2.2. In this configuration, a series of alternating pole magnets are arranged throughout the surface of the discharge chamber. These alternating pole pieces shape the magnetic field in small cusps surrounding the outer surface of the discharge chamber. The anodes are located between the magnetic poles, with the magnetic field above the anodes sufficient to prevent the direct escape of primary electrons to the anodes. The bulk of the discharge chamber volume is nearly field free. allowing a uniform distribution of electrons and 12 as Feed Cl U DUDUDPD Field I: Cathode Anades DRNUDUDUZ Daflnfln Screen grid 1 c: CJCJI: EJEDE: EJCJ r i ’TJEDEZJEDEIHZJCZHZJCZIEJI l Acceleration grid Ion beam Figure 2.2 DC Ion Source with Multipole Magnetic Field 13 ions throughout this volume. The primary electron region approximates the volume inclosed by the pole pieces. The major advantages of the multipole discharges, when used as ion sources are the uniformity of the ion beam profile and the ease of scaling. The beam uniformity is a consequence of the uniformity of primary electron and ion production distributions within the discharge chamber. Typical average-to-peak current density ratios are 0.8-0.9 for a 15 cm diameter ion source. As an example, a 30 cm diameter ion source was built18 with a 10 cm depth. The discharge losses for this configuration was about 200-400 eV/ion for Argon. 2.2.3 RADIAL FIELD. For smaller ion sources, the complexity of multipole magnetic fields can be considerably reduced. As shown in Figure 2.3, the magnetic field is given a radial orientation by introducing a pole piece at the center of the chamber, closer to the upstream end. Other magnets are positioned around this center pole and near the discharge chamber cylindrical walls. All these magnets have the same orientation which is opposite to the center one. The magnetic field orientation resulting from this configuration is predominantly radial, with a highest field concentration near the upstream end of the discharge chamber. The 14 Gas Feed ...-.--- g. H. I \\ Anode ‘\\\\\\E‘—_—’/////// \\ Field \\ l \\/ Pole pieces Cathode Screen grid 1 cat: Cicatn can: cut: r_, L IICJEZJCDCIHIJEIJCJCZICj[_, J Acceleration grid Ion beam \ \ \. Figure 2.3 DC Ion Source with Radial Magnetic Field 15 downstream end has a low magnetic field. A circular anode is positioned symmetrically between the center magnet and the wall magnets. The cathode is a heated filament at the center of the discharge chamber. A radial field ion source was designed and fabricated1 using this approach. The discharge chamber diameter was 3.8 cm, while the beam diameter was reduced to 3 cm to improve beam uniformity. The overall ion source diameter, including insulating supports for the ion optics and grounded enclosure, was 6.4 cm. The performances of this source were not published. From all these examples, it is easy to see that a multitude of discharge chambers can be conceived. with some variations of basic principles. In the same class of electrostatic discharge chambers, one can include some other ion sourceszo, such as contact ion sources and duoplasmatrons. These types of sources find most of their applications in space propulsion. 2.3 RF DISCHARGES. RF (radio frequency) discharges can be divided in two main categories, the capacitively coupled and the inductively coupled discharges. The frequencies used in both types can range anywhere between 1 KHz to 1 GHz. 9 16 2.3.1 CAPACITIVELY COUPLED DISCHARGES. 2.3.1.1 DESCRIPTION. The capacitively coupled, or more generally referred to as parallel plates plasma sources, can be thought of as an extension of the positive column discharge in the sense that as for its DC counterpart, the plasma is generated between two electrodes. The basic concept of such sources is fairly simple. A cross section of a typical RF plasma source is shown in Figure 2.4. It consist essentially of a confining chamber in which two electrodes are positioned inside the chamber and externally connected to a high power, high frequency generator. An additional DC biasing circuit for these electrodes is usually used according to the specific applications. The principal usage of the RF parallel plate plasma sources is reactive etching and sputtering deposition. Both processes are harder to achieve in a DC glow discharge if the samples used are insulators. When an electrically insulating material is covering an electrode in a DC discharge, the surface of the sample exposed to the plasma will charge up to the floating potential. In such a_ condition the fluxes of electrons and positive ions to the surface become equal. These electrons and ions will recombine at the surface, slowing down any chemical l7 Discharge chamber Electrode F~\\\ ’/’ ...—... -~unqr ’- ~ FEM”. i’l ii DC voltage biase ("m h “""'I RF power source Figure 2.4 Capacitively Coupled RF Plasma Source 18 reaction. When a glow discharge is initiated. the negatively biased target will begin to be bombarded by positive ions. The insulator will start to charge positively because it loses electrons as the ions are neutralized at the surface. The potential of the insulator. surface will then rise progressively to zero, and the discharge will be extinguished as soon as this voltage drops below the discharge sustaining value. One way to deal with this problem is to use an AC discharge so that the positive charge accumulated during one half cycle will be neutralized during the next half cycle, thus allowing the positive ions to reach the surface almost continuously. 2.3.1.2 SELF BIAS An important aspect of RF discharges is the self bias of the electrodes. The higher mobility of the electrons allows them to respond to the applied electric field much faster than the positive ions. As a result, a higher concentration of electrons around the electrodes is present at any given time. If the sinusoidal frequency is high enough, the imbalance between electron and ion concentrations will average to a constant negative voltage relative to the plasma. The applied voltage waveform will then be displaced by a negative value, with a mean known as 19 the DC offset voltage. If a sample is used around the electrodes, it acquires a net self bias voltage favorable for increasing the rate of ion bombardment of the target. From these properties, it is clear that the lower limit of the applied frequency is set by the condition that a quasi- continuous discharge is to be achieved for processing time optimization. 2.3.1.3 PLASMA PARAMETERS. The interest in RF discharges goes as far back as 1929 when they were discovered. Many investigations exploring the basic phenomena involved in these discharges have been initiated since then. The most significant progress was made in the 1960's. Harrison21 published the first paper where a number of plasma parameters were measured and correlated. In this experiment Argon gas was used in an RF discharge. The results which were summarized by Taillet22 are listed below: (a) In the absence of a magnetic field the wall potential is measured to be highly negative with respect to the plasma. Typical values of this voltage vary from 80 V to 120 V when the electronic temperature is approximately 130,000 °K. (b) The ionization ratio is very low. the maximum value is about 10". The plasma density is approximately 2x108 cm'3. 20 (c) A plasmoid, which is a concentrated discharge floating in the center between the electrodes, appears in the free- fall diffusion regime, or when the mean free path of an ion between elastic collisions with neutral particles is larger than the dimensions of the vessel. (d) Plasmoids occur only when air is present in the discharge even in very minute quantities, suggesting that oxygen is responsible for this phenomena. Additional observations from a similar geometry were made by Geller23. (a) The electron density decreases with decreasing pressures, after a certain pressure limit it stays constant, it then drops abruptly near zero when the pressure is further decreased. (b) The three domains of density (described above) correspond to different discharge regimes, diffusion glow, plasmoid and multipacting respectively. (c) The plasma density is relatively independent of small power changes in the plasmoid regime. (d) No breakdown is obtained in the plasmoid pressure region with a moderate voltage. Plasmoids are generated by decreasing the pressure once a diffusion discharge has been ignited. 21 2.3.1.4 RF PLASMA RESONANCE. Hatch24 went further in distinguishing various cases of diffusion regimes and plasmoids. He also discovered that the RF electric field inside a plasmoid has a 1800 phase shift with respect to the applied field. For the diffusion regime no phase reversal was detected. This result was a confirmation of the resonant nature of plasmoids. When the applied frequency is large compared to the electron neutral collision frequency, most of the RF energy applied to a plasma is stored as a kinetic energy of electron motion. In the regions outside the plasma, the energy is stored in the form of electric energy as a result of the quasi-static field at the electrode surface. Under such conditions the electron oscillations make the plasma behave as an inductance in the RF circuit. The quasi-static electric field at the electrodes surface makes those regions behave as a capacitance. Resonant conditions are obtained when the inductance equivalent of the plasma is matched to the capacity equivalent to the surrounding medium. Vandenplas25 presented a comprehensive review of these resonant properties. It is important to note that the RF generator has its own impedance which may vary with power. In order to maintain a resonant discharge when one or more parameters are changing, it is necessary to add an 22 additional variable impedance to the RF circuit to keep the system in resonance. 2.3.1.5 EFFICIENCY. RF discharges also have the property of being more efficient than their DC counterpart26 in promoting ionization and sustaining the discharge. As the frequency increases, the minimum operating pressure is observed to fall, reaching a value of less than 1 mtorr at 13 MHz. This seems to indicate that there might be an additional mechanism generating more electrons, not present in DC discharges. This enhanced ionization can be explained as follows. In an AC discharge the electrons cannot move freely in phase with the oscillating electric field due to the elastic collisions with the neutral particle527. If an electron makes an elastic collision at an appropriate time with respect to the phase of the electric field, its velocity could continue to increase until the next collision. The ideal case would be where an electron makes an elastic collision with a neutral particle, reversing its direction at the precise moment when the field changes direction. From this point of view. electrons could progressively build up their energies from a relatively weak electric field, until they reach ionizing energies. This 23 mechanism seems to be also accepted as the dominant ionization source in microwave discharges. 2.3.2 INDUCTIVELY COUPLED DISCHARGES. These types of discharges are predominantly high pressure discharges. They are also called induction arcs, electrodeless arcs or thermal induction plasmas. They are sustained by induction from a time varying electromagnetic field. In a descriptive manner, they may be considered as a high frequency transformer whose primary consists of a cylindrical multiturn coilza. The electrically conducting plasma inside the coil forms a secondary, which shorts out the transformer. The basic configuration of this type of discharge is shown in Figure 2.5. It consists of a multiturn coil. Typically, the diameter of the coil varies anywhere between 5 cm to 30 cm. The plasma is separated from the coil by a tube made of quartz. ceramic or a longitudinally slotted metal that permits penetration of the magnetic field. The working gas, or gas mixture, is fed from one end of the cylindrical structure. The gas pressure is controlled by the combination of the rate of the gas flow and an exhaust system located at the other end of the cylinder. The basic phenomena governing the operation of inductively coupled plasmas are similar to that of the induction heating 000000 24 r— Gas Feed l Metal plate Plasma \ \\/ F CTIOH 0—K] CID—'1 ”-0. v-C OOOOOO rtz SI‘lO Qua pla conFinement tube Figure 2.5 Inductively Coupled RF Plasma Source 25 of metals which have numerous industrial applications. The difference lies in the fact that a plasma has a substantially lower electrical conductivity. This has a direct influence on the optimal frequency. size and power combination necessary to maintain a stable discharge. In the conventional induction heating theory, the application of an oscillating magnetic field results in the generation of eddy currents in the external cylindrical shell of the load. The thickness of this shell is known as the skin depth 6=(-—-1--]% Truof where f is the applied frequency, a is the load electrical conductivity and u is the magnetic permeability which for the case of a plasma is very close to the free space permeability. For examplezg, for an induction plasma operating with argon at atmospheric pressure with an average 0K, a = 103 mhos/m. The skin depth temperature of 8,000 corresponding to this conductivity is about 8 mm for a frequency of 4 MHz. A reduction of the applied frequency would result in an increase of the skin depth. The sustaining power of an induction discharge is also dependent on the frequency. For an argon discharge at atmospheric pressure and a frequency of 960 Hz, the minimum sustaining power is close to 1 MW. The corresponding figure for 60 Hz is more than 10 MW. 26 2.4 MICROWAVE DISCHARGES. The mechanisms involved in initiating and sustaining a microwave discharge are similar to those of an RF discharge. The difference existing between the two types of discharges lies primarily in the method used to couple the electrical power to the discharge in question. Unlike RF discharges, microwave discharges are not operated with electrodes. For the case of low pressure microwave discharges there are basically two types of applicators. the propagating wave applicators and the resonant applicators. Reviews of high pressure microwave discharges can be 13 found in Ref This section will only present the basic description of low pressure discharges. 2.4.1 THE PROPAGATION WAVE APPLICATORS. There are two kinds of propagation wave applicators, the surfatrons and the surfaguides. The principle involved in these types of discharges is related to the propagation of a surface wave. The breakdown and operation of such discharges constitute a complex set of phenomena where the 32 electromagnetic wave creates its own propagation guide The propagation of the wave is possible when the electron 27 density is higher than a cutoff value, which is determined by the excitation frequency. The spatial distribution of the electron density along the axis of the discharge is strongly dependent on the amplitude of the wave and vice- versa. Many surface wave discharges using this principle of operation have been built for different applications Ref 13.30.31. An example33 of such a system is shown in Figure 2.6. It consists of a coaxial cavity with a short gap between the center conductor and the front cavity wall. A quartz tube, used to contain the discharge, runs coaxially inside the center conductor. The microwave power is introduced into the cavity by means of a microcoaxial line terminated by a magnetic field excitation loop. In this configuration, the cavity length, the gap length and the loop orientation and position can be adjusted to produce electric fields high enough to breakdown the working gas in the gap region. After breakdown of the gas in the quartz tube, the electric fields in the gap launch traveling surface waves sustaining a plasma column which extends both outside the cavity and inside the center conductor. The dimensions of this system were approximately, 2 cm for the cavity length, and 2 mm for the gap length. The discharge tubes had either 4 mm or 7 mm inside diameters. The cavity outer conductor was 2.5 cm in diameter. The excitation frequency was 2.45 GHz CW. In this experiment, two of these cavities were used at both ends of a quartz tube to create a standing wave. The gas 28 Coaxial Reentrant Cavfiy Outer Conductor —— Microwave input —— --— Gap Sliding Short '— — I ——-r\- ‘ —--——.___..t 2:: ,-—-.___.: a... G ......— ::::::: “J- J .....O........Q..... l n. e 1 l l ...—f .... .__1, —‘ ‘1:- L— Adjustable Center Conductor Quartz Discharge Chamber Microwave Slow Wave Discharge Figure 2.6 Surface Wave Microwave Applicator 29 used was argon at pressures from 0.05 torr to 330 torr. The electron density measured at the center of this system, was around 2x1012 cm'3 and the electron temperature was about 27,000 °k. 2.4.2 RESONANT APPLICATORS. In this type of applicator the concept of resonant electromagnetic fields inside a cavity is used to couple the microwave energy to the gas discharge. An example of such a system is described in detail by Asmussen34. In this system, the plasma is formed in a quartz tube located on the axis of a cylindrical cavity. The resonant cavity consists of a cylindrical waveguide terminated by a fixed short at one end. and a variable short at the other end. The cavity can be tuned to operate at a specific resonant mode by varying the length of the cylinder via the sliding short. The microwave power is coupled into the cavity-plasma system with a coupling antenna. The antenna can be an extension of the inner conductor of a coaxial cable or a loop. The choice of the geometry of this coupling system depends on the operating resonant mode. The position and orientation of this antenna can be varied to optimize the energy coupling of the system. This system was operated with argon at pressures varying between 1 mtorr to 1 atmosphere. 