Advances in
ATOMIC, MOLECULAR, AND OPTICAL PHYSICS VOLUME 44
Editors BENJAMIN BEDERSON
New York University New York, New York HERBERT WALTHER
Max-Planck-Institut fiir Quantenoptik Garching bei Munchen Germany
Editorial Board P. R. BERMAN
University of Michigan Ann Arbor, Michigan M. GAVRILA
F.O.M. Instituut voor Atoom-en Molecuulfysica Amsterdam The Netherlands M. INOKUTI
Argonne National Laboratory Argonne, Illinois W. D. PHILLIPS National Institute for Standards and Technology Gaithersburg, Maryland
Founding Editor SIR DAVID R. BATES
Supplements 1. Atoms in Intense Laser Fields, Mihai Gavrila, Ed. 2. Cavity Quantum Electrodynamics, Paul R. Berman, Ed. 3. Cross Section Data, Mitio Inokuti, Ed.
A D V A N C E S IN
ATOMIC, MOLECULAR AND OPTICA~ PHYSICS Edited by
Mineo Kimura GRADUATE SCHOOL OF SCIENCE AND ENGINEERING YAMAGUCHI UNIVERSITY YAMAGUCHI, JAPAN
Y. Itikawa INSTITUTE OF SPACE AND ASTRONAUTICAL SCIENCE SAGAMIHARA, JAPAN
Volume 44
ACADEMIC PRESS A Horcourt Science ond Technology Compony
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9 2001 by Academic Press
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Contents
CONTRIBUTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii ix
Mechanisms of Electron Transport in Electrical Discharges and Electron Collision Cross Sections Hiroshi Tanaka and Osamu Sueoka I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. M a j o r Characteristics of Collisions a n d Reactions in Discharges and P l a s m a s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Cross Sections a n d R e a c t i o n Rate C o n s t a n t s of A t o m i c a n d M o l e c u l a r Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. M e a s u r e m e n t s of Electron Collision Cross Sections a n d Illustrative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. M e a s u r e m e n t s of Partial Cross Sections with the Use of the A p p e a r a n c e P o t e n t i a l in Mass S p e c t r o m e t r y . . . . . . . . . . . . . . . . . . VI. M e a s u r e m e n t s of Cross Sections for the P r o d u c t i o n of Positive a n d N e g a t i v e Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. O u t l o o k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. A c k n o w l e d g m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23 25 29 30 31
Theoretical Consideration of Plasma-Processing Processes Mineo Kimura I. II. III. IV. V. VI. VII. VIII.
Introduction ........................................... An E x a m p l e of E l e c t r o n - M o l e c u l e Scattering . . . . . . . . . . . . . . . . . Overview of Theoretical F r a m e w o r k . . . . . . . . . . . . . . . . . . . . . . . . C u r r e n t Level of the Accuracy of Theoretical A p p r o a c h e s . . . . . . . . Excited Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Perspective and C o n c l u s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment ....................................... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33 34 37 49 53 55 56 56
Electron Collision Data for Plasma-Processing Gases Loucas G. Christophorou and James K. Olthoff I. II. III. IV.
Introduction ........................................... P l a s m a - P r o c e s s i n g Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D a t a Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assessed Cross Sections and Coefficients . . . . . . . . . . . . . . . . . . . . .
59 60 65 83
Contents
vi
V. B o l t z m a n n - C o d e - G e n e r a t e d Collision Cross-Section Sets VI. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
........
93 95 96
Radical Measurements in Plasma Processing Toshio Goto
I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. S u m m a r y of Recent D e v e l o p m e n t s in M e a s u r e m e n t M e t h o d s for Radicals in P l a s m a Processing . . . . . . . . . . . . . . . . . . III. Details of in Situ M e a s u r e m e n t M e t h o d s for Radicals in Processing P l a s m a s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Representative Results of C F x a n d Sill x Radicals in Processing Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99 100 102 108 123 124
Radio-Frequency Plasma Modeling for Low-Temperature Processing Toshiaki Makabe
I. II. III. IV. V. VI.
Introduction ........................................... R a d i o - F r e q u e n c y Electron T r a n s p o r t T h e o r y . . . . . . . . . . . . . . . . . M o d e l i n g of R a d i o - F r e q u e n c y P l a s m a s . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments ...................................... References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
127 128 141 153 153 153
Electron Interactions with Excited Atoms and Molecules Loucas G. Christophorou and James K. Olthoff I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. E l e c t r o n Scattering from Excited A t o m s . . . . . . . . . . . . . . . . . . . . . III. E l e c t r o n - I m p a c t I o n i z a t i o n of Excited A t o m s . . . . . . . . . . . . . . . . . IV. E l e c t r o n Scattering from Excited Molecules . . . . . . . . . . . . . . . . . . . V. E l e c t r o n - I m p a c t I o n i z a t i o n of Excited Molecules . . . . . . . . . . . . . . VI. E l e c t r o n A t t a c h m e n t to Excited Molecules . . . . . . . . . . . . . . . . . . . VII. C o n c l u d i n g R e m a r k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. A c k n o w l e d g m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. A p p e n d i x A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156 159 200 213 223 226 282 283 283 285
SUBJECT INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
295
CONTENTS OF VOLUMES IN THIS SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . .
305
Contributors
Numbers in parentheses indicate pages on which the authors' contributions begin LOUCAS G. CHRISTOPHOROU(59, 155), Electricity Division, Electronics and Electrical Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 TOSHIO GOTO (99), Department of Quantum Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan YUKIKAZU ITIKAWA (ix), Institute of Space and Astronautical Science, Sagamihara 229-8510, Japan MINEO KIMURA (ix, 33), Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi 755-8611, Japan TOSHIAKI MAKABE (127), Department of Electronics and Electrical Engineering, Keio University, Yokohama 223-8522, Japan JAMES K. OLTHOFF(59, 155), Electricity Division, Electronics and Electrical Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 OSAMU SUEOKA (1), Faculty of Engineering, Yamaguchi University, Yamaguchi 755-8611, Japan HIROSHI TANAKA (1), Department of Physics, Sophia University, Tokyo 102-8554, Japan
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Preface This volume is concerned with the study of electron-molecule interactions which are of particular importance in gas and plasma processing. When an electron is scattered by a molecule it feels a nonspherical, multicentered potential so that the scattering process is not simple. Quite frequently a resonance occurs in the course of scattering that is due to the complex shape of the molecular potential. Rotational and vibrational degrees of freedom give rise to a large number of channels to be taken into account. Furthermore, the nuclear motion can induce molecular dissociation. Particularly in the case of polyatomic molecules the dissociation process results in a large number of different fragments. These can be positively or negatively charged, as well as neutral. It is sometimes difficult even to identify all of the fragment species. In addition to the multiple channels of the collision process thus indicated, the existence of an enormous number of different molecular species in nature leads to a wide spectrum of collision phenomena. These issues are actively discussed at the International Conference on the Physics of Electronic and Atomic Collisions (ICPEAC) and its satellite meeting on electron-molecule collisions every other year. Electron interactions with molecules play a fundamental role in many application fields (e.g., astrophysics, atmospheric science, gaseous electronics, and radiation physics and chemistry). Recent technological applications of low-temperature plasmas (i.e., plasma processing) have developed quite rapidly and the importance of the electron-molecule collisions in these processing gases has been widely recognized. Electron collisions with molecules play two kinds of particularly important roles. First, upon collision with a molecule, electrons create a mixture of reactive species (ions, radicals, and excited atoms and molecules), which in turn induce the physical and chemical processes that are of practical use. Another importance of the electron-molecule collision is its decisive role in determining the energy distribution of the scattered and secondary electrons. In order to efficiently produce the desired reactive species by electron collisions it is necessary to control the energy distribution of these electrons. Thus detailed knowledge of relevant electron-molecule collisions is essential in the application of plasma processes to industry. This volume reviews recent progress in theoretical and experimental studies of electron-molecule collisions and their role in the diagnostics and modeling of processing gases. In this Preface we summarize specific features of the electron-molecule
x
Preface
collision in a processing gas. First, the variety of molecular species used in industry is very wide. Many of them have rarely been studied so far in atomic and molecular physics. Since the presence of active species is a main ingredient of plasma processing, the subjects of electron collisions with these (i.e., radicals and excited species) are included in this volume. Modeling or simulation of processing plasmas is carried out frequently to understand or even to control the relevent processes. For such a work, a complete set of cross-section data is required. That is, data for all the electron collision processes involved over a wide range of collision energy are required. It is practically impossible to obtain all this data from experiment. Theoretical calculations are needed in order to complement these available experimental data. Tanaka and Sueoka review experimental studies of electron-molecule collisions relevant to plasma processing. After a brief description of the characteristics of the collision phenomena, typical methods of cross-section measurement are described. These include a method of electron-beam attenuation, a swarm technique, and an electron energy-loss measurement. As the last method provides the most detailed information, it is described in detail, with particular emphasis on the recent progress in the coverage of scattering angles and the resolution of electron energy. Also mentioned are measurements of dissociation into neutral fragments and formation of negative ions, both of which are of special importance in processing plasma. In the chapter by Kimura, electron-molecule collisions are considered theoretically. Any theoretical study needs two different t h i n g s - - a method of theoretical treatment of collision dynamics and knowledge of the interaction between the incident electron and the target molecule. Both are summarized in this chapter. Owing to the recent advances in numerical techniques and computer capability, very elaborate results have been obtained using a theoretical approach. Typical comparisons are made here between theory and experiment. To understand or model the processing plasma in terms of elementary atomic and molecular processes, a comprehensive set of accurate crosssection data is necessary. Christophorou and Olthoff show how to construct such a database. From experience acquired in the recent production of databases relevant to plasma processing, this chapter indicates the kinds of procedures that have to be taken and what kinds of problems are expected to appear in the process of constructing a comprehensive database. Finally, the assessed values of the physical quantities for the electron-molecule collisions are summarized for CF 4, C2F6, C3F8, CHF 3, CC12F2, and C12. One of the specific features of the processing gas or plasma is the presence of radicals and their active roles. Hence a quantitative detection of radicals is an essential part of the diagnostics of the system under study. Recently
Preface
xi
several new techniques have been developed for that purpose. Goto introduces them and describes recent results of the research using those techniques, particularly for CFn and SiHn. In the next chapter, Makabe discusses modeling of the low-temperature radio-frequency (rf) plasmas. The rf plasmas are widely utilized in the fabrication of microelectronic devices. To understand electron transport in the rf plasmas a time-dependent problem should be solved. In relation to this, collisional relaxation times become very important. It is pointed out that the relaxation times in a molecular gas are different from those in an atomic gas. Also shown is how to model the time-dependent plasma employing knowledge of the elementary collision processes occurring in it. In the processing gas or plasma, excited atoms and molecules are produced either deliberately or concomitantly. They are normally very active and hence of practical importance. In the final chapter, Christophorou and Olthoff review the interactions of electrons with excited species. The knowledge available thus far on such interactions is not great. The authors have collected almost all the cross-section data on these and have presented them here in graphical or tabular forms. A particular emphasis is placed on the electron attachment process to vibrationally/ electronically excited molecules. As mentioned above, electron-molecule collisions play fundamental roles in many application fields other than plasma processing. This volume attempts to serve as an informative and timely review of the processes for such fields. In the industrial application of plasma processing, many other atomic phenomena, such as chemical reactions and plasma-surface interactions, are involved. For these, we recommend a previous volume of this serial, Volume 43 entitled "Fundamentals of Plasma Chemistry." Mineo Kimura and Yukikazu Itikawa
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 44
M E CHA N I S M S OF ELE C TR ON T R A N S P O R T IN E L E C T R I C A L DISCHARGES AND ELECTRON COLLISION CROSS SECTIONS H I R 0 SHI TA NA KA Faculty of Science and Technology, Sophia University, Tokyo 102-8554, Japan OSAMU SUEOKA Faculty of Engineering, Yamaguchi University, Yamaguchi 755-8611, Japan
I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. M a j o r Characteristics of Collisions and Reactions in Discharges and Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. P l a s m a Display Panel ( P D P ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. P l a s m a Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Cross Sections and Reaction Rate Constants of Atomic and Molecular Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. M e a s u r e m e n t s of Electron Collision Cross Sections and Illustrative Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. M e a s u r e m e n t s of Electron Beam A t t e n u a t i o n for D e t e r m i n a t i o n of an U p p e r B o u n d of Cross Sections . . . . . . . . . . . . . . . . . . . . . . B. The Swarm M e t h o d Leading to a Cross-Section Set . . . . . . . . . . . C. The Electron Beam M e t h o d for M e a s u r i n g the Angular Dependence of Excitation Processes . . . . . . . . . . . . . . . . . . . . . . . . 1. Differential Cross Section for Elastic Scattering . . . . . . . . . . . . . 2. Vibrational Excitation and Resonance P h e n o m e n a . . . . . . . . . . 3. M e a s u r e m e n t s of the Differential Cross Section over the Complete Range of Scattering Angles . . . . . . . . . . . . . . . . . . . . 4. Electron Spectroscopy at U l t r a h i g h Resolution . . . . . . . . . . . . . 5. Scattering of Electrons of Ultralow Energies . . . . . . . . . . . . . . . V. M e a s u r e m e n t s of Partial Cross Sections with the Use of the Appearance Potential in Mass Spectrometry . . . . . . . . . . . . . . . . . . . . VI. M e a s u r e m e n t s of Cross Sections for the P r o d u c t i o n of Positive and Negative Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Ionization Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Dissociative Electron A t t a c h m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . VII. O u t l o o k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 13 15 17 17 21 21 23 23 25 25 27 29 30 31
Copyright 92001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003844-7/ISSN 1049-250X/01 $35.00
Hiroshi Tanaka and Osamu Sueoka Abstract: The current status of experimental studies for electron scattering from polyatomic molecules is reviewed in conjunction with the electric discharge in gases and reactive plasmas. Recent developments in electron scattering experiments, total cross section, and differential cross-section measurements from high to ultralow energy regions for various processes such as ionization and dissociative attachment are described. The need for cross-section data for a broad variety of molecular species is discussed.
I. Introduction The objects of studies of electrical discharges in gases and low-temperature plasmas are numerous and diverse, ranging from laboratory experiments to natural phenomena. An example of the latter concerns the control of lightning by laser light, as recently reported (Diels et al., 1997). Although it is difficult to prevent the occurrence of thunder, attempts are being made both in the United States and in Japan to control lightning and thereby to reduce its damaging effects. The idea is to ionize air with intense laser light, which creates an electrically conductive path, and this serves to guide lightning to this path and thereby toward a more desirable destination. Another area of study is the plasma display panel (PDP). It consists of a set of fluorescent discharge lamps that generate lights of three colors--red, green and blue--assembled on a plane. A discharge lamp used in such a display panel of 40-50 in (l-m) has a linear dimension of < 1 mm. Several hundred thousand to several million of these microfluorescent discharge cells form a color display panel. Current studies in this technology aim at delineating the voltage-current characteristics of the discharge in such a cell in terms of atomic and molecular processes, through measurements of the spatial distribution of excited xenon atoms in the cell as well as through computer simulations of the glow region (Sobel, 1998). Still another example of applications is the technology of plasma processing (Lieberman and Lichtenberg, 1994; Bruno et al., 1995; Tanaka and Inokuti, 1999), which includes plasma chemical-vapor deposition (CVD) and plasma etching. This technology uses low-temperature plasmas generated by low-pressure glow discharges, which are chemically reactive, and plays a central role in efforts to enhance the function, speed, and integration of semiconductor devices. Main topics of current research include techniques of plasma diagnosis (Goto, 2000) and modeling (Makabe, 2000). An immediate goal is to elucidate plasma characteristics from the point of view of atomic, moelcular and optical physics, and thus to put the technology on a fundamentally scientific basis, rather than on the empiricism and intuition that have been relied upon so far. An eventual goal is to establish a fully developed technology that will permit one to control and design plasmas of
MECHANISMS OF ELECTRON TRANSPORT desired properties. In view of the high potential in versatility and economics, plasma-processing technology is expected to enjoy a leadership position in the twenty-first century. The central focus of competition among industrialized nations currently is the processing of materials at scales of micrometers to nanometers. Full elucidation of plasma properties used in the processing must include considerations not only of atomic and molecular processes in the gas phase, but also of boundary regions between gas and solid, as well as interactions between atoms or molecules with a solid surface, or even with bulk solid at least near the surface. Thus one deals here with an extremely complex system, containing numerous atomic or molecular species of the reactant gas and solid. However, it is the rich complexity of the system that carries the potential of diverse phenomena, and hence the possibility of control and design. A unifying aspect of complex plasma phenomena lies in its initiation, always through collisions of energetic electrons with atoms and molecules. It is also noteworthy that a preponderance of matter in the universe, well over 99%, is in a plasma state, that is, the fourth phase of matter after gas, liquid, and solid. In this sense, an understanding of plasma properties is important to astrophysics. In recent years there has been intensified recognition of the need to establish extensive databases of atomic, molecular and optical physics not only for plasma physics and chemistry but also for space research, environmental research, and energy research (Christophorou, 1984; Inokuti, 1994). Systematic programs are being developed to meet this need by the National Research Council of the U.S. (NRC, 1991, 1996). This chapter treats atomic and molecular processes in electrical discharges with an emphasis on both electron collisions with atoms and molecules and reactions of excited atoms with other atoms and molecules, discusses methods for determining cross sections and reaction rate constants, and presents some of the current data.
II. Major Characteristics of Collisions and Reactions in Discharges and Plasmas The density of electrons in the weakly ionized plasma of interest here is 109_ 1011 cm-3, with kinetic energies distributed around a mean of a few eV, corresponding to a temperature T e, of a few 10,000 K. A very few electrons with relatively high energies are responsible for excitation and ionization of
Hiroshi Tanaka and Osamu Sueoka
atoms and molecules of the gas used as the starting material. The kinetic energies of neutral atoms and molecules are much lower than the mean kinetic energy of electrons, and are characterized by nearly room temperature TN; for this reason, one describes the weakly ionized plasma as "low temperature." Such a plasma is obviously not in thermal equilibrium. Thus energy input is necessary for its generation and maintenance and is usually provided by an external electric field, which accelerates primarily electrons, rather than ions (which are much heavier). Reaction mechanisms in discharge plasmas can be classified into three stages of temporal development, starting with plasma initiation and ending with product formation, which may be designated as "physical," "physicochemical," and "chemical." The physical stage consists of excitation and ionization of atoms and molecules of the material gas by electron impact. The physicochemical stage consists of rapid reactions of highly active species, such as slow electrons, positive or negative ions, excited atoms, and radicals resulting from molecular dissociation, with atoms or molecules of the material gas, which are mostly in their electronic ground states. The chemical stage consists of thermal reactions of the products of the physicochemical stage with atoms and molecules of the material gas. We shall illustrate these stages in what follows, using the examples we gave in Section I.
A. PLASMA DISPLAY PANEL (PDP) Let us consider mechanisms of discharge in a PDP cell. Xenon is most commonly used for producing near vacuum ultraviolet (UV) light (at a wavelength of 147 nm or photon energy of 8.43 eV) efficiently and steadily. This light is emitted as a result of a transition from the resonance state to the ground state (5P 5 [-2P3/2] 6s ~ 5p6[-18o]). Sometimes a mixture of xenon at a concentration of several percent in helium or neon is used; then, excitation and ionization of helium or neon must be taken into consideration. This is the physical stage of the example. In the physicochemical stage, metastable states of atoms (He*, Ne*) produced in a discharge at appreciable pressure of about 100 torr, as used in a P D P cell, transfer energy to xenon atoms in a Penning ionization process, resulting in a lowering of the discharge voltage. Ionization processes, including electron ejection from the discharge cathode, are essential to the maintenance of the discharge. Eventually, produced chemical species undergo thermal reactions during the chemical stage. In order to allow a P D P to operate properly it is necessary to control the physicochemical and chemical stages to some extent by adjusting various conditions.
MECHANISMS
OF ELECTRON
TRANSPORT
B. P L A S M A PROCESSING
A plasma used for production of amorphous silicon (a-Si) is typically generated by applying radio-frequency power to Sill 4 gas at a pressure of 30mTorr, with a flow rate of 1 cc/s, in a reactor of volume 3 x 103 cm 3. Electron collisions lead to ionization and excitation of S i l l 4 molecules; among many product species, chemically active radicals Sill x (x = 0-3) are most important. Measurements have shown that the relative concentrations in a stationary plasma are SiHa : S i l l 2 : S i H : S i 1 0 1 2 : 101~ 101~ 109 (Goto, 2000). However, the probability of dissociation of Sill 4 in a single electron collision (Sugai, 1999) was measured only recently, as we discuss in more detail. Thus we know that the concentration of the original S i l l 4 molecules is higher than that of the radicals by two orders of magnitude. Therefore, the radicals react predominantly with the original S i l l 4 molecules. Rate constants for reactions of SiHx (x = 0-3) with Sill4 and their lifetimes are shown in Table I. Among the radicals, Sill 3 is least reactive, thus rather stable upon thermal collision with Sill4, and as a result it has a long lifetime in plasma; consequently, Sill 3 accumulates in the plasma, achieving a high density. Furthermore, Sill 3 reaches the base surface with high probability, and is considered to be the major contributor to the formation of a silicon film on the surface. The other radicals Sill x (x = 0-2) have greater reaction rate constants, shorter lifetimes, and reach the base surface in competition with reactions with S i l l 4. In particular, it is thought that successive reactions starting with S i l l 2 lead to larger silane radicals, which are precursors of the formation of fine particles in the plasma. It is possible to enhance desired chemical reactions by using a gas containing an additive that leads to additional reactive species. For instance,
TABLE I RATE CONSTANTS AND LIFETIMES (AT 50 MTORR) OF S i l l 4 AND SOME RADICALS IN THE Sill 4 PLASMAa
Reaction
Rate C o n s t a n t k (cm3/s)
Lifetime r(s)
~ ] + Sill4 ~ H 2 + Sill 3
5 x 10-12
1.1 x 10 . 4
3.3 x 10-12
1.72 x 10 -4
[-S-~+ Sill 4 ~ SizH 4 (Si2H 4 + Sill 4 ~ Si2H6) S~+
Sill 4 ~ SizH 5
(SizH 5 + Sill4 ~ SizH 6)
~-~+
Sill 4 ~ SizH 6
~ +
Sill4 --, Sill 3 + Sill 4
"Japan Society of Applied Physics.
2.3 x 10- lO
2.47 x 10 . 6 long life
Hiroshi Tanaka and Osamu Sueoka
it has been reported that amorphous silicon produced by a mixture of Xe and Sill 4 is more resistant to photodegradation than that produced by a mixture of Ar and Sill 4 (Matsuda et al., 1991). A probable reason for this observation is the difference in the excitation energies of the metastable states, which are 8.31eV and 9.45eV for Xe*, and l l.6eV and 11.7 eV for Ar*. In the plasma generated in a C F 4 - O 2 mixture and used for etching, F atoms resulting from electron-impact dissociation of CF 4 are responsible for etching both solid silicon and polymers produced by plasma-induced polymerization. In this process, active O* atoms resulting from electronimpact dissociation of 02 react with the polymers to yield CO, CO2 and C O F 2 gases, which obviously are removed from the solid phase. This phenomenon is called ashing. As a result, fewer F atoms are expended in etching the polymers, and therefore their reactions with silicon are enhanced. With expected development of organic-film semiconductors, ashing by plasmas containing 02 will be more important. The foregoing sketch illustrates our current understanding of processes in bulk plasmas. To improve this understanding, we must also learn the precise yields of Sill x (x = 0-3), F, and O*, and detailed reaction pathways initiated by Ar* and Xe* as well. Full discussion of both the physicochemical and the chemical stage must encompass a broad area of reaction kinetics, and is beyond the scope of this chapter.
III. Cross-Sections and Reaction Rate Constants of Atomic and Molecular Processes As stated in Section I, electron collisions with atoms and molecules are of general importance in the initiation of discharges and plasmas. In particular, a newer trend in etching technology is to use lower pressures, so that reactive species readily reach the base surface after a minimal number of collisions with gaseous molecules on the way. Then, the control of electron collision processes becomes even more important. In what follows, we shall concentrate first on a single collision of an electron with an atom or molecule. We first classify collisions into two kinds, namely, elastic and inelastic. In an elastic collision, the internal energy of an atom or molecule is unchanged. However, a part AE of the electron energy E is transferred to an atom or a molecule, as given by A E / E ~ m / M ~ 10 -4, where m is the electron mass and M is the mass of an atom or molecule, respectively. In an inelastic collision there is a change in the internal energy, which leads to rotational, vibrational or electronic excitation, dissociation,
MECHANISMS OF ELECTRON TRANSPORT ionization, or attachment of an electron to a molecule. For an atom, electronic excitation and ionization are the only possibilities. The energy transfer to rotational, vibrational and electronic degrees of freedom is roughly in the ratios (m/M) 1/2 :(m/M) 1/4 : 1 ~ 10- 3: 10-1 : 10. The probability of an inelastic collision is expressed in terms of the cross section defined as follows. Suppose that I o electrons of energy E o per unit area are incident on a gas consisting of N atoms or molecules per unit volume. Let the number of electrons scattered into the solid angle element df~ in the direction f~(0, qb) measured from the polar axis taken along the direction of electron incidence be written as Ion(~) = N I o dcYon(Eo,~)/d~
(1)
The subscript on indicates the transition from the ground state 0 to an excited or ionized state n. One calls the quantity dcYon(Eo,~)/d~ the differential cross section for the excitation 0 ~ n. Theoretically, the differential cross section is expressed in terms of the scattering amplitude fon(Eo,~), which is determined from the asymptotic behavior of the electron wavefunction, in the form dcYon(Eo, f~)/df~ = (k,/ko)lfo,,(Eo,
~'~)12
(2)
where ko is the magnitude of electron momentum before the collision, and k, the same after the collision. The integral of the differential cross section over all scattering angles, viz., qon(Eo)
=
f f d=on(Eo,n)/dn sin 0d0 dqb
(3)
is called the (integral) cross section for the excitation 0 -~ n. The elastic scattering cross section qo(Eo) is defined similarly, by replacing the final state n by the ground state 0 in Eqs. (1)-(3). In any discussion of the effects of elastic scattering on electron transport phenomena it is more important to use the momentum-transfer cross section defined by
q~(Eo) =
ff[d=o(Eo,
W)/d~](1 - cos0)sin0d0dqb
(4)
The sum of the cross sections given by Eq. (3) over all possible kinds of excitation (including the elastic-scattering cross section), viz.,
Q(Eo) = qo(Eo) + Y~qon(Eo) is called the total cross section.
(5)
Hiroshi Tanaka and Osamu Sueoka
If the distribution of particle speed v is given by F(v), then the reaction rate constant for a process with cross section q, is calculated as
k. = f q.V(v)v dv
(6)
Considerable progress has been made in developing theoretical approaches to the foregoing quantities. An element basic to any approach is the calculation of the electronic structure of molecules. For at least the ground and electronic state and low-lying excited states, nonempirical calculation techniques have been well advanced and thus general computer codes are available to perform calculations of electronic structure for a fixed geometry of at least a moderate number of nuclei (of not too high atomic numbers). Resulting adiabatic-potential energy surfaces are useful for treating some of the reactions involved in plasma chemistry. However, optimal calculations of this kind are still not fully automatic, and require a great deal of experience and intuition into the physics and chemistry involved, in addition to high-level computer skills. Intellectually more demanding is the scattering theory that is necessary for treating continuum states (Huo and Gianturco, 1995). A great deal of effort has been devoted to the development of various methods, including the R-matrix method, the Schwinger multichannel variational method, the close-coupling method, and the continuum multiple-scattering method, some of which have been successfully applied to problems of interest in plasma chemistry. This topic is fully discussed in the chapter by Kimura (2000) in this volume.
IV. Measurements of Electron Collision Cross Sections and Illustrative Results Several reviews (Christophorou, 1984; Trajmar and McConkey, 1994; Christophorou et al., 1996, 1997a, b, 1998, 1999) have been published on the measurements of electron-collision cross sections. In what follows, we shall concentrate on recent data pertinent to low-temperature plasmas. In view of the great variety of atomic and molecular species and of the different kinds of processes to be studied, it is necessary to choose the correct method for each measurement. There is no commercially available measurement system for general use in electron collision studies, and therefore it is a challenge to an experimenter to use the best ingenuity and insight to build a measurement system for his/her particular purposes. For applications
MECHANISMS OF ELECTRON TRANSPORT including plasma chemistry, absolute and correct cross-section values are required. Therefore, a meaningful measurement must be designed with full consideration of the limits of accuracy to be achieved. To this end, it is often necessary to improve the capability of instrumentation, and even to invent a new device based on novel ideas. As a result of continuing efforts over the last several decades, in recent years we have seen the advent of several new ways to approach quantitative data on electron-collision cross sections. Figures 1 (Zecca et al., 1996) and 2 illustrate cross-section data pertinent to plasma chemistry. Note that the behavior of the cross section differs greatly for each atomic or molecular species. For Xe, elastic scattering is the only process at kinetic energies below the (first) electronic threshold at 8.31eV, corresponding to the excitation 5 P 6 [1So] ~ 5Ps[zP3/216s. Near 0.8 eV there is a minimum of the elastic scattering cross section, known as the Ramsauer-Townsend effect (R-T). This means that an electron close to this energy is hardly scattered by Xe; in other words, Xe is virtually transparent to such an electron. The threshold for the emission of the resonance line used in the P D P is 8.43 eV. Ionization starts at its threshold of 12.13eV, above which secondary electrons are produced to sustain the plasma. Cross sections of a molecule are more complicated than those of an atom, because there are possibilities of vibrational and rotational transitions, and dissociation in addition to elastic scattering, electronic excitation,
FIG. 1. Electron collision cross sections of Xe.
10
Hiroshi Tanaka and Osamu Sueoka
FIG. 2. Total cross sections of representative molecules pertinent to plasma processing.
and ionization. Figure 2 includes the total cross sections for several important molecules as given by Eq. (5). The cross section of C4F8 shows a Ramsauer-Townsend minimum of around 3 eV. The cross sections of Sill 4 and CH 4 decrease with decreasing kinetic energy, suggesting the presence of the Ramsauer-Townsend effect at very low energies. As the authors of the data for Fig. 1 indicate, it takes efforts by many workers in many institutions to generate cross sections of a single species. More often than one would hope, results from different laboratories are discordant. Some of the data sets may be fragmentary. It is therefore necessary to collect as many sets of data as possible from the literature in order to assess their reliability and determine the most trustworthy set of data to be recommended for use in applications. Efforts toward such data compilation and analysis are being made by various groups, as described in the two chapters in this Volume by Christophorou and Olthoff (2000). A. MEASUREMENTS OF ELECTRON BEAM ATTENUATION FOR DETERMINATION OF AN UPPER BOUND OF CROSS SECTIONS
The total cross section Q given by Eq. (5) is an obvious upper bound of any of the individual cross sections. To determine Q, one may use the LambertBeer law familiar from photoabsorption. Suppose that one sends an electron beam of I o (of an ideally single momentum) per unit area energy into a gas consisting of p molecules (of a single species) per unit volume. If one determines the intensity I of those electrons passing through unit area at
MECHANISMS OF ELECTRON TRANSPORT
11
distance L in the gas, then one may write I / I o = e x p ( - p Q L ) . This relation is valid under a suitable condition of a single collision that occurs during the passage of the electron in the gas cell. Such a measurement is feasible for electrons of kinetic energies of between 0.3-1000eV or higher passing through common gases. This method has been extended recently to extremely low energies of several meV, by using photoelectrons emitted under certain conditions, as will be fully described in Section IV.C. We now describe a somewhat special apparatus, shown in Fig. 3a (Sueoka et al., 1994)], which was designed to measure the attenuation of either electrons or positrons from a radioactive source. A beam of electrons is obtained from secondary-electron emission from a thin foil of tungsten, which is used as a moderator for positrons. The resulting electron beam is stable in intensity, unlike a beam from a conventional hot-filament source, which is influenced by electron interactions with a sample gas. For determination of electron kinetic energies of < 30eV, a time-of-flight method is used, with the resulting resolution of ~0.1 eV. A uniform magnetic field is applied parallel to the electron beam so as to limit the spatial divergence of the beam. The apparatus appears to be simple in principle, but requires a great deal of ingenuity and care to achieve a precision of a few percent or better in measured results. The influence of a transmitted beam on the intensity of forward scattering must be corrected for by calculations. Measurements with positrons are fully discussed in a review article by Kimura et al. (2000). Sueoka and coworkers have carried out extensive and systematic measurements on various molecules (Kimura et al., 1999). Figure 2 shows resulting cross sections of some of the molecules often used in plasma processing. The individual cross sections that contribute to the total cross section Q of Eq. (5) have been determined by measurements using an electron-beam method as discussed fully in Section IV.C. For CH 4 for instance, the differential cross sections for elastic scattering and for vibrational excitation have been determined with considerable accuracy in order to permit good determination of the corresponding (integral) cross sections; the ionization cross section also has been carefully determined. Consequently, the knowledge of Q and these cross sections enable one to deduce from Eq. (5) that the (total) electronic-excited states of CH 4 are unbound, and dissociate into fragments CH x x = 0-3) or CH + (x = 0-3) (Kanik et al., 1993). Thus, we can determine the cross section for the formation of all fragments; however, the partition into each fragment species, viz., the determination of partial cross sections, requires separate measurements, which have recently begun to be carried out, as will be discussed fully in Section V. Concerning c-C4F 8 and the other molecules often used in plasma etching, unfortunately there are no measurements of
12
Hiroshi Tanaka and Osamu Sueoka
FIG. 3. (a) Apparatus to measure total cross sections using the attenuation method. (b) Apparatus to measure differential cross sections using the electron beam method.
MECHANISMS OF ELECTRON TRANSPORT
13
cross sections, except for the differential cross section for elastic scattering, which was obtained recently (Okamoto et al., 1999). B. THE SWARM METHOD LEADING TO A CROSS-SECTION SET
When many electrons are emitted from a source and enter into a gas of sufficiently high pressure under an applied uniform electric field, they undergo many collisions with gaseous molecules as a swarm (Crompton, 1994). Measurements can be made of many macroscopic properties of a swarm, including drift velocity, diffusion coefficient, and other transport coefficients, as well as the rate constants for excitations, ionization, and electron attachment. These macroscopic properties which are functions of the ratio of the electric-field strength to the gas density under certain conditions, can be related to electron-molecule collision cross sections through the Boltzmann equation governing the electron energy distribution. The swarm method provides a set of cross sections, especially at low electron energies (10eV), where the electron beam method is difficult to apply. However, the swarm method is incapable of giving partial cross sections for individual excitations precisely. Consequently, an analysis of swarm data usually takes into account some information from other measurements as well, and aims at determining a full set of cross sections in such a way that the set is consistent with all the available data. Figure 4 shows sets of cross sections of Sill 4 (Kurachi and Nakamura, 1990) and 0 2 (Itikawa et al., 1989; Shibata et al., 1995) thus determined. The momentum-transfer cross section q~t dominates at all kinetic energies shown. In Sill 4 for example, q~ has a minimum near 0.3 eV, where electrons pass through the gas almost freely. This minimum arises from the Ramsauer-Townsend effects, which we mentioned in connection with heavier rare gases (Ar, Kr, and Xe). To be specific, the phase shift of the s wave (1 = 0) is an integral multiple of n at this kinetic energy, and higher partial waves contribute inappreciably at such a low energy. With a minute addition of Sill 4 in Ar, transport coefficients are influenced by the vibrational excitation of Sill 4 near the Ramsauer-Townsend minimum of Ar. Indeed, N a k a m u r a and coworkers took advantage of this phenomenon to determine the vibrational-excitation cross section. The cross sections of 0 2, which are important to many applications, were determined by Itikawa et al. (1989) by considering swarm data and all other pertinent information. The cross sections for inelastic collision, including vibrational excitation, electron attachment, electronic excitation, dissociation and ionization, usually rise steeply above the corresponding threshold energies. Their behavior shows a characteristic pattern strongly dependent on molecular species. In general, numerous electronically excited states contribute to the cross sections for electronic excitation, dissociation, and ionization; even for
14
Hiroshi Tanaka and Osamu Sueoka
FIG. 4. Electron collision cross-section sets.
MECHANISMS OF ELECTRON TRANSPORT
15
02, for which the knowledge of cross sections is better than for other molecules, detailed partial cross sections currently remain obscure. Alternatively, the modeling of a discharge plasma with the use of a cross-section set and comparison of results with measurements of plasma properties provide to some extent a test of the reliability of the cross-section set. Thus, the swarm experiment and the modeling are complementary to each other, and both contribute to the elucidation of plasma properties, and at the same time to the systemization of cross sections. Indeed, the comprehensive determination of major cross sections of atoms and molecules for electron collisions is the ultimate goal of endeavors described in this chapter. C. THE ELECTRON BEAM METHOD FOR MEASURING THE ANGULAR DEPENDENCE OF EXCITATION PROCESSES The electron beam method (Trajmar and Register, 1984) is often used to study the partition of the total cross section among different excitation processes, that is, the partial (excitation) cross sections. In this method, one sends a well-collimated beam of electrons of a fixed kinetic energy E o into a molecular target at low pressure and analyzes the kinetic energies of scattered electrons. Energy analysis of electrons scattered by a fixed (measured from the direction of the incident-electron beam) leads to the determination of the differential cross section as given by Eq. (2). This method provides much more detailed information compared to that provided by the attenuation method, and certainly reflects the dynamics of electron collisions. The most commonly used of the electron analyzers include 127 ~ electrostatic cylinders and 180~ hemispheres. They are also used as monochromators, which select electrons of a chosen kinetic energy to generate an incident beam. A hot filament is commonly used as a source of electrons, with an energy spread of 0.3-0.5eV. After energy selection with a monochromator at a resolution of about 30 meV, a beam of intensity of about 10-9A is usually obtained. In general there is a reciprocal relation between energy resolution and beam intensity. In order to maintain the single-collision condition, the pressure of a gas target must be kept at about 10-3 torr, resulting in a limited scattering intensity. This is in sharp contrast with electron spectroscopy of a solid surface, which has a much higher atomic density and thus readily accomplishes energy resolution of several meV. One often plots the intensity of electrons scattered into a fixed angle as a function of the energy loss AE (i.e., the incident electron energy minus the scattered electron energy), for a fixed incident electron energy. Such a plot is called an electron energy-loss spectrum. Figure 5 shows energy-loss spectra of CF 4 (Kuroki et al., 1992)and O 2 (Allan, 1995).
16
Hiroshi Tanaka and Osamu Sueoka
FIG. 5. Overview of the electron energy loss spectra for 0 2 and
C F 4.
MECHANISMS OF ELECTRON TRANSPORT
17
1. Differential Cross Section for Elastic Scattering In an energy-loss spectrum such as the one for 0 2 in Fig. 5, the peak at zero energy loss (AE = 0) represents the elastic-scattering intensity, and is proportional to the differential cross section for elastic scattering provided that the spectrum has been taken under optimal conditions. It used to be difficult to determine an absolute scale of the differential cross section with the electron-beam method. For this purpose one now commonly uses the relative-flow method (Srivastava et al., 1975), in which the peak intensities of a molecule to be studied are compared with peak intensities of He. The established knowledge of the He differential cross sections then leads to absolute values of the differential cross sections of the molecule. Once the differential cross section for elastic scattering has been determined, the differential cross section for inelastic scattering, for which AE 4= 0, can be readily determined. This method has been established, although room for improvement still remains. Differential cross sections for elastic scattering by atoms and molecules pertinent to plasma processing have been measured for scattering angles 10-130 ~ and incident energies 15-100eV (Tanaka and Inokuti, 1999). The accuracy is almost certainly better than 10-20%. For illustration, results of measurements on CHxFy (x, y = 0-4) are shown in Fig. 6 (Tanaka et al., 1997). Here one sees the variations of the elastic-scattering cross sections upon successive substitutions of H atoms with F atoms. Moreover, peculiar angular distributions are demonstrated clearly between nonpolar and polar molecules in the results at 1.5 eV in Fig. 6.
2. Vibrational Excitation and Resonance Phenomena Those electrons that have kinetic energies below the first electronic-excitation threshold, called subexcitation electrons, slow down even more with energy losses due to elastic scattering, rotational excitation, and vibrational excitation, at a rate much smaller than electrons of higher energies. Eventually the subexcitation electrons become thermalized when the loss and gain of energy upon collision with molecules are in balance (Kimura et al., 1993). The whole process is important to plasma properties. Let us consider collisions leading to rotational and vibrational excitations. When an electron approaches a molecule, it feels a nonspherical charge distribution of the molecule, as often represented by the dipole, quadrupole, and in general multipole moments, which include both an electrostatic part (due to the initial molecular charge distribution) and an induced part (due to the polarization by the approaching electron). Therefore, it is straightforward to see that the electron exerts a torque on the molecule, leading to rotational
18
Hiroshi Tanaka and Osamu Sueoka
FIG. 6. Elastic differential cross sections for C H x d F r (x, y = 0 - 4 ) molecules. Note that data for the D C S for C F 4 are obtained for 35 eV.
excitation (or de-excitation). Molecules in plasma processing are mostly in rotationally excited states, and the distribution over rotational states should play a role in chemical reactions. Unfortunately, the electron-beam method is currently hardly capable of resolving individual energy levels (except for hydrogen and hydride molecules). Measurements so far have dealt with an envelope of rotational structure in an energy-loss spectrum, giving only gross information. Among molecules used in the etching process, data on
MECHANISMS OF ELECTRON TRANSPORT
19
chlorine have been reported (Gote and Ehrhardt, 1995; Christophorou and Olthoff, 2000). An electron approaching a molecule exerts not only a torque but also a force that causes changes in internuclear distances. This leads to vibrational excitation. In the Sill 4 molecule, which is tetrahedral, there are four normal modes with frequencies of v 1, v2, v a, and v4. As Fig. 4a shows, the excitations of v I + v 3 and v2 + v4 have appreciable cross sections. In the O2 molecule, one sees a comb-like structure in the energy-loss spectrum as in Fig. 4b, which corresponds to the X32;0- electronic state. Figure 7a shows results of recent high-resolution measurements, in which spin-orbital splitting is revealed clearly (Allan, 1995). We often invoke the idea of a resonance to interpret a sharp variation of the cross section as a function of incident energy. Theoretically, a resonance means a temporary bound state of an electron with a molecule that is formed by an effective-potential well, for instance due to the combination of the (repulsive) centrifugal force for a definite orbital angular momentum and an (attractive) molecular potential. The temporary bound state may be viewed as an excited state of a negative ion, that is, the system of the neutral molecule plus the electron, which may or may not be bound in its ground state. If the temporary bound state is sufficiently stable against auto-detachment, viz., dissociation into the original molecule and the electron, and has a lifetime much longer than a period of vibration, then the nuclei will experience forces that are different from those in the original molecule. This causes conversion of a part of electronic energy to nuclear vibrational degrees of freedom. This mechanism of vibrational excitation can be more efficient than a direct transfer of electronic energy to nuclear motion, which can occur at any electron energy above the threshold energy but is, in general, much less efficient due mostly to the large ratio of the nuclear mass to the electron mass. In this way, we understand the prominence of vibrational excitation in the examples of Figs. 4a, b. The resonance, or the temporary negative-ion state, is also important as a mechanism of dissociative electron attachment, resulting in the formation of stable negative-ion fragments. As a qualification, the structure near the threshold of vibrational excitation in Sill 4 remains a mystery. High-resolution measurements permit determination of the energy dependence of the cross section of excited electronic states, for example, the a~A and b~Eg + states of O2, as shown in Fig. 7b (Allan, 1995). The structure around 4eV diminishes for higher vibrational levels. This is due to a resonance O2(2110) occurring at 0.3-1eV, as seen in Figs. 4b and 7a. One also sees an electron energy of 8eV. The resonance at 6.5eV also is responsible for the dissociative electron attachment, viz., O2(21-I0) O-(2P)-+-O(3p), with an appreciable cross section, as seen in Figs. 4b and 5.
20
Hiroshi Tanaka and Osamu Sueoka
FIG. 7. (a) Elastic and vibrational (v = 1) excitation DCS. (b) Energy dependence of the DCS for exciting the v = 0 and selected higher vibrational levels of the alA0 and blEg +.
MECHANISMS OF ELECTRON TRANSPORT
21
3. Measurements of the Differential Cross Section over the Complete Range of Scattering Angles The electron-beam method has a main drawback, that is, scattering angles over which measurements can be carried out are limited for three reasons. First, it is difficult to extend measurements to backward scattering, usually beyond a maximum scattering angle of ~ 160 ~ because of the geometrical restrictions of an electron analyzer. Second, it is also difficult to distinguish elastic scattering at 0 ~ from unscattered incident electrons. Third, good angular and energy resolutions require minimization of magnetic fields, including the earth's magnetic field and fields due to residual magnetization of electron-analyzer materials, which markedly influence electrons of low kinetic energies. To overcome these difficulties, an innovation has been proposed. (Zubec et al., 1999; Asmis and Allan, 1997). The basic idea is to introduce into a collision region a suitably controllable magnetic field generated by several electromagnetic doils, which will guide those electrons scattered at inaccessible forward and backward scattering angles to a direction suitable for analysis. A combination of the coils is designed so that the magnetic field does not leak outside the collision region. Figure 8 (Cubric et al., 1997a, b) shows the complete angular distributions resulting from the excitation to the 23S, 21S, S3p, and 21p states of He, which is used in plasma-display panels, and as discussed in Section II.A. The excited states, except for 2a p, have long radiative lifetimes, and are energy donors in energy transfer to Xe. The integral of the differential cross sections of Fig. 8 gives the (integrated) cross sections for the excited state of He at 40eV. In the past, the integration of the differential cross section always required an extrapolation of data into scattering angles beyond a range of observation, and this was a source of significant uncertainty. The new method will eliminate this uncertainty and improve the accuracy of the measured results. It is also valuable in the sense that the forward and backward cross sections are particularly important for testing the adequacy of various approximations in scattering theory.
4. Electron Spectroscopy at Ultrahigh Resolution Energy resolution of about 10meV has been achieved recently through improvements in convergence and transmission of an electron beam through the entrance and exit of a hemispherical analyzer, optimal selection of analyzer material (e.g., molybdenum (Mo)), and care in magnetic shielding. Another improvement is the tandem use of monochromators and analyzers, which renders the shape of an energy-loss peak more accurate and the
22
Hiroshi Tanaka and Osamu Sueoka
FIG. 8. Differential cross sections for e + He scattering over the complete range of scattering angles.
baseline of the energy-loss spectrum very nearly flat. An example of such a clean energy-loss spectrum of O2, thus obtained, is seen in Fig. 5. Notice the range of intensities varying over seven orders of magnitude and representing elastic scattering, vibrational excitation, and electronic excitation. The data have been taken at the constant residual energy E, = Eo - AE = 2 eV, while the incident energy Eo is varied from 3 to 12eV; results are plotted as a function of the energy loss AE = 1-10 eV.
MECHANISMS OF ELECTRON TRANSPORT
23
As we pointed out earlier, 0 2 is important in the C F 4 - O 2 mixture used in the etching process. Electron collisions excite O2 to a band of excited states lying between 9.7 and 12.1 eV, which dissociate to produce excited O*, which are in turn effective for polymer ashing. Dissociative electron attachment occurring at an electron energy of 6.5 eV causes accumulation of O in a discharge of O 2, while excited atoms O* produced in the same process give O 2 atoms and electrons, which help in the maintenance of the plasma, as shown by a recent modeling study (Shibata et al., 1995b). Recall that cross-section data are essential to such a study.
5. Scattering of Electrons of Ultralow Energies At electron energies of < 1 eV, the electron-beam method is difficult to apply, and measurements have been made chiefly by use of either the attenuation or the swarm method. The use of photoelectrons produced by synchrotron radiation (Lunt et al., 1994) (instead of electrons from hot filaments) has been introduced for measurements of differential and integral cross sections. A beam of monochromatized light of 786.5 ~ from a synchrotron radiation source is used to excite Ar to an auto-ionizing state, which auto-ionizes into Ar+(ZP3/2) and an electron of 5meV-4.0eV, with an excellent resolution of about 5 meV, although the intensity is weak (corresponding to a current of about 10 - l ~ A). Scattered electrons are analyzed by an ordinary 180~ hemispherical analyzer. Great care is necessary to account for the contact potential of the analyzer material, and to prevent leakage of an electric field outside the electrode region. Figure 9 shows results of measurements (Lunt et al., 1994) on CH 4. The differential cross section at a fixed scattering angle is plotted as a function of the collision energy E o = 150-400meV and energy loss AE = 0 represents elastic scattering, exhibiting a Ramsauer-Townsend minimum reminiscent of Xe. At E o = 0.16eV, one sees the threshold for the vibrational excitation v2 + v4. The data shown here are on a relative scale. Efforts are now being devoted to putting differential cross sections at ultralow energies on an absolute scale, but their total cross sections have been determined in an absolute one.
V. Measurements of Partial Cross Sections with the Use of the Appearance Potential in Mass Spectrometry Molecules in general have many internal degrees of freedom and, therefore, their spectra exhibit many overlapping excited states, even in the case of
24
Hiroshi Tanaka and Osamu Sueoka
FIG. 9. Differential cross sections for e + C H , of ultralow energy.
diatomic molecules. It is difficult to obtain full information about individual excited states from an electron energy-loss spectrum alone (see the electron energy-loss spectra of 0 2 and CF 4 in Fig. 7). Now, Sugai and Toyoda (1992) have demonstrated the possibility of detecting nonfluorescent fragments resulting from dissociation of polyatomic molecules in excited states. We will discuss the production of the measurements using the fact that the appearance potential of the CF~- ion differs for different parent species: 14.3 eV for the parent molecule C F 4 and 10.4eV for the parent radical CF 3. In the first collision region electron collisions with CF4 produce CF 3 radicals, which are then led to a differentially pumped ionization chamber of a mass spectrometer and some of them are ionized by collisions with electrons from a second source. Although some of the original CF 4 also enters the ionization chamber, only those CF~ originating from CF3 radicals are detected if the electron energy in the ionization chamber is kept at < 14.3 eV, viz., the threshold for CF~ production from CF2. However, this procedure alone does not discriminate against CF~ ions originating from thermal decomposition on the hot filament used as an electron source in the ionization chamber. Therefore, the electron beam in the first collision region is turned on and off, and the part of the CF~- signal that appears simultaneously with the electron beam in the first collision region is registered. Sugai et al. (1992, 1995, 1999) have studied many radicals in this way, and contributed substantially to the elucidation of plasma chemistry.
MECHANISMS OF ELECTRON TRANSPORT
25
Another method for detecting neutral radicals has been based on the absorption of radicals on a tellurium surface (Motlagh and Moore, 1998), which revealed them to be quite different in magnitude and/or shape from the results obtained by Sugai et al. Figure 10 shows the cross sections for production of fluoromethyl radicals by neutral dissociation and dissociative ionization from electron impact on fluromethanes (Motlagh and Moore, 1998). Theoretical calculations on electron-impact excitation of polyatomic molecules have begun to be performed by Winstead et al. (1994), who applied the multichannel Schwinger variational method to calculations of cross sections for dissociation of Sill 4 through the first triplet state (at the excitation energy of 9.88 eV, leading to Sill 2 + H 2 and Sill 2 + 2H), and 1T 2 and 3T 2 states (arising from the 2t 2 ~4Saa transition) by collisions of electrons of 10-40 eV. Winsted et al. predicts the dominance of the dissociation into Sill a. A comparison of these results with recent measurements [Sugai, 1999] is urgently desired.
VI. Measurements of Cross Sections for the Production of Positive and Negative Ions A. IONIZATIONPROCESSES Ionization in general is crucial as a source of electrons to maintain discharges. The kinetic energies of secondary electrons are mostly < 20 eV, nearly independent of the incident electron energy. This fact is reflected in the energy distribution of the bulk plasma. Positive ions in general influence the quality of both a film produced by plasma chemical-vapor deposition (CVD) and a trench in the Si or SiO 2 substrate by ion-enhanced plasma etching, and therefore control of positive ions is important. A method based on combining a Nier-type ion source and a mass spectrometer is simple to use in studies on positive ions, although it may not be fully adequate for quantitative measurements. Positive ions are produced by electron-molecule collisions in an ionization chamber and are then drawn out by an electrode with three apertures. Precautions are necessary to prevent leakage of an electric field of the electrode into the collision region. The efficiency of ion collection and other items affecting the sensitivity of the mass spectrometer must be fully studied, so that correction on a measured signal may be made if necessary. Figure 11 shows the partial ionization cross sections of CF4 (Poll et al., 1992). One sees here the dominance of CF~ ions. The abundance of CF~- and CF + ions alters below and above the incident energy of about 60eV. These trends are similar to the abundance of neutral radicals seen earlier (Sugai et al., 1995).
Hiroshi Tanaka and Osamu Sueoka
26 2.0
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MECHANISMS
OF ELECTRON TRANSPORT
27
Electron energy (eV) FIc. 11. Absolute partial electron impact ionization cross sections vs electron ions of CF 4.
B.
DISSOCIATIVE ELECTRON ATTACHMENT
As already pointed out, the electron attachment process (Chutjian et al., 1996; Illenberger, 1999) is closely related to the temporary negative-ionic states. For instance, 0 2 gives rise to the reaction, for example, e + Oe(X3E~-)--, O 2 ( 2 1 - - I u ) - - - * O - ( 2 P ) -+- O(3p) upon collisions with electrons at 6.5 eV, leading to the dissociative attachment process through a short-lived negative ion. By contrast, collisions with electrons at 0.3-1.0eV leads to O2"(2I]0) in a vibrationally excited state (v~4). Subsequent thermal collisions with a third-body M stabilizes this negative ion, viz., O2 (21--I0,v < 3) -k- M. One can term this process nondissociative electron attachment. The halogen-containing molecules C F 4 , S F 6 , C12, CC14, etc. used in the etching process, as well as O2, are called electronegative, and first form short-lived and stable negative ions. The Sill 4 molecules used in CVD also provide negative ions in a similar fashion. The microwave-cavity method using pulse radiolysis (Shimamori, 1995) is suitable for measurements of cross sections for the attachment of electrons
28
Hiroshi Tanaka and Osamu Sueoka
near thermal energy. A microwave cavity is filled with a sample gas, and is irradiated with a nano-second pulse of high-energy electrons from an accelerator, or with pulsed x-rays produced by such high-energy electrons. The purpose is to generte high-energy electrons uniformly in the cavity. These electrons collide with gas molecules, and rapidly degrade down to near-thermal energies. Applied microwave powers accelerate electrons and provide a tunability of electron energies. The absorption of microwave power is readily related to electron density. Analysis at the resonance frequency of the microwave cavity as a function of time leads to the determination of the rate constant for electron attachment, and hence of the attachment cross section as a function of electron energy. Shimamori (1995) systematically studied electron attachment processes to many halogencontaining molecules. Recent topics related to electron attachment include the use of photoelectrons resulting from laser-induced ionization and of high Rydberg states (Dunning, 1995). Metastable states (3P2) of Ar produced in a discharge are led to a collision chamber filled with a sample gas. Then, light from a single-mode dye laser is used to pump the metastable states to Ar*(aD3) states, and light from another tunable laser ionizes the metastable states (Ar*(aD3)) to produce very low-energy photoelectrons. In this way, photoelectrons of energies 0-230meV are obtained with a current of about 10-12 A. Negative ions resulting from attachment of these electrons to gas molecules are detected with a mass spectrometer. Another method of study involves exciting K atoms to high Rydberg states with a dye laser, and then detecting negative ions formed in collisions with the Rydberg states of sample molecules. The time-averaged kinetic energy of the excited electron, which is equal to its binding energy, depends on the principal quantum number n and can be very small. For n = 1100, the largest value of n at which measurements have been undertaken so far, the mean electron kinetic energy is only ~ 11 geV. Very high-n atoms, therefore, provide a unique opportunity to study electron-molecule interactions at ultralow electron energies. Both of these methods provide high resolution and are complementary to the microwave-cavity method. They also promise to yield a detailed understanding of the attachment processes, including the role of rotational and vibrational degrees of freedom (Leber et al., 1999). Figure 12 shows results of measurements (Schramm et al., 1998) on SF 6. Makabe (Shibata et al., 1995a) has treated the role of negative ions in pulse radio-frequency excited plasmas to yield modeling studies, and has pointed out their importance in the processing of semiconductor surfaces.
MECHANISMS OF ELECTRON TRANSPORT 9 1
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VII. Outlook As described in Section IV, the high-resolution spectra of C F 4 (Kuroki et al., 1992) and O 2 (Allan, 1995) should contain much important information. However, angular integrated quantities based on complicated loss spectra are necessary for an application to plasma processing. Gases used in plasma processing are rather complicated polyatomic molecules, and because the energy spectra of these molecules may be rather complicated, determination of the differential cross section (DCS) from each energy spectrum may be almost impossible. On the other hand, measurements of the energy loss spectrum and the DCS of the inelastic scattering are feasible if less fine energy resolution is acceptable to use. Recently, DCS data for the energy loss spectrum of scattered electrons in the 100-3000eV range have been obtained by Grosswendt and Baek (PTB) using a resolution of 2% (Grosswendt, 1999). Observed peaks, due to ionization and electronic excitation
30
Hiroshi Tanaka and Osamu Sueoka
in the spectrum, can not be discriminated because of the energy resolution. However, the integrated cross-section data for the sum of ionization and all excitation channels may be derived from their DCS data. These data may be useful for application. Even though one's experimental method does not offer sufficiently high precision, applying this method to a wide type of molecules and obtaining cross-section data systematically is an important first step for further process in plasma processing. This chapter has focused on electron collisions with atoms and molecules, considered to be the initiator of discharge plasma. In order to be truly valuable to plasma chemistry, studies on the kind of survey noted here must aim at determining differential cross section comprehensively, that is, for a broad range of incident energy, energy loss, and a scattering angle in which the differential cross section is appreciable, and for a broad variety of atomic and molecular species. Indeed, for almost any application, the cross-section data must be comprehensive, absolute, and (of course) correct. Work toward this goal is tedious and demanding. It might appear to lack the charm of frontier science. However, studies of electron collisions with atoms and molecules are a major unsolved problem of basic physics in the sense that the subject of study concerns many-body systems (specifically in highly excited states) and there is much potential for new basic physics discoveries. For instance, an ionizing collision of an electron with any atom or molecule concerns a system with two unbound electrons in the field of a remaining ion, which remains poorly understood in general, especially when the two electrons both leave with kinetic energies that are low as compared to the binding energies. The need for cross-section data that are comprehensive, absolute, and correct points to the desirability of data compilation and assessment through joint efforts involving many knowledgable works and international collaboration. This is indeed now recognized, as seen in the ongoing program for data compilation (Christophorou and Olthoff, 1999, 2000) and in recent meetings such as the International Conference on Atomic and Molecular Data and Their Applications (Mohr and Wiese, 1997; Tennyson et al., 1998).
VIII. Acknowledgments We would like to thank Dr. M. Inokuti and Dr. M. Kitajima for their assistance in preparing this manuscript. This work was supported in part by a Grant-in-Aid from the Ministry of Education, Science, and Culture through Yamaguchi University.
MECHANISMS OF ELECTRON TRANSPORT
31
IX. References Allan, M. (1995). J. Phys. B: At. Mol. Opt. Phys. 28: 4329; J. Phys. B: At. Mol. Opt. Phys. 28:5163. Asmis, K. R. and Allan, M. (1997). J. Phys. B: At. Mol. Opt. Phys. 30: 1961. Bruno, G., Capezzuto, P., and Madan, A. (eds.). (1995). Plasma Deposition of Amorphous Silicon-Based Materials, San Diego: Academic Press. Christophorou, L. G. (ed.). (1984). Electron-Molecule Interactions and Their Applications, Orlando: Academic Press. Christophorou, L. G., Olthoff, J. K., and Rao, M. V. V. S. (1996). J. Phys. Chem. Ref Data 25: 1341. Christophorou, L. G., Olthoff, J. K., and Rao, M. V. V. S. (1997a). J. Phys. Chem. Ref Data 26: 1. Christophorou, L. G., Olthoff, J. K., and Wang, Y. (1997b). J. Phys. Chem. Ref Data 26: 1205. Christophorou, L. G. and Olthoff, J. K. (1998). J. Phys. Chem. Ref Data 27: 889. Christophorou, L. G. and Olthoff, J. K. (1999). J. Phys. Chem. Ref Data 28: 131. Christophorou, L. G. and Olthoff, J. K. (2000) two chapters in this volume. Chutjian, A., Garscadden, A., and Wadehra, J. M. (1996), Phys. Reports 264: 393. Crompton, R. W. (1994). in Cross Section Data, M. Inokuti, ed., (San Diego: Academic Press, p. 97. Cubric, C., Mercer, D., Channing, J. M., Thompson, D. B., Cooper, D. R., King, G. C., Read, F. H., and Zubek, M. (1997). in International Symposium on Electron-Molecule Collisions and Ion and Electron Swarms, Abstract of Contributed Papers, 27/1, Engelberg (Switzerland), M. Allan, ed., p. 27/1. Cubric, C., Mercer, D., Channing, J. M., Read, F. H., and King, G. C. (1997b). in International Conference on the Physics of Electronic and Atomic Collisions, Vienna, July 1997, Abstract of Contributed Papers, F. Aumary, G. Betz, and H. P. Winter, eds., p. MO 091. Deils, J. C., Bernstein, R., Stalnkopf, K. E., and Zhao, X. M. (1997). Sci. Am. Aug. 30. Dunning, F. B. (1995). J. Phys. B At. Mol. and Opt. Phys. 28: 1645. Leder, E., Weber, J. M., Barsotti, S., Ruf, M.-W., and Hotop, H. (1999). in International Symposium on Electron-Molecule Collisions and Swarms, Tokyo 1999, p. 54. Gote, M. and Ehrhardt, H. (1995). J. Phys. B: At. Mol. Opt. Phys. 28: 3957. Goto, T. (2000). Chapter in this volume: Grosswendt, B. (1999). Private communication. Huo, W. M. and Gianturco, F. A. (eds.). (1995). Computational Methods for Electron-Molecule Collisions, New York: Plenum Press. Illenberger, E. (1999). in International Symposium on Electron-Molecule Collisions and Swarms, Tokyo 1999, p-51. Inokuti, M. (ed.). (1994). Cross Section Data, San Diego: Academic Press. Itikawa, Y., Ichimura, A., Onda, K., Sakimoto, K., Takayanagi, K., Hatano, Y., Hayashi, M., Nishimura, H., and Tsurubuchi, S. (1989). J. Phys. Chem. Ref Data 18: 23. Japan Society of Applied Physics (ed.). (1993). Amorphous Silicon, Tokyo: Ohm Publ. p. 45. Kanik, I., Trajmar, S., and Nickel, J. C. (1993). J. Geophys. Res. 98: 7447. Kimura, M. (2000). See chapter in the present volume. Kimura, M., Inokuti, M., and Dillon, M. A. (1993). Adv. Chem. Phys. 84: 193. Kimura, M., Sueoka, O., Hamada, A., and Itikawa, Y. (2000). Adv. Chem. Phys. 111: 537. Kurachi, M. and Nakamura, Y. (1991). IEEE Trans. Plasma Sci. 19: 262. Kuroki, K., Spence, D., and Dillon, M. A. (1992). J. Chem. Phys. 96: 6318. Lieberman, M. A. and Lichtenberg, A. J. (1994). Principles of Plasma Discharges and Material Processing, New York: John Wiley and Sons, Inc.
32
Hiroshi Tanaka and Osamu Sueoka
Lunt, S. J., Randell, J., Zresel, J. P. Mortzek, G., and Field, D. (1994). J. Phys. B: At Mol. Opt. Phys. 27: 1407. Makabe, T. (2000). See chapter in the present volume. Matsuda, A., Mishima, S., Hasezaki, K., Suzuki, A., Yamasaki, Y., and McElheny, P. J. (1991). App. Phys. Lett. 58: 2494. Mohr, P. J. and Wiese, W. L. (eds.). (1997). in Atomic and Molecular Data and Their Application, ICAMDATA--First International Conference, Gaithersburg, Oct. 1997, Woodbury, New York: AIP. Motlagh, S. and Moore, J. H. (1998). J. Chem. Phys. 109: 432. NRC Report (1991). Plasma Processing of Materials: Scientific Operations and Technological Challenges, Washington: National Academy Press. NRC Report (1996). Modeling, Simulation, and Database Needs in Plasma Processing, Washington: National Academy Press. Okamoto, M., Hoshino, M., Sakamoto, Y., Watanabe, S., Kitajima, M., Tanaka, H., and Kimura, M. (1999). in International Symposium on Electron-Molecule Collisions and Swarms, Tokyo, July 1999, p. 191. Poll, H. U., Winkler, C., Margreiter, D., Grill, V., Mark, T. D. (1992). Int. J. Mass Spectrom. Ion Proc., 112: 1. Shibata, M. Makabe, T., and Nakano, N. (1995a). Jpn. J. Appl. Phys. 34: 6230. Shibata, M., Nakano, N., and Makabe, T. (1995b). J. App. Phys. 77: 6181. Shimamori, H. (1995). in International Symposium on Electron-and Photon-Molecule Collisions and Swarms, Berkeley, July 1995, p. B-1. Shramm, A., Weber, J. M., Kreil, J., Klar, D., Ruf, M.-W., and Hotop, H. (1998). Phys. Rev. Lett. 81: 778. Sobel, A. (1998). Sci. Am. May 48. Srivastava, S. K., Chutjian, A., and Trajmar, S. (1975). J. Chem. Phys. 63: 2659. Sueoka, O., Mori, S., and Hamada, A. (1994). J. Phys. B: At. Mol. Opt. Phys. 27: 1453. Sugai, H. (1999). in International Conference on the Physics of Electronic and Atomic Collisions, Sendai, July 1999, Invited Talk. Sugai, H. and Toyada, H. (1992). J. Vac. Sci. Technol. A10: 1193. Sugai, H., Toyoda, H., Nakano, T., and Goto, M. (1995). Contri. Plasma Phys. 35: 415. Tanaka, H. and Inokuti, M. (1999). in Fundamentals in Plasma Chemistry, M. Inokuti, ed., San Diego: Academic Press. Tanaka, H., Masai, T., Kimura, M. Nishimura, T., and Itikawa, Y. (1998). Phys. Rev. 56: R3338. Tennyson, J., Mason, N. J., Mitchell, J., and Gianturco, F. (eds.). (1998). in Electron-Molecule Collision Data for Modeling and Simulation of Plasma Processing, Lyon: Trajmar, S. and McConkey, J. W. (1994). in Cross Section Data, M. Inokuti, ed., San Diego: Academic Press, p. 63. Trajmar, S. and Register, D. (1984). Electron Molecule Collisions, K. Takayanagi, and I. Shimamura, eds., New York: Plenum Press, p. 427. Winstead, C., Pritchard, H. P., and McKoy, V. (1994). J. Chem. Phys. 101: 338. Winstead, C., Sun, Q., and McKoy, V. (1991). J. Chem. Phys. 98: 2132. Zecca, A., Karwasz, G. P., and Brusa, R. S. (1996). Rev. Nuovo Cim. 19: I. A, 56, R3338. Zubek, M., Mielewska, B., Channing, J., King, G. C., and Read, F. H. (1999). J. Phys. B: At. Mol. and Opt. Phys. 32: 1351.
ADVANCES IN ATOMIC, MOLECULAR,AND OPTICAL PHYSICS,VOL. 44
T H E O R E T I C A L C O N S I D E R A T I O N OF PLA S M A - P R 0 CESSING PR 0 CESSES M I N E O K I M URA Graduate School of Science and Engineering Yamaguchi University Yamaguchi 755-8611, Japan I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. An Example of Electron-Molecule Scattering . . . . . . . . . . . . . . . . . . . . A. N 2 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Overview of Theoretical F r a m e w o r k . . . . . . . . . . . . . . . . . . . . . . . . . . A. General Scattering Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. A Close-Coupling Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Variational M e t h o d s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. The R-Matrix M e t h o d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. C o n t i n u u m Multiple-Scattering (CMS) M e t h o d . . . . . . . . . . . . . 5. Zero-Energy Limit: The Scattering Length Theory . . . . . . . . . . . 6. The Perturbative Treatment: The Born Approximation . . . . . . . B. Electron-Molecule Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Static and Correlation-Polarization Interaction . . . . . . . . . . . . . 2. Exchange Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Current Level of the Accuracy of Theoretical Approaches . . . . . . . . . . A. An Example of CO2: Vibrational Excitation . . . . . . . . . . . . . . . . . V. Excited Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Perspective and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33 34 35 37 38 39 40 41 41 42 44 45 46 48 49 51 53 55 56 56
Abstract: Theoretical investigation for various processes resulting from electronmolecule collisions has progressed significantly in the last decade. In addition to the availability of high-power computers, the significant development of theoretical models also contributes to the prosperity of the field. Moreover, large and high-precision calculations for some processes in electron scattering from polyatomic molecules have become feasible. This chapter gives the b a c k g r o u n d of theoretical models frequently used in order to provide the rationale to measurements and data compilation discussed in other chapters of this volume.
I. Introduction Low-temperature plasma etching is effectively achieved by three major stages: (i) production of initial electrons by the electric discharge; (ii) production of a variety of ions and radicals through electron-molecule 33
Copyright 92001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003844-7/ISSN1049-250X/01$35.00
34
Mineo Kimura
collisions; and (iii) transportation of selected ions and radicals to surfaces. Initial electrons produced in the first stage occupy a wide range of the energy spectrum from a few ten electronvolts down to thermal energy, and upon collisions with "seed-gas" molecules, they initiate a variety of elastic and inelastic processes, including electronic, vibrational and rotational (ro-vibrational) excitation, ionization, attachment and dissociation (first step). Most of these electronically excited molecules, or ionized molecular ions, are not stable species, thus undergoing break-up processes to fragment neutral radicals and ions. These radicals and ionic species are chemically highly reactive, and include several different kinds of chemical species. They begin to initiate, in turn, various types of chain reactions among themselves and surfaces (second step) (Tanaka and Sueoka, 2000; Christophorou and Olthoff I and II, 2000; Goto, 2000; Makabe, 2000). Vibrationally and rotationally (ro-vibrationally) excited molecules are the more commonly produced species and are also highly reactive requiring special care to treat. In normal etching, low-pressure and high-density conditions are needed because low-radical and ion pressure reduce collision events, thereby preventing further secondary reactions from occurring. Also the high density of specific radicals increases surface reactions efficiently. Thus the whole process involves many species of fragments and a very complex series of reactions in both steps. As a result, it is impossible and not practical for a single laboratory to investigate all of these dynamical processes and species. This suggests the necessity of a close collaboration between experiment and theory. This chapter provides a theoretical basis for how one can determine necessary scattering cross sections in the plasma environment, how to understand general features and systematics of cross sections for various processes, and how to assess the accuracy of these cross sections. Finally, the current level of understanding of the scattering processes is reviewed. For more complete information of general aspects in electronic and atomic collisions, readers are advised to consult comprehensive books by McDaniel (1992), and McDaniel, Mitchell, and Rudd (1996).
II. An Example of Electron-Molecule Scattering Upon collisions with molecules, a target molecule undergoes various dynamical processes because it has a large number of quantum states (electronic, vibrational and rotational states). Depending on which quantum state the molecule initially has, a quite different final state should emerge after the collision. For example, as we will see later in more detail, the dissociative attachment cross section of a HC1 molecule is known to increase
C O N S I D E R A T I O N S OF P L A S M A - P R O C E S S I N G PROCESSES
35
by two orders of magnitude when the initial vibrational state changes from v = 0 to v = 1. Under usual conditions, the plasma-etching facility operates at room temperature and slightly above normal pressure. In this environment, most of seed gas molecules are in ro-vibrational excited states, although electronically they may be in the ground state. Hence it is important to take into account the effect of these excited states when accurate cross-section data are evaluated. Also, considering these additional conditions of excited species poses further challenges to both theorists and experimentalists. We will employ N 2 as an example because it is well studied (Itikawa et al., 1986). This allows us to overview the general cross-section features for all processes, and to examine the current status regarding: (i) how much we know about the cross sections for possible dynamical processes and their magnitude and energy-dependence; and (ii) how well theoretical tools can provide rationales to evaluate each cross section. A. N 2 MOLECULES Figure 1 shows various cross sections for electron scattering. The commonly occurring are: e(p) + N2(v, J)---,e + e + N~-
ionization Eth ~ 10 eV
~e+N~
electronic excitation Eth-- 5-9 eV,
~ e + Nz(v', J' )
ro-vibrational excitation Eth=0.1-0.01 eV
~N2~N+N
dissociative attachment
~e(p') + Nz(V,J ) m o m e n t u m transfer
(1)
where Eth represents threshold. The molecular (positive or negative) ions formed are often unstable, and after a finite lifetime, they undergo dissociation, thereby producing neutral radicals and fragmented ions. Figure 1 also summarizes some prominent features of the cross sections from those processes with a higher energy threshold. For example: (i) ionization cross section increases sharply above the threshold, reaching a magnitude of 3 x 10 -16 cm 2 at around 150 eV; (ii) electronic excitation for various low-lying states also increases sharply above each threshold, reaching the maximum at around the 20 to 30-eV region with a magnitude of 1 x 10-16cm2; (iii) vibrational excitation increases steeply above the threshold, reaching a sharp peak with some oscillatory structures. This peak is considered to be due to a resonance as described in what follows; (iv) rotational excitation also increases rapidly above the threshold, and remains rather constant at higher energies. Both
36
Mineo Kimura
FIG. 1. Cross section of N 2 by electron impact. Tot: total cross section; Mom: momentum transfer; Vib: vibrational excitation; Exc: electronic excitation; and Ion: ionization (Itikawa et al., 1986).
rotational and vibrational excitation cross sections are roughly about a magnitude of 10-16 cm2; (v) dissociative attachment is possible only at low energy (below 10 eV) and is often associated with resonance. Here we point out some very interesting and important phenomena often seen in scattering events. (i) Resonance. One notable feature is the so-called resonance in which an incoming electron is trapped temporarily within a molecular field forming a complex state and remaining a longer period of time before it escapes. Because of the longer stay near the molecular nuclei, it experiences a stronger interaction, resulting in enhancement of structures in the magnitude of the cross section. Depending upon the nature of the resonance, two different mechanisms are known to contribute to the resonance. In one, the incoming electron is trapped within the potential well, and this is called shape resonance, while in another, the incoming electron excites one of target electrons or ro-vibrational state, and loses its kinetic
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
37
energy. Then this electron falls into one of empty orbitals of the target molecule, and remains for a finite time. This is called the Feshbach resonance; (ii) The Ramsauer-Townsend effect. Another important aspect in cross sections is the Ramsauer-Townsend (RT) effect, which gives the minimum in elastic and momentum transfer cross sections normally < 1 eV. The RT effect is caused by the repulsive and attractive parts of interaction potentials canceled out by the incoming electron fields, and hence no net effect is exerted on the incoming electron. As a result, the electron appears to have undergone no scattering after the incident. The location and degree of this RT minimum in the momentum transfer cross section are important for determining electron diffusion and mobility constants; (iii) The multichannel interference. In the low to intermediate energy regions, various channels strongly couple simultaneously, thus causing a few structures in cross sections. For elastic scattering, this has been known experimentally as "threshold anomalies" or " Wigner cusp." This phenomenon occurs because of the opening of a new inelastic channel as the incident energy is slightly higher than the threshold of an inelastic process, and hence may be regarded as part of the multichannel interference. A typical example of the structures arising from the RT minimum is illustrated graphically in Fig. 2. Note that even for such a well-studied case as N2, only fragmented data are known for very limited processes at very limited energy regions. Accordingly, the data shown in the figure are constructed by using interpolation and extrapolation procedures among sparse existing data, and hence is still considered to be tentative. In what follows, we outline essential aspects of theoretical procedures that are able to evaluate these cross sections described in the foregoing with reasonable accuracy.
III. Overview of Theoretical Framework Theoretically, various types of approximations are proposed to correctly extract essential physical dynamics from each scattering event. Roughly two classes of theoretical approaches are commonly employed depending upon the scattering energy. These are the perturbative approach, which is useful for the weak interaction, or impulsive scattering at high energy above 100 eV, and one of the most notable examples is the Born approximation. Other approaches include a close-coupling, variational, R-matrix and continuum multiple-scattering approach in which many channels couple strongly and simultaneously far below 100eV. Formally, a multichannel close-coupling method can be reduced to a simpler Born formula by assuming two-channel and high-energy collision.
38
Mineo Kimura
FIG. 2. The Ramsauer-Townsend effect. Ar, Kr, and Xe show a deep minimum in the energy region of 0.3-1 eV while no minimum is seen for He and Ne. (Kauppila and Stein, 1989, with permission).
The relationship among major theoretical approaches, namely, the variational, eigenfunction expansion, R-matrix and continuum multiple scattering methods, is illustrated in Fig. 3. For more details, readers are referred to a good review article on theory by Lane (1980). A. GENERAL SCATTERING THEORY
The time-independent theory of electron scattering from molecules is based on the stationary state description of continuum states of the electron and
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
39
r xact Oesc .on l Body-Frame Close-Coupling ...... Useful:
[Laboratory-Frame [ [Close-Coupling
~
Useful:
oaway from t h r e s h o i d ~ oto describe electronic state inside molecule ~
o close to threshold o to describe electronic state
~
outside molecule
I
t
I Weakinteraction Planewaveapproximation I’B~ Appr~176
I
FIG. 3. Schematic diagram that shows the relationship among theoretical approaches frequently used for the calculation of electron-molecule scattering.
target system. The total Hamiltonian of the system considered is H = T + Veto -~- h~t
(2)
where T, Veto and h M correspond to the kinetic energy operator of the incident electron, electron-molecule interaction, and target molecule Hamiltonian, respectively. Now the problem is how to solve this Schr6dinger equation reasonably accurately. 1. A Close-Coupling Scheme
For many quantum mechanical systems a procedure is often employed to obtain the total wavefunction by an expansion in terms of the complete set
Mineo Kimura
40
of unperturbed states of the isolated molecule, viz.,
gO(r, x) = A s Fi(r)dp i(x)
(3)
where A is the usual antisymmetrization operator for electrons. In principle, the summation in Eq. (3) includes all continuum as well as bound states of the target. The one-electron scattering functions F satisfy the set of coupled equations [V 2 + k,]F,(r) = 2 ~ [V,.,(r) + W,,,(r)]F,,(r)
(4)
where the direct interaction matrix elements are defined by
V,,, = (n/Ve,,/n')
(5)
and the exchange interaction matrix elements W,,, are operators that interchange bound orbitals in ~,(r) with continuum orbitals. All exchange terms decay exponentially in the asymptotic region and thus exchange effects are characterized as short range. Expanding the function of F,(r) in terms of the spherical harmonics, Eq. (4) can be reduced to a set of the coupled equations for the radial function. Then the coupled equations can be solved numerically to obtain the scattering amplitude. Once the scattering amplitudes are obtained, the differential cross section and total cross section can be readily calculable from the conventional procedure as
dcy(O)/d~ = (k,,/ko) If.o (k,,, ko)l2
(6)
~o-~, = (k,/ko) f dk,[f,o(k,, ko)[2
(7)
and
2. Variational Methods Since a good review for describing details of the methods, which belong to this category, has appeared recently (Winstead and McKoy, 1996), only a brief description of the main features of each procedure will be given here. The Kohn variational method and the Schwinger variational method have been known to provide results with reasonable precision, and hence are widely employed for electron scattering problems. Rescigno et al. (1995) have implemented the Kohn principle for the T-matrix calculation, and applied it to some systems of electron-molecule scattering. For the Schwinger method, Winstead and McKoy have further developed the
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
41
method and applied it very extensively to study various electron-molecule scattering processes with much success (Winstead and McKoy, 1996). Interested readers can refer to the cited review articles for more detailed information. 3. The R-Matrix Method
This method was originally suggested by Wigner (1946) for the study of nuclear reactions, and later, was adopted by Burke (1979) and Burke et al. (1971) for electron scattering problems. The method has been extensively tested and applied for electron-molecule scattering (see, for example, Burke and Berrington,, 1993; Schneider, 1995; Schneider and Collins, 1984) and is now widely regarded as offering a reasonably accurate result. The basic idea of this method is the division of configuration space into two regions, an internal region and an external region. In the internal region where complicated multicenter interactions occur, one has to solve the quantumchemistry problem for the (incoming electron + all target electrons)-system accurately. In the external region, all interactions can be approximated reasonably well by a single-centered expansion provided that the asymptotic charge distribution and polarizability of the target are known. The internal region is surrounded by a sphere centered at the molecular center, and we solve two different types of Schr6dinger equations from each region separately then match the solutions at the boundary. Once the internal problem has been solved it is possible to construct the R-matrix on the boundary, which contains necessary information of scattering dynamics. In the last decade or so, this method has been applied to investigate elastic, rovibrational excitation, and electronic excitation processes resulting from electron scattering from atoms and simple molecules, and has provided much insight into mechanisms (see the review on this in Schneider, 1995). 4. Cont&uum Multiple-Scatter&g ( C M S ) Method
In a quite different theoretical category from the methods described in the foregoing, the continuum multiple-scattering (CMS) method is a simple but efficient model for treating electron scattering from polyatomic molecules as done by Dehmer and Dill (1974; 1984), and Kimura and Sato (1991). In order to overcome difficulties arising from many degrees of freedom of electronic and nuclear motions, the nonspherical molecular field in a polyatomic molecule, the CMS divides the configuration space into three regions: Region I, the atomic region surrounding each atomic sphere (spherical potentials); Region II, the interstitial region (a constant potential); and Region III, the outer region surrounding the molecule (a spherical
42
Mineo Kimura
potential). The scattering part of the method is based on the static-exchangepolarization (dipole for polar molecule) potential model within the fixednuclei approximation, in which these quantities are described in what follows. The static interaction is constructed by the electron density based on the present CMS wavefunction, and the free-electron gas model is often employed for the local-exchange interaction, while the polarization interaction is considered only for terms proportional to r -4. A simple local exchange potential replaces the cumbersome nonlocal exchange potential making the practical calculation more tractable. Under these assumptions, the Schr6dinger equation in each region is solved numerically under separate boundary conditions. By matching the wavefunctions and their derivatives from each region, we can determine the total wavefunctions of the scattered electron and hence the scattering S-matrix. Once the S-matrix is known, then the scattering cross section can easily be calculated. This approach has been employed extensively by Dehmer and Dill (1974; 1984), and successfully by Kimura and Sato (1991) for various molecules in order to provide the basic dynamics of elastic and vibrational excitation processes in electron scattering. Despite its intrinsic simplicity, today it is regarded as a useful tool for providing valuable information on the underlying scattering physics. Further, the CMS method is useful for guiding the interpolation and extrapolation of experimental data points.
5. Zero-Energy Limit." The Scattering Length Theory The behavior of the cross section at the near-zero scattering-energy limit is very interesting and practically important. In this energy domain, only elastic scattering is most likely to take place. For the attractive potential with the well depth Vo, the radial Schr6dinger equation can be written for r
(8a)
p2 = k 2 -k- V2
(8b)
with
where Vo represents well depth of the potential. The Schr6dinger equation for r > a satisfies a similar form, but without a Vo term because the potential vanishes beyond a. By the condition that the solution of Eq. (8a) can be given as fl(r) = N~sz(pr), and that for r > a, ff(r) = Sl(kr ) + Klq(kr), should match at r = a, the scattering K l matrix is
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
43
given by
Kl = tan~3l = [ k'~l(ka)sl(pa) - psl(ka)s'l(pa) ] [PCl(ka)S'l(pa) -- kci(ka)s l(pa)
(9)
For 1 = 0, K o = [k tan(pa) - p tan(ka)]/[p + k tan(ka) tan(pa)]
(lo)
g)o = - k a + tan-l[(k/p) tan(pa)]
(11)
from which
Generally, the ratio tan ~o(k)/k approaches a finite value of as as k goes to 0, where a S is known as the scattering length
a s = lim[tan ao(k)/k ]
(12)
In terms of the scattering length a S, the cross section at zero-energy limit for the s-wave can be written as
(13)
CYo(O) = lim 4rt sin(26o)/k 2 = 4rta 2
Although as usually takes a finite value, sometimes it becomes infinite when a bound state exists in the potential well. For the important case where the potential can be described in terms of an inverse fourth power for large r, that is,
U(r) = - [ ~ / r 4]
(14)
where ~ is the tensor static electric dipole polarizability. O'Malley et al. (1962) have given the effective range expansion as follows: tan 6o = Ak - (rt/3)~k 2 + (4/3)~Ak 3 log k + O(k 3) -Jr ... tan
~l --" ( r t / 1 5 ) ~
--
(Tr~
+
O(k4)
+
(15a) (15b)
...
tan 6~ = (~k2)/[(21 + 3)(21 + 1 ) ( 2 / - 1)] + O(k 4) + ...
forl>l
(15c)
The elastic cross section then becomes cy s =
4rt[A
2 -
(2/3)rt~Ak + (8/3)o~AZk 2 log k + Bk2...]
where A represents the s-wave scattering length.
(16)
Mineo Kimura
44
These results are found to be useful in guiding and extrapolation experimental data at the low-energy limit.
6. The Perturbative Treatment." The Born Approximation The basic assumption used to derive the Born approximation is that the collision time is so short that the interaction between the colliding partner is very weak. However, there are two essential assumptions: (i) the incident wave is undistorted by the interaction of both incoming and outgoing parts of the collisions, so that the plane wave may be a reasonable representation; and (ii) excitation to any final state occurs impulsively and hence very little influence from any intermediate state, namely, two-state approximation, holds. Thus we can write the total scattering wavefunction as
F(ra, rb) = exp(ikonorb)Uo(ra)
(17)
where r a and r b describe coordinates for target electron and incident electron, respectively. Uo(ra) Represents the target electronic state. Under the assumptions (i) and (ii), the infinite set of the close-coupled equations can be reduced to a single equation (V 2 + k2)F.(rb) = (2m/h)Vo. exp(ikonor b)
(18)
By solving this equation subject to the proper boundary condition F.(rb) ~ (1/rb)f.(0) exp(ik.n.rb)
(19a)
F.(0) = 0
(19b)
finally, we are able to derive the scattering amplitude
fB~
ko) = - 1/(2It) f dr' exp(-iKr')V,o(r' )
(20)
where the momentum transfer vector K is defined as K = k.-
ko
(21)
The Born approximation is considered to be valid for high-energy collisions, and has been applied for many processes including electronic excitation, ionization, and dissociation. As the incident energy lowers, higher-order terms in the Born series are expected to contribute for better description of
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
45
the dynamics. Regardless of the method adopted for solving scattering dynamics described in the foregoing, the essential part of successful calculation relies completely on how to choose and construct realistic interaction potentials between the incident electron and target molecules, which constitute the most formidable part of theory. Generally, for high-energy scattering above a few ten electronvolts, a dynamical calculation becomes less sensitive to the interaction potentials adopted, and reasonable agreement between theory and experiment for elastic and some inelastic scattering processes can often be achieved. However, it becomes more and more sensitive to the interaction potentials as the scattering energy decreases to a few-electronvolt region and below. For detailed investigations, this is the energy domain that poses a great challenge to theorists as well as to experimentalists. Next, we examine the interaction potentials in some depth. B. ELECTRON-MOLECULE INTERACTIONS In order to understand and evaluate scattering dynamics correctly, it is essential to possess an accurate knowledge of electron-molecule interactions. In principle, it is not possible to define such interactions unambiguously because some of them are dynamical in nature and interconnect with each other in a complex fashion at a certain distance between the incident electron and the target molecule. However, it is customarily considered to be reasonable, to a good approximation, that one divides the interaction potentials into three parts, namely: (a) static interaction; (b) exchange interaction; and (c) correlationpolarization interaction (Winstead and McKoy, 1996). The static interaction is the electrostatic interaction between the incident electron and the undeformed target-molecule charge distribution, while the correlation-polarization interaction is due to the electron interaction with the deformed electron distribution of the molecule. Both interactions are long range in nature. The exchange interaction is due to the exchange of the incident electron and molecular electrons. In principle, this interaction is nonlocal in nature because it is governed by the overlap of two electron wavefunctions. Hence, it decays exponentially, and is the short-range interaction. The correlation-polarization interaction is due to the deformation of the target molecular charge distribution by the approach of an incident electron at large separation. However, when the incident electron comes sufficiently close to the target charge cloud, the electron and the target electrons correlate strongly to make the correlation interaction more complex, thus making an accurate treatment more difficult. The most unique feature of a molecule is the nonspherical anisotropic
Mineo Kimura
46
nature of the potential, and very interesting scattering phenomena and uniqueness of each molecule emerge as a result of these specific characteristics of the potential. Hence, these features should be carefully built into any theory adopted as realistically as possible for a better description of the collision dynamics. Furthermore, because of these features in the potentials, even in higher-energy regions where the perturbative approach is known to be valid, it is not certain if fully converged results are attainable. Hence, a careful convergence test of the cross section with respect to the potential term should be undertaken. 1. S t a t i c a n d Correlation-Polarization Interaction The static interaction: The static interaction is given in terms of the charge distribution 9(r) inside the molecule
Vstatic(r)
-
-
q[p(r)/lr - r'l-i dr'
(22)
where q represents the electron charge, and r is the position vector of the incident electron. The charge distribution 9(r) includes both the point charges of the nuclei and the molecular electron cloud. If the contribution to the integral from the region r' > r can be safely neglected, then one can expand the term of 1 / I r - r'l and obtain Vstatic(r)
-- q Z Z r-n-1Y*m(r)[4rt/(2n + 1)-]p(r')r'nynm(r') dr'
(23)
When the incident electron is far outside the molecule, only the first few terms in the expansion are important, and hence can be expressed as Vstatic(r) ~ ZqZ/r --(D(R)q/rZ)P x(R'r) + (Q(R)q/r3)pz(R" r) + ... (24) where P I(R.r) represents the Legendre polynomial with R being the internuclear coordinate of the molecule. Note that for a polar molecule, the dipole interaction D(R) is important, while for a nonpolar molecule, the quadrupole interaction Q(R) is the leading term for the interaction although it is very weak. Note also that the preceding argument is valid only for diatomic molecules. These interactions depend on the molecular orientation relative to the direction of the incident electron, and this orientation dependence exerts a torque on the molecule, thus inducing relatively easier a rotational transition of the molecule. In addition, the moments D(R) and Q(R) depend on the intranuclear separations of the molecule, and hence the interaction can also cause a vibrational transition of the molecule.
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
47
The correlation-polarization i n t e r a c t i o n : When the electron approaches the molecule sufficiently closely, the electric field it produces is no longer uniform over the molecular dimension. Therefore, the asymptotic expansion completely breaks down. As there is no unambiguous way to describe the correlation interaction correctly except for some proposed approximate forms on the basis of the localized electron in an electron gas, one has to completely rely on a model for the description. As an example, the model potential commonly used is shown (Padial and Norcross, 1984) as g c~
=
0.0311 ln(rs) - 0.0584 + O . O 0 6 r s l n ( r s ) - O.O15rs r s < 0.7
V c~ = -0.07356 + 0.022241n(rs)
0.7 __
V c~ = - 0 . 5 8 4 r 7 x + 1.988r~- 3/2 _ 2.450rj 2 _ 0.733r7 5/2
(25a) (25b)
10.0 __
(25c)
where rs =
[3/{4pel(r)}]
1/3
(26)
If the electron is far from the molecule, the electric field produced by the electron at the molecular site is practically uniform. Then, if the system is spherical, the asymptotic polarization interaction potential is given by
Vpol(r) --~ - ~ q 2 / 2 r
4
(27)
where ~ is the electric dipole polarizability of the target molecule; Vcorr and Vpol join smoothly at intermediate r (normally, 8-10ao) to represent both short- and long-range parts of the interaction uniformly. For most molecules, the polarizability is a tensor property, depending on the orientation of the molecule relative to the applied electric field. It also depends upon the nature of the molecular bond and electron-charge distribution. For the linear molecule, the asymptotic potential is replaced by Vpol(R, r) ~ -- a q 2 / 2 r 4 -- ( ~ ' q 2 / 2 r 4 ) p 2(R "r)
(28)
where a and ~' are given by the polarizabilities along the directions parallel (~11) and perpendicular (~• to the molecular axis R in the form = (all + 2~•
(29a)
a ' = (2/3)(all- a•
(29b)
and
Mineo Kimura
48
Further, there is an additional complication, that is, there is the velocity dependence in the polarization interaction. When the incident electron velocity is small, the collision time is long, and hence the molecular electron cloud can adjust to the motion of the incoming electron adiabatically. Then the adiabatic polarization potential, given by Eqs. (25) and (28) can be used with reasonable accuracy for describing the polarization effect. When the incident electron velocity becomes higher, the collision duration becomes shorter, and hence the molecular electron cloud can not be adiabatically deformed. Therefore, the polarization interaction is expected to become less important as the collision velocity becomes higher. Such a velocity dependence of the polarization interaction in principle needs to be taken into account correctly. In reality, however, it produces a formidable task for theorists, and up to now a rigorous treatment has not been established except for some model interactions (Onda and Truhlar, 1980). 2. Exchange Interactions
The exchange effect arises from antisymmetrization of the wavefunction of the whole system with respect to the electrons including the incident one, and leads to a set of coupled integrodifferential equations rather than a set of coupled differential equations. Therefore, the exchange effect gives rise to a nonlocal interaction. In order to simplify the exchange interaction, the nonlocal interaction is often replaced by an appropriate and simpler local potential. Here the exact nonlocal exchange interaction can be written in terms of the one-electron wavefunction ~(r) of a bound electron and the incident single-electron wavefunction q~(r) as ~x~h(r) = - ~ ~(r) f ~*(r')[qe/I r - r'l]qg(r')dr'
(3o)
This nonlocal expression can be replaced by an approximate localexchange potential
l/exch(r)=[-~f~*(r’)w(r){q=/Ir
-
r'l} ~(r)~(r') dr'-I/~(r) 2
(31)
Slater (1960) derived a more realistic and tractable form of the exchange interaction by limiting the integration area within a certain boundary as follows: Vexch ~ q2/2n2 f dk'/Ik' - kl 2
(32)
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
49
The integral is taken over the region of k' occupied by the orbital electrons. For collisions of k > k', which is always the case, by integrating over k, one obtains Vexch = -(q2/g)kmax{l -[(k2-k2max)-]/(2kkmax) ] ln[(k +
kmax)/(k-kmax)]}
(33)
kmax(r ) is the maximum wavenumber in the local bound electron distribution, and is given by kmax(r ) = (37C2ne)1/3
(34)
where n e is the local bound-electron density. The incident electron wavenumber k o relates to the ionization potential I of the target molecule and kmax within the local approximation as
hZk(r)Z/2me = hZkZ/2me + hZkZax/2m e + I
(35)
Equation (33), along with Eqs. (34) and (35), are now in a local exchange model (Hara, (1967). This exchange interaction, along with other similar forms, has frequently been utilized for electron scattering as a standard exchange model. Whether this exchange interaction is attractive or repulsive depends on the initial electronic state of the molecule, and generally for the ground electronic state it is believed to be attractive. For excited electronic states, no comprehensive study exists. As an example, Fig. 4 displays spherical parts of three interactions of electron impact on CH 4 (Nishimura, 1999). Below 5a o, the static interaction contributes dominantly to the total interaction, while beyond 8a o, the polarization interaction is solely dominant. For the region in between, all three interactions become equally important, and contribute in a complex manner to scattering dynamics.
IV. Current Level of the Accuracy of Theoretical Approaches The high-precision calculation for scattering processes depends largely on: (i) how accurately one can determine electronic states of the target molecule; (ii) how properly one can select crucial channels in the close-coupling calculation or any model; and (iii) how much precision one can attain in numerical evaluation at various steps in the calculation, and so on. Of course, the level of accuracy improves significantly in conjunction with the
50
Mineo Kimura
FIG. 4. Electron-CH 4 interactions (spherical parts only). Total, static, exchange and correlation-polarization interactions are labeled, respectively, Tot, St., Ex., and Pol.
advancement of computer hardware and software, and hence it is quite possible that the present description for the accuracy would soon become obsolete in a short period of time and necessitate significant revision. Therefore, we believe that the assessment of the current level of theoretical performance described in what follows is still tentative. For ionization or electronic excitation at high energy above a few
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
51
hundred electronvolts where the perturbative approach is valid, these cross sections may be obtained within 30 to 40% by using different variations of the Born-type approximation, provided that we know reasonably accurate wavefunctions of the target electronic state. As the incident energy decreases to the intermediate energy regime between 100 and 10 eV, many channels couple strongly, begin to interfere each other and hence influence the magnitude and energy-dependence of cross sections. This is the region where most theories work rather poorly. Even for the successful case based on the most rigorous and careful but very exhaustive computation such as the R-matrix method, the agreement between theoretical and experimental results for vibrational excitation of O2 is considered to be qualitative (Noble, 1996). Below this energy domain, elastic cross sections for various molecules become dominant and as a result are rather well studied in various types of computing environments including a parallel processor. However, the theoretical calculation of ro-vibrational excitation for such molecules as CO2, N 2 0 and other triatomic molecules was unthinkable only a couple of years ago (Winstead and McKoy, 1996). Therefore, it may be viewed as a success story of theory to study those processes for such a "large" molecule. An essential difference for larger molecules compared to a simpler molecule such as N 2 as discussed in the preceding is that the more the number of atoms increases, the more additional modes for rotational, vibrational and electronic excited states become available, which results in a variety of possibilities for paths of excitation. Furthermore, because of the additional atoms, the potential created from the molecular field becomes more complex, thus increasing the possibility of a shape-resonance. Because of the variety of additional states, these new states are expected to lead to a variety of paths for fragmentation, producing a variety of species of fragmented radicals and ions. Therefore, the increase of the molecular size dramatically increases the complexity of dynamical aspects and hence numerical computation. A. AN EXAMPLE OF C 0 2 : VIBRATIONAL EXCITATION
An example of the result for C O 2 is shown in Fig. 5, in which the revision is suggested for vibrational excitation based on the most recent theoretical calculation. The original data obtained from the combination of swarm measurements, beam experiments and theoretical calculations were compiled, critically evaluated, and determined (Kurachi and Nakamura, 1990). These data have been widely utilized in various applications from environmental science and atmospheric science to semiconductor manufacturing. However, it should be noted that most of the available data for inelastic
52
Mineo Kimura
FIG. 5. Cross sections for C O 2 (Kurachi and Nakamura, 1990, with permission). Recent theoretical results for vibrational excitations are included. O: (001) asymmetric stretching excitation; and I1: (010) bending excitation (Takekawa and Itikawa, 1998).
processes are very fragmented in the collision energy, and their accuracy is not well examined. Furthermore, very little knowledge of scattering dynamics is available. Briefly, we overview the general features of the cross sections. From the high-energy side, ionization (qi) begins to grow sharply above its threshold of about 12 eV, becoming the dominant process beyond --~500eV. There should be a variety of electronic excitational processes (qex2) beyond their thresholds of a few electronvolts, and they are represented as a band because details of electronic states are not yet known and no cross-section data are available. A sharp peak around at 8 to 9 eV is due to dissociative electron attachment (qa), which may lead to fragmentation. This process is due primarily to the resonance in which the incoming electron is trapped temporarily within a molecular field and therefore has a significant influence on the nuclear motion. This induces a shoulder at the same energy in
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
53
vibrational excitations. Vibrational excitation processes for symmetric stretching (100), bending (010), and asymmetric stretching (001) modes with corresponding threshold energies of 0.165, 0.083, and 0.291 eV, respectively, are seen to increase sharply above each threshold. Then above around 10eV, the present three vibrational excitation cross sections drop rather sharply. Below these thresholds, only the elastic process is possible, which is equal to the total cross section. Below roughly 0.1 eV, the cross section should be dominated by rotational excitation processes, but these cross sections are not known. At much lower energies, the elastic scattering is a sole contributor whereby only the s-wave contributes to the scattering and the scattering length theory may provide a guide to the shape and magnitude of the elastic cross section. With regard to vibrational excitation, the recent calculation of vibrational excitation for (100), (010) and (001) modes based on the closecoupling method (Takekawa and Itikawa, 1998) shows different energy dependence as included in the figure, where the theoretical results do not die off so quickly in the high-energy side. Because electronic excitation is always expected to accompany ro-vibrational excitation processes, the sharp decrease of ro-vibrational excitation would not be expected. This finding by theory is another clear example of the important contribution from theory to provide the correct assessment of measured data. One crucial difference between a small molecule and polyatomic molecule is the variety of fragment products, neutral or ionic species. In the plasma, these fragments go through inelastic processes by electron collisions as a part of a series of chain reactions, thus producing different secondary products. As described, these radicals initiate further reactions with other radicals and ions, thus making all reaction processes very complex. A knowledge of all of these radicals and ions provides basic information of fragment energy and spatial distributions that constitute a basis for application. Basically, one has to determine the 3D potential surface quantum chemically, and then study collision dynamics in conjunction with the potential surface. Accurate determination for the 3D potential surface for polyatomic molecular systems is one of the formidable tasks for theorists. Unfortunately, however, very little study on this subject has been carried out, and hence no assessment of the accuracy of the theoretical results can be made.
V. Excited Species So far, we have considered the case in which the target gas is in an electronically and ro-vibrationally ground state, that is, near zero-temperature condition. However, this situation is somewhat too ideal and not
Mineo Kimura
54
realistic. In the practical operational condition of the plasma processing, it is common to apply the room temperature and low pressure, and the weak external field. Also, in this condition, most of the seed gases is likely to be in the electronically ground state, but they must be in ro-vibrationally excited states. Therefore, it is important to consider the scattering dynamics from these excited molecules, which is expected to be grossly different from that of the ground state. Unfortunately, there is very limited study on collision dynamics from electronically or ro-vibrationally excited molecules. (See the review by Christophorou and Olthoff II (2000), for the current status on excited species.) Among possible electron scattering processes, dissociative electron attachment, followed by its fragmentation for ionic and neutral species is one of those most influenced by the ro-vibrationally excited state. In the example shown in Fig. 6 (Morgan, 1991), we illustrate C1- formation through dissociative attachment from various initial vibrational states of the parent HC1 molecule in Fig. 6. In other words, the figure shows how C1formation depends on the initial vibrational state of the parent molecule as a function of the incident electron energy. Even though the vibrational excitation energy is roughly 0.4eV, HC1 appears not to be significant
10 "14
--
’
’
’
’
’
|’
|
’
i
’
’
’
’
’
|
’
’
’
I
’
’
i
,
,
,
,
-
D,sso+i.,,ve o,ectro, attachme.t of
v = 2
~
e + HCI(v) --> CI"
q
10 "15
z
@ .=.,
r~
@
lO
-16
@ o~ I=
~
10 "17 r,,)
v=0
10-Is 1.5
0.5 Electron energy (eV) FIG. 6. Dissociative attachment of HC1.
CONSIDERATIONS OF PLASMA-PROCESSING PROCESSES
55
enough to cause the drastic change of the system. But as the vibrational quantum state increases, the intranuclear separation between H and C1 atoms increases, thus changing the electron-charge distribution of the molecule rather drastically, and hence increasing the possibility of a strong coupling with one of the dissociation channels. Therefore, when the vibrational state of the parent HC1 molecule increases from the ground v = 0 state to the first excited v = 1 state, the C1- formation cross section increases by two orders of magnitude. In addition, its energy dependence also changes drastically by shifting the peak of the cross section toward lower energies from 0.85 to 0.65 eV. When the vibrational state increases to the v = 2 level from the v = 1 level, the C1- formation cross section again increases rapidly by an order of magnitude, and its peak also moves toward much lower energy from 0.65 to 0.25 eV. It is intriguing and important to realize that such a large change of the cross section occurs by such a small change of the vibrational energy. For semiconductor manufacturing, the plasma temperature used is normally a room temperature, and at this temperature, most of the seed gases are in their electronic ground state, but some are in the vibrationally excited state. For example, if the temperature of CO2 gases is raised from 300 to between 400-500 K, then 20-30% of the (010) vibrational excited state is produced, and most of the rotational states should be much higher. This is particularly the case for larger molecules. More theoretical and experimental study on electronically and ro-vibrationally excited molecules should be carried out.
VI. Perspective and Conclusion Theoretical approaches are complementary to experimental methods and quite often the obtaining of cross-section data must rely solely on theoretical means. Theoretical approaches can provide the following basic support to understanding physics, measurements and data compilation: (i) rationales of underlying physics of collisions dynamics; (ii) tools for extrapolation and interpolation for experimental data that are merely fragmented; (iii) correct magnitude of cross sections and their energy dependence, and hence they can be employed to critically assess the reliability and precision of experimental data. In plasma processes, there are three major reaction stages that must be considered: (i) electron-molecules reactions; (ii) radical- and ion-radical reactions; and (iii) ion- and radical-surface reactions. In this section, we have been concerned with and discussed mainly stage (i) because reactions in this
56
Mineo Kimura
stage are relatively well known for some species albeit qualitatively. Knowledge for reaction cross sections and dynamics in stages (ii) and (iii), however, is far less satisfactory, and much more of an orchestrated effort from all disciplines in investigating these reactions is essential for further progress of this field. Particularly, as the nanoscale fabrication of larger wafers 300 mm in diameter is now a goal in the new century, the control of the production of radical and ionic species as well as these reactions themselves at the atomic-level is essential. Furthermore, because of the greenhouse effect, new types of etching-gas molecules, which are far less hazardous to the earth environment than these currently used, should be employed and this means we must understand the physical and chemical natures of these new molecules. All these problems we are now facing are so enormous that no one group, working independently, can handle them. What is required is a greater collaborative and orchestrated effort in the areas of theory and experiment in scientific and engineering research sectors in all countries that is indispensable for the twenty-first century.
VII. A c k n o w l e d g m e n t The work presented here was supported in part by a Grant-in-Aid from the Ministry of Education, Science, and Culture through Yamaguchi University.
VIII. R e f e r e n c e s Burke, P. G., (1979). Advances in Atomic and Molecular Physics 15: 471. Burke, P. G. and Berrington, K. A. (1993). R-Matrix Theory of Atomic and Molecular Processes, Bristol, UK: IOP Publishing. Burke, P. G., Hibbert, A., and Robb, W. D. (1971). J. Phys. B4: 153. Christophorou, L. and Olthoff, J. K. (2000). Electron collision data for plasma processing gases, Advances in Atomic, Molecular, and Optical Physics 44, San Diego: Academic Press. Christophorou, L. and Olthoff, J. K. (2000). Electron interactions with excited atoms and molecules, Advances in Atomic, Molecular, and Optical Physics 44, San Diego: Academic Press. Dehmer, J. L. (1984). In Electron-Molecule and Photon-Molecule Collisions, T. Rescigno, V. McKoy, and B. Schneider, eds., New York: Plenum Press. Dill, D. and Dehmer, J. L. (1974). J. Chem. Phys. 61: 692. Goto, T. (2000). Radical measurements in plasma processing, Advances in Atomic Molecular, and Optical Physics 44, San Diego: Academic Press. Hara, S. (1967). J. Phys. Soc. Jpn. 22: 710. Itikawa, Y., Hayashi, M., Onda, K., Sakimoto, K., Takayanagi, K., Nakamura, M., Nishimura, H., and Takayanagi, T. (1986). J. Phys. Chem. Ref. Data 15: 985. Kauppila, W. E. and Stein, T. S. (1989). Advances in Atomic, Molecular, and Optical Physics 26: 1.
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Kimura, M. and Sato, H. (1991). Comment At. Mol. Phys. 26: 333. Kurachi, M. and Nakamura, Y. (1990). Proc. Thirteen Symp. on Ion-Sources and on Assisted Technology, ISIAT-90. Lane, N. F. (1980). Rev. Mod. Phys. 52: 29. Makabe, T. (2000). Radio-frequency plasma modeling for low-temperature processings, Advances in Atomic, Molecular, and Optical Physics 44, San Diego: Academic Press. Morgan, W. L. (1991). JILA Data Center Report, No. 34. Nishimura, T. (1999). Proc. Workshop for Atomic and Molecular Processes in Low-Temperature Plasma, ISAS, p. 104. Noble, C. J. et al. (1996). Phys. Rev. Lett. 76: 3534. For general aspects resulting from atomic collisions, see, for example, McDaniel, E. W. (1992). Atomic Collisions (Electron and Photon Projectiles), New York: John Wiley & Sons, Inc.; McDaniel, E. W., Mitchell, J. B. A., and Rudd, M. E. (1996). Atomic Collisions (Heavy Particle Projectiles), New York: John Wiley & Sons, Inc. O'Malley, T. F., Spruch, L., and Rosenberg, L. (1962). Phys. Rev. 125: 1300. Onda, K. and Truhlar, D. G. (1980). J. Chem. Phys. 72: 1415. Padial, N. T. and Norcross, D. W. (1984). Phys. Rev. A29: 1742. Rescigno, T., Lengsfield, B. H., and McCurdy, C. W. (1995). In Modern Electronic Structure Theory, D. F. Yarkony, ed., p. 501, Singapore: World Scientific. Schneider, B. I. (1995). In Computational Methods for Electron-Molecule Collisions, W. M. Huo and F. A. Gianturco, eds., New York: Plenum Press. Schneider, B. I. and Collins, L. A. (1984). Phys. Rev. A30: 95. Slater, J. C. (1960). Quantum Theory of Atomic Structure, New York: McGraw-Hill. Takekawa, M. and Itikawa, Y. (1998). J. Phys. B31: 3245; 1999). J. Phys. B32: 4209. Tanaka, H., and Sueoka, O. (2000). Mechanisms of electron transport in electrical discharges and electron collision cross sections, Advances in Atomic, Molecular, and Optical Physics 44, San Diego: Academic Press. Wigner, E. P. (1946). Phys. Rev. 70: 15. Winstead, C. and McKoy, V. (1996). Advances in Chemical Physics XCVI: 103.
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 44
E L E C T R O N C O L L I S I O N D A T A FOR PLA S M A - P R 0 CESSING GASES L O U C A S G. C H R I S T O P H O R O U and J A M E S K. O L T H O F F Electricity Division, Electronics and Electrical Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. P l a s m a - P r o c e s s i n g Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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III. D a t a Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Synthesis, Assessment, a n d R e c o m m e n d a t i o n of D a t a . . . . . . . . . . . B. D e d u c t i o n of U n a v a i l a b l e D a t a a n d U n d e r s t a n d i n g from Assessed K n o w l e d g e , N e w M e a s u r e m e n t s , a n d D a t a N e e d s
......
C. D i s s e m i n a t i o n a n d U p d a t i n g of the D a t a b a s e . . . . . . . . . . . . . . . . . IV. Assessed Cross Sections a n d Coefficients
.......................
V. B o l t z m a n n - C o d e - G e n e r a t e d Collision Cross-Section Sets VI. C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
..........
65 65 72 83 83 93 95 96
I. Introduction Low-temperature plasma applications require detailed understanding of the physical and chemical processes occurring in the plasmas themselves. For instance, as the push for smaller feature sizes and higher quality devices in the semiconductor industry has increased, so has the need for sophisticated models with predictive capabilities that can guide the technology, and the need for advanced diagnostics to probe the details of the plasmas used to etch features, deposit materials, or clean reactor chambers. In addition, environmental concerns have fostered the demand for the more efficient use of global warming gases used in plasma processes. Advancement in each of these areas inherently requires detailed understanding of the physics and chemistry occurring within the discharge, which itself requires knowledge of the basic collision processes taking place between the species existing in the plasma. The most fundamental of the discharge processes are collisions between electrons and atoms, radicals, or molecules. These collisions are the precursors of the ions and the radicals that drive the etching, cleaning, or deposition processes. Hence, a quantitative understanding of the fundamental electron collision processes in terms of cross sections and rate coefficients is of utmost importance. 59 All rights of reproduction in any form reserved. ISBN 0-12-003844-7/ISSN 1049-250X/01 $35.00
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This chapter deals with fundamental data necessary for targets of importance in the plasma etching of silicon. It draws heavily from the work we have conducted at the National Institute of Standards and Technology (NIST) over the last four years under a project aimed at building a database for electronic processes in plasma processing gases, including cross sections, and electron transport and rate coefficients. To date, this effort has yielded six comprehensive publications, each containing detailed information on and assessed values for electron-molecule interaction cross section and ratecoefficient data for an important plasma processing gas: CF4 (Christophorou et al., 1996), CzF 6 (Christophorou and Olthoff, 1998a), C3F 8 (Christophorou and Olthoff, 1998b), CHF 3 (Christophorou et al., 1997a), CClzF 2 (Christophorou et al., 1997b), and C12 (Christophorou and Olthoff, 1999a). In this chapter we emphasize the methodology of the assessment adopted and its value, the assessed cross sections and coefficients derived and their significance, the differences between independently assessed cross sections and those determined as cross-section sets from Boltzmann codes and the significance of the former to guide the latter, and fundamental data needs. This effort is but one example of the many critical reviews that have been made on a number of species (e.g., see Morgan, 1992a, b). Its basic goal is to show how critically assessed data can provide recommended cross sections for the various electron collision processes from often widely differing sets of data, and how such knowledge can serve to establish correlations between the various collision cross sections and molecular physical properties. Such correlations are a prerequisite of a physical understanding of the magnitude and energy dependence of the cross sections, and provide the capability to predict these quantities for gases for which such knowledge is not available. A list of the basic electron collision processes considered here and their respective cross sections and coefficients are given in Table I. See, also, the Introduction to this volume by Itikawa (2000), Christophorou (1971), Csanak et al. (1984), and Christophorou et al. (1996).
II. Plasma-Processing Gases In general, there are four groups of gases of interest to plasma processing. Those used in etching, deposition, or cleaning (e.g., CF4, CHF 3, C2F6, C3F8, c-C4F8, C12, SF6, BC13, NF 3, HBr, HC1), those used as buffer gases (e.g., He, Ar, N2) , those used as additives (e.g., O 2, CO), and those that are present in virtually all practical systems as unavoidable impurities (e.g., O2, Nz, H20 ). These gases are, of course, the gases comprising the initial gaseous media. It should be realized, however, that in a discharge a large
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TABLE I ELECTRON COLLISION PROCESSES CONSIDERED IN THIS CHAPTER, THEIR RESPECTIVE CROSS SECTIONS AND SYMBOLS, AND ELECTRON-IMPACT IONIZATION, ATTACHMENT, AND TRANSPORT COEFFICIENTS Electron Collision Process
Respective Cross Section/Coefficient
Electron scattering
Total electron scattering cross section Differential electron scattering cross section(s) a Total rotational electron scattering cross section Total elastic scattering cross sectionb/ Total elastic integral b Momentum transfer cross section (elastic) Total vibrational excitation cross section Total direct vibrational excitation cross section Total indirect vibrational excitation cross section Electronic excitation cross section Total dissociation cross section Total cross section for electron-impact dissociation into neutrals Total ionization cross section Partial ionization cross section Multiple ionization cross section Density-reduced ionization coefficient Effective ionization coefficient Total electron attachment cross section Total dissociative electron attachment cross section Density-reduced electron attachment coefficient Total electron attachment rate constant Cross section for ion-pair formation Electron drift velocity Transverse electron diffusion coefficient to electron mobility ratio
Rotational excitation Elastic electron scattering
Vibrational excitation
Electronic excitation Dissociation
Ionization
Attachment
Ion-pair formation Electron drift Electron diffusion
Symbol
(Ysc,t(~) (Ysc,diff(~) O'rot,t(E) (Ye,t(~)/O'e,int (~;) (Ym(E) O'vib,t(~) O'vib,dir,t(E) O'vib,indir,t(~)
O'diss,t(~) (Ydi...... t,t(E)
O'i,t (8) O'i,partia, (~) O'i,mult(8)
a/N ( ~ - q)/U O'a,t(~) O'da,t(~)
q/N ka,t O'ip (8) w
DT/~
a For total or for a particular electron scattering process. bThese two cross sections refer to the same quantity (see Christophorou, 1971 and Csanak, 1984).
f r a c t i o n o f t h e m o l e c u l e s o f t h e i n i t i a l feed g a s ( e s ) m a y be d i s s o c i a t e d i n t o a t o m s , r a d i c a l s , a n d ions. A d d i t i o n a l l y , d e p e n d i n g o n t h e d i s c h a r g e c o n d i t i o n s a n d t h e g a s itself, t h e i n i t i a l g a s m o l e c u l e s c a n h a v e c o n s i d e r a b l e v i b r a t i o n a l excitation e n e r g y a n d the d i s c h a r g e - p r o d u c e d species can also
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be vibrationally (and/or electronically) excited. Therefore, besides the knowledge on electron-molecule interactions presented in this chapter on the initial feed gases, there is a need for basic electron-collision data for vibrationally excited molecules and radicals, and electronically excited atoms, radicals, and molecules. Although this latter kind of knowledge is sparse, its acquisition is necessary because the cross sections for electron collisions with excited (energy-rich) targets are normally much larger than for the corresponding ground-state (unexcited) species (e.g., see Christophorou, 1991; Christophorou et al., 1994) and hence a small amount of excited species can influence the behavior of electrons in a plasma and, consequently, the discharge properties. Important as these processes are, they are not dealt with here, but are presented in detail later in this volume (Christophorou and Olthoff, 2000, this volume). This chapter focuses on the fundamental primary interactions of electrons (mostly with kinetic energies below 100 eV) with the neutral, unexcited feed-gas molecules, and reviews critically the current state of our knowledge on these interactions. The practical significance of these electron-collision processes and their respective cross sections depends on the nature of the application, as illustrated by the examples that follow. a. Plasma Models. Many models have been designed to emulate various aspects of reactive plasmas (see for example, Ventzek et al., 1994; Lymberopoulos and Economou, 1995; Bukowski et al., 1996; Meyyappan and
Govindan, 1996). The fundamental parameters required for the accurate modeling of reactor plasmas are electron-energy distributions, electron densities, positive ion fluxes and energies, negative ion densities, and reactive radical densities. Knowledge of these parameters is the precursor to the calculation of other more industrially significant parameters, such as etch and deposition rates, etch profiles, and plasma uniformity. The calculation of the fundamental quantities relies heavily on knowledge of the magnitude of electron-collision cross sections, since virtually all physical processes in the discharge are determined or initiated by electron motion through the gas. For example, the electron-energy distributions are determined by the elastic and inelastic electron-scattering processes. Especially significant are the latter, even when they lie at low energies such as those inelastic processes due to strong vibrational excitation of molecules. Such processes can indeed determine the probability of high-energy processes via their effect on the electron energy distribution function. The determination of these energy distribution functions for the electrons in the discharge is the initial calculation in models based upon Boltzmann or Monte Carlo techniques (see, for instance, Bordage et al., 1996), and relies for its success on the
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availability of detailed and accurate electron scattering and electron transport coefficient data. Similarly, electron transport parameters and rate coefficients are often the first parameters calculated by plasma models. Accurate measurements of these values are, thus, essential to validate model calculations. The transport parameters commonly calculated in such models include the electron drift velocity, the transverse (and logitudinal) electron diffusion coefficient to electron mobility ratio, the density-reduced ionization coefficient, the density-reduced electron attachment coefficient, and the total electron attachment rate constant. The electron density in a plasma is primarily determined by electronimpact ionization processes (which produce free electrons), electron attachment processes (which remove free electrons by creating negative ions), and by secondary electron emission from surfaces. The first two processes are described by the ionization and the electron attachment cross sections, respectively, and the third process, while important and worthy of investigation, is a surface process and is not discussed here. Ionization and attachment cross sections are of particular importance as they determine the ionization balance within the plasma and thus influence the plasma properties. Another process of interest in this regard is the ion-electron recombination reactions, but since these are secondary processes they are not covered in the present discussion. Positive ion bombardment is one of the main drivers of plasma surface reactions, and the ion flux is a direct result of electron-impact ionization. Although the final identity and magnitude of the positive ion flux may be dependent upon secondary reactions, such as ion-molecule reactions occurring as the ion travels through the discharge, the initial ion-formation process is driven by electron-impact processes. Partial ionization cross sections are required to determine the identity and quantity of the initial ions created in the plasma. Moreover, since positive ion and negative ion recombination processes influence the positive ion densities, the production of negative ions by resonant electron attachment processes also plays a critical role. Dissociative electron attachment is significant both as an efficient source of negative ions and as a source of free radicals because for many molecules the cross section for this process is very large at low electron energies ( < 1 eV) (Christophorou et al., 1984). b. New Diagnostic Techniques. The need to measure the identity and density of gas-phase plasma products, including reactive radicals, in industrial plasmas has led to the development of new diagnostic techniques such as negative-ion mass spectrometry and threshold-ion mass spectrometry. Negative-ion mass spectrometry detects gas-phase plasma products by monitoring negative ions formed by electron attachment to radicals, excited
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species, and molecules formed by reactions in the plasma (Stoffels et al., 1997; Rees et al., 1998). Cross sections for electron attachment and dissociative electron attachment are required for the feed gas and for the species to be detected in order for this technique to be effective. Threshold-ionization mass spectrometry, on the other hand, detects radicals by monitoring positive ions generated by collisions of radicals with electrons whose kinetic energy is above the ionization threshold of the radical, but below the ionization threshold of the feed gas (Sugai et al., 1995a; Nakamura et al., 1997; Schwarzenback et al., 1997). This allows detection of radicals even when the mass spectra of the radicals are similar to those of the feed gas. This technique, too, requires detailed electron-impact ionization cross sections for the feed gas and for the radicals at energies near threshold. This same technique can be used to detect excited species. Additionally, optical emission diagnostic techniques rely on light emission from a processing plasma and are often used to monitor plasma uniformity, excited species densities, and electron-energy distributions. The latter two applications require electron-impact excitation cross sections for the feed gas and for the gas-phase products generated in the discharge. c. Environmental Applications. Environmental concerns over the use of fluorinated compounds that are often global warming gases have prompted significant interest in increasing and optimizing the efficiency of plasmaassisted cleaning techniques (Sobolewski et al., 1998), and in the development of post-processing emission abatement techniques (i.e., the destruction or conversion of any remaining feed gas being exhausted from the reactor). Both of these processes, cleaning and abatement, require the dissociation of the feed gas into reactive radicals by three basic processes, electron-impact dissociative ionization, where a positive ion and a radical are produced; dissociative electron attachment, where a negative ion and a radical are produced; and neutral dissociation, where two neutral fragments are produced by electron impact. Knowledge of the cross sections for electronimpact dissociation, dissociative electron attachment, and partial ionization are necessary to optimize such industrial processes. d. N e w Applications. Fundamental research in electron collision processes involving transient species such as radicals and excited species (such as electronically excited atoms and electronically and/or vibrationally excited molecules) will undoubtedly avail new possibilities for applications. Little is known about these reactions and their effect on the plasma itself at the current time. As already indicated in this section, the data show that electron interactions with energy-rich species have large cross sections that often are orders of magnitude greater than for similar interactions with the feed gas (Christophorou and Olthoff, 2000, this volume).
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llI. Data Assessment For discharges utilized in industrial plasma processes, the most significant electron collisions occur in the electron energy range < 100 eV. The generic primary processes are elastic and inelastic electron scattering, electronimpact ionization, electron-impact dissociation, and electron attachment (Table I). No discussion is given here of electron interactions with energy rich gases (vibrationally and/or electronically excited), or with discharge decomposition products such as radicals. The three principal components of our effort to provide electron-impact reference data relevant to plasma processing are: (1) synthesis, assessment, and recommendation of electron collision data; (2) deduction of unavailable data and understanding from the assessed knowledge, including identification of new measurements and data needs; and (3) dissemination and updating of the database. We provide examples for each of these components in the following three subsections.
A. SYNTHESIS, ASSESSMENT, AND RECOMMENDATION OF DATA
This component begins with thorough literature searches and contacts with researchers in the field, followed by a critical review and assessment of the available data, and a recommendation of data. The critical review and assessment requires understanding of the physical processes themselves, which itself requires auxiliary and complementary information on the physical and chemical properties of the molecules under consideration. In general, there exist three main sources of electron collision data. These are experimental measurements (obtained principally by electron beam and electron swarm techniques), calculations (of varied levels of sophistication), and Boltzmann- and Monte Carlo-based computations. The first provides directly--and at times indirectly--cross sections or coefficients for individual electron collision processes. The second gives in principle cross sections for any process, but they are in practice limited in their utility by the complexity the calculations themselves entail, especially for polyatomic molecules. The third relies on electron transport data and other inputs and yields only self-consistent sets of cross sections, not independent and unique cross sections for each individual collision process (see discussion in Section V). Assessment of these cross sections is essential as the values determined from each of these sources are often contradictory. In addition, assessment of the cross sections from each of these sources is often difficult. The uncertainty of the measurement, the limitation of the calculation, and the
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physical reasonableness of the data obtained as sets rather than for each individual reaction are the main issues. Any assessment of data relies upon some established protocol for determining which data are the most reliable. For our work performed at NIST, "recommended" or "suggested" values of cross sections and transport coefficients are determined, where possible, for each type of cross section and coefficient for which data exist. These values are derived from fits to the most reliable data, as determined by the following criteria: (i) the data are published in peer reviewed literature; (ii) there is no evidence of unaddressed errors; (iii) the data are absolute determinations; (iv) multiple data sets exist and are consistent with one another within combined stated uncertainties over common energy ranges; and (v) in regions where both experimentally and theoretically derived data exist, the experimental data are preferred. Cross sections and coefficients for the various processes that meet these criteria are designated as "recommended" and fits to these data represent the best current estimates for the cross sections and coefficients for each of these processes. For cross sections and coefficients for which the only data that are available do not meet all of the forementioned criteria, the best available data may be used to designate a ~ cross section or coefficient. In cases where no reasonable data exist, or where two or more measurements are in an unresolved contradiction, the raw data are presented for information and no recommendation is made. To identify most clearly the reliable data for electron interactions with a given gas, all published data for each cross section are considered in our assessment, even those which have been subsequently superseded. This is done in order to aid the understanding of the evolution of the data, assist in the determination of the reliability of the data, and draw attention to these changes for researchers who might have used the earlier data in their work. When possible, data are obtained from published tables. For data presented only in graphical form, the published figures are scanned and the data are digitized for use in this work. Depending on the quality of the original figure, the values of the data obtained in this manner are within 1 - 3 % of the original values. No uncertainty values are assigned to our recommended data since no means exist of confirming the experimental uncertainties reported by the original authors (see Christophorou et al. 1996, 1997a, 1997b; Christophorou and Olthoff, 1998a, 1998b, 1999a). Some measure of uncertainty can be obtained from an analysis of the combined relative uncertainties of the original data, which are fitted to derive the recommended set. It should be stressed that although for many cross sections there exist published values that differ by as much as two orders of magnitude, critical analysis of these data allows the determination of cross sections whose uncertainties
ELECTRON COLLISION DATA
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are expected to be between 10 and 20% for most cases. We wish to illustrate this assessment process with four examples. One shows how reasonable data may be extracted from conflicting data, another shows how a recommended cross section for a particular electron collision process can be determined by considering its relationship to known cross sections for other electron collision processes, a third shows where the magnitude of electron-beam determined cross sections is adjusted based on knowledge provided by the electron swarm method, and finally, an example of the required consistency between different cross sections is provided.
a. Determination of the Recommended Cross Section for Momentum Transfer Cym(e) for CF 4. Figure 1 shows an example of how a recommended cross section is extracted from multiple sets of experimental and theoretical data. It refers to the m o m e n t u m transfer cross section Cym(e) of CF 4 for which some values in the literature differ by more than two orders of magnitude.
FIG. 1. Extraction of a recommended cross section for the momentum transfer cross section tyro(e) of CF 4 from multiple sets of experimental and theoretical data (see text and Christophorou et al., 1996).
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Loucas G. Christophorou and James K. Olthoff
The data in Fig. 1 cover the energy range 0.001-1000 eV and come from three sources, direct measurements, calculations, and swarm-based Boltzmann codes. The Cym(e) derived from direct measurements are the highenergy data of Sakae et al. (1989) and Boesten et al. (1992), which are in agreement within their combined uncertainty [ ~ 10% (Sakae et al., 1989) and 15-20% (Boesten et al., 1992)], and the low-energy values of Mann and Linder (1992), which were determined from their elastic differential crosssection measurements (uncertainty 20-30%) and modified effective range theory. The calculated cym(~) are the results of three investigations, one using an independent-atom model with partial waves (Raj, 1991), and the other two using the static exchange approximation (Huo, 1988; Winstead et al., 1993), and agree only partially with the experimental measurements of Sakae et al. and Boesten et al. The swarm-based Boltzmann-code cross sections (Hayashi, 1987; Masek et al., 1987; Nakamura, 1991; Stefanov et al., 1988; Curtis et al., 1988; Bordage et al., 1996) are model dependent and have different degrees of uncertainty depending on the electron transport data used and on other inputs. None agrees well with the measurements. In spite of these disparities, a recommended cross section can be obtained (Christophorou et al., 1996) over the energy range 0.001-700eV (solid black line in Fig. 1) from a least squares fit to the experimental cross sections of Mann and Linder for energies <0.5 eV, those of Sakae et al. and Boesten et al. > 1.5 eV, and an interpolation between 0.5-1.5 eV. b. Determination of the Recommended Total Electron Scattering Cross Section CYsc,t(e) for CF 4 below ~ 1 eV. A recommended value for the total electron scattering cross section Cysc,t(~) of the CF 4 molecule was derived with confidence for energies > 1 eV because there exist reliable experimental measurements over wide energy ranges that agree within specified uncertainties (Christophorou et al., 1996). However, for energies < 1 eV this is not the case. Nonetheless, recommended values for the (Yse,t(E) of the CF 4 molecule down to 0.003 eV were determined by considering the relationships between other known types of cross sections as shown in Fig. 2. First, measurements of ~sc,t(e) for e >0.5 eV by Jones (1986) (solid circles) and by Szmytkowski et al. (1992) (open triangles) were accepted as accurate high-energy reference data points. Second, measurements of Mann and Linder (1992) for the elastic integral cross section eYe,ant(e) of < 2 eV (long-dash curve in Fig. 2) were accepted because they were determined from their differential electron scattering cross-section measurements and a sound analysis. Third, below the lowest vibrational threshold of CF 4 at 0.054 eV, Cysc,t(e) was taken equal to (3"e,int(~), that is, (3"sc,t(~) = (3"e,int(E). Fourth, as there are no known negative ion states of CF 4 for energies < 2 e V (Christophorou et al., 1996), it was assumed that all vibrational excitation below 2 eV is due to the direct
ELECTRON COLLISION DATA
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FIG. 2. Determination of the recommended total electron scattering cross section Cysc,t(e)of CF4 below ~ 1 eV (see text).
excitation by electron impact of the two modes v 3 and v 4 of CF 4. Furthermore, since in this energy range electronic excitation is absent and rotational excitation is negligible (the CF 4 molecule has neither a dipole nor a quadrupole moment) it was assumed that between ~0.06 eV and 2 eV, (5"sc,t(~) "--(Ye,int(~)+ O'vib.dir,t(~), where (Yvib,dir,t(~) is the sum of the cross sections for the direct excitation of the v 3 and v4 infrared active modes of CF 4 as calculated (Bonham, 1994) in the Born-dipole approximation (short-dash curve in Fig. 2). The dotted curve in Fig. 2 is C~sc,t(e) = cr~,int(e) + O'vib,dir,t(~) and was obtained by using the recommended values of Christophorou et al. (1996) for ~e,int(e) and O'vib,dir,t(E ). The cross section %c,t(e) estimated in the manner just outlined from 0.08 to 2 eV was used, along with the measurements of Jones (1986) and Szmytkowski et al. (1992) for ~c,t(e) at energies ~>0.5eV and the c~,i~t(e) below 0.08eV to obtain a best estimate of Crsc,t(e) from 0.003 to ~ 1 eV. This then allowed recommended values to be delineated for ~sc,t(~) from 0.003 to 4000 eV (Christophorou et al., 1996). A subsequent measurement by Lunt et al. (1998), shown in Fig. 2 by the cross ( • point, is in excellent agreement with the assessed cross section. The results of a recent ab initio calculation by Isaacs
70
Loucas G. Christophorou and James K. Olthoff
et al. (1998) are also in general agreement with the recommended cross section. c. Determination of the Recommended Total Electron Attachment Cross Section O'a,t(t~) for Cl 2. The total electron attachment cross section of C12 has been measured by Kurepa and Beli6 (1978) using a beam experiment. From a critical assessment of the available swarm data, Christophorou and Olthoff (1999a) adjusted the Kurepa and Beli6 cross section upward by 30%. It is instructive to see how this adjustment was made, for it shows an example of the assessment process itself and is also an excellent example of the value of absolute electron-swarm measurements to adjust (normalize) the absolute magnitude of electron beam data. The process essentially utilizes the strength of each experimental procedure--the determination of well-resolved relative cross sections by electron beam experiments and the determination of absolute magnitude by electron swarm experiments. Let us then first refer to the measurements of McCorkle et al. (1984) of the rate c o n s t a n t ka, t of electron attachment to C12 in a buffer gas N 2 over a wide range of density-reduced electric fields E/N. Since for these measurements the content of C12 in N 2 was kept very small, the electron energy distribution function in the mixture is virtually the same as in the pure buffer gas N 2. Furthermore, since the electron energy distribution functions in N 2 can be reliably calculated at the E/N values for which the ka,t measurements were made, the ka, t (E/N) data can be plotted as a function of the mean electron energy (e), that is, the quantity ka,t((8)) was accurately determined. The ka,t((8)) m e a s u r e m e n t s determined this way at room temperature ( ~ 298 K) are shown in Fig. 3a. In Fig. 3a three sets of calculated values for ka,t((g)) are also plotted. One was calculated by McCorkle et al. using the electron energy distributions in N 2 and the total electron attachment cross section of Kurepa and Beli6 (1978), and the other two were calculated by Kurepa et al. (1981) and by Chantry (1982) using the Kurepa and Beli6 (1978) cross section and a Maxwellian electron energy distribution function for the electron energies. Clearly, the assumption of a Maxwellian distribution function for the electron energies is unrealistic at high E/N as is shown by the large difference in the calculated rate by the last two groups and the measurements. In the low-energy region (around the ka,t((t~)) maximum) all three calculated values of ka,t((t~)) using the Kurepa and Beli6 (1978) total electron attachment cross section have an energy dependence similar to the directly measured rate constants of McCorkle et al. (1984). However, each of the calculated values is lower in magnitude by ~ 30%, suggesting that the Kurepa and Beli6 electron attachment cross section is lower than its true value by this amount. Hence the swarm-based
71
ELECTRON COLLISION DATA
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Electron Energy (eV) FIG. 3. (a) Total electron attachment rate constant as a function of the mean electron energy <e), ka,t((~;)), for el 2 (T ~ 298 K) (from Christophorou et al., 1999). O, (McCorkle et al., 1984). • (ka,t)th [average of the two most recent values (McCorkle et al., 1984; Smith et al., 1984) of the thermal (T ~ 300 K) electron attachment rate constant]. -.-., Chantry (1982) using the CYa,t(e) of Kurepa and Beli6 (1978) and a Maxwellian distribution function for the electron energies. ..... Kurepa et al. (1981) using the O'a,t(~ ) of Kurepa and Beli6 (1978) and a Maxwellian distribution function for the electron energies. ---, McCorkle et al. (1984) using the Cra,t(e) of Kurepa and Beli6 (1978) and the electron energy distribution functions they calculated for N 2. (b) Total dissociative electron attachment, ~da.t(~), for CI 2 (from Christophorou and Olthoff, 1999). Q, measurements of Kurepa and Beli6 (1978). , cross section of Kurepa and Beli6 (1978) adjusted upwards by 30% (see text).
72
Loucas G. Christophorou and James K. Olthoff
adjustment of + 30% to the electron-beam dissociative electron attachment data for C12 shown in Fig. 3b. A similar adjustment would be in order for the Kurepa and Beli6 (1978) cross section for ion-pair formation. d. Consistency between Assessed Cross Sections. Finally, it is important to stress the significance of the total electron scattering cross section in efforts to establish the consistency of the independently assessed cross sections for the various electron collision processes for a given gas. This cross section is usually measured with the lowest uncertainty compared to the other cross sections. While this cross section is rarely used in plasma models, it provides a way to normalize or validate the other cross sections: the sum of the independently assessed cross sections of all possible electron-collision processes should add up to and not exceed the total electron scattering cross section. This has been nicely shown by Christophorou et al. (1996) for the CF 4 molecule for which the sum of the independently assessed cross sections nearly adds up to the independently assessed total electron scattering cross section as can be seen from Fig. 4. The small dip around 20 eV in the sum of the independently assessed cross sections may be an artifact due to the significant discrepancy in this energy range between the two experimental measurements of 13"e,int(t~) (Boesten et al., 1992; Mann and Linder, 1992). Indeed, if instead of taking the average of the two sets of experimental measurements of O'e,int(E ) in this energy range, one considers only the values of Boesten et al. (1992), the dip in the sum of the independently assessed cross sections disappears and the sum agrees well with the assessed values of Crsc,t(e) in this region as well. Conversely, this suggests that the cross section from Boesten et al. may be preferred to that of Mann and Linder in this energy range, and that further measurements of O'e,int(t~) in this energy range are needed. B. DEDUCTION OF UNAVAILABLE DATA AND UNDERSTANDING FROM ASSESSED KNOWLEDGE, NEW MEASUREMENTS, AND DATA NEEDS
A thorough and critical assessment of the available knowledge on electronmolecule collisions and related physical and chemical properties for each plasma processing gas often helps deduce needed data, which at the time are not otherwise available. It also enhances our understanding of the dependence of the cross sections of the various electron collision processes on the structural and electronic properties of molecules, leads to new measurements, and identifies needed critical data. Examples of these benefits are given in what follows. a. Deduction of Unavailable Data from Assessed Knowledge. Two examples of cross sections deduced from critically assessed data are given in this
73
ELECTRON COLLISION DATA
0.001
0.01
0.1 Electron
1
10 energy
100
1000
(eV)
FIG. 4. Recommended and suggested electron-impact cross sections for CF 4. The data are from Christophorou et al. (1996) except as follows: O'vib,indir,t(~ ) (Fig. 5a, Section III.B), O'di...... t,t(E) (Fig. 7, Section III.B), and O'i,t(~ ) (Fig. 14, Section IV). Note the excellent agreement between the sum of the independently assessed cross sections (dotted curve) and the total electron scattering cross section (see text).
subsection (for other examples and additional details see Christophorou et al., 1996, 1997a, 1997b; Christophorou and Olthoff, 1998a, 1998b, 1999a). The first example is the deduced cross sections for indirect (resonance enhanced) vibrational excitation cross sections for C F 4 and C12. Figure 5a shows the sum of the cross sections for direct vibrational excitation of the two infrared active modes v 3 and v 4 of CF 4 as calculated in the Born-dipole approximation (Bonham, 1994). This sum is taken to give the cross section, O'vib,dir,t(~ ) for total direct vibrational excitation of CF 4. This cross section is compared in Fig. 5a with the total inelastic cross section O'inel,t(E ) [which is approximately equal to O'vib,dir,t(S ) in this energy range] ( x ) measured by Mann and Linder (1992), and with the values (O, O) of the total inelastic cross section O'inel,t(S ) = [(O'sc,t(S ) --O'e,int(S)] deduced from the assessed values of Christophorou et al. (1996) for Crsc,t(s) and Cre,int(e). Since electronic excitation is not energetically possible below the electronic excitation
a n d J a m e s K. O l t h o f f
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Electron e n e r g y (eV) FIG. 5. (a) Total indirect vibrational excitation cross section CYvib,indir,t(E) for CF 4. (-.-) Total direct vibrational excitation cross section CYvib,dir,t(~) for C F 4 [sum of the Bornapproximation calculation (Bonham, 1994) for the two infrared active modes of CF,]. • measurements of (Yvib,dir,t(~) ~,~ (Yinel,t(~) by Mann and Linder (1992). O, (~, (Ysc,t(E) -- (Ye,int(~), where the values of these two cross sections are those assessed in Christophorou et al. (1996). ---, assessed total dissociative electron attachment cross section CYda,t(e) (Christophorou et al., 1996). _ _ , Deduced (Yvib,indir,t(~) (see text). (b) Total vibrational excitation cross section CYvib,t(E) for C12 (from Christophorou and Olthoff, 1999). Results of Boltzmann-code analyses: (. . . . ) (Rogoff et al., 1986), (. . . . . ) (Pinh~o and Chouki, 1995); , Deduced by Christophorou and Olthoff (1999) from assessed cross sections (see text).
ELECTRON COLLISION DATA
75
threshold at 12.5 eV, the difference between (~inel,t(~) and the Born O'vib,dir,t(~ ) gives the cross section for indirect inelastic electron scattering O'inel,indir,t(E ) for CF4. The indirect vibrational excitation cross section O'vib,indir,t(E) can then be obtained by subtracting the assessed total dissociative electron attachment cross section C~da,t(e) from (Yinel,indir,t(E) for energies < 12.5 eV, that is,
(Yvib,indir,t(E)
= [(Ysc,t(~)
--
O'e,int(E)]
--
[(Yvib,dir,t(~)
+ (Yda,t(~)]
This is shown by the solid line in Fig. 5a. The data shown in the figure by the open circles were not considered in this process because the values of CYe,int(e) are less reliable in the 10-20eV range due to the large difference between the two experimental sets (Mann and Linder, 1992; Boesten et al., 1992) of measurements used to derive the recommended values of CYe,int(e). The work of Boesten et al. (1992) did not indicate any contribution to the scattering cross section in this energy range due to the existence of negative ion resonances. The deduced cross section clearly shows that indirect vibrational excitation is a dominant inelastic electron scattering process in the energy range from ~ 7 to ~ 13 eV. It plays a crucial role in the yield of the various discharge products by virtue of its effect on the electron energy distribution function. This effect results not only from the large value of the cross section (3"vib,indir,t(~), but also from the large electron energy loss associated with indirect vibrational excitation (as compared to direct vibrational excitation) via the negative ion states of CF 4 in this energy range (see further details in Christophorou et al., 1996 and Bordage et al., 1999). The second example is the deduction of an estimated cross section for electron-impact vibrational excitation for the C12 molecule. In this case, one can use the "suggested" values (Christophorou and Olthoff, 1999a) derived from the assessment of the cross sections for total electron scattering Cysc,t(e), total elastic electron scattering (Ye,t(l~), total ionization (Yi,t(l~), total dissociation into neutrals (Ydiss,neut,t(l~), and total dissociative electron attachment (Yda,t(l~) to calculate a cross section for total vibrational excitation of C12 by electron impact, O'vib,t(e),t(l~), from the expression (3"vib,t(e),t(E)
= (Ysc,t(E) -- [(3"e,t(E ) + (Yi,t(~)
"lI- (3"diss,neut,t(~)
-ll- (Yda,t(~)]
Moreover, since C12 is a homopolar molecule, direct vibrational excitation is expected to be small and the total vibrational excitation cross section can be taken to be the cross section for the total vibrational excitation O'vib,indir,t(l~), that is, (3"vib,indir,t(l~) ~,~ O'vib,t(l~ ). The O'vib,t(t~) deduced this way is shown in Fig. 5b, where it is compared with the total vibrational
76
Loucas G. Christophorou and James K. Olthoff
excitation cross section of C12 obtained from two Boltzmann-code analyses. It bears no similarity to them. In spite of the uncertainty involved in the derivation of O'vib,indir,t(E), the derived cross section shows that the indirect vibrational excitation cross section of C12 is large. In the absence of any direct measurement of O'vib,t(~), the cross section O'vib,t(E ) deduced from the assessed data is to be preferred to those provided by the Boltzmann codes. b. Better Understanding from Assessed Data. The critical review and assessment of existing data on electron collisions with the six plasma processing gases covered in this chapter has enhanced our understanding of electronmolecule interactions in a number of ways. This is illustrated by the following two examples. The first example pertains to the enhancement of our knowledge on the negative ion states (NIS) of these molecules, their effects on the various types of electron collision processes, and their respective cross sections. Let us then look at a specific molecule, namely, CC12F 2, and the number and energy positions of its negative ion states that fall below 10 eV. The available data on the number and energy positions of the negative ion states of CC12F 2 are summarized in Fig. 6. The last column in the figure lists the assessed energies of the negative ion states of the CC12F 2 molecule. This assessment is based on published data on the electron affinity, electron attachment using the electron swarm method, electron attachment using the electron beam method, electron scattering, electron transmission, indirect electron scattering deduced in the assessment process, and related calculations (see References in Christophorou et al., 1997b). Thus, the lowest negative ion states of CC12F 2 have been identified with the average positions as follows: aI(C-Clcy* ) at +0.4eV and -0.9eV, b2(C-Clcy*) at - 2 . 5 e V , al(C-Fcy* ) at - 3 . 5 eV, and bl(C-Fcy*) at - 6 . 2 eV. The lowest negative ion state al(C-Clcy*) accounts for both the production of C12 with a binding energy of +0.4 eV and the production of C1- via the lowest negative ion state of C12 at - 0 . 9 eV. [Note that the + and - signs are used here and in Fig. 6 to indicate, respectively, a positive electron affinity and a negative electron affinity (vertical attachment energy) for the various negative ion states of CC12F2.] Similar information has been obtained for other molecules (see Christophorou et al., 1996, 1997a, 1997b; Christophorou and Olthoff, 1998a, 1998b, 1999a). The second example pertains to an increased understanding of electron collisions with the perfluoroalkanes. For example, a thorough review of the literature used to determine the assessed data leads one to a rather simple picture of the collisional behavior of the CF 4 molecule with low-energy electrons.
ELECTRON COLLISION DATA
77
FIG. 6. Energy positions of the negative ion states of C C l z F 2 < 10eV obtained from various experimental and theoretical sources. The last column gives the assessed energies of the negative ion states and their assignments [see text and Christophorou et al. (1997b) for original sources of data].
9Vibrational excitation is the dominant inelastic process for energies < 12.5 eV, that is, below the threshold for electronic excitation. It is dominated by the excitation of the infrared active modes v 3 and v4 via direct dipole scattering below the negative ion resonance region 6 - 8 eV, and via indirect scattering in the resonance region. 9All electronic excitations of C F 4 lead to dissociation (Winters and Inokuti, 1982). Therefore, no separate cross sections for electronic excitation are required. 9Dissociation of CF 4 into neutral fragments begins at ~ 12.5 eV, dominates until ionization sets in, and progressively yields to dissociative ionization. 9Cross sections for positive ion-negative ion pair formation, and multiple ionization, are generally smaller than those for single ionization in the low-energy range of interest.