30 13 In some experiments the quartz tube diameter was varied between 4 mm and 13 mm with the plasma length approximately constant and equal to about 16 cm. The resonant mode was TM012. The absorbed power density, defined as the total power absorbed by the plasma divided by the volume of the plasma, ranged between 0.6 - 10.0 Watt/cm3. The gas was argon at pressures ranging from 0.3 Torr to 1.0 Torr. For these experimental conditions, the measured electron density 12 -3 m-3 and 8x10 cm , the higher varied between 3x1011 c densities correspond to higher pressures. The electron 0 temperature varied from 25,000 0K to 50,000 K. the higher temperatures correspond to the lower pressures. 2.4.3 ECR SOURCES. Many applications of ion sources in material processing require a high density ion beam to minimize the processing time. One way to achieve these ion currents is by applying higher powers to any ion source. This solution however, has some practical limitations. Some materials cannot withstand the heat produced by such high energy discharges. Also the cost of high power electrical equipment makes this idea somehow less attractive. Another solution is to increase the efficiency of the ion source. In the case of microwave discharges. this can be done by introducing a static magnetic field to promote electron cyclotron resonance. 31 35 tested a 26-cm ECR ion source for reactive ion Miyamura beam etching. The discharge chamber is a waveguide type applicator with external tuning. The magnetic field is produced by three external electromagnetic coils surrounding the discharge chamber. The magnetic field strength varies along the axis of the discharge from 1.5 KG to 0.5 KG. The lowest value is near the extraction grids system. The excitation frequency was 2.45 GHz. A stable plasma was 5 4 generated at pressures between 2x10' and 2x10- Torr. For an argon plasma, the measured electron temperature and the 10 ions/cm3, plasma density were about 3 ev and 5x10 respectively. The ion beam current density for CAFB at an energy of 1 Kev was 0.3 mA/cmz. Another ECR ion source was tested by Tokiguchi36. In this experiment, the plasma chamber was a cylindrical coaxial waveguide. The impedance matching between the plasma and the 2.45 GHz microwave circuit was performed by a movable short flange. A 1.5 KG magnetic field was supplied by two electromagnetic coils surrounding the discharge chamber. For an argon discharge a current density of 7 mA/cm2 was obtained at a microwave power of 850 W. 2.5 ION SOURCE PERFORMANCE EQUATIONS The evaluation of ion sources involves the experimental determination and calculation of several figures of merit. 32 The definitions of these quantities used in this thesis are briefly outlined in this section. The first of these is is the degree of ionization, D. It is defined as being equal to the number density of ionized particles in the discharge divided by the equivalent number density of neutral particles and ions present in the discharge. 0 = Ni / (Nn + Ni ) The ion density Ni can be directly measured with a Langmuir probe and the neutral particles density can be estimated in the case of a weakly ionized discharge if the discharge pressure is known. The mass utilization efficiency. Um' is defined as the number of ions extracted from the source divided by the number of neutral particles introduced into the discharge. Um 8 Nb / "f The number of extracted ions ND is directly calculated from the measured ion beam current while the number of neutral particles Nf introduced to the discharge can also be calculated from the measured input gas flow rate. The ion production power cost of an ion source is defined as the power absorbed by the discharge in Watt divided by the ion beam current (in Amperes) extracted from the discharge. Pc = Pa / Ib The power cost can also be expressed as the energy cost to produce an ion in electron volts per ion. 33 The ion beam current density jb is defined as the ion beam current Ib divided by the total extraction area of the extraction grid system. Note that the grid extraction area defined as the total area of the grids where the extraction holes are located is different than the total holes or aperture area. The aperture area is the total area of the extraction holes. The ratio of the aperture area and the grid extraction area is called the geometrical transparency of the grid system. 2.6 REVIEW OF RF AND MICROWAVE ION SOURCES Numerous recent applications in material processing, such as ion implantation, ion milling and plasma assisted deposition of thin films has stimulated interest in developing RF and microwave discharges for ion and plasma material processing. A review of many microwave ion and plasma sources including an analysis of different energy coupling methods is presented in Ref 7. An overview of some RF and microwave ion source536'37'38'39'40'41 is presented in Table 2.1 where some figures of merit defined in the preceding section are displayed for each ion source. It should be noted that these ion sources are designed for different purposes. For example the ion source in Ref37 was designed and optimized for low energy ion beams (< 1 KeV), whereas the ion source in Ref36 was designed to achieve high 34 m0¢XOio Chg—my: mzsmnmqi+ n12 21..on Oz mm 8cm. a 3 a ad“ 8o m8... 2.... «Sh .u so .zz<2mozm 8365 Oz 3 a: as 8 I S 8 o.v ii 2: _a so _=m_z‘ «.6 39¢; :08 55...... 6:45.35 p.80 :32"... End-=0 3336» 3: 3:82... add 9:3!6 EEBSEH- 9:5. 3Q: .6559:- 83. 332 23- 23- 22513.!— aie 3.4-33 mochsom coH mmOHOUOHuoofim meow mo comfimeEoo ~.N OHQMH 35 ion beam currents. All the ion sources reviewed Utilize flat-type multiaperture extraction grids and argon as the working gas except Ref41 where oxygen gas was used. CHAPTER III DEVELOPMENT OF A SIMPLE MODEL 3.1 INTRODUCTION. The objective, in this chapter is to develop a semi-empirical model applicable to a low pressure microwave generated discharge. This model is derived from the fluid equations42. These equations are simplified using some justified approximations. The simplified theory results in a macroscopic treatment of the problem. The predictions Of this model are also limited to low pressure discharges ( p < 0.5 torr ) where ambipolar diffusion is the dominant charged particle loss mechanism. Also for the purpose of simplicity, the discharge considered is free of any static magnetic field. The main reason for developing such a model is to derive a set of equations that will correlate the controlled experimental parameters to the discharge characteristics without having to solve the exact problem which is considerably more complicated. The controlled experimental parameters are; the discharge pressure, the gas type. the gas flow, the microwave power absorbed and the diffusion 36 37 length. The parameters characterizing the discharge are; the electron density and temperature, the ion temperature and the charged particles flux. Starting from the Boltzmann equation and Maxwell's equations, expressions for particle conservation, momentum transfer and energy conservation are derived for each particle species. All these equations are then separated into a time varying part and a time independent part. The time varying part is used to derive expressions for the plasma complex conductivity, equivalent complex dielectric constant and the absorbed power density. The time independent part is used to derive expressions for the parameters associated with the diffusion of the charged particles. 3.2 DERIVATION OF THE FLUID EQUATIONS. The behavior of a gas discharge can be modeled by using the kinetic theory of gases. The most common model consists of treating the plasma as a mixture of different interpenetrating subgases, such as electron. positive ion and neutral gases. Each subgas is described by a separate Boltzmann equation. For a distribution function f(r,v,t) describing the position and velocity of some particles at a 38 certain time t, the Boltzmann equation is: QJICL) c-e H1 4. <1! 8|”?! 1 .Vrf + .va = [fa—t], (3.1) This is a conservation equation in a six dimensional space‘z, where dn = f(F,V,t) d3r d3v represents the number of particles in a volume of phase space d3r d3v. The term V.vrf represents the diffusion of particles in the three dimensional configuration space. The effect of external accelerating forces applied to the particles is described by the 3': F/m term, and 6%}. is the collision term representing a change in the distribution of particles in a 3r d3v due to elastic and six dimensional elementary volume d inelastic collisions. This equation can be written for each species existing in a plasma discharge. A set of macroscopic equations can be derived from the Boltzmann equation by multiplying equation (3.1) with a specific function of velocity ¢(V), and integrating over the velocity space. l d3v (13(7) + i d3v ah?) VVrf rot-01 .. (3.2) + i d3v oi?!) m 7.; = l d°v mix?) [35%]. Using vector identities. some of the terms in equation (3.2) 39 can be simplified yielding 3 N<0lVl> at + Vr.N<¢(v]v> 8<¢lVl> (3’ 3) + + + 00C 1 This equation is sometimes called the Boltzmann transport equation where N is the particle density and A¢c is the collision term. The symbol "<...>" represents the average over the velocity space. If ¢(v) is explicitly independent of time and position, and if F is independent of velocity, then equation (3.3) becomes 3N . - .- —<—a“—’f—"13 + V..[ N i - %. = ADC (3,4, In all the previous equations, the total instantaneous velocity v of an individual particle is equal to V=U+V (3,5) where U is the random or thermal velocity (also called peculiar velocity) and V is the average velocity. Note that > N1. In the course of these calculations, complex phasor notation is used and thus care should be taken in the manipulation of nonlinear terms. Only the real part of the complex expressions have a physical meaning and special attention must be given to nonlinear operations. For example, it can 42 be shown that Rela+bejwtheic+dejwtl (3.13) = Rel ac + :Ebd' + [ac+bd]ej"’t + %‘odez*"”t ] Under such conditions the continuity equations become; for the electrons Vu+N V h?” e1 e0 ijeley‘Jt + vr'HNeoVeo + éRemeI-Velj + [N CO (3.14) + éNelveieZJm] = [Neo+NeIert][vi ‘ a[NiO+Nilert] ' VA] and for the positively charged particles j‘i’Niiejmt I vr'HNioVIO 1' .12-Re[Nilvil.] 1' [Niovi1+NiIVio]ejwt _ . . (3.15) + é—Nllvilezju’t] = [Nio+NiIeJWt)[vi ' a[Neo+NeleJWtD where the subscripts e and i are for electron and positive ion respectively. The particle conservation equation for the neutral species remains unchanged since it is not affected directly by the applied electric field. 43 3.2.2 THE MOMENTUM TRANSFER EQUATION. The momentum transfer equation for each subgas is obtained by letting ¢(v) = mV in equation (3.3) aNm at where ”m is the momentum transfer collision frequency Nm all + mV £35 + Vr.Nm(L-JU+W] ~FN = - Nvam (3, 81 at Nm 33!— . m7 9N— + v} + VrileWD - EN = — Nvam (3. 31 Nm 4! + m'V' All + 75 + Nm[V.Vr]\-/ + mVVrlNl-l] - EN = - Nvam at at (3. From the particle conservation equation we have v 91 _ - - - m at - - mVVr.[NV] + mVNZ (3. where all the inelastic collision processes have been included in the term 2. For the electrons Ze=Vi-01Ni-VA and ”me = is the momentum transfer collision frequency for the electrons + Vr.[Nm] - EN = - Nm<17>vm (3. 16) 42 17) 18) 19) 20) 44 For the ions and V . = is the momentum transfer collision frequency for the ions. For the neutral gas Zn = Gain - Loss Substituting equation (3.20) in (3.19), we obtain Nm 33—? + v} + NmiVVrlv - TN = ml (3.21) Calling I: = - vamV - NmVZ where E=Nm is the pressure tensor, C is the collision term ,F is the applied force and m is the particle mass. for the electrons we have Nm 4+7? +Nmiiivii7 -‘F’N =c (3.22) where Ce is the electron collision term. Ce 3 ' Nemevmeve “ vaz (3.23) 8888 similarly for the ions; av. = _ .. _ .... Nimi 737‘ + ‘7r.Pi + NinthYVFJVi - FiN1 = C. (3.24) l 45 where C1 = ' Nirnivmivi ‘ Nimivizi (3'25) and for the neutrals; 3V = .. _ Nnmn ——’l + VFPn + meWVrivn - 1"ann = C (3.26) Tl where En : - Nnmnvmnvn - Nnmnvnzn (3'27) Replacing E, N and V by their steady state expressions, equations (3.22) and (3.24) become respectively iwt . " iwt meiNeo+Nele leVele + vrfe[Neo+Nelejth[v-eo+ Ve1ejwtlvr][\-]eo+_l\7ei ejwt] (3 . 28) + e[NEOEO + %Ne1Ei + [NBOEIflVeIEOJBJwt + é—Nelfilezjwt] : E3e and mimio+Niiemth‘t’viieMt 1.. wt ‘ " wt - _ (at + VI'PI[NIO+‘P\IIIeJ )[[Vio+ VileJ ]'Vr][vio+vileJ ] (3.29) + e [NIOEO + é—NIIE ” [N E ”11150181001 + %NllEle‘jwt] = 46 Equation (3.26) remains unchanged since the neutral particles are not directly affected by the electric field. 3.2.3 THE ENERGY CONSERVATION EQUATION. the energy conservation equation is obtained from equation (3.3), by letting leading to BailN‘é’mwzfl + %mV,.N = Fill/2’ ” <§I[N%V2]>C (3.30) “AZ 3 1 2 where (379% >2 is the collision term which includes all the . . . . 42 collis1on processes such as elastic, superelastic . recombination, excitation, ionization etc. = (3.3.1) (V2) = + v2 (3.32) E = éflKUz> (3.33) <[\7.V]‘7> = + VZV + V + 2617217 (3.34) 'Substituting the expression for the pressure tensor I)" = IHN (3.35) 47 and the heat flow If : lmN 1 (3. 36) we obtain %[%mNV2 + N5] + vr_[q + NEV + lmNVZV + 5.17] = N + CE 2 (3.37) where the term CE symbolizes all collision processes. For the case of a time varying plasma, N and V have to be replaced by the time varying equivalent expressions. 3.2.4 MAXWELL'S EQUATIONS. All the preceding basic equations are coupled to Maxwell's equations which are listed bellow VEOE = “Ni-Ne] (338) in1 = e[NiVi-Ne.\7€] + (o {33% (3.39) VXE = -uo %% (3.40) VII: 0 (3.41) 3.3 SIMPLIFYING ASSUMPTIONS. Some additional assumptions are to be considered in order to find a reasonable solution to these equations. 48 3.3.1 ASSUMPTIONS. a.) For the isotropic plasma approximation, the pressure tensor 3 is considered as a scalar quantity p = NkT and not a diatic. Implied in this assumption is that the gas particles have a Maxwellian distribution. b.) The electron and ion temperatures are uniform throughout the discharge and constant with respect to time. The effect of non uniform gas temperature becomes noticeable at high currents and/or high pressures in a plasma column. Ecker43 treated the case of a thermally inhomogeneous plasma column. When the assumption of constant temperature is dropped, the problem becomes much more complicated since the coefficients in the particle conservation law show a radial dependence. The electron temperature is no longer an eigenvalue of the problem , but becomes related to the electron density through the energy balance equation. The assumption of uniform temperature is used in the simple model presented in this thesis. A more complete model should include temperature nonuniformities. C-) The inertia term Nm(v.vr)V in the momentum transfer equation for both the electrons and ion gases is neglected. d.) There is no static magnetic field. 49 e.) The time dependent motion of the ions is neglected with respect to the electron motion for the case of a high frequency excitation field. f.) Only diffusion losses are important. Volume recombination and attachment are neglected. The assumption that only diffusion losses are important is justified if the discharge pressure and plasma density are low enough. Kagan44 studied, experimentally, contractions in a positive column in the pressure range of 1—50 Torr for inert gases. Under such conditions it was shown that the volume occupied by the electrons does not change as the pressure is increased, suggesting that volume recombinations do not play a major role. All the experimental measurements presented in this thesis correspond to discharge pressures lower than 1 Torr, so the assumption that volume recombination can be neglected is justified for this model. At higher pressures, however, contraction of the region occupied by electrons is observed. The mechanism of contraction is explained by the fact that, at relatively high pressures, the the charged particles, produced mainly in the center of the column, recombine before reaching the tube walls and thus the discharge contracts into a narrow region. The high pressure allows volume recombination since the probability of a three body .45 collision increases with pressure. Eletskii estimated 10_ l3cm-3 that, at electron densities in the order of 10 10 50 and an ambipolar diffusion coefficient of 10-100cm2/sec, only a predominance of molecular ions can cause contraction. 05kam46 found that,at room temperature,atomic Ar+ and Ne+ ions change into molecular Ar + and Ne + at pressures higher 2 2 than 10 Torr. 9.) Only singly ionized positive ions are present. This assumption is good for rare gases and relatively low input power. h.) Only one step ionization is considered. A complete theory of low pressure discharges would require an exact solution to the Boltzmann equation for both electron and ion subgases. In order to solve these equations one would have to take into account all of the atoms and ions excited states. This requirement by itself makes the problem very hard, if not impossible to solve since many of the cross-sections for excitation and ionization from excited states are not very well known. This is an example that justifies why a common practice is to use simplified models for calculations. Kagan47 developed a method that takes into account multistep ionizations. In this method the electron energy distribution was calculated for Neon gas for the pressure range of 5-20 Torr taking into account both elastic and inelastic collisions between electrons and atoms and between electrons and electrons. The number of direct ionizations 51 was calculated using this distribution function and so was the number of stepwise ionization events. The interesting result of this stepwise ionization treatment is that, in considering the number of stepwise ionization obtained by this method, further calculations give the same order of magnitude as the calculation based on the Maxwellian distribution assuming direct ionization. The fact that these two results are similar is a coincidence and does not imply a physical similarity. It is important, however, to note that the combination of the non-Maxwellian distribution and multistep ionization tends to give roughly the same results as the assumed one step ionization and a Maxwellian distribution. i.) Ambipolar diffusion assumption. The plasma model developed in this thesis is that of a gas discharge in which the loss mechanisms are assumed to be dominated by the diffusion of charged particles to the discharge chamber walls. The case where the diffusion of these particles is ambipolar is developed. This means that the plasma is assumed to be quasineutral, and that both electrons and positive ions diffuse to the discharge chamber walls at the same rate. The process of ambipolar diffusion is explained by the fact that the higher mobility of electrons allows them to move faster toward the walls. As a consequence, a negative voltage, with respect to the plasma voltage, begins to build near the walls. This negative 52 voltage will slow down the electron diffusion and increase the ion diffusion rate until the system reaches a steady state, where the diffusion rates of both species are equal. This model has been developed elsewhere42 and is reviewed here by using part of the equations of Section 3.2. The assumptions related to this model are: 1. The flux of electrons entering or leaving an elementary volume is equal to the flux of positive ions; Fe: n 2. The discharge is quasineutral i,e and N = N.= N It is a well known fact that free diffusion dominates in very low density discharges. In the free diffusion process, electrons and positive ions diffuse to the discharge walls independently of each other. Gerber48 investigated the transition from ambipolar-to-free diffusion as a function of gas pressure and discharge tube size in Helium afterglow. Both theoretical and experimental results show that the transition begins when A/< 2 D> = 86 independent of pressure and size of the discharge tube,where < x > is the D 53 Debye length ‘ T RD 2 69 —9- [in m] Ne Ne is the average value of the electron density in m-3 and Te is the electron temperature in degrees K. The transition happens progressively over several orders of magnitude in A/< 10>. The ions diffuse free by space charge effects when A/< 10> is smaller than 0.25 All the experimental gas discharges obtained for this thesis correspond to a value of A/< 10> larger than 50. Thus it is reasonable to assume that most of our experimental discharges correspond to the ambipolar diffusion regime. However, note that some discharge conditions ( A/< 10> < 86 ) would correspond to the ambipolar-to-free fall diffusion transition regime. These conditions are obtained for the lower discharge pressure range. 3.3.2 PRACTICAL SIMPLIFICATION OF THE BASIC EQUATIONS. Along with the previous assumptions we can further simplify the basic equations by adding the following approximations: NOE >> N E NOE1 >> N N V >> N V N V >> N >> N. 54 All these approximations are related to the assumption that the terms N1 are considered as small perturbations about the steady states No. Second harmonic terms are also neglected. With the application of these approximations, the particle conservation equation for the electrons becomes: Vr.[Neol/-eo + [N V Neill—whim] + ijeleJ‘”t = [N80+Nelej“’t]vi eo 9.1+ (3.42) this equation can be separated into a dc part vr'meoveo] -_- Neovi (3.43) and an AC part ijel + vr'[NeoVe1+Nelveo] = Nelvi (3,44) For the ions, the DC part of the particle conservation equation is io] = N- V- (3.45) <3 V .[N rio and the AC part is iju + Vr'[N \ZNNuVio) = 0 (3.46) io 55 The momentum transfer equation for the electrons becomes 1'me V ejmt + eNEOIE-0 + eNeoEIejm + kTer[Neo+Nelej°’t] 820 81 't = meVeo[vme-vi][Neo+Neler ] (3 . 47) where ”me is the total collision frequency for momentum transfer due to binary elastic collisions between electrons and neutral particles and between electrons and ions, it often can be expressed as a sum of these two processes. vme = 1)men + vmei (3'48) where and are the collision frequencies for U . men ”MET momentum transfer between electrons and neutrals and between electrons and ions respectively. At moderate pressures (0.01-1 torr) in a weakly ionized gas u . and U men >> me1 ”me = ”men’ However, for the case of a low pressure plasma (less than 0.01 Torr) when the discharge is no longer weakly ionized, may become important. Also, an additional V . "I91 computation arises when “men is a function of velocity. A correction to “men must be made using the isotropic part of the distribution function. The result is an effective collision frequency for momentum transfer42 I 00V:3 vaM 9:9- dv o v Ud‘i'ufl 8v v = ”‘9“ (3.49) e m 3 l 3% Jo‘v [ 2 a 53-dv vmen V] + 0" 56 8f where sf-is the first term of the expansion of the velocity distribution function of the electrons in spherical harmonics. Equation (3.47) can also be separated into a DC part eNeoEo + kTeVrNeo = N v mv + N v mv (3,50) eoeoee eoeoei and an AC part [ve +jw1mN V = - eN El (3.51) e eo e1 eo Similarly the momentum transfer equation for the ions is - eNmEo + kTV N. = - Niovionyvmi (3.52) lflO where umi is the ion collision frequency for momentum transfer. 3.4 RF PLASMA MODEL. Using the time varying part of the electron momentum transfer equation (3.51) and the effective collision frequency, we obtain - eE ve1:_[ 1 M (3-53) Thus the expression for the time varying electron current 57 density is ._ _ 2 N _ __ ‘ J81 : -8N80Vel = [ve+jw]me l : 0E1 (3.54) where the RF plasma conductivity is 2 e HNeo 2N _ eN m... . w 0 “5:032 )vezwz ] (3.56) The expression for the plasma conductivity can be used to determine the power absorbed by the discharge in terms of the plasma parameters. The time average RF power absorbed by the plasma in an elementary volume is given by Pam: %R M[JE] Re[0 E2 1 (3.57) substituting for a from equation (3.55), we obtain e21\‘eoveE2 : t 3 o 58 Pabs 2va fun“) ) Multiplying the numerator and denominator of equation (3.55) by the free space dielectric constant 50 , we get 2 _ mp 60 O — ve+jw (3.59) where wp is the plasma frequency defined as w = m (3.60) 58 From the expression of the conductivity we can find the plasma complex dielectric constant 6C , From Maxwell's equation '0) ”N Vfli==of +6 o at (3.61) m? = waOU-jmgé-gf (3.62) - 0%20 _ = - - ' . 3.63 VXH jOJEOU J m] E ( ) we can write Q = Er +15) (3.64) where 2 0.) pe 6r = 1' V2+0J2 (3.65) ' 2 v w e W (3.66) E.=‘--———- 1 U) [v82+w2] For a steady state discharge the power absorbed by the plasma is equal the power losses in the plasma. It can be shown that the power loss by the electron gas per unit volume can be expressed as 2:25 - i __D_., 2111.35 _ K. v _ [ZkTe][A2] + vmen[rnn]2[Te Tn]+ eveivi + fii8v exlvexl (3.67) where Da = Ambipolar diffusion constant (defined later in this chapter). A = Diffusion length (defined later in this chapter). 59 ... ll Electron temperature. TN = Neutral gas temperature. V -= Ionization potential V . . = ' ' ‘ ' ' ex) and vexJ eXC1tation potentials and eXC1tation frequencies of the atoms The first term of eq (3.67) represents the energy loss by the electrons diffusing to the discharge chamber walls. The second term represents the energy transfer from the electron gas to the neutral gas due to elastic collisions. The third term represents the energy lost to ionization. The last term accounts for the energy loss by inelastic collisions. 3.5 THE AMBIPOLAR DIFFUSION MODEL FOR A CYLINDRICAL GEOMETRY. the geometry considered in this thesis is that of a cylindrical microwave generated discharge. The discharge region is located at one end of a cylindrical microwave resonant cavity as shown in Figure (3.1). The plasma region is confined by a quartz disk forming one end of a cylinder, the other end of the cylinder consists of a circular opening in the lower base of the resonator and an electrically conducting plate adjacent to the bottom of the cavity. The inner radius of the discharge chamber is R = 4.7 cm and the 60 ['1 I CFOWQVE cavity dischorge chamber~ 'Q j X discharge oxls Figure 3.1 discharge geometry 61 length L is made variable by interchanging quartz dishes of different heights. The relatively low loss dielectric constant of quartz allows the resonant microwave fields to be transmitted to the discharge region without significant losses. The electric fields interact with the electrons inside the chamber to break-down and maintain the discharge. The electromagnetic field distribution in the discharge chamber is directly related to the type of resonant mode selected. At this point we should note that the DC part of the particle conservation equation and the DC part of the momentum transfer equation are completely uncoupled from the time varying parts (see eq. 3.43 to 3.46 and 3.50 to 3.52). This was made possible with the use of approximations. If we consider the time independent part of the momentum transfer equation for the electrons and ions. Substituting the expressions for the particle flux e = Neoveo for the electrons and Pi = Niovio for the thS, equations (3.50) and (3.52) can be written as. F = - {BM—01%. - w (3.68) 8 m8 v8 me v8 - eNE kTVN r.=——*°—2- ‘ 1° (3.69) m}? = De ; mivl. = Bi (3.70) 62 and the mobilities n1v = “e ‘ mjvmi = H (3.71) equations (3.68) and (3.69) become F. = - Neon-5.. - DeVNeo (3.72) r. = Niouifo - DiVNio (3.73) 1 Substituting these terms in (3.43) and (3.45) and neglecting recombinations and attachments yields (3.74.) <1 :3 3—1 ._, u u 4 <3 c: (3.75) using the assumption that Ne=Ni=N and multiplying (3.72) by #i and (3.73) by “e and taking the sum (1.08m D. 2 [W1V N = " NVI- (3.76) where uD-H1D —fiififJ-= a (3.77) is the ambipolar diffusion constant Equation (3.76) can be expressed as Nvi + DaVZN = 0 (3.78) 63 for the case of a cylindrical symmetry and steady state 2 vi . The radial solutions to this equation are the Bessel functions of the first kind, since the density has a finite value on the z axis, only the Jn(x) functions are to be retained. Furthermore we can consider only J0(x) since higher order modes decay more rapidly. The axial solution is a combination of sin and cos functions. If the origin is chosen at the center of the cylinder as in Figure (3.1), the solution can be written as N[r,z] = N0 Jomor] cos(az] (3.80) where N0 is the density along the axis of the cylinder and 80 = “i/Da . The boundary conditions are N(r,z)=0 for r=R and for 2: :L/2, where R is the cylinder radius and L is the height. Taking the first zero of Jo( Bop) [30R = 2.405 and - fl 0‘ ' L Substituting (3.80) in (3.79) and carrying out the derivation we obtain .1.— A 1! 2 2.405 2 = [—L-l + (T) x) (3.81) :1 I”: Q) I where A is defined as the diffusion length of the cylindrical discharge volume. Equation (3.81) defines a 64 relation between the ionization frequency and the geometry of the discharge. The ionization frequency is a function of the electron temperature Te' pressure pe and the gas type. It can be 42 determined from vi = N < 0.1V.) V. > (3.82) where ai(ve) is the ionization cross section and Ve is the electrons speed < 04v.) = 10 o.tv.1v.rtv.1 av. (3.83) For a Maxwellian distribution m '3- 2kTe 7 “V81 = 411 [m] 8 V“ (3.84) e 01‘ e 446 'fi; f(ee] = ———-e——- e e m [Hf (3-85) where 5e is the electron kinetic energy. Figure 3.2 shows a typical superposition of a Maxwellian distribution and an ionization cross section. The ionization cross section can be approximated by two straight lines as shown in Figure 3.3, line (2) can be omitted in the integration when the distribution function goes to zero faster than the ionization cross section. If ai is the slope of line (1), 65 IODIZDIiOD on cross- bUtiOD section electron energy Figure 3.2 superpOSition oF the electron distribution and the ionization cross section r-sp I'D- s—a _ electron energy Figure 3.3 lineor opproxinotion oF the ionization cross section 66 integral (3.83) becomes 3 m —iL 3 _ m 3 FE— kTe 2&5 - [anTe] 41m}. Lo sze e [me] d6 (3.86) and the ionization frequency is 8 _ 4E % ‘T'; 6. vi “me Nali [kTe] e [1+ 2kTe] (3.87) substituting in (3.81) e. IJa 4“)? g - RT; 6) 'A— = 4717-11; Na; [kTe] 8 [1+ m] (3.88) but D _ IJ'iD‘? + IJeni a fle+ A and since ue >> I’ll and Te >> Ti then R T . Da = g ”1 (3.89) Equation (3.88) leads to 1 Q 6 — ET I 2 e 4 . “2' e (6’7 [FT-1 e A2 N2[ 3.14 N511 l: e 6 (3.90) ,le me “'i 1 + l 67 using the ideal gas approximation p=Nnan, we get E e L EL _4_2 e 2 2 2 [kTe] e C p A : 61 (3.91) 1+ ——- 2kTe where C2: 1E5? fig; 1- (3 92) (It me N Hi [an14 ' ’ Equation (3.91) can be represented by a curve expressing ei/kTe versus Cp A which is a universal curve for all atomic gases. The interpretation of this equation is that for a given gas the electron temperature is a unique function of the pressure diffusion length product and is independent of the electron density. Many applications of plasma and ion sources require the knowledge of electron and positive ion currents flowing to the discharge chamber walls. In the case of an atomic gas the value of these currents can be derived from this model. Combining equation (3.72) and (3.73) along with the ambipolar diffusion assumption ri=re=r an expression for the charge particles flux is obtained -— n-n r: —131 VN + ”1111+ L1évN (3.93) ‘3 l This equation can be simplified knowing that ”e >> pi and 68 — D . F=-DiVN-uifi—:VN (3.94) -‘ kT r = ' ”i 778 VN (3.95) The total current flowing to the walls is obtained by multiplying F by the electron (or ion) electric charge and integrating over the walls surface. Substituting the expression for N from equation (3.80) in equation (3.95), one can express the particles flux in two cylindrical components, the component of 'F in the‘V direction being zero because of the azimuthal symmetry of the problem. In the r direction 3.142.405 £1 H F, = - (11 —eg NO cos[{-z] 8r R (3.96) using the identities dlhd 2 3x = Jn_l[x] - JMM and J_1[X] = " J1[X] we find H I} = ui 7,—9- No —%—S 11(2405 £1 cod—£12] (3.97;, 69 and RT r = u. ~5- N0 % JO(2.405 1%] sinI—Ez) (3.98) 2 1 The radial current is then Ir 2 (ii We No' L‘ [5.002] (3.99) and the current flowing to one end of the cylinder R I0 Jo[2.405 1%] 1‘ dr (3.100) N 12 = 2 n2 kTe I? u. 1 using the following identity and integrating d J -' (135") = 1.-.th -J.tx1 The total current of electrons or positive ions flowing to the walls is 2 I = ui kTe N0 [ 2 3f [4.268) + L (5.002] 1 (3.101) The ion mobility “i is given by the relation u: : poTI (3.102) in where go is the ion mobility measured at temperature TO degree Kelvin and at a pressure of one Torr, p and Ti are the experimental pressure (in Torr) and ion temperature (in Kelvin) respectively. In Raferenceag it is shown that the ion mobility is dependent of the ratio E/P, where E is the applied electric 70 field in a DC discharge, in the following way E -L n, = u,‘[ 1+ aoip-l] 2 (3.103) )K where ”i and a0 are constants that can be determined from experimental measurements of the mobility. Frost50 shows an experimental plot of ”i versus E/p for Argon at 1 Torr and * 300 0K. From this data, “i and a0 were calculated to be 2 1.3x103 (cmz/Volt—sec) and 2.3x10- (Torr/Volt cm) respectively. Using this result the ion mobility becomes 3 “i _ 1.3x10 Ti (3.104) - L [ 1 + 2.3x10‘2 [%1 1?- 300 p In an RF discharge E has to be replaced by the RF effective electric field which is defined in Chapter 5. Substituting equation (3.104) in (3.101), we obtain an expression for the currents flowing to the walls, in terms of the gas pressure and temperature, the electron temperature, the electron density, the dimensions of the discharge chamber and the applied electric field. 