Loucas G. Christophorou and James K. Olthoff
78
Similarly, a s y s t e m a t i c review of the assessed d a t a for all three p e r f l u o r o a l k a n e m o l e c u l e s ( C F 4 , C2F6, C3F8) reveals: 9large direct v i b r a t i o n a l e x c i t a t i o n cross sections at low energies, a n d very large indirect v i b r a t i o n a l e x c i t a t i o n cross sections in the e n e r g y r e g i o n s of the n e g a t i v e ion r e s o n a n c e s ; 9m a x i m a in the v a r i o u s cross sections at the l o c a t i o n of n e g a t i v e i o n states; 9v a r i a t i o n of the cross sections with m o l e c u l a r p o l a r i z a b i l i t y ( T a b l e II); 9existence of a R a m s a u e r - T o w n s e n d (R-T) m i n i m u m in the total, elastic, a n d m o m e n t u m s c a t t e r i n g cross section a n d its d e p e n d e n c e o n the m o l e c u l a r p o l a r i z a b i l i t y ( T a b l e II); a n d 9d i s s o c i a t i o n of all electronic states into c h a r g e d a n d / o r n e u t r a l fragm e n t s (a p r o p e r t y largely s h a r e d also by C H F 3, CC12F2, a n d C12).
TABLE II ELECTRONSCATTERINGDATA FOR CF 4, C2F6, AND C3F 8 Physical Quantity
CF4
C2F6
C3F8
Position of R-T minimum in eV (cross-section value at the minimum in
CYsc,t(8): 0.13(1.30) (Ym(1~): 0.15(0.13) Cre,i,t(e): 0.18(0.55)
<0.04(< 10.8) 0.15(0.32) 0.18(1.67)
< 0.025( < 9.4)
(Ysc,t(l~):
<0.003( > 12.7) 9.0(21.8) 25(20.4) O'm (~): <0.001(> 13.0) ~20.0 (14.1) CYe,int(e): <0.003(> 12.7) ~20.0 (16.1) O'diss,t (8)" '~ 120(5.6) (Yi,t(l~): 120(5.7)a CYda,t(e): 6.9(0.016)
'~ 5.1(26.4) "~9.1(28.6) > 20( > 27.1) <0.01(>9.5) ~ 17.0 (22.7) <0.01(> 12.2) ~ 20.0(28.0) ~ 120(8.6) ~ 120b(~ 8.0)b 4.0(0.14)
9.0(38.7)
27.3; 29.3; 39.1 (31.9) e'/
46.0; 50.6; 65.0 (53.9)
64.7; 73.6; 94.0 (77.4)
10-20 m 2)
Position of cross section maximum in eV (cross-section value at the maximum in units of 10- 20 m 2)
Static polarizability (10 -25 cm3)d
.~ 9.5(41.3) 9.0(45.0) ~ 120(11.8) ,~ 120c(> 13.0)c 2.9(0.15)
"From revised data (Fig. 14, Section IV). bEstimated from data presented in Fig. 12a of Christophorou and Olthoff (1998a). cEstimated from data presented in Fig. 9 of Christophorou and Olthoff (1998b). dFrom Beran and Kevan (1969). e Average of three values. I The average of two recent experimental values (Au et al., 1997) for this molecule is 28.3 x 10 -28 cm 3.
ELECTRON COLLISION DATA
79
c. Determination of Data Needs, and N e w Related M e a s u r e m e n t s and Calculations. The data assessment for each molecular species naturally identifies gaps in the database. In general, there are two types of data needs: (i) new data to replace existing data judged to be incorrect; and (ii) data that are needed, but are not available. In connection with the first kind of data needs we give as an example the cross section for electron-impact dissociation of molecules into neutral fragments. At the time the CF 4 review (Christophorou et al., 1996) was performed, there was only one direct measurement (Nakano and Sugai, 1992; revised by Sugai et al., 1995b) of the cross section for the production of CF 3, CF2, and CF radicals by electron impact on CF 4. The sum of the revised cross sections for the three radicals was determined (Christophorou et al., 1996) as the recommended value of (3"diss,neut,t(l~). This previously determined cross section is plotted (short dashed curve) in Fig. 7. For comparison, the cross sections for total electron-impact dissociation CYais~,t(~) (Winters and Inokuti, 1982) and ionization cYi,t(~) are also plotted in the figure. An estimated value (dotted curve) of (3"diss,neut,t(l~) deduced from cYai~s,t(e)- cYi,t(e) for energies < 7 0 e V [using the currently recommended values of cYi,t(~) derived in Section IV], is also shown in Fig. 7. Clearly, the measurements of Sugai et al. (1995b) are inconsistent with the recommended values of CYai~s,t(e) and cYi,t(e) by more than one order of magnitude. The need for more accurate measurements of the cross section for this important process led to new measurements by both Mi and Bonham (1998) and Motlagh and Moore (1998). The results of both of these groups are also shown in Fig. 7 and confirm the conclusions of the initial assessment, namely that the cross section from Sugai et al. (1995b) is much too small. The new suggested cross section (3"diss,neut,t(l~) is shown in the figure by the solid line. The fairly large discrepancy remaining between the values of Motlagh and Moore and the values deduced from CYdiss,t(e) -- CYi,t(e) requires further investigation. In connection with the second kind of data, we point to the situation with C H F 3, a gas used in place of CF 4 because of its lower global warming potential. In this instance, when the review and assessment work was begun about 2 yr ago by Christophorou et al. (1997a), there were no measurements of electron scattering cross sections or electron transport coefficients. The cross section from Sugai et al. (1995b) for electron-impact dissociation into neutrals was judged to be incorrect, and there were no absolute cross-section measurements for dissociative electron attachment. Partly as a consequence of the discussions during the review and assessment process, measurements have since been made of the cross section for total electron scattering (Sanabia et al., 1998; Sueoka et al., 1998; Tanaka, 1998), dissociation into C H F 2 and CF 3 neutrals (Motlagh and Moore, 1998), elastic differential
80
Loucas G. Christophorou and James K. Olthoff
FIG. 7. Cross sections for electron-impact dissociation of CF4 into neutrals. . . . . , ~di...... t,t(e) (Sugai et al., 1995b) .....
(3"diss,t(E) - - ~ i , t ( E )
C), t~di . . . . . . t,t(g) (Motlagh and Moore, 1998) x, crai...... t,t(8) (Mi and Bonham, 1998) , Suggested. For comparison, the total dissociation cross section craiss,t(8)(O) (Winters and Inokuti, 1982) and the assessed cri,t(13) (___) are also plotted in the figure.
electron scattering cross section (Tanaka et al., 1997; Tanaka, 1998), electron drift velocity (Wang et al., 1998; Clark et al., 1998), and electron attachment coefficient (Wang et al., 1998; Clark et al., 1998; Jarvis et al., 1997). In addition, a study has been made of the ion chemistry in CHF 3 using Fourier-transform mass spectrometry (Jiao et al., 1997) in which it was reported that at 60 eV the total cross section for the production of CHF~, CF~, CF~-, and CF § was measured to be (3.4 _+ 0.4) x 10-16 cm 2. Figure 8a shows the updated total electron scattering cross section ~i.t(~) for CHF a and Fig. 8b the recently measured electron drift velocities in pure CHF 3 and in mixtures with argon. The small measured (Wang et al., 1998) small electron attachment rate constant ( ~ 13 x 10-14 cm 3 s- 1 for E / N < 50 x 10-17 V cm 2) is thought to be due to traces of electronegative impurities.
ELECTRON COLLISION DATA
81
FIG. 8. (a) Updated total electron scattering cross section (3"sc,t(l~) for CHF 3. 7-1, Cyso,t(e) [calculation, Christophorou et al., 1997a) 9 cysc,t(e) [measurement, Sanabia et al., 1998) 0, Osc,t(~) [measurement, Sueoka et al., 1998) _ _ , Recommended. (b) Electron drift velocity w as a function of E/N for CHF a and mixtures of CHF 3 with Ar (from Wang et al., 1998).
In terms of determining remaining data needs, it is useful to review the state of our knowledge regarding electron-collision data for the six gases we have considered so far. This is summarized in Table III. In general, our knowledge is the best for CF 4 and the worst for CHF 3. With the sole exception of CF4, the database for the other five gases needs much
Loucas G. Christophorou and James K. Olthoff
82
T A B L E III THE STATE OF CURRENT KNOWLEDGE ON ELECTRON-COLLISIONDATA FOR CF4, C2F6, C3F8, CHF3, CC12F2, AND C12
Cross Section/ Coetficient
CF 4
C2F 6
C3F 8
CHF 3
CC12F 2
C12
O'sc,t (8)
R" R Md/C R R/D e R R M M M R S R R R R R
R Sb M/C S None C S M None None R None R R R R R
R S M S None None R M None None R None R R R Ry R
R None None None None None S M None None R M None None None None None
R Cc M/C S D R S M None M None None S R R R R
R C None S D None S None S None None S S S S S S
R
R
S
None
S
M
Crm(~;) Cre,diff(~;) Cre,int(~;)
(3"vib,indir,t (~) Crvib,~ir,t(e) cri,t(e)
(Yi,part (~) (3"ip(~) (3"i,mult(~) cYaiss,t(~)
(3"di...... t,t(~) O'a,t (~) a/N(E/N) q/N(E/N) ( ~ - rl)/N(E/N) ka,t((g))
w(E/N) DT/~t(E/N)
R
R
R
R = Recommended. b S = Suggested. c C = Calculated. d M = Measured. e D = Deduced. YDeduced in this work from the recommended values of values of q/N(E/N).
S
S
M
a
a/N(E/N) and the density-independent
improvement. The cross sections for total electron scattering, elastic integral, total ionization, total dissociation, and total electron attachment are better known than the cross sections for momentum transfer, vibrational excitation, partial ionization, multiple ionization, ion-pair formation, and dissociation into neutrals. Existing data for electron transport and electron attachment and ionization rate coefficients are reliably known for CF4, C 2 F 6 , and C3F8, and to some degree also for C C l z F 2. However, such knowledge is meager for C12 and CHF 3. For some of the molecules, the coefficients, although accurately known in a restricted E/N range, are not known or are poorly known in other or wider E/N ranges.
ELECTRON COLLISION DATA
83
C. DISSEMINATIONAND UPDATING OF THE DATABASE
For the review and assessment process being performed at NIST, the end product is a comprehensive article for each gas published in the Journal of Physical and Chemical Reference Data. These critical reviews contain our best effort to provide a complete, yet concise, review of data relevant to electron collision cross sections for these gases. A much briefer summary of relevant data, containing primarily the recommended and suggested cross-section data and coefficients for the plasma processing gases studied, is also available on the Worldwide Web at http.'//www.eeel.nist.gov/811/refdata. These data are updated as new measurements become available (Christophorou and Olthoff, 1999b).
IV. Assessed Cross Sections and Coefficients A complete assessment of data for all electron collision processes for a single gas is useful in many instances--for example, to the industry using the gas or to the modeler performing calculations on a system containing the g a s - - a n d this is the approach used in the articles resulting from our assessment process. However, the complementary approach, namely, of following the variation of the cross section for each particular electroncollision process for all gases and highlighting its dependence on molecular physical properties is also productive. It allows for the possible understanding of the physics of the collision processes themselves, from which deductions and generalizations can be inferred that can be used to deduce knowledge on collision processes for which no data exist. Thus, in this subsection we follow the latter approach and present in graphical form the recommended or suggested cross sections and coefficients for the following gases, CF 4 (Christophorou et al., 1996), CzF 6 (Christophorou and Olthoff, 1998a), C3F 8 (Christophorou and Olthoff, 1998b), CHF 3 (Christophorou et al., 1997a), CClzF 2 (Christophorou et al. 1997b), and C12 (Christophorou and Olthoff, 1999a) (see the respective references for details and more data, and also the summary in Table III). In both subsequent sections and Figs. 9-21, all quoted assessed data are as discussed in the respective references just mentioned, and no further reference will be made to these articles. When, however, assessed cross sections are reported that incorporated new or revised data, full citation of these sources is made. a. Total Electron Scattering Cross Section (Ysc,t(E). Figure 9a presents the recommended values of the total electron scattering cross section Osc,t(e), for CF4, C2F6, and C3F8, and Fig. 9b gives the recommended values of CYsc,t(e)
Loucas G. Chr&tophorou and James K. Olthoff
84
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Electron energy (eV) FIG. 9. Total electron scattering cross sections (Yse,t(~). (a) Recommended data for
CF 4 ( - - ) , C2F 6 (--), and C3F 8 (-.-) [as revised in this work (see text)]. (b) Recommended data for CC12F 2 (--), CHF 3 ( - - ) [as revised in this work (see text)], and C12 ( - . - ) .
for CC12F2, C H F 3 , and C12. The recommended cross section of Christophorou and Olthoff (1998b) for C3F 8 has been revised in this work to include the recent measurements of Tanaka et al. (1999). Similarly, the cross section for CHF 3 of Christophorou et al. (1997a) has been revised in this work in view of the recent measurements discussed in the previous section (see Fig. 8a). It is interesting to note the deep RamsauerTownsend (R-T) minimum exhibited by the Cysr of CF 4. Such a minimum is expected in the Cysr of C 2 F 6 and C3F8, but the direct electron transmission measurements are unable to locate it possibly because of poor energy resolution in this low energy range. A new, direct, high-resolution measurement of Cysr has been made for C12 ( G u l l e y et al., 1998), which resolves such a low-lying minimum for this gas. Similar high-resolution
ELECTRON
0.001
0.01
85
COLLISION DATA
0.1
1
Electron
10
energy
100
1000
(eV)
FIG. 10. Elastic integral electron scattering cross sections ( Y e , i n t ( ~ ) . Recommended data for CF 4 ( for C2F 6 (_____), C3F 8 ( - . - ) (Christophorou and Olthoff, 1998b; Tanaka et al., 1999), CC12F 2 (_-_) (Christophorou et al., 1997b; 1992), and C12 the cross section plotted is the total elastic CYe.t(e).
tt3-1 ~,~ |
0.001
........
,
0.01
........
,
........
0.1 Electron
J
........
1 energy
J
10
1000
(eV)
11. Momentum transfer cross sections (Ym([;). Recommended data for CF 4 ( suggested data for C2F 6 (____) and C3F 8 (-.-).
Loucas
86 15
Chr&tophorou and James K. Olthoff ’
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=
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FIG. 12. Total electron-impact dissociation cross sections C3F8(11), and CHF3(O ) (data of Winters and Inokuti, 1982).
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Electron energy (eV) FIG. 13. Suggested total cross sections for electron-impact dissociation into neutrals CYdi...... t.t(e) for CF 4 (O) (from Fig. 7), and C12 (A) (Cosby and Helm, 1992).
ELECTRON COLLISION DATA
87
O4
E 0
~J
~-
Electron e n e r g y (eV) FIG. 14. Total ionization cross sections (Yi,t(~). Recommended data for CF4( ) (see text and Christophorou et al., 1996; Rao and Srivastava, 1997; Nishimura et al., 1999); suggested data for C2F6(____), C3F8(-.-), CHF3(...---...), (_-_) CCI2F 2, and C12 (---).
Electron
energy (eV)
Electron energy
(eV)
FIG. 15. Total electron attachment cross section CYa,,(~) (T ~ 300K). (a) Recommended data for CF 4 ( ), CzF 6 (____), and C3F8 (.-.-); (b) Suggested data for CClzF 2 (____), and C12
(- - - ) .
Loucas G. Chr&tophorou and James K. Olthoff
88
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300
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500
600
700
800
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FIG. 16. Density-reduced electron-impact ionization coefficient, ot/N(E/N)(T ~ 300 K). Recommended data for CF 4 ( ), C2F 6 (____), C3F 8 (.-.-), and CC12F 2 (__-__); suggested data for C12 (---).
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E/N ( 10 .21 V m 2) FIG. 17. Density-reduced electron attachment coefficient q / N ( E / N ) ( T ~ 300 K). Recommended data for CF4 ( ), C2F 6 (____), C3F 8 (-’-), and CC12F 2 (__-__); suggested data for C12 (---). The q/N(E/N) for C3F 8 are the density-independent data of Hunter et al. (1987).
ELECTRON
COLLISION
89
DATA
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E/N (10 21 Vm 2) FIG. 18. Density-reduced effective ionization coetficient (or- rl)/N(E/N)(T ,~ 300 K). Recommended data for CF 4 ( ), C2F 6 (____), C3F 8 (.-.-), and CC12F 2 (__-__); suggested data for C12 (---).
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.........
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........
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Mean electron energy (eV) FIG. 19. Total electron attachment rate constant ka,t((g))(T - - ~ 3 0 0 K). Recommended data for CF4 ( ), C2F 6 (____), C3F 8 (.-.-), and CC12F 2 (__-__); suggested data for C12
(---).
Loucas G. Christophorou and James K. Olthoff
90
30
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E/N (10 "17 Vcm 2) FIG. 20. Electron drift velocity w(E/N) (T = ,-, 300 K). Recommended data for CF 4 ( ), C2F6(_____), and C3F s (.-.-); suggested data for CClzF 2 (__-___) and CHF 3 (-...- ...-) (data of Wang et al., 1998).
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E/N ( 1 O-17 V c m 2) FIG. 21. DT/~t(E/N)(T -- ~300 K). Recommended data for C F 4 ( _ _ .) and C 2 F 6 (. suggested data for C3F 8 (.-.-), and CClzF 2 (-_-_).
__);
ELECTRON COLLISION DATA
91
measurements for the other molecules discussed here would be useful in this regard. The Cysr of CF 4, C2F6, and C3F 8 increase with increasing molecular dipole polarizability (Table II). It is also interesting to observe the large increase in the CYsc,t(e)of CHF 3 as the electron energy is decreased below 1 eV (Fig. 9b). This is due to the large (5.504 • 10-30 C m = 1.65 D) (McClellan, 1963) permanent electric dipole moment of this molecule. Similar behavior is to be expected for other polar gases (Christophorou, 1971). b. Elastic Integral Electron Scattering Cross Section O'e,int(E ). Figure 10 presents the recommended values of the elastic integral electron scattering cross section CYe,int(e) for CF4, and suggested data for C2F6, C3F 8 (Christophorou and Olthoff, 1998b; Tanaka, 1998; Tanaka et al., 1999), CClzF 2 (Christophorou et al., 1997b; Mann and Linder, 1992), and C12. The R-T minimum is clearly evident in the cY~,int(e) of both CF 4 and CzF 6 and is located at about the same energy (see Table II). c. Momentum Transfer Cross Section (3"m(E). Figure 11 presents the recommended values of the momentum transfer cross section crm(e), for CF4, and suggested data for CzF 6 and C3F s. The cross section CYm(e) of both CF 4 and CzF 6 exhibits--as does the cross section CYe,int(e) of both molecules--a pronounced R-T minimum located at roughly the same energy (see Table II). A similar minimum is expected for C3F 8. d. Total Dissociation Cross Section O'diss,t(t~). Figure 12 presents the values of the total dissociation cross section CYdiss,t(e) for CF 4, C2F6, C3F8, and CHF3. These are measurements made by Winters and Inokuti (1982) and they are the only data available at this time. The cross section CYdiss,t(e) for CF4, C2F6, C3F s increases with increasing molecular dipole polarizability. e. Total Cross Section for Dissociation into Neutrals O'diss,neut,t(g ). Figure 13 shows the suggested total cross sections for electron-impact dissociation into neutrals for CF 4 (from Fig. 7) and C1a (Cosby and Helm, 1992; Cosby, 1998). It is interesting to note the profound difference in the energy dependence of O'diss,neut,t(E ) for the two molecules. The O'diss,neut,t(E ) for C12 is accounted for by considering the excitation of the C12 molecule to its lowest five excited electronic states (3H u, XHu, 3I-Ig, l l-Ig, 3~E+) (Rescigno, 1994; Christophorou and Olthoff, 1999a). This would indicate that higher electronic states of the C12 molecule preionize with high efficiency, a conclusion consistent with the observed preponderance of C13~ compared to C1 + in electron collisions with the C12 molecule. In contrast, the cross section CYdiss,neut,t(e) of CF 4 indicates that for this molecule dissociation into neutrals and dissociative ionization are competitive processes to high energies [CF~ is rarely formed for the CF 4 molecule (Christophorou et al., 1996)].
92
Loucas G. Chr•tophorou and James K. Olthoff
f Total Ionization Cross Section (Yi,t(~). Figure 14 presents the recommended values of the total ionization cross section cYi,t(e), for CF4, and suggested data for C2F6, C3F8, CHF 3, CC12F2, and C12 . The recommended data for CF 4 in Fig. 14 are based on the cross sections discussed in Christophorou et al. (1996) and two new sets of measurements (Rao and Srivastava, 1997; Nishimura et al., 1999) that have appeared since. g. Total Electron Attachment Cross Section CYa,t(~). Figure 15a,b gives the recommended values of the total electron attachment cross section Oa,t(e) for CF 4, C2F6, and C3F 8, and suggested data for CClzF2, and C12. These data are for T ~ 300 K. It is important to specify the temperature at which the electron attachment cross sections have been measured, since both dissociative and nondissociative electron attachment processes are often strong functions of gas temperature (Christophorou, 1991; Christophorou et al., 1994). With the exception of C3F8 for which there is some evidence for parent anion formation in addition to dissociative attachment, for the rest of these molecules all electron attachment processes are dissociative. It is interesting to note (Fig. 15a) the progressive increase in the magnitude and the progressive shift to lower energy of the O'a,t(E ) of the three perfluoroalkane molecules. It is also interesting to note the increase in both the attachment cross section and the number of negative ion states of the chlorine-containing molecules compared to the perfluoroalkane molecules. For CC12F 2, negative ions (mostly C1-) are produced via a number of negative ion states < 6 e V (Christophorou et al., 1997a), and for C12, C1negative ions are produced at N0. 0 eV, 2.5 eV, and 5.5 eV (Christophorou and Olthoff, 1999a). These negative ion states are also responsible for the peaks in the total electron scattering cross section around these energies. h. Density-Reduced Electron-Impact Ionization Coefficient ot/N(E/N). Figure 16 presents the recommended values of the density-reduced electron-impact ionization coefficient, ct/N(E/N) for CF4, CzF 6, C3F 8, and CC12F2, and suggested data for C12. These data are for temperatures of ~ 300 K. The ot/N(E/N) for CF 4 was extended here to higher E/N than in the earlier study by Christophorou et al. (1996). i. Density-Reduced Electron Attachment Coefficient rl/N(E/N). Figure 17 shows the assessed values of the density-reduced electron attachment coefficient, rl/N(E/N): recommended data for CF4, CaF 6, C3F 8, and CClaF a, and suggested data for C1a. These data are for temperatures of ~ 300 K. The rl/N used for C3F 8 are the density-independent values (Hunter et al., 1987) because for this gas, q / N varies with gas pressure.
ELECTRON COLLISION DATA
93
j. Density-Reduced Effective Ionization Coefficient (o~- q)/N(E/N). Figure 18 presents the recommended values of the density-reduced electron-impact effective ionization coefficient, (0~- q)/N(E/N) for CF4, C2F 6, C3F 8, and CC12F2, and suggested data for C12. The recommended coefficient for C3F 8 was determined in this work using the recommended values of a/N(E/N) in Christophorou and Olthoff (1998b) and the densityindependent values of q/N(E/N) given by Hunter et al. (1987). Note the progressive increase in the value of E/N at which (0~- q)/N = 0 with increasing electron attachment for the perfluoroalkanes.
k. Total Electron Attachment Rate Constant ka,t((E)). Figure 19 presents the recommended values of the total electron attachment rate constant ka,t((~;)) (T ~ 300 K) for CF4, C2F6, C3F8, and CC12F 2, and suggested data for C12. The larger electron attachment cross sections for the chlorine-containing gases (CC12F2 and C12) are clearly evident. I. Electron Drift Velocity w(E/N). Figure 20 shows the recommended values of the electron drift velocity w(E/N) (T ~ 300K) for CF 4, C2F6, and suggested data for C3F 8 , CC12F2, and CHF 3. The data for CHF 3 are recent measurements by Wang et al. (1998). It is interesting to observe the reduction in the negative differential conductivity as the size of the perfluorocarbon molecule is increased. It is also interesting to observe the profound differences in w(E/N) between CF 4 and CHF 3 due to the large permanent electric dipole moment of the latter. m. Ratio of Lateral Electron Diffusion Coefficient to Electron Mobility Dr/lx(E/N ) . Figure 21 shows the recommended values of Dr/Ix(E/N ) (T ~ 300 K) for CF 4 and C2F6, and suggested data for C3F 8 and CClzF 2. Further measurements of this quantity are indicated.
V. Boltzmann-Code-Generated Collision Cross-Section Sets Boltzmann and Monte Carlo codes have provided useful information on electron collision cross sections for a number of gases including those discussed in this chapter. For instance, in the past decade, a number of cross-section sets for electron interactions with CF 4 have been derived that are based upon Boltzmann modeling of electron swarm parameters (Hayashi, 1987; Nakamura, 1991; Bordage et al., 1996; Hayashi and Nakamura, 1998; Bordage et al., 1999). In these investigations a cross-section set is assumed, which is modified iteratively until the electron-transport parameters calculated using the Boltzmann equation best agree with their measured values. Such calculations rely heavily on electron swarm transport
94
Loucas G. Christophorou and James K. Olthoff
coefficients measured over wide ranges of E/N, and on knowledge of collision cross sections from other sources used as input to the procedure. A serious difficulty of this procedure is that the derived electron-interaction cross section set is not a unique solution, and if little is known about the cross sections for the molecule under study, the Boltzmann-code-generated cross sections for individual processes may be physically unrealistic [see, for instance, in Fig. 1 the most recent values of Cym(e) calculated this way by Bordage et al. (1996)], or, in some cases, fictitious [e.g., the cross section for electronic excitation by Hayashi and Nakamura (1998)]. A solution to this problem is to use as inputs to such calculations the assessed data on electron-impact cross sections, to consider them as essentially invariant (within experimental uncertainties) in the iterative process, and to use the assessed electron transport coefficients as a reliable reference for their computed values. In this way, these codes can serve as a means of computing cross sections and coefficients that are not available, and/or as a means of checking the validity of questionable data. The assessed cross sections for C F 4 have indeed been used in such a manner by Bordage et al. (1999). That is, the assessed cross sections and coefficients for C F 4 w e r e used without modification using the solution of the Boltzmann equation under the hydrodynamic regime (Bordage et al., 1996). It was found that the agreement between the calculated and the measured values of the swarm parameters was good for the drift velocity in CF4 and in its mixtures with Ar, for the transverse diffusion coefficient in C F 4 , for the longitudinal coefficient in CF 4 and in its mixtures with Ar, and for the attachment coefficient in C F 4. This rather satisfying agreement between the measured and the calculated electron-transport parameters using the independently assessed cross sections validates both the cross sections and the model, and removes the usual arbitrariness and lack of uniqueness that are often characteristic of cross-section sets derived from Boltzmann analyses. The agreement was, however, not as good for the ionization coefficient at low E/N values. Analysis of the input of the different cross sections on the output of the code enables reasonable conjectures of possible reasons for the lack of agreement between the calculated and the measured values of the ionization coefficient at low E/N. For instance, it was found that the magnitude of the cross section for indirect vibrational excitation and the associated energy loss influence the calculated coefficient significantly as do also the energy thresholds for the various inelastic processes and the angular distributions of the elastically and inelastically scattered electrons. Clearly, this indicates the effect of such processes on the high-energy tail of the electron energy distribution function on which the low E/N values of the ionization coefficient critically depend. In addition, such calculations, by relying on
ELECTRON COLLISION DATA
95
invariant inputs of assessed cross sections, can be employed to assess the effects of excited molecules, as well as the validity of methods used to extrapolate differential scattering cross sections to 0 ~ and to 180 ~ scattering angles from measurements in restricted ranges of electron scattering angles.
VI. Conclusions At this time a reasonably complete set of electron collision cross sections and coefficients exists only for CF 4. The assessed knowledge for this prototype of many plasma processing gases can serve as a benchmark for experimental, theoretical, and model-calculation studies. All the other gases assessed and discussed in this chapter have significant gaps in the known cross sections and coefficients. Data needs for electron interactions with plasma processing gases vary from gas to gas, as can be seen from Table III. Two nearly universal needs for these and other plasma processing gases are experimentally derived cross sections for vibrational excitation and for dissociation into neutrals. Both of these processes play a critical role in industrial plasmas and a minimal amount of data are currently available for CF 4, with virtually no data available for the other gases. To these needs must be added the need for electron-impact electronic excitation cross sections and differential elastic and inelastic cross sections. In connection with angular distribution measurements, there is a need for differential cross sections at small ( ~ 0 ~ and large ( ~ 1 8 0 ~ scattering angles. While such measurements have not been possible to perform in the past, two new recent techniques (Read and Channing, 1996; Zubek et al., 1996; Trantham et al., 1997) may allow such measurements over the entire scattering-angle range from near 0 ~ 180 ~ There are still some electron-collision cross sections that are nearly universally needed for all cases. Foremost among these are electron collision cross sections for radicals and excited species commonly produced in industrial plasmas. Electron-impact ionization cross sections have been measured for only some radicals produced in CF 4 plasmas (Tarnovsky et al., 1993). Boltzmann-code analyses require accurate transport coefficients over wide energy ranges, angular distribution measurements that extend to 0 ~ and to 180 ~ scattering angles, and energy losses assigned to each particular electron-collision process. These analyses require assessed data as "invariant" inputs, and knowledge of electron scattering from and electron attachment to excited species. The effects of such processes on the electron energy distribution functions in plasmas need to be considered.
96
Loucas G. Christophorou and James K. Olthoff
VII. References Au, J. W., Burton, G. R., and Brion, C. E. (1997). Chem. Phys. 221: 151. Beran, J. A. and Kevan, L. (1969). J. Phys. Chem. 73: 3860. Boesten, L., Tanaka, H., Kobayashi, A., Dillon, M. A., and Kimura, M. (1992). J. Phys. B 25: 1607. Bonham, R. A. (1994). Jpn. J. Appl. Phys. 33: 4157. Bordage, M.-C., S6gur, P., and Chouki, A. (1996). J. Appl. Phys. 80: 1325. Bordage, M.-C., S6gur, P., Christophorou, L. G., and Olthoff, J. K. (1999). J. Appl. Phys. 86: 3558. Bukowski, J. D., Graves, D. B., and Vitello, P. (1996). J. Appl. Phys. 80: 2614. Chantry, P. J. (1982). in Applied Atomic Collision Physics, vol. 3, Gas Lasers (H. S. W. Massey, E. W. McDaniel, and B. Bederson, eds., New York: Academic Press, p. 35. Christophorou, L. G. (1991). in lnvited Papers, Proc. XXth Intern. Conf. on Ionization Phenomena in Gases, V. Palleschi, D. P. Singh, and M. Vaselli, eds., Pisa, Italy: Institute of Atomic and Molecular Physics, CNR, July 8-12, 1991, p. 3. Christophorou, L. G. (1971). Atomic and Molecular Radiation Physics, New York: WileyInterscience, Ch. 4. Christophorou, L. G., McCorkle, D. L., and Christodoulides, A. A. (1984). in Electron-Molecule Interactions and Their Applications, L. G. Christophorou, ed., New York: Academic Press, vol. 1, Ch. 6. Christophorou, L. G. and Olthoff, J. K. (1998a). J. Phys. Chem. Ref Data 27: 1. Christophorou, L. G. and Olthoff, J. K. (1998b). J. Phys. Chem. Ref. Data 27: 889. Christophorou, L. G. and Olthoff, J. K. (1999a). J. Phys. Chem. Ref Data 28: 131. Christophorou, L. G. and Olthoff, J. K. (1999b). J. Phys. Chem. Ref Data 28: 967. Christophorou, L. G. and Olthoff, J. K. (2000). Electron interactions with excited atoms and molecules, in Advances in Atomic, Molecular, and Optical Physics, B. Bederson and H. Walther, eds., Boston: Academic Press, vol. 44, p. 155. Christophorou, L. G., Olthoff, J. K., and Rao, M. V. V. S. (1996). J. Phys. Chem. Ref Data 25: 1341. Christophorou, L. G., Olthoff, J. K., and Rao, M. V. V. S. (1997a). J. Phys. Chem. Ref Data 26: 1. Christophorou, L. G., Olthoff, J. K., and Wang, Y. (1997b). J. Phys. Chem. Ref Data 26: 1205. Christophorou, L. G., Pinnaduwage, L. A., and Datskos, P. G. (1994). in Linking the Gaseous and the Condensed Phases of Matter, the Behavior of Slow Electrons, L. G. Christophorou, E. Illenberger, and W. F. Schmidt, eds., New York: Plenum Press, p. 415. Clark, J. D., Wright, B. W., Wrbanek, J. D., and Garscadden, A. (1998). in Gaseous Dielectrics VIII, L. G. Christophorou, and J. K. Olthoff, eds., New York: Plenum Press, p. 23. Cosby, P. C. (1998). Private communication. Cosby, P. C. and Helm, H. (1992). Wright Laboratory Report No. WL-TR-93-2004, Wright Patterson AFB, OH 45433-7650. Csanak, G., Cartwright, D. C., Srivastava, S. K., and Trajmar, S. (1984). in Electron-Molecule Interactions and Their Applications, L. G. Christophorou, ed., New York: Academic Press, vol. 1, Ch. 1. Curtis, M. G., Walker, I. C., and Mathieson, K. J. (1988). J. Phys. D 21: 1271. Gulley, R. J., Field, T. A., Steer, W. A., Mason, N. J., Lunt, S. L., Siesel, J.-P., and Field, D. (1998). J. Phys. B 31: 2971. Hayashi, M. (1987). in Swarm Studies and Inelastic Electron-Molecule Collisions, L. C. Pitchford, B. V. McKoy, A. Chutjian, and S. Trajmar, eds.), New York: Springer, p. 167.
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Hayashi, Y. and Nakamura, Y. (1998). in International Conference on Atomic and Molecular Data and Their Applications, W. L. Wiese, and P. J. Mohr, eds., N I S T Special Publication 926 (National Institute of Standards and Technology, Gaithersburg, MD), p. 248. Huo, W. M. (1988). Phys. Rev. A 38: 3303. Hunter, S. R., Carter, J. G., and Christophorou, L. G. (1987). J. Chem. Phys. 86: 693. Isaacs, W. A., McCurdy, C. W., and Rescigno, T. N. (1998). Phys. Rev. A 58: 309. Jarvis, G. K., Mayhew, C. A., Singleton, L., and Spyrou, S. M. (1997). Intern. J. Mass Spectrom. and Ion Processes 164: 207. Jiao, C. Q., Nagpal, R., and Haaland, P. D. (1997). Chem. Phys. Lett. 269:117. Jones, R. K. (1986). J. Chem. Phys. 84: 813. Kurepa, M. V., and Beli6, D. S. (1978). J. Phys. B 11: 3719. Kurepa, M. V., Babi6, D. S., and Belib, D. S. (1981). Chem. Phys. 59: 125. Lunt, S. L., Randell, J., Ziesel, J.-P., Mrotzek, G., and Field, D. (1998). J. Phys. B 31: 4225. Lymberopoulos, D. P. and Economou, D. J. (1995). IEEE Trans. Plasma Science 23: 573. Mann, A. and Linder, F. (1992). J. Phys. B 25: 533. Masek, K., Laska, L., D'Agostino, R., and Cramarossa, F. (1987). Contrib. Plasma Phys. 27: 15. McClellan, A. L. (1963). Tables of Experimental Dipole Moments, San Francisco: W. H. Freeman and Company, p. 38. McCorkle, D. L., Christodoulides, A. A., and Christophorou, L. G. (1984). Chem. Phys. Lett. 109: 276. Meyyappan, M. and Govindan, T. R. (1996). J. Appl. Phys. 80: 1345. Mi, L. and Bonham, R. A. (1998). J. Chem. Phys. 108: 1910. Morgan, W. L. (1992a). Plasma Chem. Plasma Proc. 12: 449. Morgan, W. L. (1992b). Plasma Chem. Plasma Proc. 12: 477. Motlagh, S. and Moore, J. H. (1998). J. Chem. Phys., 109: 432. Nakamura, Y. (1991). in Gaseous Electronics and Their Applications, R. W. Crompton, M. Hayashi, D. E. Boyd, and T. Makabe, eds., Tokyo, Japan: KTK Scientific, p. 178. Nakamura, K., Segi, K., and Sugai, H. (1997). Jpn. J. Appl. Phys. 36: L439. Nakano, T. and Sugai, H. (1992). Jpn. J. Appl. Phys. 31: 2919. Nishimura, H., Huo, W. M., Ali, M. A., and Kim, Y.-K. (1999). J. Chem. Phys. 110: 3811. Pinh~o, N. and Chouki, A. (1995). in Proceedings X X I I International Conference on Phenomena in Ionized Gases, K. H. Becker, W. E. Carr, and E. E. Kunhardt, eds., Hoboken, USA, July 31-August 4, 1995, Contributed Papers 2, p. 5. Raj, D. (1991). J. Phys. B 24: L431. Rao, M. V. V. S. and Srivastava, S. K. (1997). in Proceedings X X Intern. Conf. on the Physics of Electronic and Atomic Collisions, Scientific Program and Abstracts of Contributed Papers, F. Aumayr, G. Betz, and H. P. Winter, eds., Vienna, Austria, 23-29 July, 1997, vol. II, p. M O 150. Read, F. H. and Channing, J. M. (1996). Rev. Sci. Instrum. 67: 2372. Rees, J. A., Seymour, D. L., Greenwood, C. L., and Scott, A. (1998). Nuc. Instrum. Methods in Physics Research B 134: 73. Rescigno, T. N. (1994). Phys. Rev. A 50: 1382. Rogoff, G. L., Kramer, J. M., and Piejak, R. B. (1986). IEEE Trans. Plasma Science PS-14: 103. Sakae, T., Sumiyoshi, S., Murakami, E., Matsumoto, Y., Ishibashi, K., and Katase, A. (1989). J. Phys. B 22: 1385. Sanabia, J. E., Cooper, G. D., Tossell, J. A., and Moore, J. H. (1998). J. Chem. Phys. 108: 389. Schwarzenback, W., Tserepi, A., Derouard, J., and Sadeghi, N. (1997). Jpn. J. Appl. Phys. 36: 4644. Smith, D., Adams, N. G., and Alge, E. (1984). J. Phys. B 17: 461. Sobolewski, M. A., Langan, J. G., and Felker, B. S. (1998). J. Vac. Sci. Technol. B 16: 173.
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Stefanov, B., Popkirova, N., and Zarkova, L. (1988). J. Phys. B 21: 3989. Stoffels, W. W., Stoffels, E., and Tachibana, K. (1997). Jpn. J. Appl. Phys. 36: 4638. Sueoka, O., Takaki, H., Hamada, A., Sato, H., and Kimura, M. (1998). Chem. Phys. Lett. 288: 124. Sugai, H., Nakamura, K., Hikosaka, Y., and Nakamura, M. (1995a). J. Vac. Sci. Technol. A 13: 887. Sugai, H., Toyoda, H., Nakano, T., and Goto, M. (1995b). Contrib. Plasma Phys. 35: 415. Szmytkowski, C., Krzysztofowicz, A. M., Janicki, P., and Rosenthal, L. (1992). Chem. Phys. Lett. 199: 191. Tanaka, H. (1998). Private communication. Tanaka, H., Masai, T., Kimura, M., Nishimura, T., and Itikawa, Y. (1997). Phys. Rev. A 56: R3338. Tanaka, H., Tachibana, Y., Kitajima, M., Sueoka, O., Takaki, H., Hamada, A., and Kimura, M. (1999). Phys. Rev. A 59: 2006. Tarnovsky, V., Kurunczi, P., Rogozhnikov, D., and Becker, K. (1993). Int. J. Mass Spectrom. Ion Processes 128: 181. Trantham, K. W., Dedman, C. J., Gibson, J. C., and Buckman, S. J. (1997). Bull. Amer. Phys. Soc. 42: 1727. Ventzek, P. L. G., Grapperhaus, M., and Kushner, M. J. (1994). J. Vac. Sci. Technol. B 12: 3118. Wang, Y., Christophorou, L. G., Olthoff, J. K., and Verbrugge, J. K. (1998). in Gaseous Dielectrics VIII, L. G. Christophorou, and J. K. Olthoff, eds., New York: Plenum Press, p. 39. Winstead, C., Sun, Q., and McKoy, V. (1993). J. Chem. Phys. 98: 1105. Winters, H. F. and Inokuti, M. (1982). Phys. Rev A 25: 1420. Zubek, M., Gulley, N., King, G. C., and Read F. H. (1996). J. Phys. B 29: L239.
ADVANCES IN ATOMIC, MOLECULAR,AND OPTICAL PHYSICS,VOL. 44
R A D I C A L M E A S U R E M E N T S IN PLA S M A PR 0 CESSING TOSHIO GOTO Department of Quantum Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. S u m m a r y of Recent Developments in Measurement M e t h o d s for Radicals in Plasma Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Details of in Situ Measurement Methods for Radicals in Processing Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Laser Absorption Spectroscopy (LAS) . . . . . . . . . . . . . . . . . . . . . . 1. I R L A S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. I C L A S and RLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Laser-Induced Fluorescence Spectroscopy (LIF) . . . . . . . . . . . . . . . IV. Representative Results of C F x and Sill x Radicals in Processing Plasmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. C F x Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Characteristics of CF~ Radicals in E C R F l u o r o c a r b o n Plasmas . 2. Behaviors of CF~ Radicals in On-Off M o d u l a t e d Plasmas (Takahashi et al., 1993, 1994; G o t o and Hori, 1996) . . . . . . . . . . 3. Control of Silicon Oxide Etching by Injection of Radicals (Goto and Hori, 1996; Takahashi et al., 1996b) . . . . . . . . . . . . . . 4. Comparisons of C F x Radical Densities in I C P and C C P (Hikosaka et al., 1994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Sill x Radicals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
100 102 102 102 106 106 108 108 108
111 114 119 120 123 124
Abstract: In plasma processing, radicals such as CFx, SiHx, and C H x (x = 1-3) play important roles in both thin-film formation and etching. Various measurement methods for important radicals whose measurements were impossible in the past have recently been developed. With these methods, behaviors of these radicals in plasmas and their correlations with thin-film formation or etching have been clarified. Control techniques for behaviors of radicals have also been developed. This chapter describes recent findings.
I. Introduction Thin-film processing using nonequilibrium plasmas has many practical advantages and, therefore, further development of techniques is strongly desired. Quantitative and physical investigations of plasmas are indispensible in this endeavor. 99
Copyright 92001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003844-7/ISSN1049-250X/01$35.00
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Toshio Goto
Because reactive plasmas with high frequency discharges are used in plasma processing, induction noise and window contamination occasionally occur. These make quantitative measurements of processing plasmas difficult. In particular, the meaurements of neutral nonemissive radicals (in the electronic ground state) such as CF x, SiHx, and CH~ (x = 1-3), which play important roles in thin-film formation or etching, encounter difficulty. However, various new measurement methods for important radicals whose measurements were impossible in the past have recently been developed. Behaviors of radicals in plasmas have now been clarified and control techniques have also been developed with the aid of these methods. In this chapter, a summary of the measurement methods for radicals in processing plasmas developed in recent years will be introduced in Section II. Details of the major in situ measurement methods for radicals in processing plasmas will be described in Section III, and representative results on CF~ and SiH~ radicals will be described in Section IV.
II. Summary of Recent Developments in Measurement Methods for Radicals in Plasma Processing In processing plasmas there exist emissive radicals in electronic excited states and nonemissive radicals in the electronic ground state. Table I shows the radical measurement methods developed to date and the radicals measured using these methods. In these methods, the most common optical emission spectroscopy (OES) has been used to measure emissive radicals and monitor processing plasmas. On the other hand, nonemissive radicals that exist abundantly in plasmas and play important roles in thin-film formation and etching must also be measured, using incoherent optical absorption spectroscopy and especially using the laser spectroscopy that has been developed in recent years. Optical absorption spectroscopy (OAS) using an incoherent hollow cathode lamp as a light source employs compact experimental apparatus and many spectral lines are needed for radical measurements. This OAS is used to measure atomic radicals such as Si (Sakakibara et al., 1991) as well as C. Infrared diode laser absorption spectroscopy (IRLAS) (Itabashi et al., 1988, 1989) has recently experienced particularly significant development among laser spectroscopic methods. With the development of IRLAS, in situ measurements of important radicals such as Sill3, CH3, and CF 3, for which measurements were never made, as well as many other radicals in processing plasmas, have now become possible.
R A D I C A L M E A S U R E M E N T S IN P L A S M A P R O C E S S I N G
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TABLE I SUMMARYOF RADICALMEASUREMENTMETHODSAND MEASUREDRADICALS Measurement Methods (abbreviations in this chapter) Incoherent spectroscopy Optical emission spectroscopy (OES) Optical absorption spectroscopy (OAS) Laser absorption spectroscopy Infrared diode laser absorption spectroscopy (IRLAS) Intracavity dye laser absorption spectroscopy (ICLAS) Ring dye laser absorption spectroscopy (RLAS) Laser-induced fluorescence spectroscopy Conventional laser-induced fluorescence spectroscopy (LIF) Modified laser-induced fluorescence spectroscopy (MLIF) Multiphoton excitation laser-induced fluorescence spectroscopy (MPLIF) Other laser spectroscopy Coherent anti-Stokes Raman spectroscopy (CARS) Laser resonant ionization spectroscopy (RIS) Laser optogalvanic spectroscopy (LOGS) Mass spectroscopy Appearance potential mass spectroscopy (AMS)
Measured Radicals
Various emissive radicals Si, C, F, etc. Sill3, Sill2, Sill, CH3, CF3, CF2, CF, SiF, etc. Sill 2 Si, C
Sill, CH, CF, CFz, etc. Sill 2 H,N,F
Sill 4, Si2H6, GeH4 Sill 3, CH 3, GeH 3
CH3, CH2, CF3, CF2, CF, etc.
As for laser absorption spectroscopy (LAS) using a dye laser, intracavity laser absorption spectroscopy (ICLAS) has been developed in which an RF silane plasma is placed inside the laser resonator to obtain a long absorption length, and the low-density Sill 2 radical density has been measured (Tachibana et al., 1992). In addition, Si atom density in the silane plasma has been measured using laser absorption spectroscopy with a ring dye laser that has narrow linewidth (RLAS) (Hiramatsu et al., 1991). Laser-induced fluorescence spectroscopy (LIF) is the common laser spectroscopic measurement method used to measure many diatomic radicals such as CH, CF, and Sill. Improved LIF have been developed recently, namely a modified laserinduced fluorescence spectroscopy (MLIF) that combines photon counting and plasma modulation techniques, and a multiphoton excitation laserinduced fluorescence spectroscopy (MPLIF). In RF silane plasmas, the Sill 2
Toshio Goto
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radical has been measured using MLIF (Kono et al., 1993) and the H atom has been measured using M P L I F (Kajiwara et al., 1990). Among the other laser spectroscopic measurement methods, there are a coherent anti-Stokes Raman spectroscopy (CARS) used for measuring parent molecules such as Sill 4 and GeH4 (Hata et al., 1985), a laser resonant ionization spectroscopy (RIS) used for investigating fundamental processes of radicals such as Sill 3 and CH 3 (Okada and Maeda, 1989), and the laser optogalvanic spectroscopy (LOGS) used for measuring the electric field strength in plasma. In addition to laser spectroscopic methods, an appearance potential mass spectroscopy method (AMS) has been developed, and measurements of several radicals have been made (Toyoda et al., 1989; Kojima et al., 1989). Using the various radical measurement methods shown in Table I, fundamental processes of radicals have also been investigated (Goto, 1993; Tanaka et al., 1996). To date measurements of the reaction rate constant and diffusion coefficient of the Sill 3 and CF radicals by IRLAS, the reaction rate constant of the CH 3 radical, and the formation cross sections of the CH x, CFx, and SiFx radicals by electron impact on parent molecules have been made.
III. Details of in Situ Measurement Methods for Radicals in Processing Plasmas Regarding the radical measurement methods shown in Table I, the OES and OAS are well known and therefore the explanation is abbreviated here. Among laser spectroscopic methods, LAS and LIF are used as in situ measurement methods for radicals in processing plasmas. Therefore, details will be introduced here, with a focus on IRLAS.
A. LASER ABSORPTION SPECTROSCOPY (LAS) 1. I R L A S
Table II shows radicals measured with IRLAS, transitions used for measurements, measured plasmas, and references. The IRLAS is a useful method by which in situ measurements of many important radicals such as Sill 3, CF 3, and CH 3 in processing plasmas are possible. The Sill 3 and CH 3 radicals are the most important precursors of amorphous silicon and diamond thin-film formations, respectively. For CF x (x = 1-3) radicals, many measurements
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TABLE II SUMMARYOF RADICALSMEASUREDUSING IRLAS Parent Molecules
Radical
Transition (~tm)
Sill4
Sill 3
v2(15)
Sill 2 Sill
v2(10) v = 0-1(5)
CH 4
CH 3
v2(16)
CHF 3 CF,, CzF 6 C4F8 CHF3 CF4
CF 3 CF2 CF
V3(8) Vl(9) t v -- 0-1(8)
CF 3 CF2 CF
v3(8) ] Vl(9) I v = 0-1(8)
Plasma
Reference
P CCP
Itabashi et al. (1988, 1989) Itabashi et al. (1990) Nomura et al. (1994) Yamamoto et al. (1994)
ECR (CCP) P, CCP ECR CCP
ECR
Yamamoto et al. (1994) Naito et al. (1992, 1993, 1994) Wormhoudt et al. (1990) Davies and Martineau (1990) Takahashi et al. (1993, 1994) Miyata et al. (1995, 1996)
RF
Maruyama 1995)
HF
et al.
(1993, 1994,
P is dc-pulsed plasma; CCP is a capacitively coupled RF plasma; HF is a high-frequency plasma; and ECR is the electron cyclotron resonance plasma.
have been m a d e in various E C R and R F f l u o r o c a r b o n plasmas. W i t h IRLAS, in s i t u and almost simultaneous m e a s u r e m e n t s of CF, CF2, and C F 3 radicals in p l a s m a are possible using the same experimental conditions. Figure 1 shows the schematic d i a g r a m of a radical m e a s u r e m e n t system based on IRLAS. The w a v e n u m b e r of the infrared diode laser is varied by changing the cooling t e m p e r a t u r e in the t e m p e r a t u r e region a few tens K as well as the excitation current of the diode laser. The o u t p u t of the laser is 0.1 m W or less, and its linewidth is a p p r o x i m a t e l y 10 M H z or slightly more, which is m u c h n a r r o w e r than the width of the radical a b s o r p t i o n line to be measured. The infrared diode laser b e a m is divided into three parts; they are sent to the reference gas cell for determining the absolute w a v e n u m b e r , the etalon for providing the relative scales of the w a v e n u m b e r , a n d the E C R or R F p l a s m a cell to be measured. The reference gas and etalon signals are m e a s u r e d with the infrared detectors and phase sensitive detection m e t h o d , a n d the a b s o r p t i o n signal from the radical in p l a s m a is m e a s u r e d with the infrared detector and transient wave m e m o r y .
Toshio Goto
104
Trigger
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Figure 2 illustrates examples of the absorption profile of the CF 3 radical and the transient absorption waveform of the R18 (18) line of the v3 band observed in the RF CHF 3 plasma (Maruyama et al., 1993). The derivation method of the CFx radical densities from the measured absorption data shown in Fig. 2 is described very briefly here (Maruyama et al., 1993). The absorption coefficient k(v) is obtained by substituting the measured I A(v)/I o(V) into the following application of Lambert's law. k(v) = - ~ l n
1
io(vl/
(11
Here L is the absorption length, I A(V) is the laser intensity absorbed in plasma and Io(v) is the laser intensity without absorption. Because in the ECR fluorocarbon plasma the lifetimes of the CFx radicals were long enough (around 1 s), the CF x radicals were assumed to distribute uniformly between the mirrors placed at intervals of 200 cm, and the absorption length L was estimated to be 200 cm x the number of passes. The CF x radical density N(N", K") of the lower level of the measured absorption line is obtained by integrating the absorption coefficient k(v) over the Gaussian profile corresponding to the translational temperature assumed to be 300 K and substituting it into the following equation:
N(N", K") = 8~cv 2 gN"gK"gr' gN'gK'gI'
1 f A(N', K' - N", K") k(v)dv
(2)
RADICAL MEASUREMENTS IN PLASMA PROCESSING
105
FIG. 2. Examples of (a) the absorption profile of the CF 3, radical and (b) the transient absorption waveform of the R18 (18) line observed in the on-off modulated RF CHF 3 plasma.
Here c is the light velocity, v is the wavenumber of the absorption line, 9 are the statistical weights of the upper and lower states with the quantum numbers N, K, and I, and A(N', K'-N",K") is the A coefficient. The total CFx radical density N(X) in the electronic ground state is obtained by substituting the measured N(N", K") and the rotational temperature assumed to be 300 K into the partition function (Gordy and Cook, 1970).
Toshio Goto
106
Ar+
i
I RF power source
Dye laser
laser
M2" Timing
pulse generator I
I ]
1
t
i Monochro" I~ mator
L
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FIG. 3. Schematic diagram of the Sill 2 radical measurement system based on ICLAS.
2. I C L A S and R L A S
Figure 3 shows the schematic diagram of ICLAS. The ICLAS is a measurement method for obtaining a long absorption length, in which an RF silane plasma is placed inside a resonator of a cw dye laser that was devised in such a way that the laser light is able to go back and forth inside the plasma many times and can be used to measure the Sill 2 radical density of the order of 10 9 cm 3 or less (Tachibana et al., 1992). The RLAS is an absorption method that uses a ring dye laser with a narrow linewidth as a light source, and it can be used to investigate density characteristics of the Si atoms in an RF silane plasma (Hiramatsu et al,, 1991).
B. LASER-INDUCED FLUORESCENCE SPECTROSCOPY (LIF)
Conventional LIF is a method in which we excite radicals in the electronic ground state to the electronic excited state using a tunable pulsed dye laser, measure the LIF signal emitted after excitation, and then determine the density and temperature of some radical. Figure 4 shows the schematic diagram of the conventional LIF system. The M L I F is a method in which we detect the very weak LIF signal after cut-off of the plasma by combining the on-off modulated plasma and photon counting technique, and then determine the low radical density. This has been developed for measuring the Sill 2 radical in an RF silane plasma. Figure 5 shows one example of the LIF spectrum observed using M L I F (Kono et al., 1993). Since the Sill 2 radical is reactive with a parent silane
RADICAL M E A S U R E M E N T S IN PLASMA P R O C E S S I N G
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Boxcar integrator
Pump FIG. 4. Schematic diagram of a radical measurement system of the conventional LIF.
molecule, its density is low in the R F silane p l a s m a a n d because the excited Sill 2 radical is predissociated, m e a s u r e m e n t of the Sill 2 radical using c o n v e n t i o n a l L I F was difficult. M e a s u r e m e n t s of a t o m s such as H a n d N are difficult because the a b s o r p t i o n lines transiting from their g r o u n d state are in the v u v w a v e l e n g t h region. H o w e v e r , with the d e v e l o p m e n t of M P L I F , m e a s u r e m e n t s of those a t o m s is n o w possible. T h e M P L I F is a m e t h o d in which we excite a t o m s in the g r o u n d state to the excited state with two or three p h o t o n a b s o r p t i o n
300 ~1
I
I
I
I
I
I
"J200 E
._~ ----" 100 ...I cM
.:g_ if3
_ 0/I 579.6
I
I 579.8
I
I 580.0
V~velength (nm)
I
I 580.2
FIG. 5. The LIF spectra of the Sill 2 radical observed with MLIF.
Toshio Goto
108
using a high-power uv excimer laser, observe the LIF signal emitted in the visible wavelength region, and then determine atom density.
IV. Representative Results of CF x and Sill x Radicals in Processing Plasmas Using the measurement methods described in Section III, many investigations on characteristics of important radicals in processing plasmas have been made over the last 10 yr. In this section, only representative results concerning CFx and SiH~ radicals will be described. These results have been obtained with three kinds of plasma sources as shown in Fig. 6. The capacitively coupled RF plasma (CCP) has been used widely in the plasma processing field. It is obtained by supplying RF power (13.56 MHz) to 2-plane parallel electrodes and has a relatively low electron density of 109-101~ cm -3 and a low electron temperature of about 2eV. The CCP source shown in Fig. 6 consists of a stainless-steel plasma chamber 40-cm in diameter and 40-cm in length with plane parallel electrodes of 20-cm diameter. The chamber also has a White-type multireflection system 200-cm long. The laser beam is passed across the plasma 10 or more times to obtain a larger absorption signal. The electron cyclotron resonance plasma (ECR) is obtained in the low-pressure region (< 1 Pa) using microwave power (2.45 GHz) and a magnetic field. It has a high electron density of around 1012 cm -3 and a high electron temperature of more than 5 eV. It is suitable for ultrafine semiconductor processing. The ECR source shown in Fig. 6 consists of a stainless steel plasma chamber 15-cm in diameter, 28-cm long, and a stainless-steel process chamber 40-cm in diameter and 40-cm long. A stainless-steel substrate plate is placed at an axial position 20 cm downstream from the end of the plasma chamber. The process chamber also has a White-type multireflection system 200-cm long. The inductively coupled RF plasma (ICP is obtained by supplying RF power (a few tens MHz) to a loop antenna. It has a high electron density of approximately 1012 c m - 3 and a medium electron temperature. A. CFx RADICALS 1. Characteristics o f CF x Radicals in E C R Fluorocarbon Plasmas
Figure 7 shows the CFx radical densities as a function of microwave power obtained in four kinds of ECR fluorocarbon plasmas (Miyata et al., 1996).
FIG. 6. Typical plasma processing chambers in which radical measurements have been made.
10 14 . . . . .
..
,
.
10 14
10 14 o
i---1
~
~-
CF2
u
CF3
10 13~
10 13
I
I
"
4
CF
10 13
, ..43...--- --.--.O ~ - ’ - ’ -
~1012
10
-o
1011
o
CF
z~ CF 2 u CF 3 1010 0
'
200
'
'
' 400
'
' 600
Microwave
power
(a)
C4F 8
'
800
[W]
12 ~
Lx
10
11 - ~ 1 7 6 1 7 6 1 7 6 1 7 6
/M/p'/5"
"~ z~ CF2 []
f[ 10 10/ 0
. . . . . 200 400
600
M i c r o w a v e power (b)
C2F6
,
, 800 [W]
10 I0 0
. . . . . . . . 200 400 Microwave (c)
power CF4
CF 3
9 CF 4 , , 600 800 [W]
o u
0
0
'
CF CF 2 CF 3
9 CHF 3 . . . . . 400 600 80(
~ 200
M i c r o w a v e power (d)
[W]
CHF 3
FIG. 7. The C F x radical densities as a function of microwave power in various ECR fluorocarbon downstream plasmas measured using IRLAS. The pressure and flow rate of each fluorocarbon gas are 0.4 Pa and 3 sccm, respectively.
RADICAL MEASUREMENTS IN PLASMA PROCESSING
111
They are of the order 1011~ 1013cm -3 and apparently show rather complicated behavior. However, taking the ratio (C/F) of the numbers of C and F atoms in a parent molecule and comparing those behaviors, the C F and C F 2 radical densities increase with the C / F ratio but the C F 3 radical density scarcely changes. This difference occurs mostly for the following reason. The C F x radicals are formed primarily by the dissociation of parent molecules t h r o u g h electron impact. However, in the case of the C F 3 radical as reproduced from fluorocarbon thin film deposited on the electrodes and wall, its rate is large and this depends only marginally on discharge conditions. As this reproduced fraction is added to the primary fraction, the behavior of the C F 3 radical density differs from the other two.
2. Behaviors of CFx Radicals in On-Off Modulated Plasmas (Takahashi et al., 1993, 1994; Goto and Hori, 1996) All results shown here were obtained at a C H F 3 pressure of 0.4 Pa, a C H F 3 flow rate of 5 sccm, and a pulse cycle of 100 ms in the on-off m o d u l a t e d E C R C H F 3 plasma. Figure 8 shows the CF, CF2, and C F 3 radical densities as a function of duty ratio at a microwave power of 300 W (Takahashi et al., 1993, 1994).
2. C
f
0
51.5
CF 9
CF2
Z&
CF3
,
,
0 ,m
0.5
o.(] ?
,
,
,
I
,
5O Duty ratio
,
!
100 (~)
FIc. 8. The CFx radical densities as a function of duty ratio at a microwave power of 300 W in the ECR CHF 3 downstream plasma measured using IRLAS. The pressure and flow rate of CHF 3 gas are 0.4 Pa and 5 sccm, respectively. The pulse period is lOOms. The CF x radical densities are normalized to unity at a duty ratio of 15%.
Toshio Goto
112 40
Si Si02 ,
E
30
E E
O
Q
50 W
/k
A
300 W
F1
I
600 W
2O .iJ L
E O
.+2_ 10 0
0
50
Duty r a t i o
1O0
( % )
FIG. 9. Deposition rates on Si and SiO 2 surfaces as a function of duty ratio at microwave powers of 50, 300, and 600 W obtained under the same conditions as in Fig. 8.
The CF 3 radical density changes slightly but the CF and CF 2 radical densities increases considerably with a decrease in duty ratio. Although interpretation of the behaviors of the CFx radicals is currently difficult, the production and extinction processes during the on-period may make important contributions; additionally, for CF 3, reproduction from the fluorocarbon films deposited on the chamber wall by ion bombardment during the on-period may also contribute (Miyata et al., 1996). It has been found by this measurement that the ratios of these radical densities change with the duty ratio. This result indicates that the ratio of the radical densities can be controlled with simple on-off plasma modulation. The fluorocarbon films were deposited on the Si and SiO 2 surfaces in the downstream plasma region at relatively high microwave powers. Figure 9 shows deposition rates of the fluorocarbon films on Si and SiO 2 surfaces as a function of duty ratio at microwave powers of 50, 300, and 600 W. There are reports that the bombardment of charged species of low energy promotes the activation of the surface sites followed by the reaction with the
RADICAL MEASUREMENTS IN PLASMA PROCESSING
113
CFx radicals for growth of fluorocarbon films (d'Agnostino et al., 1983; Kitamura et al., 1989). Therefore, assuming that fluorocarbon films are deposited mainly during the on-period of microwave power, the deposition rates have been obtained by dividing the fluorocarbon film thickness by the plasma duration of the on-period. The behavior of the deposition rate of the fluorocarbon films at 300 W as shown in Fig. 9 is similar to those of the CF and CF 2 radical densities shown in Fig. 8. Moreover, those at 50 and 600 W were similar only to the behavior of the CF 2 radical density. Therefore, it is believed that the CF 2 radical contributes dominantly to the growth of the fluorocarbon films in the present ECR CHF 3 plasma. The actual etching rates of SiO 2 and Si were also measured as a function of duty ratio of 300 W microwaves. In this experiment, the rf (400 kHz) bias voltage of 150 V was applied to the substrate. The result is shown in Fig. 10. Here the etching rate represents the etching depth divided by the on-period of plasma assuming that the fluorocarbon film is assumed to be etched mainly during the on-period of plasma. The etching rate of SiO 2
40
.
.
.
.
I
.
.
.
0
.
Si
Q SiO2
30 l= E
~.
20
Q
b.8
r
,"
o
10
u.I
0 ~
.
.
~
~
i
0
~
[
!
!
50 Duty
ratio
|
!
100 (~)
FIG. 10. Etching rates of Si and SiO 2 as a function of duty ratio at a microwave power of 300 W obtained under the same conditions as in Fig. 8.
114
Toshio Goto
increases with a decrease in the duty ratio while that of Si does not change appreciably. It is said that SiO 2 etching occurs by the reaction of C and F atoms in the fluorocarbon film with the Si and O atoms on the SiO 2 surface, and with the assistance of ions that bombard the fluorocarbon film deposited on the SiO 2 substrate (Mayer and Barker, 1982). The behavior of SiO 2 etching in Fig. 10 is similar to that of the deposition rate of fluorocarbon film at 300 W as shown in Fig. 9. This supports the belief that the SiO2 etching is enhanced by the fluorocarbon film deposition on the SiO 2 surface. On the other hand, Si etching is suppressed by the deposition of fluorocarbon film, which prevents Si from being etched by F atoms, and as a result the Si etching rate does not change appreciably. It is seen from Fig. 10 that the selectivity of SiO2/Si increases with a decrease in the duty ratio. This suggests that the selectivity of SiO2/Si etching can be controlled with the simple on-off modulation of plasma. When H 2 gas was added to C H F 3 gas the behaviors of the CF x radicals in the Hz/CHF 3 plasma differed from those in the pure C H F 3 plasma. Figure 11 shows CF and CF 2 radical densities (after pure C H F 3 plasma exposure) as a function of H 2 partial pressure at a duty ratio of 15%, microwave power of 300 W, and C H F 3 pressure of 0.4 Pa (Takahashi et al., 1996a). With the increase in H 2 pressure, CF 2 radical density decreases monotonously but the CF radical density increases rapidly and then decreases. Therefore, although the C F 2 radical density is five times as high as the CF radical density in the pure C H F 3 plasma, the CF radical density becomes even higher than the C F 2 radical density at H 2 pressure of above 0.02 Pa. As already mentioned here, although the dominant precursor of fluorocarbon film formation in the pure C H F 3 plasma is believed to be the CF 2 radical, it is expected from the result shown in Fig. 11 that the contribution of the CF radical to fluorocarbon film formation increases rapidly with the increase in H 2 pressure and the CF radical becomes the dominant precursor of the fluorocarbon film formation.
3. Control of Silicon Oxide Etching by Injection of Radicals ( Goto and Hori, 1996; Takahashi et al., 1996b) a. Experimental Apparatus for a Radical Injection Technique. In the CF 2 radical injection technique (RIT), the ECR plasma process system shown in Fig. 6b was used with the following modifications. The CF 2 radical injection source was attached to the sidewall of the ECR plasma chamber and the Ar or Hz/Ar mixture was introduced into the top. This structure enabled us to obtain the ECR Ar and Hz/Ar downstream plasmas with CF 2 radical
RADICAL
MEASUREMENTS
5
'
I
IN PLASMA
'
!
'
115
I
CF2
~4
0
PROCESSING
CF
1
0 0
,
0
I
0.2
,
I
0.4
,
I
0.6
H2 partial pressure ( Pa ) FIG. 11. The CF and CF 2 radical densities (after pure C H F a plasma exposure) as a function of H 2 partial pressure at a duty ratio of 15%, microwave power of 300 W, and C H F a pressure of 0.4 Pa in the ECR C H F 3 / H 2 downstream plasma.
injection. The 1.3-cm wide tube was set at the boundary between the plasma and process chambers to prevent hexafluoropropyleneoxide ( H F P O ) from being dissociated by electron impact in the ECR region. The resonance region was moved about 10 cm downward by changing the coil current, and the substrate was moved about 15 cm upward. Under this condition, the electron density and temperature were estimated to be of the order of 108 cm -3 and about 2 eV, respectively, from the probe measurement, in the ECR Ar downstream plasma at an Ar pressure of 0.8 Pa and 800-W of microwave power. The CF 2 radical was selectively created from pyrolysis of H F P O in a resistively heated one-eighth-in-stainless steel tube. The heated H F P O gas pressure and flow rate were 0.67 Pa and 10sccm, respectively. The CF 2 radical density increases with inner wall temperature, reaching about 1 x 1013 cm -3 at 900 K, which was measured using IRLAS. The CF 2 radical is injected into the ECR downstream plasma through the tube. Here it was confirmed using IRLAS that the CF and CF 3 radical densities were of the order of 1011 cm -a or less, respectively, which were negligibly small compared with the CF 2 radical density.
116
Toshio Goto
b. Results in ECR Ar and H2/Ar Downstream Plasmas with C F 2 Radical Injection. Figure 12 shows the deposition rates of fluorocarbon films formed on Si surfaces as a function of microwave power in the ECR Ar and Hz/Ar downstream plasmas with C F 2 radical injection. In the Ar plasma, the Ar pressure and flow rate are 0.8 Pa and 14 sccm, respectively. In the Hz/Ar plasma, the H 2 pressure and flow rate are 0.26 Pa and 10 sccm, respectively, and the Ar pressure and flow rate are 0.4 Pa and 7 sccm, respectively. The C F 2 radical density is fixed at about 1 x 1013 cm -3. The fluorocarbon film formed is negligible without plasma exposure and the deposition rates increases linearly with the microwave power in the Ar and Hz/Ar plasmas, although the injected C F 2 radical density is fixed. It has been suggested that the fluorocarbon film formation occurs due to the reaction of CF and C F 2 radicals with the surface activated by ion bombardment (d'Agnostino et al., 1983). Then the deposition rate R of the fluorocarbon film by the C F 2 radical can be given by
R = K[CF2]F
(3)
where K is constant, [CF2] is the C F 2 radical density and F is the flux of the charged species bombarding the surface. As the Ar emission intensity increased linearly with increasing microwave power in both plasmas, so did the flux F of the charged species that bombarded the surface. Then film deposition rate R can increase linearly with increasing microwave power, which agrees with the result shown in Fig. 12. Moreover, when ions were removed with a magnetic field of 0.3 T, the film formed was negligible. These show that the fluorocarbon film is formed from the C F 2 radical with the assistance of the ion flux. The fluorocarbon films deposited on the Si surfaces were analyzed using x-ray photoelectron spectroscopy (XPS). Figure 13a, b shows the C (1 s) photoelectron peaks in the XPS spectra of the films formed on the Si surfaces at microwave powers of 200 and 800 W in the ECR Ar and H2/Ar downstream plasmas with the C F 2 radical injection of 1 x 1013cm -3, respectively. The other experimental conditions are the same as in Fig. 12. In Fig. 13a, the strong peaks are those o f - C F 2 components and these films are fluorine-rich whereas in Fig. 13b, the strong peaks are those o f - - C - - C components and the carbon-rich films are formed. This suggests that the H atoms in the plasma scavenge the F atoms in the film formed by the C F 2 radical as follows: H + F--C(s)--o HF + - - C ( s )
(4)
In this case, because the H atom density incident on the surface increases
RADICAL MEASUREMENTS IN PLASMA PROCESSING
4 I,2. 3~
i
i
,
I
9 Ar plasma 0 H2 /Ar plasma
i
I
i
117
,
////'tO
P,
0
500 Microwave power (W)
I
1000
FIG. 12. Deposition rates of fluorocarbon films formed on the Si surfaces as a function of microwave power in the Ar and Hz/Ar ECR downstream plasmas. The injected CF 2 radical density is fixed at 1 x 1013 cm-3. In the Ar plasma, the Ar pressure and flow rate are 0.8 Pa and 14 sccm, respectively. In the Hz/Ar plasma, the Hz/Ar pressures are 0.26/0.4 Pa and the Hz/Ar flow rates are 14/10sccm.
with increasing microwave power, the density of the F atoms, in the film scavenged by the H atoms increases with the H atom density. However, these H atoms do not appreciably affect the deposition rate of the film, as shown in Fig. 12. Thus the H atoms merely change the composition of the film. Next the effect of the fluorocarbon films formed by the surface reaction of the CF 2 radical on the SiO2/Si etching selectivity was investigated by applying an rf (400 kHz) bias voltage to the substrate in the E C R Ar and Hz/Ar downstream plasmas. Figure 14 shows the etching rates of Si and SiO2 as a function of bias voltage to the substrate at microwave power 800 W in the E C R Ar and Hz/Ar downstream plasmas with CF 2 radical injection of 1 x 1013 cm-3. The other conditions are the same as those in Fig. 12. In the E C R Ar plasma, the fluorine-rich (F/C = 1.5) fluorocarbon films shown in Fig. 13a are formed on the Si and SiO 2 surfaces at bias voltages of up to - 30 V. At bias voltages of above - 50 V, the etching rates of SiO2
Toshio Goto
118
-C.F2 j(
-C-C 200W
200W -C-CFx
-CF
"C'CFx, ~
e-
I
v
I-
I
I
I
i
i
i
I
I
I
i
I
I
I
I
I
I
I
I
I
I
I
I
800W
ffl e-
om
I
800W
t-
I
298
I
!
294
I
I
290
I
I
286
1
Binding energy (eV) (a)
I
282
298
,I
I
294 290 286 282 Binding energy (eV)
. . . .