1.3x103 T. 2 1 = I kTe N0 [ 2%[4268] + L[S.002l l L [ 1 + 2.3x10“"(%1]2 300 p (3.105) 71 3.6 POSSIBLE IMPROVEMENT OF THIS MODEL. The most frequently used method, for explaining some of the gas discharges properties, is based on the assumption that the electrons have a Maxwellian distribution. This is justified when the electron density is high enough to make the Coulomb relaxation the dominant energy transfer involving the electrons. For electron densities lower than 1013 cm-3, the inelastic electron-atom collisions play a more important role in depleting the high energy tail of the electron distribution. Vriens51 described a simple method that enables one to account for the large deviations from Maxwell distribution. The main purpose of the method is to obtain accurate values of averages over the electron velocity distribution without making it necessary to calculate the exact distribution function. The energy conservation relation for the electrons in a gas discharge can be written as P +P E +P =P +P +P sel rec el exc ion +Pdiff (3.106) where PE'P represent the electron energy gain such sel'Prec as from the electric field, superelastic collisions and recombinations respectively. P p el' P and Pdiff are the energies lost through elastic collisions, exciting and exc’ ion ionizing collisions, and diffusion respectively. In Vriens method, the electron temperature Te is neither constant nor continuous. Instead, a subdivision is 72 made in two or possibly more energy regions. The region below the threshold of the first dominant inelastic process 51, corresponds to the bulk electrons. The region of energy higher than E1 corresponds to the tail electrons. The bulk electrons are described by an effective temperature T equal b to 2/3k, where is the average electron energy. This is a good approximation if is smaller than £1. The tail electrons are described by a temperature Tt which is determined uniquely by solving the system of two equations similar to equation (3.106), each of these corresponds to a different electron group. In this case a term is added to each equation to account for the Coulomb interaction between the two groups. Tb is clearly greater than Tt which value is determined by the atoms excitation levels considered in the method. Results from this method were calculated for an Argon discharge, with a pressure of 5 Torr, and compared to experimental results. In these calculations the recombination and diffusion terms have being omitted because, the difference between these two terms in the energy equation is smaller than the sum of the terms representing the direct ionization and the ionization from excited states. The values for the electric field, electron density and temperature used in these calculations were taken from experimental measurements. The following conclusions were drawn; 73 a) Deviations from the Maxwell distribution are found to be very large for the excitation and direct ionization terms b) Calculated excited state densities are very close to the measured values, in contrast to calculations using the Maxwell distribution which predict much higher values. c) The energy flow to the tail is implemented mainly by Coulomb collisions. The superelastic collisions and electric field terms are negligible. d) Excitation is responsible for more than 85% of the energy lost by the tail electrons. e) Excited atoms are lost mainly by radiation, while ionization is of lesser importance in the loss process. L.Vriens52 extends this method to a three electron group model. The three groups consist of one bulk and two tails. The tail electron temperatures are determined by considering two thresholds energies for inelastic collisions instead of one. The results of this three electron group model are in better agreement with measured values than the two group model. However, as more groups of electrons are considered in the calculations, the results converge toward the same values. Other improvements of the model should include 1) The study of free fall diffusion regime at very low discharge pressures. 2) The characterization of the ion sheath region for 74 a better understanding of the processes involved in the plasma surface processing applications. 3) The study of the effects of a nonuniform applied electric field. CHAPTER IV EXPERIMENTAL SYSTEMS 4.1 INTRODUCTION This chapter describes the experimental systems used to generate and measure the data presented in this thesis. The first part of this chapter, Section 4.2, presents the description of two microwave applicators used to generate and characterize a plasma and ion beam. The first applicator (applicator I) consists of a cylindrical microwave cavity without a static magnetic field. This applicator is later retrofitted with small samarium cobalt magnets to study the effect of a multicusp static magnetic field on the microwave discharge. Using the experimental results of the retrofitted applicator, a new applicator was designed and built. This new applicator included a total of 34 rare earth magnets which were positioned in a multicusp configuration to produce charged particle confinement and electron cyclotron resonance zones within the discharge volume. The second part of this chapter describes the microwave circuit, gas flow and vacuum systems used in the experiments related to this thesis. Also described are the double 75 76 Langmuir probes and extraction systems and methods used to characterize the plasma and ion beam obtained with both applicators. 4.2 DESCRIPTION OF THE MICROWAVE ION SOURCES 4.2.1 MICROWAVE PLASMA DISK ION SOURCE, APPLICATOR I 4.2.1.1 THE CAVITY APPLICATOR DESCRIPTION A cross-sectional view of the microwave plasma disk ion source3 is shown in Figure 4.1. This ion source consists of a 17.8 cm-i.d. brass cylinder (1) forming the outer conducting shell of the cavity applicator. The sliding- short (2), the cavity end plate (3) and the cylinder (1) form the cylindrical cavity microwave excitation zone. The end plate is water cooled by means of an embedded circular water channel (19). The sliding short (2) is a movable circular end of the cavity and it is surrounded with a ring of silver coated finger stock (4) to insure good electrical contact with the cylindrical shell. The end plate (3) with a thickness of 0.9 cm is soldered to the other end of the cylinder (1). The working gas is introduced into the discharge chamber (5) by means of an annular ring (6), and the gas feed tube (7). A disk shaped quartz tube of 9.4 cm inside-diameter (8) confines the working gas to region (5), 77 H w H 4.4 11 LLP.’ #4 ) g L: 12 a 13 a filo 19 J p.20 — 7 ...-.....- —W\/\/\/\p—— 23 Figure 4.1 Cross Section of Applicator I 78 where the microwave fields produce a disk shaped plasma adjacent to the ion extraction grid system (9). The ion extraction grid system consists of either a single grid or double grid assembly and a neutralizer (23). The ion source is designed to allow quartz disks of different heights to be easily interchanged and thereby allows plasma discharges of different thicknesses (or diffusion lengths) to be experimentally investigated. A silicon rubber gasket (20) positioned between the base of the quartz disk and the end plate provide a seal isolating the discharge region from the atmospheric pressure present in the cavity. The gasket is held in a 0.5 mm deep grove on the end plate. The discharge region is exposed to the vacuum system through the extraction grid holes. The pressure difference applied on the quartz disk holds it firmly to the end plate thus providing an adequate self vacuum seal. A screen port (10) is cut in the cavity side wall for viewing the discharge.The microwave power is coupled into the cavity through the coaxial input port (11) via the length-adjustable coaxial input probe (12). Similar to the sliding short, silver plated finger stock (13) provide the required good electrical contact for the adjustable probe. The probe is connected to a coaxial feed line via an Andrew type N connector. A radial choke (24), shown later in Figure 4.20, is placed between this connector and the coupling probe to provide the DC electrical isolation of the 79 cavity from the ground potential when the high grid voltages are applied during ion extraction. The sliding short and the adjustable excitation probe provide the impedance tuning required to match the applicator with and without the plasma. This cavity can be tuned to resonate in several electromagnetic modes such as TE TE and TM 211' 111 011' TE211 mode was used because it was the mode choice of earlier experimentsa. The tuning process involves the In this thesis however, only the adjustment of the sliding short position LS and the coupling probe position Lp. The method used for matching the cavity 3'14'53'54. The sliding short is is described in References driven by a low RPM AC servo motor when the extraction high voltages are applied. 4.2.1.2 APPLICATOR OPERATION In order to start a gas discharge, the cavity applicator has to be adjusted to resonate at the chosen mode (in this case the TE mode). For this purpose, a 211 calibrated measuring system is designed to indicate the position of the sliding short LS relative to the end plate which is a measure of the cavity length. Also, the excitation probe is calibrated to indicate its position LP relative to the cavity side wall. A list of theoretical and 80 experimental values of LS and LP for several resonant modes is given in Table 4.1. An initial calibration of the applicator is necessary since the values of the adjustable parameters Ls and L vary p with each mode. Furthermore, they also depend on the size and shape of the quartz disk used. This calibration procedure is described in details elsewhere‘s. It consists of using a microwave circuit in which the frequency can be constantly varied by means of a sweep generator to display the power absorbed by the cavity versus the excitation frequency. This method can yield the quality factor Q of the cavity and the exact positions of the sliding short and the excitation probe for all the resonant modes allowed with or without the quartz disk present in the cavity. The identification of these resonant modes can be further verified by means of a micro-coaxial electric field probe. The experimental procedure which is employed when using the microcoax probes is also described in detail in Reference14. The electromagnetic field pattern as well as LS and L for p the TE211 mode are shown in Figures 4.2 and 4.3. When the empty cavity (with the quartz disk) is tuned to the chosen resonant mode the discharge breakdown can be induced at relatively low microwave power (no more than 100 Watts) by a hand held Tesla coil. Since the electric field required to breakdown a discharge has a minimum value55 at saressures typically between 100 mTorr to 10 Torr, it is c>ften necessary to increase the the gas pressure Table 4.1 81 Applicator I Tuning Parameters SLIDING SHORT LENGTH L AND COUPLING PROBE POSITION L CORRESPONDING TO DIFFERENT RES NANT MODES FOR APPLICATOR I EMPTY CAVITY TE111 TM011 TE211 TE011 TM111 6.2 7.1 8.05 10.85 11.0 +0.4 +0.5 +0.2 +0.15 +1.3 6 69 7.21 8 24 11.27 11.27 CAVITY WITH 1.8 cm DISK 6.85 7.1 9.4 9.45 12.15 +0.3 +0.25 +0.5 +0.3 +0.2 Measured sliding short position. Measured probe position. Theoretical sliding short position. TE112 13.1 +0.4 13.39 14.1 +0.25 82 Cross Section of TE 211 Mode Cavity Walls 7 Electric Field Lines —-J —- Magnetic Field Lines Figure l..2. Cross Section of Cavity Mode 83 ~ ~ -~~ ’ ‘ - ’ --~ ‘ "Eigflf'tifies Electric Field lines 'I I I 1 L / [\I ’ ’ —' ’ ' 1 : 1 I I ' I I I 1 I ' I I I 1 I I \ ‘“ "’C I (I I : . ' I I I I I I I ' I I I I I 1 : Figure 4.3 Three Dimensional View of the Electromagnetic Cavity Resonant Fields for the TE211 Made -==-_rJ--r.r.r.rJ-_r.r.r-.r.r.r_r.r_&-J-.r.r—r.rA‘J—r—r—y' o ——.-.-.a—o.—-— — ... --w—-.-— .———- . 84 to > 10 mTorr by increasing the gas flow to ignite the plasma. Once the discharge is ignited, the cavity has to be retuned to compensate for the change of the dielectric constant in the discharge region. The expression for the plasma dielectric constant is given in equation (3.64). This operation requires the sliding short to be pulled out until the new matching condition is found. In practice, the cavity is considered to be tuned when the reflected power from the cavity-plasma system is brought to a minimum by iteratively varying the sliding short and the excitation probe positions. The discharge pressure can then be decreased by reducing the gas flow rate. Note that as seen in Chapter 3, any significant variation of the discharge pressure is followed by some variations of the discharge parameters such as plasma density, electron temperature, etc. Since the plasma dielectric constant is a function of the plasma density, it is then necessary to retune the cavity as these parameters are varied. This process of tuning the cavity as the discharge conditions are changing is easily achieved when the discharge pressure remains higher than about 1 mTorr. When the pressure is further decreased the discharge becomes unstable and difficult to tune. An improvement of this system was needed in order to easily operate the discharge at very low pressures. 85 4.2.2 APPLICATOR I RETROFITTED WITH A MULTICUSP MAGNETIC FIELD. At very low pressures the ion mobility increases since it is inversely proportional to the pressure as seen in equation (3.102). The increase of the ion mobility will result in a proportional increase in the ambipolar diffusion constant eq. (3.77 and 3.89). For example, argon gas at room temperature and at 1 mTorr has an atomic mean free path of about 8 cm and an electron mean free path of a same order of magnitude. These lengths are comparable to the discharge dimensions. As a result of this, the electrons in the low pressure discharge have a higher probability to diffuse to the chamber walls before they can make an ionizing collision with the neutral gas particles. This low pressure limitation can be solved by the application of a static magnetic field to the discharge. The potential benefits of the addition of a static magnetic field are to (i) improve the microwave coupling efficiency at low pressures through electron cyclotron resonance (ECR). The condition for such a resonance exists when the rotation frequency of the electron around the magnetic field lines is equal to the microwave 86 excitation frequency. This condition can be expressed as NC = eB/me where wc is the cyclotron frequency, 8 is the magnetic field, e and me are the electron charge and mass respectively. The value of 8 corresponding to wc a 2.45 GHz, is 875 Gauss. (ii) improve discharge efficiency by reducing charged particles losses. As a first step in applying a static magnetic field to the microwave discharge, applicator I described above was modified to include rare earth magnets. The modifications of this plasma disk ion source7 are displayed in Figure 4.4. In this configuration the 9.4 cm.i.d disk shaped zone (8) is surrounded by 17 2.54 x 2.54 x 1 cm samarium cobalt magnets. Each magnet has a maximum field strength of approximately 2.5 KG which is well in excess of the 875 6 required for the electron cyclotron resonance at the excitation frequency of 2.45 GHz. Eight magnets (14) are positioned on a soft iron keeper (18) in a circle around and adjacent to the outer circumference of the disk. The poles of these magnets are alternated thus providing eight magnetic cusps. The magnetic field of all the rare earth magnets is oriented 87 parallel to their 1 cm thickness. There are two different ways for positioning these magnets. The first configuration consisted in placing these magnets in an upright position with the 2.54 cm square magnetic pole faces tangent to the quartz enclosure. This position maximized the radial magnetic field exposed to the discharge chamber. This configuration was tested and a discharge was obtained. In this discharge eight distinct very bright plasma regions were observed near the eight surrounding magnets. These bright regions correspond to the ECR zones in the discharge. However, as the discharge pressure was further reduced during the experiment, the discharge became instable. This instability was attributed to the fact that in the upright position, the eight magnets surrounding the discharge created a conducting shield preventing the microwave resonant fields from efficiently reaching the discharge region. In addition the intrusion of these magnets in the cavity region caused a substantial perturbation of the resonant modes. A second configuration was tested where the eight rare earth magnets surrounding the discharge were positioned as shown in Figures 4.4 and 4.5 to minimize the resonant fields perturbation. In this configuration, more stable discharges were obtained at lower pressures, but since the orientation of the magnets was not optimum, no ECR zones could be sighted in the discharge. This magnetic field geometry was 88 I I. I J." wen-com m 0 £0 '71-- i to m ... O 00 7 ---------- —‘_/\/\/\/\/\_,.r— 33 Hr/ Figure 4.4 Cross Section of Applicator I Retrofitted with Rare Earth Magnets 89 preferred over the first configuration because it provided stable low pressure discharges.) The other 9 alternating pole magnets (15) are positioned on a circular soft iron plate (22) at the bottom side of the sliding short. The magnetic fields obtained with this configuration are sketched in Figure 4.5. The main improvement achieved with this configuration is a better stability of the gas discharge at low pressures. The plasma stability is the result of the magnetic field confinement of the charged particles. However, there is no evidence of electron cyclotron resonance mainly because the optimum position of the magnets around the discharge region could not be achieved. Due to their limited field strength, the best position for these magnets to promote ECR is upright and as close as possible to the quartz disk side walls. However, in such a location the magnets would partially shield the discharge from the microwave excitation fields. In addition, the intrusion of the magnets inside the microwave cavity causes a perturbation of the resonant electromagnetic fields. The result is a limitation in matching the microwave power into the cavity-plasma system. The reflected power could not be reduced to a value lower than 10% of the incident power. \ Rare earth Vx "”' magnets\\\\ \\\V6?7 90 O \ ‘ CICUNF8F8\ e 1 I 8 Flag" ‘1 ‘\\ um 82 Sof’ Iron keeper h v I P r I "]\ I \ 3 IS 3 . I I r L f ‘ ’1 \ II \ 7 \ / x I \ I \ I I \ / \. I. ‘\ (I I \\ // A \‘ -// ‘ \ I \ I “\ / \\ I \ \ // \ Discharge// /’ \\ \ I I \reglan / q ‘\I / ‘\ ~ /\di/Rm ¢”\mg~.. I 1 . - 1 I . g \ I I ‘ I ' \. ,1 ‘ z I 1 I I I I EFL-“3901‘” I I 14 I f '\ :34; #4_I / [SH \\ I I, ‘\ ./ 1;: \E/ \\\ ...:f/f <\ :_--”/,/ Ib‘ Crass seztlanai VIQN Figure 4.5 Magnetic Field Lines in Applicator I Retrofitted 91 4.2.3 MULTICUSP MICROWAVE ION SOURCE Using the experimental knowledge acquired with applicator I, a new design was developed. This new design is based on the original ion source where the end plate and the sliding short have been modified to remove the rare earth magnets from the electromagnetic excitation region in the cavity. The advantage here is to prevent the conducting magnets from interfering with the microwave resonant fields and use the static magnetic field more efficiently. Figures 4.6 to 4.8 display a cross-sectional view and photographs of this ECR ion source. Similar to the earlier design the ion source consists of a 17.8 cm i.d. brass cylinder (1) where the screen viewing port (10) and the coaxial input port (11) have been positioned closer to the end plate to allow the sliding short to reach lower cavity lengths. Silver plated finger stock ((4) and (13)) is used for good electrical contact. The end plate (3) can be pulled apart from the brass cylinder (1) when not in operation allowing for easy examination or replacement of the quartz disk (8). During cavity excitation, four threaded bolts (16) firmly hold the end plate (3b) onto the cylinder (1). The end plate consists of two separate pieces (3a) and (3b) bolted tightly together. The piece (3a) adjacent to the interior of the cavity is made from brass, while piece (3b), which is 92 33 . _3L._, I— 'a ' 1 4 (1 P 3 E i 10 8 16 1 A. 5 _ D 1"“ 3:: ,.g_ ‘ "—" 3b 9 " 3 83 Figure 4.6 Cross Section of ECR Applicator Figure 4.7 93 Photograph of Assembled ECR Applicator 94 Figure 4.8 Photograph of the ECR Applicator Disassembled 95 exposed to the discharge and the downstream high vacuum, is machined from nonmagnetic stainless steel. These two cylindrical pieces enclose sixteen 2.54 x 2.54 x 1 cm samarium cobalt magnets (17). Each magnet has a maximum field strength of approximately 2.5 KG. Eight pairs of magnets (17) are equally spaced on a circle around and adjacent to the radial gas feed annular ring (6) and quartz discharge chamber (5). The magnet pairs are placed in series and are arranged on a soft iron keeper (18) with alternate poles in the circumferencial direction forming a multicusp, octapole, static magnetic field across a radial plane as shown in the cross-sectional view of Figure 4.9. Field maps of the multicusp magnetic fields are also displayed in Figures 4.9 and 4.10. The magnetic fields mapping was obtained with a method utilizing iron filings, the method is described in more detail in Appendix A. The magnetic field strength produced by these magnets is near zero at the center and increases in the radial direction. Each magnetic pole pair produces a pole face with a maximum field strength of approximately 3 KC which is well in excess of the 875 G required for electron cyclotron resonance. The strength and position of these magnet pairs produces a radial magnetic field surface in excess of 875 G in the discharge zone and thus, as shown in Figure 4.9, results in an undulating radial ECR layer inside the quartz chamber. The iron keeper (18) has an L-shaped cross-section and is placed on the outer radius and under the magnet pairs, and 96 Caupfing Antenna _. Soft Iran Keeper (22) // \\\\\\\ _ t\\\\\\3 'l , .. | W == gfifface m Rare Earth Magnets (17) T03 VEW CF PLASMA DISCHARGE REGION SI-Dwm MAGNETC FELD (T- RARE EARTH MAGI‘ETS AND ASSOCIATED ELECTRON CYCLOTRON RESONANT ZONES Figure 4.9 Radial Magnetic Field Lines in the ECR Applicator 97 Soft “‘0:1 7 Magnets (21) Sliding Short (2) *1 (E—L ECR Surface :I i . i ' I "I ,Quartz «— . Disk \j L ) I- __'____3=+_= I ran Keeper (18) Magnets (I 7) Extraction Grid Figure 4.10 Crass Sectional View Showing the Static Magnetic Field Lines in the ECR Applicator ‘ 98 thus reduces the fringing static field in the grid extraction zone. Also shown in Figure 4.6, nine rare earth magnet pairs (21) identical to the above-mentioned magnets, are arranged in a 3 x 3 square array with a 14 cm diagonal. They are placed on a circular, thin, soft iron keeper (22) and are either located on the interior surface of the sliding short as described earlier in Figure 4.4, or as is shown in Figure 4.6, are located outside the cavity excitation zone. Similar to the radial octapole, the poles of the nine magnet pairs alternate. This nine-pole array is aligned so that the poles of the eight outer magnets alternate with the poles of the radial octapole. Thus, a multicusp magnetic field is also formed over the flat circular end surface of the discharge, and the magnetic field lines from magnets (21) also interconnect with the radial octapole field from magnets (17). 4.3 GENERAL EXPERIMENTAL SYSTEM 4.3.1 VACUUM AND GAS FLOW SYSTEMS. The gas flow system and vacuum system are shown in Figure 4.11. Starting from the gas cylinder and regulator, the gas flow is divided in two parallel paths. The upper 99 path is designed to function with manual controls and is mainly used for the higher flow rates (20 sccm - 100 sccm). It consists of a rotameter, a pressure gage and two needle valves. The valves are used to control the gas flow rate and the back-pressure. The pressure gage is used to accurately monitor the gas pressure before reaching the rotameter. This pressure control is needed since the rotameter is calibrated for a constant back-pressure. The lower gas path is designed for the lower flow rates (0.5 sccm - 50 sccm). It consists of a Tylan mass flow controller and two valves used to isolate this path if needed. These two paths converge toward a common line connected to the microwave cavity. On this line, a 30 cm long quartz tube is used to electrically isolate the microwave cavity from the rest of the gas flow system. This isolation is necessary since the cavity is held at a high potential during ion beam extraction. The ion source is located on top of a 45.7 cm radius by 45.7 cm cylindrical 6 Torr. bell jar which could be pumped down to 10- The vacuum system consists of a 10 inch NRC diffusion pump with a water cooled cold trap and a roughing pump. This system is separated from the bell jar by an air pressure driven throttle valve. The bell-jar pressure is directly measured by means of a thermocouple gage and ion gage as shown in Figure 4.11. The discharge pressure was deduced from the bell-jar pressure and the gas flow rate using a thermodynamic 100 ratcheter back ressure err 89 II mass Flow ’:F controler needle qg> gg?valve I.____J :ééigegulator quartz Isolator as I I gyl 111er U D COVIty Flow meter --—-—-—-i I vacuum bell-Jar Ion . thermocouple D vacuum , 0099 1::. valve [,7 i\\ecold I J "'99 roughing dIFFUSIon (NM) 6 PU"? E3 I- Figure 4.11 Gas Flow and Vacuum Systems IOI calculationss. This calculation takes into account the total area of the grids holes linking the discharge chamber to the bell-jar. The equation for the gas pressure in Pascal inside the discharge chamber is Nit-e _ 0011ka TC) pd — A \IT—d I pbj Tbj (4-1) where m in Kg is the gas particles mass, Td is the discharge temperature in degree Kelvin, q is the gas flow rate in particles per second , A is the total area of the holes in 2 m , ij temperature. is the bell-jar pressure and Tbj is the bell-jar 4.3.2 MICROWAVE SYSTEM. The microwave circuit used in these experiments is shown in Figure 4.12. It consists of a variable power (0.0 to 400 Watts) CH Holaday microwave power source. The frequency of this source is 2.45 GHz and is very frequency stable at operating powers higher than 70 Watts. The waveguide output of the source is connected to a three part circulator via a 3 in x 1.5 in rectangular waveguide. The circulator is used to prevent any reflected power from returning to the magnetron tube and causing possible damage from overheating. The reflected power is directed to a 500 Watt water cooled matched load where it is absorbed. The output power from the microwave source and the power 102 Power meters E: 1%” 3—port Ineldent ReFleczed ctrculator fl 28.81;“ IO O ; Udveg ICONS «%¢E;:::§§ji:tanuotors II .J ______J >185th Directional -—'3" coupler u1d coax1 ITI Ceylty C O O l n Pr Rectan ular wavegu de pI Microwave ower ource OOOOO Figure 4.12 Microwave System 103 reflected from the resonant cavity are measured through a 20 db Microlab/FXR directional coupler. These powers are further reduced with a 40 db attenuator for the incident power and 20 db attenuator for the reflected power and then measured with two Hewlett-Packard 432A power meters. The power coupled into the cavity-plasma system was measured and calibrated for this circuit as follows P = 230 x Pm C - 18.6 x Pm I R' where Pm is the incident power read on the power meter and I PmR is the reflected power also read on the meter. The microwave power is then coupled into the cavity with a type N coaxial cable. 4.3.3 ELECTRON DENSITY AND TEMPERATURE MEASUREMENTS. The method used to determine the ion density and the electron temperature is described in Reference57. The experimental setup consists of a double Langmuir probe shown in Figure 4.13. The probes length is 0.356 cm, the diameter is 0.0254 cm for each probe and the separation between the two probes is 0.35 cm. The reason for this choice is the reasonable accuracy obtained in measuring the electron temperature due to the fact that the size of the probes is small enough not to disturb the plasma. Also, the 104 dmu_ppdmpfiga Ca Ow Figure 4.19 Double Grids Dimensions and Potential 119 regions the ions tend to follow the electric field lines passing from the screen grid hole through the accelerator grid hole.. The important aspect of a double grid system design is to shape these electric field lines to achieve a good focusing and a maximum ion beam density. A comprehensive experimental investigation of two—grid accelerator systems is found in Referenceso. In this work a wide range of geometrical grid parameters and grid set operating conditions were investigated for their effect on ion beam divergence. Other investigations61 showed that three-grid accelerator systems offer significant improvements in ion beam focusing over two-grid systems. A three-grid system is similar to a two-grid system except that a third grid which is spaced as close as practically possible to the accelerator grid, is added downstream from the beam and is biased to decelerate the ions. The hole diameter in this deceleration grid is about 25% larger than the accelerator hole diameter. The effect of electrodes misallignement and ion current variations on the beam thrust from a single aperture of a two-grid system have been investigated using a computer simulationsz, In this investigation four types of perturbations have been considered: changes in ion emission rate, changes in axial spacing of the electrodes, transverse misallignement and tilt between the electrodes. It was found that apart from the changes in the ion emission rate, the dominant effect on the thrust was caused by the axial 120 changes in the electrodes spacing. The other perturbations were found to have negligible effects on the thrust or ion beam extraction. 4.3.5 VOLTAGE EXTRACTION SYSTEM The high voltage circuit used for ion extraction is shown in Figure 4.20. It consists of two high voltage power supplies connected in series. The positive terminal of this power supply combination is connected to the metallic cavity base plate. The negative terminal is connected to the metal part of the single extraction grid for the case when a single grid is used or to the acceleration grid for double grid operation. The electrical ground is connected between the two power supplies to allow two ammeters to separately read the electrical currents flowing through each power supply. The cavity is isolated from the ground potential by means of a DC radial choke (24). The beam neutralization system consists of a tungsten filament (23) placed downstream from the extraction grids and connected to the terminals of a high current power supply. The positive terminal of this power supply is connected to ground potential through an ammeter that measures the electron current extracted from ground and thermally emitted through the heated tungsten filament. The vacuum system bellow the bell-jar is also connected to ground potential. 121 C AV I T Y __1 L__ _[_—"L (2“) ‘ - :1: -_. —%L>‘—_ ' HIGH . i . VOLTAGE rowan SUPPLY ’ (23) I Vo lat _ HEATER w SUPPLY g. s V., i. . ‘ " an in vomace rowan caouuoep SUPPLY vncuuw V- svsreu L. - Figure 4.20 Electrical Circuit for Ion Beam Extraction 122 The measured voltages and currents are labeled as follow: v+, 1+ V_, 1_ Vh' In ID The electron and system are shown e1 1e2 e3 e4 i. 11 i2 voltage and current between ground and the cavity base plate and screen grid. voltage and current between the single grid or the acceleration grid and ground. voltage and current applied to the neutralizer tungsten filament. current flowing from the neutralizer to ground. electron current discharge to the screen grid. electron current discharge to the electron current ion currents involved in the ion extraction in Figure 4.21 where flowing from the gas cavity base plate and flowing from the gas bell—jar environment. backstreaming from the bell-jar environment to the cavity base plate. electron current emitted from the neutralizer. ion current through the ion current grid. extracted from the gas discharge grids. collected by the acceleration 123 Quartz disk Discharge region ii ii Screen 1 '2 e1 grid 1 \ —__7 C::] C::] CZZJ 1 C2223 C2223 E:__J E’ J l j Accelegation 9C , /i\ /\ 7’ il e2 ‘ q ' Q \\ \\/ \// 11d ‘ec Neutralizer VACUUM Figure 4.21 Electron and Ion Currents Involved in Ion Beam Extraction 124 ii3 = ion current backstreaming to the base plate and acceleration grid. During an ion extraction operation the cavity base plate and the screen grid are held at a high potential relative to ground (1600 V > V+ > 300 V). The single grid or the acceleration grid are biased negatively relative to ground potential (-200 V < V_ < 0 V). This voltage bias minimizes some of the electron and ion currents. For example ie2 and i1.3 can be neglected at very low pressures. The current i1.3 cannot be neglected at bell-jar pressures higher than 1 mTorr since the ions in the bell-jar have a higher probability to collide with neutral particles and return to the negatively biased acceleration grid. A metal screen, shown in Figure 4.22 is placed bellow the base plate and biased with the same potential as the acceleration grid to prevent the electrons emitted by the neutralizer from reaching the positively biased base plate, thus minimizing ie3' The rest of the currents are accounted for by the ammeters in the extraction system as follow: J I H el- + (4.14) in = I_ (4.15) ied =ie1-i1.2 = 1b (4.16) 125 Sliding short COVIty Discharge region Double grid COVlty assembly support *‘Metal screen With a negative potential. used to revent lectrons Fran back treaning to the caVity base plate Figure 4.22 Cross Sectional View Showing the Double Grid Assembly and the Shielding Metal screen 126 then .il (4.17) As shown in these equations the ion beam current i1.1 can be deduced from a balance of the measured currents. This is done in practice by adjusting the tungsten filament voltage Vh and current Ih so that the electron emitted current Ib is made equal to the difference (I+ - I_). When this currents balance is achieved, the ion beam current can be read directly from an ammeter. This method however, does not indicate how well the ion beam is focused. For this reason a Faraday cup was added to the system. 