(b)
FIG. 13. (a) C (1 s) photoelectron peaks in the XPS spectra of the films formed on the Si surfaces at microwave powers of 200 and 800 W in the ECR Ar downstream plasma and (b) those in the ECR Hz/Ar downstream plasma. The other conditions are the same as in Fig. 12.
and Si increase in the same manner when bias voltages is higher. The SiO2/Si etching selectivity does not vary with bias voltage. On the contrary, in the ECR H z/Ar plasma where the carbon-rich (F/C = 0.4) fluorocarbon films shown in Fig. 13b are formed, Si is not etched even when a bias voltage of - 4 0 0 V is supplied and it is covered with the fluorocarbon film. Although the SiO 2 is also covered with the fluorocarbon film at bias voltages < - 2 0 0 V, it is etched at a bias voltage > - 2 0 0 V, where an etching rate of 33 nm/min at - 4 0 0 V is attained. Thus, the carbon-rich film is highly resistive to etching and high etching selectivity is obtained. It has been suggested by Mayer and Barker (1982) that SiO 2 etching is caused by the reaction of Si and O atoms on the SiO 2 surface with F and C atoms in the fluorocarbon film, and with the assistance of ion bombardment. As shown in Fig. 14, bias voltages > - 2 0 0 V are needed for SiO 2 etching in Hz/Ar plasma, while SiO 2 is etched at low bias voltages > - 5 0 V
RADICAL MEASUREMENTS IN PLASMA PROCESSING '
I'
l
I
-
3O-
/// (2.8)
~ 20~
!
/
9
Si02 //,l (2.6)
0
,
I
'
S102
/
/ Ar plasma
/
/
O i /L
'
;
,/
/ ,(7,1-1"/"
~ 10~-
....
I
119
/ H2/Ar plasma
_1 . . . . . . . . . . . . . . . . . I
_
,
-200 -400 Bi as vol tage (V) I
,
I
i
I
FI6. 14. Etching rates of Si and S i O 2 a s a function of the bias voltage at a microwavepower of 800 W in the ECR Ar and H2/Ar downstream plasmas. The other conditions are the same as in Fig. 12.
in Ar plasma. In H2/Ar plasma with CF 2 radical injection, the carbon-rich film is formed on the S i O 2 surface. As this carbon-rich film protects the S i O 2 surface against ion bombardment, Ar ion energy > - 200 V is needed for SiO 2 etching. The results obtained in this study suggest that the CF 2 radical contributes greatly to fluorocarbon film formation and SiO 2 etching.
4. Comparisons of CF x Radical Densities in ICP and CCP (Hikosaka et al., 1994) The measurements of the CFx radical densities in inductively coupled RF plasma (ICP) and capacitively coupled RF plasma (CCP) were also made using AMS. Table III shows them. Here the F atom densities are relative values obtained with actionmetry. In low-pressure, high input power ICP, the F density is high and the CF x radical densities are low due to high dissociation of radicals and parent molecules. On the contrary in highpressure, low input power CCP, the CFx radical densities are high and the F atom density is low.
Toshio Goto
120
TABLE III COMPARISONS OF THE CF x AND F RADICAL DENSITIES IN THE INDUCTIVELY COUPLED R F PLASMA (ICP) AND CAPACITIVELY COUPLED R F PLASMA ( C C P ) USING C F x GAS; THE UNIT IS 1012 c m - 3 FOR THE C F x RADICALS; THE F ATOM DENSITY IS THE RELATIVE ONE MEASURED USING ACTINOMETRY
ICP RF power 1000 W CF4 pressure 1.3 Pa CCP RF power 30 W CF4 pressure 13.3 Pa
CF 3
CF 2
CF
F
CF~-
CF +
2.5
0.9
0.7
(10)
~0.01
~0.1
13
2
3
(0.8)
<0.01
B. S i l l x RADICALS
Amorphous silicon thin films used widely in solar cells and liquid crystal displays are formed using RF silicon plasmas. The Sill x radicals contribute this amorphous silicon thin-film formation dominantly. Figure 15 shows the spatial distribution of the S i l l 3 radical density measured in capacitively coupled SiH4/H 2 plasma using IRLAS for the first time (Itabashi et al.,
~?
10.0
~
• v
.~...~--0-"0-0 9
7.5
-
5.0 t"0 t~
2 "0
2.5
=5_ 0.0 co
,
0
C~D elect rode
I
10
,
I
20
Distance (mm)
30
RF electrode
FIG. 15. Spatial distribution of the Sill 3 radical density in the capacitively coupled RF SiH4/H 2 plasma measured using IRLAS for the first time. The RF power is 125 W, the SiH4/H 2 pressures are 6.7/4 Pa, and the flow rate is 16 sccm.
RADICAL MEASUREMENTS IN PLASMA PROCESSING 1010
."
121
.......
E
o
v
>., .i.a [-. "o
SiH4/A r
U)
m
u "o
"C~~
109 ) SiH4/H 2
C~l
r 108
9
1
.
,
|
,
,
|
|I
9
,
10 S iH 4 concen t ra t ion
100 (~)
FIG. 16. The Sill 2 radical density as a function of Sill 4 concentration in the capacitively coupled SiHg/Ar, H 2 plasmas measured using ICLAS. The RF power is 15W, the total pressure is 26.7 Pa, and the total flow rate is 10 sccm.
1990). The Sill 3 radical density is close to 1012 cm -3 and increases slowly from the grounded electrode to the RF electrode. Using the incident flux density of the Sill 3 radical to the substrate obtained from the slope of that distribution, the deposition rate of amorphous silicon thin film by the Sill 3 radical was estimated. This explains the large fraction of the measured rate. Moreover, it was observed that the Sill 3 radical density and the deposition rate had a good correlation. It has been demonstrated from these results that the Sill 3 radical is the most important precursor for film formation in CCP. Figure 16 shows the Sill 2 radical density as a function of Sill 4 concentration in capacitively coupled SiH4/Ar, H 2 plasmas using ICLAS (Tachibana et al., 1992). Since the very long absorption length can be obtained in ICLAS, low Sill 2 radical density of the order of 109 cm -3 or less can be measured. The Sill 2 radical density was measured also using MLIF. The two results by ICLAS and M L I F were in good agreement considering the difference in the experimental conditions. The Sill radical density was measured using LIF and IRLAS, and the Si atom density was measured using incoherent OAS and RLAS. Figure 17 shows the Sill 3, Sill 2, Sill, and Si radical densities as a function of Sill4 concentration at an RF power density of 0.6 W/cm 2 and a
Toshio Goto
122 1012 ~:
i
,
i
i
i
i
i
,
i
_ 1011 E O 4.a itl e-
t-
1010 -~
I011
-o
o
o -ID
b; =2
.=2_
09
1010
109
& -.1-.
I
0
I
I
20
I
I
40
I
I
60
I
I
80
I
-
m
o'~
100
Sill 4 concent rat ion ( ~ ) FIG. 17. Sill3, Sill2, Sill, and Si radical densities as a function of Sill 4 concentration in the capacitively coupled SiH4/Ar plasma measured using various spectroscopic methods. The RF power density is 0.6 W/cm 2 and the total pressure is 5 Pa.
total pressure of 5 Pa in capacitively coupled SiH4/Ar plasma. As shown in Fig. 17, in CCP the density of the Sill 3 radical with a long lifetime (a few ms) is very high ( 1 0 1 1 - 1 0 1 2 c m - 3 ) and increases with an Sill 4 mixture ratio. On the contrary, the densities of the Sill 2, Sill, and Si radicals with short lifetimes, < 100 gs, are in the order of 10 9 cm-3 or less, respectively, and they decrease with Sill 4 concentration. In the H 2 gas mixture, similar results were obtained but Si atom density decreased significantly. It has been found in the Xe gas mixture that Si Sill 3 radical density increases with Xe pressure. This occurs due to the selective formation of Sill 3 by collisions of Xe metastable atoms and parent molecules. The Sill3, Sill2, Sill, and Si radical densities were also measured in ECR SiH4/H 2 plasma. Table IV shows the orders of those densities measured in ECR plasma together with them in CCP (Yamamoto et al., 1994). In high-pressure, low input power CCP, Sill 3 radical density is high (close to 10 x2cm -3) while Si atom density is <108 cm -3. On the contrary, in low-pressure, high input power ECR where the dissociation rate of parent molecules is very high, Sill 3 radical density falls ( ~ 10 l~ cm-3), whereas Si atom density increase ( ~ 10 9 cm-3).
RADICAL MEASUREMENTS IN PLASMA PROCESSING
123
T A B L E IV ORDERS OF THE Sill3, S i l l 2, Sill, AND Si RADICAL DENSITIES IN THE CAPACITIVELY COUPLED R F PLASMA ( C C P ) AND THE ELECTRON CYCLOTRON RESONANCE PLASMA ( E C R ) USING S i H g / H 2 MIXTURE GAS
CCP R F p o w e r 125 W S i H 4 / H 2 p r e s s u r e 6.7/4 P a ECR R F p o w e r 400 W S i H 4 / H 2 pressure 0.67/0.67 P a
Sill 3
Sill 2
Sill
Si
7 • 1011
~ 10 9
'~ 10 9
'~ l 0 s
1 • 109
1 x 109
2 x 101~
As already mentioned here, the development of radical measurement methods and systematic investigations in recent years have clarified the various behaviors of Sill x radicals and the contribution of these radicals to amorphous silicon thin-film formation.
V. Conclusions The in situ measurement method for radicals in plasmas used in semiconductor processing (using the infrared diode laser absorption spectroscopic method (IRLAS) as well as other methods) has undergone considerable development during the last 10 yr. These developments have made it possible to investigate the behaviors of many radicals as well as the contributions of many radicals to either thin-film formation or etching. In etching processing the behaviors of CF x (x = 1-3) radicals in various fluorocarbon plasmas and their correlation with fluorocarbon film formation and etching have also been clarified. For thin-film formation processing, the behaviors of SiHx radicals in silane plasmas and their contribution to amorphous silicon thin-film formation as well as those of the CH 3 radical in hydrocarbon plasmas have been clarified. The in situ measurement method for radicals in plasmas will be further developed in the future and behaviors of various radicals also will be clarified quantitatively. These areas of research are expected to contribute very significantly to further plasma processing field developments.
124
Toshio Goto
VI. References d'Agnostino, R., Cramarossa, F., Colaprico, V., and d'Ettole, R. (1983). Mechanisms of etching and polymerization in radiofrequency discharges of CF4-H2, CF4-CEF4, CF6-H 2, CaFs-H 2. J. Appl. Phys. 54: 1284-1288. Davies, P. B. and Martineau, P. M. (1990). Infrared diode laser diagnostics of methane plasmas produced in a deposition reactor. Appl. Phys. Lett. 57: 237-239. Gordy, W. and Cook, R. L. (1970). Microwave Molecular Spectra, New York: Interscience. Goto, T. (1993). Recent advances in radical measurements on plasmas used for semiconductor processing. O YO BUTURI 62:666-675 (in Japanese). Goto, T. and Hori, M. (1996). Radical behavior in fluorocarbon plasma and control of silicon oxide etching by injection of radicals. Jpn. J. Appl. Phys. 35: 6521-6527. Hata, N., Matsuda, A., and Tanaka, K. (1985). CARS as a diagnostic tool of silane discharge plasmas. O YO BUTURI 54:208-214 (in Japanese). Hikosaka, Y., Nakamura, M., and Sugai, H. (1994). Free radicals in an inductively coupled etching plasma. Jpn. J. Appl. Phys. 33: 2157-2163. Hiramatsu, M., Sakakibara, M., Mushiga, M., and Goto, T. (1991). Measurement of the density and translational temperature of Si (3pE1D2) atoms in RF silane plasma using uv laser absorption spectroscopy. Meas. Sci. & Technol. 2: 1017-1020. Itabashi, N., Kato, K., Nishiwaki, N., Goto, T., Yamada, C., and Hirota, E. (1988). Jpn. J. Appl. Phys. 27: L1565-L1567; (1989). Jpn. J. Appl. Phys. 28: L325-L328. Itabashi, N., Nishiwaki, N., Magane, M., Naito, S., Goto, T., Matsuda, A., Yamada, C., and Hirota, E. (1990). Spatial distribution of Sill 3 radicals in RF silane plasma. Jpn. J. Appl. Phys. 29: L505-L507. Kajiwara, T. Takeda, K., Kim, H. J., Park, W. Z., Okada, T., Maeda, M., Muraoka, K., and Akazaki, M. (1990). Application of laser fluorescence spectroscopy by two-photon excitation into atomic hydrogen density measurement in reactive plasmas. Jpn. J. Appl. Phys. 29: L154-L156. Kitamura, M., Akiya, H., and Urisu, T. (1989). Polymer deposition and etching mechanisms in CEF 6 radio-frequency plasma as studied by laser-induced fluorescence. J. Vac. Sci. & Technol. 137: 14-18. Kojima, H., Toyoda, H., and Sugai, H. (1989). Observation of CH 2 radical and comparison with CH 3 radical in a rf methane discharge. Appl. Phys. Lett. 55: 1292-1294. Kono, A., Loike, N., Okuda, K., and Goto, T. (1993). Laser induced fluorescence detected of Sill 2 radicals in a radio frequency silane plasma. Jpn. J. Appl. Phys. 32: L543-L546. Maruyama, K. and Goto, T. (1995). Variation of CF3, CF 2 and CF radical densities with RF CHF 3 discharge duration. J. Phys. D 28: 884-887. Maruyama, K., Ohkouchi, K., Ohtsu, Y., and Goto, T. (1994). CF3, CF 2 and CF radical measurements in RF CHF 3 etching plasma using infrared diode laser absorption spectroscopy. Jpn. J. Appl. Phys. 33: 4298-4302. Maruyama, K., Sakai, A., and Goto, T. (1993). Measurement of the CF 3 radical using infrared diode laser absorption spectroscopy. J. Phys. D 26: 199-202. Mayer, T. M. and Barker, R. A. (1982). Simulation of plasma-assisted etching processes by ion-beam techniques. J. Vac. Sci. & Technol. 21: 757-763. Miyata, K., Hori, M., and Goto, T. (1996). CF x radical generation by plasma interaction with fluorocarbon films on the reactor wall. J. Vac. Sci. & Technol. A 14: 2083-2087; (1996). Infrared diode laser absorption spectroscopy measurements of CF x radical densities in electron cyclotron resonance plasmas employing C4F 8, C2F 6 and CHF 3 gases. J. Vac. Sci. & Technol. A 14: 2343-2350.
RADICAL MEASUREMENTS
IN PLASMA PROCESSING
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Miyata, K., Takahashi, K., Kishimoto, S., Hori, M., and Goto, T. (1995). CF x (x = 1-3) radical measurements in ECR etching plasma employing C 4 F 8 gas by infrared diode laser absorption spectroscopy. Jpn. J. Appl. Phys. 34: L444-L447. Naito, S., Ito, N., Hattori, T., and Goto, T. (1994). Correlation between CH3 radical density and carbon thin film formation in RF discharge CH 4 plasma. Jpn. J. Appl. Phys. 33: 5967-5970. Naito, S., Ikeda, M., Ito, N., Hattori, T., and Goto, T. (1993). Effect of rare gas dilution on CH 3 radical density in RF discharge CH 4 plasma. Jpn. J. Appl. Phys. 32: 5721-5725. Naito, S., Nomura, H., and Goto, T. (1992). Measurements of CH 3 radical in RF methane/rare gas plasma using infrared diode l'aser absorption spectroscopy. Rev. Laser Eng. 20: 746-751. Nomura, H., Kono, A., and Goto, T. (1994). Effect of dilution gases on the Sill 3 radical density in an RF Sill4 plasma. Jpn. J. Appl. Phys. 33: 4165-4169. Okada, T. and Maeda, M. (1989). Application of laser ionization spectroscopy to plasma processing and its related fields. Rev. Laser Eng. 17:536-545 (in Japanese). Sakakibara, M., Hiramatsu, M., and Goto, T. (1991). Measurement of Si atom density in radio frequency silane plasma using ultraviolet absorption spectroscopy. J. Appl. Phys. 69: 3467-3471. Tachibana, K., Shirafuji, T., and Matsui, Y. (1992). Measurement of Sill 2 densities in an RF discharge silane plasma used in the chemical vapor deposition of hydrogenated amorphous silicon film. Jpn. J. Appl. Phys. 31: 2588-2591. Takahashi, K., Hori, M., and Goto, T. (1996a). Fluorocarbon radicals and surface reactions in fluorocarbon high density etching plasma. II. H 2 addition to electron cyclotron resonance plasma employing CHF 3. J. Vac. Sci. & Technol. A14: 2011-2019. Takahashi, K., Hori, M., Inayoshi, M., and Goto, T. (1996b). Evaluation of C F 2 radical as a precursor for fluorocarbon film formation in highly selective S i O 2 etching process using radical injection technique. Jpn. J. Appl. Phys. 35: 3635-3641. Takahashi, K., Hori, M., and Goto, T. (1993). Control of fluorocarbon radicals by on-off modulated electron cyclotron resonance plasma. Jpn. J. Appl. Phys. 32: L1088-L1091; (1994). CF x (x = 1-3) radicals controlled by on-off modulated electron cyclotron resonance plasma and their effect on polymer film deposition. Jpn. J. Appl. Phys. 33: 4181-4185; (1994). Characteristics of fluorocarbon radicals and CHF 3 molecule in CHF 3 electron cyclotron resonance downstream plasma. Jpn. J. Appl. Phys. 33: 4745-4751. Takahashi, K., Hori, M., Maruyama, K., Kishimoto, S., and Goto, T. (1993). Measurements of the CF, C F 2 and CF 3 radicals in a CHF 3 electron cyclotron resonance plasma. Jpn. J. Appl. Phys. 32: L694-L697. Tanaka, H., Boesten, L., and Hatano, Y. (1996). Fundamental processes in reactive plasmas-- a report on the current status of research. O YO BUTURI 65:568-577 (in Japanese). Toyoda, H., Kojima, H., and Sugai, H. (1989). Mass spectroscopic investigation of the CH 3 radicals in a methane rf discharge. Appl. Phys. Lett. 54: 1507-1509. Wormhoudt, J. (1990). Radical and molecular product concentration measurements in CF4 and CH 4 radio frequency plasmas by infrared tunable diode laser absorption. J. Vac. Sci. & Technol. A 8: 1722-1725. Yamamoto, Y., Nomura, H., Tanaka, T., Hiramatsu, M., Hori, M., and Goto, T. (1994). Measurements of absolute densitie3s of Si, Sill and Sill 3 in electron cyclotron resonance SiH4/H 2 plasma. Jpn. J. Appl. Phys. 33: 4320-4324.
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ADVANCES IN ATOMIC, MOLECULAR,AND OPTICAL PHYSICS, VOL. 44
RADIO-FREQ U E N C Y P L A S M A M O D E L I N G FOR L 0 W- TEMPERA TURE PR 0 CESSING TO SHIA K I M A KA BE Department of Electronics and Electrical Engineering, Keio University, Yokohama 223-8522, Japan I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. R a d i o - F r e q u e n c y Electron T r a n s p o r t T h e o r y . . . . . . . . . . . . . . . . . . . . A. Semiquantitative T h e o r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Expansion P r o c e d u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Direct Numerical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. M o d e l i n g of R a d i o - F r e q u e n c y Plasmas . . . . . . . . . . . . . . . . . . . . . . . . A. G o v e r n i n g E q u a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Local Field A p p r o x i m a t i o n M o d e l . . . . . . . . . . . . . . . . . . . . . . . 2. Q u a s i t h e r m a l Equilibrium M o d e l . . . . . . . . . . . . . . . . . . . . . . . . 3. Relaxation C o n t i n u u m M o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . 4. H y b r i d M o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. System E q u a t i o n s in Inductively Coupled P l a s m a . . . . . . . . . . . IV. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
127 128 130 132 136 141 142 142 145 146 147 149 153 153 153
Abstract: P l a s m a processing using a radio-frequency (rf) plasma for semiconductor device fabrication has been developed rapidly during the last decade. As the basis of plasma processing, an rf electron swarm t r a n s p o r t under nonequilibrium conditions is described by the B o l t z m a n n equation. The system equations and the various m e t h o d s of rf plasma modeling are given.
I. Introduction Radio-frequency (rf) glow discharges have been used widely in microelectronic device fabrication and new material manufacture (Graves, 1994; Makabe and Garscadden, 1998). They differ from dc glow discharge plasmas in that the plasma is maintained even in an electrodeless chamber as well as between metallic and/or dielectric electrodes. They are used to produce the radicals and ions responsible for surface reactions in plasma etching and in plasma chemical vapor deposition. Detailed knowledge of ion and radical transports as well as of the electrical properties of an rf glow discharge is of 127
Copyright 92001 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-003844-7/ISSN 1049-250X/01 $35.00
128
Toshiaki Makabe
great importance for prediction and design of plasma processes. The area of interest is obtained in the vicinity of the boundary between the collisiondominated nonequilibrium plasma and the collisionless plasma. It is of utmost importance, therefore, that we study electron transport under microscopic collisions with gas molecules in an rf field. The purpose of this chapter is first to describe rf electron swarm transport under nonequilibrium conditions in an alternating field over a wide frequency range in order to gain an understanding of the energy and momentum relaxation phenomena of the electrons. In principle, there are three methods to investigate the rf electron swarm. One is a kinetic approach based on the Boltzmann equation (Chapman and Cowling, 1978). The difficulty of solving the Boltzmann equation is considerable and only in trivial cases can an analytical solution be found even in a dc field. The most popular approach is the expansion procedure of the velocity distribution in terms of spherical harmonics (Robson and White, 1997). A second method is the Monte Carlo particle model based on first principles. The model calculates the transport histories of each individual electron by choosing random numbers for times of flight, scattering events, scattering angles, etc. It requires large computational time because statistical accuracy increases only as the reciprocal of the square root of the sample size. The third method uses the deterministic probability related to collisional scattering instead of random numbers to calculate velocity changes based on the electron collision in an rf field (Maeda et al., 1997). This method is similar to the Monte Carlo particle model in the sense of the direct tracking of electron trajectories in phase space. On the other hand, it resembles the Boltzmann equation method in its use of collision integrals. As computers become more powerful, this new method promises to be of great use for the analysis of the electron swarm. In the following, the modeling technique is given for studying the low-temperature rf plasma and for predicting the surface processing. For the last 15 years, rapid advances in a quantitative understanding of rf glow discharge plasmas have been made by fluid models and the Monte Carlo particle model on the basis of the fundamental collision processes of the electron, ion, and neutral species, and of the swarm parameters.
II. Radio-Frequency Electron Transport Theory For the treatment of nonconservative electron swarm transport subject to ionization and electron attachment in addition to elastic and excitation collisions in the presence of a spatially uniform, time-varying sinusoidal field with the amplitude of Eo (the RMS value, ER) and the angular frequency
RADIO-FREQUENCY PLASMA MODELING
129
E(t) = E o cos(ot) = Re[E o exp(iot)]
(1)
of co
we employ the spatially homogeneous Boltzmann equation. The essential characteristic of electron swarm transport in an rf field in comparison with dc is the appearance of a phase-shift with respect to the applied field E(t). This phase-shift is expressed by introducing a complex velocity-distribution function. The governing equation is the Boltzmann equation
c~ eE(t) c~ G(v, t) + - - ' - G(v, t) = J(G, F) c~t m c~v
(2)
where v and t are velocity and time, e and m are the electronic charge and mass, and J is the collision term, respectively. By considering the time evolution of the electron number density ne(t ) due to ionization and attachment, the time-dependent distribution function G(v, t) may be separated into the product of a time-varying number density ne(t ) and a velocity-distribution function g(v, t) normalized to unity under a periodic steady-state condition:
G(v, t) = ne(t)g(v, t)
(3)
f g(v, t) dv - 1
(4)
where
ne(t ) and g(v, t) are separated by substituting Eq. (3) into Eq. (2) using a separation function RT(t ). Following substitution, we obtain 0 eE(t) 0 & g(v, t) -~ --'m c~v g(v, t) = J(G, F) - RT(t)g(v, t)
(5)
where the separation function RT(t ) represents the difference between the ionization and attachment rates Ri(t ) - Ra(t) and is related to the electron number density by
ne't>
Toshiaki Makabe
130
where n o is the density at t = 0. In this chapter we deal with two of the methods of obtaining the time-dependent velocity distribution and the related swarm parameters: ionization rate and drift velocity.
A. SEMIQUANTITATIVETHEORY
We will begin our discussion by describing the conventional theory, which uses the 2-term approximation of the Boltzmann equation. In this case, the isotropic random and the directional-drift components of the velocity distribution go(V, t) and g~(v, t) are written as follows: 0 Ot g~
t) + ~[E, o), gl(v, t)] = -go(V, t)/Ze(V )
(7)
0 at g ~(v, t) + ~[E, co, go(V, t)] = - g ~(v, t)/'Cm(V)
(8)
where Te(V) and ~,,(v) are, respectively, the collisional relaxation times (Fig. 1) for energy and momentum transfer for an electron with velocity magnitude v. They are expressed as follows:
"l~e(V)- 1 ~,~
NI(2m/M)Qm(v) + ~ Qj(v) + Qi(v) + Qa(v)lv
(9)
N IQm(v) + ~ Qj(v) + Qi(v) + Qa(v)l v
(10)
J
Tm(V) - 1
=
J
where m / M is the electron-to-molecule-mass ratio, and N is the molecular number density; Qm(v) denotes the elastic momentum transfer cross section, Qj(v) denotes the jth excitation cross section, and Qi(v) and Qa(v) are the cross sections for ionization and electron attachment, respectively. In atomic gases such as Ar and He, up to moderate E/N, most of the energy loss of electrons is due to elastic collision with neutral particles. Under those conditions, and for the angular frequencies of interest here, L(v) is much longer than the period of the rf field 2rt/o3, whereas Zm(V) is much shorter (see Fig. 1). The time dependence of the velocity distribution g(v, t) can then be expressed as
g(v, t) = go(V) + cos 0gl(v ) Re[exp(i~0t)]
(11)
RADIO-FREQUENCY
(a)
PLASMA
10 -2
I
r~
10 .4 . . . .
I
I
,. /
x ,,
"~e
"-. -.
x
I; ex
i
", =
131
MODELING
i ’
10 -6-
-i"
~
,7,,
~ 9Imi
i
i
-
,
10 8 ~'~..........
10 I~ t
~'~
i
i
10 .2
10 -1
I
I
1.0
10
Electron energy
1 0 -4
(b)
f
I
I
10 2
[ eV ]
I
I
L-----n
106
"l~e
/ / i
i! ,
~
@ .*=-t
10 .8
~v2
"~" /:i ', r'L, I
~D
"-__1
9
- ~
I /I
'1" ,,
"t
.
10 -’~
10 .3
...... ]........ i 10 .2 10 -1
i 10 0
Electron energy
, 101
, 10 2
10 3
[ eV ]
FIG. 1. Collisional relaxation times of electrons for energy and m o m e n t u m transfer at 1 torr in (a) Ar and (b) C F 4. The quantity t m is the total m o m e n t u m relaxation time. The quantities re, Zv, rex, and t i are the energy relaxation times for elastic, vibrational, total excitation, and ionization collisions, respectively.
Toshiaki Makabe
132
in terms of an effective dc electric field Eeff(v) given by
1 Eo Eeff(v) -" { 1 -~- [03"l~m(V)]2) 1/2 N/~
(12)
The method of employing an effective dc field, Eq. (12), instead of a time-varying field, Eq. (1), is very simple and has been widely used to study swarm transport. With this procedure, the swarm parameters defined in terms of go(V), such as the ensemble average of the energy and the ionization rate, are constant in time although the drift velocity given by g l(v, t) has a periodic time response. For atomic gases, the application of this conventional theory is therefore limited to the high-frequency range where re(V) >> 03-1. For the complex molecular gases frequently employed in plasma processing, however, the situation is not so simple even at high frequency. The difference between atoms and molecules from the viewpoint of electron impact is that molecules have large cross sections for vibrational excitation Qv(v), with energy losses of the order of 0.1 eV over a large range of electron energies. The magnitude of Qv(v) may sometimes be comparable to that for momentum transfer from elastic scattering. In that case, the isotropic part of the distribution go(V, t) as well as g~(v, t) will be modulated in time owing to %(v)< 03-1 even at high frequency. As a result, the conventional theory is inadequate for these cases and a more reliable method is needed. In particular, the concept of the collisional relaxation time becomes important as well as the collision cross sections required for calculation in a dc field for an understanding of the temporal behavior of the electron swarm in a periodic rf field.
B. EXPANSION PROCEDURE Because the velocity distribution g(v, t) is asymmetrical parallel to the field even for low values of E(t)/N, the velocity distribution can be expanded in terms of spherical harmonics, and the temporal behavior is determined by the sum of the higher-order harmonics of the fundamental wave with frequency 03. Expanding g(v, t) in spherical harmonics in velocity space and in a Fourier series in time, we obtain
,vt, Re
0,
l
(13)
RADIO-FREQUENCY PLASMA MODELING
133
where 0 is the angle between - E ( t ) and v expressed as 0 = cos- 1[ _ (v" E)/vE];
g~(v) is real for k = 0 and complex for k > 0, expressing the phase lag of electron transport with respect to the applied alternating field, Eq. (1). It should be noted that the isotropic part of the distribution gko(v) possesses only even harmonics in time, whereas the directional-drift part g](v) possesses only odd harmonics in sinusoidal field. Physically, this is due to the fact that under a pure sinusoidal field, Eq. (1), the energy gain described by the isotropic velocity component is proportional to E(t) 2, that is, even time harmonics. The directional-drift component is a function of E(t), that is, odd harmonics. It is convenient to define an energy distribution f~(e) according to the relation f~(a) = (4rc/m)vg~(v);
e. = mv2/2
(14)
where the normalization conditions of f~(~), from Eq. (4), are expressed as follows:
f o f~
d~ - 1
(15)
In a pure sinusoidal field, symmetry considerations show that only components ff(e), where (s + k) is an even number, can exist, that is, s + k = 2[3, [3 = 1, 2,.... In that case, insertion of expansion (13) into Eq. (5) gives a set of coupled differential/difference equations of the form (Goto and Makabe, 1990).
iko(m/2g) ' /2f sk(~,)
s {d
x/~ 2s -- 1 ~ [~1 f)ll(E)
nt-
f f +~(e)l
s
k - 1 (l~) -1L ds_l f k +1 (t~)] -- ~ [~1 fs-1
eERS+I {d k-X S+I x/~ 2s + 3 ~ [L,fs +, (e) + f/++ x(e)] + ~ [~1 f~k+1 - i (~:)+ rr =
+i +1
s=0 + To] -NEQm(g) + ~ Qj(g) + Qi(e,) + Qa(g)] fsk(~) s4=O
(E)]
} }
(16)
Toshiaki Makabe
134
where 9~1 = 1 for all k 4= 1, and )~ = 2 for k = 1; To is the gas temperature, and I~(e) satisfies the relation
1 and can be expressed as L 0 R~fk-k'(e) ik(e) = -2-2~~ k'=
~ +-~1 k'= ~o
[Rk+ kffi' *(e) +
R~*fk +k'(e)]
(18)
where )~o = 1 for all k 4= 0, and )~o = 2 for k = 0; R~ is the kth component in the Fourier series of RT(t), and the symbol 9denotes the complex conjugate. The collision term in Eq. (16) is expressed as follows: JEfk(e), To] = ~ - ~
~
fNQm(e)ea/2fok(e)+ kBToNQm(e)e2 d
~ Ee- 1/2fok(e)]
+ _1/2 ~9d
t
el/ZNQj(e) fog(e) de
+e_x/2 ~d f~ ~/~N(L(~)fo~(~)d~ a
-~8
+
81/2NQi(8) fk(e) de
(19)
where kB is the Boltzmann constant; ej, e i, and ea are the threshold energies for excitation, ionization and electron attachment, respectively; 8:(1 - 5) is the energy partition ratio between two ejected electrons after ionization. In particular, at ultrahigh frequency, most of the component f~ lies in an energy range less than the electronic excitation threshold ej, and collisions are almost completely limited to elastic, rotational and vibrational scatterings. Under these circumstances, if(e) can be expressed in analytical form from the Boltzmann equation (16) as
fo(~) = Ax/~ ex p
{ - f~
l+EEQr(8)er+Qv(8)ev]/(2m/M)eQm(e) (eER/N) 2 / 2m kBTo+ 3 eQm(e) Z Q(e) 1 + [(o/w/2e/m N Z Q ( e ) ] 2 , -M(20)
RADIO-FREQUENCY PLASMA MODELING
135
This is identical to the expression of Margenau and Hartman (1948), except for the presence of rotational and vibrational collisions. In atomic gases subject only to elastic scattering, the distribution fo~ in the limit o - 1 << "Cm(e) has a Maxwellian form with an effective gas temperature
L
Weff -- g 9 1 -1--k,,~//
(21)
The presence of rotational and vibrational collisions with low threshold energies in molecular gases changes the shape of the distribution substantially in comparison with that obtained in atomic gases. That is, fo(e) can be expressed in the asymptotic form of Eq. (20) as
fo(~) = Ax~ exp
kBTeff
1+
(2m/M)~Qm(~)
The integral in Eq. (22) shows the collisional energy-loss ratio between inelastic and elastic scattering. Recalling the fact that the higher the threshold energy, the faster the energy relaxation time, one would expect that e/ej should be weighted by the energy relaxation time for inelastic scattering and that the effective relaxation time is expressed as Z~eff(e)- 1 =
N [(2m/M)Qm(~) + ~ Qj(~)~j/~] v
(23)
when referring to inelastic collision processes. The electrons with energy will follow closely the time-varying field when m-1 >> .c~ff(e). The macroscopic behavior of the swarm is described in terms of swarm parameters (transport parameters), which are ensemble averages of quantities with respect to the time-dependent velocity (energy) distribution. The mean energy (~(t)) is expressed as
R.I 2.eeik 'f:m 4,2k ,,,,l
25,
ToshiakiMakabe
136 the ionization rate
Ri(t) is expressed as
Ri(t)=RelfNQi(v)vg(v,t)dv] = ReI~k4rte2ik'~
(27)
1
(28)
k (2/m)l/ZeZik~ i NQi(e)~l/Efo2k(e)de
= Re ~
(29)
the excitation rate to level j from the ground state is expressed as
Rj(t)= Re[fvNQj(v)vg(v , t) dv1
(30)
--ReI~k4rte2ikc~
(31)
=Re[~k(2/m)l/2e2ik~~ f~?NQj(g)gl/2fEk(~)de,1
(32)
and the drift velocity is expressed as
Ef
l
I~k-~4~ei(2k+l)t~ v392k+l(v) dv1 = Re [~k-~ 1(2/m)l/Zei(Zk+1)o~t fO ~l/2f?k+l(g) de1 = Re
Diffusion coefficients parallel and perpendicular to the field E(t), Maeda et al. (1997) (see Fig. 3).
Dr(t ), are defined by
(33)
(34)
(35)
DL(t) and
C. DIRECT NUMERICAL PROCEDURE
It is difficult and sometimes very difficult to obtain the time-dependent energy distributions from the set of equations (16) by using the expansion procedure both in velocity space and in time as described in the preceding
RADIO-FREQUENCY PLASMA MODELING
137
FIG. 2. (a) Set of cross sections of Ar/CF4; and (b) related rate coefficients in Ar/CF 4 (5%) as a function of dc-E/N.
Section II.B. Recent developments in large memory computing hardware, however, permit application of direct numerical methods. In this section, a direct numerical procedure (DNP) for solution of the Boltzmann equation in an rf field is briefly described (Maeda et al., 1997), and the results are shown to illustrate the usefulness of the procedure. Because the spatially homogeneous Boltzmann equation represents the time evolution of the velocity distribution only in velocity space, the Boltzmann equation (2) is completely equivalent to the expression g(v + Av, t + A t ) = g(v, t) + J(G, F)At
(36)
where the velocity increment Av is related to At as follows: Av = [eE(t)/m]At
(37)
Equation (36) suggests that it should be possible to calculate the time evolution from an arbitrary initial distribution to a final periodic steady state under the rf field by a differential method. It is essential to consider the change both of the incident angle and of the energy at collision in terms of a deterministic finite probability for each type of collision. For this purpose, it is convenient to evaluate the collisional scattering in spherical coordinates. The electron velocity also changes, however, due to acceleration or deceleration in the electric field, and Cartesian coordinates are more suitable for
Toshiaki Makabe
138
this case. In fact, the transformation of quantities between the two coordinate systems is a serious practical problem, and therefore the simulation in velocity space instead of energy space may be essential. The collision term is expressed in the case of a cold gas To = 0 as
J(G, F) = N
-~ g(v'x, t)v'l (~el(V~l,~) d~'~
+ N ~. fn V'Zvg(v'2, t)V'zCyj(v'2,9)d~ +N
1
(1 -
v_33g(v'3, t)v'3cYi(v'3,8 ) d ~
6)
v
+ N-~1 fn --v' v 4g(v'4, t)v'4cYi(v'4,~) d~ -
N fn g(v, t)V[CYet(V, ~) + ~E(Yj(V, ~) + (Ya(V, ~) + C~i(V, 0)] d~'~ (38)
Here, cy(v, 8) is a differential cross section, defined as the number of electrons scattered into a solid angle d~ = v2 sin OdOdd? dv at scattering angle 0. The subscripts of cy(v, 8), el, j, a, and i denote elastic, excitation, attachment and ionization collisions, respectively. The velocity v~ of the incoming flux prior to elastic scattering is related to the velocity of the outgoing flux v as
!
/)1 =
V
1 --(re~M)(1 - cos 0)
(39)
For excitation, v~ is expressed as vh = ( v 2 7 t- 2e.j/m) 1/2. Similarly, v~ = (v2/~) + 2e.i/m) x/2 and vk = (v2/(1 - 8 ) + 2el~m) 1/2 are the velocity relations for two electrons after ionization. When the scattering is not strongly dependent on angle 0, we may make the approximation of isotropic scattering, which means that the differential cross section cy is independent of 0. For isotropic scattering, cr(v, 8) is replaced by Q(v)/47r, and Eq. (36) can be rewritten in a form for numerical calculation of the time evolution as
9(Vx, vy, v~ + (eE(t)/m)At, t + At) - g(Vx, Vy, vz, t) + J(v~, vy, v~, t)At (40)
RADIO-FREQUENCY PLASMA MODELING
139
where
fn g(v'1, t) d~ J(vx, Vy, vz, t) = NQm(v'l)v'~ 4roy3 +N
XQ~(v' 4roy ~)v'f~g(v'2, t) d~
NQi(v'3)v'32 f
+ 4roy(1 - 6)
v'
g( 3, t) df~
+ nQi(v4)v4~2f g(v] t) dfl 4try8
- N[Qm(v)+ ~ Qj(v)+Qa(v)+ Qi(v)]vg(v, t) (41) Because there is axial symmetry around the z-axis, g is only stored as a function of vz and vx (or Vy) in such a way that the velocity increment Avz satisfies the relation Av~ = (eE(t)/m)At. By so doing, evaluation of g in Eq. (40) merely involves a shifting of the 2D array g(Vx, v~) along v~ at each time interval At, and addition of the corresponding collision term J(vx, Vy, v~, OAt to each array element. The collision integrals for each Vx and vz at time t are calculated by integrating the distribution of v and 0 over both the velocity v and the polar angle 0. The time step At in an explicit method is limited to a very short time in order to satisfy the Courant-Friedrichs-Lewy condition, relating to the velocity-cell-size Av
[eE(t)/m]At % Av
(42)
and to satisfy the differential expression Max[,Cm(V)- x] x At << 1
(43)
A method not restricted by the relation in Eq. (42) is proposed (Matsui et al., 1998). Figure 3 shows the time modulation of the electron swarm parameters in HC1 at ER/N = 100Td as a function of applied frequency f(=c0/2r0 (in detail, as a function of o/N), obtained from D N P (Section II.C). The ensemble average of the energy (a(t)) has several interesting characteristics. One is its time modulation with frequency 2o, and another is the dependence of its time-averaged value on o/N. The time average has a maximum for o/N. Both of these characteristics can be understood from the form of
Toshiaki Makabe
140 1M [Hz]
(a)
10M [Hz]
20M [Hz]
50M [Hz]
200M [Hz]
,8.0 r
oE 4.0 0.0 ~. -4.0 " -8.0
-12.0
(b)
0
n
,
2n 0
~
2n 0
.~.'-">3.0
n
’~ ’
'
'
2n 0
n
,
2~ 0
,
,
i
i
!
,
,
,
n
21
2.0
f
~" 1.0
V
0.0
0
n
.
2n 0
,---,
(C)
a.
~
.,
.
n
,
~'r 2"4
~
.
,
.
.
2n 0 ,
~',_~.,
. ,
,
" _
' .,...' ..._ , , ,' . t s,,..
1.2 0.8
R~x2
(d)
-9
'1::: 1.61
. ,
{
7t
,-',NDT
.
2n 0
.
.
n
,,
2n
0
n
27
,. ,.'i'
1i
R= x 2
0.00
2n 0
Ra
0.4 n"
|
n
,
,, ,._~._-, ,,"
/ ',
i
2n 0
n
2n 0
RI x 2
2n 0
n
~;
2r
,, NDT ND-r
~ ('9
NDL
a 0.8 Z " 0.4 a Z 0.0 0
NDL
n
~t
2n 0
,
i
n
cot
,
!
2n 0
n
~t
2n 0
|
n
(JOt
i
2n 0
n
~t
2r
FIG. 3. T h e time m o d u l a t i o n of the electron s w a r m p a r a m e t e r s in HC1 for different values
of a p p l i e d f r e q u e n c y f at Ee/N = 100 T d in rf fields. (a) Drift velocity; (b) m e a n energy; (c) i o n i z a t i o n a n d a t t a c h m e n t rates; a n d (d) l o n g i t u d i n a l a n d transverse diffusion coefficients.
fo(e, t). A phase lag occurs in (e(t)) with increasing coiN due to the time for collision energy relaxation. The drift velocity Vd(t) in Fig. 3(a) varies with frequency co, and the amplitude of Vd(t) increases gradually as a function of co/N without phase shift. The effect of collision on the drift velocity is due to a rise in the collision rate for inelastic scattering, in particular, vibrational excitation. As coiN further increases, a phase lag appears in the drift velocity.
RADIO-FREQUENCY PLASMA MODELING
141
This coincides with the beginning of electron trapping. Finally, collisionless phenomena occur between electrons and molecules during a cycle of the driving field. The electron swarm will behave as a group vibrating in vacuum under the effect of the field E o cos cot. The instantaneous group velocity has the form Vd(t ) = Re[(eEo/mco ) exp{i(cot + rc/2)}]
(44)
and its magnitude decreases with coiN.
III. Modeling of Radio-Frequency Plasmas In a collision-dominated plasma, two different methods can be used to simulate the radio-frequency (rf) discharge plasma based on the database of molecular collision/reaction processes in gas and surface phases. One is the fluid model and the other is the Monte Carlo (MC) particle model. The particle in cell (PIC) method is primarily developed for collisionless plasmas under a Maxwellian distribution of electrons and ions (Birdsall and Langdon, 1991). The PIC/MC simulation is available for a collision-dominated plasma (Boswell and Morey, 1990; Boswell and Vender, 1990; Birdsall, 1991; Nanbu et al., 1999). In a low-pressure discharge including a strong nonequilibrium region, a hybrid model that combines a fluid and MC model is of practical use (Sommerer and Kushner, 1992; Ventzek et al., 1994); rf plasma is sustained in a periodic steady state in a capacitively or inductively coupled reactor. With increasing the applied frequency to the range of ultrahigh frequency, some of antennas are used in practice to couple the external source and the plasma. The fluid theory is also designated as the moment or continuum theory. The discharge plasma structure and related properties of the active species are modeled as a fluid on the basis of particle continuity, and momentum and energy conservation derived from the velocity moments of the Boltzmann equation (Chapman and Cowling, 1970), c~ ~t
c~ eE(r, t) G(v, r, t) + v .-;- G(v, r, t) + ~ ' - or
m
c? c3v
G(v, r, t) = J(G, F)
(45)
and Maxwell's equations. Figure 4 shows the governing equation systems and related external quantities. The system of equations is not closed and it requires the auxiliary equation, as an equation of state is required to complete the specification in a strongly ionized plasma in thermal equilib-
Toshiaki Makabe
142
FIG. 4. Governing equation system in rf plasma reactors and related external quantities.
rium. The processing plasma for etching or new material production is characterized as a nonequilibrium system, and the electron velocity distribution is far from Maxwellian. Some encouraging fluid models of rf discharge plasmas have been presented in the past decade. In this section, we consider a dynamic rf discharge plasma, mainly maintained between two plane-parallel electrodes separated by a distance d (see Fig. 5). When the voltage source Vo cos(cot) is connected to the reactor by way of a blocking capacitor, the applied voltage between two parallel plates has the form Vapp(t ) :
V o cos(cot)
-- Vdc
(46)
where Vac is the dc self-bias voltage due to the presence of the series blocking capacitor to the powered electrode. A. GOVERNING EQUATIONS 1. Local Field Approximation Model
The electron and ion swarms attain a quasiequilibrium independent of time and space after a finite relaxation time ~ or relaxation distance ~ under a
RADIO-FREQUENCY PLASMA MODELING
143
FIG. 5. Capacitively coupled parallel plate electrode system in an rf glow discharge.
constant reduced field E/N. When it is adequate to assume zero relaxation time or distance, that is, a local field approximation (LFA), the normalized velocity distributions of charged particles depend only on the local instantaneous field E(z, t)/N under a spatially distributed rf field. As a result, the swarm parameters are completely determined as a function of E(z, t)/N alone. Nonequilibrium glow discharges can be simulated under the local field approximation, because we have a considerable amount of database concerning the swarm parameters over a wide range of E/N. The local field approximation has been used successfully to simulate dc and rf glow discharges (Boeuf, 1987), and the approach has provided basic insight into glow-discharge behavior. It consists of conservation equations for electrons and ions and Poisson's equation. In a 1D-t space, these are,
63ne(Z , t) c~t
= -- Vde ( Z , t)
(~ne(Z , t) C~~
nt- D Le ( Z' t)
632ne(Z, t) 63Z ~
+ {Ri(z, t) - R~ (z, t)}ne(Z, t) - R~e(Z, t)ne(Z, t)np(z, t)
(47)
c~np(z, t) c~nv(z, t) c~2np(z, t) c3t = - Vdp(Z, t) c3z + DLp(Z, t) C~Z2 -+-Ri(z , t)ne(Z, t) -- R.e(z, t)ne(Z, t)np(z, t) -Rri(z, t)n.(z, t)np(z, t)
(48)
Tosh&ki Makabe
144
FIG. 6. Time averaged-electron number density in reactive ion etcher in Ar for f = 100 MHz, Vo = 100 V, and p - 50 mtorr, obtained by RCT modeling.
c3n,(z, t) - Vd,(Z, t) c3n,(z, t) c32n,(z, t) c3t = c3--------~+ D L" ( Z ' t) C3z-------W~ + Ra(Z, t)ne(Z, t) -- Rr
~E(z, t)
t)n.(z, t)np(Z, t)
(49)
~ V(z, t)
Oz
Oz 2
_
e
-- e'o {np(Z, t) -- ne(Z, t) -- n,(z, t)}
(50)
where ne, np and n, are, respectively, the number densities of electrons, positive and negative ions; Vds and DLs are the drift velocity and longitudinal diffusion coefficient, where the subscript s is replaced by e for electrons, and by p and n for positive and negative ions; Ri and R , are the ionization and electron attachment rates by direct electron impact; Rre and Rri are the electron/positive ion and positive/negative ion recombination coefficients; and ~o is the permittivity. It should be noted that the governing equations (47) to (50) form a self-consistent closed system, as all of the swarm parameters are given as a function of the local instantaneous field E(z, t)/N (see Fig. 2).
RADIO-FREQUENCY PLASMA MODELING
145
2. Quasithermal Equilibrium Model It is well known that the electron obeys a Maxwellian distribution with temperature T e
fM(8) Tcl/2(kTe)3/2 e
exp
-
(51)
when the system is in thermal equilibrium. If that is the case, the ionization rate under a constant ionization cross section Qz(e)= Q~o can be written analytically as
Ri(z, t) = Nkio exp - k Te(z, t)
(52)
where kio = (8kTe/rcm)X/2(1 + ei/kTe)Qi o. The excitation and electron attachment rates can also be expressed similarly to Eq. (52). The reaction rate in a form of Eq. (52) is called an Arrhenius form if k~o is constant. The electron temperature Te(z, t) in Eq. (52) can be derived from the energy conservation equation in 1D-t space as
~t
ne(Z, t)k re(z, t) +
-~z
= eE(z, t) - ne(Z, t)Vde(Z, t) + D L
One(Z t)} e - -
--eine(Z , t)Nkio exp -- kTe(z, t) -~.ane(Z, t)Nkao exp -- k Te(z, t) --ejne(Z, t)Nkjo exp { -
ej kTe(z,t)}
(53)
where qe(Z, t) is the electron energy flux and is expressed as
5
{
qe(Z, t) = -~ k Te(z , t) rte(Z , t)Yde(Z , t) -- O L One(Z'~z e ~ t)}
(54)
As a result, the structure of an rf glow discharge in quasithermal equilibrium (QTE) can be simulated from the set of Equations (47) to (50) and (53), provided that Vas and DLs are adequately known (Graves, 1987; Lymberopoulos and Economou, 1994).
Toshiaki Makabe
146
3. Relaxation Continuum Model In an rf glow discharge, a positive ion-sheath is formed with high field in front of both electrodes. It is necessary to consider the momentum and energy relaxation of electrons in the sheath regions, where the high field changes rapidly in both time and space (Maeda et al., 1997; Goto and Makabe, 1990). In other words, the electron motion depends on time and on the position of its generation in a sheath and there exists a memory effect. As stated earlier in Section II, the essential characteristic of electron swarm transport in a high-frequency field is the appearance of a phase-lag with respect to the applied field waveform. As a result, we have to consider the relaxation kinetics of momentum and energy of charged particles in order to model the rf glow discharge in nonequilibrium in both time and space (Okazaki et al., 1989). The relaxation equation for momentum is obtained by taking the average of my over the Boltzmann equation (45) in 1D-t space as follows:
= {n~(z, t)mVd~(z, t)} = eE(z, t)n (z, t)
-
ne(Z, t)mVne(z, t)
c~t
--ne(z, t)mVn~(z, t)
0 Vd~(z, t)
Oz
(55)
where (%,) is the time constant for momentum transfer, and is expressed as m Vd~ using the dc value of the drift velocity Vd~ as a function of E(z, t)/N. The energy relaxation time is generally much larger than the momentum relaxation time. Therefore, the mean energy ~,,, the ionization and excitation rates Ri and R;, and the longitudinal diffusion coefficient DL~ are not directly dependent on the instantaneous field but on effective fields. For example, ~m(Z, t) is given by the energy conservation equation from the moment of my2~2 over the Boltzmann equation (45) as
0
(
0n(Z,t)}z
{~m(Z, One(z, t)) = eE(z, t) ~-- Va~(z, t)n~(z, t) + D L e ~
(
-I2--~Rm~,m(Z,t)+~Rj8j-kRi~,ilne(Z,t) --
~z
{[Vale(Z, t)ne(z, t) - DLe(Z, t)c~n~(z, t)/OZ]am(Z, t)} (56)
RADIO-FREQUENCY
PLASMA
147
MODELING
If we define the effective field for era(Z, t) by Ee2f = 8m/eg, then the relaxation equation for Ee2f is derived from Eq. (56) as follows:
~t {Eeff(Z'
where
t)Zne(Z'
{Eeff(Z
t)} :
, t) 2 --
--
E(Z, t)2}ne(Z, t)
COqe(Z,t)
~Z
(57)
q'e(Z, t) denotes the energy flux and is given by
q'e(Z, t)
= Vde(Z ,
t)ne(Z, t)Eeff(z,
t) 2 --
DLe(Z, t)
c~[ne(Z, t)Eeff(z, 0z
t) 2]
(58)
{'Ce> is the energy relaxation time and is estimated to a first approximation as the reciprocal of the energy loss frequency or Eq. (23); e,,(z, t) at position z and time t is then given as a function of Eeff(z, t)/N from values obtained under a uniform and constant field. Consequently, the relaxation continuum (RCT) model consists of the number density continuity and the momentum relaxation of charged particles, and the energy relaxation of electrons in each range of energy as well as Maxwell's equation.
4. Hybrid Model The hybrid model consists of both fluid and particle models. The model is suitable for the simulation of a low-pressure discharge plasma strongly subject to a nonequilibrium transport of the electron that keeps the spatio-temporal memory of production. For example, in a sheath region at low pressure, the fast electron is traced individually under the field E(z, t)
cot r(t)
=
v(z, t) t
ft
e E(z, t) m
(59)
v dt + r(t - At)
(60)
- At
by considering the various kinds of collisions between the electron and the neutral molecule by the Monte Carlo simulation (MCS). The collision between the time ( t - At, t) and the type are judged by using a pseudorandom number (~) uniformly distributed between 0 and 1
N{Qm(v ) +~.Qj(v)+Qi+Qa}vAt'~,
(61)
148
Toshiaki Makabe
FIG. 7. Time-averaged number density distribution of charged particles in reactive ion etcher in Ar and CF4(5%)/Ar for f = 13.56 MHz, Vo = 100 V, and p = 100 mtorr, obtained by RCT modeling.
RADIO-FREQUENCY PLASMA MODELING
149
When the electron at r(t) satisfies the relation { V(z + ;~sh, t - - A t ) -
V(z, t) + g(z, t)} ~< gex
(62)
the fast electron changes to the bulk slow electron that is not able to excite or ionize the neutral molecule. Here, ;~sh is the sheath width. The ensemble average of the fast electron will give the net production rates of the ionization and the bulk electron A i and Abe. Then, the continuity equations of the number density of the bulk electron nbe and all the ions np are written in 2D-t space, respectively, g3t nbe(r' t) q- div Fbe(r , t) -- Abe(r , t) - - Rre(v, t ) n b e n p
(63)
c3t nv(r' t) + div Fv(r, t) = Ai(r, t) - Rre(r , t)nen p
(64)
where Fbe and Fp are the fluxes of the bulk electron and all the ions; Abe is the net production rate of the bulk electrons, and A i is the net ionization rate obtained by the MCS. The total number density of electrons is given by n e = nfe + nbe. Here, the density of the fast electron nfe(r, t) is given by the MCS (Shidoji et al., 1999). The series of equations (59) to (64) are calculated to the satisfaction of Poisson's equation (50). Figure 8 exhibits the 2D spatial distributions of n e, nfe and space potential in the dc magnetron reactor, maintained at 160 V at 30 mtorr in At. The steady-state plasma is confined in front of the target(cathode) under the influence of the external magnetic field (Shidoji et al., 1999). Some kinds of hybrid model analogous to that described here are used to simulate a highly nonequilibrium plasma (Sommerer and Kushner, 1997; Sato and Tagashira, 1991). In addition, there exist a phase-space continuity model by using the Boltzmann equation (Kortshagen et al., 1995; Kaganovich and Tsendin, 1992) and the particle-in-cell Monte Carlo model (Boswell and Morey, 1990; Boswell and Vender, 1990; Birdsall, 1991; Nanbu et al., 1999). The details are in the references. 5. System Equations in Inductively Coupled Plasma
An inductively coupled plasma (ICP) is driven by an rf current source l(t) = Io cos o~t
(65)
150
Toshiaki Makabe
FIa. 8. Two-dimensional spatial profile in dc magnetron discharge maintained for 160 V, 30mtorr in Ar. (a) Total electron density he(X, z) and (b) fast electron density nfe(X , z) and (c) space potential V(x, z).
supplied to a coil arranged around/on a reactor. Therefore, ICP is also named transformer coupled plasma (TCP); ICP is mainly maintained by the induced electric and magnetic fields E(r, t) and B(r, t) given by Maxwell's equations. By introducing the vector potential A(r, t) defined by B(r, t) = rot A(r, t), Maxwell's equations under the presence of electric and magnetic fields is replaced by
(
RADIO-FREQUENCY PLASMA MODELING
V2 - g g ~
,')
(,)
A(r,t)-V
gg-~V(r,t)
V 2 V(r, t) + V. c3A(r, t) = _ np(r, t) 0t
=-gJ(r,t)
-- rle(r , t) -- nn(r , t)
151 (66) (67)
where ~ and la are the permittivity and permeability, and J is the current density of charged particles. We can obtain E(r, t) and B(r, t) by solving the simultaneous partial differential equations (66) and (67) with respect to the vector and scalar potentials A(r, t) and V(r, t) E(r, t) .
.
~A(r, t) .
. ~t
VV(r, t)
B(r, t) = V • A(r, t)
(68)
(69)
In a fluid model of ICP, Poisson's equation (50) in each of the models, Sections III.A.1-4 is replaced by Maxwell's equations (66) to (69). Electron and ion fluxes incident on the wafer contacted with the ICP maintained for the external current source 13.56MHz and 20A in Ar at 50mtorr, are shown in Fig. 9 (Kamimura et al., 1999). The wafer is driven by a low-frequency voltage source of 678kHz and 100V to accelerate ions. The phase-space continuity model of ICP is described in Kortshagen et al., 1995. The boundary conditions for ne, np, nn, etc., are generally of the first or second kind. A boundary condition of the first kind for the electron number density corresponds physically to a fixed density at the boundary, and a condition of the second kind indicates a fixed diffusion flux. The drift-diffusion equations (47) to (49) have second derivatives with respect to position. Boundary conditions must therefore be imposed on both electrodes. A numerically stable solution is, in principle, obtained if time and position steps At and Az for a numerical calculation satisfy the relations At ~< min {A~, (A2)2 }2D L
(70)
’ V~ J
(71)
Az ~< min
where VaAz/D L is the Pecl6t number and K is the spatial wave number. In particular, if the diffusion flux is predominant as compared with the drift,
152
Tosh&ki Makabe
FIG. 9. Electron and ion fluxes incident on the wafer exposed to ICP at 50 mtorr in Ar. ICP is driven at 13.56MHz with amplitude of 20 A. The wafer is biased by low frequency voltage of 678 kHz and 100 V.
the solution is numerically stable. On the other hand, it is not easy to solve the pure drift-diffusion equation without reactions under a dominant drift flow. That is, when the boundary conditions on both electrodes are of the second kind, the solution is not unique. Then, it is useful to employ the Scharfetter and Gummel method (Scharfetter and Gummel, 1969). When the time evolution of an rf plasma is explicitly simulated, the dielectric r e l a x a t i o n time "Cd ,
A t ~ "cd
-- e ( l a p n p 8~ + laene) t
(72)
has to be satisfied to solve Poisson's equation. In a high-density plasma, Eq. (72) gives a very short time At as compared to the rf period, and it requires huge computational time. In order to avoid the time-consuming procedure, an implicit method is proposed to solve Poisson's equation (Ventzek et al., 1994).
RADIO-FREQUENCY PLASMA MODELING
153
IV. Conclusions I have tried to compile the typical models of a low-temperature rf plasma in a collision dominated and nonequilibrium situation, the goals that motivate predictive study of plasma processings in gas and surface phases, and the physics that support plasma etching and deposition. Radio-frequency electron transport theory is first introduced as the basis of the rf plasma in a collision-dominated region. Each of rf plasma models is stably solved in a time-evolved scheme from an arbitrary initial condition by using a workstation or PC machine. A periodic steady-state profile of the rf plasma is obtained in both continuous wave (CW) and pulsed operations. Extraction of an important and active function from an rf plasma produced from a feed gas in the reactor unique in its geometrical and electrical profile is possible through the numerical modeling.
V. Acknowledgments The author wishes to express his gratitude to Z. Lj. Petrovic, R. E. Robson, and N. Nakano for their stimulating discussions in the course of research in rf swarm transport and rf plasma modeling. Thanks are also due to M. Kimura for his considerably patient editing during the preparation of this manuscript.
Vl. References Birdsall, C. K. (1991). IEEE Trans. Plasma Sci. 19: 65-85. Birdsall, C. K. and Langdon, A. B. (1991). Plasma Physics via Computer Simulation, Bristol: Adam Hilger. Boeuf, J.-P. (1987). Phys. Rev. A 36: 2782-2792. Boswell, R. W. and Morey, I. J. (1990). J. Appl. Phys. 52: 21-23; Vender, D. and Boswell, R. W. (1990). IEEE Trans. Plasma Sci. 18: 725-732. Chapman, S. and Cowling, T. G. (1970). The Mathematical Theory of Non-Equilibrium Gases, Cambridge: Cambridge University Press. Goto, N. and Makabe, T. (1990). J. Phys. D 23: 686-693. Graves, D. B. (1994). IEEE Trans. Plasma Sci. 22: 31-42. Graves, D. B. (1987). J. Appl. Phys. 62: 88-94. Kaganovich, I. D. and Tsendin, L. D. (1992). IEEE Trans. Plasma Sci. 20: 66-75. Kamimura, K., Iyanagi, K., Nakano, N., and Makabe, T. (1999). Jpn. J. Appl. Phys. 38: 4429-4435. Kortshagen, U., Pukropski, I., and Tsendin, L. D. (1995). Phys. Rev. E 51: 6063-6078. Lymberopoulos, D. P. and Economou, D. J. (1994). J. Vac. Sci. Technol. A 12: 1229-1236.
154
Toshiaki M a k a b e
Maeda, K., Makabe, T., Nakano, N., Bzenic, S., and Petrovic, Z. Lj. (1997). Phys. Rev. E 55: 5901-5908. Makabe, T. and Garscadden, A. (eds.). (1998). Papers from the Int. Workshop on Basic Aspects of Nonequilibrium Plasmas Interacting with Surfaces. J. Vac. Sci. Technol. A 16: 212-382. Margenau, H. and Hartman, L. M. (1948). Phys. Rev. 73: 309-315. Matsui, J., Shibata, M., Nakano, N., and Makabe, T. (1998). J. Vac. Sci. Technol. A 16: 294-299. Nanbu, K., Morimoto, T., and Suetani, M. (1999). IEEE Trans. Plasma Sci. 27: 1379-1388. Okazaki, K., Makabe, T., and Yamaguchi, Y. (1989). Appl. Phys. Lett. 54: 1742-1744; Makabe, T., Nakano, N., and Yamaguchi, Y. (1992). Phys. Rev. A 45: 2520-2531. Robson, R. E. and White, R. D. (1997). Annals of Physics 261: 74-112. Sato, N. and Tagashira, H. (1991). IEEE Trans. Plasma Sci. 19: 102-112. Scharfetter, D. L. and Gummel, H. K. (1969). IEEE Trans. Electron Devices 16: 64-77. Shidoji, E., Ohtake, H., Nakano, N., and Makabe, T. (1999). Jpn. J. Appl. Phys. 38: 2131-2136; Shidoji, E., Nakano, N., and Makabe, T. (1999). Thin Solid Films 351: 37-41. Sommerer, T. J. and Kushner, M. J. (1992). J. Appl. Phys. 71: 1654-1673. Ventzek, P. L. G., Hoekstra, R. J., and Kushner, M. J. (1994). J. Vac. Sci. Technol. B 12: 461-477.
ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 44
E L E C T R O N I N T E R A C T I O N S WITH EXCITED A T O M S A N D M O L E C U L E S L O U C A S G. C H R I S T O P H O R O U and J A M E S K. O L T H O F F Electricity Division, Electronics and Electrical Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Electron Scattering from Excited A t o m s . . . . . . . . . . . . . . . . . . . . . . . . A. G e n e r a l C o n s i d e r a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. T o t a l a n d Elastic Electron Scattering by Excited A t o m s . . . . . . . . . 1. Rare Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Alkali Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. D e p e n d e n c e of the Total Electron Scattering Cross Section on the A t o m i c Electric Dipole Polarizability . . . . . . . . . . . . . . . . . . C. Inelastic Scattering of Electrons by Excited A t o m s . . . . . . . . . . . . . 1. Cross Sections: Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Rare Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Alkali Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Superelastic Scattering of Electrons by Excited A t o m s . . . . . . . . . . E. Differential Scattering of Electrons by Excited A t o m s . . . . . . . . . . . 1. Differential Elastic Electron Scattering Cross Sections . . . . . . . . 2. Differential Inelastic Electron Scattering Cross Sections . . . . . . . 3. Differential Superelastic Electron Scattering Cross Sections . . . . III. E l e c t r o n - I m p a c t I o n i z a t i o n of Excited A t o m s . . . . . . . . . . . . . . . . . . . . A. Rare Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. O t h e r A t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Electron Scattering from Excited Molecules . . . . . . . . . . . . . . . . . . . . . A. Scattering of Slow Electrons from " H o t " ( V i b r a t i o n a l l y / R o t a t i o n a l l y Excited) Molecules . . . . . . . . . . . . . . . B. Scattering of Slow Electrons from Electronically Excited Molecules C. Superelastic Scattering of Slow Electrons f r o m Excited Molecules . D. Effect of V i b r a t i o n a l E x c i t a t i o n on Electron T r a n s p o r t . . . . . . . . . . V. E l e c t r o n - I m p a c t I o n i z a t i o n of Excited Molecules . . . . . . . . . . . . . . . . . VI. Electron A t t a c h m e n t to Excited Molecules . . . . . . . . . . . . . . . . . . . . . . A. Electron A t t a c h m e n t to " H o t " ( V i b r a t i o n a l l y / R o t a t i o n a l l y Excited) Molecules . . . . . . . . . . . . . . . 1. Dissociative Electron A t t a c h m e n t . . . . . . . . . . . . . . . . . . . . . . . . 2. N o n d i s s o c i a t i v e Electron A t t a c h m e n t . . . . . . . . . . . . . . . . . . . . . B. Electron A t t a c h m e n t to Electronically Excited Molecules . . . . . . . . 1. D a t a on Dissociative Electron A t t a c h m e n t to Electronically Excited Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156 159 159 162 162 172 173 177 177 178 186 188 190 190 191 197 200 203 210 213 215 218 221 222 223 226 228 230 259 268 270
155 All rights of reproduction in any form reserved. ISBN 0-12-003844-7/ISSN 1049-250X/01 $35.00
Loucas G. Christophorou and James K. Olthoff
156
VII. VIII. IX. X.
2. Data on Nondissociative Electron Attachment to Electronically Excited Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
280 282 283 283 284
Abstract: Elastic, inelastic, and superelastic scattering of electrons by and electronimpact ionization of excited atoms are reviewed and discussed and the role of the electric dipole polarizability in the interaction of slow electrons with excited atoms is indicated. The meager knowledge on the scattering of slow electrons from vibrationally and electronically excited molecules is also summarized and discussed, as well as the available information on excitation and ionization by electron impact of electronically excited molecules. The available data on the processes of electron attachment to vibrationally/rotationally and electronically excited molecules and the processes of electron detachment from energy-rich transient anions are also summarized and discussed.
I. Introduction While the investigations of interactions of slow electrons (kinetic energies mostly below ~ 100 eV) with ground-state atoms and molecules are abundant and trace back over a century, studies of the interactions of slow electrons with excited atoms and molecules as a function of the internal energy of the target a t o m or molecule are meager and relatively recent, especially for molecules. The findings of a limited n u m b e r of early investigations have been discussed by Massey and Burhop (1969) and Moiseiwitsch and Smith (1968). M o r e recent work on excitation into and out of metastable levels of rare-gas atoms has been reviewed by Lin and Anderson (1992) and cross-section measurements for electron-excited a t o m collisions have been surveyed by T r a j m a r and Nickel (1993). Recent work on molecules has been briefly summarized by C h r i s t o p h o r o u (1992), Christ o p h o r o u et al. (1994), and M a s o n et al. (1994). One of the reasons for the paucity of experimental data on electron collisions with excited atoms and molecules is the difficulty of producing sufficient numbers of excited species to study under controlled conditions. Traditionally, three methods have been employed to generate excited (mostly atomic) species (Trajmar et al., 1993); these are discharges (dc, RF, or microwave), electron beams (transverse, or coaxial), and charge-exchange processes. The first m e t h o d relies on recombination, direct excitation, and cascade processes and can give relative populations of excited to unexcited
EXCITED ATOMS AND MOLECULES
157
species of <10 .4 (excited-state fluxes of 1012-1014 atoms sr -1 s-l). The second method relies on direct excitation and cascade processes and can give relative populations of excited to unexcited species of < 10 - 4 (excitedstate fluxes of 101~ atoms sr- 1 s- 1). The third method relies on recombination processes and can give relative populations of excited to unexcited species of ~0.5 (excited-state fluxes of 1010-1016 atoms sr-1 s-1). Another difficulty associated with the study of electron interactions with excited atoms and molecules relates to the production of excited species in precisely defined, well-characterized states. This is especially difficult for molecules that have closely spaced excited states and dissociate or predissociate quickly, thus depleting the excited-state populations. However, recently this situation has changed considerably with the availability of pulsed lasers. Direct laser excitation (or indirect excitation and cascade) can produce excited-tounexcited atom ratios of ~0.25, and excited atomic-state fluxes of < 1017 atoms st-1 s-1. Today, the much higher number densities and selectivity of excited states achieved by lasers allow such studies to be performed both in low-pressure electron beam experiments and also in high-pressure electron swarm experiments. As pointed out by Jaduszliwer et al. (1980), however, because in the former experiments the excited species normally live for 10-8 s and at thermal speeds they travel only ~ 10-3 cm during this time interval, observation of collisions of electrons with such excited species requires good overlap of the atomic, electron, and laser beams. The study of electron interactions with excited atoms and molecules opens up a new field of endeavor of basic and applied significance. It offers unique new opportunities to study the electronic structure of atoms and molecules and electron-atom interactions, especially the dynamics of electronic and atomic collisions and energy transfer processes. Large differences are expected--and are indeed observed--in the cross sections for electron scattering from excited atoms as compared to ground-state atoms. For instance, considering the large values of the static polarizability of the excited rare-gas atoms (see Table II later in this section), it seems unlikely that the cross sections for electron scattering by the excited heavier rare-gas atoms will exhibit the well-known Ramsauer-Townsend (R-T) minimum, a prominent feature in the cross section of electron scattering by the groundstate heavier rare-gas atoms. In view of both this and the larger cross sections for scattering of slow electrons by excited atoms (often 100 to 1000 times larger, see later in this section), the electron transport properties of excited rare gases would be expected to differ from those of the ground-state rare gases. Similarly for molecules, vibrational and electronic excitation play important roles in electron scattering and in electron attachment (see, respectively, Sections IV and VI).
158
Loucas G. Christophorou and James K. Olthoff
On the applied side, it is generally known that collisions of low-energy electrons with electronically excited atoms and molecules and vibrationally/rotationally excited ("hot") molecules affect the behavior of partially ionized gases, gas discharges, and plasmas, and play a prominent role in many applied fields such as electron beam or discharge pumped lasers (Massey et al., 1982a), atmospheric phenomena (Allen, 1984), planetary ionospheres (Massey et al., 1982b), low-temperature plasmas (Delcroix et al., 1976; Den Hartog et al., 1988; Lymberopoulos and Economou, 1993; Malyshev and Donnelly, 1996) and pulsed power switches (Schaefer and Schoenbach, 1986; Saporoschenko et al., 1988; Schaefer et al., 1988; Christophorou, 1990; Christophorou and Pinnaduwage, 1990). They offer unique opportunities to change and/or modulate the electrical properties of matter using pulsed lasers. The effects on the practical properties of such systems may be large even when the percentage of excited species is small because the excited species are normally much more reactive with slow electrons than the respective ground-state species. Since the electron energies in many practical systems are low (a few eV), the larger number of slow electrons in such systems coupled with the larger cross sections and lower excitation thresholds of excited species compared to the respective ground states make the role of excited states in many applied areas significant. Indeed, the lowering of the ionization threshold energy for the excited species compared to the ground-state species makes electron-impact ionization energetically a more favorable process (e.g., step-wise ionization is a dominant process in many gas discharges). This is especially striking for the alkali metal atoms, which due to the low ionization threshold energies of their excited states can act as good electron donors. In this work we first review and discuss elastic, inelastic, and superelastic scattering of electrons by and electron-impact ionization of excited atoms and stress the role of the electric dipole polarizability in the interaction of slow electrons with excited atoms. Subsequently, the meager knowledge on the scattering of slow electrons from vibrationally and electronically excited molecules is summarized and discussed, as well as the available information on excitation and ionization by electron impact of electronically excited molecules. Finally, the available data on the processes of electron attachment to vibrationally/rotationally and electronically excited molecules and the processes of electron detachment from energy-rich transient anions are summarized and discussed. The goal of the present work is to be as comprehensive and complete as possible in order to provide an up-to-date account of the field and stimulate further work. We shall use the same symbols for the cross sections of the various processes involving excited states as for the ground state, but will
EXCITED ATOMS AND MOLECULES
159
signify the respective quantities and symbols for the excited species by a superscript asterisk (*).