4.3.6 FARADAY CUP A cross-section of the Faraday cup used in these experiments is shown in Figure 4.23. It consists of a cylindrical aluminum cup 2.54 cm in diameter and 2.5 cm high. The outer surface of the cup is shielded from the ion beam by means of a 1.6 mm thick circular stainless steel plate positioned on top of the cup. This stainless steel plate has a diameter of 15 cm and a 2.54 cm diameter circular hole at the center. The cup is electrically isolated from the plate by an insulating ring. The Faraday cup assembly was positioned about 30 cm downstream from the 127 \ / la) Top View Stainless steel plate L i [--E ‘_4L1 Isalatar Metal cup (b) Cross section Figure 4.23 Faraday Cup 128 grids on a movable cart driven by a small electric motor, allowing the cup to be accurately centered on the ion beam axis. The stainless steel plate is held at ground potential while the cup is biased negative with respect to ground to collect ions and repel electrons. This Faraday cup was used to control the ion beam collimation and to confirm the ion beam current measurements, thus no explicit measurements involving the Faraday cup are presented in this dissertation. For the double grids, the focusing of the ion beam can be controlled by the magnitude of the negative voltage applied to the acceleration grid. The negative voltage controls the ion optics between the grids which affects the beam collimation. The ion beam focusing can be monitored by positioning the Faraday cup around the beam axis and as close as possible to the acceleration grid. In this location, the current collected by the Faraday cup is maximum when the beam is focused since the beam divergence is minimized. The experimental results showed that for screen grid voltages higher than 800 V, the proper acceleration grid voltage, for optimum beam focusing, is approximately -50 V. It was also found that the optimum acceleration voltage 129 ‘ depends on the magnitUde of the ion beam current extracted. Experimental measurements obtained with the Faraday cup also confirmed the accuracy of the method used to measure the value of the ion beam current. CHAPTER V EXPERIMENTAL MEASUREMENTS 5.1 INTRODUCTION This chapter presents the experimental measurements performed to characterize microwave discharges and the extracted ion beams under different experimental conditions. Argon and oxygen gases were used in these experiments. In Section 5.2 applicator I is used without static magnetic field, and the measurements for electron density, electron temperature and extracted ion beam currents are presented for different experimental conditions where gas flow rate, pressure, microwave input power and extraction voltages are varied. In Section 5.3 Applicator I is retrofitted with rare earth magnets to allow an initial investigation of the effect of a multicusp static magnetic field on the microwave discharge. Only ion beam extraction results are presented in Section 5.3 since the applied static magnetic field introduces errors in the double probe electron density and electron temperature measurements. Section 5.4 presents the results of the same type of measurements performed with a 130 131 new Electron Cyclotron Resonance (ECR) microwave applicator. All experimental results are discussed and summarized in the last section of this chapter. 5.2 APPLICATOR I WITHOUT STATIC MAGNETIC FIELD 5.2.1 EXPERIMENTAL DISCHARGE CONDITIONS In this experiment applicator I shown in Figure 4.1 was used to characterize a microwave discharge without static magnetic field. The experimental set up is shown in Figure 4.11 and the microwave system diagram is shown in Figure 4.12. Electron density and electron temperature measurements were performed using the double Langmuir probe described in Chapter 4 and shown in Figures 4.13 and 4.14. Ion beam extraction was performed using the single grid and double grid systems described in Chapter 4 and shown in Figures 4.16, 4.17 and 4.20. Three different quartz disks were used to investigate the effects of the discharge chamber volume variation. All quartz disks have a same inside diameter of 9.4 cm, but different heights which are 0.5 cm, 1.8 cm and 4.0 cm corresponding to discharge volumes of 97.2 cm3, 187.4 cm3 3 and 340 cm respectively and diffusion lengths (defined in Chapter 3 equation (3.81)) of 0.43 cm, 0.79 cm and 1.22 cm respectively. For the calculations of the diffusion lengths and volumes, the 132 discharge height is the quartz disk height augmented by the base plate thickness which is 0.9 cm for the case of applicator I. Argon and oxygen gases were used. The discharge pressure was varied from 6x10.3 Torr to 0.5 Torr corresponding to a bell-jar (or environmental) pressure 4 Torr to 6x10-1 Torr. In the 2 variation ranging from 1x10- higher discharge pressure range (p > 3x10- Torr) only the vacuum roughing pump was used whereas for the lower discharge pressures the roughing pump and the diffusion pump were used. The gas flow rate ranged between 20 scam to 170 sccm. The microwave power was varied from 80 H to 200 w. No static magnetic field was applied to the discharge chamber. 5.2.2 EXPERIMENTAL RESULTS OF ELECTRON DENSITY AND ELECTRON TEMPERATURE MEASUREMENTS. It was observed that for the TE211 mode, the sliding short position LS and the coupling probe position LP are dependent on the discharge chamber height, the input microwave power and the discharge pressure. The parameters LS and LP along with the cavity tuning procedure are described in Chapter 4. For argon gas at a pressure of 10.2 Torr and a microwave power of 80 w, the sliding short and probe 133 positions corresponding to the three quartz disks are as follows: for the 0.5 cm disk L8 = 7.7 cm LP = + 0.7 cm for the 1.8 cm disk L8 = 7.8 cm LP = + 1.2 cm for the 4.0 cm disk LS = 8.0 cm LP=+1.9 cm It was also observed that for all these discharge geometries, a power increase of 100 w from 80 H to 180 w corresponds to an increase in the sliding short position LS of about 0.2 cm, but the coupling probe position decreases by about 0.1 cm. The same kinds of variations of LS and LP are observed when the discharge pressure is increased to about 0.5 Torr. During experimentation it is important to implement such adjustments as one or more discharge parameters are varied so that the optimum power match is always maintained. Reflected microwave power could always be adjusted to be less then or equal to 0.2% of the incident power for the 0.5 cm disk. For the 4.0 cm disk the lower limit of the reflected power was about 1% of the incident power. 134 Examples of typical experimental measurements of electron density and electron temperature versus discharge pressure for argon discharges are shown in Figures 5.1 and 5.2. The results for the 1.8 cm and the 4.0 cm disks are displayed for a constant input microwave power of 100 w as the discharge pressure is reduced from 0.5 Torr to 6x10"3 Torr. Note that for the same input microwave power the electron density obtained with the 1.8 cm disk is higher than the electron density for the 4.0 cm disk. The discharge obtained by using the 0.5 cm disk was harder to tune and maintain at the lower pressures. Thus measurements are not displayed for this diffusion length. The incertainties involved in these measurement can only be estimated from the systematic errors since the method used in determining the results is not based on an exact theory. For example the electrons energy was assumed to have a Maxwellian distribution and the effect of the ion sheath is only approximated in the calculations. The relative incertainties evaluated from repeated measurements are 10% for the electron density and 20% for the electron temperature. Figures 5.3 and 5.4 show the electron density and electron temperature dependence on the microwave input power for the three quartz disk sizes. These experimental measurements were performed at constant pressure with a varying input microwave power. The discharge pressure was ELECTRON oewsmr (cm-'3) 135 10'2 q 1011‘ 10 1O .3 T TllllllIz l lllllllf l IIFTT 10 10" 10" PRESSURE (Torr) Gas - Argon U- 1.8 cm Disk. L3 - 7.8 cm Applicator ' A . 0.79 cm ' L 1- +1.2 cm No Magnets P Power =- 100 W O- 4.0 cm Disk. Ls I 8.0 cm A . 1.22 cm Lp = +2.0 cm Figure 5.1 Electron Density Versus Discharge Pressure 136 10s ELECTRON TEMPERATURE (K) a 10‘ l ITTITTTI T ETITIIII T’TTTITII to“ 10'2 10"1 1 PRESSURE (Torr) Gas - Argon D-1.8 cm disk Applicator I _ o- 5.0 cm disk Na Magnets Power - 100 in Figure 5.2 Electron Temperature Versus Discharge Pressure For Two Disk Sizes 137 1012 1 q A .1 m I E —i 3 (I) 2 Lu 0 1 Z O O: '— 0 ui _‘ .1 1...: 10" ' TllllllllllllTITllT‘llIllllTllllllTIIIIITIIIlllTT 60 80 100 120 140 160 POWER (W) Gas- Argon U- 1.8 cm disk Applicatorl A- 0.5 cm disk Na Magnets o- 5.0 cm disk Discharge Pressure - 1.5x10'3Torr Figure 5.3 Electron Density Versus Input Power Par Three Disk Sizes 138 LN (luv ELECTRON TEMPERATURE (K) .1 1O ‘ lTTFTlTTllTTTITllllfrlllllllllflfliillilllflllfl‘r 60 80 100 120 140 160 POWER (W) Gas - Argon A - 0.5 cm disk Applicatari D -1.8 cm disk Na Magnets o- «.0 cm disk Discharge Pressure - 1.5x10'zTarr Figure 5.1. Electron Temperature Versus input Power Far Three Disk Sizes ‘1 139 maintained constant at 1.5x10'2 Torr and the flow rate was 60 scam. Note that an increase of power by a factor of two corresponds to an increase of the electron density by approximately the same factor of two, however the corresponding electron temperature remains relatively unchanged for the same power increase. The smallest disk yields the highest electron temperature but not the highest electron density. Using the same experimental data shown in Figures 5.3 and 5.4, Figures 5.5 and 5.6 display the electron density and electron temperature versus the microwave input power density for the three quartz disks. The microwave power density is calculated by dividing the input microwave power by the discharge volume in cm3. In an attempt to assess the electron density and temperature variation over the cross section of the discharge chamber, a second Langmuir double probe was added to the system. This probe was located 2.5 cm from the cavity axis and centered on the radius passing through the coupling probe axis as shown in Figures 5.7.a and 5.7.b. The plane containing the two tungsten wires of each double probe was oriented perpendicular to the coupling probe axis minimizing any effect that the microwave fields may have on the measurements. Both double probes were also carefully positioned in the vertical direction to expose the same length of tungsten extremities to the plasma. However, an 140 10 '2 .mf" 'E - 3 ('7) 2 Lu 0 .1 2 o a: f— 0 Lu A d LL! 1011 ITTITTIIIIFVI TTYTTVTTI llfifflIl—rlljflll 0.0 0.5 1.0 1.5 2.0 POWER DENsrnr (W/cma) Gas-Argon A-0.Scmdisk Applicatarl t: «- 1.8 cm disk NaMagnets o-lo.0cmdisk Discharge Pressure - 1.5x10’zTarr Figure 5.5 Electron Density Versus input Power Density For Three Disk Sizes 141 10‘ ': ELECTRON TEMPERATURE (K) .1 ‘104 IlTITIlll]IflrlllTIrTlFTITlTlll[ITII'EIF 0.0 0.5 1.0 ;.5 2.0 ' POWER DENSilY (W/cm ) Gas - Argon A - 0.5 cm disk Applicatorl 0-1.8 cm disk N0 Magnets O - h.0 cm disk Discharge Pressure - 1.5x1ti'a Torr Figure 5.6 Electron Temperature Versus Input Power Far Three Disk Sizes 142 C ii 1 p38 c "9 3 Ouortz disk Discharge region r '1" c__ii:ihoai lDDDEiL__J CW”, base Biate Probe Center logated probe . CH T'Ofl the axiq r. 5.7( ) CR0 3 s CTI NA v1 u OF THE TVO 9 ° DOUBLE EROBES EOSITIONS Quartz disk Discharge region Cougling pro e Fig 5.7(bl TOP VIEW SHOWING THE ORIENTATION OF BOTH PROOES RELATIVE TO THE COUPLING AN NNA 143 estimated 10% incertainty in determining the relative position of these probes should be considered due to the systematic errors involved in measuring their exact positions. Here, the plasma is assumed to have the same sheath thickness.around both double probes. The same relative incertainty should be added to the measured electron density since this measured value is proportional to the current collected by each single probe which in turn is proportional to the area of the probes exposed to the plasma. Experimental measurements obtained with the two double probes are shown in Figures 5.8 and 5.9. The gas used was argon, the input microwave power was 125 w and the quartz dish was 1.8 cm in height. Note that at the higher pressure range the electron density is higher at the center of the discharge, but as the discharge pressure is decreased the measured electron densities converge to approximately the same value. This convergence can be interpreted as a result of longer electron and ion mean free paths at lower pressures and a different diffusion process at lower pressures. The electron temperature however is lower at the center of the discharge. This can be explained by the fact that the electrons acquire their energy from the electric fields which are higher near the the plasma surface exposed to the microwave cavity through the quartz disk. The amplitude of the electric field is decreased as it penetrate the 144 1O 12 ' A .. m 16 4 3 t .4 (7: 2 Lu 0 - Z O a: .- 0 Lu _‘ -1 L0 10 11 l T I I l T 1 If 1 l 1 l l 1 TI 10 ‘1 1o '3 10 -1 PRESSURE (Torr) Gas - Argon U - Center Of Discharge Applicator I O - 2.5 am From Center No Magnets Power - 125 iii Disk - 1.8 cm Figure 5.8 Electron Density Versus Discharge Pressure in Two Probe Locations 145 105 electron temperature (K) ' S 3 T T T T T T T T I T T T T T T TT 10‘ 10'2 10‘1 pressure (torr) Gas - Argon D - Center Of Discharge Applicator I O - 2.5 am From Discharge Na Magnets Disk - 1.8 cm Power - 125 in Figure 5.9 Electron Temperature Versus Discharge Pressure For Two Probe Locations flu 146 discharge since the plasma frequency is higher than the excitation frequency. The electron plasma frequency wpe is defined as 2 2 2 . wpe ‘ e Ne /me&0 where e, Ne' me are the electron charge, density and mass respectively, 2.0 is the vacuum dielectric constant. If Ne is expressed in m-3, the electron plasma frequency becomes w = 56 4(N )1/2 radians/second pe ' e For and electron density of 2x1011 cm'3, "pe = 2.52x1010 radians/second 9 or fpe - 3.98x10 Hz which is higher than the 2.45 GHz excitation frequency. Oxygen gas was also used is this experiment to characterize an oxygen microwave discharge used for oxide 63 and to also demonstrate the growth on a silicon substrate capability to produce an oxygen ion beam with a microwave applicator. The measured electron density and electron temperature are shown in Figures 5.10 and 5.11. Here again the 1.8 cm high quartz disk was used. The microwave power was held constant at 200 w. The bell-jar pressure was 4 varied from 2x10- Torr to 0.1 Torr and the gas flow ranged from 30 sccm to 130 sccm. 147 1012 ELECTRON DENSITY (cm“3) l 1011 r T llTlll] T l TIIIIIT T 1 llTTll 10* 10‘2 10“ 1 PRESSURE (Torr) Gas - Oxygen Applicator I No Magnets Disk - 1.8 cm Power - 200 Ill Figure 5.10 Electron Density Versus Discharge Pressure Far Oxygen Gas 148 10s ELECTRON TEMPERATURE (K) 10‘ r 1 llTTll] l l TT—Trllf T T‘lefll 10* 10'2 10‘1 1 PRESSURE (Torr) Gas - Oxygen Disk - 1.8 cm Applicator I Power . M w No Magnets Figure 5.11 Electron Temperature Versus Discharge Pressure for Oxygen Gas 149 5.2.3 ION BEAM EXTRACTION. 5.2.3.1 SINGLE GRID. Ion beam extraction using applicator I without magnets and the single grid was performed for argon gas. The extraction grid system and procedure are described in Chapter 4, Figures 4.16 and 4.20. Figure 5.12 shows the ion beam current versus extraction voltage obtained with the 1.8 cm high quartz disk versus different constant input microwave powers. The extraction voltage is defined as the sum of the voltages V+ and V_ applied between the cavity base plate and the single extraction grid. The bell-jar pressure was 4x10"4 Torr corresponding to a discharge pressure of 7x10'3 Torr, the argon flow rate was 20 sccm. Each curve in Figure 5.12 was obtained for a constant input power, while the extraction voltage was varied from 800 V to 1500 V in 100 V increments. The irregularities observed on the curves of Figure 5.12 can be attributed to the fact that the conditions for matching the microwave power to the cavity-plasma system do change for each extraction voltage increment. When the extraction voltage is increased, more ions are extracted from the discharge resulting in a reduction of the discharge pressure which causes a change in the ion density in the discharge. Since the plasma dielectric constant is a function of the electron density , a change in the ion 150 100 q 807: £5 2 v I E : Lu 60-! . _ l m ‘ a, 0‘ 3 150 u D o 3 ” g 2’ ’, 125 w -i 9 -—i m 40 ‘1 ” z : 5 > e 9. I ’I 5 5 80 w i ’, / 5 20: g . 5 z " 3 E 5 j 3 I 0 IIITTTITIFTIIIFTITI‘TTITFTTTTIIIIITTTTITFTTTITITT 600 800 1000 1200 1400 1600 EXTRACTION VOLTAGE (V) Gas-Argon GasFlow-ZOsccm .3 Applicator I Discharge Pressure - 7x10 Torr N0 Magnets Disk - 1.8 cm Single Grid Lr- 7.7 cm Made T52“ L,- +0.65 cm Figure 5.12 ion Beam Extraction Versus Extraction Voltage For Different Powers 151 density will result in a change in the electrical properties of the plasma. To compensate for these changes, the cavity has to be retuned for each voltage increment. This was done in practice by readjusting the sliding short position which was driven by a small electric motor. This motor is controlled by a separate unit which is electrically isolated from the high voltages applied to the cavity. When the 1.8 cm quartz disk is used, the process of tuning the cavity was very sensitive to the sliding short displacements. When the 4.0 cm high quartz disk was used under the same conditions of pressure and flow, the plasma became much more stable under all extraction conditions. The results of the beam current versus the extraction voltage for the 4.0 cm quartz disk are shown in Figure 5.13. In this case the power matching conditions became less sensitive to the extraction voltage variations and to the sliding short displacements. This reduced sensitivity can be attributed in part to the fact that a larger plasma volume inside the cavity will absorb more microwave power, thus reducing the quality factor of the cavity for resonance. Figure 5.14 illustrates the reduced sensitivity of the tuning parameters by showing that an ion beam can still be extracted when the sliding short position LS has been reduced by 4 mm and the coupling probe position L has been p reduced by 1.25 cm simultaneously from the previous values. 152 100 s 1 .1 I 80- %. 3 v I t- “ 150 w E 60- 0: 2 a: .. 3 - 0 2 0%: ‘01 125 w -( Z i 9 d .1 20 I u-( '1 80 w .. 1 -i l a TIIIITFIIIIIIIITTITTIIIIIllTllllTlllllrllTllTlllT 600 800 1000 1200 1400 1600 EXTRACTiON VOLTAGE (V) Gas-Argon GasFlaw-ZOsccm a Applicator I Discharge Pressure - 7x10’ Torr N0 Magnets Disk - 4.0 cm Single Grid L5- 7.9 cm M008 TE“. LP. 1’1.9 cm Figure 5.13 ion Beam Current Versus Extraction Voltage with The 4.0 Cm Disk 153 100 d I .1 30: I A q E, 1 ._ i A E 60: E : :3 .. o 2 cl g : 150 w a: 1°: 5 Z _ 3 100 w 205 I : o IllIllllllrlTllTTllflTlllllTrrTTTFTTTTIr1ITIFIWT 600 800 1000 1200 1400 1600 EXTRACTiON VOLTAGE (V) Gas ' Argon Gas Flow - 20 scam .3 Applicator 1 Discharge Pressure - 7x10 Torr N0 Magnets Disk - 4.0 cm Single Grid L3- 7.5 cm Mode TEzii Lp' *0.65 Cm Figure 5.14 Ian Current Versus Extraction Voltage uihen The Cavity is Not Perfectly Tuned 154 In this case however a critical power match was not achieved and the ion beam intensity is lower than the one obtained earlier for the same discharge conditions of pressure and input power. 5.2.3.2 DOUBLE GRIDS. Applicator I was also used for ion beam extraction with the double grids described in Chapter 4 and shown in Figure 4.17. The total area of the screen grid holes is equal to 3.8 cm2 2 which is 86% of the 4.42 cm total area of the single grid holes. The difference in geometry between the two types of grids is that the single grid has its extraction holes distributed over a total area of 24 cm2 whereas the double grids have their extraction holes distributed over an area of only 4.9 cm2. Also the double grids provide a better collimation of the ion beam. Because the double grid system has a smaller grid hole area, the discharge can be operated at lower gas flow rates. When the double grids are used, the acceleration voltage V_ has to be more carefully adjusted since it has a direct effect on the ion beam optics. Moreover, when the absolute value of V_ is too small, electrons from the bell— jar can possibly backstream and reach the positively biased screen grid. On the other hand, if the absolute value of V_ 155 is too large the acceleration grid will attract and collect a large percentage of ions from the beam. The effect of varying the acceleration grid voltage is illustrated in Figure 5.15 where argon gas is used for the same conditions of flow, pressure and input power but the acceleration grid voltage is varied from -3.5 V to -100 V. Note that the ion beam current appears higher when the acceleration voltage is low, but this result is somehow erroneous, because as explained in Chapter 4, the method used to estimate the ion beam current consists of measuring the electron current falling on the screen grid and cavity base plate and the ion current collected by the acceleration grid. The difference between these two currents is considered to be approximately equal to the ion beam current. However, when the acceleration voltage is not low enough electrons emitted from the neutralizer can possibly backstream to the screen grid over estimating the value of the electron current measured between the screen grid and ground. This problem can be eliminated by applying a higher negative voltage to the acceleration grid but in such a case it was observed that the ion beam was no longer focused. In order to find the optimum value of the accelerating voltage, a Faraday cup (described in Chapter 4) was positioned directly on the beam path to measure the intensity of the beam over a constant cross section. Using the Faraday cup, the acceleration voltage could be adjusted to simultaneously minimize the neutralizer electrons collected by the screen 156 ‘6‘ 8 N O lllillljllllllllllJlLllllllelllLllllJJljlllllllI iON BEAM CURRENT (mA) 1 1’ to 0 IITTTTTTTIPTITTTTTTYITTITTTTTTTTW rrrrlrrTlfirTTTT 800 Gas - Argon Applicator i No Magnets Double Grids "Ode TEz“ Power-250m 1000 1200 1400 1600 1800 DCTRACTION VOLTAGE (V) Disk - 1.8 cm Gas Flow - 6.0 scam O -Acceleratian Voltage - -3.5 V A - Acceleration Voltage - -100 V Figure 5.15 ion Current Versus Extraction Voltage For Different Acceleration Voltages - 157 ‘6‘ 3 N O llulljlllllljllljjjlllllllllllllLLlJlI11111]llJJ ION BEAM CURRENT (mA) o TUTTIITTTITTTTTIIlIITTTTTTTTTTITTTTTTTTITTTTITTWTTTTTTTTIT 600 800 1000 1200 1400 1600 1800 EXTRACTTON VOLTAGE (V) Gas - Argon Disk - 1.8 cm Applicator I U- Gas Flow Rate - 3.5 scam N0 Magnets Power - 200 ui Double Grids O - Gas Flow Rate - Z scam Mode T52,“ Power - 240 111 Figure 5.16 Ian Current Versus Extraction Voltage For Low Gas Flow Rates 158 grid and optimize the beam focusing. It was found that the optimum value for the acceleration voltage was approximately -50 V. The value of this voltage could vary by about 10% depending on the discharge conditions and the screen grid voltage. Figure 6.16 shows ion beam currents obtained for very low argon flow rates and low discharge pressures. The quartz disk used was 1.8 cm high. One curve is obtained for a flow rate of 3.5 scam , a discharge pressure of 1.5x10"3 Torr and an input power of 200 W. The second curve is obtained for a flow rate of 2 sccm, a discharge pressure of 8.7x10'4 Torr and an input power of 240 W. In such a pressure range the discharge was unstable and very sensitive to the gas flow adjustments. In order to maintain the discharge, the input microwave power had to be increased as the gas flow was progressively reduced to 2 scam. The discharge could not be maintained at lower pressures with this applicator. 5.2.3.3 OXYGEN ION BEAM EXTRACTION. An oxygen ion beam was extracted using applicator I and the double grids. Figures 5.17 and 5.18 show the results obtained with the 1.8 cm quartz disk. The gas flow rates range from 15 sccm down to 3.4 sccm corresponding to 3 discharge pressures between 5.3x10’3 Torr and 1.2x10' Torr. 159 ‘6‘ 8 N O LlLllJlllllillllllllLllLlJlJlllllljlljjlllllllllj iON BEAM CURRENT (mA)' o TITTTTITIIIIPTTTTTI‘ITTTITTTTIWTTTTTTTTIITTTTTTTT 0 Gas - Oxygen Applicator I No Magnets Double Grids "Ode T62" Disk - 1.8 cm 400 800 1200 1600 2000 EXTRACTiON VOLTAGE (v) Power - 156 in Gas Flow - 15 sccm DISCharge Pressure - 7.2xia" Torr Figure 5.17 Ian Current Versus Extraction Voltage For Oxygen Gas ‘- 160 ‘6‘ 3 N O lliLLl iiiliuuiiiiliu LiiiiiliiuLiuilLuiiuii iON BEAM CURRENT (mA) o TTTTTTTTTIFTTTTTTTTTTIITITITTIflTTIFTTTTTITIIITTT 0 400 300 1200 1600 2000 EXTRACTION VOLTAGE (V) Gas-Oxygen A--Fiow--ésccm Applicator I PM? ' 2m 11’ N0 Magnets Double Grids 0 - Flow - lo sccm Mode 1'53" Power - 250 iii Disk - 1.8 cm 0 - Flow - 3.4 scam Power - 290 111 Figure 5.18 ion Current Versus Extraction Voltage Far Oxygen At Low Flow Rates 161 The input microwave power was varied from 150 W to 290 W in order to maintain the discharge when the flow was decreased. The 4.0 cm quartz disk was also used and the results for an oxygen flow rate of 2 sccm are shown in Figure 5.19. In all these measurement an abrupt increase of the ion beam current is observed as the extraction voltage is progressively changed from 800 V to 1000 V. This transition is also observed when argon gas is used for ion beam extraction. The transition has been visually confirmed during the experiment. When the extraction voltage is lower than 800 V the ion beam cannot be seen but rather a diffuse glow fills the whole bell—jar. When the extraction voltage reaches a threshold value, a well collimated beam suddenly appears downstream from the grids. The threshold voltage varies between 800 V and 1000 V depending on the operating discharge conditions. The change in the beam behavior could be explained by the fact that for lower screen grid voltages the plasma sheath near the screen grid holes does not reach an optimum configuration to allow for an optimum ion Optics focusing between the two grids. 5.3 APPLICATOR I RETROFITTED. Electron density and electron temperature measurements were not possible when the samarium-cobalt magnets were added inside the cavity. The multicusp static magnetic 162 8 (d O iON BEAM CURRENT (mA) N llllLllJLllllLll111?L111L1JjjllI'lllllllll'llllljll o TTTTTTTTTTTTTITTTII‘lTTITTTrTITTTrrTITT]TTTTTITTT 800 1000 1200 1400 1600 1 800 EXTRACTTON VOLTAGE (V) Gas - Oxygen Gas Flow - 2 seem -3 Applicator I Discharge Pressure - 1x10 Torr N0 Magnets A -' Power - 200 111 Double Grids O - Power - 300 iii ”Ode TE)... Disk - 4.0 cm Figure 5.19 Ian Current Versus-Extraction Voltage For Oxygen with The 4.0 cm Disk 163 fields were measured to be non zero around the Langmuir probe position. A magnetic field applied in the probe region will disturb the plasma in that region by forcing the electrons to follow the field lines in a specific pattern. This electron trajectory disturbance will adversely affect the probe measurements since the method is based on sampling thermal electrons. Ion beam extraction measurements were taken for argon gas using the single grid. The 4.0 cm high quartz disk was chosen for this experiment because the 8 rare earth magnets located around the discharge region as described in Chapter 4, produce a conducting shield preventing part of the resonant electric fields from reaching the discharge region. When the 1.8 cm disk was used the plasma manifested instabilities and an ion beam could not be extracted. The 4.0 cm quartz disk was high enough to expose a larger discharge surface to the resonant field for more stability. Figure 5.20 shows results of ion beam extraction when only 8 magnets were positioned around the discharge area. The argon flow rate was 20 sccm and the discharge pressure was 5.1x10"3 Torr, the microwave input power was varied from 80 W to 150 W. The discharge was stable under all conditions. A comparison of these results with the case where no magnets are present (Fig. 5.13) shows that the beam intensities obtained are comparable for the same discharge 164 120 q , I ..i -i :1 100-3 ’5? 2 is E 80- 1— I z - Lu Ci 0: I Q: : D - O 60: m E z 40: 2 a 20% S I o lillTlTIllmlilllilllIITTTTIIIITTWIII[llrllllli]ilTWllll 600 800 1000 1200 1400 1600 1800 EXTRACTlON VOLTAGE (V) Gas - Argon ' Discharge Pressure - 7x10'3Tarr Applicatori Single Grid A - 150 iii Mode T53,“ -125 ll] Flow - 20 scam o- 100 iii Disk - 4.0 cm *- 80 111 Figure 5. 20 ion Extraction Applicator I Retrofitted liiith Only 8 Magnets Surrounding The Discharge 165 conditions. The stability of the discharge however, has been considerably improved. Figure 5.21 shows the results of ion beam extraction when the nine magnets array was added in the cavity. These 9 magnets were positioned on the sliding short as described in Chapter 4. For the same discharge conditions as the preceding case, extracted ion beam currents were substantially decreased. This ion beam reduction can be explained by the fact that the nine magnets array causes an important disturbance of the resonant cavity electromagnetic fields even when these magnets were covered with an aluminum foil sheath. 5.4 ECR APPLICATOR. 5.4.1 PRELIMINARY CALIBRATIONS. The cavity resonant modes were investigated using a frequency sweep generator and microwave circuit described elsewhere13, The resonant modes obtained with an excitation frequency of 2.45 GHz are characterized by the sliding short positions and the coupling probe positions. The results are displayed in Table 5.1 for the empty cavity and the cavity loaded with three different quartz disk sizes. These modes could not easily be identified with the resonant modes 166 100 , q q I d 80'-1 q A ‘1 d g A .i v -I d 1— " z .1 Ld 60“ m 4 0: I I :2 u o c: : a g A 40‘ a o co -1 -i V 5 z : ‘ c O " 5 t — .1 ' 4 g'.,‘. :1 v’ q q - I d o WTTTTTTTITTTTTTTTTTTTTTTT'TTT]TTTTTTTTWTTTTTTTTIITTTTTTTTT 600 800 1000 1200 1400 1 600 1 800 EXTRACTlON VOLTAGE (V) Gas - Argon Flow - 20 scam _3 Applicator 1 Discharge Pressure . 7x10 Torr Single Grid Disk - 4.0 cm ‘ ' D - 150 in o- 125 111 x - 100 iii Figure 5.21 Ian Extraction with Applicator i Retrofitted with 17 Magnets 167 Table 5.1 ECR Applicator Tuning Parameters SLIDING SHORT LENGTHS L AND COUPLING PROBE POSITIONS L CORRESPONDING TO DIFFERENT RESON NT MODES FOR THE ECR APPLICATOR EMPTY CAVITY LS (cm) 7.3 7.65 7.7 9.05 LP (cm) +0.7 +0.95 +0.3 +0.50 CAVITY WITH THE 1.8 cm DISK LS (cm) 7.0 8.0 12.5 LP (cm) +1.15 +0.37 +0.8 CAVITY WITH THE 4.0 cm DISK LS (cm) 6.85 8.48 8.5 10.75 11.95 11.98 LP (cm) +0.7 +0.35 +0.5 +0.65 +0.2 +1.35 168 5.4.2 ELECTRON DENSITY AND TEMPERATURE MEASUREMENTS. Electron density and electron temperature measurements were performed using a set of two Langmuir double probes positiOned as described earlier. All the magnets had to be removed from the applicator in order to make these measurements because the magnetic fields were found to interfere with the accuracy of the results. The interference from the magnetic field was apparent when the probes current versus voltage curves were plotted. The current versus voltage curves showed a relatively high asymmetry between the currents collected by each individual probe. The results of electron density and electron temperature measurements obtained with no static magnetic field for argon gas at different pressures and a constant input microwave power, are shown in Figures 5.22 and 5.23. 5.4.3 ION BEAM EXTRACTION. Argon ion beams were extracted using the double grids. Figure 5.24 shows the ion beam current for two different gas flows 5.6 scam and 4.5 sccm corresponding to discharge pressures of 2.4x10'3 Torr and 1.9x10-3 Torr respectively. The microwave input power was held constant at 200 W. These measurements were taken with all the magnets removed from 169 10 ‘2 A d _'0 . d E u v <3 2 1.0 D —i Z O O! l"- 0 L.) A «- id 10" I fir lTTlrl] 1 l fiTllll 10 ‘3 1O '2 10 -l PRESSURE (Torr) Gas-Argon DISK'A'Dcm.n-1.420m Power - 150 iii 13 - Probe Position At Center ECR Applicator O - Probe At 2.5 cm From Na Magnets , Center Figure 5.22 Electron Density Versus Discharge Pressure For ECR Applicator 170 10 5 d A .1 X v T m d 0: D 5 . 1.1.1 0. E .— a Z O m ’— Q U _. .1 1.1.1 10‘ l T T rr111[ T T T TIT'FT 10“ 10'2 10“ PRESSURE (Torr) Gas-Argon. 013k.1,,gcm.A-1.42cm ECR Applicator n - Probe At Center of Power - 150 111 Discharge Na Magnets O - Prabe At 2.5 cm From Center Figure 5.23 Electron Temperature Versus Discharge Pressure For ECR Applicator 171 ‘6‘ 8 N O lllLilljllllllllljlllllLllJlllllllllluIlJJLllle ION BEAM CURRENT (mA) O TTTTTTTITTTTTTTTIWITTHITWITTTIITTTTTTTIITITUITITTTTIITTT 600 800 1000 1200 1400 1600 l 800 EXTRACTiON VOLTAGE (V) Gas-A on O-Fiow-Sésccm 3 Double l1.:agi'ids Discharge Pressure - 3x10 Torr No Ma 9113 Powergrzm 111 0- Flow- 4. 5 scam Discharge Pressure- -.2 5x103 Torr Figure 5.24 Ian Extraction For ECR Applicator without Magnets ‘ 172 calculated theoretically for and ideal resonant cavity with the same size. A positive identification of the experimental modes would require the use of a micro-coaxial electric field probe to provide a mapping of the electric field pattern near the cavity walls. This method requires a number of holes to be drilled across the cavity walls, and the results would be useful if the exact solution for the theoretical resonant modes was known for this particular geometry. This applicator differs from an ideal cylindrical cavity by the fact that the base plate has a relatively large opening in the lower part of the discharge chamber. This cylindrical opening has a height of 2.54 cm and cannot be treated as a cavity perturbation because of it's large size relative to the cavity dimensions. After these calibrations were completed argon discharges were obtained with each of the three quartz disks. The discharge obtained with the 1.8 cm quartz disk was observed to be unstable at low pressure conditions. Because of the geometry of this applicator, the 1.8 cm disk allows only 0.5 cm of the discharge height to be directly exposed to the cavity region. The 4.0 cm disk was found to have the optimum size. 173 the applicator so that the results can be compared to the case were the magnets are in place. Figure 5.25 shows the results of ion beam extraction with all magnets in position. In this case a stable discharge was obtained with a gas flow as low as 0.86 sccm. This configuration worked very well at the very low pressures and flow rates conditions. Figure 5.26 shows measurements of the extracted ion beam current when the argon flow rate was varied from 0.86 sccm to 24 sccm while the power was maintained constant at 250 H. Figure 5.27 displays the extracted ion beam current versus microwave input power. In this experiment the argon flow rate was 2.4 sccm corresponding to a discharge pressure of 1.3x10'3 Torr. Note that the beam extraction appears to vary with power in a manner similar to the electron density. Maximum beam extraction at constant input power occurs at a gas flow of approximately 3.6 sccm, here again we note a similarity between the curves representing beam extraction and electron density versus discharge pressure. Comparing the ion beam extraction results obtained with the ECR applicator and applicator I, we note that modest improvements in ion beam extraction were obtained. However, Important improvements in ease of operation were achieved with the ECR applicator. 174 3 ION BEAM CURRENT (mA) N on O O llLLlLlJJlIllllllJiLllllllllllllJllJliJlllllllle ... O O Illfllfil]rlllrrllI‘lrlIWITTIIIIFITIIIIIIIIllfir 0 400 800 1200 1600 2000 DCTRACllON VOLTAGE (V) Gas-Argon O-Flow-Z.Ssccm ECR Applicator Double Grids D - Flow - 3.5 sccm Disk - 4.0 cm Power-2min A-Flow-5.63ccm Figure 5.25 lon Beam Extraction with ECR Applicator with All Magnets 175 3 lDN BEAM CURRENT (mA) 8 ‘6‘ IllllLllllJlLllLLllllllllIlllJlllllllJJlLllLUlll a O 0 IIITIITIT]IIIITIIIFIFTI‘IITTIITUITITIIIITTWIIIIIIUITIIIITT -5 o 5 1o 1 5 20 25 GAS FLOW (sccu) Gas - Argon ECR Applicator with All Magnets Disk - All cm Power-2mm Figure 5.26 Ion Extraction versus Gas Flow 176 ‘6‘ 8 N O llllLlllJlllllllllllLLllllllllllllllLlllllllLlle ION BEAM CURRENT (mA)' o I T I I I I r I I I If T I I T I T I [ I T O 200 400 POWER (W) Gas - Argon . Flow - 2.1. sccm ECR Applicator Discharge _ re - with All Magnets 1.3x10 Torr Disk - 10.0 cm Figure 5.27 Ion Current Versus Power CHAPTER VI COMPARISON OF THE EXPERIMENTAL RESULTS NITH THE THEORETICAL DISCHARGE MODEL 6.1 INTRODUCTION This chapter presents a comparison of the experimental measurements with the results of the corresponding predictions obtained with the simple model developed in Chapter 3. In the first section, a list of the quantities that were directly measured is reviewed along with the plasma parameters calculated using the measured data. The experimental measurements such as electron temperature and ion current available for beam extraction are compared to their corresponding theoretical values in the following sections using argon as the working gas. 6.2 MEASURED QUANTITIES The methods used in this thesis, for measuring and calculating the plasma parameters, are summarized in this section. The quantities that were directly measured with 177 178 the equipment available were: 1. The environmental (or bell jar) pressure. 