II. Electron Scattering from Excited Atoms A. GENERAL CONSIDERATIONS As mentioned in Section I, four general methods have been used to produce excited atoms for electron impact studies; these include discharge (dc, RF, microwave), electron beam, charge exchange, and laser. The number density of excited species compared to the ground-state species is generally < 10 - 4 in the former two methods and between 25 and 50% in the latter two. The last method, with its distinct advantages of energy selectivity, intensity, and pulse duration, is uniquely suited for such studies. Some details of the specific methods used to obtain the results referred to in this work will be elaborated upon in the respective sections where the cross sections are presented. Laser applications in the study of electron interactions with excited molecules are discussed in Section VI. On the theoretical side, a number of approaches have been employed to calculate elastic, inelastic, and superelastic cross sections (total, integral, or differential) for electrons scattered by excited atoms (mostly excited rare-gas and alkali-metal atoms). These approaches are generally similar to the ones employed to calculate such quantities for electron-ground state atom/ molecule collisions (e.g., see Csanak et al., 1984). They include calculations using the first Born approximation, the close-coupling approximation, the polarized-core distorted-wave approximation, the extended polarization approximation, the Glauber approximation, the multichannel eikonal, effective range, R-matrix, and other theoretical treatments. While the results of such calculations often differ among themselves and the available experimental data (Sections II and III), they clearly show that the cross sections for scattering of slow electrons by excited atoms can be very large. They also show that the excited-state scattering cross sections are characterized by a large contribution of higher angular momenta to the total cross section as opposed to the cross sections for electron scattering by ground-state atoms where most of the contributing partial waves have small angular momentum L values. This is a direct consequence of the larger dipole polarizabilities of the excited atoms and the resultant dominance of the polarization potential. Furthermore, the calculations show that due to the long-range dipole character of the electron-excited atom interaction and the significant role played by high angular momentum partial waves, the
160
Loucas G. Christophorou and James K. Olthoff
polarization, rather than the central atomic and exchange potentials dominate the scattering process. Thus, while normally the scattering process is treated using polarization and distortion potentials together with exchange effects, the exchange effect between the incident and the bound electrons generally does not influence significantly the overall behavior of the computed cross section. In most instances, an approximate form of the polarization potential consistent with the polarizability of the excited atom may give a reasonable description of the scattering process. Two groups of atoms are best suited for such studies--the rare gas atoms and the alkali metal atoms. The prototypical atom within the first group is He; within the second group it is Na. Most of the discussion on elastic, inelastic, superelastic, and differential electron scattering cross sections in this chapter will be on those two atoms. To aid our subsequent discussion, we give in Fig. 1 the energy-level diagram for the He (Delcroix et al., 1976) and Na (Stumpf and Gallagher, 1985) atoms and list in Table I information (Jaduszliwer et al., 1980; Delcroix et al., 1976) on the lowest excited states of rare gas atoms and sodium. The metastable states of He that have been mostly studied experimentally are the 2 3S and the 2 1S states. The energy gap between these two metastable levels is 0.79 eV, and the first excited state that can decay radiatively to the ground state is the 2 ip, which lies 0.59 eV above the 2 iS state. For Na, the state 3 2P3/2 is the one most studied experimentally. It lies 2.1 eV above the ground state 3 2S1/2. The processes of elastic, inelastic, and superelastic electron scattering by excited atoms can be represented, respectively, by reaction equations (1), (2), and (3):
e(ei) + A*(E 3 --->e(a:) + A*(E:)
Ei = E f
(1)
e(~:3 + A*(E 3 --->e(~::) + A**(E:)
~: = e,~ - (E: - E,)
(2)
e(~) + A*(E,)~ e(~:) + A(E:)
~I = ~i + El.
(3)
In the above reactions ~i and e: are the initial and final energies of the electron (i.e., the energy of the electron before and after the collision); Ei and E I are the energies of the target atom before and after the collision [E I > Ei in expression (2) and E I = 0 in expression (3)]; and A, A*, and A** are, respectively, an atom in the ground state, the excited state, and an excited state that lies energetically higher than the initial excited atom A*.
EXCITED ATOMS AND MOLECULES 25-
...~51D ,~.51p ~ 51S
\4922015 ~281 A
UJ
5875/~ '3289/t'~ 7065/~
~
22-
v
.m.,53D-....53p .~..53S _.._.43D ,~\33p 43p 4713/~ ~ 43S "~ \33D
,&, 41p 5048 "~41S
"~'41D
23-
>
Ionization
24.6
24-
6678~k~i t ~3965,&,
\~ ~3188,&,
21,.08
584A
2019-
~ e singlet
23S He triplet
l f, ’
(a) 11S
0
40000 -
.i9 6S
5S 30000-
! E v0
LLI
161
6P
5D
5F
5P
4D
4F 3D
4P
4S
Electron Excitation /
/ / 8 1 9 nm
20000 -
3P Optical 10000 -
/ Excitation / /
//
Na
589 nm
(b)
_
3S
FIG. 1. Energy levels of (a) He (Delcroix et 1985).
al.,
1976) and (b) Na (Stumpf and Gallagher,
Loucas G. Christophorou and James K. Olthoff
162
TABLE I LOWEST EXCITED STATES OF THE RARE-GAs ATOMSa AND SODIUM
Atom
Ground State (X)
He
1 1So
Ne
21S o
Ar
3 xSo
Kr
41So
Xe
5 1So
Na
3 2S1/2
Metastable State (M)
Energy E M of Excitation of M (eV)
Radiative Lifetime z of M (s)
Nearest Lower-Energy State (eV) b'c
2 3S 1 21S o 3 3P 2 3 3P o 4 3P 2 4 3P o 5 3P 2 5 3P o 6 3P 2 6 3P o 3 3P3/2
19.82 20.61 16.62 16.72 11.55 11.72 9.92 10.56 8.32 9.45 2.105
6 x 105 2 • 10 -2 >0.8 >0.8 > 1.3 > 1.3 > 1 > 1
X (19.82) 23Sx (0.79) X (16.62) 3 3P 1 (0.05) X (11.55) 4 3P 1 (0.10) X (9.92) 5 3P 1 (0.53) X (8.32) 6 3P 1 (1.01)
1.6 x 10 T M
aFrom Delcroix et al. (1976). b Energy difference of this state and that of M. CNearest higher-energy states are the 1,3p states, which lie ~<0.12eV above the energy of the respective M, except for He, for which they lie 0.30 and 0.59 eV higher. dFrom Jaduszliwer et al. (1980).
A fourth reaction, namely, excited state-continuum state inelastic scattering (ionization by electron impact of an excited atom), can be represented by e(ei) + A*(Ei) ~ e(e I) + A +t*) + e(es)
(4)
The energetics of reaction equation (4) are e i = e I + es + I* + Eexc
(5)
where es, I*, and E exc are, respectively, the kinetic energy of the ejected electron, the ionization energy threshold of the excited atom A*, and the internal energy (if any) of the positive ion A +t*).
B.
TOTAL AND ELASTIC ELECTRON SCATTERING BY EXCITED ATOMS
1. Rare Gases
He*(2 3S). A number of experimental and theoretical studies have been conducted on the scattering of slow electrons by excited helium atoms. The
163
EXCITED ATOMS AND MOLECULES ’
10
3
o
Ckl
b o
02
-
2-.
~
101
’"1
’
’
’
’’
’"1
’
’
’
’
’ ’ " 1
’
’
' '''
’
.~n0
0.01
-
-
.::
"".,....
_
9 9
O*sc,t - Neynaber (1964) O*sc,t Wilson (1976) O*e,t - Husain (1967) s - Sklarew (1968) ......... O'*e,t Robinson (1969) + O'e, t Taylor (1975) ..... o 9 O
0 if)
/U
’’
.""::"' ~ . . . . , ,. , . .~""'"' "" ::
E
’
........ ::. "'".... :" -.... .. ..
’
O'*e,t a*sc,t Osc,t (~sc,t " ’
" " ,.i .............. .~. ".+
He
Fon (1981) Bray (1995) Kennerly (1978) Nickel, (1985)
’ ’ " ’ "
’
0.1
(1
9
9
9 9o o
"
....
’
O
...
"., ,.
1S) 9OOoo O0
, ’
o ~
~
",k
"'+,.., ,,...,
~
, ’
’
’
' " ' "
1
O?,q~ ’
10
’
’’
100
Electron energy (eV) FIG. 2. Electron scattering cross section for He(2 as). O's~c,t(l~): Experimental measurements: I, Neynaber et al. (1964); A, Wilson and Williams(1976) (data as given in Trajmar and Nickel, 1993). o*t(e): Calculations: , Husain et al. (1967);---, Sklarew and Callaway (1968); ..... Robinson (1969); +, Taylor (1975); -.-, Fon et al. (1981); ~ (cy*c,t),Bray and Fursa (1995). cysc,t(e):Experimental measurements: 0, Kennerly and Bonham (1978); O, Nickel et al. (1985).
first absolute measurement of the total electron scattering cross section, cy*c,t(e), for the metastable helium atom He*(2 as) was made by Neynaber e t al. in 1964. Similar measurements were reported by Wilson and Williams in 1976. In both studies the metastable states were produced in a gas discharge. These measurements of cy%,t(e) for He*(2 3S) are shown in Fig. 2 as a function of the impacting electron energy e. A comparison of cy*,t(~) with the total electron scattering cross section, Cys~,t(~), for the ground-state He(1 1So) (Kennerly and Bonham, 1978; Nickel e t al., 1985; Fig. 2 here) shows that cy%,t(e) exceeds C~s~,t(e) by about two orders of magnitude. The much higher value of the dipole polarizability of He*(2 as) compared to He(1 So) accounts largely for this enhancement in the excited-state scattering cross section (the dipole polarizability 0~, of He*(2 as) and He (1 aSo) is, respectively, 316 ao3, and 1.38 a~; see Table II). Indeed, as was indicated earlier in this section, a number of calculations emphasized the significance
TABLE II STATIC POLARIZABILITIES 0t OF GROUND STATE AND EXCITED STATES OF He, Ne, Ar, Na, AND K IN ATOMIC UNITS 3 3 ao(ao=0.1482 x 10-2'1- cm 3 = 0.1482 A3)a,b
r
Atom
3)
1 1S 0 1.270 c Lamm and Szabo (1980) 1.363 d Dalgarno (1962) 1.366 Miiller et al. (1991) 1.382 Victor et al. (1968) 1.383 Glover and Weinhold (1976) 1.383 e Miller and Bederson (1977) 1.384 Dalgarno and Kingston (1960) [1.38] I
23S 312.6 Miiller et al. (1991) 315.63 Chung and Hurst (1966) 316.2 Victor et al. (1968) 316.24 Glover and Weinhold (1976) 318.7 c Lamm and Szabo (1980)
21S o 2.571 d Dalgarno (1962) 2.66 Matthew and Yousif (1984) 2.663 Dalgarno and Kingston (1960) 2.665 e Miller and Bederson (1977) 2.676 Werner and Meyer (1976) [2.66] -r
3 3P 2 180.1& (ms = 2) Molof et al. (1974) 187.58 g'h Molof et al. (1974) 191.63 g (ms = 1) Molof et al. (1974)
Ar, Ar*
31S o 11.066 e Miller and Bederson (1977) 11.07 d Dalgarno (1962) 11.08 Dalgarno and Kingston (1960) [11.07] -r
4 3P 2 301.60 (mj -- 2) Molof et al. (1974) 323.2 ~ Molof et al. (1974) 3340 (ms = 1) Molof et al. (1974) [319.4] I
Na, Na*
3 2S1/2
S states (4s) 2939 Vign6-Maeder (1984) 2962 c'i Lamm and Szabo (1980)
He, He*
Ne, Ne*
150.47 d Dalgarno (1962) 159.24 e Miller and Bederson (1977) 159.24 ~ Molof et al. (1974) 159.5 Gruzdev et al. (1985) 160.0 c L a m m and Szabo (1980) 160.59 Adelman and Szabo (1973)
2iS 773.1 Miiller et al. (1991) 790.8 c Lamm and Szabo (1980) 801.95 Chung and Hurst (1966) 802.3 Victor et al.(1968) 803.31 Glover and Weinhold (1977)
[316] y [794.3] I
[186.5] y
P states (3p) 362.0 Vign6-Maeder (1984) 368.15 j Lamm and Szabo (1980) 441.15 Schmidt et al. (1985) 340.760 Duong and Picqu6 (1972) Na*(3 2P1/2) 367.32 c Lamm and Szabo (1980) Na*(3 2P1/2) 355.3 ~ Duong and Picqu6 (1972) Na*(3 2P3/2)
162.6 Mfiller et al. (1984)
368.93 c Lamm and Szabo (1980) Na*(3 2P3/2)
164.640 Hall and Zorn (1974) 164.75 / Fantucci et al. (1989) 165.02 Reinsch and Mayer (1976) 165.52 Schmidt et al. (1985) [161.9]" K, K*
41S o 275.3 a Dalgarno (1962) 286.7 c Lamm and Szabo (1980) 287.6 Werner and Meyer (1976) 288.1 Miiller et al. (1984) 291.50 Adelman and Szabo (1973) 292.8 g Molof et al. (1974)
[-362.2]" S states (4s) 4585 Vign6-Maeder (1984)
P states (4p) 625.0 Vign6-Maeder (1984) 645.37 Schmidt et al. (1985) 587.00 Marrus and Yellin (1969) K*(4 2P x/2, -t-12) 614.00'0 Marrus and Yellin (1969) K*(4 2P3/2) 622.9 c Lamm and Szabo (1980) K*(4 2P3/2) 635.0 c Lamm and Szabo (1980) K*(4 2P3/2)
292.85 e Miller and Bederson (1977) 298.04 Sternheimer (1969) 301.4 ~ Fantucci et al. (1989) 305.00 Hall and Zorn (1974) 308.57 Schmidt et al. (1985) [298.9]" a For polarizabilities of ground-state atoms see Miller and Bederson (1977) and Teachout and Pack (1971). b The polarizabilities of high-lying excited electronic states can be very large. Polarizabilities on the order of 10a~ 3 have been measured for atoms in Rydberg orbits (Miller and Bederson (1977). c Extended coulomb approximation results. d Average of values listed in column b of Table 5 of this reference. e Value recommended by these authors. I The bracketed values are the ones referred to in the text and are also the ones used in Fig. 7. 0 These are experimental values, h Average polarizability, i For the 4 2S1/2 state. J Average for the P states as quoted in this reference. k Average of 0~(3 2P3/2, Mj = _+ 89 and ~(3 2P3/2, M r = _+3/2) given in this reference. t Effective core potential-core polarization potential value (ECP-CPP). " Average of two experimental values. "Average of two values listed for Na*(3 2P3/2). o Average of two listed values.
166
Loucas G. Chr&tophorou and James K. Olthoff
of the polarization potential in electron-excited atom scattering. The results of a number of these calculations (Husain et al., 1967; Sklarew and Callaway, 1968; Robinson, 1969; Taylor, 1975; Fon et al., 1981; Bray and Fursa, 1995) are compared with the experimental measurements in Fig. 2. In general, the calculated values lie below the experimental data. One of the earliest calculations of the total elastic electron scattering cross section o*,t(~) for He*(2 3S) was made by Husain et al. (1967), who used the polarized-core, distorted-wave approximation. They identified the potential terms as the static central and induced polarization. The large polarization of He*(2 as) implies a large polarization of the core in the presence of the scattered electron and, thus, participation in the scattering process of a large number of states near the isolated He*(2 3S) level. Indeed, Husain et al. concluded that the polarization rather than the central potential dominates the entire scattering process and hence the calculated cross section is not significantly affected by the omission of the effect of electron exchange, and that the major contribution to cy*,t(~) comes from higher partial waves. Subsequent calculations confirmed these conclusions. Thus, Sklarew and Callaway (1968) calculated the cross section cy*,t(~) for elastic scattering of electrons by He*(2 as) using various forms of the polarized orbital method. Their cross section in the adiabatic exchange approximation is in reasonable agreement with the experiment. Elastic scattering cross sections for the 2 3S excited state of helium (and also for the 3P 2 excited states of neon, argon, and xenon) were calculated by Robinson (1969). He performed an adiabatic calculation based on an electron-excited atom interaction potential of the form r = VHFS 't- (e21r)(1 -
e -r/a) -
89
2 + r~)2]
(6)
In Eq. (6), the first term on the right-hand side is the Hartree-Fock-Slater potential for the atom, the second term removes the coulomb tail of the VHFS, and the third term represents the effect of polarization. The quantity is the electric dipole polarizability, rp2 is chosen to approximate the mean-square radius of the valence-electron orbital, and a is an adjustable parameter. The cross section ~*,t(a) determined by Robinson contains large contributions from higher angular momenta at low energies. At very low energies (~0.04 eV) it shows a peak with a large cross section and at higher energies it is in fair agreement with the experiment. Similarly, the 5-state R-matrix calculation of Fon et al. (1981) showed that for the optical, spin-allowed transitions 2 as ~ 2 3p and 2 1S ~ 2 Xp, a large number of partial waves contribute to the calculated elastic cross sections. This they attributed to the long-range dipole character of the interaction resulting from the coupling between the 2 ~'3S and the 2 ~,ap
EXCITED ATOMS AND MOLECULES ’
E
’
’
x.
10 3
x.
~ ~’"1
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He* (2 1S1 ~ {
,,
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o
...... ,.,9....... . . . . .9
.qr-=
~ . ~-
.
10 2
~.
9
-It
\
r O
x.
(Y*sc,t " Wilson (1976) O * e , t - Husain (1967)
.........
2-.
...~.,, -,~x.
-...
+ ,,., ",,.
~*e,t " Burke (1969) (~*e,t - Oberoi (1973)
~
10 ~
+ ......
9
.....
O’*e, t -
Fon
9
9 O
+
"...+ .,
9 0 0 0 0
(1981)
Oleo
""'".,,
ap e
(:Y*sc,t " Bray (1995) C~sc,t - Kennerly (1978)
O
100 0.01
".,
He (1 1S)
~*e,, " Taylor (1975) (3*e,t - Berrington (1975)
- "
i
~sc,t " Nickel(1985) I
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t
0.1
~o0 I
I
J IItli
J
t
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~ ~ J l
1
I
10
t
1
'
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100
Electron energy (eV) FI6. 3. Electron scattering cross section for He*(21S). (3s~c,t(~): Experimental measurements: &, Wilson and Williams (1976). cr*t(e): C a l c u l a t i o n s : - - , Husain et al. (1967); . . . . . . Burke et al. ( 1 9 6 9 ) ; - - , Oberoi and Nesbet (1973); + , Taylor (1975);-...-, Berrington et al. (1975);-.-, Fon et al. (1981); ~ (cy*c,t), Bray and Fursa (1995). Cysc,t(e): Experimental measurements: O, Kennerly and Bonham (1978); 9 Nickel et al. (1985).
states. Their results on 2 3S --, 2 3S elastic electron scattering lie considerably lower than the experimental measurements (Fig. 2). Figure 2 also shows the cr*t(e) computed by Taylor (1975) in the first Born approximation. These computed cross sections are lower than the experimental data. Also shown are the integral cross sections to n ~< 4 states calculated by Bray and Fursa (1995) using the convergent close-coupling method. He*(2 ~S). Figure 3 compares the experimental data on the total electron scattering cross section, Cr*c,t(e), for the excited He*(21S) helium atom (Wilson and Williams, 1976), with the cross section, Cysc,t(e), for the ground state He(1 1So) helium atom (Kennerly and Bonham, 1978; Nickel et al., 1985). Also plotted in Fig. 3 are the calculated values of ~*.t(e) by Husain et al. (1967), Burke et al. (1969), Oberoi and Nesbet (1973), Taylor (1975), Berrington et al. (1975), and Fon et al. (1980), and the integral cross section
168
Loucas G. Christophorou and James K. Olthoff
for n ~ 4 states of Bray and Fursa (1995). As for the He*(2 3S) metastable, the calculated values of cy*,t(e) are generally lower than the experimental data on cy*,t(e). However, both theory and experiment show that cr*,t(e) exceeds Crsr by a large factor. He*(21'3P). There have been a few calculated cross sections (Fon et al., 1981; Burke et al., 1969; Oberoi and Nesbet, 1973; Berrington et al., 1975) for elastic electron scattering by He*(21,3p), namely, for the reactions e(e,) + He*(2 3p) ~ e(es ) + He*(2 3p) and e(ei) + He*(21 P) ~ e(e s) + He*(2 ~P) The values of ~*e,t(E) calculated by Fon et al. (1981) are generally larger than those of the earlier calculations (Burke et al., 1969; Oberoi and Nesbet, 1973; and Berrington et al., 1975) possibly because the earlier calculations considered only one parity (Fon et al., 1981). Cross sections for step-wise excitation of the helium atom from metastable levels have also been measured (e.g., Mityureva and Penkin, 1975, 1989; Goster et al., 1980; Rall et al., 1989; Lockwood et al., 1992; and Table III). At the maximum, the cross-section functions for such excitations are about 100 times larger than the corresponding cross sections for the ground-state atom (Table III; see further discussion in Section II.C.2). Ar*(4 3P2 + 4 3P0). Besides He*(2 1'3S), the only other excited rare gas atom for which cr*c,t(e) has been measured is the excited argon atom in an unspecified mixture of 4 3P 2 and 4 3P o metastables (Celotta et al., 1971). The 4 3P o state lies 0.17 eV above the 4 3P 2 state, which itself lies 11.55 eV above the ground state 3 1So. The measurements of Celotta et al. (1971) were made using the atom-beam-recoil method and have an overall estimated uncertainty of ___13%. They are given in Fig. 4 where they are compared with the measured cross sections for the ground state 3 1So of the argon atom [(3"sc,t(E) (Nickel et al., 1985; Jost et al., 1983; Ferch et al., 1985a), and O'm(E) (Milloy et al., 1977)]. Robinson (1969) calculated the elastic scattering cross section cy*,t(e) for the 4 3P 2 metastable state of argon. This cross section is also plotted in Fig. 4. In comparing their experimental results with the cross section calculated by Robinson for elastic electron scattering, Celotta et al. found that correcting Robinson's cr* ~,t (e) for the angular resolution of their apparatus changed the cross section by only ~ 10% at 1 eV. Clearly the experimental cross section Cy*c,t(e) lies higher than the calculated cross
EXCITED
ATOMS
AND
169
MOLECULES
T A B L E III MEASURED ABSOLUTE APPARENT CROSS SECTIONS (Y* FOR ELECTRON-IMPACT EXCITATION OUT o r METASTABLE He*(2 3S OR 2 1S) TO THE EXCITED He*(n 3L OR n 1L) LEVELS AT A NUMBER OF INCIDENT ELECTRON ENERGIES 13; COMPARISON WITH THE CROSS SECTIONS G" FOR THE TRANSITIONS TO THE n3L OR n IL LEVELS FROM THE GROUND STATE He(1 1So)
Transition
M e t a s t a b l e He*
G r o u n d State He
(3"*(E)(10-16 cm 2)
O.peak(Epeak)(lO-16 cm2)a
3.5 e V - 5 eV b
6 eV
10 eV
16 eV
Transition
~ 35 e V - 50 eV ~
2.8 e 2.75 e 2.3`/ 1.84 e 5.8`/ 5.40 e 1.0`/ 0.63 c 0.44 e 1.2`/ 1.14 e 0.27 e
0.0107
~ 3 3p
0.0097
~ 3 3D
0.0031
~ 4 3S
0.0035
~ 4 3D
0.0012
~ 5 3D
0.0006
0.07(4) e
0.39 e
5.6`/ 3.01 e 3.0`/ 2.23 e 9.4`/ 6.79 e 1.5`/ 0.66 e 0.56 e 1.5 d 1.26 e 0.25 ~ 0.24`/ 0.40 e 0.11 a
1 1S ~ 3 3S
0.41(4) e 0.12(4) e
9.5 e 3.50 e 3.8 `/ 3.20 e 13`/ 7.30 e 1.5`/ 0.87 e 0.86 e 1.6`/ 1.12 e 0.3&
--, 6 3D
0.0004
1 1 S ~ 3 IS ~ 4 1S ~ 3 1p ~41 p
0.0049 0.0024 0.0350 0.0159
1 1 S ~ 3 1S ~ 41S ~ 3 1p ~ 41p ~ 3 ID ~ 4 ID
0.0049 0.0024 0.0350 0.0159 0.0042 0.0018
2 3S ~ 3 3S 5.70(4) e
3 3pC 4.56(4) e
3 3D~ 4.40(4) e 4 3S 4 3p 4 3Dh 5 3S 5 3D
0.33(4) e 0.15(4)e
---~6 3D 23S ~ 3 1S 41S 3 1p 4 ~P 21S ~ 3 IS 41S 3 1p 41p 3 1D --~4 1D
0.9(3.5) / 0.6(4.5) i 1.5(4.8)i.j 0.5( ~ 5) i 5.2 / 1.9 / 1.3 / 2.4 / 32 / 4.8 i
0.39 e
section value at the peak of the cross section function m e a s u r e d by St. J o h n et al. (1964). See this reference for other values. b The actual energy at which or* was m e a s u r e d is given in the parentheses. CThis is the a p p r o x i m a t e energy range over which the cross section function peaks, except for the transitions 2 3S ~ 3 1p a n d 2 3S--, 4 1 p for which the cross section function peaks at 100eV (see St. J o h n et al., 1964). aRall et al. (1989) r e p o r t e d u n c e r t a i n t y a b o u t _ 35%. e Piech et al. (1997) r e p o r t e d u n c e r t a i n t y + 4 5 % . See this reference for d a t a at other energies below 18 eV. I F o r this t r a n s i t i o n G o s t e v et al. (1980) r e p o r t e d ,-~7 x 10 -16 cm 2 at , ~ 5 e V a n d M i t y u r e v a and P e n k i n (1989) r e p o r t e d 270 x 10 -16 cm 2 at ~ 5 e V . g F o r this t r a n s i t i o n G o s t e v et al. ( 1 9 8 0 ) m e a s u r e d ,-~ 100 x 10 -16 cm 2 at -~3 eV. h F o r this t r a n s i t i o n G o s t e v et al. (1980) m e a s u r e d ,-~7 x 10 -16 cm 2 at ~ 5eV. / L o c k w o o d et al. (1992) estimated t h a t the absolute uncertainties in the cross sections for the transitions out of the 2 3S and 2 1S m e t a s t a b l e levels are, respectively, +__3 5 % a n d + 30% ,except for the transitions to the 4 1 p level, which are a b o u t ___60%. J F o r this t r a n s i t i o n Gostev et al. ( 1 9 8 0 ) r e p o r t e d ,-~10 x 10 -16 cm 2 at ~ 3 e V .
a Cross
Loucas G. ChrL~tophorou and James K. Olthoff
170
i
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+++ ++++
100 :-
.+ ++++++ v,,~++%,~.++, ~z~p ~
-
9 9 9 1 4 9- 1 4 9 O
O
00o
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~
~,~
~. O !~! ~TQ _
+
Ar
~7 ~7 ~ m ~
_
i
o% OooO
g*se,t (43P2 + 43Po): exp - Celotta (1971) a'e, t (43P2): calc- Robinson [1969) a s c , t (31So): exp - Jost (1983) a s c , t (31 So): exp - Nickel (1985) asc,t (31So): exp - Ferch (1985) O m (31So): exp- Milloy (1977)
0 -
,,i,-*
|
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o
b
i
-
13 ~s 10-~ t3 I
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0.01
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10
Electron energy (eV) FIG. 4. Comparison of the electron scattering cross section from the excited Ar*(4 3P 2 + 4 3Po) and unexcited Ar(3 XSo) argon atoms. (Tys~c,t(~) (4 3P2 -t-4 3Po): O, Experimental measurements (Celotta et al., 1971) as reported by Trajmar and Nickel (1993). cy*,t(~;)(43P2): Q), calculated values of Robinson (1969). Crsr Experimental measurements: i , Jost et al. (1983); A, Nickel et al. (1985); V, Ferch et al. (1985a). CYm(~;)(31So): Experimental measurements: +, Milloy et al. (1977).
section O'e*,t(~), and they are both larger than the scattering cross section for the ground state. As in the case of He, the large enhancement is due to the large electric dipole polarizability of the excited argon atom (for the 4 3P 2 state cx = 319.4 ao3; see Table II). The large value of cx for the excited atom also accounts for the absence of the R-T minimum in cr*,t(e), although such a minimum is most prominent in the Crm(e) and ~sr of the unexcited Ar atom. Cross sections for step-wise excitation of the argon atom from metastable levels have also been measured (e.g., Mityureva, 1985; Mityureva et al., 1989a, b). At the maximum, the cross-section functions for such excitations are about 100 times larger than the corresponding cross sections for the ground-state atom. Ne*(3 3P2); Kr*(5 3P2); Xe*(6 3P2). Elastic scattering cross sections CYe*,t03) for these excited species have been calculated by Robinson (1969). Robinson's
171
EXCITED ATOMS AND MOLECULES 10 4
_
_
_
He* (23S)
--
-
_
10 3
_ Kr* (53P2),
Xe* (63P2) -
Ar* (43p CXl
E 10 2
O CXl
~ Xe (51S~ -
Ne* (3
v
-g
I1)
t~
101
t-t~
He (11So)
E
100 Ne (21So) Ar (31 So)
10-1 0.001
0.01
0.1
1
10
Electron energy (eV) FIG. 5. Comparison of cy*t(e), open symbols, for He*(23S), Ne*(3P2), Ar*(43P2), Kr*(5 3P2), and Xe*(6 3P2) with the Crm(e), closed symbols, for He(1 1So) Ne(21So), Ar(3 ~So), Kr(4 ~So), and Xe(5 ~So). cy*t(e): Calculated cross sections by Robinson (1969). O, He*; A, Ne*; [3, Ar*; V, Kr*; ~, Xe*. tyro(e): Experimental results, e, He (Crompton et al., 1970); A, Ne (Robertson, 1972); II, Ar (Milloy et al., 1977); V, Kr (Hunter et al., 1988); II,, Xe (Hunter et al., 1988).
(Ye*,t(~;) for these excited rare gas atoms and for He*(2 3S1) and Ar*(4 3P2) are presented in Fig. 5, where they are compared with the respective momentum transfer cross sections CYm(e) for the ground-state atoms. The cross sections cr*,t(e) for all the rare gas atoms are similar and large in contrast to their respective Crm(e). This similarity largely reflects the similarity in the magnitude of the polarizabilities of the excited states of all these rare gas atoms. The R-T minimum in the Cym(e) of Ar, Kr, and Xe is distinctly absent from the cr*t(e) of all the heavier rare gas atoms. The ratio
Loucas G. Christophorou and James K. Olthoff
172
O’e*,t(S)/O’m(S) depends on the electron energy and is always much greater than 1. For Ar at ~0.2 eV, (3"e*,t(~)/(Ym(~) ~ 104. Step-wise excitation functions of metastable atoms of Ne, Kr, and Xe are discussed in Section II.C [see also Mityureva and Penkin (1975) for Ne, Mityureva et al. (1989a,b) for Ar, and Mityureva et al. (1989c) for Kr]. 2. Alkali Metals
Na*(32Pm, m j = _+3/2). The alkalis are effectively one-electron systems. Their high electric dipole polarizabilities in the ground state (see Table II) result in large elastic, inelastic, ionization, and reactive cross sections in their ground state. These properties, coupled with their low ionization threshold energies, make them ideal for many applications. A number of investigators (Jaduszliwer et al., 1980; Hertel and Stoll, 1974; Bhaskar et al., 1977; Jaduszliwer et al., 1985) studied inelastic electron scattering from excited sodium atoms using crossed-beam arrangements. Figure 6 shows the total
i
’
800
’
’
I
. . . .
700 Cq
I
E
600
’
’
’
I
. . . .
I
. . . .
O
a*sc,t,
Na*(32P3/2; m j = 3 / 2 ) - J a d u s z l i w e r
(1980)
A
(~*sc,t' Na*(32P3/2; m j = 3 / 2 ) - J a d u s z l i w e r
(1985)
.......
C~*e,t, N a * ( 3 P --, 3P) - M o o r e s (1974)
9
O
’
O'sc,t, Na(32S1/2) - K a s d a n (1973)
..............
(~sc,t, N a ( 3 2 S v 2 ) "
M o o r e s (1972)
Ckl
500 v
~,o 400 I! 300 o ~
0
200
,, 9o .
"t
I O0 0
,
0
', ~
~
--’-o.o,, 9 9 9 9
,
f
,
I
5
r
,
,
,
I
10
15
20
25
Electron energy (eV) FIG. 6. Total electron scattering cross section O’s*c,t(8) as a function of electron energy for the excited Na*(3 2P3/2) (O, Jaduszliwer et al., 1980); A, Jaduszliwer et al., 1985) and the ground state Na(3 2S1/2) (O, Kasdan et al., 1973) sodium atom. ---, cy*t(e) for Na*(3P-~ 3P) (Moores et al., 1974); ..... Cysc,t(e) for Na(3 2S1/2) (Moores and Norcross, 1972).
EXCITED ATOMS AND MOLECULES
173
electron scattering cross section O's~e,t(~) for Na*(3 2P3/2) measured by Jaduszliwer et al. (1980, 1985) using an electron and photon atomic-recoil technique. The data have an estimated uncertainty of _+35%. Also shown in Fig. 6 is the total electron scattering cross section ~sr for the ground state Na(3 281/2) sodium atom measured by Kasdam et al. (1973). Many electron scattering processes contribute to the total scattering cross section in the 6-25 eV energy range--elastic (3P ~ 3P), superelastic (3P ~ 38), as well as excitation and ionization. It is interesting to note that the cy*r of the sodium atom does not exceed Cysr by as large a factor as in the case of the rare gas atoms. This clearly reflects the fact that the difference in the electric dipole polarizability of the excited and unexcited Na atom is small (only about a factor of 2.2; see Table II), while for the rare gases it is very large [by a factor of 229, 575, and 29 for He*(23S), He*(21S), and Ar*(4 3P2) , respectively]. The ground-state rare-gas atoms have low polarizabilities in their ground states due to their closed-shell structure, but when excited, the loosely bound electron substantially increases their polarizability. On the other hand, the polarizability of the alkali metal atoms is already large in their ground state because a single outer valence electron is loosely bound in an s-orbital of large radius. Four-state close-coupling calculations (Moores and Norcross, 1972) of the %c,t(e) of Na agree well with the measured (Kasdan et al., 1973) O'sc,t(t~ ). Similar calculations by Moores et al. (1974) of the elastic and superelastic electron scattering cross section by the sodium atom in the first excited state cannot be compared directly with the cy*~,t(e) measurements of Jaduszliwer et al. (1980) because they describe the scattering of electrons by a sodium atom in which all three P states are populated. The cy*,t(e) values of Moores et al. (1974) are shown in Fig. 6 by the broken line and are seen to lie higher than the measurements at low energies. There is a need for more calculations. 3. Dependence o f the Total Electron Scattering Cross Section on the Atomic Electric Dipole Polarizability
The consistently larger values of the cross sections cy* sc,t(a) for excited atoms compared to the cysc,t(e) of the ground-state atoms and the theoretical results discussed earlier in this section show the dominant role played by the electric dipole polarizability in the electron scattering process. Indeed, Christophorou and Illenberger (1993) drew attention to a rather quantitative correlation between the total electron scattering cross section and the electric dipole polarizability of the ground and excited states of atoms as was predicted by Vogt and Wannier (1954). They considered the motion of ions or electrons in gases when the interaction potential between the
174
Loucas G. Christophorou and James K. Olthoff
charged species and the atoms/molecules making up the gas is simply the polarization function V(r) = - (e 2o0/(2r')
(7)
In Eq. (7) e is the electron charge, a is the atomic polarizability, and r is the distance between the electron and the atom. From a quantum mechanical description of the polarization potential they obtained for the capture cross section the expression CYv,w= 4rt[(eZoO/(mvZ)] 1/2
(8)
where m and v are, respectively, the mass and the velocity of the electron. The Ov,w in Eq. (8) is twice the classical capture cross section for spiraling orbits over a wide range of v. Equation (8) can be rewritten as CYv,w= 4rta2o(O~/2g)1/2 = 2.487 • 10-
16(~/E)1/2
(9)
where a o is the Bohr radius (5.29172 • 10 -9 cm), a is in atomic units (1 atomic unit (a.u.)= ao3 = 0.1482A3), e is the electron energy in atomic units (1 a.u. = 1 Hartree = 27.21165 eV), and Ov,w is in cm 2. Figure 7 gives the plot of the cross-section data discussed earlier in this section (see the caption for Fig. 7) for He(1 a So), He*(2 aS), He*(23S), Ar*(4 3P 2 q- 4 3Po) , Na(3 2S1/2), Na*(3 2P3/2) , and K(4 aSo) as a function of (a/e)a/2 using the corresponding values of a given in brackets in Table II for each species. The cross sections decrease monotonically, and the measurements - - especially those for the alkali m e t a l s - - a r e in rather good agreement with the predicted dependence of Crv,w on (a/e) 1/2 (Eq. (9)). The magnitude of a accounts largely for the magnitudes of Crsr and cr*r The dominant role of the electric dipole polarizability is further seen from 1 • , electron scattering cross-section data the differential inelastic, (3"diff,ine shown in Fig. 8 for the transitions e(g~) + He*(2 3S) - He*(2 3p) -k- e(e s = 30 eV)
(10)
e(e~) + He(1 1So) ~ He*(2 3p) A- e(g~ = 30 eV)
(11)
and
measured by Miiller-Fiedler et al. (1984) keeping the scattered-electronkinetic energy ~I at 30eV. These cross sections refer to electron-impact
175
EXCITED ATOMS AND MOLECULES
103
’
’
’
’ ’’"I
Oy
9
'
'''
:,;:/
,,1 O4
o04E b
1 02
O
A
~V,W
~d
9
1 01
100
*,
I
1
I
I
I I IIII
10
I
I
I
is0) He* (21S) He* (23S)
He (1
9
9
He*
9 z~ [] O
Ar* (43P2 + 43P0) Na (32Sl/2) Na* (3 2P3/2) K (4180)
I l llll
100
(23S)
I
I
I
’
; ~[
1000
((z/e) 1/2 (a.u.)1/2 FIG. 7. Total electron scattering cross sections for atomic species plotted as a function of (0~/e)1/2 (from Christophorou and Illenberger, 1993). O, He (1 1So) (Kennerly and Bonham, 1978; Nickel et al., 1985); , , He* (2 IS) (Wilson and Williams, 1976); V, A, He*(23S) (V, Wilson and Williams, 1976; A, Neynaber et al., 1964); II, Ar*(4 aP 2 4- 4 3Po) (Celotta et al., 1971); A, Na(3 2S~/2) (Kasdan et al., 1973); E], Na*(3 2P3/2) (Bhaskar et al., 1977; Jaduszliwer et al., 1980, 1985); C), K(4 ]So) (Kasdan et al., 1973);--, cy....
excitation of the 2 3p excited state of He, respectively, from the excited state 2 3S and from the ground state 1 1So and show that the differential electron scattering cross section for the excited state (reaction (10)) is up to 10 5 times larger compared with that for the ground state (reaction (11)) (Fig. 8). The maximum enhancement is for small angles (forward scattering) as is to be expected for the distant collisions involved in the electron-induced dipole scattering. The excited-state enhancement is a function of the excited state itself and the electron energy. It can thus be concluded from these rather limited studies that electron scattering from excited atoms (and possibly but to a lesser extent from electronically excited molecules) can be as much as 10 5 times larger
Loucas G. Christophorou and James K. Olthoff
176
10 3 _
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101
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i
20
o J
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Scattering angle (deg) FIG. 8. Differential inelastic electron scattering cross section O’diff,ine1 as a function of scattering angle for excitation of the He*(2 3p) state from the excited state 2 3S and from the ground state 1 1S o of the He a t o m . . , Excited-state measurements of Mfiller-Fiedler et al. (1984) for a scattered-electron energy es of 30 eV. O, [--3,Ground-state measurements for 30-eV incident electron energy ei (O, Brunger et al., 1990; D, Trajmar et al., 1992).
compared to their respective ground states depending on the excited state, the electron energy, and the scattering angle. These increases are principally the consequence of the large polarizabilities of the excited states. The Vogt-Wannier "limiting-case" equation (Eq. 9) predicts reasonably well the magnitude of the total electron scattering cross section and clearly indicates that the cross section can be very large depending upon the magnitude of both 0~ and ~. For instance, for cx = 3 x 103 a.u. and ~ = 5 meV, CYv,w= 10-12 c m 2. Such high cross sections may be characteristic of atomic Rydberg states for which polarizabilities as high as 101~ have been measured (Miller and Bederson, 1977).
EXCITED ATOMS AND MOLECULES
177
C. INELASTIC SCATTERING OF ELECTRONS BY EXCITED ATOMS
1. Cross Sections: Definitions To aid the discussion in this section we first define cross sections that are determined experimentally. To this end, we refer to the schematic energylevel diagram in Fig. 9 and follow the discussion by Trajmar and Nickel (1993). Let us assume that there are N i atoms in the initial state i in the interaction region of the experiment and that they are uniformly irradiated by a monoenergetic electron beam of energy a. These atoms are excited by electron impact to higher-lying j, 1 states. In Fig. 9 these electron-impact excitation processes are designated by the vertical broken arrows. The solid arrows between the 1,j levels and between the j, k levels represent, respectively, the l ~ j cascade and the j---, k emission transitions. Experimentally one usually measures the total photon flux in the interaction region, ~jk (photons/s), for the particular j ~ k transition emitting photons of wavelength Xj,k. If Je is the electron flux, Ni is the number of target atoms in level i, I e is the electron current, ni is the target atom number density, and L is the interaction length, a line excitation cross section cyj,k for the production of photons of wavelength Xj,k can be defined from (~j,k = JeNiCYj,k = (Ie/e)niLcyj,k
(12)
The line excitation cross section as a function of electron energy e, CYj,k(e), is
i
I
FIG. 9. Schematic energy-level diagram showing electron-impact excitation (vertical broken arrows), radiative decay from level j to level k (j ~ k transition), and population of level j by cascading from level 1(1 ~ j transition) (from Trajmar and Nickel, 1993).
178
Loucas G. Christophorou and James K. Olthoff
often referred to as the optical excitation function. The sum of the cross sections for emission of light from a level j to all lower levels k isreferred to as the apparent level excitation cross section for that particular level (j) and is designated by crA. The cross sections crj,k and crA are related by
crA = CYj,k/?j,k
(13)
where
Yj,k :
Aj,k/k~<jAj, k
(14)
is the branching ratio, Aj, k is the Einstein spontaneous emission coefficient, and the summation is over all levels k to which the level j can decay radiatively. The quantity cyA represents the cross section for all excitation processes which populate the level j. The level j can be populated directly by electron impact from level i and indirectly by cascading from all electron-impact levels l, which lie energetically above j and can decay to level j by radiative emission. Thus the apparent level excitation cross section cyA is equal to the cross section for direct electron-impact excitation of level j from level i (e.g., the integral electron-impact excitation cross section, crj) plus the cascade contribution. The integral electron-impact excitation cross section ~j is defined by
Nij = J e N i g j
(15)
where Nij is the direct production rate of level j from level i. The cross sections crA and crj are related by
cy,: .A(1--l~>l.l.,/k~
(16)
The term in the parenthesis accounts for the cascade contributions from levels 1 higher than j. In the absence of cascade contributions into level j , ~ j = ~A.
2. Rare Gases Most of the experimental studies in this area involve the 2 3S and the 2 1S metastable states of helium. Absolute apparent excitation cross sections crjA for electron-impact excitation out of the 2 3S metastable level of helium to
EXCITED ATOMS AND MOLECULES
179
several (3 3S, 4 3S, 3 3p, 3 3D, 4 aD, 5 3D, and 6 3D) higher triplet levels n 3L have been measured by Rallet al. (1989) and to several (3 ~S, 4 ~S, 3 ~P, and 41p) higher singlet levels n IL by Lockwood et al. (1992). Their measured cyA for these transitions at a number of incident electron energies are given in Table III. Also listed in Table III are measured cyA for transitions out of the 2 1S metastable state of helium to several higher singlet levels n 1L (Lockwood et al., 1992). In the experiments by R a l l e t al. (1989) and Lockwood et al. (1992) the metastable atoms were crossed by an electron beam and the emission from the excited states was detected. Absolute calibration was made by measuring the ratio of the electron excitation cross section to the known optical absorption cross section using knowledge of pertinent branching ratios (Rall et al., 1989). The cross section for the 2 3S ~ n 3L transitions was determined by measuring the intensity of light emitted from the n 3L levels. Lockwood et al. (1992) indicated that the direct cross sections for excitation out of the metastable levels into the 3 IS and 4 ~S levels are virtually identical to the apparent cross sections, as cascades into the 3 1S and 4 1S levels from the higher xp levels are negligible due to the very much larger transition rates from the 1p level to the ground state. Also listed in Table III are the cross sections of St. John et al. (1964) for the transitions to the n 3L and n 1L levels out of the ground state 1 1So of the He atom. F r o m a comparison of the measured cross sections for excitation by electron impact of the n 3L and n 1L levels from the helium metastable levels and from the He ground state, it can be seen that the cross sections out of the metastable levels are several orders of magnitude larger than out of the ground level. The metastable atom is larger, more loosely bound, and energetically closer to the upper levels. Furthermore, it can be seen from the measurements in Table III that the variation of the excitation cross section with the quantum number of the final state is different for excitation from the metastable and from the ground state, that is, the pattern of excitation out of the metastable levels differs from that out of the ground level. Thus, R a l l e t al. (1989) pointed out (see Table III) that the apparent cya they measured for the 2 3S ~ 3 3p transition is smaller than for the 2 as--, 3 3S and 2 3S ~ 3 3D transitions, a trend that is different from the results of excitation from the 1 1So state where excitation to levels optically connected to the initial level has a larger cross section. These experimental observations are consistent with both the results of Born approximationtype calculations (Kim and Inokuti, 1969) and the results of calculations based on multichannel eikonal theory (Flannery and McCann, 1975a). It should be noted that Flannery and McCann's calculations give for the direct cross sections of the transitions 2 as ~ 3 ap, 2 3S ~ 3 3S, and 2 3S ~ 3 3D at 10eV the values of 0.615 x 10 -16 cm 2, 1.51 x 10 -16 cm 2, and 5.54 x
180
Loucas G. Christophorou and James K. Olthoff
10-16 cm 2, which are substantially smaller than the experimental values but exhibit the same overall trend as indicated by the measurements. This conclusion, however, is different from that reached by Lockwood et al. (1992) for excitation from the 2 aS level into the 3 aS, 3 ap, and 3 aD levels. The apparent cy* for the 2 aS ~ 3 ap transition is smaller than for the 2 aS ~ 3 aD transition, but larger than for the 2 IS ~ 3 aS transition. The relative cross sections from the 2 IS into these levels are different than for excitation into the same levels from the ground state 1 1So. Excitation from 1 aSo into the optically allowed 3 ap is much larger than into the 3 aS or 3 I D levels (see Table III). Measurements of cross sections for excitation of the helium atom out of the 2 3S level to higher levels (3 3p, 3 3D, 4 3D, and 3 ap) for electron energies < 1 eV have been performed by Gostev et al. (1980) (see footnotes to Table III). Similar measurements have also been conducted by Mityureva and Penkin (1989) for the transitions 2 3S ~ 3 3p, 2 aS ~ 3 ap, 2 ap ~ 3 ID, and 2 3p ~ 4 3 D . The peak values of the cross sections for these transitions were reported to be, respectively, 240• 10 -16 cm 2, 30x 10 -16 cm 2, 370• 10 -a6 cm 2, and 50 • 10 -16 cm 2. Clearly, the cross-section values of these latter investigators are much higher than those of Rall et al. The difference between the cross-section values of the two groups is often more than two orders of magnitude. More recently, Lagus e t al. (1996) and Piech et al. (1997) reported measurements of the direct cy* cross section for electron-impact excitation from the metastable He*(2 3S) to various n 3L states. These data are listed in Tables IV and V. The reported uncertainty in these data is _+35% for Lagus et al. (1996) and _+45% for Piech et al. (1997). For those transitions studied by both groups, the data are within the combined uncertainties as can be seen from Tables IV and V and Fig. 10, where the data of both groups are compared for the transitions from He*(2 3S) to 3 3S (Fig. 10a), 3 3p (Fig. 10b), 3 3D (Fig. 10c), and 4 3D (Fig. 10d). The experimental data for each of these four transitions are compared with the results of a number of calculations: the Born approximation (Kim and Inokuti, 1969; Flannery et al., 1975), multichannel eikonal theory (Flannery and McCann, 1975), R-matrix method (Berrington et al., 1985), distorted-wave approximation (Mathur et al., 1987), updated multichannel eikonal theory (Mansky and Flannery, 1992), two versions of first-order many-body theory (Cartwright and Csanak, 1995), and the convergent close-coupling method (Bray and Fursa, 1995). The R-matrix method values show good agreement with the measurements in both shape and magnitude. The distorted-wave approximation cross section for 3 3S in the energy range 13-23 eV also agrees with the measurements. Although both the multichannel eikonal theory and the updated multichannel eikonal theory give cross sections smaller than the
EXCITED
181
ATOMS AND MOLECULES
TABLE IV MEASURED DIRECT ABSOLUTE CROSS SECTIONS Or* FOR ELECTRON-IMPACTEXCITATION OUT OF METASTABLE He*(2 3S) TO THE EXCITED He*(n 3L) LEVELSAT A NUMBER OF INCIDENT ELECTRON ENERGIES (data of Lagus et al., 1996) cry'(~)(10-16 cm 2) Electron Energy (eV)
He*(3 3S)
3.5 6 10 16 27 40 50 100 200 500
8.1 + 2.8 2.2 __+0.9 2.5 + 0.7 2.2 + 0.8 1.6 + 0.6 1.2 + 0.4 1.0 + 0.35 0.61 + 0.21 0.36 + 0.13 0.16 + 0.06
He*(3 3p)
1.6 + 0.7 1.2 + 0.4
He*(3 3D) 5.1 + 1.8 6.7 __+2.3 6.3 + 2.2 5.4 + 1.9 4.5 + 1.6 3.5 + 1.2 2.9 + 1.0 1.5 + 0.5 0.90 + 0.31 0.30 + 0.11
He*(4 3D)
1.0 +__0.4 1.1 + 0.31 0.93 + 0.33 0.75 + 0.26 0.63 + 0.22 0.56 + 0.20 0.25 + 0.09
measurements, the general energy dependence of the 3 aD cross section from these two methods is consistent with the measurements. The first-order many-body theory cross section (Fig. 10c) is larger than the experimental data below ~ 6 eV and smaller above this energy. The convergent closecoupling method gives low values and so do the Born approximation calculations. Besides the calculations already referred to here, other earlier calculations of excitation cross sections from the 21'3S metastable states of He to higher-lying states have been conducted by Moiseiwitsch (1957), Ochkur and Bratsev (1966), Burke et al. (1969), Flannery et al. (1975), Fort et al. (1981), and Franca and da Paixfio (1994). Figure 11 shows the 5-state R-matrix calculation results of Fort et al. (1981) for the spin-forbidden transitions 2 3S ~ 2 1S, 2 3S --, 2 xp, 2 IS ~ 2 3p, and 2 ap ___,2 ~P, and for the optically allowed transitions 2 3S ~ 2 3p and 2 IS --, 2 xp of He (see this reference for comparison with other calculations). In contrast to the cross sections for the spin-allowed and optically allowed transitions, the cross sections for the spin-forbidden transitions are dominated by short-range exchange potentials and hence one may expect only a few low-lying partial waves to contribute to the calculation of integral cross sections. The contribution from higher partial waves is particularly dominant for optically allowed transitions. In their calculation, Fort et al. (1981) concluded that for energies < 10 eV, it is sufficient to include partial waves up to L = 13.
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183
EXCITED ATOMS AND MOLECULES
. . . . . . . .
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1000
Electron energy (eV) FIG. 10. Cross sections g*(e) for the transitions (a) 23S--, 33S, (b) 23S--, 33P, (c) 2 3S --, 3 3D, and (d) 2 3S --, 4 3D. Direct cross section measurements: O, Lagus et al. (1996); A, Piech et al. (1997). Calculated results: Born approximation:- .-, Kim and Inokuti (1969); . . . . . Flannery et al. (1975). Multichannel eikonal t h e o r y : - - , Flannery and McCann (1975). R-matrix method: ---, Berrington et al. (1985). Distorted-wave approximation: V, Mathur et al. (1987). Updated multichannel eikonal t h e o r y : - - - - , Mansky and Flannery (1992). Two versions of first-order many-body theory: . . . . . , Cartwright and Csanak (1995). Convergent close-coupling method: +, Bray and Fursa (1995).
Loueas G. Christophorou and James K. Olthoff
184
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215
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_
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10 -2 -
-
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..........
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....
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Electron energy (eV) FIG. 11. Cross sections for the spin-forbidden transitions 23S ~ 2 1 S , 2 3S--, 2 ap, 21S --, 2 3p, and 2 3p .._, 2 ap, and for the optically allowed transitions 2 3S --, 2 3p and 2 aS ~ 2 ap of He (5-state R-matrix calculation results of Fon et al., 1981).
While the preponderance of electron collision studies with metastable atoms have been made with metastable helium, some accurate similar work has been reported recently for metastable argon. Foremost among these recent studies is the work of Piech et al. (1998), who measured apparent electron-impact excitation cross sections out of the ls3 and lss metastable levels of the argon atom into eight levels of the 3p54p manifold (see Fig. 12). Table VI shows the apparent cross sections they measured at two values of the incident electron energy. The absolute uncertainty of the measurements is about + 35%. To obtain the direct cross section from the values of the
185
EXCITED ATOMS AND MOLECULES
J=2 1 0 1 s5 s4 s3 s2
1
3
2
1
2
0
1
2
1
0
P~o P9 P8 P7 P6 P5 P4 P3 P2 Pl
14 _
m
m
m
13
2p
3p54p
> v
12
r UJ
m m m
--
Argon
ls
3p54s
11 /
I
/
I
01 G r o u n d s t a t e
/
I"
1s22s22063s2305(1So)
FIG. 12. Energy-level diagram for the first two excited configurations of the Ar atom. The two metastable levels in the 3p54s configuration are indicated by the letter m. At the top of the figure the Paschen designation is indicated for each level along with the corresponding value of J (from Piech et al., 1998).
TABLE VI A APPARENT CROSS SECTIONS O'j FOR EXCITATION O U T OF THE 1S 3 AND 1S 5 METASTABLE LEVELS INTO THE LEVELS OF THE
3pS4pCONFIGURATION
OF THE A R G O N ATOM
(from Piech et al., 1998)
Apparent Cross Section (10-16 c m 2) Electron Energy (eV)
Initial Level
J = 0 2Pl
2.5
1s 3
< 1.28 0.28
10
1S3
<0.85
2.5
ls 5
10
ls 5
0.15 +0.13 <0.09
2ps
+0.19 <0.14 0.46 +0.16 0.13 +0.05
J = 1
J=3
J = 2
2P2
2p 4
2p 3
2p 6
2p 8
2p 9
8.54 +3.38 10.76 +4.26 0.36 +0.17 0.61 +0.26
13.63 +5.63 18.79 +7.76 0.33 +0.17 0.24 +0.12
1.14 +0.58 0.94 +0.48
7.50 +2.67 8.86 +3.16
5.62 +1.96 4.67 +1.73
19.92 +6.93 23.00 +8.0
186
Loucas G. Christophorou and James K. Olthoff
apparent cross sections in Table VI one needs to subtract the cascade contribution. This was done for only the 2P9 and 2P6 levels. For the 2P9 level, Boffard et al. (1996) estimated that the cascade cross section is much less than 20% of the apparent cross section, and for the 2P6 level Piech et al. (1998) estimated that the cascade cross section is less than 10% of the apparent cross section. The cross section value for the 2P9 in Table VI is much smaller than was measured earlier by Boffard et al. (1996) due to earlier calibration errors (Piech et al., 1998). Earlier measurements by Baranov et al. (1999) and Mityureva et al. (1989b) for excitation out of the 3p54p manifold are much larger than the values in Table VI. For instance, at 10eV they are larger by about a factor of 10. Recent multistate semirelativistic R-matrix calculations (Bartschat and Zeman, 1999) of the direct excitation cross sections of the states in the 3p54p manifold from the initial metastable states ls5 (J = 2) and ls3 (J = 0) are in general agreement with the measurements of Piech et al. (1998). Based on the data in Table VI, Piech et al. (1998) concluded that the cross sections for excitations corresponding to dipole-allowed optical transitions are usually large and vary slowly with electron energy, and that their magnitudes are qualitatively related to the oscillator strength of the transition. Excitations corresponding to dipole-forbidden transitions typically exhibit sharper energy dependencies and smaller cross sections than excitations corresponding to optically allowed transitions.
3. Alkali M e t a l s
Cross sections for electron-impact excitation of Na*(3P) atoms to the 3D state (Fig. l b) have been measured from threshold to 1000eV by Stumpf and Gallagher (1985). The excited sodium atoms Na*(3P) were produced in the 3P (M L = 1, M s = 89level by optical pumping. Excitation from this state to the 3D level was accomplished by an electron beam (having an energy resolution of ~0.3 eV) which was coaxial with the laser beam. The subsequent 3D ~ 3P fluorescence at 819 nm was detected at 90 ~ to the electron/ atom beams as a function of the electron energy. In Fig. 13 the results of Stumpf and Gallagher are shown for the total cross section cYt*,cas(3P, M L = 1, M s = 89 ~ 3D, 90 ~ including cascades from higher excited states, and the total cross section o't,cas(3S ~ 3D, 90 ~ for excitation of the 3D state from the ground state under the same experimental conditions. These cross sections were obtained by normalization to the Born and Born-Ochkur approximation values at high energies. Excitation of the 3D state from the excited 3P state is seen to be about a factor of 10 larger than from the ground state 3S.
EXCITED ATOMS AND M O L E C U L E S 0
~
4-"
40
2
3o
g
~
'c
~
~
~ ~ l
....
~
~
~
~
~
~ ~Ul
187 ~
a
2o s
0
10 ........................ vt,cas
0
/
~ ,...’, , , . , . I
1
. 10
. . . . . .
..,..~ . . . . . . . . . . . . . . . . . . . . . . .
[
i
100
I
I I
1000
Electron e n e r g y (eV) FIG. 13. Normalized cross sections cyt.... and ~*t , c a s for electron-impact excitation of Na*(3D) via, respectively, the Na(3S)~ Na*(3D) and Na*(3P)-~ Na*(3D) transitions. The symbols cyt.... and O'*t,casrefer to the total cross sections for excitation including cascades from higher states (from Stumpf and Gallagher, 1985).
Finally, K r i s h n a n a n d S t u m p f (1992) calculated e l e c t r o n - i m p a c t excitation cross sections for optically allowed excited state-excited state transitions in Li, Na, K, Rb, a n d Cs in the first B o r n a p p r o x i m a t i o n for incident electron energies from 1.02 to 1000 in t h r e s h o l d units. These a u t h o r s give t a b u l a t e d results for the following transitions: Li: np --, n's (n = 2 to 4; n' - 3 to 6) a n d np --, n'd (n = 2 to 4; n' - 3 to 6) Na: np ~ n's (n = 3 to 5; n' = 4 to 7) a n d n p - - , n'd (n = 3 to 5; n' = 3 to 6) K: np --, n's (n = 4 to 6; n' = 5 to 8) a n d np --, n'd (n = 4 to 6; n' = 3 to 6) Rb: np --, n's (n = 5 to 7; n' = 6 to 9) a n d np --, n'd (n = 5 to 7; n' = 4 to 7) Cs:np--,n's(n=6to8;n'-7to
10) a n d n p - - , n ' d ( n = 6 t o 8 ; n ' - 5 t o 8 )
188
Loucas G. Christophorou and James K. Olthoff
D. SUPERELASTIC SCATTERING OF ELECTRONS BY EXCITED ATOMS Early studies of the superelastic scattering of electrons from excited atoms have been discussed by Massey and Burhop (1969) and Moiseiwitsch and Smith (1968). One of the superelastic collisions that had been the subject of early investigations--both experimental (Phelps, 1955) and theoretical (Marriott, 1957, 1966)--is He*(2 IS) + e ~ He*(2 3S) + e + 0.78 eV
(17)
The exothermic reaction (17) is a spin-exchange s-wave process with a large cross section at low energies. Phelps (1955) reported the cross section for (17) to be 3 x 10 -14 cm 2 for thermal (T = 300 K) electrons, and Marriott (1957) calculated a cross section of 5 x 10 -~5 cm 2 for thermal electrons (T = 300 K). Reaction (17) has been shown to be the dominant process that suppresses the population of singlet metastables in helium glow discharges (Den Hartog et al., 1988). Another superelastic reaction that has been the subject of early investigations (see Burrow, 1967, and references cited therein) is Hg*(3P1) + e --, Hg(1So) + e + 4.89 eV
(18)
More recently, there has been a close-coupling calculation of the cross section for superelastic scattering of electrons by excited Na* sodium atoms (3p ~ 3s transition) as a function of electron energy by Moores et al. (1974) (Fig. 14a), and a Born-approximation calculation of the cross section for superelastic scattering for various transitions of alkali metal atoms by Krishnan and Stumpf (1992). In Fig. 14b are shown the Born approximation results of Krishnan and Stumpf for the following superelastic transitions of Na* (see this reference for similar calculations on Li*, K*, Rb*, and Cs*): Na*(5p) + e ~ Na(4d) + e(0.0616 eV) Na*(4p) + e --, Na(3d) + e(0.1361 eV) Na*(5p) + e ~ Na(5s) + e(0.2283 eV) Na*(4p) + e ~ Na(4s) + e(0.5617 eV) Na*(5p) + e ~ Na(3d) + e(0.7277 eV) and Na*(5p) + e ~ Na(4s) + e(1.153 eV)
189
EXCITED ATOMS AND MOLECULES Od
E
200
b
150
0 Od
v
tO
om
0 (1)
O3 r~ 0
(.9
'
'
'
c
'
'
'
I
'
(a)
100 50 0
j
,
,
,
,
,
i
I
3
........
/.
I
.... "'~.....~
J
,
,
] 03
,
4
'"'1
.......
I
5
........
I
........
"'"-....
104
10
I
2
I
(b) "" ~'%"4
t
!
0 ~
I
I
105 E o~,
'
2
0
o o3
101 00
......
5p~4d
.....
4p~3d
......
5p -~ 5s
0
0
~'"" ~ . . ",<.. ~... ":'" ~'...
4p -* 4s
10-1 10 -2 0.01
\,~,....
5p -> 3d ...... ........
\
""
".
5p -~ 4s I
O. 1
........
I
1
........
I
10
,
, ,,,,,,I
1 O0
,
~ ~,,~,Jl
1000
Electron energy (eV)
FIG. 14. (a) Cross section for the superelastic collision Na*(3p) + e--, N a ( 3 s ) + e (close coupling calculations of Moores et al., 1974). (b) Born cross sections of Krishnan and Stumpf (1992) for superelastic collisions.
The values in parentheses are the energy gains in the superelastic collision as listed by Krishnan and Stumpf (1992). These Born-calculation results (Fig. 14b) show that the cross section for superelastic electron scattering increases sharply as the energy gain in the collision decreases. There have been a number of determinations of the differential superelastic collision cross sections, CYdimsuper,*which are discussed in Section II.E.
Loucas G. Christophorou and James K. Olthoff
190
E. DIFFERENTIAL SCATTERING OF ELECTRONS BY EXCITED ATOMS
1. Differential Elastic Electron Scattering Cross Sections Differential elastic electron scattering cross sections (Y~iff,e(~) have been measured for Na*(3 2P3/2, F --- 3) by Zuo et al. (1990). Their results on the ~iff,e(~) for 3P ~ 3P electron scattering are shown in Fig. 15. These investigators used an electron and photon double-recoil technique and generated the excited sodium atoms using circularly (c~-light) and linearly (x-light) polarized laser light. The measurements in Fig. 15 are for 3-eV unpolarized electrons and cover the angular range 25-40 ~ For comparison, the differential elastic scattering cross section O’diff,e(~ ) for the ground state (3S-~ 3S) is also shown in the figure in the same angular range. The
x
200
[]
Na
[]
160
e=3eV
L._
[]
04
E
150
o 04
140
m
e=2eV X
-
b
i
120
-
tl.}
100
3P 0
"o
i
,
40
i
42
,
[]
44
"-> 3 P
X
_
50
,
Linearly polarized 0
X
0
.m
n
38
m -
"13
,
36
_
v
..It
[]
180
-
3P
"-> 3 P
_
Circularly polarized
X
o
0
o
x
_ 9
+
9
-
9
9
9
9 3 S --> 3 S
-
0
9
n
25
I
J
I
I
30
r
i
I
i
I
I
i
I
35
+
t
I
40
Scattering angle (deg) FIG. 15. Differential elastic electron scattering cross section (~diff,e*for Na*(3P --, 3P) at 3-eV incident electron energy (O, circularly polarized light; x, linearly polarized light) (measurements by Zuo et al., 1990). Also plotted for comparison are CYaiff,e(~), for ground-state Na(3S ~ 3S) elastic electron scattering for 3eV (O, measurements by Zuo et al., 1990; +, calculations by Moores and Norcross, 1972). Inset: E], measurements by Jiang et al. (1991) for 2-eV incident-electron energy with circularly polarized light.
EXCITED ATOMS AND MOLECULES
191
uncertainty of these cross sections has been quoted to be less than _ 15% for the ground-state cross section and _+25% for the excited-state cross are l a r g e r - - b y a factor of about 4 for section. The cross sections O'diff,e(t~) * G-light and by a factor of about 10 for re-light--and more forward peaked than O'diff,e(E ). The 4-state exchange, close-coupling calculation result of Moore and Norcross (1972) for O'diff,e(E ) agrees well with the experimental measurements for the ground level (Fig. 15). However, the results of a 7-state R-matrix calculation by Zhou et al. (1991a) for the 3P --* 3P O'diff,e * (E) at 3 eV above the 3P threshold lie significantly lower than the measurements for atoms pumped by circularly and linearly polarized light. ) for Na*(3 2P3/2,F--3) have also been reMeasurements of O'diff,e(E * ported by Jiang et al. (1991). These investigators used circularly (cy+) polarized light for the generation of the excited atoms and measured CYdiff,e(e) in the angular range 36-44 ~ for 2-eV incident electron energies. Their measurements are plotted in the inset of Fig. 15 and are seen to be about 2.5 times larger than those by Zuo et al. (1990) at 3 eV. 2. Differential Inelastic Electron Scattering Cross Sections
Experimental measurements of the differential cross section for inelastic electron scattering by excited atoms r have been made for He*(2 3S) (Miiller-Fiedler et al., 1984), Na*(3 2P3/2,M L = _+ 1) (Jiang et al., 1992), and Ba*(6s6p 1P1) and Ba*(6s5d 1D2) (Register et al., 1978). Mfiller-Fielder et al. (1984) measured cy~iff,in(e) for the transitions
3p)
(19a)
e(ss) + He*(3 3S)
(19b)
--* e(es) + He*(3 3p)
(19c)
3D)
(19d)
e(es) + He*(n = 4 triplet states)
(19e)
e(ai) + He*(2 3S) ~ e(ss) + He*(2
e(es) + He*(3
The helium metastables were produced in a gas discharge with a ground-tometastable state population ratio of 10s: 1. The various excitation processes were separated by energy analysis of the electrons before and after the collision. The energy difference ~ i - aI represents the energy loss AE according to the energy difference of the two states 2 3S and n3L. The cross-section measurements have been made for el = 15, 20, and 30 eV and for scattering angles from 10-40 ~. Their overall uncertainty depends on the scattering angle. It increases from ~ 35 to 50% between 10 and 40 ~ for the transition to 2 3p and from 45 to 65% between 10 and 40 ~ for the other
192
Loucas G. Christophorou and James K. Olthoff
TABLE VII DIFFERENTIAL INELASTIC ELECTRON SCATTERING CROSS SECTIONS (~iff,in(~) FOR EXCITATION FROM He*(2 3S) TO He*(2 3p), He*(3 3S), He*(3 3p), He,(33D), AND He*(n - 4) AT FINAL (DETECTION) ELECTRONENERGIES~;f OF 15, 20, AND 30 eV (MEASUREMENTSBY M/.DLLER-FIEDLER, 1984 AS LISTED IN TRAJMAR AND NICKEL, 1993; SEE TEXT FOR QUOTED UNCERTAINTIES) ~iff,in(E)(lO -20 m 2 sr-1) Angle (deg)
2 3p
3 3S
3 3p
3 3D
n = 4 triplets
8.97 2.11 0.98 0.69 0.83
4.09 2.19 2.13 1.71 0.48
28.4 13.28 5.87 1.84 1.19
15.66 5.89 3.56 1.33 1.43
4.4 1.16 0.90 0.55 0.35
4.63 1.75 2.00 0.69 0.53
21.73 9.59 3.68 1.49 0.32
8.57 4.80 1.47 0.68 0.43
4.71 0.71 0.67 0.89 1.17
2.36 3.05 1.79 0.48 0.27
23.93 7.49 1.80 0.81 0.42
8.55 4.29 1.37 0.99 0.49
~I -- 15 eV
10 15 20 25 30 35 40
522.5 117.9 34.57 10.29 3.58 2.01 1.41 ~I = 20 eV
10 15 20 25 30 35 40
276.2 75.74 23.3 7.02 2.52 1.30 0.84 ~y = 30 eV
10 15 20 25 30 35 40
279.7 57.09 9.68 3.51 1.49 1.06 0.68
transitions. The differential inelastic electron scattering cross sections cY]’iff,in(e) measured by Mtiller-Fielder et al. (1984) for reactions (19a-19d) at three values--30, 20, and 1 5 e V - - o f the final electron energy ~y are listed in Table VII and are plotted in Fig. 16a, b, c, and d. For comparison, the cross section CYdiff,in(e) for the transitions He(1 1So)~ He*(3 3S) and H e ( l l S o ) ~ H e * ( 2 3 p ) is also shown in Fig. 16a, b for ~ i = 3 0 e V . The dominant excitation to the 2 3p state (reaction 19a) is evident. The differential cross section for reaction (19a) is much larger than the cross sections associated with excitation of the same level from the ground state 1 1So, and it is especially strongly forward peaking. The differential cross section for
193
EXCITED ATOMS AND MOLECULES
10 3
'
'
'
' I
. . . .
I
. . . .
I
. . . .
I
10 2 101 10 0 (a)
10-1
He* (23p)
1 0 -2
, , v’~-’,r’~’~,,_-~;-_-_,~ ~ - - - ~-"
1 0 -3 101
....
I
....
i ....
lo 0 Or)
1 0-2
0 04 |
1 0-3
.E_
6 o
I
(b) .
10 4 101
He* (33S)
.... _,
.
.
.
. . . .
~ .... ,,i
~ ....
....
i .... I He* (33p)
100
.-~ 9
-9 "o
13
._...._ ' ....
i .... (c)
II 13
i
lo-1
cJE
,-~ 9
i ....
9
1
0.1
0
15 eV
9
20 eV
9
10. 2 10 2
._.
30 e
,,i
....
i ....
i,
,
i
''J
....
I ....
I'
'
I
io
II
100
9 (d)
10-1 10. 2
He* (330)
, , ,
0
. . . .
10
I
20
,
,
,
,
I
,
,
30
I
40
Scattering a n g l e (deg) FIG. 16. Differential inelastic electron scattering cross sections (Ydiff,in* for excitation from excited He* (2 3S) to (a) He*(2 3p), (b) He*(3 as), (c) He*(3 3p), and (d) He*(3 30), for three values of the final (detection) electron energy el: 15eV (O), 20eV ( 9 and 30eV (A) (measurements by Miiller-Fiedler, 1984 as listed in Trajmar and Nickel, 1993). For comparison, the O'diff,in for excitation of the He*(2 3p) and He*(3 as) states of helium from the ground state He(1 1So) for ei - 30 eV are shown in, respectively, Figs. 16a, b (-.-, measurements of Brunger et al., 1990; ---, measurements of Trajmar et al., 1992).
194
Loucas G. Christophorou and James K. Olthoff
process (19a) also decreases slightly with increasing energy from 15 to 30 eV for all scattering angles. Interestingly, excitation to the optically forbidden 3 3D state is more probable than to the optically allowed 3 3p state. This is consistent with the findings of Rall et al. (1989) (Table III) and with the calculations of Flannery and McCann (1975), who attributed this behavior to the abnormally small line strength of the 2 3S ~ 3 3p transition. Flannery and McCann (1975) calculated differential electron scattering cross sections for excitation of the 2 1,3p, 3 ~'3S, 3 ~,3p, and 3 l'3D levels of the He atom from the He*(2 ~'3S) metastables for energies between 5 and 100eV using 10-channel eikonal treatment with electron exchange effects neglected. Similar calculations using semiclassical multichannel eikonal theory were made more recently by Mansky and Flannery (1992) for the transitions He*(2 3S) ~ He*(2 3p, 3 3S, 3 3p, and 3 3D). The principal difference between the two calculations is an increase in the numerical accuracy of the recent work. These authors argued that while electron exchange is important in electron-ground state helium atom scattering, for larger scattering angles (>140 ~ and intermediate energies its neglect in electron scattering from metastable atoms will result in small error. This is because scattering is predominantly in the forward direction due to the strong He*(2 3S) ~ He*(2 3p, 3 3p) dipole polarization coupling effects. Figure 17 compares the experimental measurements of Miiller-Fielder et al. (1984) for el = 20eV with the results of the multichannel eikonal theory of Mansky and Flannery (1992) and with the distorted-wave approximation calculation results of Mathur et al. (1987). The earlier results using multichannel eikonal theory (Flannery and McCann, 1975) are not plotted because they have been superseded by those of Mansky and Flannery (1992) and they were for ~i = 20 eV rather than for es = 20 eV. There is generally a satisfactory agreement between the calculated and the experimental data for the He*(2 3S)~He*(2 3p) (Fig. 17a) and He*(2 3S)~He*(3 3S) (Fig. 17b) transitions, but the experimental data lie higher than the calculated values for the transitions He*(23S)~He*(33p) (Fig. 17c) and He*(23S)~ He*(3 3D) (Fig. 17d). The experimental data also do not show the deep minimum indicated by the theory for the He*(2 3S) ~ He*(3 3p) transition (Fig. 17c). Differential cross sections for electron-impact excitation of helium from 2 IS to n IS states (n = 3, 4) have been calculated by Sharma et al. (1980) in the 2-potential modified Born approximation. These calculations covered the electron energy range 20 to 200 eV and included the effect of electron exchange. As expected, the results of the Born approximation calculation at large scattering angles differ considerably from the measurements. These calculations showed that for the transitions investigated, the contribution of electron exchange is small in comparison with the direct scattering, and it decreases as the energy increases from 20 to 200 eV.
195
EXCITED ATOMS AND MOLECULES
104 103
10 2
~ o
(a) He*(23S) ~ He*(23p)
101 04 o
10-1
E
04
(b) He*(23S)~ He*(33S)
101
102 100
I
100 ,
0
,
,
,
I
10
,
20
30
40
10 -1
....
0
, ....
10
~
20
'
~
"
30
40
'11'-" v
E :_
o
o,F,
"
I
10o 10o
10-1 10 -2
0
10
(d) 9 He*(23S) ---> He*(33D)
20
30
40
10-1
L
0
10
20
30
40
Scattering angle (deg) FIG. 17. Comparison of the experimental results for the differential inelastic electron scattering cross sections O'~iff,i n for excitation from excited He*(2 3S) to (a) He*(23p), (b) He*(3 3S), (c) He*(33p), and (d) He*(33D) with theory. O, Experimental data, Mfiller-Fiedler (1984);--, multichannel eikonal theory, Mansky and Flannery (1992); . . , distorted-wave approximation, Mathur et al. (1987). All data are for aI = 20eV (from Mansky and Flannery, 1992).
Besides He, differential inelastic electron scattering cross sections have been measured for excited sodium and excited barium atoms. Figure 18 shows the measurements of Jiang et al. (1992) for the transition Na*(3 2p 3/27 ML ~ i+ 1) ~ Na*(4 28 3/2) for 2-eV incident-electron energy. The results of a 10-state close-coupling calculation (Zhou et al., 1991b) lie higher than the measured values. Similarly, Register et al. (1978) measured differential inelastic cross sections for the excited barium atoms Ba*(6s6p IP1) and Ba*(6s5d 1D2) for 30- and 100-eV incident-electron energies. Their results are summarized in Table VIII and have a reported uncertainty of about 4- 50% when their magnitude
Loucas G Christophorou and James K. Olthoff
196
102
~
'
I
'
'
I
'
'
I
'
'
'
'
I
'
'
'
'
I
'
Na*(32P3/2, ML= 1) --> Na*(4 2S1/2) 7 04
E
0 04
101
o ’T"-V r
13
100 0
I
I
I
1
5
10
15
20
25
30
Scattering angle (deg) FIG. 18. Differential inelastic electron scattering cross section (Ydiff,in* for the transition Na*(32p3/2, ML = + 1 ) ~ N a * ( 4 2S1/2) for 2-eV incident-electron energy. O, Experimental results, Jiang et al. (1992);--, 10-state close-coupling calculation data, Zhou et al. (1991b).
is larger than 10 - 1 7 c m 2 sr - 1 , and within about a factor of 5 for smaller cross section magnitudes. The data in Table VIII show that all cross sections are forward peaking, especially those for optically allowed transitions. They also show that the dominant cross sections are associated with AJ = _+1 transitions. The measured differential inelastic scattering cross sections for the excited barium atom Ba*(6s6p ~P~) at 30-eV incident electron energy are compared in Fig. 19 with the "unitarized distorted-wave approximation using multiconfiguration wavefunctions" calculation results of Clark et al. (1992) at this same energy. As noted by Clark et al., both the calculated and experimental cross sections represent cross sections summed over final and averaged over initial sublevels with the assumption of equal population in the magnetic sublevels of the initial 1p 1 level. The calculations of Clark et al. reproduce the shape of the experimental cross sections reasonably well, but agreement between the magnitudes is not as good (see Fig. 19).
197
EXCITED ATOMS AND MOLECULES
TABLE VIII DIFFERENTIAL INELASTIC ELECTRON SCATTERING CROSS SECTION (Y~iff,in(a) FOR Ba*(6s6p 1P1) AND Ba*(6s5d 1D2) FOR 30- AND 100-eV INCIDENT ELECTRON ENERGIES (from Register et al., 1978)
(y~iff,in(E)(l O- 20 m 2 sr- 1) 30eV Inelastic Transition
6s6p 1P 1--*5d21D 2 ~5d6plD2 6s6p 1P1---~5d 2 3P 2 6s6p IP 1~6s7s 3S 1 6s6plPx ~6s7slSo 6s6p 1P 1~6s6d 1D2 6s6p 1p1 ~6s7p 1p I 6s6p IP 1~6s7d XD2 6s6p 1P 1~6s8d 1D2 6s5dlDz~6S6plP 1 6s5dXDz~5d6plF3
100eV
Energy Loss (eV) 5~
10~
15 ~
20 ~
5~
15 ~
0.620
43.0
5.5
0.77
0.57
12.7
0.57
0.725 1.003 1.259 1.508 1.794 2.400 2.539 0.828 1.912
11.0 1.4 44.7 69.3 4.6 21.9
0.93 0.24 5.9
0.14
0.06
2.9 0.25 12.0 31.0
2.5 2.0 0.42 1.9
0.37 0.57 0.05 0.07
2.7 50.6
0.28
0.37 0.40 0.07 0.06
9.0 12.0 1.00 13.3
0.07
0.10 0.05
3. Differential Superelastic Electron Scattering Cross Sections
There have been a limited number of measurements of superelastic differential electron scattering cross sections from excited helium He*(90% 23S + 10% 21S) (Jacka et al., 1995), excited barium Ba*( .... 6s6pXp1) (Register et al., 1978), and excited sodium Na*(3 2P3/2, M L = _+ 1) (Jiang et al., 1992) atoms. These results are presented in Figs. 20-22 where a comparison is made with the results of various calculations. Figure 20 shows the measurements of Jacka et al. (1995) for the differential cross section for superelastic scattering of electrons from metastable helium (90% 2 3S + 10% 2 1S) for 10- and 30-eV incident electron energies and scattering angles from 35 to 125 ~. They are compared with the results of three calculations, convergent close-coupling (Bray et al., 1994), first-order many-body theory (Trajmar et al., 1992), and 29-state R-matrix calculation (Fon et al., 1994). The experimental data were normalized to the close-coupling calculation result at a scattering angle of 85 ~ and the theoretical cross sections plotted are a combination of the He*2 3S (90%) and He* 21S (10%) superelastic cross sections. The error bars indicate the uncertainties estimated by Jacka et al. The shape of the experimental data angular distribution, especially for 10 eV, favors the close coupling calculation over the other two (Jacka et al., 1995).
198
Loucas
104 103 102 101 100 10-1
~L__
(/)
E
E) Oa
b
v
tom om
.it "o t3
k
G.
Chr&tophorou
Ba*(5d6plD2 + 5d2 1D2)
James
K.
Olthoff
03 02
(b)
o,i. 0o )-1 ).2
101 100 10-1 10-2 10-3 10-4 10-5
, , , . , , . , , , , , i , , ,
(c) i o
0203 X
I
(d)
0o 9-1 ,
,
,
i
~
3-2
104 103 102 101 100 10-1 10-2 102 101 100 10-1 10.2 10.3
and
(e) l
. . . . . . . . . . .
, , , , ,
102 ~
(f)
101
.
10-1 102 (h)
101 100 10-1 0
10
20
30
40
10.2
Ba*(6s8d 1 D 2 ) ~ _ , , , i , , , i , , , i i i l
10
20
30
40
Scattering angle (deg) FIG. 19. Comparison of the experimental and theoretical differential inelastic electron scattering cross sections O'diff,in * for excitation from the excited barium atoms Ba*(6s6p1P1) for 30-eV incident electron energy. Q, Experimental data, Register e t al. (1978);--, unitarized distorted-wave approximation calculation results, Clark e t al. ( 1 9 9 2 ) .
The differential superelastic (3P-~ 3S) cross section, O'd, iff,super * has been measured by Jiang e t a l . (1992) for 3-eV electron scattering by excited sodium atoms initially prepared by circularly polarized light. Their measurements were made in the angular range 0 - 3 0 ~. They are compared in Fig. 21 with the 10-state close-coupling calculation of Zhou e t a l . (1991b). Table IX
199
EXCITED ATOMS AND MOLECULES 10
-2
’\’
a, oev
I ’ ’
I ’ ’
i ’ ,
i ’ ’
i
’
’ 1
1 0 -2
'
'
I
9
\
"7,
'
'
I
'
'
I
'
'
I
'
'
I
'
t
(b) 3 0 e V
\
L_
em
i/
2
,k
ii//
E
10 -3
O
o
1-" v
1 0 -3
x_
ca. --,
c~
/ /
\
:I=
\
9
/
Jacka
-o
0_ 4
(1995)
Bray (1994) Trajmar ........ 10.
4
,
0
,
,
(1992)
Fon (1994) ,
,
i
,
,
,
,
,
i
,
,
t
,
,
30 60 90 120 150 180 Scattering angle (deg)
10. 5
, , I , , I , , I , , I , , I
0
, ,
30 60 90 120 150 180 Scattering angle (deg)
FIG. 20. Differential cross section (3"diff,super*for superelastic electron scattering from metastable He*(2 3S)(90%)+ He*(21S)(10%) at 10-eV (a) and 30-eV (b) incident electron energy. il, Measurements of Jacka et al. (1995) normalized to the close-coupling calculation result at a scattering angle of 8 5 ~ convergent close-coupling calculation, Bray et al. (1994); ---, first-order many-body theory calculation, Trajmar et al. (1992);-.-, R-matrix calculation, Fon et al. (1994) (from Jacka et al., 1995).
lists the O'diff,super * for Na*(3 2P3/2, ML = + 1) ~ Na(3 2S1/2) superelastic transition for incident electron energies of 3, 5, 10, and 20 eV (data provided by Dr. Luskovi6, 1992). At all energies the cross section O'dire,super*is forwardpeaking. Register et al. (1978) measured superelastic differential electron scattering cross sections for 30- and 100-eV incident electrons scattered by laserexcited Ba*(6s6p 1p) barium atoms. Their measurements are listed in Table X. The uncertainty of these cross sections was estimated to be + 50% for cross sections larger than 10-17 cm 2 sr-1 and about a factor of 5 for smaller cross sections. The experimental data of Register et al. (1978) on the superelastic differential electron scattering cross section O'diff,super* for excited barium Ba*(6s6p ~P~) for 30-eV incident electron energy are compared with the unitarized distorted-wave approximation calculation results of Clark et al. (1992) in Fig. 22. Both theory and experiment show that the O'diff,super* of the excited barium Ba*(6s6p 1P1) atom is forward-peaking. -
Loucas G. Chr&tophorou and James K. Olthoff
200
'
'
'
'
I
'
'
~
'
I
'
'
~
]
I
'
'
'
'
I
'
'
'
'
I
'
'
'
'
I
'
Na* (3 2P3/2, ML=_+1) --> Na(3 2S1/2)
102 m
3eV
o
b ,_
101
~ 9
"0
Jiang
[]
Zhou
100
~
0
L
J
r
I
5
J
~
(1992)
Vugkovid
~
r
I
10
~,
(1992)
(1991
)
~
~
I~
I
15
f
~
~,
1
~
~ 1 ~
20
~
25
K
~
I
~
30
Scattering angle (deg) FIG. 21. Differential superelastic electron scattering cross section O'diff,super* for the Na*(3 2P3/2, M L -- -I- 1) --~ Na(3 2S1/2) superelastic transition at 3-eV incident electron energy. Measurements: 0, Jiang et al. (1992); l-], Vu~kovi~ (1992). Calculation:--, 10-state closecoupling calculation, Zhou et al. (1991b).
These experimental studies on superelastic scattering of electrons from excited atoms have been basic in understanding the extent to which theory can describe electron scattering from various atomic states. In this regard, experiments have been conducted on superelastic differential electron scattering from optically pumped sodium atoms with the goal of determining alignment and orientation parameters in order to facilitate a comparison of the results of various experimental methods and the results of experiment and theory (e.g., Hermann et al., 1977; Hermann and Hertel, 1982; Scholten et al., 1988; Scholten et al., 1993). Similarly, experiments were conducted on superelastic scattering of spin-polarized electrons from laser-excited atoms (McClelland, 1989) and on spin polarization of electrons superelastically scattered by laser-excited Na atoms (Hanne et al., 1982).
III. Electron-Impact Ionization of Excited Atoms The lower ionization threshold energies and the higher polarizabilities of the excited states of atoms compared to their respective ground states cause a
201
EXCITED ATOMS AND MOLECULES '
103
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102
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1)-*Ba(6s5d 1D2)
101 100 10 -1 10-2
o
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o
20
30
40
50
Scattering angle (deg) FIG. 22. Superelastic differential electron scattering cross section O'diff,super* for excited barium Ba*(6s6plp1) for 30-eV incident electron energy. (a) Superelastic transition Ba*(6s6plP1) -, Ba(6s 2 1So); (b) superelastic transition Ba*(6s6plP1) --. Ba(6s5daO2); (c) superelastic transition Ba*(6s6plP1)~ Ba(6s5dlD2). 9 Experimental data, Register et al. (1978);--, unitarized distorted-wave approximation calculation results from Clark et al. (1992).
shift of the ionization cross section cy*(e) to lower energies and an increase in its magnitude compared to cy/(e), which in turn affects the rate coefficients of various plasma discharges. The data on electron-impact ionization of excited atoms are mostly on rare gases and a few other atoms. In terms of plasma processing applications, data on excited states of atoms such as Cu and A1 are desirable.
Loucas G. Chr&tophorou and James K Olthoff
202
TABLE IX SUPERELASTIC DIFFERENTIAL ELECTRON SCATTERING CROSS SECTION O'diff,super * (8) FOR Na*(3 2P3/2, M l = _+ 1) -o Na(3 2S1/2) SUPERELASTIC TRANSITIONAT INCIDENT ELECTRON ENERGIES OF 3, 5, 10, AND 20eV (data of Vu~kovi6, 1992) , (Ydiff,super (~)(10 - 20 m 2 sr- 1)
Scattering Angle (deg)
3 eV
5 eV
10 eV
20 eV
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 25 30
110 100 99 92 85 75 61 48 37 32 24 21 16 12 9.6 5.3 3.3
380 240 150 120 94 75 62 51 44 38 30 21 14 10 8.4 5.2
820 560 360 270 210 180 150 130 120 98 73 50 36 18 7.4
1300 1100 850 510 340 170 95 55 34 21
TABLE X SUPERELASTIC DIFFERENTIAL ELECTRON SCATTERING CROSS SECTION O'dire,super(g * ) FOR Ba*(6s6p 1Px) AND Ba*(6s5d XD2), Ba*(6s5d 1D) FOR 30- AND 100-eV INCIDENT ELECTRON ENERGIES (from Register et al., 1978) O'd~iff,super(E)(IO- 20 m 2 sr- 1)
30eV
100eV
Superelastic Transition
Energy Loss (eV) 5~
10 ~
15 ~
20 ~
5~
15 ~
6s6p 1P 1---~6S2 XSo 6s6p 1P 1~6s5d3D2 6s6p 1P 1~6s5d 1D2 6s5d 1D2 ~ 6 s 21S o 6s5d 1D~6s21S~
-2.240 - 1.098 -0.828 - 1.412 - 1.412
11.8 0.12 0.70 0.46 0.92
1.4
0.70
0.43
0.08 0.06 0.42
0.12 0.08 0.19
36.0 0.29 1.7 0.30 1.7
Calculated.
91.3 1.4 4.6 1.6 1.7
0.08 0.08 0.25
EXCITED ATOMS AND MOLECULES
203
A. RARE GASES
In this section the electron-impact ionization cross sections cy*(e) are presented and discussed for He*(2as), He*(21S), Ne*(3 3P2,o) , a n d Ar*, Kr*, Xe*, and Rn*. He*(23S). The first experiments (Fite and Brackmann, 1964; Vriens et al., 1968; Long and Geballe, 1970) designed to measure cy*(e) for metastable He*(2 3S) were performed in the 1960s. They were limited in energy range from the metastable-state ionization threshold energy (4.77eV) to the ground-state ionization threshold energy (24.58eV). This energy-range limitation is inherent in most experiments utilizing a discharge or direct excitation beam source. The metastable-to-ground state ratios in these beams range from 10 -7 to 10 -4 and the ground-state contribution to the ionization signal swamps the metastable contribution at electron energies above the ground-state threshold. Fite and Brackmann (1964) measured cy*(~) for an unknown mixture of 2 as and 2 IS metastable helium using an RF discharge metastable source and a crossed electron-atom beam arrangement. Vriens et al. (1968) also used a crossed-beam apparatus and employed direct electron-beam excitation on a helium atomic beam in an attempt to produce only 2 as metastables (plus ground state atoms) in their beam. They attempted to eliminate the 2 1S contribution by adjusting the energy of their excitation electron beam below the 2 IS threshold. They reported or* (e) for an unknown 23S and 2 IS mixture. Long and Geballe (1970) made a measurement of cy*(e) for 2 3S using an electron-beam excitation technique. The experimental data of these three groups, extracted from the published curves by Trajmar and Nickel (1993), are shown in Fig. 23. Subsequent experiments by Dixon et al. (1973, 1976) employed an atomic beam generated by the fast-beam technique in a crossed electron-atom beam configuration. The metastable beam was produced by charge exchanging a fast (2-6 keV ) singly charged He + ion beam in a low-density cesium vapor cell where single-collision conditions prevailed. This technique allowed an extension of the electron energy range above the ground-state energy threshold. The measurements by Dixon et al. (1976) of the cy*(e) of He*(2 as) are listed in Table XI and plotted in Fig. 23. The lower values are their data corrected for charge exchange of metastables with trapped ions. The systematic errors in these measurements are < _+6% for ~ > 13 eV (see Dixon et al., 1976). The experimental data of Dixon et al. in Fig. 23 offer a comparison with the predictions of various calculations. Thus, we have plotted in Fig. 23 the Born approximation and the binary-encounter result of Ton-That et al. (1977) and the semiclassical and classical binary-encounter approximation
204
L o u c a s G. C h r i s t o p h o r o u a n d J a m e s K. O l t h o f f
FIG. 23. Cross section cr*(e) for electron-impact ionization of He*(2 3S) in comparison with the cross section cri(e) from the ground state He(1 1So). cr*(e): Measurements: A (unknown
mixture of 2 3S and 21S, Fite and Brackmann, 1964); V (unknown mixture of 2 3S and 2 ~S, Vriens et al., 1968); ~ , (23S), Long and Geballe (1970); II, 9 (23S), Dixon et al. (1976). Calculations:-.-., binary encounter (BE) calculation, Ton-That et al. (1977); . . . . . Born (full-range)-approximation calculation Ton-That et al. (1977); .-...- .... Born (half-range)approximation calculation, Ton-That et al. ( 1 9 7 7 ) ; - - - - , semiclassical (SC) calculation, Margreiter et al.. (1990);---, classical binary encounter (CBE) approximation calculation, Margreiter et al. (1990). cri(e): O, Measurements by Krishnakumar and Srivastava (1988).
results of Margreiter et al. (1990). The agreement between the calculations and the measurements depends on the electron energy range. The Margreiter calculations underestimate the cross section at low energies, and the Ton-That data underestimate the cross sections at high electron energies. Also shown in Fig. 23 are values of Krishnakumar and Srivastava (1988) of the electron-impact ionization cross section cy/(~) for the ground-state
205
EXCITED ATOMS AND MOLECULES TABLE XI CROSS SECTION CY*(e) FOR ELECTRON-IMPACTIONIZATIONOF He*(2 3S) (experimental data of Dixon et al., 1976) ,
,
Electron Energy (eV)
cy*(~)(i0-16 cmZ)a
Electron Energy (eV)
cr*(e)
6.1 6.6 7.1 7.6 8.6 10.6 12.6 15.1 17.6 20.1 22.6 27.6 32.6 37.6 47.6 58 68 78
4.03 5.09 5.63 5.59 6.20 6.98 7.23 7.15 7.19 6.70 6.43 6.14 4.99 5.02 4.27 4.07 3.50 3.26
88 98 123 148 173 193 198 248 298 348 398 498 598 698 798 898 988 998
2.98 (2.73) 2.72 (2.49) 2.45 (2.21) 2.11 (1.87) 1.93 (1.70) 1.79 (1.58) 1.70 (1.49) 1.44 (1.24) 1.30 (1.12) 1.12 (0.95) 1.06 (0.90) 0.88 (0.745) 0.736 (0.615) 0.651 (0.542) 0.605 (0.505) 0.553 (0.460) 0.516 (0.428) 0.503 (0.414)
(6.38) b
(4.89) (4.11) (3.87) (3.28) (3.04)
(10-16cm2)a
"Systematic errors are typically less than +_6% for energies above 13eV. bValues in parentheses are data corrected for charge exchange of metastables with trapped ions.
helium atom. Clearly, the cross section cy*(e) of He*(2 3S) far exceeds the cyi(e) of the ground state helium He(1 aSo), especially at low energies. He*(2~S). There are no measurements of cy*(e) of He*(21S). Figure 24 presents the Born (full and half range) and binary-encounter approximation results of Ton-That et al. (1977), and the semiempirical and classical binary-encounter approximation results of Margreiter et al. (1990). Ne*(33p2,0). There have been two measurements of the cross section cy*(e) for electron-impact ionization of metastable Ne*(33P2,o)--the early measurement was by Dixon et al. (1973) and a more recent measurement was made by Johnston et al. (1996). The latter measurements have been made in the energy range from threshold to 200eV and were put on absolute scale in comparison with the ground-state ionization data of Krishnakumar and Srivastava (1988). The two sets of experimental data are shown in Fig. 25a. The data of Dixon et al. have a quoted uncertainty of +_ 30%. The total (systematic and statistical) error of the data of Johnston
L o u c a s G. Christophorou and J a m e s K. O l t h o f f
206
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Electron energy (eV) FIG. 24. Calculated cross section ~*(e) for electron-impact ionization of He*(21S) in comparison with the cross section cyi(e) from the ground state He(1 1So). . . . . . . Born (full-range)-approximation, Ton-That et al. (1977)..-...- .... Born (half-range)-approximation, Ton-That et al. (1977) . . . . Binary-encounter approximation, Ton-That et al. (1977). , Semiclassical, Margreiter et al. (1990) ---, Classical binary-encounter approximation, Margreiter et al. (1990). cyi(e): O, Krishnakumar and Srivastava (1988).
et al. are listed in Table XII and for some data points are shown in Fig. 25a. Also shown in Fig. 25a is the electron-impact ionization cross section cri(e) for the ground state Ne atom (Krishnakumar and Srivastava, 1988). The measured cr*(e) for Ne*(3 3P2,o) are compared in Fig. 25b with the predictions of a number of calculations (Margreiter et al., 1990; Vriens, 1964; Ton-That and Flannery, 1977; McGuire, 1979; Hyman, 1979; Mann et al.,
207
EXCITED ATOMS AND MOLECULES .
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Electron e n e r g y (eV) FIG. 25. (a) Measured electron-impact ionization cross section cy*(e) for Ne*(3P2 + 3P o) in comparison with the cross section cri(e) from the ground-state Ne(21So). cy*(~): O, Johnston et al. (1996); C), Dixon et al. (1973). cri(e):-.-, Krishnakumar and Srivastava (1988). (b) Comparison of the measured values of cy*(~) for Ne*(3P2 + 3P o) (Fig. 25a) with the results of various calculations. Measurements: 0, Johnston et al. (1996); O, Dixon et al. (1973). Calculations: (BEI), Vriens (1964); .... (BEI), Ton-That and Flannery (1977);-.- (BHR), Ton-That and Flannery (1977); (BFR), Ton-That and Flannery (1977); (SBI), McGuire (1979); -...- (SBE), Hyman (1979); (DWA), Mann et al. (1996); . . . . (BE), Margreiter et al. (1990); ..... (SC), Margreiter et al. (1990).
208
Loucas G. Christophorou and James K. Olthoff
TABLE XII CROSSSECTIONO*(E)FORELECTRON-IMPACTIONIZATIONOFNe*(aP2 -at- 3Po) (experimental data of Johnston et al., 1996) Electron Energy (eV)
cy*(e) (10-16 cm2)
_+Systematic Error (10-16 cm 2)
4.92 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25.0 30.0 40.0 50.0 75.0 100.0 125.0 150.0 200.0
0.0 0.64 1.75 3.75 4.99 4.69 5.34 5.25 4.33 3.92 3.52 3.50 3.82 2.94 3.05 2.43 1.62 1.52 1.56 1.30
0.45 2.00 1.60 1.50 1.30 1.15 1.10 1.00 0.90 0.95 0.90 0.80 0.75 0.75 0.70 0.70 0.65 0.65 0.70
1996). The binary encounter calculations of Vriens (1964) and Ton-That and Flannery (1977) included inner-shell contributions and their results are higher than the measurements for most of the electron energy range covered by the measurements. The Born half-range (BHR) calculation of Ton-That and Flannery (1977) is in good agreement with the measurements, and so is their Born full-range (BFR) above 50eV. Similarly, the symmetric binary encounter (SBE) (in which the indistinguishability of the incident and bound electrons is taken into account) result of Hyman (1979), the scaled Born approximation including inner-shell contributions (SBI) of McGuire (1979), and the distorted-wave approximation (DWA) of Mann et al. (1996) are in good agreement with the measurements. In contrast, the binary encounter (BE) and semiclassical model ( M D M ) of Margreiter et al. (1990) are much higher than the measurements at energies above ~ 20 eV. Ar*, Kr*, Xe*, and Rn*. For metastable Ar* there have been some preliminary measurements of c~ (e) by Dixon et al. (1973) with a quoted uncertainty of + 5 0 % . These are compared with the results of a number of calculations in Fig 26a. The Born half-range (BHR) calculation result of
209
EXCITED ATOMS AND MOLECULES
12 8
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Electron Energy (eV) FI~. 26. Cross sections cy*(e) for electron-impact ionization of metastable Ar*, Kr*, Xe*, and Rn* in comparison with the respective cross sections cyi(e) for the ground-state atoms. (a) Metastable Ar*. Measurements: e , Dixon et al. (1973). Calculations:--- (BEI), Vriens (1964); - - (BE), Ton-That and Flannery (1977); (BHR), Ton-That and Flannery (1977);-...(BFR), Ton-That and Flannery (1977); - - - (SBI), McGuire (1979); --- (CBE), Margreiter et al. (1990); ... (SC), Margreiter et al. (1990). (b) Metastable Kr*. Calculations:-.- (BE), Ton-That and Flannery (1977); (BHR), Ton-That and Flannery ( 1 9 7 7 ) ; - . . . - (BFR), Ton-That and Flannery (1977); - - (SBI), McGuire (1979); --- (BE), Margreiter et al. (1990); ... (SC), Margreiter et al. (1990). (c) Metastable Xe*. Calculations: as in Fig. 26b. (d) Metastable Rn*. Calculations:--- (BE), Margreiter et al. (1990); ... (SC), Margreiter et al. (1990);--, Total ionization cross sections c~i(e) for the ground-state atoms (data of Krishnakumar and Srivastava, 1988).
Ton-That and Flannery (1977) and the scaled Born (SB) approximation calculation result of McGuire (1979) are in better overall agreement with the experimental data than the results of the other calculations. It is worth noting that while cy*(e) far exceeds cyi(e) at low electron energies, the two cross sections become similar in magnitude at energies > 100 eV. To our knowledge there exist no experimental data for the cy*(e) of metastable Kr*, Xe*, and Rn*. In Fig. 26b, c, and d are shown the results of various calculations for the electron-impact ionization of metastable Kr*, Xe*, and Rn*. They are compared with the ionization cross section cyi(e) for
L o u c a s G. Christophorou and J a m e s K. O l t h o f f
210
the respective ground-state atoms (Kr and Xe) (Krishnakumar and Srivastava, 1988). The agreement between the calculations of Margreiter et al. (1990) and the other calculations appears to become progressively worse as the atomic number increases. B. OTHER ATOMS
H*(2s). Figure 27 shows the experimental (Koller, 1969; Defrance et al., 1981; Dixon et al., 1975) and calculated (Margreiter et al., 1990; Prasad,
18
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Electron energy (eV) FIG. 27. Measured and calculated values of the cross section o*(~) for electron-impact ionization of H*(2s) in comparison with the cross section ~i(e) for the ground-state H(ls). Experimental data: O, Koller (1969) (data as given in Defrance et al., 1981); O, Dixon et al. (1975); A, Defiance et al. (1981). Calculated data: . . . . , Born-A, Prasad (1966);--, Born B, Prasad (1966); -..., Born-Ochkur, Prasad (1966);--, Born-exchange, Prasad (1966); -.-, Bethe, Vriens and Bonsen (1968); ...... semiclassical calculation, Margreiter et al. (1990);--, classical binary-encounter approximation, Margreiter et al. (1990). i , Ground-state data are from Kieffer (1970).
EXCITED ATOMS AND MOLECULES
211
1966; Vriens and Bonsen, 1968) values for the cy*(e) of the excited hydrogen atom H*(2s) in comparison with the cross section cy~(e) of the ground-state hydrogen atom H(ls) (Kieffer, 1970). The experimental data are listed in Table XIII. The uncertainties in the data of Defrance et al. (1981) are believed to be < _+ 10%, and the standard deviation of the Dixon et al. (1975) measurements varies from < _+10 to + 50% depending on the value of the incident electron energy (they are mostly between +_ 10 and _+30%). Below about 100eV the experimental data are in agreement within the quoted uncertainties but above this energy the data of Defrance et al. are systematically below those of Dixon et al. With the exception of the semiclassical results of Margreiter et al. (1990) at < 100eV the calculations give cross-section values that are substantially larger than the experimental data. The Born-Ochkur calculation of Prasad (1966) is in better overall agreement with the measurements. (See also an early review of the ionization cross section for ground H(ls) and excited H*(2s) hydrogen atoms by Rudge, 1968). Ba*. Electron-impact ionization cross sections, cy*(e), for laser-excited 138Ba*( .... 5p66s6p; 1P1, M = - 1) and cascade-populated 138Ba*( .... 5p66s5d; ID + 3D) barium atoms have been measured by Trajmar et al. (1986). These cross sections and the cross section cri(e) for the ground-state atom ~3SBa(.... 6s 2, ~S) (Dettmann and Karstensen, 1982) are shown in Fig. 28 along with typical uncertainties. They are also listed in Table XIV. At the peak the cross section cy*(e) exceeds cri(e) by about a factor of 2. Trajmar et al. found that in the case of ~38Ba*(~P1), the cy*(e) for both the M = 0 and the M = +_1 sublevels are equal within their experimental error limit. These measurements were made on the isotope 138, but they are isotope independent. For cross sections for inner (5p) shell ionization of Ba by 6-keV electrons with the barium atoms in the ground state and in the laser-excited metastable 6s5d(~'3D) state see Azizi et al. (1994). Sr*. Aleksakhin and Shafranyosh (1974) measured the electron-impact ionization cross section of Sr*(41D2) using a 2-electron beam technique. They reported a value of 8 x 10 -14 cm 2 at 10eV for cy*(~), which is about two orders of magnitude larger than the eye(e) of the ground-state atom. Note added in proof: Since the completion of this work, Boffard et al. (1999) [Boffard, J. B., Piech, G. A., Gehrke, M. F., Anderson, L. W., and Lin, C. C. (1999). Phys. Rev. A 59: 2749] reported measurements of cross sections for electron-impact excitation of metastable Ar, and Boffard et al. (1999) [Boffard, J. B., Lagus, M. E., Anderson, L. W., and Lin, C. C. (1999). Phys.
Loucas G. Christophorou and J a m e s K. Olthoff
212
TABLE XIII ELECTRON-IMPACTIONIZATIONCROSS SECTION (~i(~;) FOR THE GROUND H(ls) (from Kieffer, 1970) AND cr*(e) FOR THE EXCITED H*(2s) HYDROCEN ATOM (from Dixon et al., 1975 and Defrance et al., 1981) Cross Section (10-16 cm 2) Electron Energy (eV) 6.3 8.3 8.5 10.3 12.3 13.5 14.3 18.3 23.3 23.5 25.3 31.8 33.3 38.3 38.5 48.3 68.3 68.5 98.3 98.5 148.3 148.5 198.3 198.5 218.3 218.5 248.3 298.3 348.3 348.5 398.3 498.3 498.5 748.3 998.3
H(ls) Kieffer (1970)
H*(2s) Dixon et al. (1975)
H*(2s) Defiance et al. (1981) 5.94 8.75
(7.25) a 10.5 7.67 9.5 (9.1) 8.06 7.56 6.22 0.40
7.3 (6.7) 6.92 6.63 5.39 4.93
0.65
4.94 (5.7) 4.08 3.14
0.70
3.84 (3.58)
0.61
3.11 (2.84)
0.50
2.61 (2.19)
0.42
2.05
0.40
(1.83)
2.91 1.93 1.75 1.61
1.54 1.26 1.15 0.28
1.63 (1.27)
1.04 0.867 0.20
1.19 0.655 0.482
"Data taken using an apparatus with lower signal-to-noise ratio (SNR).
213
EXCITED ATOMS AND MOLECULES i
’ ! I
’
’
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I
40
’
138Ba
E
h,
o
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30
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0
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0
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01
z~z~
o~O i
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4
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1
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z~
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,,a z~
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I
L
i
i
6
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t
8
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10
Electron energy (eV) FIG. 28. Measured cross section cy*(e) for electron-impact ionization of excited 138Ba*(1P) and 138Ba* (1D + 3D) in comparison with the cross section cyi(e) for the ground-state atom ~38Ba(~S). Representative error bars are indicated in the figure (from Trajmar et al., 1986). C), Q, Trajmar et al. (1986); A, Dettmann and Karstensen (1982).
Rev. A 59: 4079] of metastable He. Also, Shafranyosh and Margitich (2000) [Shafranyosh, I. I. and Margitich, M. O. (2000). J. Phys. B 33: 905] reported measurement of the electron-impact ionization cross section of metastable Ca, and Deutsch et al. (1999) [Deutsch, H., Becker, K., Matt, S., and M~irk, T. D. (1999). J. Phys. B 32: 4249] semiempirical calculation of the electronimpact ionization cross section of metastable rare-gas, mercury, and cadmium atoms.
IV. Electron Scattering from Excited Molecules Vibrational and electronic excitation of molecules plays an important role in electron attachment processes (see Section VI). It is also generally known that collisions of low-energy electrons with vibrationally/rotationally excited ("hot") or electronically excited molecules affect the behavior of gas dis-
214
Loucas G. Christophorou and James K. Olthoff TABLE XIV
CROSS SECTION O*(E) FOR ELECTRON-IMPACT IONIZATION OF Ba*(1P), AND Ba*(1D + 3D), AND (ri(8) FOR ELECTRON-IMPACT IONIZATION OF Ba(1S); EXPERIMENTAL DATA
(Trajmar et al., 1986; Dettmann and Karstensen, 1982) as given in Trajmar and Nickel (1993) Electron Energy (eV) 3.1 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0
oi(e) (10 -16 cm 2) Ba(~S)
1.00 2.00 2.80 3.90 4.80 5.70 6.60 7.40 8.30 9.20 10.00 10.60 11.40 12.1 12.8 13.3 14.0 14.5 15.0
o*(e) (10 -16 cm 2) Ba*(~D + 30)
0.45 1.3 2.3 3.3 4.7 5.7 7.5 9.1 11.4 13.3 14.5 16.2 15.8 18.0 17.6 17.5 19.3 20.3 20.6 20.3 20.7 21.7 22.0 22.6 23.4 23.0 23.9
o'*(g) (10 -16 cm 2) Ba*(~p) 1.66 2.04 3.6 4.62 6.40 8.42 11.0 13.0 16.2 21.7 24.6 30.7 33.0 35.5 34.6 35.4 39.1 33.0 30.8 32.2 32.7 30.2 30.4 27.6 28.5 28.4 28.5 29.4 26.9 30.0
charges, plasmas, gaseous dielectrics, and pulsed power switches (e.g., see Schaefer and Schoenbach, 1986; Christophorou, 1990; Phelps, 1979; Pejovi6 and Dimitrijevi~, 1982), and the need for such knowledge to model these systems is generally recognized. While electron attachment to hot molecules has been relatively well investigated, little is known experimentally about the scattering (elastic, inelastic, superelastic) of slow electrons from vibrationally excited molecules mainly because of the difficulties in producing excited
EXCITED ATOMS AND MOLECULES
215
species in sufficient number densities and properly characterizing them. Production of vibrationally excited molecules in the few electron-swarm and electron-beam studies to date was accomplished by heat, photon, or electron impact. Similarly, our knowledge is poor regarding the scattering of slow electrons from electronically excited molecules. While the available data on the scattering of slow electrons from excited molecules are meager, they indicate that vibrational and electronic excitation of molecules enhances electron scattering. This is clearly consistent with the results of a number of calculations (Ton-That and Flannery, 1977; McCann et al., 1979; Huo, 1990; Capitelli et al., 1994; Capitelli and Celiberto, 1998). A. SCATTERINGOF SLOW ELECTRONS FROM "HOT" (VIBRATIONALLY/ROTATIONALLY EXCITED) MOLECULES
The few experimental studies to date on vibrationally excited molecules employed heat, laser photons, or monoenergetic electrons to excite the molecules vibrationally. The first means is not state selective, the second is initial-state selective, and the third c a n - - i n certain cases--be made in such a way as to favor excitation of a particular vibrational level. CO 2. A number of studies have been made with the aim of measuring the cross section for electron scattering from vibrationally excited CO2. Buckman et al. (1987) measured the total electron scattering cross section for both unexcited and vibrationally excited CO2 molecules using a time-offlight electron spectrometer. They produced vibrationally excited CO~ molecules principally in the first bending mode (010 at 0.083 eV) by heating the gas from 37 to 300~ Their measurements are shown in Fig. 29. At energies ~< 2 eV, the excited-state cross section is considerably larger than that for electron scattering from the ground-state CO2 molecule. The CO2 bending vibration has an associated electric dipole moment (~0.1debye) and it was suggested (Buckman et al., 1987; Haddad and Elford, 1979) that the observed increase in the cross section for "hot" CO 2 comes principally from enhanced electron scattering (elastic, inelastic, superelastic) due to the electric dipole moment associated with the lowest bending vibration of CO 2. Earlier calculations (Davis and Schmidt, 1972) indicated that sizable inelastic electron-molecule scattering cross sections can arise from electron scattering by the electric dipole moments associated with molecular bending and stretching vibrations. The cross sections for scattering of slow electrons by polar molecules have long been known (Christophorou, 1971) to be very large. A subsequent study of CO 2 by Ferch et al. (1989) confirmed the earlier work of Buckman et al. (1989) below ~ 2 eV, but, in contrast, showed a
L o u c a s G. Christophorou and J a m e s K. O l t h o f f
216 T
100
. . . .
,
. . . .
,
. . . .
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.
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energy
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J
~
,
2
(eV)
FIG. 29. T o t a l cross s e c t i o n for e l e c t r o n s c a t t e r i n g f r o m C O 2 in the e n e r g y r a n g e ~ 0 . 1 2 eV. V i b r a t i o n a l l y excited CO~': 0 , B u c k m a n et al. (1987). G r o u n d state C O 2 : C), B u c k m a n et al. (1987); V-l, F e r c h et al. ( 1 9 8 1 ) ; - - , c a l c u l a t e d v a l u e s b y M o r r i s o n et al. (1977) ( f r o m B u c k m a n et al., 1987).
significant increase in the total electron scattering cross section beyond 2 eV, especially between 3 and 5 eV where the 21--[ u negative ion state of CO2 is located. These data are shown in Fig. 30. Also shown in Fig. 30 is the more recent cross section for vibrationally excited CO2 molecules determined by Strakeljahn et al. (1995). They determined their cross section from measurements they made of the total electron scattering cross section for CO2 at 320 and 520 K and a knowledge of the population fractions of the relevant vibrational states at these two temperatures. While the measurements of Strakeljahn et al. (1995) are in qualitative agreement with the earlier measurements of Ferch et al. (1989) they differ significantly in magnitude, energy dependence, and position of the maximum. The enhancement in the scattering cross section in the energy range 3-5 eV was attributed principally to the indirect population of the bending mode of CO2 via the decay of the 21--[ u r e s o n a n c e of CO2". The position of
EXCITED ATOMS AND MOLECULES
217
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:
i
I
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i
6
i
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I
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10
Electron energy (eV) FIG. 30. Total cross section for electron scattering from C O 2 molecules in the vibrational ground state (solid line) and from C O 2 molecules in excited states of bending vibration (dashed line) (Ferch et al., 1989). The dotted line is a subsequent determination of the cross section for electron scattering from vibrationally excited C O 2 molecules by Strakeljahn et al. (1995).
the cross-section peak is shifted to lower energy by 0.3 to 0.4eV as is expected from calculations of the potential energy surface of CO2" (21-Iu) (Ferch et al., 1989; Krauss and Neumann, 1972; Christophorou et al., 1984). To our knowledge no theoretical data exist for the excited-state cross section. A technique has been described by Srivastava and Orient (1983) whereby vibrational excitation of molecules is accomplished by an electron beam rather than by heat, or by laser photons. The technique employs a crossed electron beam-target beam geometry. The target beam is crossed at 90 ~ by two electron beams--whose energies can be varied independently--traveling in opposite directions. One of the electron beams is used to excite the molecules and the other is used to observe the scattering from the excited molecules. Srivastava and Orient (1983) employed this technique for the study of dissociative electron attachment to vibrationally excited CO2. They
218
Loucas G. Christophorou and James K. Olthoff
tuned the excitation electron beam to ~ 1.2eV because at about this electron-impact energy the vibrational excitation for the CO2 molecule is the largest (Boness and Schulz, 1968) and is due mainly to the asymmetric stretch mode (001). They found that the cross section for dissociative electron attachment to CO2 at 4.4 eV - - where a negative ion resonance is located--increases when the CO2 molecule is vibrationally excited. However, no measurements of electron scattering from vibrationally excited CO2 molecules were reported. N zO. Strakeljahn et al. (1995) used their measurements of the total electron scattering cross section for N20 at 320 and 520 K in the energy range 0.36 eV and the population fractions of the relevant vibrational states at these two temperatures to determine the cross section for total electron scattering from vibrationally excited N20*. The cross sections they determined for the ground N20 and the vibrationally excited N20* molecule are shown in Fig. 31. The cross section maximum due to the shape resonance (2E +) at 2.3 eV shifts to lower energy by ~0.4 eV for the vibrationally excited molecule. Finally, Capitelli and collaborators (e.g., Capitelli et al., 1994; Capitelli and Celiberto, 1998; Celiberto et al., 1999) performed a series of calculations on the effect of vibrational excitation of H2, D2, N2, and O2 on the cross sections for electron-impact electronic excitation, dissociation, and ionization of these molecules. Their calculations indicate that the cross sections for these processes depend on the initial state of vibrational excitation of the molecule. SF 6. More recently, Stricklett and Burrow (1991) used an infrared laser to pump vibrational transitions in SF 6 expanded from a nozzle and then passed an electron beam through the free jet downstream from the laser. They modulated the laser beam and measured synchronously the change in the attenuated electron beam current, which was found to be "a sensitive measure of the changes in the cross section upon vibrational excitation" (Stricklett and Burrow, 1991). They found that electron scattering was most strongly affected at electron-impact energies of below 2 eV and in the energy ranges where negative ion states are located. B. SCATTERINGOF SLOW ELECTRONSFROM ELECTRONICALLYEXCITED MOLECULES As in the case of vibrationally excited molecules, our knowledge on the scattering of slow electrons from electronically excited molecules is very limited. It seems that the only electronically excited molecule that has been experimentally studied to date is singlet oxygen O~(a lag). The metastable
EXCITED ATOMS AND MOLECULES
35
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Electron energy (eV) FIG. 31. Total electron scattering cross section from ground state (--) and vibrationally excited (. . . . ) N20 molecules (data of Strakeljahn et al., 1995).
state a 1Ao lies 0.98 eV above the ground state (X 3~-) of 0 2 and has a radiative half-life of about 45 min (Badger et al., 1965). The excited O~'(a 1A0) species is relatively easy to produce in reasonable quantities in microwave discharges. The differential and integral cross sections for scattering of 4.5-eV electrons by the ground s t a t e 0 2 ( X 3]~O) and by the excited state O~(a ~A0) species in the - 2 . 0 to + 2 . 0 e V energy-loss range have been measured by Hall and Trajmar (1975). Figure 32 shows the differential cross sections for excitation of the b ~Z~ state (located at 1.63 eV above the ground state of O2) from the a ~A0 and X 3Z0- states of O2. The differential cross section for the transition O~(a ~Ao) + e(4.5 eV) --, O~'(b ~2;o+) + e
(20)
was found (Fig. 32) to be about a factor of 10 larger than that for excitation from the ground state, viz., O2(X
3 Z o- )
+ e(4.5 eV) --, O~(b ~Z~) + e
(21)
Loucas G. Christophorou and James K. Olthoff
220
10-1
’
’
’
I
’
’
’
I
’
’
’
I
’
’
’
_
02* (a lAg) + e(4.5 eV) --->02* (blT_,g+)+ e
if)
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_
E
02* (alAg) +
_
e(4.5 eV) ---> 02
(X3Eg") +
e
_
(xl
b
v
"o
10-3
-
g'" 0 e (xaZg") + e(4.5 eV) ~ 02* (blZg+) + e
_
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I
40
,
,
~
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,
160
Scattering angle (deg) FIG. 32. Differential cross s e c t i o n for 4 . 5 - e V e l e c t r o n s s c a t t e r e d f r o m g r o u n d state O 2 ( X 3Z~-) ( I ) a n d e x c i t e d O ~ ( a 1A0) ( Q ) o x y g e n m o l e c u l e s . T h e d a t a ( V ) r e p r e s e n t the m e a s u r e d differential s u p e r e l a s t i c s c a t t e r i n g cross s e c t i o n for 4 . 5 - e V e l e c t r o n s ( d a t a of H a l l a n d Trajmar,
1975).
The integral cross sections for reactions (20) and (21) for 4.5-eV electrons were measured by Hall and Trajmar (1975) to be 23 x 10 -18 c m 2 and 2.1 x 10-18 c m 2, respectively. They estimated the former value’s uncertainty to be _+35%, with the latter at _+25%. Huo (1990) calculated cross sections for excitation to various electronic states of N 2 from the ground state N z ( X 1]~o) and from the excited states N~(a 11-[0) , N~(A 3]~u+), and N~’(B 3I]o) , and found that the cross sections for the excited states far exceed those for the ground state. This is seen from the data in Fig. 33 where the Schwinger multichannel calculation cross sections obtained by Huo (1990) for excitation of the B 31-[o and W 3A u excited states of N 2 from the ground state and from the excited states N~’(A 3E+) and N~’(B 3I]o) are shown as a function of the scattered electron energy. Similar
EXCITED ATOMS AND MOLECULES '
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)
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o
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,
I
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I
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N 2 ( X 1 Z g * ) --, N 2 * ( W 3 A u )
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0 ~
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0 2 4 6 8 10 12 Scattered electron energy (eV)
0
I O,
I
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I
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0 2 4 6 8 10 12 Scattered ,electron energy (eV)
FIG. 33. Cross sections for excitation of the B 3[] 0 and W 3Au excited states of N 2 from the ground state N2(X 122) (---) and from the excited states (a) N~'(A 3Eu+) and (b) N*(B 3F10) ( - - ) as a function of the scattered electron energy (Huo, 1990). The open circles are the ground-state measurements of Cartwright et al. (1977) as normalized by Trajmar et al. (1983).
results were obtained by Huo for other transitions. The structure in the calculated cross sections has been attributed by Huo to negative ion resonances.
C. SUPERELASTIC SCATTERING OF SLOW ELECTRONS FROM EXCITED MOLECULES
In a superelastic collision the electron gains energy from the excited target, which itself reverts to a lower energy state. In spite of the practical significance of superelastic electron scattering there are few studies on the subject. Notable are the early work by Burrow and Davidovits (1968) on superelastic electron scattering from vibrationally excited nitrogen and the subsequent work by Khakoo et al. (1983) on superelastic scattering of slow electrons from singlet oxygen. The electron energy-loss spectrum of O~'(a 1Ao) showed an energy-gain peak at -0.98 eV, which they attributed to superelastic electron scattering, that is, to the electron-collision-induced
222
Loucas G. Christophorou and James K. Olthoff
decay of the a 1Ao state down to the ground state. Hall and Trajmar (1975) measured the differential scattering cross section for this superelastic collision in the range 20-135 ~. Their data are shown in Fig. 32 and are seen not to depend strongly on the scattering angle. They have an estimated uncertainty of _ 35%. From their differential cross section measurements (extrapolated to 0 and 180~ Hall and Trajmar estimated an integral cross section for this superelastic collision of ~ 10-17 cm 2 for 4.5-eV electrons.
D. EFFECT OF VIBRATIONAL EXCITATION ON ELECTRON TRANSPORT
The higher cross sections for electrons scattered off vibrationally excited molecules (Section IV.A) are expected to make the transport properties of gases temperature dependent. Indeed, Haddad and Elford (1979) found that the momentum transfer cross section they deduced for CO2 using their electron-swarm drift velocity measurements depended strongly on the gas temperature below ~ 1 eV. This they attributed to enhanced electron scattering at the higher temperatures, which resulted from increased population of excited vibrational levels of CO 2, principally the lowest lying bending vibration. More recently, Christophorou et al. (1991) demonstrated the effect of vibrational excitation on electron transport by measuring the drift velocity w of slow electrons in C H 4 and CzF 6 as a function of the density reduced electric field E/N, in the temperature range 300-700 K. Their thermal electron mobility data (laN)th(T) (deduced from the slopes of the initial linear portions of the w(T) vs E / N plots) are shown in Fig. 34. Interestingly, while at 300 K the value of (laN)t h is almost the same for the two molecules, at 700 K the (gN)t h for CzF 6 is ~ 5 times smaller than for CH 4. The momentum transfer cross section tYro(e) of both molecules possesses a Ramsauer-Townsend (R-T) minimum, which occurs at ~0.4eV for C H 4 (Ferch et al., 1985b; Alvarez-Pol et al., 1997) and at ~0.15eV for CzF 6 (Christophorou and Olthoff, 1998). In view of this, the (btN)th of both molecules would be expected to increase with increasing T. This is indeed the case for CH 4 for which the population of higher vibrational states is negligible in the temperature range investigated. [the energies of the four fundamental frequencies of C H 4 are: 0.162eV, 0.190eV, 0.362eV, and 0.374eV (Shimanouchi, 1972)]. However, for C2F6, which has very low vibrational thresholds [6 of its 12 fundamental vibrational frequencies lie below 0.077eV and all 12 lie below 0.155eV (Shimanouchi, 1972)], the opposite behavior is observed due at least in part to enhanced electron scattering from vibrationally excited C z F 6 molecules as T is increased. Evidence for efficient vibrational excitation of CzF 6 by slow (<0.5eV)
223
EXCITED ATOMS AND MOLECULES
oo
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4
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--
...,....,.,.o,~ . - . . . - ’ ’ ’ ’ ’ ~
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700
Gas temperature (K) FIG. 34. Density-normalized thermal electron mobility (gN)t h as a function of gas temperature T for CH4( 9) and C2F6(O ) (Christophorou et al., 1991).
electrons was also obtained in an electron cyclotron resonance study of C z F 6 by Morris et al. (1983).
V. Electron-Impact Ionization of Excited Molecules In sharp contrast to the many experimental and theoretical studies on electron-impact ionization of ground-state molecules (e.g., M/irk, 1984), there is only limited information on electron-impact ionization of electronically excited molecules. The few studies that have been conducted in this area include calculations of electron impact ionization of metastable rare-gas excimers [Ne~' ( 1 ' 3 2 + ) and Ar~(l'aE +) (McCann et al., 1979)], and N~(A 32,+), N~(a' ~22), and CO* (a3H) (Ton-That and Flannery, 1977), and experimental measurements on N~'(A 32;2) (Armentrout et al., 1981). Ionization of metastable N* and CO* is important in gas-laser dynamics. In this connection, Wang et al. (1989) observed that when they irradiated N 2 molecules using the ArF excimer line (193 nm), the production of N § by electron-impact dissociative ionization was enhanced. They attributed this
Loucas G. Christophorou and James K. Olthoff
224 C O
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Electron e n e r g y (eV) FIG. 35. Experimental nondissociative electron-impact ionization cross section for: N2(X 1s + ) ( ) and N~'(A 3s (O) (Armentrout et al., 1981); calculated cross section for the ionizing transition N*(A as + e ~ N~-(A 2FI,) + 2e ( - . - . - , Ton-That and Flannery, 1977) (from Armentrout et al., 1981).
enhancement to electron-impact ionization of laser-excited nitrogen in the A 3Z+ state. In Fig. 35 the experimental and the calculated cross sections for the nondissociative ionization of N~'(A 3s are compared with that from the ground s t a t e N z ( X 1 ~ + ) , viz., e + N~(A 3 2 + ) ~ N f ( X 2s
+ 2e
(22)
e + N~(A 3E~+) ~ N f ( A 2II.+) + 2e
(23)
e + Nz(X ']~+) --+N~-(X2~0+) + 2e
(24)
Armentrout et al. (1981) extracted their cross sections from the apparent ionization cross section of a beam of nitrogen molecules, ~ 50% of which were in the ground state (X xE~) and ~ 50% of which were in the excited state (A 32+). They formed this mixed-state beam by charge transfer neutralization of a 1-keV N~ beam with NO. The threshold energies for
225
EXCITED ATOMS AND MOLECULES i
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Electron energy (eV) FIG. 36. Binary-encounter cross sections o* for ionization of metastable N~(A 3Eu+) ( ), N~(a' 1E~-) (---), and CO*(a3H) (...) as a function of electron energy. The final state of the residual positive ion is, respectively, N~(A 2I-Iu), N~-(A 21-Iu), and C O + ( X / Z +) (from Ton-That and Flannery, 1977).
reaction expressions (22), (23), and (24) are, respectively, 9.35 eV, 10.47 eV, and 15.58eV (Armentrout et al., 1981). While the variation with electron energy of the ionization cross section for processes (22) and (24) is similar, the peak value for expression (22) is surprisingly lower than that for expression (24). It was suggested by Armentrout et al. (1981) that this may be due partly to the fact that the A state lrt0 orbital is occupied by one electron while the X state 3or0 orbital is occupied by two electrons. It should be noted, however, that higher-lying states of N~ (e.g., the A 21--[u state that lies ~ 1.12eV above the X 2~]; state) may not be neglected. Indeed, the theoretical curve in Fig. 35--obtained by Ton-That and Flannery (1977) in the binary-encounter approximation--is for reaction (23) and not for reaction (22). Figure 36 presents the binary-encounter approximation results of TonThat and Flannery (1977) for the ionization of metastable nitrogen N*(A 3 ] ~ : ) , N*(a’ 1Z~-) and metastable carbon dioxide CO* (a 31-I), namely,
226
Loucas G. Christophorou and James K. Olthoff
for reactions (23), (25), and (26): e + N~'(a' 12;~-)~ N~(A 21-I+) + 2e
(25)
e + CO*(a 31-I) ~ CO +(X 2Z +) + 2e
(26)
The threshold energies for reaction expressions (25) and (26) are, respectively, equal to 8.56 and 8.274 eV. Cross sections for ionization of the metastable excimers Ne~ and Ar~ by electron impact, namely for the reactions e + Ne~(1'32; +) --. Ne~-(zE +) + 2e
(27)
e + Ar~(l'3Z2)~ Ar~(2E.+) + 2e
(28)
have also been computed by McCann et al. (1979) in the binary-encounter approximation for electron energies of between 5.0 and 50 eV. The calculations of McCann et al. (1979) indicated that for these reactions the cross sections have maximum values of ,-~ 10 -15 c m 2 and the excited electron in the 1'32;+ states behaves like a Rydberg electron attached to its parent 2Z+ ion with a binding energy of ,~ 3-4 eV. It should be noted that ionization of rare gases initially in atomic and molecular metastable states is important in the kinetic modeling of excimer lasers.
VI. Electron Attachment to Excited Molecules Electron attachment reactions depend strongly on both the structure of the molecule and the kinetic energy e of the attached electron (Christophorou et al., 1984; Christophorou, 1971; Massey, 1976; Smirnov, 1982). They also depend strongly on the internal energy (~)int of the electron attaching molecule. As (~)int is increased, delicate and often profound changes occur in the electron attaching properties of molecules that depend on the molecules themselves and on the mode (dissociative or nondissociative) of electron attachment (e.g., see Christophorou et al., 1984, 1994, and other references cited later in this section). The effects of the internal energy of excited targets on electron attachment are of intrinsic value (e.g., in determinations of thermodynamic data from electron attachment studies where the energetic onsets are functions of gas temperature) and of interest to many applied areas (employing temperatures higher than ambient) where electron densities are affected by negative ion formation. These effects are
EXCITED ATOMS AND MOLECULES
227
best understood via the resonance scattering theory of electron attachment (e.g., Bardsley et al., 1966; O'Malley, 1966; Chen and Peacher, 1967). Within this theory an electron e of kinetic energy e is initially captured by the molecule AX, forming a transient anion AX-* which subsequently decays by electron attachment (A + X- or AX-) or by autodetachment (AX e) + e), viz., e(e) + AX ~ AX-* --+ A + XAX(*) + e(e') e(e) + AX ~ A X - * ( + S) ~ AX- + energy --, AX e) + e(e')
(29a) (29b) (30a) (30b)
where e'(~ 10 -~4 cm 2) depending on the molecule and the energy position of the negative ion state with respect to that of the neutral molecule (Fig. 37; Christophorou et al., 1984; Christophorou, 1971). Similarly, the autodetachment lifetime of the isolated AX-* anion varies by more than 13 orders of magnitude (from --~10- is to > 10-2 S; see, e.g., Christophorou et al., 1984; Christophorou, 1971, 1978). As the internal energy of the molecule is increased, changes may occur in cy0(e) and orb(e) due to variations in the Franck-Condon factors and the fact that as the internal energy is increased electrons with lower kinetic energy can reach the negative ion state. As will be seen from the discussion in the following sections, while these changes affect the electron attachment cross sections, the reported dependencies of the electron attachment cross sections on the internal energy of molecules are rather attributable to the large changes in the quantities p(e) and p'(e) with changes in the internal energy (l~)int of the molecules.
Loucas G. Christophorou and James K. Olthoff
228
10-13 _! 10-14
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Electron energy (eV) FIG. 37. Dissociative electron attachment cross sections as a function of electron energy for a number of molecules. The quantity n(X/2n) 2 is the s-wave capture cross section (from Christophorou et al., 1984).
A. ELECTRON ATTACHMENT TO " H O T " (VIBRATIONALLY/ROTATIONALLY EXCITED) MOLECULES
It has generally been observed (e.g., Christophorou et al., 1984, 1994; Christophorou, 1987) that an increase in temperature T produces large increases in the magnitude of O'da(8 ) and changes in the energy dependence of O'da(~). These effects are due to increases in p(e) and changes in the Franck-Condon factors resulting from the increase in the internal energy of AX with increasing T. At elevated temperatures electron attachment occurs
EXCITED ATOMS AND MOLECULES
229
over larger internuclear distances and over larger excited-vibrational-state amplitudes. As T increases the probability p(~) for reaction (29a) increases and the transient ion AX-* dissociates faster into A + X-. However, this generalization is not without exceptions as will be seen from the results presented later in this section. For instance, when the negative-ion potential energy curve crosses that of the neutral molecule near-zero energy, an increase in T may result in a decrease of ~da(a). Conversely, the effect of T on nondissociative electron attachment has generally been a decrease in the magnitude of ~naa(~) attributed (Christophorou, 1987, 1994; Christophorou et al., 1984) to a decrease in p'(~) (i.e., an increase in autodetachment) as the anion's internal energy is increased with increasing T. This, however, requires further scrutiny (Christophorou, 1994; Christophorou and Datskos, 1995) (Section VI.A.2). The techniques that have been used to study electron attachment to energy-rich ("hot") targets in their electronic ground state are generally conventional electron swarm methods with provisions for temperature control (e.g., see Christophorou, 1994; Christophorou and Datskos, 1995; Spyrou and Christophorou, 1985a; Datskos et al., 1990, 1993b), and electron-impact mass spectrometers with similar provisions (e.g., see Allan and Wong, 1978; Chantry and Chen, 1989; Pearl and Burrow, 1993; Orient et al., 1989). Measurements dealing only with the effect of T on thermal electron attachment have been made using the flowing afterglow/Langmuir probe technique (e.g., see Alge et al., 1984; Smith and Spanel, 1994) and other afterglow-based methods (e.g., see Burns et al., 1996). While gas heating is the easiest way to increase the internal energy of a molecule, the resultant ro-vibrational excitation is not state selective. There have been few studies that employed selective vibrational excitation of molecules prior to electron attachment using lasers (Chen and Chantry, 1979; Kiilz et al., 1996). There has also been one study of electron attachment to vibrationally excited fragments whereby the vibrationally excited fragments were generated by laser photodissociation of the parent molecules (Rossi et al., 1985). With regard to the effects of T on nondissociative electron attachment, the development of a time-resolved electron swarm technique (Christophorou and Datskos, 1995; Datskos et al., 1993b) that allows simultaneous determination of the effect of T on both the electron attachment and detachment processes has been a major advancement. This technique (see Section VI.A.2) has been useful in unraveling and quantifying the effects of T on both the electron attachment and detachment processes in nondissociative electron attachment processes involving polyatomic molecules.
230
Loucas G. Christophorou and James K. Olthoff
1. Dissociative Electron Attachment
In this section the available data on electron attachment to ro-vibrationally excited molecules is summarized and discussed. Few investigators have reported on the absolute uncertainties regarding their measurements. For a number of electron-swarm studies the uncertainty is a function of T. It is usually about +_ 10% for room-temperature data, but it can exceed _+ 15% at higher values of T. a. Diatomic Molecules. The effects of temperature on the magnitude and
energy dependence of the cross section for dissociative electron attachment to diatomic molecules has been investigated experimentally, using both electron beam and electron swarm methods, as well as theoretically. Both the theoretical and experimental work has shown the effect of rotational and vibrational excitation on dissociative electron attachment, and has highlighted the significance of the total internal energy content of the target molecule on dissociative attachment for diatomic (and polyatomic) molecules. As a rule, the threshold energy for the dissociative attachment cross section decreases, the energy position of the resonance maximum decreases, and the magnitude of the cross section and the resonance width increase with increasing gas temperature. H2;D 2. Experimental (Allan and Wong, 1978) and early theoretical (Wadehra and Bardsley, 1978; Bardsley and Wadehra, 1979; Wadehra, 1984) work on the production of H - from H 2 via the 3.75 eV H2 resonance has shown an increase by over a factor of 10 with each increase in vibrational quantum, and by a factor of 3 for rotational level increase from J = 0 to J = 7. The results of Bardsley and Wadehra (1979) employing resonance scattering theory with semiempirical parameters are shown in Fig. 38a. They indicate that although the effect of rotational excitation is not as high as that of vibrational excitation and not as significant as suggested earlier (Chen and Peacher, 1967), it is nonetheless considerable. The results of the initial calculations have by-and-large been borne out by a number of subsequent theoretical studies (e.g., Capitelli and Celiberto, 1998; Miindel et al., 1985; Gauyacq, 1985; Atems and Wadehra, 1990; Hickman, 1991; Ci~ek et al., 1998) as can be seen from Fig. 38b, where the peak cross section for dissociative attachment to H 2 is plotted as a function of the internal energy of the molecule. It is interesting to observe the bending over of the cross-section maximum for vibrational quantum numbers in excess of v = ~ 8, which is close to the exoergic threshold. The differences between the cross sections for H - from H 2 and D - from D 2 show the existence of an isotope effect (Fig. 38a), which is a function of temperature (Christophorou, 1985).
EXCITED
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Internal e n e r g y (eV) FIG. 38. (a) Internal-state energy dependence of threshold dissociative electron attachment cross sections in H 2 and D 2 via the "Z + resonance. The numbers indicate the value of the vibrational quantum number v (from Bardsley and Wadehra, 1979). O, Allan and Wong (1978); D, Wadehra and Bardsley (1978); A, Bardsley and Wadehra (1979). (b) Peak cross section for dissociative electron attachment, CYaa(epeak)to H 2 as a function of the internal energy of the H 2 molecule (from Hickman, 1 9 9 1 ) . - - , Hickman (1991); . . . . . . Wadehra and Bardsley (1978); . . , Gauyacq ( 1 9 8 5 ) ; - - , Miindel et al. (1985); O, Allan and Wong (1978).
Liz. McGeoch and Schlier (1986) investigated dissociative electron attachment to optically pumped lithium molecules. They populated metastable vibrationally excited lithium molecules by laser excitation of a supersonic lithium beam. They found that the dissociative electron attachment rate constant does not vary significantly for Liz(X 1~2~-)between the v ~ 10 and
232
Loucas G. Chrk~tophorou and James K. Olthoff
v-~ 13 states that lie energetically above the attachment energy threshold, and that there is no significant rotational variation between J ~ 0 and J ~ 20. The rate constant for dissociative attachment of thermal electrons (~0.05 eV) to these states, that is for the reaction, e(,~0.05 eV) + Li~(X i X ; , v = 10 to 13) ~ Li2*(A 2Z0+ ) --, Li(2S) + Li- (1S) has been measured to be (2 _+ 1) x 10-8 cm a s-1. The A 2]~; state is bound and the threshold for dissociative attachment of zero-energy electrons lies between v = 10 and 11. Nv Measurements by Huetz et al. (1980) showed that the cross section for the process (7-13 eV) e + N2(X ~Z~, v = 0 ) ~ N2*(A 211.)~ N-*(3P) + N(4S)
i N(4S) + e is about the same as that for N 2 in the v = 1 level. Calculations by the same authors indicated that the dissociative electron attachment cross section for N2 in the v = 4 level is about a factor of 4 higher compared to that for N 2 ( X 12~o, v = 0).
02. Work on the temperature dependence of dissociative electron attachment to O 2 via the O2"(21-Iu) resonance is the first quantitative experimental result of this type (Fite and Brackmann, 1963; Henderson et al., 1969). Their measurements on the production of O - from O 2 at 300 and 2100 K are shown in Fig. 39. The threshold energy shifts from ~ 4 eV at ~ 300 K to ,~ 1.2 eV at 1930 K. At the higher T the energy position of the resonance maximum is decreased and the magnitude of both the cross section and the resonance width are increased. The measurements in Fig. 39 were explained theoretically by O'Malley (1967). He assumed that the direct effect of T on O2 is to produce a Maxwellian distribution of vibrational (v) and rotational (j) states, and thus the effective cross section CY~a@, T) for dissociative electron attachment is the Boltzmann average of the cross section cy~(e) from each of the individual states. In his treatment, O'Malley considered the effect of rotational states to be negligible. The excellent agreement of his predictions on the threshold, magnitude, width, and energy position of the O - from O2 resonance with the experimental results justifies this assumption. As T is increased, higher vibrational levels are populated, the internuclear distances increase significantly, and although even at 2000 K there is
233
EXCITED ATOMS AND MOLECULES t
'
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Electron energy (eV) FI6. 39. Cross section for the production of O- by dissociative electron attachment to 0 2 as a function of the electron energy at 300, 2100, and 3000K (from O'Malley, 1967). 0, O, measurements (Fite and Brackmann, 1963; Henderson et al., 1969);--, theoretical results (O'Malley, 1967).
only a limited amount of vibrational excitation, the probability p(a) is increased considerably and dominates the temperature dependence of the cross section. F 2. McCorkle et al. (1986) measured the dissociative electron attachment rate constant kaa(E/N ) for F 2 in mixtures with nitrogen buffer gas over a range of E/N values corresponding to mean electron energies between 0.04 and 0.75 eV at three temperatures, 233, 298, and 373 K. From the measured kda(E/N ) and a knowledge of the electron energy distribution functions in pure nitrogen they deduced the rate constants as a function of the mean electron energy (~), /(;da((t~)), which are shown in Fig. 40a. (In this and in subsequent similar cases for other molecules discussed in this work, only the functions kaa((e)) will be given. The connection between kda((~;)) and kda(E/N ) can be made easily by considering the data listed in Appendix A on the variation of ( e ) with E/N at various values of T for the two buffer gases, nitrogen and argon, normally used in these studies.) The kda((e), T)
Loucas G. Christophorou and James K. Olthoff
234
2.5
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1.0
FIG. 40. (a) Dissociative electron attachment rate constant kda((~;)) as a function of the mean electron energy, (e), for F 2 at T = 233, 298, and 373 K (data of McCorkle et al., 1986). In the inset is shown the variation with T of the thermal value (kda)th of the electron attachment rate constant (C), data of McCorkle et al., 1986; O, data of Sides et al., 1976). (b) Calculated cross sections for dissociative electron attachment to F 2 as a function of the electron energy e in the vibrational levels v = 0, 1,2, and 3 . - - , Hazi et al. ( 1 9 8 1 ) ; - - - , Bardsley and Wadehra (1983).
data in Fig. 40a show a rather small increase in the magnitude of the rate constant with increasing T in this temperature range. The variation of the thermal value (kda)th of the electron attachment rate constant with temperature is listed in Table XV and is plotted as an inset in Fig. 40a. While the two sets of measurements of (kda)th (T) agree in that the magnitude of the
EXCITED
ATOMS
AND
235
MOLECULES
TABLE XV VARIATION OF THE (kda)t h OF DIATOMIC MOLECULES WITH GAS TEMPERATURE"
Temperature Molecule
(K)
(kda)th (cm 3 s -
F2
233 298 373 350 600
1.2 x 10 - 8 1.8 x 1 0 - s 1.9 x 10 - 8 (3.1 _ 1.2) x 10 . 9 (4.6 ___1.2) x 1 0 - 9
McCorkle
213 233 253 273 298 323 293 300 300 350
1.22 x 10 - 9 1.35 x 10 - 9 1.51 • 10 - 9 1.67 x 10 - 9 1.86 x 1 0 - 9 2.14 x 10 - 9 3.1 x 1 0 - l O (2.8 ___0.4) x 1 0 - lO 1.1 x 10 - 9 (3.7___ 1.7) x 10 - 9
McCorkle
Christodoulides et al. (1975) E C W Ayala et al. (1981) P S a Schultes et al. (1975) E C W Sides et al. (1976) F A
300 295 253 467
( 1 . 3 6 + 0 . 2 8 ) x 10 - l ~ 1.8 x 10 - l ~ 0 . 9 x 10 -10 4.2 x 1 0 - 1 o
Ayala et al. (1981) P S T r u b y (1968) M W C e T r u b y (1969) M W C T r u b y (1969) M W C
C12
1)
Reference/Method
Sides
et
et
al. (1986) Swarm
al. (1976) F A b
et
al. (1984) Swarm
" F o r some relevant data on Br 2 and 12 see Christophorou et al. (1984). b F A = Flowing afterglow technique. c E C R = Electron cyclotron resonance technique. P S = Pulsed sampling technique. e M W C = Microwave cavity technique.
rate constant shows a small increase with increasing temperature, they are not compatible in terms of their absolute magnitudes of (kda)th. Figure 40b gives the calculated cross sections by Hazi et al. (1981) and by Bardsley and Wadehra (1983) for dissociative electron attachment to F 2 in the vibrational levels v = 0, 1, 2, and 3. The results of the two calculations are in good agreement with each other. There are no measurements for a comparison. Na~. An elegant study of dissociative electron attachment to Na 2 molecules excited to selected vibrational states was conducted recently by Kiilz et al. (1996). They employed a crossed electron-molecule beam arrangement and two optical methods (Franck-Condon pumping and stimulated Raman scattering) for preparing Na~(v, j) molecules in selected excited vibrational states v. Their data show an increase of more than 3 orders of magnitude in
Loucas G. Christophorou and James K. Olthoff
236
the state-dependent dissociative electron attachment rate constant as a function of the vibrational level up to v = 12 (Fig. 41a). For v > 12, which is close to the exoergic threshold, further increase in v resulted in a decrease of the dissociative electron attachment rate constant. This was also consistent with their ab initio calculations, which showed the potential-energy curve of the dissociating negative ion state Naz(A 2 E o+ ) crossing that of Na2( X 1 ~ ) between v = 11 and v = 12 in agreement with the experiment. Kiilz et al. (1996) also calculated the cross section for dissociative electron attachment to Na~(v, j) in j = 9 and v = 0 to 24. These calculated cross sections are shown in Fig. 4lb. The reversal in the temperature dependence behavior of the cross section for dissociative attachment seen for Na~(v > 12) is similar to that indicated by the calculations in the case of H - from H 2 (Fig. 38b) and may be exhibited by other molecules having similar dissociative attachment characteristics. For instance, this may be the case when the negative-ion state crosses the ground state in such a way that population of vibrational levels higher than the v = 0 of the neutral molecule results in the initial neutral {E (1)
i
,,=,
3000 .... , .... , .... , .... , .... Na2*(v) ~ (a) 2500 ~
~L/14' 103~24
1500 1000
~
500
| (b) 1
10 2
2000
~ <
' ' i ....
v
101
1o0
.-~ o
0
0
~
5 10 15 20 25 Vibrational level v
10 ~ 0.00
0.25
0.50
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FIG. 41. (a) Dissociative electron attachment rate-constant enhancement for vibrationally excited Na* as a function of the excited vibrational level v (from Kfilz et al., 1996). @, M e a s u r e m e n t s ; - - , - - - , calculations. (b) Calculated dissociative electron attachment cross sections (in units of a 2) as a function of electron energy for ro-vibrationally excited Na* with j = 9 and v = 0 to 24 (from Kiilz et al., 1996).