2. The gas flow. 3. The cavity length. 4. The microwave coupling probe position. 5. The microwave input power. 5. The microwave reflected power. 7. The discharge wall temperature. 8. The discharge chamber dimensions. 9. The voltage and current collected by the Langmuir probes. 10. The different currents and voltages involved in the ion beam extraction. 11. The excitation frequency. From combinations of these measured values and in some cases with the proper assumptions, plasma parameters were calculated. For instance, the discharge pressure is obtained by using the bell jar pressure along with a thermodynamic calculation. This calculation involves the geometry of the aperture used as the limiting boundary between the discharge region and the vacuum chamber. The assumption used here is that of an ideal gas conditions. This method along with the other calculation methods used in this thesis are described in Chapter 4. 179 The plasma parameters that were directly calculated are: a. The ion temperature. b. The discharge pressure. c. The plasma density. d. The electron temperature. e. The extracted ion beam current. f. The power absorbed by the cavity-discharge system. 9. The power density. h. The degree of ionization. i. The mass utilization. j. The diffusion length of the discharge. These quantities are then used to determine some additional parameters. 6.3 CALCULATION OF THE DISCHARGE ELECTRIC FIELD As mentioned earlier in Chapter 3, a value for the electric field inside the discharge is required in order to have an estimate of the ion mobility. In the case of a microwave discharge, and in particular for the geometry of a discharge partially filling a resonant cavity, it is very hard to measure or calculate the exact value of the electric field inside the gas discharge. In order to do so , one A 180 would have to solve the Boltzmann equation coupled with a set of Maxwell's equations. The coupling of these equations appears explicitly in the momentum transfer equation for the electrons(or ions) as shown in equations (3.22) and (3.24) where F is the Lorentz force applied on the charged particles F = q ( E + 3x5 ) where E-is the applied electric field and B is a static magnetic field (B=0 in this case). Even with the assumption that the plasma parameters are known, it is still very hard, if not impossible, to find the exact solution for the electric field. The reason for such a difficulty is that the geometry of this particular problem is relatively complicated, in the sense that it involves a large number of boundaries. One alternative to this direct approach is to work out a relatively simple model first. If this simple model is in reasonable agreement with the experiment, the results from this model could be used to make some justified simplifying assumptions that would make the direct approach within reach. In the present model we assume that quantities such as the electric field, the electron collision frequency for momentum transfer and the electron temperature are uniform within the discharge. In doing so we are limiting the model to the prediction of the macroscopic properties of the discharge. 181 The average electric field over the plasma volume can be calculated if the effective electron-neutral collision frequency for momentum transfer ”a and the discharge absorbed power density are known. The expressions for these two quantities are shown in equations (3.49) and (3.58) respectively. we is calculated using a numerical integration Of equation (3.49) and plotted data for the electron collision frequency for argonss. The values used for Te were obtained from the langmuir probe measurements. The results are shown in Figure 6.1 where ”e is plotted versus the discharge pressure. The expression for the total microwave power absorbed by the plasma is 1 2 PabsziRer 0E (IV (6.1) Using equation (3.56) for a and the assumption that E and are uniform throughout the discharge. 2 2 eveE IJabs = 2me[ve2+w2] Iv Ne[r,z] dv (6.2) where w is the excitation frequency, e is the electron charge, me is the electron mass, E is the average electric field in the discharge and Ne(r,z) is the electron density distribution. Substituting expression (3.80) for Ne(r,z) and integrating 10‘0 O o 1 1 111111 10' Effective collision freq (l/s) 182 11111 1 1 .1 107 r I IIIIIT] r T TTTTTTr T ru1rrTr 10 " 10 “ 10 " 1 Pressure (torr) Figure 6.1 Calculated Electron-Neutral Effective Collision Frequency Versus Discharge Pressure 183 over the discharge volume yields 2 e2 E ve abs " 2me(ve2+w2] P NO I. R2 [0.865] (6.3) where No is the electron density at the center of the discharge, L and R are the discharge chamber dimensions. From this expression we can calculate the value of the electric field using the previously measured values for N 0 I L, R, Pabs and the calculated we. 2 2 1 2Pzalrsn‘lehzje +0) 1 12' (6 . 4) ezveNoLR [0.86 S] The value used for Pabs is approximated by the incident microwave power minus the reflected power (Pi-PR). In this approximation it is assumed that all the microwave energy in the resonant cavity is absorbed by the discharge. This is obviously an over estimation of P This approximation is abs' justified by the fact that microwave discharges are very efficient in general. Rogers13 measured the power absorbed by an Argon plasma column positioned along the axis Of a microwave cylindrical resonant cavity similar to the one used in this thesis. The experimental conditions were as follows; the resonant mode was the TM012, the tube radius was 13mm, the discharge pressure ranged between 0.01 and 1 Torr and the electron density was between 1011 cm“3 to 1012 cm-a. He found that the microwave coupling efficiency 184 defined as E _ Power absorbed by the discharge 8”“ 7 Power stored in the cavity varies from 85% to 98%. The highest efficiency corresponds to the higher pressure range which is where he measured the largest electron density. He also found that the largest tube size had the best coupling efficiency. In our case, the cavity is excited with the TE211 mode and the plasma is disk shaped. The electron density measured ranges between 8x1010 cm-3 and 6x1011 cm'3. This comparison seems to indicate that the assumption of a high coupling efficiency is reasonable for the purpose of this simple model. A further investigation of the coupling efficiency for the particular geometry used in this thesis is necessary for more accurate calculations. The other assumption made here, is that NO is considered to be equal to the plasma density measured in the lower region of the discharge. Using the calculated value for we we can determine E from equation (6.4). The results obtained from these calculations are displayed in Figure 6.2 where E is plotted versus the product Of the discharge pressure p and the diffusion length A. These calculations correspond to an argon discharge in applicator I with a constant input microwave power of 100 w and three diffusion length 0.43 cm. 0.79 cm and 1.22 cm. In Figure 6.3, E/va is plotted against poA. 185 10" .1 .J - D " E] [D - O A El E {102 > : V g [30 DJ _ J 10 F I IFIIIIf I I IIIIITf I I IIIIII To“ 10‘2 10“ 1 PA (Torr—cm) A-A=U.A3 cm U-A=0.79cm 'o-A=1.22cm Figure 6.2 Calculated Average Electric Field Versus Discharge Pressure Diffusion Length Product 186 10‘ 1 lLllll l __L O u 1 L 1 111111 E / PA (V/cmE-Torr) ES i _ E] ..l 10’; .. C] 102 O T I ITIIIII I ITPWIII r 1 TTTFT 10" 10'2 10" P/\ (Torr-cm) A - A: 07.3 cm El - A= 0.79 cm 0 - A=1.22 cm Figure 6.3 Calculated E/pA Versus pA 187 10’ .. D I D A D C] A 1 E l 1 ($1 .1 E1 E s O 3102‘: E I 0 ‘3 \ -1 a" —1 LL] —u g [:1 O 10 1 1111111] T 1111111] 1 1111111 10* 10'2 10“ 1 PA (Torr-cm) A -l\ = 0.113 cm 1'3 - A = 0.79 cm C - I\= 1.22 cm Figure 6.11 Calculated Average Effective Electric Field 188 The average effective electric field Ee is defined as E 2 E2 V82 8 - 2(ve2+w2] (6.5) It represents the effective value Of the electric field for a microwave discharge. This effective field term is comparable to the electric field Of a DC discharge. Note that the term 2 2 P = 82 E v6 e meve 2[ve2+w21 represents the average power density transferred to the electrons from the electric field between two collisions. 2 E is calculated for the This power is proportional to Ee a measured experimental conditions, and plotted as Ee/p A versus p A in Figure 6.4. 6.4 ION MOBILITY. Knowing the average electric field E, the ion mobility can be calculated from equation (3.104). It should be noted that equation (3.104) was derived empirically for a DC argon discharge50 and that an equivalent expression for an RF discharge was not available. The effect of an RF field can be included in equation (3.104) provided the electric field in the equation is replaced by the effective electric field described earlier. The results for the calculated ion 189 mobility are plotted against the discharge pressure p for argon in Figure 6.5. For a comparison, this figure includes two curves, curve 1 represents the ion mobility without E field correction, curve 2 includes the average effective electric field correction. 6.5 ELECTRON TEMPERATURE We have seen, in Chapter 3 that the electron temperature is independent of the plasma density, but varies with the product Cp A . An expression for C was obtained in Chapter 3 equation (3.92) __ 48-5 3116—1 1 (6.6) c2 _ 1171112 Nani [an]2 where 3i is the slope of ionization cross section versus electron energy curve described in Chapter 3, Si is the ionization threshold energy, Nn and Tn are the neutral particles density and temperature respectively. In all experimental measurements the measured value for the gas temperature was found to vary from approximately 400 0K to 480 0K. The results of the theoretical calculations for kTe/ 5i versus Cp A using equation (6.6) are shown in Figure 6.6 (solid curve). In Figure 6.6, the results from the experimental measurements using the ion mobility corrected with the effective electric field, are compared to the 190 O 10 j I ‘ (l) Mobility Not Corrected A -l O Q) U.’ . <10 3 a (2) r1 .1 g _ Mobility éfi - Corrected with q the Effective E; Electric Field :é - DD 2 10‘: z: s S2 2 q .103 WTTTHH] I I IIIIIII I TITIIIT 10‘3 10'2 10" 1 PRESSURE (Torr) Figure 6.5 Calculated Ion Mobility 191 10 1 E - I w‘ _ \ - Cl .1 [9» 1— a :2 Q? 10 "j a 10.2 T I IIIHI] I IIIIIIH TTT IIIIH] T I III” 10 " 1 10 10 ’ CP/\ (Torr cm) Cl- A.= 0.43 cm 2; - /\ = 0.79 cm C>- fix= 1.22 cm 10‘ Figure 6.6 Comparison Between Experimental Measurements and Theoretical calculations of the Electron Temperature 192 theoretical curve. The experimental data correspond to an argon discharge in applicator I for a constant microwave input power of 100 w and three diffusion lengths 0.43 cm. 0.79 cm and 1.22 cm. The constant ai and were calculated from published data for the ionization cross section for argon gas‘g. Note that the experimental results of the electron temperature measurements are in fairly good agreement with the predictions of this simple model for the higher pressure range. In the low pressure region however, the experimental data do not match with the theoretical curve. This can be interpreted as the domain of transition from ambipolar to free fall diffusion‘a. 6.6 ION CURRENT AVAILABLE FOR BEAM EXTRACTION An expression for the ion current available for beam extraction can be derived from equation (3.100) in Chapter 3. In this case however the ion flux has to be integrated over the total area of the extraction apertures of the extraction grids. Since these extraction holes are distributed over a circular area defined as the grid extraction area (see Figure 4.16), the ion flux has to be integrated over this extraction area and then multiplied by the geometric transparency Of the extraction grid in order to obtain the ion current falling on the extraction holes F4‘ 1 193 area. The expression for this ion current is REX N 1811 = 2 “2 kTe 12 ll, 10 1012.405 111] 1‘ (11‘ (6.7) where Rex is the extraction area radius, R is the discharge chamber radius and L is the discharge chamber height. Using the identity d if") = Jam - 1.1x] and integrating by parts, Iex becomes N R2 R Iax = 21r2id‘eui EA—g—S—L 11(2405 T?) (1%!) To: - (6.8) where “i is the ion mobility, k is the Boltzmann constant, Te is the electron temperature, N0 is the ion density at the center of the discharge and TGE is the grid geometric transparency. For the case Of the double grids the extraction area has a radius of 1.25 cm and a geometric transparency of 77%. the results Of the calculated ion current available for extraction obtained for the case of the ECR applicator (when the magnets were removed) with the 4.0 cm quartz disk and an input power of 200 w, are shown in Figure 6.7. This figure displays the results of the calculated ion current available for extraction for the case where the ion mobility is corrected with the effective electric term. Figure 6.7 also includes the measured ion beam currents obtained with the double grids using the ECR applicator with the 4.0 cm quartz 10' ION BEAM CURRENT (mA) 8 194 1111 l C) .1 q ——- Theory 0 Experiment TIWITIIIITIIITFIWYIITTIIIII[IIIIITIII]IIIIIIIII O 5 10 15 20 25 GAS FLOW (SCCM) Figure 6.7 Comparison Between Experimental Measurements and Theoretical Calculations of Extracted Ion Beam Currents 195 disk and an input microwave power of 200 N. In this experiment the argon flow rate was varied from 0.85 sccm to 22 sccm corresponding to a discharge pressure variation of 5x10’4 Torr to 1.5x10-2 Torr. The theoretical curves were obtained by using the previously measured values for the electron density and the electron temperature corresponding to each data point. Figure 6.7 shows that the calculated ion current available for extraction corresponds almost exactly to the experimental measurements when the ion mobility term is corrected with the calculated average effective electric field. It should be reminded that in the theoretical calculations, measured values for the electron density and electron temperature were used. These measurements could not be performed when the ion beam was being extracted, however they were performed under similar gas flow conditions. This method of measuring the electron density and electron temperature could induce some errors since the ion beam extraction can result in a discharge pressure drop due to this forced ion extraction. This incertainty in the discharge pressure evaluation could be resolved by measuring directly the discharge pressure with a transducer located in ’the discharge chamber. CHAPTER VII SUMMARY AND CONCLUSIONS 7.1 INTRODUCTION In the experiments described in this dissertation, three microwave applicators were successfully tested as plasma and ion sources. All three applicators were capable of producing high density plasmas, with densities in excess of 5x1011 cm-3 at discharge pressures of less than 5x10-3 Torr. Applicator I and applicator I retrofitted with rare earth magnets were tested as ion sources and yielded ion beam currents that were comparable to other RF and microwave ion sources in the literature36'37’38'39’40. The ECR applicator was also tested as an ion and plasma source. The extracted ion beam currents obtained with the ECR applicator did not show any substantial improvements in extracted ion beam current and power cost over the performances of the first two applicators. However, the new ECR applicator design allowed easy operation as a plasma and ion source at very low discharge pressures and gas flow rates. For example. An ion beam was extracted with argon gas flow rates as low as 0.84 sccm under very stable plasma 196 CO 118 TH al3 ex ex Th be pr 51' Ni va fr is sif 9’“ Ni 49 10 4.1 197 conditions. The discharge pressure at these low flow rates was calculated to be approximately 3x10'4 Torr. 7.2 COMPARISON BETWEEN THE THREE APPLICATORS TESTED IN THIS THESIS The performance and figures of merit of the three applicators tested are summarized in Table 7.1. The experimental data displayed in Table 7.1 was taken at an excitation frequency of 2.45 GHz for argon gas discharges. The results are shown for different discharge conditions because each applicator had a different low discharge pressure limitation. Applicator I was tested with both single and double grids and the ECR applicator was tested with only the double grids. The input microwave power varied from 150 w to 350 w and the extraction voltage varied from 1400 V to 1600 V. Note that the grid extraction area is different for the single and double grid systems, The 2 single grid has a 24 cm extraction area while the double 2 extraction area. grid has a 5 cm Applicator I and Applicator I retrofitted were tested with the single grid, for the samedischarge conditions. 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