237
EXCITED ATOMS AND MOLECULES
state lying above the dissociating negative-ion state. Recent calculations (Hor~t~ek et al., 1997; Horfi6ek, 1998) indicate that this is the case for dissociative electron attachment to HI, for which Hor~t~ek (1998) calculated dissociative electron attachment cross sections decreasing in the order HI(v = 0) > HI*(v = 1) > HI*(v = 2). CIr. The dissociative electron attachment rate constant kaa(E/N) for C12 has been measured by McCorkle et al. (1984) as a function of E / N in N 2 buffer gas for temperatures in the range of 213 to 323 K. From these measurements McCorkle et al. deduced the kda((e)) for C12, which are shown in Fig. 42. As for the case of F2, a small increase in electron attachment is observed as T is increased in the indicated T range. The variation of the thermal value of the electron attachment rate constant (kda)th with T is listed in Table XV and plotted in the inset of Fig. 42.
i
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Mean electron energy (eV) FIG. 42. Dissociative electron attachment rate constant kda((g)) as a function of the mean electron energy for C12 at various temperatures (data of McCorkle et al., 1984). Inset: Thermal value, (kda)th, of kda((e)) as a function of T. O, McCorkle et al. (1984); I , Christodoulides et al. (1975); 9 Ayala et al. (1981); x, Schultes et al. (1975); A, Sides et al. (1976).
238
Loucas G. Christophorou and James K. Olthoff
12. Measurements of (kaa)th have been made at room temperature by Truby (1968) and Ayala et al. (1981) and at temperatures from 253 to 467 K by Truby (1969) (see Table XV). The latter measurements show an increase in (kda)th from 0.9 x 10-~~ cm 3 s-X at 253 K to 4.2 x 10-~~ cm 3 s- 1 at 467 K. Similarly, Brooks et al. (1979) observed the electron attachment coefficient of a 1% 12 in 99% N 2 mixture to increase with increasing T between 35 ~ and l l 0 ~ for the E / N range between ~ 7 • 10 -17 V cm 2 and 50 • 10-17 V cm 2 they investigated. Laser optogalvanic effects in 12 under the second harmonic of Nd:YAGlaser irradiation have been reported by Beterov and Fateyev (1982, 1983) and they were attributed to enhanced electron attachment to vibrationally excited I~'. No attachment cross-section data were given. HF. Allan and Wong (1981) studied the temperature dependence of dissociative electron attachment to H F using an electron-impact mass spectrometer. They found that the cross section for F - from H F shows an order-of-magnitude increase with each increase of vibrational quantum (v = 0, 1, and 2). In Table XVI is shown the vibrational enhancement in the threshold cross section of dissociative electron attachment to H F as measured by Allan and Wong (1981). The experimental uncertainty of these cross-section ratios is _+30% for the v = 1 and _+50% for the v = 2 ratio (Allan and Wong, 1981). Interestingly, Rossi et al. (1985) showed that the electron attachment properties of a gas mixture of helium containing trifluoroethylene (CzHF3) can be altered from nonelectron attaching to strongly electron attaching by irradiation with a low-energy laser pulse at 193 nm. In effect the CzHF 3 molecule is photodissociated, producing vibrationally excited HF* (and other) fragments that strongly attach slow electrons. The measurements of Rossi et al. on the attaching gas density-normalized electron attachment coefficient q / N for CzHF 3 mixtures with He with and without laser irradiation showed that under laser irradiation q / N is as much as a factor
TABLE XVI VIBRATIONAL ENHANCEMENT IN THE THRESHOLD CROSS SECTION OF DISSOCIATIVE ELECTRON ATTACHMENT TO HC1, DC1, AND H F
(data of Allan and Wong, 1981) O-v>o/o-v=o
HC1
DC1
HF
O-v=a/o-v=o O'v=2/o-v=O
38 880
32 580
21 300
EXCITED
239
ATOMS AND MOLECULES
of 103 larger than for the unexcited sample. Actually this enhancement is more like a factor of 105 since the attachment coefficient q was normalized to the unexcited attaching-gas number density, which was estimated in these experiments to be about 100 times the excited-gas number density. HCI; DCI. An electron-impact mass spectrometric study by Allan and Wong (1981) of the temperature dependence of dissociative electron attachment to HC1 and DC1 in the energy range 0 to 4 eV has shown that the cross section for the production of C1- from HC1 and DC1 increases by an order-of-magnitude with each increase of vibrational quantum (v = 0, 1, and 2). The threshold cross section for C1- from HCI*(v = 2) at 0.1 eV reaches a value of (7.8 _+ 4.7) x 10 -15 c m 2. In Fig. 43a are shown the measured energy dependencies of C1- produced by electron impact on HC1 at four values of T. The four spectra have approximately the same vertical scales. As T is increased, the spectra show additional C1- peaks at lower energies, which are due to rotationally and vibrationally excited HC1. Allan and Wong determined the cross sections for electron attachment to different vibrational states relative to the ground state by comparing the correspond-
a) HCI
1 l~ ~
HCI
10"15
104
l~:~, ~=o~ o
(c)
~" 103 D
i=2, d=o)
102 /i 0
I
10"17
v=l
10.18
0.0 0.5 1.0 1.5 2.0 Electron energy (eV)
,
0.0
0.5
9 (v=l,
a=-o)
101
,
,
1.0
Electron energy (eV)
100 0.0
, d=5 . . .
.
I
0.5
. . . .
i
,
1.0
Internal ienergy (eV)
FIG. 43. Effect of T on the dissociative electron attachment to HC1 and DC1. (a) Measured energy dependence of the formation of C1- by electron impact on HC1 at 300, 880, 1000, and 1180 K (data of Allan and Wong, 1981). (b) Calculated cross sections for dissociative electron attachment to HC1 in the v = 0, v = 1, v = 2, and v = 3 levels, averaged over a thermal distribution of rotational states (from Bardsley and Wadehra, 1983). (c) Ratio of ~da(V, J)/ CYda(V = 0, J = 0) for HC1 and DC1 as a function of the internal energy of the molecule. The error bars are the experimental data of Allan and Wong (1981). The rest of the data are the calculated results of Teillet-Billy and Gauyacq (1984) (25 meV above the thermodynamical threshold) for: HC1 (v, J -- 0 ) levels (Q), DC1 (v, J - - 0 ) levels (O), and HC1 (v = 0, J) levels (ll) (from Teillet-Billy and Gauyacq, 1984).
240
Loucas G. Christophorou and James K. Olthoff
ing signal intensities with the thermal population of these states. Table XVI gives their results for the relative cross sections for the v = 1 and v = 2 vibrational levels of HC1 and DC1. The experimental errors for the ratios given in Table XVI are + 30% for the v = 1 and + 50% for the v = 2 states. From a knowledge of the peak cross section for dissociative electron attachment to the ground state ( v - 0) molecule (Christophorou, et al., 1968; Azria et al., 1974; Sze et al., 1982; Orient and Srivastava, 1985), absolute cross sections for dissociative electron attachment to HC1 and DC1 molecules excited in the v = 1 and v = 2 states can be obtained. Cross sections for dissociative electron attachment to vibrationally and rotationally excited HC1 and DC1 molecules have been calculated by a number of workers, including Bardsley and Wadehra (1983), Teillet-Billy and Gauyacq (1984), and Fabrikant (1993). In Fig. 43b the early resonantscattering theory results of Bardsley and Wadehra (1983) are shown on the cross section for dissociative electron attachment to the HC1 in the v = 0, 1,2, and 3 vibrational levels averaged over a thermal distribution of rotational states. The effect of rotational excitation on ~da(V,j) can be seen from the data in Fig. 43c taken from an article by Teillet-Billy and Gauyacq (1984). The experimental values (Allan and Wong, 1981) of the ratio O'da(/) , j ) / O ' d a ( V - - 0,j = 0) are plotted as a function of the internal energy of the HC1, DC1 molecules and compare well with the prediction of the calculation by Teillet-Billy and Gauyacq (1984) as to the variation of this ratio with increasing rotational energy of the target. The quantity of significance here and in the dissociative electron attachment processes in many other systems is the total internal energy content of the target molecule Finally, Rossi et al. (1985) showed that the electron attachment properties of a gas mixture of helium containing vinyl chloride (C2H3C1) can be altered from nonelectron attaching to strongly electron attaching by irradiation with a laser pulse at 193 nm. According to Rossi et al., the molecule is photodissociated, which produces vibrationally excited HCI* (and other) fragments that strongly attach slow electrons. Rossi et al. found that under laser irradiation the vl/N of CzH3C1/He mixtures is as much as a factor of 103 larger than for the unexcited (without laser irradiation) sample. Moreover, as the ratio of excited to unexcited C2H3C1 molecules in this experiment was estimated to be 10 -2, this enhancement, as in the case of CzHF3, is more like a factor of 105. b. Triatomic Molecules. N20. Chaney and Christophorou (1969) found the total electron attachment rate constant ka,t(E/N) for N20 measured in Ar buffer gas to increase with increasing temperature (323 to 473 K) for E / N < 0.5 x 10-17V cm 2 ((~) ~< 1.5 eV) and to be T independent for
241
EXCITED ATOMS AND MOLECULES 10 3
,
c 0
I
’
I
’
I
’
I
’
-
O’/N20
10 2
-
.--..,
(9
09
101
0
0
(9
>
10 0
,....--.
d)
r
10-1
10 -2
I
0
1
l
I
2
i
I
3
l
4
Electron energy (eV) FIc. 44. Dependence of the relative cross section for the production of O - from N 2 0 on gas temperature. All but the highest temperature curve have been normalized at 2.25 eV and coincide at higher energies. The 1040-K curve was normalized also to coincide with the rest of the data at higher energies (from Chantry, 1969).
E/N >~ 1 x 10-17V cm 2. These findings are consistent with the electron beam data of Chantry (1969) in the T range 160 to 1040K that show (Fig. 44) that the relative cross section for the production of O - from N 2 0 is very sensitive to T close to thermal and epithermal energies and insensitive to T for electron energies in excess of ~ 2.3 eV. It appears that two states of N 2 0 - are involved in the production of O - from N 2 0 below ~4eV. The strongly temperature sensitive portion of the cross section involves the lowest (ground) state of N 2 0 - and is due to excitation of the bending mode of vibration (Chantry, 1969). The strong temperature dependence of the production of O - via this state is thought to arise from the dependence on bond angle of the energy separation of the electronic ground states of N 2 0 and N 2 0 - since the potential energy of the lowest
Loucas G. Christophorou and James K. Olthoff
242
state depends significantly on bond angle (Chaney and Christophorou, 1969; Chantry, 1969; Ferguson et al., 1967). The temperatureindependent peak at ~ 2 . 3 e V is ascribed (Chantry, 1969) to dissociative electron attachment via the second N 2 0 - state connected to the electronic ground state N 2 4- O - . N20-
SO s. Spyrou et al. (1986) measured the total dissociative electron attachment rate constant kaa,t(E/N) for SO2 as a function of E / N in Ar buffer gas over a range of values corresponding to mean electron energies from 1.9 to 4.8 eV. Their data for T = 300 to 700 K are shown in Fig. 45a. The cross sections unfolded from these data using the electron energy distributions in Ar are shown in Fig. 45b. It is interesting to observe the rather unique temperature dependence of kda,t((~;)) and ( 3 " d a , t ( l ~ ) for this gas. Although the peak value of O ' d a , t ( t ~ ) a t ~4.5 eV increases by more than a factor of 2 when T is increased from 300 to 700 K, the peak position and the onset of (3"da,t(l~) shift only slightly to lower energy. The small shift of the onset and the peak contrasts the larger shifts observed for other molecules (e.g., CC1F 3, C2F6) for which the negative-ion state involved in the electron attachment process is purely repulsive. It has been attributed (Spyrou et al., 1986) to a "vertical
2.5
"7,
if/
_'
I''
f I''
(a)
; 9
/
2.0
10
' I '_
9
..e"
600
K
~.
-
!
:
'
'
I
'
I
'
8
o 300 K
E
o
6
o ~
300 K
-
~i-o ..o .~." !i/, , ..
I
500 K
..ei~400K~
.." o" _." .o'" /~_.':: ".w...-'e'"o . . e ' ~
1.0
'
K
O~ ..o"
.e ? ..'"
-
T'--
-
." "9
- "
1.5
o
"O
' 700
:: e'" .e.~ - ...o" : :.
E o~
'~' .e.
i I ~
o
v 700 K
v
-cff
.."
4
0:.:/ " :'6/.e
0.5 0.0
.i.e /:i::~!.. . . . .
802 I
,
,
,
I
,
,
,
J
,
2 3 4 5 Mean electron energy (eV)
0
3
4
5
6
7
8
Electron energy (eV)
FIG. 45. (a) Total dissociative electron attachment rate constants as a function of the mean electron energy kda,t((l~)) for SO 2 measured in Ar buffer gas at temperatures of 300, 400, 500, 600, and 700 K. (b) Total dissociative electron attachment cross sections as a function of the electron energy ~aa,t(~) for SO 2 unfolded from the data in Fig. 45a (from Spyrou et al., 1986).
243
EXCITED ATOMS AND MOLECULES
onset" dissociative electron attachment process, that is, to electron attachment via a negative ion state that is attractive in part of the Franck-Condon region. c. Halogenated Compounds. CH3CI. In a swarm study of mixtures of CH3C1 with N 2 , Datskos et al. (1990) found that the weak electron attachment exhibited by CH3C1 below ~1 eV at room temperature increases very strongly as the gas temperature is increased above ambient. Their measurements are reproduced in Fig. 46a and show that the kda,t((e>) for CH3C1 increases by 3 to 4 orders of magnitude when the T is raised from 300 to 750 K. In Fig. 46b are shown the cross sections unfolded (Datskos et al., 1990) from these measurements. Two T-dependent peaks are seen, one at near-zero electron energy and another at ~0.8 eV. Results of a subsequent electron-beam study by Pearl and Burrow (1993) were interpreted as having provided evidence that the peak in the Datskos et al. data at ~ 0.8 eV is due to electron attachment to HC1 produced by decomposition of the CH3C1 molecules on the walls of the hot chamber, in contrast with the zero-energy peak that "appears to arise from the parent molecule." A further
100 ~fl
100 10-1 E o 10-2
_~,,..__. . . . . . .
..-. 10 E o
500 K
1.0
t
(c) CH3CI
0.8
o,i
600 K
e3
(b) CH3CI I .
.--.-..
oE 0.6
o
~
10-a
----"~-o
4O0 K
-o
10.4 10-5 0.0
,~ 0.4 0.1
"~
0.2
'~300 K
!a! CH3CI , 0.5
,
1.0
Mean electron energy (eV)
0.01
0.0
0.5
1.0
1.5
Electron energy (eV)
0.0
0.0
0.2
0.4
Electron energy (eV)
FIG. 46. (a) Total dissociative electron attachment rate constants as a function of the mean electron energy kda,t(<~)) for CH3C1 measured in N 2 buffer gas at temperatures of 300, 400, 500, 600, 700 and 750 K. The solid and broken lines indicate data taken by two different swarm methods. The data at 300 K (A, total pressure = 20 kPa; V, total pressure = 6.66 kPa) are uncertain due to the very low values of the rate constant (from Daskos et al., 1990). (b) Total dissociative electron attachment cross sections as a function of the electron energy CYda,t(~) for 400, 500, 600, and 750 K for CH3C1, unfolded from the respective kda.t(<~)) data in Fig. 46a (from Daskos et al., 1990). (c) Dissociative electron attachment cross section ~aa(e) as a function of electron energy at 600 K. The data points are measurements by Pearl et al. (1995) normalized at the peak to the solid curve, which is the result of a calculation at this temperature (from Pearl et al., 1995).
Loucas G. Chr&tophorou and James K. Olthoff
244
electron-beam study of the T dependence of dissociative electron attachment to CH3C1 by Pearl et al. (1995) provided cross sections that are about a factor of 10 lower than those indicated by the swarm study of Datskos et al. Figure 46c shows the relative cross-section data of Pearl et al. for 600 K, which were normalized to the their mixed ab initio semiempirical calculation result for this temperature (see also Fabrikant, 1994; Fabrikant et al., 1994). Clearly, while the strong effect of T on the dissociative electron attachment to the CH3C1 molecule is shown by all these studies, there is still a substantial difference in the absolute values of the reported cross sections. CH3Br. Datskos et al. (1992a) measured the temperature dependence (300 to 700 K) of the dissociative electron attachment to CH3Br in a swarm experiment using N 2 as the buffer gas. Their measurements covered the E / N range 0.062 x 10-17 V c m 2 to 6.21 x 10-17 V c m 2, which for T = 300 K corresponds to a mean electron energy range of --,0.046 to 0.872eV (see Appendix A). Figure 47a shows the large increases in the magnitude of kda,t() with increasing gas temperature, and Fig. 47b shows the Crda,t(e) deduced by an unfolding procedure from the rate constants in Fig. 47a. Such large variations of kda,t(<e)) and Crda,t(e) with T are consistent with those observed for CH3C1 and other halocarbons that attach slow electrons
0K
,~"
4
CH3Br
101
102
(b) _
(a) ~'~
E
E
CH3Br
'~ 101 E
t__i/700K
3
i/y
600K
o
~, 1o0
o
N
..
100 o
10-1 0.0
0.5
1.0
Mean electron energy (eV)
,
lk g ,oo
0N2 0.0
0.5
~ 10-1
(c) CHaBr
1.0
Electron energy (eV)
10-2 f 2OO
,,1~,
400
, I J l
600
9
800
Gas temperature (K)
FIG. 47. (a) Total dissociative electron attachment rate constants as a function of the mean electron energy kda,t(<e>) for CH3Br measured in N 2 buffer gas at temperatures of 300, 400, 500, 600, and 700 K (from Daskos et al., 1992a). (b) Total dissociative electron attachment cross sections as a function of the electron energy CYda,t(e)for CH3Br unfolded from the data in Fig. 47a (from Daskos et al., 1992a). (c) Variation of (kda,t)th with T. 0, Alge et al. (1984); O, Petrovi6 and Crompton (1987);/~, Datskos et al. (1992a); V, Burns et al. (1996).
245
EXCITED ATOMS AND MOLECULES
weakly at room temperature. In Table XVII are listed the thermal values (kda,t)t h of the total electron attachment rate constant as a function of temperature along with values of this quantity as a function of T measured for this molecule by other investigators (Alge et al., 1984; Burns et al., 1996; Petrovi6 and Crompton, 1987). These data are plotted in Fig. 47c. CH2CI 2. Figure 48a shows the recent measurements of Pinnaduwage et al. (1999) on the temperature dependence of the total dissociative electron attachment rate constant kda,t((e)) for CHzC12 and Fig. 48b gives the variation of the thermal value (kda,t)t h of the total dissociative electron attachment with gas temperature (Table XVII). The value at 300 K is the average of the four values listed by Christophorou (1996).
50
’
E o "2 o
’
’
’
I
’
’
’
I
’
’
’
(a) CH2Cl 2
500 K
30 - 9
20 "o
I
ari•
40
03
’
~
400 K
9C
%
10 K
~~~ ~ 0~ 0
, ~",,
,,,,,
1
,
,
e
2
o ~,
3
Mean electron energy (eV) 103 03
E O
10 2
o
101
’
I
’
I
(b) CH2Cl 2 0 I
J
I,-
v
’
r
100 O v
10-1
,
200
I
300
~
I
400
I
500
,
I
600
,
I
700
,
800
Temperature (K) FIG. 48. (a) Total dissociative electron attachment rate constant as a function of the mean electron energy kda,t((~;)) for CHzC12 measured in N 2 (solid symbols) and Ar (open symbols) buffer gases at temperatures of 300, 400, and 500 K (from Pinnaduwage et al., 1999). (b) (kda,t)th as a function of temperature: 0, Burns et al. (1996); C), Christophorou (1996).
Loucas
246
G. C h r i s t o p h o r o u a n d J a m e s K. O l t h o f f
T A B L E XVII VALUES OF (kda,t)th AS A FUNCTION OF T FOR POLYATOMIC MOLECULESa Temperature (K)
(kda,t)th(Cm 3 S- 1)
Reference/Method/Comment
300 452 585 293 445.3 498.8 300 400 500 600 700 293 615 777
6.0 x 10-12 2.3 x 10- lo 2.5 x 10 -9 (6.78 +0.2) x 10-12 (1.83 ___0.07) x 10- lo (4.40+0.18) • 10 -1~ 1.08 • 10-11 1.68 x 10-1o 7.13 • 10- lo 1.64 x 10- 9 3.28 • 10- 9 6 • 10- ~2 8.3 x 10-1o 9.5 • 10 -9
Alge et al. (1984) F A L P b dissociative a t t a c h m e n t
CH2C12
467 579 777
1.8 • 10- lo 6.4 • 10-1 o 2.1 • 10 -9
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
CHC13
293 467 579 777
4.7 6.2 1.7 2.3
x x x x
10 . 9 10 . 9 10 -8 10 -8
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
CF3C1
293 467 579 777
4.2 1.4 2.4 9.5
x x x x
10-13 10 -11 10-1 o 10-lO
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
CFzC12
298 400 500 205 300 455 590 293 467 579 777 74 e 82 123 159 168
1.66 • 10 -9 6.0 • 10 -9 < 1 . 4 • 10 -8 < 1.0 • 10- 9 3.2 • 10 -9 1.6 • 10 -8 5.3 x 10-8 1.9 x 10 . 9 1.4 x 10 -8 2.4 x 10 -8 4.2 x 10 -8 1.25 x 10 -xle 2.33 x 10 -11 2.34 x 10 -11 7.71 x 10 -11 2.44 x 10 -1~
293 467 579 777 294
2.4 • 10-7 1.8 • 10 -7 2.1 • 10 -7 1.9 • 10- 7 2.38 • 10- v
Molecule CH3Br
CFC13
Petrovi6 and C r o m p t o n (1987) Swarm Datskos et al. (1992a) Swarm
Burns et al. (1996) FAC/ECR a
W a n g et al. (1998) S w a r m / dissociative a t t a c h m e n t Smith and Spanel (1994), Smith et al. (1984) F A L P
Burns et al. (1996) F A / E C R
LeGarrec et al. (1997a) C R E S U f
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
Orient et al. (1989) Swarm
EXCITED
ATOMS
AND
MOLECULES
247
T A B L E XVII (Continued) Temperature (K)
(kda,t)th(Cm3 S -1 )
404 496
2.16 x 10 . 7 2.01 x 10- 7
293 467 579 777 294 400 500
3.6 x 10- 7 2.1 x 10 -7 1.4 x 10-7 1.2 x 10- 7 3.79 x 10- 7 2.96 x 1O- 7 2.33 x 10- 7
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
SO2F 2
300 400 500 600 700
8.4 • 10- lo 3.11 x 10 -9 1.09 x 1O- 8 2.08 • 10 - s 3.07 x 10- s
D a t s k o s and C h r i s t o p h o r o u (1989) Swarm/dissociative attachment 0
SF 6
298-418
2.7 x 10 -7
>~ 300 293-523 205 300 455 590 294 500 300 329 362 411 449 498 545 49 85 126 162 174 304
3.1 • 10-v 2.2 x 10- v 3.1 x 10 -7 3.1 x 10-v 4.5 • 10- 7 4.0 • 10- 7 (2.27 +0.09) x 10 -7 (2.20+_0.09) • 10 .7 2.3 x 10- v 2.6 x 10- 7 2.8 x 10- 7 3.1 x 10 -7 2.8 x 10- 7 2.7 x 10- 7 2.2 • 10 -7 1.41 x 10 -Te 1.44 x 10-7 1.42 x 10- 7 1.65 x 10 .7 1.73 x 10 -7 2.77 x 10- 7
( C o m p t o n et al., 1966; C h r i s t o p h o r o u et al., 1971) Swarm/dissociative and nondissociative a t t a c h m e n t M a h a n and Y o u n g (1966) M W h Fehsenfeld (1970) F A Smith et al. (1984) F A L P
Molecule
CC14
Reference/Method/Comment
Orient et al. (1989) Swarm
Petrovi6 and C r o m p t o n (1985) Swarm Miller et al. (1994a) F A L P
Le G a r r e c et al. (1997a) CRESU f
a F o r r o o m t e m p e r a t u r e values of (kda,t)t h for some of these molecules see C h r i s t o p h o r o u et al. (1984), Burns et al. (1996), and C h r i s t o p h o r o u (1996). b Flowing a f t e r g l o w / L a n g m u i r probe technique. c Flowing afterglow method. d Electron cyclotron resonance technique. e Values taken off the graph given in Le G a r r e c et al. (1997a). s Cin6tique de R6action en E c o u l e m e n t Supersonique Uniforme. 0 P r e d o m i n a n t l y dissociative attachment; small nondissociative a t t a c h m e n t at near-zero electron energy at the lowest T. h M i c r o w a v e method.
Loucas G. Christophorou and James K. Olthoff
248
CHCI 3. Rough estimates of the cross section for the production of C1- by electron attachment t o C H C 1 3 for temperatures ranging from 310 to 430 K were reported by Matejcik et al. (1997). In this temperature range the cross section increases with increasing T over the energy range (~<2eV) they investigated. This is in accord with swarm-unfolded total electron attachment cross sections for 300, 400, and 600 K reported for this molecule (Shimamori and Sunagawa, 1997). In Table XVII are listed the thermal values (kda,t)t h of the total dissociative electron attachment rate constant as a function of gas temperature (Burns et al., 1996). C F 3 C I ; CF2C12; CFCI3; C C I 4. The total dissociative electron attachment rate constant kda,t(<8)) for C F 3 C 1 has been measured in an electron swarm study as a function of the mean electron energy from 0.41 to 4.81 eV using both argon and nitrogen as buffer gases (Spyrou and Christophorou, 1985a). These data were taken over the T range from 300 to 750 K and are shown in Fig. 49a. The total dissociative electron attachment cross sections O'da,t(~ ) unfolded using the data in Fig. 49a are shown in Fig. 49b. Table XVII lists
14|",~,
,,
,,,,,,,,,|
i,i60OK-:
12 ~L O O~ K [.
Eo
,.,~-
t
8
1
";.
.:
/ :~"i ,.",,,, : i:!lbO
2pOo o~
I
"'-,," .. ..... ..,.., j
, U ~ ; 4 o o K,,’ . I-
x J
"
... . . . ."-.._1 1 .... . .""9. ....... . .... .......... :",,.1
llo.o.
CF3CI
-]
1
0 1 2 3 4 5 Mean electron energy (eV)
,
,
,
,
'7, o ~
i
2
, /
(b) 1
I-iii L/ ~176
4
:i : 4 4 " .
1/:~: I It` I!S']
o
,
c,c 1
l il
oo
-4
,'"
,
4 I [i/7oo K
(a)_]j
+u .... .:.o .....,..-.. ....-.. "-o o : :i~r.v,- 9
I-;,Z,,
6
|
0
~'..
,I;~k~;t
,~
~"
/
|
2 4 6 8 Electron energy (eV)
FIG. 49. (a) Total dissociative electron attachment rate constants as a function of the mean electron energy kda,t(<13>)for CF3C1 measured in N2(O ) and Ar(O) buffer gases at temperatures of 300, 400, 500, 550, 600, and 700 K (from Spyrou and Christophorou, 1985a). (b) Total dissociative electron attachment cross sections as a function of the electron energy CYda,t(l~) for CF3C1 unfolded from the data in Fig. 49a for Ar buffer gas (from Spyrou and Christophorou, 1985a).
249
EXCITED ATOMS AND MOLECULES
the thermal values (kda,t)t h of the total electron attachment rate constant as a function of temperature (Burns et al., 1996). A recent electron swarm study of the temperature dependence of the total dissociative electron attachment rate constant kda,t(<e)) for CF2C12 has been made by Wang et al. (1998). They used N 2 as the buffer gas and changed T from 298 to 500 K. Their measurements of kda,t(
100
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oo
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L e G a r r e c (1997)
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Temperature (K)
800
FIG. 50. (a) Total dissociative electron a t t a c h m e n t rate constants as a function of the mean electron energy kda,t(<E)) for CF2C12 measured in N 2 buffer at temperatures of 298, 400, and 500 K (from W a n g et al., 1998). (b) Variation of (kda,t)th with T. O, W a n g et al. (1998); A, Smith et al. (1984); E], Burns et al. (1996); C), Le G a r r e c et al. (1997a).
Loucas G. Christophorou and James K. Olthoff
250
function of T have been made for CC14 and show a slight decrease of (kda,t)th with T between 293 and ~ 5 0 0 K (Table XVII). A somewhat similar behavior is exhibited by the yield of C1- from CFC13 and by the values of (kda,t)th(T) for CFC13 (Orient et al., 1989; Burns et al., 1996; Table XVII). C2H3CI; C2HsCI; 1,I-C2H4CI 2. Chantry and Chen (1989) measured the
T-dependence of the predominant ion C1- produced in the dissociative attachment of slow electrons to C2H3C1 (vinyl chloride). Their data are shown in Fig. 51. The higher temperature data were put on an absolute scale by normalization to the room temperature data. At 290 K, the C1- ion has an onset at 0.85 eV and a peak at 1.35 eV with a peak cross-section value of 3.2 • 10-17 cm 2. At 850 K the cross section at the peak is a factor of 2.6 larger and lower in energy by 0.33 eV.
I
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Electron e n e r g y (eV) FIG. 51. Cross section O'da,C1- (1~) for dissociative electron attachment to C2H3C1 producing C1- as a function of electron energy at 290, 510, 730, and 850 K (data of Chantry and Chen, 1989).
251
EXCITED ATOMS AND MOLECULES
The variation of the total electron attachment rate constant of C2HsC1 with T has been measured by Datskos et al. (1991) in a swarm experiment using N 2 as the buffer gas at 400, 500, 600, and 700 K. These data are shown in Fig. 52a. The cross sections unfolded from the data in Fig. 52a are shown in Fig. 52b. The peak value of the cross section increases in magnitude and shifts to lower energy with increasing T. This latter behavior seems to rule out any effect of thermal decomposition products on the measurements, as was suggested (Pearl and Burrow, 1993) for CH3C1 for which the energy position of the peak at 0.8eV remains unchanged with increasing T. Fabrikant et al. (1994b) calculated cross sections for dissociative electron attachment to this molecule as a function of T. Consistent with the experimental data in Fig. 52b, these calculations show a broad peak at about 1.5 eV that shifts to lower energy with increasing T, and the appearance of another peak at thermal energies as T increases above ~ 500 K. The absolute magnitudes of the calculated cross sections are not incompatible with those in Fig. 52b, but significant differences exist between the calculated and the experimentally derived cross sections as a functionof T.
25
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o 0
1
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Electron energy (eV)
FIG. 52. (a) Total dissociative electron attachment rate constants as a function of the mean electron energy kaa,t((e)) for C2H5C1 measured in N 2 buffer gas at temperatures of 400, 500, 600, and 700 K (data of Datskos et al., 1991). (b) Total dissociative electron attachment cross sections as a function of the electron energy (Yaa,t(0 for C2H5C1 unfolded from the data in Fig. 52a (data of Datskos et al., 1991).
Loucas G. Chr&tophorou and James K. Olthoff
252
An increase of kda,t((~3>) with T has also been observed (McCorkle et al., 1982) for 1,1-C2H4C12 when studied in a swarm experiment at temperatures of 333, 373, and 473 K. CaF 8. The total dissociative electron attachment rate constant kda,t((~;)) for CEF 6 has been measured by Spyrou and Christophorou (1985a) using an electron swarm method and argon as the buffer gas. Their measurements covered the E / N range between 0.155 x 1 0 - 1 7 V c m 2 and 4.35 x 10-17V cm 2, which corresponds to a mean electron energy range of 0.976 to 4.81 eV and was conducted over the T range of 300 to 750 K. Figure 53a shows their data o n k d a , t ( ( S ) ) and Fig. 53b shows the respective unfolded total dissociative electron attachment cross sections O'da,t(E ). The single peak in the cross section is due to F - and CF3 production. It shifts from 3.9 eV at 300K to ~ 3.3 eV at 750 K and the corresponding threshold shifts from 2.3 to 1.5 eV. As for other similar cases, the observed changes in the rate constant and cross section with increasing T were attributed (Spyrou and Christophorou, 1985a) to the increase with T of the total internal (~vibrational) energy of the molecule. C2F6;
8
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FIG. 53. (a) Total dissociative electron attachment rate constant as a function of the mean electron energy kda,t((~;)) for C2F 6 measured in Ar buffer gas at temperatures of 300, 500, 650, and 750K (data of Spyrou and Christophorou, 1985a). (b) Total dissociative electron attachment cross section as a function of the electron energy ~da,t(e) for C2F 6 unfolded from the data in Fig. 53a (data of Spyrou and Christophorou, 1985a).
253
E X C I T E D A T O M S AND M O L E C U L E S
T h e T d e p e n d e n c e of l o w - e n e r g y e l e c t r o n a t t a c h m e n t p r o c e s s e s in C 3 F 8 is r a t h e r c o m p l i c a t e d , b u t u n d e r s t o o d . T h e s w a r m s t u d y of S p y r o u a n d C h r i s t o p h o r o u (1985b) s h o w e d t h a t the t o t a l a t t a c h m e n t r a t e c o n s t a n t ka,t(<~)) for this m o l e c u l e first d e c r e a s e s a n d t h e n i n c r e a s e s with i n c r e a s i n g T a b o v e a m b i e n t (Fig. 5 4 a ) . This is b e c a u s e l o w - e n e r g y e l e c t r o n a t t a c h m e n t to C3F8 u n d e r s w a r m c o n d i t i o n s leads to the f o r m a t i o n of b o t h p a r e n t a n d f r a g m e n t n e g a t i v e ions. T h e rate c o n s t a n t for the f o r m e r p r o c e s s d e c r e a s e s with i n c r e a s i n g T d u e to i n c r e a s e d a u t o d e t a c h m e n t f r o m the t r a n s i e n t a n i o n a n d the r a t e c o n s t a n t for the l a t t e r p r o c e s s increases with T d u e to i n c r e a s e d
~.
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.... .....
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8
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Electron energy (eV)
FIG. 54. (a) Total electron attachment rate constant as a function of the mean electron energy ka,t(<e)) for C3F 8 measured in Ar buffer gas at temperatures between 300 and 750 K (data of Spyrou and Christophorou, 1985b). (b) Total electron attachment cross section as a function of the electron energy aa,t(~) for C3F s unfolded by Spyrou and Christophorou (1985b) from their ka,t(<e)) data in Fig. 54a for 300, 425, and 450 K. (c) As in Fig. 54b but for T equal to 500, 600, 675, and 750 K. The 300 K data shown in the figure are the dissociative attachment part of ~a,t(E) at this temperature (data of Spyrou and Christophorou, 1985b). (d) Cross-section for the production of F - by electron impact on C3F 8 at gas temperatures of 300, 370, 510, and 730 K as measured in an electron-beam experiment (data of Chantry and Chen, 1989). For comparison the O'da,t(~) for T = 750 K from Fig. 54c is also shown.
254
Loucas G. Christophorou and James K. Olthoff
autodissociation of the transient anion. In light of the data in Fig. 54a, the total electron attachment cross section (Ya,t(~) of the C3F 8 molecule is expected first to decrease and then to increase with increasing T above 300 K as is indeed the case. Figure 54b shows the O'a,t(~) for the T range between 300 and 450 K, in which the cross section has a contribution from both parent and fragment anions and in Fig. 58c the cross sections for only the dissociative electron attachment part of the cross section are shown. Actually, for the data in Fig. 54c only those for 300 K are the dissociative attachment part of the total electron attachment cross section at this temperature. The data for temperatures > 500 K are entirely dissociative attachment cross sections because at these temperatures there is no contribution to the cross section from the production of parent negative ions (Spyrou and Christophorou, 1985b). The threshold of the dissociative attachment cross section shifts from 1.8 eV at 300K to 1.0eV at 750K. Consistent with the swarm data in Fig. 54c are the electron-beam measurements made by Chantry and Chen (1989) on the production of F - by electron impact on C3F 8 as a function of T shown in Fig. 54d. The fragment anion F - is by far the most abundant dissociate attachment negative ion for this molecule (see Christophorou and Olthoff, 1998b). n-C4F10. The dependence of the total electron attachment rate constant ka,t((~)) on T for this molecule has been investigated (Datskos and Christophorou, 1987) in the mean electron energy range 0.634 to 4.81 eV over temperatures ranging from 300 to 750 K. As for the case of CaF 8, both dissociative and nondissociative electron attachment processes take place simultaneously over a given energy range and thus the overall variation of ka,t((~)) with T depends on the value of (e). The ka,t((g)) first decreases slowly with T between 300 and 400 K, then decreases precipitously between 400 and --~500 K, and subsequently increases for T > 500 K. This is seen in the data shown in Fig. 55a,b where the measurements of Datskos and Christophorou (1987) for ka,t((e), T) and kda,t((g), T), respectively, are plotted. The kda,t((~), T) in Fig. 55b for 300, 400, and 500 K are for only the (total) dissociative electron attachment part of the ka,t((g), T) and the data in Fig. 55b for T > 500 K are the measured values of ka,t((~), T), because at these temperatures kda,t((e), T) = ka,t((~), T). It should be noted that the data shown in Fig. 55a, b are for "infinite" buffer-gas pressure and thus all parent anions must have been stabilized. It should also be noted that in this study (see Section VI.A.2) it is difficult to quantify the effect on the measurements of thermally induced detachment from the stabilized negative ions. For this reason, we present in Fig. 55c only the cross section for dissociative attachment at various temperatures as deduced by Datskos and Christophorou (1987) from the data in Fig. 55b. The value of the
255
EXCITED ATOMS AND MOLECULES 30 In-C4F13ooK (a)
;~
7 350K
20
4 10/
12 ~
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(b) l
8
2.5
~ ~
2
_~X~.o.OOoo .... o. ~_~'~1
0.5
0
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0
1
2
3
4
5
Mean electron energy (eV)
0
1
=’ 2
’’ 3
’’ 4
[ 5
Mean electron energy (eV)
(C)
]["..I n'C4Flo / / ~ F 600K
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.,,~, ,'Jl,,,
0
2
,~..~.~
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Electron energy (eV)
FIG. 55. (a) Total electron attachment rate constant as a function of the mean electron energy ka,t((~;)) for n-C4Flo measured in Ar buffer gas at 300, 350, 400, 450, and 500 K (data of Datskos and Christophorou, 1987). The data shown are for "infinite" buffer-gas pressure. (b) Total dissociative electron attachment component kaa,t((E), T) of the total ka,t((E), T) for 300, 400, and 500 K. For 600, 675, and 750 K the rate constant is entirely due to dissociative electron attachment and kaa,t((E), T ) = ka,t((E), T) (data of Datskos and Christophorou, 1987). (c) Total dissociative electron attachment cross section CYaa,t(e)as a function of electron energy for n-C4Fx0 at T between 300 and 750 K (data of Datskos and Christophorou, 1987).
electron energy at which the dissociative electron attachment cross-section peaks shifts from 2.85 eV at T = 300 K to 2.20eV at T = 750 K and the peak cross-section value increases from 6.0 x 10 - 1 7 c m 2 at 3 0 0 K to 26.0 x 10 - 17 cm2 at 750 K.
d. Other Polyatomic Molecules. S O 2 F 2. Low-energy electrons attach to the SO2F2 molecule both dissociatively and nondissociatively (Datskos and Christophorou, 1989; Sauers et al., 1993). A weak parent anion is formed at near-zero energy and three fragment anions ( F - , F2, S O E F - ) a r e produced at somewhat higher energies (Sauers et al., 1993). The total electron attachment rate constant ka,t((~;)) for SOEF 2 has been measured (Datskos and Christophorou, 1989) in a buffer gas of N 2 as a function of the mean electron energy from 0.046 to 0.911 eV for T between 300 and 700 K. These data are shown in Fig. 56a and the total electron attachment cross sections CYa,t(~) unfolded from these are shown in Fig. 56b. At 300 K the cross section exhibits a maximum at -~0.22eV, which is due to dissociative electron attachment, and an increase below ~0.1 eV, which is due to the formation of parent negative ions SO2F2 at near-zero energy (Sauers et al., 1993). At T - 400 K, the cross section has only one main peak at ~0.13 eV, which is due only to dissociative electron attachment and reflects the depletion of the
Loucas G. Christophorou and James K. Olthoff
256 ~ )
'
'
30
'
'
-----o----
9
........ - - ~ - -
7+,
---o---
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S02F 2
20
"-"
15
13
10
v
"".,,.,,.,,
0 0.0
'
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7o0
20 15
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~
9
1.0
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0 00
'r-- ~'--m"" ~ ~
01
02
~
03
I.
04
05
Electron energy (eV)
FIG. 56. (a) Total electron attachment rate constant as a function of the mean electron energy ka,t((~3)) for SO2F2 measured in N 2 buffer gas at temperatures of 300, 400, 500, 600, and 700 K. The solid points are extrapolated data to 3/2kT (data of Datskos and Christophorou, 1989). (b) Total electron attachment cross section as a function of the electron energy c&,t(e) for SO2F 2 unfolded from the data in Fig. 56a (data of Datskos and Christophorou, 1989).
parent anions and the prevalence of the fragment negative ions as T is increased. The main peak of the cross section shifts to lower energies with increasing T such that at 700 K the peak is located at ~0.03 eV. The value O'da,t(~max) of the total cross section at the peak energy 8max increases by a factor of ,~ 32 as T is increased from 300 to 700 K. This increase results mainly from an increase with T of the internal vibrational energy of the molecule. Table XVII lists the thermal values (ka,t)th of the total electron attachment rate constant of SO2F2 as a function of the gas temperature (Datskos and Christophorou, 1989). SF 6. Figure 57 shows the relative cross-section measurements of Chen and Chantry (1979) for the production of SF~ from S F 6 for temperatures from 300 to 8 8 0 K . Two peaks are seen in the energy dependence of the production of SF~, one at -~0.0eV and the other at ~0.38eV. The near-zero energy peak is very sensitive to T, has an activation energy of ~0.2eV, and is due to dissociative electron attachment to "hot" S F 6 molecules, that is, due to the attachment of near-zero-energy electrons to vibrational/rotational states of S F 6 lying at energies 0.2eV above the
257
EXCITED ATOMS AND MOLECULES
1000
I
’
’
"",880 K
’
’
1
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~!..t"~._~._~ 607 K
I|;
c
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il
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0
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i.
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10 rr
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SF=’/SF~ ,, ,,
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-9"
K
---- ~9 .
9
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0.5
1
Electron energy (eV) FIG. 57. Dependence of the production of SF~ by electron impact on SF 6 on electron energy and gas temperature (data of Chen and Chantry, 1979).
ground state, viz. SF] (v,r > 0.2 eV) + e ( ~ 0 e V ) ~ SF~ + F. The 0.38-eV peak is broad, rather independent of T, and results from the capture of ~0.38 eV electrons by unexcited S F 6 molecules reaching the lowest repulsive negative ion state of SF6, that is, due to the reaction S F 6 ( / ) = 0) + e(~0.38 eV) ---, SF;- + F (see, however, Matejcik et al., 1995; Smith et al., 1995). It is interesting to observe that in spite of this large increase in the formation of SF~ with increasing T the total electron attachment cross section for SF 6 at near-zero electron energy is independent of T (Table XVII, Section VI.A.2). This may imply that at ~0.0eV, the formation of SF6 in electron beam experiments where the SF6* is not stabilized by collisions decreases with T. Indeed, such a decrease has been observed (Hickam and Berg, 1958) and it would be consistent with the decrease in the autodetachment lifetime with increasing internal energy of the transient anion (Christophorou, 1978). The data in Fig. 57 can be put on an absolute
258
Loucas G. Christophorou and James K. Olthoff
scale by considering the magnitude of the cross section for the production of SF5 at 0.38 eV at room temperature. A value of ~0.5 x 10 -16 cm 2 can be discerned from the work of Hunter et al. (1989) and Kline et al. (1979). The strong increase of the cross section for the production of SF~- from SF 6 with increasing vibrational excitation energy of the SF 6 molecule has led Chen and Chantry (1979) to anticipate that the zero-energy peak in Fig. 57 could be photoenhanced. They thus used specific lines from a CO2 laser to produce (via n-photon absorption processes, n 1> 1) vibrationally excited SF 6 molecules SF~ and observed the production of SF~- from electron impact on SF~ as a function of electron energy, viz. rt(hv)laser + S F 6 ~ (SF~)lase r
followed by (SF~)laser .qt_ e ~ (SF5)l~se r At- F
Chen and Chantry found that the production of SF~- from electron impact on SF~ is enhanced and that this infrared enhancement of SF~ production is different for the 32S and 34S isotopes. Thus the formation of SF~- was found to be radiation-wavelength dependent. For the 936.856cm -1 CO 2 line the 32SF~- enhancement was optimized and the 34SF~- was unaffected. For the 920.810 cm-1 C O 2 laser line the 34SFs line was optimized and the 32SF~- was unaffected. This high isotope specificity is an illustration of possible isotope separation processes using knowledge of low-energy electron-molecule reactions. It is consistent with the earlier observations of Beterov et al. (1978) and Beterov and Fateyev (1983) of optogalvanic effects when they used a CO2 laser to vibrationally excite SF 6 molecules. Their finding that electron attachment to SF 6 is sensitive to the vibrational excitation energy led them to suggest the use of lasers in laser isotope separation of electronegative molecules. Table XVII lists the thermal values (ka,t)th of the total electron attachment rate constant for SF 6 as a function of gas temperature (Smith et al., 1984; Le Garrec et al., 1997a; Compton et al., 1966; Christophorou et al., 1971; Mahan and Young, 1966; Fehsenfeld, 1970; Petrovi6 and Crompton, 1985; Miller et al., 1994a). Although the data listed in Table XVII show (ka,t)th to be virtually constant for T between about 300 and 600 K, the more recent measurements of Le Garrec et al. (1997a) below room temperature indicate a small increase with increasing T in the low-temperature range they investigated (see Table XVII). In closing this section we refer to a few other studies on the effects of T on electron attachment to polyatomic molecules. First, a measurement has been made by Spence and Schulz (1973) of the "integrated total attachment
EXCITED ATOMS AND MOLECULES
259
cross sections" as a function of T for a number of halogenated compounds. These data are not included in this work because of the difficulty in quantifying the physical meaning of the measured quantity and because of the way in which the defined quantity was normalized. Second, a number of investigators made measurements of only (/r as a function of T for a number of molecules other than those listed in Table XVII. These "thermal" data are listed in Table XVIII. In some cases these data may be uncertain. This is the case, for instance, when the molecule thermally decomposes as T is elevated above ambient, or when both dissociative and nondissociative electron attachment processes occur at thermal energies and the latter are affected by the method of measurement. It should be noted also that only the data of studies dealing with the T dependence of (ka,t)th are listed in Table XVIII. A listing of just room-temperature values is not given. However, for most of the molecules discussed in this work, room-temperature values of (/r can be found in Christophorou et al., 1984; Burns et al., 1996; Christophorou, 1980, 1996). A representative set of data on (ka,t)th from Tables XVII and XVIII are plotted in Fig. 58. For each molecule the various sets of (/r are plotted using the same symbol. For F 2 the data of Sides et al. (1976) were normalized to those of McCorkle et al. (1986) for the convenience of display. For the same reason, the data of Burns et al. (1996) for CHzBr 2 were normalized to those of Alge et al. (1984). While these rate constants are designated as "total," in reality for all but a few cases indicated in the tables, they are due to dissociative attachment processes. For this reason we use the notation (kda,t)t h in Fig. 58. These data show that there is a spread of several orders of magnitude in the room-temperature values of (ka,t)th for exoergic electron attachment reactions. The data also show that there is a wide variation in the effect of T on (/r In general, the smaller the value of (ka,t)th at room temperature, the stronger its T dependence. When the room-temperature value of (ka,t)th is very large, (]r shows little or no dependence on T. 2. Nondissociative Electron A t t a c h m e n t
The understanding of the effect of T on electron attachment processes leading to parent anions requires knowledge of the effect of T on the autodetachment lifetime ~a of the initially formed transient anion AX-*, namely of the reaction AX-* ~ AX(*) + e
(31)
In electron-beam studies an increase in T increases the internal energy of
260
L o u c a s G. C h r i s t o p h o r o u a n d J a m e s K. O l t h o f f T A B L E XVIII VALUES OF (kda,t)th AS A FUNCTION OF T FOR POLYATOMIC MOLECULESa Temperature
Molecule
(K)
(kda,t)th(Cm 3 S- 1)
Reference/Method/Comment
CH3I
205 300 452 585 293 467 579 777 250 e 298 347
8.5 • 1.2 • 1.8 • 1.1 • 1.0• 1.1 • 1.2 • 1.2 • 5.9 x 8.6 x 1.1 x
10 -8 10-7 10 -7 10-7 10 -7 10 -7 10- 7 10- 7 10 -8e 10- 8 10-7
Alge et al. (1984) F A L W / dissociative a t t a c h m e n t
205 300 452 585 293 467 777
8.1 9.3 1.6 2.2 3.5 4.2 4.5
• • • • • • •
10 -8 10-8 10- 7 10- 7 10 -8 10 -8 10-8
Alge et al. (1984) F A L P / dissociative a t t a c h m e n t
CHFC12
293 467 579 777
6.1 1.2 6.6 2.0
• • • •
10 -12 10- lo 10-1 o 10 -9
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
CF3Br I
205 300 452 585 293 615 777 49 g 76 84
5.3 1.6 4.9 7.7 1.2 3.9 1.2 1.3 1.6 1.4
• • • • • • • • • •
10- 9 10 -8 10 -8 10 -8 10 -8 10 -8 10- 7 10 -1~ 10-10 10-10
Alge et al. (1984) F A L P / dissociative a t t a c h m e n t
125 158 172
1.2 • 10 -9 2.0 x 10 -9 2.1 x 10 -9
293 615 777 250 e
2.2 2.4 2.2 1.5
298 347
1.7 • 10- 7 2.0 • 10- 7
CH2Br 2
CF3I
• • • •
10- 7 10-7 10- 7 10-7e
Burns et al. (1996) FAC/ECR d
S h i m a m o r i and N a k a t a n i (1988) Swarm
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t
Burns et al. (1996) F A / E C R
Le Garrec et al. (1997a); Le Garrec et al. (1997b) C R E S U h
Burns et al. (1996) F A / E C R / dissociative a t t a c h m e n t S h i m a m o r i and N a k a t a n i (1988) Swarm
EXCITED
ATOMS
AND
MOLECULES
T A B L E XVIII ( C o n t i n u e d ) Temperature (K)
(kda,t)th(Cm 3 S- 1)
Reference/Method/Comment
CF2Br 2
298 380 475
3.0 x 10- 7 3.7 x 10- 7 4.0 x 10- 7
Smith et al. (1990) F A L P
CFBr 3
298 380 475
4.8 x 10- 9 7.4 x 10- 9 9.6 x 10 -9
Smith et al. (1990) F A L P
CC13Br
300 540
6.2 x 10- 8 1.3 x 10-7
Spanel et al. (1997) F A L P / dissociative a t t a c h m e n t
CH2C1CH2Br
298 380 475
1.0 x 10- 9 3.6 x 10 . 9 9.7 • 10 . 9
Smith et al. (1990) F A L P / dissociative a t t a c h m e n t
CH2BrCH2Br
298 380 475
1.5 x 1 0 - s 3.1 x 10 - s 4.1 x 10 - s
Smith et al. (1990) F A L P / dissociative a t t a c h m e n t
CH2C1CHC12
298 385 470
3.1 x 1 0 - l o 9.5 x 10- lo 5.0 • 10 -9
Smith et al. (1989) F A L P / attachment
CH3CCI 3
298 385 470
1.5 x 10-8 3.9 x 10 -8 9.3 x 10 -8
Smith et al. (1989) F A L P / dissociative a t t a c h m e n t
CF3CC13
298 385 470
2.4 x 10-7 2.4 x 10-7
Smith et al. (1989) F A L P / dissociative a t t a c h m e n t
CF2C1CFC12
298 385 470
1.1 x 10 -8 2.0 x 10 -8 5.5 x 10 -8
Smith et al. (1989) F A L P / dissociative a t t a c h m e n t
CF2BrCF2Br
298 380 475
1.6 x 10- 7 2.5 x 10-7 3.0x 10 -7
Smith et al. (1990) F A L P / dissociative a t t a c h m e n t
C2H5I
250 e
3.1 • 10 -9e
298 347
5.2 X 10- 9 7.2 X 10 . 9
Shimamori and N a k a t a n i (1988) Swarm/dissociative attachment
250 e 298 347
7.8 x 10- 9e 1.2 X 10- 8 1.6 X 10 -8
Shimamori and N a k a t a n i (1988) Swarm/dissociative attachment
Molecule
1-C3H7I
261
262
L o u c a s G. Christophorou a n d J a m e s K. O l t h o f f T A B L E XVIII (Continued) Temperature
Molecule
(K)
(/r
3 S- 1)
2-C3H7I
250 e 298 347
7.1X 10 - l ~ 1.1 X 10 . 9 2.0 X 10 . 9
Shimamori and N a k a t a n i (1988) Swarm/dissociative attachment
C6F6
200 i 300 350 450 300 j 450 500 550 600 650
1.4 x 10-7i 1.1 x 10 -7 4.3 x 10 -8 ~ 1 x 10 . 9 1.3 x 10-vj 3.8 x 10 -8 1.1 x 10 -8 3.5 x 10 . 9 1.1 x 10 . 9 5.2 x 10- lo
Adams et al. (1985) F A L P / nondissociative attachment
C6F5C1
300 450
8.4 x 10 -8 1.3 x 10 . 7
Herd et al. (1989a) F A L P / predominantly nondissociative attachment
C6FsBr
300 450
8.3 • 10-8 2.4 • 10-7
Herd et al. (1989a) F A L P / dissociative and nondissociative attachment
C6F5I
300 450
3.1 • 10 -8 1.2 • 10- 7
Herd et al. (1989a) F A L P / predominantly dissociative attachment
CF3803CH 3
300 385 475
1.8 • 10- lO 1.0 • 10 -9 2.3 • 10 -9
Herd et al. (1989b) F A L P / predominantly dissociative attachment
CF3SO3C2H 5
300 385 475
2.7 • 10- lo 6.7 • 10- lO 6.5 • 10-lO
Herd et al. (1989b) F A L P / dissociative attachment
c-C7F14
205 300 452 585
4.5 6.8 1.3 1.6
Alge et al. (1984) F A L P / dissociative and nondissociative attachment
SO3
300, 400, 505
(3 ___1) • 10 -9
Miller et al. (1995) F A L P / nondissociative k
PC13
296 372 457 552
6.4 9.1 1.1 1.4
Miller et al. (1998) F A L P / dissociative attachment
• • • •
• • • •
10- 8 10-8 10- 7 10- v
10- 8 10 -8 10-7 10-'z
Reference/Method/Comment
Spyrou and C h r i s t o p h o r o u (1985c) Swarm
263
EXCITED ATOMS AND MOLECULES TABLE XVIII (Continued) Temperature Molecule
(K)
(kda,t)th(Cm 3 S - 1)
Reference/Method/Comment
POC13
296 372 457 552
1.8 x 2.1 x 1.8 x 1.5 x
Miller et al. (1998) F A L P / dissociative and nondissociative attachment
10 -7 10 -7 10-7 10 -7
" F o r room temperature values of some of these molecules see Christophorou et al. (1984), Burns et al. (1996), and Christophorou (1996, 1980). b Flowing afterglow/Langmuir probe technique. c Flowing afterglow. d Electron cyclotron resonance technique. e Values obtained from Fig. 3 of Shimamori and Nakatani (1988). I See also Shimamori and Sunagawa (1997). ~ taken off the graph given in Le Garrec (1997a). h Cin6tique de R6action en Ecoulement Supersonique Uniforme. iTaken from Fig. 1 of Adams et al. (1985). JThese values are the lowest data points in Fig. 1 of Spyrou and Christophorou (1985c). They correspond to mean electron energies <0.1 eV (see Spyrou and Christophorou, 1985c). k This rate constant is for the formation of SO3 measured in a helium buffer in the pressure range 53-160 Pa.
9
A 9
9 9 A O 9 O 9
12 CI2 F2
CF31 CF3Br CHFCI2 CH31 CF3CI CHCI 3 CH3Br
9 9 9 O V
10 -6
10 .7
10 .6
0
10 -8
0
d -'o
"o
t (a)
10-11 200
400
600
Temperature (K)
10-8 <>
.-o
10-11
O
10 -9
10-12 10 -13 200
O O
eo
E o ~. 10 "10
10-9
10 -7
0
10.9
10-1o
~7~v
10-7
9
10 8
CF2Br 2 CH2Br2 CH2CI 2 CCI2F2 CCI 4
9 ,
f
(c)
(b) ,
I
400
~
,
r
I
r
,
600
Temperature (K)
L
800
10-1o ,,, ~,,, f , , , 200 400 600 800 Temperature (K)
FIG. 58. Sets o f (kda,t)th as a function of T for diatomic molecules (a) and polyatomic molecules (b and c). The data are as listed in Tables XVII and XVIII. For each molecule the symbols refer to all data sets for that molecule. For F 2 the data of Sides et al. (1976) were normalized to those of McCorkle et al. (1986), and for CH2Br 2 the data of Burns et al. (1996) were normalized to those of Alge et al. (1984).
264
Loucas G. Christophorou and James K. Olthoff
AX-* and this is expected to decrease Xa because it has been found experimentally that the ~a of an isolated AX-* metastable anion, besides depending on the negative ion state and selection rules, depends also on the total internal energy of AX-*, which includes the captured electron's energy and the capturing molecule's temperature (see Christophorou et al., 1984; Christophorou, 1978). Direct measurements of Za for reaction (31) as a function of the kinetic energy e of the captured electron that led to the formation of AX-* have clearly shown that ra decreases with increasing (see, for example, Christophorou, 1978; Collins et al., 1970; Johnson et al., 1975). However, the situation is different in high-pressure electron swarm experiments where the anion AX-* is quickly stabilized by collisions producing AX- ions [reaction (30a)] predominantly in their lowest state of excitation. In swarm experiments, therefore, the effect of T mostly originates from an enhancement in the electron detachment frequency zd 1 via the reaction (Christophorou and Datskos, 1995; Datskos et al., 1992b, 1993a, b; Knighton et al., 1992; Miller et al., 1994b) AX- + heat (energy)--. AX + e
(32)
that is, from the effect of T on the stabilized AX- rather than from the effect of T on the unstable AX-*. Moreover, as the internal energy of polyatomic negative ions is appreciable even at temperatures within a few hundred degrees above ambient, reaction (32) becomes significant especially when the electron affinity of the molecule is small (<0.5 eV) and its effect on the measured electron attachment rate constant as a function of T can be large. There have been a number of studies on molecules attaching slow electrons nondissociatively that reported profound decreases in the measured total electron attachment rate constants/cross sections with increasing T. The more detailed of these are those on the ka,t((~3), T) of C6F 6 (Adams et al., 1985; Spyrou and Christophorou, 1985c; Datskos et al., 1993a; Wentworth et al., 1987), c-C4F a (Christodoulides et al., 1987), and c-CgF 6 (Datskos et al., 1992b, 1993b). The lifetimes of the isolated ions [reaction (31)] C6F6", c-C4Fff*, and c-C4Fg* have been reported to be ..~ 12 ~s for C6Fff* , > 10 ~ts for c-C4Fff*, and > 6 ~ts for c-CgFg* (Christophorou et al., 1984). An example of the reported (Spyrou and Christophorou, 1985c) large decreases in ka,t((e), T) with increasing T is shown in Fig. 59a for C6F 6. Similar data (Adams et al., 1985; Spyrou and Christophorou, 1985c) for the (ka,t)th (T) of this molecule are shown in Fig. 59b. The decrease in ka,t((~), T) and (ka,t)th (T) of C6F 6 with increasing T has been attributed to an increase in the autodetachment rate and/or to a decrease in the capture cross section as T increases. However, subsequent studies (Christophorou and Datskos, 1995; Datskos et al., 1992b, 1993a,b) have shown the domi-
265
EXCITED ATOMS AND MOLECULES i
I
10 3 ~ - % J
or) O3
E o
O
o
,T=.. V
C6F 6
3o0 K
103
~ l m mmmm 9mm 10 2 - ~ 450K 9mm’m40oK-:
-
,OOOOoo
" ",~so K
101 - ~ V v v v --
-
% _
99
DODD
%e
-
9
10 ~ -
-,,:
<>o oosoo K -
%<>0 -
10_ 1 . . . . 0.0
90 % o
q
, II
. .9
9.
O
5
102
"
o
b
101 v
_
b
_ _ _
%
I .... 0.5
i
r
[][]0 600K_
(a)
I
(b)
.. 9
or)
VV
6soK - , , ,
i
,.., . 9 ,, 9
_
%or)
OOn vv*~v -
i
, _ .....
_
1.0
Mean electron energy (eV)
100 200
C6F 6
400
600
Temperature (K)
FIG. 59. (a) ka,t((E), T) for C6F 6 (data of Spyrou and Christophorou, 1985c). (b) (ka,t)th(T) for C6F 6. D, Spyrou and Christophorou (1985c) [the data plotted are the values of k, at the lowest mean electron energy (<0.1 eV) at which these measurements were made]; @, Adams et al. (1985).
nant effect of reaction (32) on the measured values of ka,t(~S), T), especially when the electron binding energy in AX- is small. It is likely that the strong T dependence of reaction (32) has affected the measurements in Fig. 5 9 - - a n d similar ones on c-C4F 8 (Christodoulides et al., 1987)--to various degrees. These data then represent only apparent values of ka,t((l~), T). Indeed, this realization led to the development (Christophorou and Datskos, 1995; Datskos et al., 1993a; Wen and Wetzer, 1989) of the time-resolved electron swarm technique, which allowed information on electron attachment and detachment processes to be obtained simultaneously from an analysis of the transient electron waveforms in high-pressure electron swarm experiments. From such recorded electron-current waveforms the electron attachment rate constant and the electron detachment frequency have been determined using a nonlinear least squares fit to the current waveforms obtained at each E / N and at each temperature employed (Christophorou et al., 1994; Christophorou and Datskos, 1995; Datskos et al., 1993a,b). The technique has been applied to the study of C6F 6 (Christophorou and Datskos, 1995; Datskos et al., 1993a), c-C4F 6 (Christophorou and Datskos, 1995; Datskos et al., 1992b, 1993b) and SF 6 (Christophorou and Datskos, 1995; Datskos et al., 1993b).
Loucas G. Christophorou and James K. Olthoff
266
Figure 60a shows the measured k a , t ( ( 8 ) , T) for C 6 F 6. In contrast to the initial measurements (Fig. 59a), the changes in k a , t ( ( 8 ) , T) are not as profound as the earlier studies indicated. The data in Fig. 60a show that k a , t ( ( 8 ) , T) first increases slightly with increasing T and then decreases. This behavior is better seen in Fig. 60b where for a number of fixed values of the mean electron energy ka,t is plotted as a function of the internal energy ( 8 ) i n t ( Z ) of the molecule. The quantity ( 8 ) i n t ( T ) itself was estimated (Christophorou and Datskos, 1995; Datskos et al., 1993a) by assuming that the vibrational frequencies of the anion and the neutral molecule are the same and using published vibrational frequencies for the neutral molecule. The rather weak dependence of k a , t ( ( g ) ) o n T suggests that orb [reaction (30a)] is not a strong function of T. In contrast to this small effect, an increase in gas temperature enhances rather dramatically the thermally induced detachment of C6Fg [reaction (32)]. This is clearly shown by the data in Fig. 60c where the electron detachment frequency rE 1 is seen to increase sharply with increasing internal energy ( 8 ) i n t ( T ) (corresponding to a T range of 450 to 575 K). Interestingly, zd-1 varies little with the value of the mean electron energy of the attached electron. This heat-activated electron detachment process was found (Datskos et al., 1993a) to have an activation energy of 0.477eV. Studies of thermal electron detachment
5.5
(a)
5.0 4.5
~
4.0 CO | v
"
9 300 K ', 400 K o 450 K
(~>(ev)~ ' ~ 0 231 r -
,~ 2.0
o 500K
%
9 550 K
S"
3.0
0.647" / / J 0.759,/f
2.5 0.0
;6F6 ,
,
~ f I
0.5
(c)
"~
,.,- \{
.oo4 ,~
" ~ , r ~ ,
,, /E)
2.5
\
3.5
2.0
3.0
b)
a
0.238 e V 9 0.556 eV
t
./• _.1~
1.5 1.0 0.5
C6F6
0.0
1.0
Mean electron energy (eV)
0.0
0.2
0.4
0.6
Mean internal energy (eV)
0.3 0.4 0.5 0.6 0.7
Mean internal energy (eV)
FIG. 60. (a) ka,t((g)) for C6F 6 at 300, 400, 450, 500, 550, and 575 K. (b) ka, t for C6F 6 as a function of the internal energy (e)i.t of the molecule (taken to be the average vibrational energy of the molecule at each T) for the indicated values of the mean electron energy (a). The data points correspond to values of T equal to 300, 400, 450, 500, 550, and 575 K. (c) Thermally induced electron detachment frequency z~- ~ for C6F 6 as a function of the internal energy <~)int of the anion. The data points correspond to values of T equal to 450, 500, 550, and 575 K (Fig. 60 (a), (b) and (c) are from Christophorou and Datskos, 1995).
EXCITED ATOMS AND MOLECULES
267
(Knighton et al., 1992) at ms times (rather than at ps times in the experiments by Christophorou and co-workers) gave a value for the electron affinity of the C6F 6 molecule equal to 0.52 eV. Electron attachment and detachment processes using the time-resolved electron swarm technique have been made for two other molecules, namely, c-C4F 6 and SF 6. Both of these molecules attach strongly thermal and near-thermal energy electrons that form long-lived (isolated anion lifetimes > 1 ps) parent anions, but differ in the value of their electron affinity. The electron affinity of SF 6 is ~ 1 eV (see Christophorou and Datskos, 1995; Datskos et al., 1993b) and that of c-C4F 6 is most likely < 0 . 5 e V [the heat-activated electron detachment process for c-C4F6- was found (Christophorou and Datskos, 1995; Datskos et al., 1993b) to have an activation energy of 0.237 eV]. Figure 61a shows the effect of T on the rate constant ka,t((E)) of formation of c-C4Fg and Fig. 61b shows the effect of T on the process of thermally induced electron detachment from the c-C4Fg ions. These studies have been made in a buffer of gas N 2 over the temperature range of 300-600 K and for mean electron energies in the range 0.2-1.0 eV.
7
. . . .
6
~
~ ....
10
'
(a)
5
~,~
O3
E
0 co|
o
v
~ ,
4 3
.,-,
21
o
300 K
[]
450 K
~ 400 K
&~
o sooK
'
I
'
I
'
I
o c4 ~
8 %o~
I
t1 J
-
_ o 0.:~) eV
'~
_
_
4
//
:
~176 /
2
//t
~
t
- r
0
~
0.0
L
J
~
I
0.5
~
J
J
1.0
M e a n electron e n e r g y (eV)
0 0.1
0.2
0.3
0.4
0.5
0.6
M e a n internal e n e r g y (eV)
FIG. 61. (a) Electron attachment rate c o n s t a n t ka,t((E)) as a function of the mean electron energy for c-C4F 6 measured in mixtures of c-C4F 6 with nitrogen at gas temperatures of 300, 400, 450, 500, and 600 K. (b) Thermally induced electron detachment frequency -cd-1 for c-C4F6 as a function of the internal energy (l~)int of the anion for a number of values of the mean electron energy (e). The data points correspond to values of T equal to 450, 500, 550, and 600 K (Fig. 61 (a) and (b) are from Christophorou and Datskos, 1995).
268
Loucas G. Christophorou and James K. Olthoff
Under these experimental conditions the formation of the parent anion c-C4Fg depends only very slightly on T, but increases in T from ambient to 600 K enhance dramatically the frequency of thermally induced electron detachment from c-C4Fg. As for the case of the C6F6 ions, the detachment frequency ~d-l((~)int ) varies little with the mean electron energy. Under the same experimental conditions as for c-C4Fg, the stabilized SFg anions do not undergo thermal detachment in the T range ( < 600 K) investigated (Christophorou and Datskos, 1995; Datskos et al., 1993b). No evidence of any detached electrons was observed in the electron-current waveforms for this molecule for temperatures of up to 600 K. This was attributed (Christophorou and Datskos, 1995; Datskos et al., 1993b) to the higher value ( ~ 1 eV) of the binding energy of the electron in the SFg anion. The total electron attachment rate constant ka,t for SF 6 was found (Christophorou and Datskos, 1995; Datskos et al., 1993b) to be independent of T at all mean electron energies < 1 eV investigated (Fig. 62). Based on the study of the three molecules C6F6, c-C4F6, and SF 6 using the time-resolved electron swarm technique, it is evident that for molecules which attach electrons nondissociatively and have electron affinities < 1 eV, increases in T above ambient strongly enhance thermal detachment from the stabilized parent anions. The cross section for formation of the parent anions is slightly, if at all, affected by increases in T above ambient to 600 K. B. ELECTRON ATTACHMENT TO ELECTRONICALLY EXCITED MOLECULES In this section we focus on dissociative attachment of slow electrons to electronically excited molecules prepared by laser light prior to or concomitantly with the generation of the attaching electrons. The electronically excited species can be in a metastable long-lived (lifetimes > 10-5 s) state, or in a short-lived (lifetimes < 10 -6 s) state, or in a very short-lived (lifetimes < 10 -9 s) state. Such excited states can be produced directly by single or multiple photon absorption, or indirectly via internal conversion and intersystem crossing from higher-lying excited electronic states initially reached by photoexcitation, viz. nhv(n >>.1) + AX ~ AX*(+e) ~ AX*- ---,AX ~*) + e
A + X-
(33a) (33b)
or
nhv(n ~ 1) + AX -* AX** -* AX*(+e) -. AX*- -* AX (*) + e
-~ A + X-
(34a) (34b)
269
EXCITED ATOMS AND MOLECULES
10
'1
,
i
I
’
’
’
’
= 300!) #,.
400 (Christophorou, 1995) 500 550 300 K (Hunter, 1989)
r r
E
oo
b
v
4
SF 6 I
0
I
I
I
]
I
I
I
0.5
I
1
Mean electron energy (eV) FIG. 62. Total electron attachment rate constant ka,t((8)) as a function of the mean electron energy for SF 6 measured (Christophorou and Datskos, 1995; Datskos et al., 1993b) in mixtures with nitrogen at gas temperatures of 300, 400, 500, and 550 K. The broken line indicates the data of Hunter et al. (1989) for 300 K (from Christophorou and Datskos, 1995).
where AX** is a short-lived excited electronic state lying energetically above AX*, and AX*- refers to a transient anion formed by addition of an electron to the electronically excited molecule AX*. Both AX** and AX* may dissociate prior to electron collision. Observation of electron attachment to electronically excited molecules requires production of an appropriate number of excited molecules under conditions such that electron attachment to the excited molecules occurs within their lifetimes. Depending on the lifetime of the excited electronic state, a number of techniques have been developed (Christophorou et al., 1987; Kuo et al., 1988; Pinnaduwage et al., 1991; Jaffke et al., 1992, 1993; Krishnakumar et al., 1997) for electron attachment studies using lasers. For instance, when the excited states are long-lived (lifetimes > 10-5 s), tradi-
270
Loucas G. Christophorou and James K. Olthoff
tional high-pressure electron swarm experiments (Christophorou, 1994; Christophorou et al., 1987; Pinnaduwage et al., 1989) and low-pressure electron beam/mass spectrometers (Christophorou, 1994; Jattke et al., 1993; Krishnakumar et al., 1997) can be used in conjunction with pulsed lasers. With regard to high-pressure swarm experiments, Christophorou and collaborators used a pulsed-Townsend swarm technique (Christophorou, 1994; Christophorou et al., 1989) in which the gas under study was mixed with Ar or N 2 at total pressures of 1-100 kPa. Briefly, a pulsed laser enters the interaction region through a gridded electrode (anode), excites a fraction of the electron attaching molecules in the interaction region (but not the buffer gas), and produces a pulse of electrons at the cathode electrode. The electron pulse injected into the drift region at the cathode quickly (within < 10-8 s) reaches a known steady-state energy distribution and drifts as an electron swarm to the anode electrode through the partially excited gas. The drift time taken by the electron swarm to reach the anode is normally ~ 10-5 s and thus electron attachment to the excited molecules can take place if their lifetime is > 10-5 s. Other versions of this arrangement were employed to allow excited states to be generated independently of the attaching electrons, to separate negative from possible positive charges, and for indirect identification of the negative ions (Pinnaduwage et al., 1989; Pinnaduwage and Christophorou, 1994). With regard to low-pressure electron beam/mass spectrometric experiments, measurements of electron attachment to long-lived excited electronic states under isolated conditions (pressures < 10 - 2 Pa) was accomplished using various modes of pulsing the laser, electron, and ion extraction beams (Jaffke et al., 1993; Krishnakumar et al., 1997). Measurement of electron attachment to short-lived excited species having a lifetime ~, produced via a laser pulse of duration ~L, requires arrangements whereby the electron attachment time ~, is less than the maximum of the quantities z and ~L, that is, arrangements where electron attachment takes place before the excited species decays. If ~L > ~, this limit is set by ~L because excited species are continuously being generated within the duration of the pulse. A number of techniques have been introduced for the study of electron attachment to short-lived excited states whereby the excited species and the attaching electrons are produced concomitantly by a single laser pulse via photoionization of the gas under study or a suitable additive. Because in these arrangements the excited species and the electrons are produced in close proximity, electron attachment can take place in spite of the short lifetime of the excited states (see Christophorou et al., 1994; Pinnaduwage et al., 1991; Pinnaduwage and Christophorou, 1991).
EXCITED ATOMS AND MOLECULES
271
1. Data on Dissociative Electron Attachment to Electronically Excited Molecules
H~. The only theoretical work on electron attachment to electronically excited states seems to be that of Bottcher and Buckley (1979), who predicted that dissociative electron attachment to the metastable hydrogen molecule H~(c 3IIu) is substantially larger than that from the low-vibrational states of the ground-electronic state Hz(X 1~2~-,v -- 0). They found the cross section to be ~ 10-18 cm 2 for dissociative electron attachment to H~(c 3IIu) #:_ proceeding via the H2 (21--Iu)resonance, that is, for the reaction e + H~-(c 3H.)--*
H~-(2II.)--. H - ( l s 2) +
H(2p)
The value is insensitive to the initial vibrational level v, in contrast to dissociative electron attachment to the ground state of H 2 (see Section VI.A). The insensitivity to vibrational-state excitation is consistent with other subsequent studies referred to in Section VI.A, which showed that the dissociative attachment cross section does not appreciably increase and may actually decrease for vibrational levels that lie at or above the dissociative attachment threshold. Pinnaduwage and Christophorou (1993) observed photoenhanced dissociative electron attachment to H 2 under ArF laser irradiation that they attributed to electron attachment to high-lying excited electronic (possibly Rydberg) states. In a subsequent study Pinnaduwage and Christophorou (1994) provided evidence through photodetachment and ion-mobility measurements that the efficient formation of negative ions Pinnaduwage and Christophorou (1993) observed in ArF-laser-irradiated H 2 is due to the formation of H - ions. They argued that under their experimental conditions [gas pressure = 0.67 kPa, laser intensities = (~0.7 to 3) x 1025 photons cm-2 s-1, laser wavelength = 193 nm, applied electric fields = (25 to 100) V cm-1] electron attachment to laser-excited hydrogen molecules has a rate constant as large as ~ 10 .6 cm a s-1. O~. Measurements of electron attachment to electronically excited 0 2 molecules were first carried out by Burrow (1973) on singlet oxygen O~(a 1A0). The a 1A s state of 0 2 has a lifetime of ~ 4 5 min (Badger et al., 1965) and lies 0.98 eV above the ground state 32;0-. A trochoidal electron beam apparatus was employed for these studies and the excited molecules were produced in a microwave discharge. The cross section measured by Burrow for the reaction e + O~(a
lag)~ O~-(2rlu).-40-(2p) +
O(sp)
(35)
272
Loucas G. ChrL~tophorou and James K. Olthoff
is compared in Fig. 63a with that (Rapp and Briglia, 1965; Christophorou, 1971) for the ground state, viz., e + O 2 ( 3 Z ; ) ~ O2*(21-Iu) ~ O-(2P) + O(3p)
(36)
In these and similar reactions for other molecules the notation O~- is used to represent a transient anion formed by electron attachment to the electronically excited molecule O~ and it should be distinguished from the notation Of*, which is used to represent a transient negative ion with excess internal energy. As expected, the energy dependence of the cross section for reaction (35) resembles that for reaction (36), but the cross section is shifted to lower energies by 0.98 eV. According to the measurements of Burrow (1973) it has a peak value of (4.6 ___ 1.3) x 10 -~8 c m 2, which exceeds the peak value of the ground-state cross section by a factor of 3.5 ___ 1 times. The width of the cross section measured by Burrow for reaction (35) is the same as that for reaction (36) and this finding is consistent with the similarity of the potential energy curves for singlet and triplet 0 2 and the fact that both reactions proceed through the same negative ion s t a t e 2I-Iu. A subsequent study by Beli6 and Hall (1981) using an electron-impact spectrometer and a microwave discharge confirmed the findings of Burrow for reaction (35) and the additionally reported observations of two other dissociative electron attachment processes involving singlet oxygen, viz. e + O ~ ( a X A 0 ) ~ O ~ - 2 Z 0+ ) ~ O
(2p)+O(~D)
(5.61eVlimit)
(37)
e + O~(a ~Ag) -~ O~ -(2 Z o+ ) -~ O (2p) + O(~S)
(7.89 eV limit)
(38)
and
These processes can be visualized through the aid of the schematic potentialenergy diagram in Fig. 63b. The cross sections for reactions (37) and (38) were found (Beli~ and Hall, 1981) to peak, respectively, at 8.5 and 9.5eV, with respective peak crosssection values equal to 1.8 • 10-~8 c m 2 and < 10 - 2 0 c m 2. A third similar study of dissociative electron attachment to singlet oxygen was conducted by Jattke et al. (1992). They measured the cross sections for reactions (35) and (37), which they put on an absolute scale by normalization to the peak cross section value for reaction (36) taken to be 1.3 • 10-x8 c m 2 at 6.5 eV. Their data are shown in Fig. 63a. Table XIX summarizes the results of dissociative electron attachment to O*(a 1Ao) [reactions (35) and (37)] in comparison to the results o n O2(3]~]g) [reaction (36)].
273
EXCITED ATOMS AND MOLECULES 7
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4 _l
6 8 10 12 Electron energy (eV) 4
o
O*2(alAg)
~
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-2
Internuclear separation -->
FIG. 63. (a) Cross sections for the production of O - by dissociative electron attachment to O2(3E~-) via O2"(2H,) (--, Rapp and Briglia, 1965), and to O~(a 1A0) via O~-(2I-I,) (--, Jaffke et al., 1992;---, Burrow, 1973) and via O*-(2E +) (-.-, Jaffke et al., 1992). (b) Schematic potential-energy diagrams for O2(3E~-), O~(a 1Ao), O~-(2I-I,), and O~-(2E +) (from Jaffke et al., 1992).
TABLE XIX PEAK ENERGIES 8 . . . . PEAK CROSS-SECTION VALUES (~da(~max) AND RATIO R OF (~da(~max) FOR REACTION (35) TO THAT FOR REACTION (36) I~max
O'da (~max)
Electron Attachment Reaction
(eV)
(10 -18 cm 2)
e + O2(3E~-)~O;*(2H.)~O-(2P)+ O(3p) e + O~(a 1ao)--, O* - (2Hu)-, O - (2p) + O(3p)
6.5 a 5.45 b 5.5d
1.3" 5.73 b (4.6 + 1.3)'t
5.5 e 7.5 e
3.8 e 1.8 e
e+O~’(a
1Ag)---~O ~ - ( 2 ]~g+ )---+O (2p)+O(~D)
4.5 c
3.54 't 2.92 e
1.5c aRapp and Briglia (1965). See Christophorou (1971) for a comparison of the data of various investigators for this process. bAverage of two values given in Jaffke et al. (1993). c Jaffke et al. (1992). Burrow (1973). e Beli6 and Hall (1981).
274
Loucas G. Christophorou and James K. Olthoff
Kuo et al. (1988) studied dissociative electron attachment to excited NO*(A 2Z+) by allowing a pulsed molecular beam to interact simultaneously with a beam of low energy (kinetic energy <0.5 eV) electrons and a pulsed tunable dye laser beam. As the laser wavelength was scanned, several peaks appeared for the mass-resolved O - ion signal in the wavelength range near 226 nm. The wavelengths at which this enhancement occurred were shown to correspond to the (0, 0) band of the xzI-[ ~ A 2 ] ~ + band system of NO and thus the photoenhanced signal was attributed to dissociative electron attachment to the electronically excited molecule NO*(A 2Z+). Subsequently, Kuo et al. (1994) estimated the cross section for dissociative electron attachment to NO*(A 22+) to be (2.0 _+ 0.5) x 10-15 cm 2. This value, however, must be too low because it was obtained by normalization to the total electron attachment cross section of CC14 at 0.5 eV, for which a value of 0.88 x 10-16 cm 2 was assumed. A number of other studies (Christophorou et al., 1984; Christodoulides and Christophorou, 1971) indicate a much larger (by about a factor of ~20) cross section for CC14 at this energy. Thus, the dissociative electron attachment cross section for the electronically excited-state reaction NO*.
e + NO*(A 2Z+)--, O-(2P) + N(4S)
(39)
is over 3 orders of magnitude larger than the cross section for the ground-state reaction e + NO(X 2 H ) ~ O-(2P) + N*(2D)
(4o)
Reaction (39) is exoergic by 0.45 eV while reaction (40) requires a threshold energy of ~ 7.5 eV (Chantry, 1968) and has a maximum cross-section value of 1.11 x 10 -18cm 2 at 8.1eV (Rapp and Briglia, 1965; Chantry, 1968). Photoenhanced electron attachment to NO has been observed by Pinnaduwage and Christophorou (1991). They used various excimer laser lines and also several wavelengths from a dye laser pumped by an XeCl-excimer laser to excite NO molecules by multiphoton absorption and to concomitantly produce the attaching electrons by multiphoton ionization. No cross-section data were given by these investigators, but the observed signals due to negative ions generated in the laser-irradiated gas and attributed to dissociative electron attachment to excited electronic states of NO lying above the ionization threshold indicated cross-section values many orders of magnitude larger than for the ground state. SO~. Dissociative electron attachment to the ground state SO2(X 1A1) molecule is known (Christophorou et al., 1984; Spyrou et al., 1986) to lead
EXCITED ATOMS AND MOLECULES
275
to the production of O - , SO-, and S- with maximum intensities around 4.5 eV, viz. e+SOz(X 1A1)--.SO2"~O- + S O --.SO- + O
(O'da peaks at 4.5 and 7.3eV)
(41a)
(Cyaapeaks at 4.8 eV)
(41b)
~ S - + O 2 (~da peaks at 4.2 and 7.4eV)
(41c)
Jattke et al. (1993) used a trochoidal electron monochromator, a quadrupole mass spectrometer, and an excimer laser arrangement and investigated electron attachment on XeCl-laser-irradiated SO2. They looked at the changes in the energy dependence and the magnitude of the cross section for reaction (41a) under XeCl-laser irradiation of SO2. Figure 64a shows their findings. The solid line is the relative cross section for the production of O - from SO2 in the absence of laser irradiation where the two peaks due to the ground-state process are clearly seen, and the dots are the signal (corrected for the variation of the electron beam current with electron energy, but not for the fraction of excited to ground-state gas number density) detected for a few gs following each irradiating laser pulse. With the laser beam on, besides the peaks due to the ground state attachment, an enhanced peak of O - signal is seen at electron energies <0.5 eV. The magnitude of this peak is much larger than indicated in Fig. 64a, because only a small fraction of the SO 2 molecules is excited by each laser pulse. A rough estimate of the excited-state number density led Jattke et al. to conclude that the value of the cross section at the peak of the photoenhanced O - signal at near-zero energy is at least 2 orders of magnitude larger than the peak cross-section value (2.5 x 10 -18 cm2; Spyrou et al., 1986) of the O - formed from the ground state. The observed photoenhanced O production from XeCl-laser-irradiated SO 2 was attributed (Jaffke et al., 1993) to the reaction hv(308 nm)+ SO2(X 1A1)---~SO~(1B 1 or 1A2)( + e < 0.5 eV)---,SO~- ~ O - + SO (42) that is, to dissociative electron attachment to the electronically excited SO~(1B1 or 1A2) molecule. This excited state is long-lived (Jaffke et al., 1993) (lifetime longer than 50gs). The electron energy required for the transition from SO~(IB1 or 1A2) to SO~- is small and thus the photoenhanced resonance appears close to zero energy. Following the work of JatIke et al., Krishnakumar et al. (1996, 1997) also studied dissociative electron attachment to electronically excited SO 2 using
Loucas G. ChrL~tophorou and James K. Olthoff
276
I
,
I
,
from
O
, m
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(a)
9
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..# 9
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-,: f
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9
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o
9 S from SO 2 (xlO)
o
9 SO- from SO 2
20
v .Ic "0
13
10 ~%~
"" oA
--7
0
2
i
4
,
; ......
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,
8
10
Electron energy (eV) FIG. 64. (a) Relative cross section for the production of O - from the ground state SO2(X IA1) ( - - ) and electronically excited SO~(1BI or 1A2) ( .... ) molecules as a function of the electron energy. The relative cross sections were normalized at 8 eV and the excited-state cross section was not corrected for the fraction of excited to unexcited gas number density (data of Jaffke et al., 1993). (b) Partial (for O - , S-, and S O - ) dissociative electron attachment cross sections from the ground-state SO2 (solid symbols) and the electronically excited S O / ( o p e n symbols) molecule. Note the multiplication factor for the S- data (data of Krishnakumar et al., 1997).
a triple-crossed beam geometry in which a pulsed laser beam (XeC1-308 nm) excited the molecules in an effusive beam, a pulsed electron beam intersected the effusive beam immediately after the laser pulse, and the resultant negative ions were extracted by a pulsed electric field into a time-of-flight mass spectrometer and detected by a channel electron multiplier. They
EXCITED ATOMS AND MOLECULES
277
looked at all three channels (O-, S-, and S O - ) of reaction (41) and their results are shown in Fig. 64b. Besides the higher energy peaks due to ground-state attachment, photoenhanced O - a n d SO- peaks appeared at near-zero energy. While these results confirm the earlier findings of Jaffke et al. as to the very-low energy position of the photoenhanced peak, they show a much smaller photoenhancement factor. The cross section of Krishnakumar et al. for the production of O - from the excited state has a peak at 0.4 eV with a value of 36 x 10-18 cm 2 as compared to a peak value of 5.9 x 10-18 cm 2 at 4.6eV they measured for O - from ground state SO2. Thus, for this fragment anion the photoenhancement factor is only ~ 6 compared to a factor of ~ 175 estimated by Jaffke et al. This discrepancy and similar large uncertainties for other systems stress the need for a reliable method to quantify the magnitudes of the cross sections for electron attachment to electronically excited molecules. For the other two fragments, Krishnakumar et al. reported that the SOcross section peaks at 0.6eV with a peak value of 6.6 x 10 - i s cm 2, while their measured cross section for SO- from ground state SO2 peaks at 4.8 eV and has a peak value of 4.3 x 10- is cm 2. According to Krishnakumar et al., the S- signal was too weak to investigate. The sum of the cross section for the formation of O - and SO- from the excited SO~(1B1 or 1A2) molecule peaks at 0.4eV and has a peak cross-section value of 42 x 10 -18 cm 2 as compared with the corresponding cross section from the ground state SO 2 (X1AI) molecule, which they found to peak at 4.6 eV with a peak cross-section value of 10.2 x 10 -18 cm 2. CS~. Rangwala et al. (1997) used the method of Krishnakumar et al. (1996, 1997) and investigated the formation of S- and CS- by dissociative electron attachment to excited CS~(1B2) produced from the ground-state molecules by absorption of 308-nm photons from an excimer laser pulse. They found the peak for S- and CS- from dissociative electron attachment to the excited state to occur, respectively, at 0.5 and 0.7 eV. The cross-section peaks for these fragment anions from the ground state occur at 3.6 and 6.2 eV for S-, and at 6.2 eV for CS- (Christophorou et al., 1984; Krishnakumar and Nagesha, 1992; Ziesel et al., 1975). Rangwala et al. reported that the peak value of the cross section for S- from dissociative electron attachment to the excited molecule CS~(1B2) is 3 x 10 -18 cm 2 as compared to the maximum of 0.35 • 10-~8 cm 2 they measured from the ground state. Similarly, the cross section for the formation of CS- from the excited state was found to be 1.7 • 10 -19 cm 2 as compared to 0.67 • 10 -19 cm 2 from the ground state. Once again it is stressed that the cross-section values for the excited states may be uncertain mainly because of difficulties in establishing the correct excited-state number density.
278
Loucas G. Christophorou and James K. Olthoff
Recent observations by Bhardwaj et al. (1998) of "dramatically different" dissociative electron attachment patterns in laser-irradiated CS2 gas compared to dissociative electron attachment to the ground-state molecule are consistent with the possible involvement of electronic excitation of CS2 in dissociative attachment under laser irradiation in their experiments. C6HsSH*. The first observation of optically enhanced electron attachment to electronically excited molecular states was reported by Christophorou et al. (1987) for the first excited triplet state T 1 of the thiophenol (C6HsSH) molecule. The T~ state lies ~3.4eV above the ground state and has a lifetime of ~ 6 ms. It was excited indirectly via internal conversion and intersystem crossing from higher optically allowed singlet states using the 249-nm KrF excimer line. The measured electron attachment coefficient normalized to the unexcited attaching gas number density N a, q / N , , for the thiophenol molecule in its ground and in its first excited triplet state is shown in Fig. 65. The data designated by the open circles are for the ground-state molecule and were obtained in a separate high-pressure swarm experiment without laser irradiation. The data designated by the solid squares were obtained with the 308-nm XeC1 excimer laser line and are almost identical to those without laser irradiation, that is, those for the ground state. The photon energy (4.03 eV) for the 308-nm XeC1 excimer line lies below the first excited singlet state (at ~4.4 eV) of C6HsSH and thus no excited molecules are produced by single-photon absorption at this wavelength. The data designated by the solid circles were obtained using the KrF line and show a large enhancement in electron attachment at low E / N values (low electron energies). Since in these experiments only ~ 1% of the molecules are excited by the laser pulse, the actual enhancement in electron attachment at thermal and near-thermal energies is over a factor of 105 (Christophorou et al., 1987; Pinnaduwage et al., 1989). This enhancement was attributed to dissociative electron attachment to the first excited triplet state of the thiophenol molecule C6H5SH*(T1) produced indirectly via internal conversion and intersystem crossing from higher optically allowed electronic states reached by laser excitation. p - B e n z o q u i n o n e * ; T r i e t h y l a m i n e * ; SIH4; " * cH~. Mock and Grimsrud (1990) irradiated p-benzoquinone and a number of its methylated derivatives with a xenon arc lamp using a monochromator of 20-nm bandwidth for wavelength selection, and monitored the electron capture detector current during the gas chromatographic introduction of these compounds with and without light irradiation. The electron capture detector response was simply the decrease in current due to electron attachment. Similar to the study on C6HsSH*(T~), the first excited triplet states of p-benzoquinone and its
EXCITED ATOMS AND MOLECULES ,.,9
~
279
m!
10 2 __
04
E
0 oo
%-, o
101 --
C6H5SH in N 2
_
,,f--
v
PN2 = 133 k P a
Z
Pa = 0 . 0 0 4 k P a
100 XL=249 nm, E=2.5 mJ
-
XL_=308 nm, E = I . 0 mJ o
10-1 0.01
I
I
[
I
i IIIII
I
I
High Pressure Swarm Exp~
I III11
[
0.1
1
E/N ( 1 O-17
V
I
I
r r i+il
I
I
I0
cm 2)
FIG. 65. Electron attachment coefficient q/N, normalized to the unexcited attaching gas number density N, as a function of E/N for C6HsSH in N 2 for the ground state ( 9 high-pressure swarm experiment without laser irradiation), (B, swarm experiment under 308 nm, 1.0 mJ laser pulse irradiation, C6HsSH pressure = 0.004 kPa, N 2 pressure = 133 kPa), and for the first-excited triplet state (0, swarm experiment under 249 nm, 2.5 mJ laser pulse irradiation, C6HsSH pressure = 0.004kPa, N 2 p r e s s u r e - 133kPa) (Christophorou et al., 1994, 1987; Pinnaduwage et al., 1989).
methylated derivatives were populated indirectly via higher-lying optically allowed excited singlet states. The lifetimes of the first excited triplet states of these molecules are ~30 gs and were found to be independent of the pressure of the buffer gases argon or nitrogen employed. Mock and Grimsrud (1990) concluded that electron attachment to p-benzoquinone and methylated p-benzoquinone molecules excited in their respective lowest triplet states is 105-10 "7 times larger than for the respective ground-state molecules. This is similar to the enhancement estimated earlier (Christophorou et al., 1987) for C6HsSH*(Ta) compared to the ground state.
280
Loucas G. Christophorou and James K. Olthoff
A more recent investigation of optically enhanced electron attachment to p-benzoquinone was conducted by Gordon et al. (1997) in the energy range 0-3 eV using a trochoidal electron monochromator in combination with a negative-ion mass spectrometer. Gordon et al. reported that near 0 eV the attachment cross section for the UV/visible light-excited p-benzoquinone molecule is ~ 105 times larger than that for the ground-state molecule. Finally, photoenhanced electron attachment has been reported for excimer laser irradiated silane (Pinnaduwage et al., 1994; Pinnaduwage and Datskos, 1997), triethylamine (Pinnaduwage et al., 1991; Pinnaduwage and McCorkle, 1996), and methane (Pinnuduwage et al., 1995). These studies have indicated as well that the photoenhanced dissociative electron attachment cross sections are many orders of magnitude larger compared to those for the unexcited molecules. 2. Data on Nondissociative Electron A t t a c h m e n t to Electronically E x c i t e d Molecules
Electron attachment accompanied by simultaneous electronic excitation of the molecule (leading to two electrons in normally unfilled molecular orbitals) has long been known to manifest itself as resonances in both dissociative electron attachment and electron scattering (e.g., Christophorou, 1971; Christophorou et al., 1984; Schulz, 1973). The reaction can be represented as e: + AX ---, [AX*
.
.
.
.
eth] ~ AX*- ~ AX (*) + e a + X-
(43a) (43b)
It involves the concomitant electronic excitation of the molecule AX by a "fast" electron e: which, having lost virtually its entire kinetic energy to electronic excitation of AX, is "thermalized," eth, in the very vicinity of the electronically excited molecule it produced and is quickly and efficiently captured by it. The unstable anion AX*- normally decays rapidly (within < 10 -12 s) by autodetachment (reaction 43a), and/or by dissociative electron attachment reaction 43b). It has, however, been found that in the case of p-benzoquinone (Collins et al., 1970; Christophorou et al., 1969) and possibly in the case of aromatic hydrocarbons with electron affinities larger than 0.5 eV (Tobota et al., 1992), the intermediate AX*- lives long enough (lifetime longer than 10 -6 s) to be detected directly as a parent anion in conventional mass spectrometers. This accounts (Collins et al., 1970; Christophorou et al., 1969; Tobota et al., 1992) for the observation of negative
EXCITED ATOMS AND MOLECULES
P.C6H402 ~Ar '
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b
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C"
0.01
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C2H4~:~
"o c-
(a) 0.001 0.01
I
I
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0.1
I
i
i illll
i
1
I
I
(b) I liJH
10
Mean ]electron energy (eV)
0 1.5
i
i
2.0
i
i
2.5
i
3.0
Electron energy (eV)
FIG. 66. (a) Rate constant k da({e)) for nondissociative electron attachment to the P-C6H402 molecule measured in each of the buffer gases CzH 4 (O), N 2 (O), and Ar (A) (Christophorou et al., 1969; Collins et al., 1970). (b) Cross section for the production of P-C6H40~- as a function of the electron energy (Christophorou et al., 1969; Collins et al.,
1970).
ion resonances due to long-lived parent negative ions at electron energies well above thermal and with cross sections much larger than at thermal energies. Figure 66a shows the rate constant knda({e)) for nondissociative electron attachment to p-benzoquinone as a function of the mean electron energy measured by Collins et al. (1970) and Christophorou et al. (1969) in three different buffer gases (C2H4, N2, and Ar). Although the parent molecule has a positive electron affinity (Christodoulides et al., 1984), the rate constant is more than two orders of magnitude larger at a mean energy of ~ 2 eV compared to thermal. Consistent with the electron swarm data in Fig. 66a are the electron beam mass spectrometric data shown in Fig. 66b, which identified the negative ion peak at 2.1 eV with the formation of the parent p - C 6 H 4 0 ~- anion at 2.1 eV. The peak cross-section value was measured to be 6.7 • 10 -17 cm 2 and the unstable parent negative ion P-C6H40 ~- was found to have an autodetachment lifetime ~. of ~ 30 gs at 2.1 eV under isolated (low-pressure) conditions. The formation of this anion
Loucas G. Christophorou and James K. Olthoff
282
at this energy was attributed to electron attachment into the field of the lowest n ~ p* transition, that is, to a long-lived electron-excited Feshbach resonance via the reaction P-C6H402
if-
e(~ 2.3 eV) ~
(P-C6H40~)n~,(triplet) -at- eth(,~ 0.0
eV)
P-C6H40 ~- ~ autodetachment (z, ~ 30 gs) (44) The existence of this resonance, its long lifetime %, and the measured decrease of z, with decreasing electron energy beyond the resonance maximum (Collins et al., 1970) were confirmed in a subsequent electronbeam study by Cooper et al. (1975). These workers found the resonance at a lower (1.4 eV) energy and, in addition, to mechanism (44), they proposed that the resonance could be a shape resonance formed by internal conversion following electron attachment to a higher unfilled n* orbital. The decay characteristics of the long-lived parent negative ion of p-benzoquinone formed by electron impact of ~ 2 eV electrons on p-benzoquinone have been further investigated by Allan (1983) using time-resolved electron-energy-loss spectroscopy, and more recently by Schiedt and Weinkauf (1999) using resonant photodetachment.
VII. Concluding Remarks It can be concluded from this work that with the exception of electron scattering from excited atoms and electron attachment to ro-vibrationally excited molecules for which reliable data exist, the current state of our knowledge on electron interactions with excited atoms and molecules is quite limited. Especially meager are the data on electron scattering from excited molecules. It can be further concluded that the cross sections for electron interactions with excited atoms and molecules are generally much larger than the cross sections for the respective ground-state species. The enhancement depends on the species itself, the excited state (especially its polarizability), the electron energy, and for differential scattering cross sections, on the scattering angle. A considerable body of knowledge and understanding has been achieved on electron attachment to ro-vibrationally excited molecules. The crucial quantity here is the total internal energy of excitation of the molecule. Its effect on the electron attachment properties of molecules depends on the mode (dissociative/nondissociative) of electron attachment, the negative ion
EXCITED ATOMS AND MOLECULES
283
state(s) involved, and the location of the negative ion state with respect to the ground state of the neutral molecule. The effect of molecular internal energy on the electron attachment cross sections/rate constants is due primarily to the enhanced autodissociation of the transient anion for dissociative electron attachment and to enhanced electron detachment for nondissociative electron attachment. While a number of studies on electron attachment to electronically excited molecules have shown that the cross sections are much larger than for the ground-state molecules, the cross sections for the former are not even known on the-order-of-magnitude scale of accuracy. Reliable new methods are needed for such studies. The larger dissociative electron attachment cross sections for the excited electronic states compared to the ground state of molecules may in part be due to the higher polarizability of the excited states and the lower energies of the captured electrons. The higher reactivity of slow electrons with excited atoms and molecules would affect the properties of electrically stressed gaseous matter even when the density of excited species is relatively small. In efforts to consider these "excited-state" effects in practical systems--such as the assessment of the role of electron collisions with excited states in Boltzmann codes and other electron transport analyses and m o d e l s - - t h e diverse dependence of excitedstate cross sections on the individual targets seen from the data presented in this work should be fully recognized. Finally, it can be concluded that the field of electron interactions with excited atoms and molecules is still young and although more complicated than the study of electron interactions with ground-state atoms/molecules, it is full of challenge and potential for applications.
VIII. Acknowledgment We wish to thank Ms. Robin J. Martucci of the Electricity Division, National Institute of Standards and Technology (NIST) for her assistance with the literature.
IX. Appendix A Mean electron energies {e) as a function of E/N in the buffer gas Ar at 300 K (Spyrou and Christophorou, 1985b) and in the buffer gas N 2 at 300, 400, 500, 600, 700, and 750 K (from Datskos et al., 1990, 1992a).
Loucas G. Christophorou and James K. Olthoff
284
TABLE AI MEAN ELECTRON ENERGIES <~;> AS A FUNCTION OF E/N IN THE BUFFER GAS Ar AT 300 K (from Spyrou and Christophorou, 1985b)
E/N (10-~TVcm 2)
<e> (eV)
E/N (10-~7 Vcm2)
<e> (eV)
0.0932 0.109 0.124 0.155 0.186 0.217 0.249 0.311 0.373 0.466 0.528 0.621 0.777
0.764 0.822 0.876 0.976 1.07 1.15 1.23 1.37 1.50 1.67 1.77 1.92 2.14
0.932 1.097 1.24 1.55 1.86 2.17 2.49 2.79 3.11 3.42 3.73 4.04 4.35
2.33 2.52 2.69 3.00 3.29 3.55 3.80 4.03 4.26 4.43 4.58 4.71 4.81
TABLE A.II MEAN ELECTRON ENERGIES <~;> AS A FUNCTION OF E/N IN Tim BUFFER GAS N 2 AT 300, 400, 500, 600, 700, AND 750 K (from Datskos et al., 1990, 1992a)
E/N (10-1v Vcm 2)
<e> (eV) 300K
<e> (eV) 400K
<e> (eV) 500K
<e> (eV) 600K
<e> (eV) 700K
<e> (eV) 750K
0.062 0.093 0.124 0.155 0.186 0.217 0.248 0.310 0.373 0.457 0.528 0.621 0.776 0.931 1.087 1.24 1.55 1.86 2.17 2.48 3.10 3.73 4.66 5.28 6.21
0.046 0.055 0.065 0.076 0.087 0.099 0.111 0.133 0.154 0.184 0.204 0.231 0.279 0.327 0.374 0.417 0.493 0.555 0.601 0.647 0.711 0.759 0.812 0.839 0.872
0.058 0.065 0.075 0.085 0.096 0.107 0.118 0.138 0.159 0.189 0.213 0.235 0.283 0.330 0.376 0.419 0.494 0.555 0.601 0.647 0.711 0.759 0.812 0.839 0.872
0.070 0.076 0.085 0.095 0.104 0.115 0.125 0.144 0.164 0.193 0.217 0.238 0.286 0.333 0.378 0.421 0.495 0.556 0.601 0.647 0.711 0.759 0.812 0.839 0.872
0.083 0.086 0.096 0.104 0.113 0.123 0.132 0.144 0.168 0.198 0.221 0.242 0.289 0.336 0.381 0.423 0.496 0.556 0.601 0.647 0.711 0.759 0.812 0.839 0.872
0.092 0.097 0.104 0.112 0.121 0.130 0.139 0.157 0.176 0.202 0.221 0.249 0.296 0.343 0.388 0.429 0.503 0.556 0.601 0.647 0.711 0.759 0.812 0.839 0.872
0.097 0.102 0.108 0.116 0.124 0.133 0.142 0.160 0.178 0.204 0.223 0.250 0.297 0.344 0.389 0.431 0.504 0.556 0.602 0.647 0.711 0.759 0.812 0.839 0.872
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Index
A Alkali metals, electron scattering by excited atoms inelastic, 186-187 total and elastic, 172-173 AMS, s e e Appearance potential mass spectroscopy Appearance potential mass spectroscopy, 102 Ar, and H zAr, ERC downstream plasmas, with CF 2 radical injection, 116-119 Ar*, electron-impact ionization, 208210 Ar*(43P2 + 43Po), total and elastic electron scattering, 168-172 Atomic electric dipole polarizability, dependence of total electron scattering cross section on, 173-176 Atoms excited alkali metals electron scattering, 172-173 inelastic electron scattering, 186187 differential electron scattering from elastic, 190-191 inelastic, 191-196 alkali metals, 186-187 cross sections, definition, 177178 rare gases, 178-186 superelastic, 188-189, 197-200 total and elastic alkali metals, 172-173 rare gases, 162-172 total electron scattering cross section, dependence on atomic electric dipole polarizability, 173-176 electron-impact ionization of, 200202 Ba*, 211
H*, 210-211 rare gases, 203-210 Sr*, 211 hydrogen and nitrogen, measurement with MPLIF, 107-108
Ba*
differential inelastic scattering cross sections, 196-197 electron-impact ionization, 211 Boltzmann equation, 93-94, 130, 134, 146, 149 Born approximation, 37, 44-45, 180 C Capacitively coupled RF plasma, CF x radical densities in, comparison with ICP, 119-120 CARS, s e e Coherent anti-Stokes Raman spectroscopy CC14, ro-vibrationally excited, electron attachment to, 248-250 CC12F2, negative ion states, 76 C3F6, ro-vibrationally excited, electron attachment to, 252-254 C3F8, ro-vibrationally excited, electron attachment to, 252-254 CF 4 below l eV, recommended total electron scattering cross section, determination, 68-70 momentum transfer for, determination of recommended cross section, 67-68 vibrational excitation cross section, 73-74 n-C4 F1 o, ro-vibrationally excited, electron attachment to, 254-255 CFzC1 , ro-vibrationally excited, electron attachment to, 248-250
295
296
INDEX
CF3C1, ro-vibrationally excited, electron attachment to, 248-250 CFC1 a, ro-vibrationally excited, electron attachment to, 248-250 CFx, radical densities, 108-113 CFx radicals densities in ICP and CCP, 119-120 injection, in control of SiO etching, 114-119 measurements in plasma processing, representative results, 108 behaviors in on-off modulated plasmas, 111-114 characteristics in ECR fluorocarbon plasmas, 111 CHaBr, ro-vibrationally excited, electron attachment to, 244-245 1,1-C2H4C12, ro-vibrationally excited, electron attachment to, 250-252, 252-254 CH2C12, ro-vibrationally excited, electron attachment to, 245 C2H3C1 , ro-vibrationally excited, electron attachment to, 250-252 C2H5C1 , ro-vibrationally excited, electron attachment to, 250-252 CH3C1, ro-vibrationally excited, electron attachment to, 243-244 CHC1 a, ro-vibrationally excited, electron attachment to, 248 CHF 3, 79-80 CzHsSH* , electronically excited, dissociative electron attachment to, 277-279 C12, ro-vibrationally excited, electron attachment to, 237-238 C14 electron-impact cross sections, 73 recommended total electron attachment cross section for, determination, 70-72 CO2, vibrationally excited, electron scattering cross section, 215-218 Coefficients, assessed, 63-64 density-reduced effective ionyization, 93 density-reduced electron attachment, 92 density-reduced electron-impact ionization coefficient, 92
elastic integral electron scattering cross section, 91 lateral electron diffusion, ratio to electron mobility, 93 Coherent anti-Stokes Raman spectroscopy, 102 Collisional reaction time, 132 Collisions, electron data assessed cross sections and coefficients, 63-64 density-reduced effective ionization coefficient, 93 density-reduced electron attachment coefficient, 92 density-reduced electron-impact ionization coefficient, 92 elastic integral electron scattering cross section, 91 electron drift velocity, 93 momentum transfer cross section, 91 ratio of lateral electron diffusion coefficient to electron mobility, 93 total cross section for dissociation into neutrals, 91 total dissociation cross section, 91 total electron attachment cross section, 92 total electron attachment rate constant, 93 total electron scattering cross section, 83-91 total ionization cross section, 92 Boltzmann-code-generated collision cross-section sets, 93-95 diagnostic techniques, 63-64 environmental applications, 63-64 plasma models, 62-63 data assessment process, 65 CF4 below leV, recommended total electron scattering cross section, 68-70 momentum transfer for, determination of recommended cross section, 67-68
INDEX C14, recommended total electron attachment cross section, 70-72 consistency between cross sections, 70-72 database dissemination and updating, 83 deduction of unavailable data, 72 from assessed knowledge, 72-76 better understanding from assessed knowledge, 76-78 data needs, determination, 79-82 in discharges and plasmas, major characteristics, 3-6 elastic versus inelastic, 6-7 Cross-sections, electron collision atomic and molecular processes, 6-8 Boltzmann-code-generated, 93-95 CO 2, 51-52 data assessed cross sections and coefficients, 63-64 elastic integral electron scattering cross section, 91 momentum transfer cross section, 91 total cross section for dissociation into neutrals, 91 total dissociation cross section, 91 total electron attachment cross section, 92 total electron scattering cross section, 83-91 data assessment process CF 4 below l eV, recommended total electron scattering cross section, 68-70 momentum transfer for, determination of recommended cross section, 67-68 C14, recommended total electron attachment cross section, 70-72 consistency between cross sections, 70-72 database, 83 definition, 177-178 differential measurement over complete range of scattering angles, 21 elastic scattering, 7
297
energy dependence, determination, 19 measurement and illustrative results, 8-23 electron beam attenuation for determination of upper bound, 10-13 electron beam method, for angular dependence of excitation process, 15-23 swarm method, 13-15 partial, measurement with appearance potential in mass spectrometry, 23-25 positive/negative ion production, measurement dissociative electron attachment, 27-28 ionization process, 25 total electron scattering, dependence on atomic electric dipole polarizability, 173-176 CS2", electronically excited, dissociative electron attachment to, 277
D D z, ro-vibrationally excited, electron attachment to, 230 DC1, ro-vibrationally excited, electron attachment to, 239-240 Diatomic molecules, ro-vibrationally excited, electron attachment to, 230-240 Dielectric relaxation time, 152 Dissociative electron attachment to electronically excited molecules, 270-280 HC1, 54
ECR, s e e Electron cyclotron resonance plasma Elastic scattering cross section, 7, 17 Electron attachment, to excited molecules, 226-227 electronically excited molecules, 268270 dissociative electron attachment, 270-279
298
INDEX
Electron attachment (Continued) nondissociative electron attachment, 280-282 vibrationally/rotationally excited molecules, 228-229 dissociative electron attachment, 230-259 nondissociative electron attachment, 259-268 Electron attachment process, 27 Electron beam method, for angular dependence of excitation process, 15 differential cross section measurement over complete range of scattering angles, 21 elastic scattering, differential cross section for, 17 electron spectroscopy at ultrahigh resolution, 21-23 scattering of electron of ultralow energies, 23 vibrational excitation and resonance phenomena, 17-19 Electron collisions data assessed cross sections and coefficients, 63-64 density-reduced effective ionization coefficient, 93 density-reduced electron attachment coefficient, 92 elastic integral electron scattering cross section, 91 electron drift velocity, 93 momentum transfer cross section, 91 ratio of lateral electron diffusion coefficient to electron mobility, 93 total cross section for dissociation into neutrals, 91 total dissociation cross section, 91 total electron attachment cross section, 92 total electron scattering cross section, 83-91 total ionization cross section, 92 Boltzmann-code-generated collision cross-section sets, 93-95
diagnostic techniques, 63-64 environmental applications, 63-64 data assessment process, 65 CF4 below leV, recommended total electron scattering cross section, 68-70 momentum transfer for, determination of recommended cross section, 67-68 C14, recommended total electron attachment cross section, 70-72 consistency between cross sections, 70-72 database dissemination and updating, 83 deduction of unavailable data, 72 from assessed knowledge, 72-76 better understanding from assessed knowledge, 76-78 data needs, determination, 79-82 in discharges and plasmas, major characteristics, 3-6 elastic versus inelastic, 6-7 eleastic versus inelastic, 6-7 Electron cyclotron resonance plasma, 108 fluorocarbon, CF x radicals in, characteristics, 108-111 H2Ar, with C F 2 radical injection, 116-119 Electron energy distributions, 62 Electron-impact ionization of excited atoms, 200-202 Ba*, 211 H*, 210-211 rare gases, 203-210 Sr*, 211 of excited molecules, 223-226 Electron-molecule interactions, 45-46 exchange interactions, 48-49 static and correlation-polarization interaction, 46-48 Electron molecule scattering, 34 N 2 molecules, 35-37 resonance, 35-37 Electron scattering from excited atoms differential scattering elastic scattering, 190-191
INDEX inelastic scattering, 191-196 superelastic scattering, 197-200 inelastic scattering alkali metals, 186-187 cross sections, definition, 177178 rare gases, 178-186 superelastic scattering, 188-189 total and elastic scattering alkali metals, 172-173 rare gases, 162-172 total electron scattering cross section, dependence on atomic electric dipole polarizability, 173-176 from excited molecules, 213-215 slow electrons from electronically excited molecules, 218-220 slow electrons from vibrationally/ rotationally excited molecules, 215-218 superelastic scattering of slow electrons from excited molecules, 221-222 vibrational excitation effects on electron transport, 222-223 N 2 molecules, 35-37 of ultralow energies, 23 Electron spectroscopy, at ultrahigh resolution, 21-23 Excited molecules electron attachment to electronically excited molecules, 268-270 dissociative electron attachment, 270-279 nondissociative electron attachment, 280-282 to excited molecules, 226-227 vibrationally/rotationally excited molecules, 228-229 dissociative electron attachment, 230-259 nondissociative electron attachment, 259-268 electron scattering from, 213-215 slow electrons from electronically excited molecules, 218-220 slow electrons from vibrationally/ rotationally excited molecules, 215-218
299 superelastic scattering of slow electrons from excited molecules, 221-222 vibrational excitation effects on electron transport, 222-223
ro-vibrationally excited, electron attachment to, 233-235 Feshbach resonance, in electron N 2 molecule scattering, 36 Fourier-transform mass spectroscopy, CHF 3, 80 F z,
H
H*, electron-impact ionization, 210-211 H*(2s), electron-impact ionization, 210-211 H z* , electronically excited, dissociative electron attachment to, 270-271 H2, ro-vibrationally excited, electron attachment to, 230 Halogenated compounds, rovibrationally excited, electron attachment to, 243-255 HzAr, ERC downstream plasmas, with C F 2 radical injection, 116-119 HC1, ro-vibrationally excited, electron attachment to, 239-240 He*, electron-impact excitation, differential cross sections, 194 He*(21S) electron-impact ionization, 205 total and elastic electron scattering, 167-168 He*(23S) electron-impact ionization, 203-205 total and elastic electron scattering, 162-167 HF, ro-vibrationally excited, electron attachment to, 238-239
s e e Capacitively coupled RF plasma ICLAS, s e e Intracavity laser absorption spectroscopy
ICC,
300
INDEX
ICP, see Inductively coupled RF plasma Inductively coupled RF plasma CF x radical densities in, comparison with CCP, 119-120 fluid model of, 151 Infrared diode laser absorption spectroscopy, 100, 102-105 Intracavity laser absorption spectroscopy, 101, 106 Ionization density-reduced effective coefficient, 93 electron-impact of excited atoms, 200-202 Ba*, 211 H*, 210-211 rare gases, 203-210 Sr*, 211 of excited molecules, 223-226 total cross section, 92 Ion production, cross section measurement for dissociative electron attachment, 27-28 ionization process, 25 IRLAS, see Infrared diode laser absorption spectroscopy J Journal o f Physical and Chemical Reference Data, 83
K
Kr*, electron-impact ionization, 208210
Lambert-Beer law, 10 LAS, see Laser absorption spectroscopy Laser absorption spectroscopy, 101 in radical measurement infrared diode LAS, 102-105 intracavity LAS, 106 ring dye LAS, 106 Laser-induced fluorescence spectroscopy, 101, 106-108 Laser optogalvanic spectroscopy, 102
Li2, ro-vibrationally excited, electron attachment to, 230-232, 231-232 LIF, see Laser-induced fluorescence spectroscopy Local field approximation model, for radio-frequency plasma modeling, 142-144 LOGS, see Laser optogalvanic spectroscopy
M
Mass spectrometry, with appearance potential, in measurement of partial cross-sections, 23-25 Maxwell's equation, 151 MLIF, see Modified laser-induced fluorescence spectroscopy Modified laser-induced fluorescence spectroscopy, 101 Molecules electron interactions, 45-46 exchange interactions, 46-48 static and correlation-polarization interaction, [46-48 electron scattering, 34-35
N2, 35-37 excited electron attachment to, 226-227 electronically excited molecules, 268-270 dissociative electron attachment, 270-279 nondissociative electron attachment, 280-282 vibrationally/rotationally excited molecules, 228-229 dissociative electron attachment, 230-259 nondissociative electron attachment, 259-268 electron-impact ionization, 223-226 electron scattering from, 213-215 slow electrons from electronically excited molecules, 218-220 slow electrons from vibrationally/ rotationally excited molecules, 215-218
INDEX superelastic scattering of slow electrons from excited molecules, 221-222 vibrational excitation effects on electron transport, 222-223 scattering dynamics, 54 Momentum transfer, for CF4, determination of recommended cross section, 67-68 Monte Carlo simulation, 147, 149 MPLIF, s e e Multiphoton excitation laser-induced fluorescence spectroscopy Multichannel interference, in electron N 2 molecule scattering, 36 Multiphoton excitation laser-induced fluorescence spectroscopy, 101 N Na2, ro-vibrationally excited, electron attachment to, 235-237 Ne*(3 3P2,o), electron-impact ionization, 205-208 NO*, electronically excited, dissociative electron attachment to, 273-274 N20 , vibrationally excited, electron scattering cross section, 215-218 Nondissociative electron attachment, 27, 259, 263-268 data on, 280-282 Nonequilibrium glow discharges, simulation, 143 O electronically excited, dissociative electron attachment to, 271-273 O2, ro-vibrationally excited, electron attachment to, 232-233 OAS, s e e Optical absorption spectroscopy OES, s e e Optical emmission spectroscopy Optical absorption spectroscopy, 100 Optical emmission spectroscopy, 100 02* ,
P
Plasma chemical-vapor deposition, 2
301
Plasma display panel, 2, 4 Plasma etching, low-temperature, 33-34 electron-molecule interactions, 37-49, 45-49 Plasma phenomena, initiation, 3 Plasma processing, 5-6 gases, 61-62 diagnostic techniques, 63-64 environmental applications, 64 plasma models, 62-63 low-temperature, radio-frequency plasma modeling for, 127-128 direct numerical procedure, 136141 expansion procedure, 132-136 governing equations hybrid model, 147-149 local field approximation model, 142-144 quasithermal equilibrium model, 144-145 relaxation continuum model, 146-147 system equations in inductively coupled plasma, 149-152 semiquantitative theory, 130-132 processes electron-molecule interactions, 4546 exchange interactions, 48-49 static and correlationpolarization interaction, 46-48 excited species, 53-55 theoretical approaches, current accuracy, 49- 53 theoretical framework, overview electron molecule scattering, 3435 N 2 molecules, 35-37 general scattering theory, 37-38 close-coupling scheme, 39-40 continuum multiple-scattering method, 41-42 R-matrix method, 41 variational methods, 40-41 zero-energy limit, 42-44 radical measurements in in s i t u methods, 102 laser absorption spectroscopy infrared diode LAS, 102-105
302
INDEX
Plasma processing (Continued) intracavity LAS, 106 ring dye LAS, 106 laser-induced fluorescence spectroscopy, 106-108 representative results CF~ radicals behaviors in on-off modulated plasmas, 111-114 characteristics in ECR fluorocarbon plasmas, 108, 111 densities in ICP and CCP, 119120 injection, in control of SiO etching, 114-119 SiH~ radicals, 120-123 summary of recent developments, 100-102 Plasmas ECR fluorocarbon, CF~ radicals in, characteristics, 108-111 electron density in, 63 inductively coupled, system equations in, 149-152 on-off modulated, CFx radicals in, behaviors, 111-114 RF, inductively and capacitively coupled. CF x radical densities, 119 Poisson's equation, 143, 152
Quasithermal equilibrium model, for radio-frequency plasma modeling, 144-145
Radical injection technique, experimental apparatus for, 114-115 Radical measurements, in plasma processing in situ methods, 102 laser absorption spectroscopy infrared diode LAS, 102-105 intracavity LAS, 106 ring dye LAS, 106 laser-induced fluorescence spectroscopy, 106-108
representative results CF x radicals behaviors in on-off modulated plasmas, 111-114 characteristics in ECR fluorocarbon plasmas, 108, 111 densities in ICP and CCP, 119120 injection, in control of SiO etching, 114-119 SiHx radicals, 120-123 summary of recent developments, 100-102 Radio-frequency electron transport theory, for low-temperature processing, 128-130 direct numerical procedure, 136-141 expansion procedure, 132-136 semiquantitative theory, 130-132 Radio-frequency glow discharges, 127128 Radio-frequency plasma, modeling governing equations hybrid model, 147-149 local field approximation model, 142-144 quasithermal equilibrium model, 144-145 relaxation continuum model, 146147 system equations in inductively coupled plasma, 149-152 methods, 141-142 Ramsauer-Townsend effect, 9, 10, 23, 38 in electron N 2 molecule scattering, 36 Rare gases, electron-impact ionization, 203-210 Rate constants atomic and molecular processes, 6-8 Sill reactions, 5 total electron attachment, 93 Reactions, in discharges and plasmas, major characteristics, 3-6 Relaxation continuum model, for radiofrequency plasma modeling, 146147 Resonance, in electron N 2 molecule scattering, 36 Ring dye laser absorption spectroscopy, 101, 106
INDEX RIT, s e e Radical injection technique RLAS, s e e Ring dye laser absorption spectroscopy R-matrix method, 40-41, 51, 180, 181, 186 Rn*, electron-impact ionization, 208210 S
Scattering amplitude, 7 Scattering length theory, 42-44 Scattering theory, 8, 38-39 Born approximation, 44-45 close-coupling scheme, 39-40 continuum multiple-scattering method, 41-42 general, 38 close-coupling scheme, 39-40 continuum multiple-scattering method, 41-42 perturbative treatment, 44-45 R-matrix method, 41 variational methods, 40-41 zero-energy limit, 42-44 R-matrix method, 41 scattering length theory, 42-44 vibrational methods, 40-41 Semiquantitative theory, radiofrequency electron transport, 130132 SF6, ro-vibrationally excited, electron attachment to, 256-259 Shape resonance, in electron N 2 molecule scattering, 36 Sill4, cross sections, 13-14 Sill x radicals, measurements in plasma processing, representative results, 108, 120-123 SiO, etching control by radical injection
303
CF 2 radicals, ECR Ar and H2Ar downstream plasmas, 116 CF x radical densities, in ICP and CCP, 119 experimental apparatus for radical injection technique, 114-115 rates, 113-114 SO~', electronically excited, dissociative electron attachment to, 275-277 SO 2, ro-vibrationally excited, electron attachment to, 242-243 802F2, ro-vibrationally excited, electron attachment to, 255-256 Sr*, electron-impact ionization, 211 Swarm method, 13-15
Time-resolved electron swarm technique, 266-267 Triatomic molecules, ro-vibrationally excited, electron attachment to, 240-243 V Vibrational excitation, 17-19, 51, 52-53, 77 W
Wigner cusp, in electron N 2 molecule scattering, 36 X
Xe*, electron-impact ionization, 208210 Xe, pressure, and Sill radical densities, 122
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Contents of Volumes in This Serial Volume 1
Molecular Orbital Theory of the Spin Properties of Conjugated Molecules, G. G. Hall and A. T. Amos
Electron Affinities of Atoms and Molecules, B. L. Moiseiwitsch
Atomic Rearrangement Collisions, B. H. Bransden
Volume 3
The Quantal Calculation of Photoionization Cross Sections, A. L. Stewart Radiofrequency Spectroscopy of Stored Ions I: Storage, H. G. Dehmelt Optical Pumping Methods in Atomic Spectroscopy, B. Budick Energy Transfer in Organic Molecular Crystals: A Survey of Experiments, H. C. Wolf
The Production of Rotational and Vibrational Transitions in Encounters between Molecules, K. Takayanagi
Atomic and Molecular Scattering from Solid Surfaces, Robert E. Stickney
The Study of Intermolecular Potentials with Molecular Beams at Thermal Energies,
Quantum Mechanics in Gas Crystal-Surface van der Waals Scattering, E. Chanoch
H. Pauly and J. P. Toennies
High-Intensity and High-Energy Molecular Beams, J. B. Anderson, R. P. Andres, and J.
Beder
Reactive Collisions between Gas and Surface Atoms, Henry Wise and Bernard J. Wood
B. Fen
Volume 2
The Calculation of van der Waals Interactions, A. Dalgarno and W. D.
Volume 4
H. S. W. Massey--A Sixtieth Birthday Tribute, E. H. S. Burhop Electronic Eigenenergies of the Hydrogen Molecular Ion, D. R. Bates and R. H. G.
Davison
Thermal Diffusion in Gases, E. A. Mason, R.
Reid
J. Munn, and Francis J. Smith
Applications of Quantum Theory to the Viscosity of Dilute Gases, R. A.
Spectroscopy in the Vacuum Ultraviolet, W. R. S. Garton
Buckingham and E. Gal
The Measurement of the Photoionization Cross Sections of the Atomic Gases, James
Positrons and Positronium in Gases, P. A. Fraser
A. R. Samson
Classical Theory of Atomic Scattering, A. Burgess and I. C. Percival
The Theory of Electron-Atom Collisions, R. Peterkop and V. Veldre
Born Expansions, A. R. Holt and B. L. Moiselwitsch
Experimental Studies of Excitation in Collisions between Atomic and Ionic Systems, F. J. de Heer
Resonances in Electron Scattering by Atoms and Molecules, P. G. Burke
Mass Spectrometry of Free Radicals, S. N.
Relativistic Inner Shell Ionizations, C. B. O. Mohr
Foner
305
306
CONTENTS OF VOLUMES IN THIS SERIAL
Recent Measurements on Charge Transfer, J. B. Hasted Measurements of Electron Excitation Functions, D. W. O. Heddle and R. G. W. Keesing Some New Experimental Methods in Collision Physics, R. F Stebbings Atomic Collision Processes in Gaseous Nebulae, M. J. Seaton
The Diffusion of Atoms and Molecules, E. A. Mason and T. R. Marrero Theory and Application of Sturmian Functions, Manuel Rotenberg Use of Classical Mechanics in the Treatment of Collisions between Massive Systems, D. R. Bates and A. E. Kingston
Collisions in the Ionosphere, A. Dalgarno
Volume 7
The Direct Study of Ionization in Space, R. L. F Boyd
Physics of the Hydrogen Master, C. Audo&, J. P. Schermann, and P. Grivet Molecular Wave Functions: Calculations and Use in Atomic and Molecular Processes, J. C Browne
Volume 5
Flowing Afterglow Measurements of IonNeutral Reactions, E. E. Ferguson, F C. Fehsenfeld, and A. L. Schmeltekopf Experiments with Merging Beams, Roy H. Neynaber Radiofrequency Spectroscopy of Stored Ions II: Spectroscopy, H. G. Dehmelt The Spectra of Molecular Solids, O. Schnepp The Meaning of Collision Broadening of Spectral Lines: The Classical Oscillator Analog, A. Ben-Reuven The Calculation of Atomic Transition Probabilities, R. J. S. Crossley Tables of One- and Two-Particle Coefficients of Fractional Parentage for Configurations S~S'upq, C. D. H. Chisholm, A. Dalgarno, and E. R. Innes
Localized Molecular Orbitals, Harel Weinstein, Ruben Pauncz, and Maurice Cohen General Theory of Spin-Coupled Wave Functions for Atoms and Molecules, J. Gerratt Diabatic States of Molecules--QuasiStationary Electronic States, Thomas F. O'Malley Selection Rules within Atomic Shells, B. R. Judd Green's Function Technique in Atomic and Molecular Physics, Gy. Csanak, H. S. Taylor, and Robert Yaris A Review of Pseudo-Potentials with Emphasis on Their Application to Liquid Metals, Nathan Wiser and A. J. GreenfieM
Relativistic Z-Dependent Corrections to Atomic Energy Levels, Holly Thomis Doyle
Volume 8
Volume 6
Interstellar Molecules: Their Formation and Destruction, D. McNally
Dissociative Recombination, J. N. Bardsley and M. A. Biondi
Monte Carlo Trajectory Calculations of Atomic and Molecular Excitation in Thermal Systems, James C. Keck
Analysis of the Velocity Field in Plasmas from the Doppler Broadening of Spectral Emission Lines, A. S. Kaufman
Nonrelativistic Off-Shell Two-Body Coulomb Amplitudes, Joseph C. Y. Chen and Augustine C. Chen
The Rotational Excitation of Molecules by Slow Electrons, Kazuo Takayanagi and Yukikazu Itikawa
Photoionization with Molecular Beams, R. B. Cairns, Halstead Harrison, and R. I. Schoen
CONTENTS OF VOLUMES IN THIS SERIAL The Auger Effect, E. H. S. Burhop and W. N. Asaad
307
Scattering: An Information-Theoretic Approach, R. B. Bernstein and R. D. Levine
Volume 9
Inner Shell Ionization by Incident Nuclei, Johannes M. Hansteen
Correlation in Excited States of Atoms, A. W Weiss The Calculation of Electron-Atom Excitation Cross Sections, M. R. H. Rudge
Chemiluminescence in Gases, M. F. Golde and B. A. Thrush
Collision-Induced Transitions between Rotational Levels, Takeshi Oka
Volume 12
The Differential Cross Section of Low-Energy Electron-Atom Collisions, D. Andrick Molecular Beam Electric Resonance Spectroscopy, Jens C. Zorn and Thomas C. English Atomic and Molecular Processes in the Martian Atmosphere, Michael B. McElroy
Volume 10
Relativistic Effects in the Many-Electron Atom, Lloyd Annstrong, Jr. and Serge Feneuille The First Born Approximation, K. L. Bell and A. K. Kingston Photoelectron Spectroscopy, W C. Price Dye Lasers in Atomic Spectroscopy, W. Lange, J. Luther, and A. Steudel Recent Progress in the Classification of the Spectra of Highly Ionized Atoms, B. C. Fawcett A Review of Jovian Ionospheric Chemistry, Wesley T. Huntress, Jr.
Stark Broadening, Hans R. Griem
Nonadiabatic Transitions between Ionic and Covalent States, R. K. Janev Recent Progress in the Theory of Atomic Isotope Shift, J. Bauche and R.-J. Champeau Topics on Multiphoton Processes in Atoms, P. Lambropoulos Optical Pumping of Molecules, M. Broyer, G. Goudedard, J. C. Lehmann, and J. ViguO Highly Ionized Ions, Ivan A. Sellin Time-of-Flight Scattering Spectroscopy, Wilhelm Raith Ion Chemistry in the D Region, George C. Reid
Volume 13
Atomic and Molecular Polarizabilities-- A Review of Recent Advances, Thomas M. Miller and Benjamin Bederson Study of Collisions by Laser Spectroscopy, Paul R. Berman
Volume 11
Collision Experiments with Laser-Excited Atoms in Crossed Beams, I.V. Hertel and W Stoll
The Theory of Collisions between Charged Particles and Highly Excited Atoms, I. C. Percival and D. Richards
Scattering Studies of Rotational and Vibrational Excitation of Molecules, Manfred Faubel and J. Peter Toennies
Electron Impact Excitation of Positive Ions, M. J. Seaton The R-Matrix Theory of Atomic Process, P. G. Burke and W. D. Robb
Low-Energy Electron Scattering by Complex Atoms: Theory and Calculations, R. K. Nesbet
Role of Energy in Reactive Molecular
Microwave Transitions of Interstellar Atoms and Molecules, W B. Somerville
308
C O N T E N T S O F V O L U M E S IN THIS SERIAL
Volume 14
Resonances in Electron Atom and Molecule Scattering, D. E. Golden The Accurate Calculation of Atomic Properties by Numerical Methods, Brian
Inner-Shell Ionization, E. H. S. Burhop Excitation of Atoms by Electron Impact, D. W. O. Heddle
Coherence and Correlation in Atomic Collisions, H. Kleinpoppen
C. Webster, Michael J. Jamieson, and Ronald E. Stewart (e, 2e) Collisions, Erich Weigold and Ian E. McCarthy
Theory of Low Energy Electron-Molecule Collisions, P. G. Burke
Forbidden Transitions in One- and TwoElectron Atoms, Richard Marrus and Peter
Volume 16
J. Mohr
Semiclassical Effects in Heavy-Particle Collisions, M. S. Child Atomic Physics Tests of the Basic Concepts in Quantum Mechanics, Francis M. Pipkin Quasi-Molecular Interference Effects in IonAtom Collisions, S. V. Bobashev
Atomic Hartree-Fock Theory, M. Cohen and R. P. McEachran
Experiments and Model Calculations to Determine Interatomic Potentials, R. Diiren
Sources of Polarized Electrons, R. J. Celotta and D. T. Pierce
Rydberg Atoms, S. A. Edelstein and T. F.
Theory of Atomic Processes in Strong Resonant Electromagnetic Fields, S. Swain
UV and X-Ray Spectroscopy in Astrophysics,
Spectroscopy of Laser-Produced Plasmas, M.
Gallagher
A. K. Dupree
Volume 15
Negative Ions, H. S. W. Massey Atomic Physics from Atmospheric and Astrophysical Studies, A. Dalgarno Collisions of Highly Excited Atoms, R. F. Stebbings
H. Key and R. J. Hutcheon
Relativistic Effects in Atomic Collisions Theory, B. L. Moiseiwitsch Parity Nonconservation in Atoms: Status of Theory and Experiment, E. N. Fortson and L. Wilets
Volume 17
Theoretical Aspects of Positron Collisions in Gases, J. W. Humberston
Collective Effects in Photoionization of Atoms, M. Ya. Amusia
Experimental Aspects of Positron Collisions in Gases, T. C. Griffith
Nonadiabatic Charge Transfer, D. S. F.
Reactive Scattering: Recent Advances in Theory and Experiment, Richard B.
Atomic Rydberg States, Serge Feneuille and
Bernstein
Ion-Atom Charge Transfer Collisions at Low Energies, J. B. Hasted Aspects of Recombination, D. R. Bates The Theory of Fast Heavy Particle Collisions, B. H. Bransden
Atomic Collision Processes in Controlled Thermonuclear Fusion Research, H. B. Gilbody
Crothers Pierre Jacquinot
Superfluorescence, M. F. H. Schuurmans, Q.
H. F. Vrehen, D. Polder, and H. M. Gibbs
Applications of Resonance Ionization Spectroscopy in Atomic and Molecular Physics, M. G. Payne, C. H. Chen, G. S. Hurst, and G. W. Foltz
Inner-Shell Vacancy Production in IonAtom Collisions, C. D. Lin and Patrick Richard
CONTENTS OF VOLUMES IN THIS SERIAL Atomic Processes in the Sun, P. L. Dufton and A. E. Kingston
309
The Vibrational Excitation of Molecules by Electron Impact, D. G. Thompson Vibrational and Rotational Excitation in Molecular Collisions, Manfred Faubel
Volume 18
Theory of Electron-Atom Scattering in a Radiation Field, Leonard Rosenberg
Spin Polarization of Atomic and Molecular Photoelectrons, N. A. Cherepkov
Positron-Gas Scattering Experiments, Talbert S. Stein and Walter E. Kauppila
Volume 20
Nonresonant Multiphoton Ionization of Atoms, J. Morellec, D. Normand, and G. Petite
Ion-Ion Recombination in an Ambient Gas, D. R. Bates
Classical and Semiclassical Methods in Inelastic Heavy-Particle Collisions, A. S. Dickinson and D. Richards Recent Computational Developments in the Use of Complex Scaling in Resonance Phenomena, B. R. Junker Direct Excitation in Atomic Collisions: Studies of Quasi-One-Electron Systems, N. Anderson and S. E. Nielsen Model Potentials in Atomic Structure, A. Hibbert Recent Developments in the Theory of Electron Scattering by Highly Polar Molecules, D. W. Norcross and L. A. Collins Quantum Electrodynamic Effects in FewElectron Atomic Systems, G. W. F Drake
Volume 19
Electron Capture in Collisions of Hydrogen Atoms with Fully Stripped Ions, B. H. Bransden and R. K. Janev Interactions of Simple Ion-Atom Systems, J. T. Park High-Resolution Spectroscopy of Stored Ions, D. J. Wineland, Wayne M. Itano, and R. S. Van Dyck, Jr.
Atomic Charges within Molecules, G. G. Hall Experimental Studies on Cluster Ions, T. D. Mark and A. W. Castleman, Jr. Nuclear Reaction Effects on Atomic InnerShell Ionization, W. E. Meyerhof and J.-F. Chemin Numerical Calculations on Electron-Impact Ionization, Christopher Bottcher Electron and Ion Mobilities, Gordon R. Freeman and David A. Armstrong On the Problem of Extreme UV and X-Ray Lasers, I. L. Sobel'man and A. V. Vinogradov Radiative Properties of Rydberg State, in Resonant Cavities, S. Haroche and J. M. Ralmond Rydberg Atoms: High-Resolution Spectroscopy and Radiation Interaction-Rydberg Molecules, J. A. C. Gallas, G. Leuchs, H. Walther, and H. Figger
Volume 21
Subnatural Linewidths in Atomic Spectroscopy, Dennis P. O'Brien, Pierre Meystre, and Herbert Walther Molecular Applications of Quantum Defect Theory, Chris H. Greene and Ch. Jungen
Spin-Dependent Phenomena in Inelastic Electron-Atom Collisions, K. Blum and H. Kleinpoppen
Theory of Dielectronic Recombination, Yukap Hahn
The Reduced Potential Curve Method for Diatomic Molecules and Its Applications, E. Jen~
Recent Developments in Semiclassical Floquet Theories for Intense-Field Multiphoton Processes, Shih-I Chu
310
C O N T E N T S O F V O L U M E S IN THIS SERIAL
Scattering in Strong Magnetic Fields, M. R. C. McDowell and M. Zarcone
Volume 24
Pressure Ionization, Resonances, and the Continuity of Bound and Free States, R. M. More
The Selected Ion Flow Tube (SIDT): Studies of Ion-Neutral Reactions, D. Smith and N. G. Adams Near-Threshold Electron-Molecule Scattering, Michael A. Morrison
Volume 22
Positronium--Its Formation and Interaction with Simple Systems, J. W. Humberston Experimental Aspects of Positron and Positronium Physics, T. C. Griffith
Angular Correlation in Multiphoton Ionization of Atoms, S. J. Smith and G. Leuchs Optical Pumping and Spin Exchange in Gas Cells, R. J. Knize, Z. Wu, and W. Happer Correlations in Electron-Atom Scattering, A. Crowe
Doubly Excited States, Including New Classification Schemes, C. D. Lin Measurements of Charge Transfer and Ionization in Collisions Involving Hydrogen Atoms, H. B. Gilbody Electron-Ion and Ion-Ion Collisions with Intersecting Beams, K. Dolder and B. Pearl Electron Capture by Simple Ions, Edward Pollack and Yukap Hahn Relativistic Heavy-Ion-Atom Collisions, R. Anholt and Harvey Gould Continued-Fraction Methods in Atomic Physics, S. Swain
Volume 23
Vacuum Ultraviolet Laser Spectroscopy of Small Molecules, C. R. Vidal Foundations of the Relativistic Theory of Atomic and Molecular Structure, Ian P. Grant and Harry M. Quiney Point-Charge Models for Molecules Derived from Least-Squares Fitting of the Electric Potential, D. E. Williams and Ji-Min Yan
Volume 25
Alexander Dalgarno: Life and Personality, David R. Bates and George A. Victor Alexander Dalgarno: Contributions to Atomic and Molecular Physics, Neal Lane Alexander Dalgarno: Contributions to Aeronomy, Michael B. McElroy Alexander Dalgarno: Contributions to Astrophysics, David A. Williams Dipole Polarizability Measurements, Thomas M. Miller and Benjamin Bederson Flow Tube Studies of Ion-Molecule Reactions, Eldon Ferguson Differential Scattering in He-He and He +He Collisions at KeV Energies, R. F. Stebbings Atomic Excitation in Dense Plasmas, Jon C. Weisheit Pressure Broadening and Laser-Induced Spectral Line Shapes, Kenneth M. Sando and Shih-I Chu Model-Potential Methods, G. Laughlin and G. A. Victor
Transition Arrays in the Spectra of Ionized Atoms, J. Bauche, C. Bauche-Arnoult, and M. Klapisch
Z-Expansion Methods, M. Cohen
Photoionization and Collisional Ionization of Excited Atoms Using Synchroton and Laser Radiation, E. J. Wuilleumier; D. L. Ederer, and J. L. Picquk
Fine-Structure Transitions in Proton-Ion Collisions, R. H. G. Reid
Schwinger Variational Methods, Deborah Kay Watson
C O N T E N T S O F V O L U M E S IN THIS SERIAL Electron Impact Excitation, R. J. W. Henry and A. E. Kingston Recent Advances in the Numerical Calculation of Ionization Amplitudes, Christopher Bottcher The Numerical Solution of the Equations of Molecular Scattering, A. C. Allison High Energy Charge Transfer, B. H. Bransden and D. P. Dewangan Relativistic Random-Phase Approximation, W. R. Johnson Relativistic Sturmian and Finite Basis Set Methods in Atomic Physics, G. W. F. Drake and S. P. Goldman Dissociation Dynamics of Polyatomic Molecules, T. Uzer
311
Volume 27
Negative Ions: Structure and Spectra, David R. Bates Electron Polarization Phenomena in Electron-Atom Collisions, Joachim Kessler Electron-Atom Scattering, I. E. McCarthy and E. Weigold Electron-Atom Ionization, I. E. McCarthy and E. Weigold Role of Autoionizing States in Multiphoton Ionization of Complex Atoms, V. /. Lengyel and M. I. Haysak Multiphoton Ionization of Atomic Hydrogen Using Perturbation Theory, E. Karule
Photodissociation Processes in Diatomic Molecules of Astrophysical Interest, Kate P. Kirby and Ewine F. van Dishoeck
Volume 28
The Abundances and Excitation of Interstellar Molecules, John. H. Black
The Theory of Fast Ion-Atom Collisions, J. S. Briggs and J. H. Macek
Volume 26
Comparisons of Positrons and Electron Scattering by Gases, Walter E. Kauppila and Talbert S. Stein
Some Recent Developments in the Fundamental Theory of Light, Peter W. Milonni and Surendra Singh Squeezed States of the Radiation Field, Khalid Zaheer and M. Suhail Zubairy Cavity Quantum, Electrodynamics, E. A. Hinds
Electron Capture at Relativistic Energies, B. L. Moiseiwitsch The Low-Energy, Heavy Particle Collisions-- A Close-Coupling Treatment, Mineo Kimura and Neal F. Lane Vibronic Phenomena in Collisions of Atomic and Molecular Species, V. Sidis Associative Ionization: Experiments, Potentials, and Dynamics, John Weiner, Franfoise Masnou-Sweeuws, and Annick Giusti-Suzor On the J3 Decay of 187Re: An Interface of Atomic and Nuclear Physics and Cosmochronology, Zonghau Chen, Leonard Rosenberg, and Larry Spruch Progress in Low Pressure Mercury-Rare Gas Discharge Research, J. Maya and R. Lagushenko
Volume 29
Studies of Electron Excitation of Rare-Gas Atoms into and out of Metastable Levels Using Optical and Laser Techniques, Chun C. Lin and L. W. Anderson Cross Sections for Direct Multiphoton Ionization of Atoms, M. V. Ammosov, N. B. Delone, M. Yu. Ivanov, I. I. Bondar, and A. V. Masalov Collision-Induced Coherences in Optical Physics, G. S. Agarwal Muon-Catalyzed Fusion, Johann Rafelski and Helga E Rafelski Cooperative Effects in Atomic Physics, J. P. Connerade
312
CONTENTS OF VOLUMES IN THIS SERIAL
Multiple Electron Excitation, Ionization, and Transfer in High-Velocity Atomic and Molecular Collisions, J. H. McGuire
Volume 30
Differential Cross Sections for Excitation of Helium Atoms and Helium-Like Ions by Electron Impact, Shinobu Nakazaki Cross-Section Measurements for Electron Impact on Excited Atomic Species, S. Trajmar and J. C. Nickel The Dissociative Ionization of Simple Molecules by Fast Ions, Colin J. Latimer Theory of Collisions between Laser Cooled Atoms, P. S. Julienne, A. M. Smith, and K. Burnett Light-Induced Drift, E. R. Eliel
Electron-Atom Scattering Theory and Calculations, P. G. Burke Terrestrial and Extraterrestrial H3 +, Alexander Dalgarno Indirect Ionization of Positive Atomic Ions, K Dolder Quantum Defect Theory and Analysis of High-Precision Helium Term Energies, G. W. F Drake Electron-Ion and Ion-Ion Recombination Processes, M. R. Flannery Studies of State-Selective Electron Capture in Atomic Hydrogen by Translational Energy Spectroscopy, H. B. Gilbody Relativistic Electronic Structure of Atoms and Molecules, I. P. Grant The Chemistry of Stellar Environments, D. A. Howe, J. M. C. Rawlings, and D. A. Williams
Continuum Distorted Wave Methods in IonAtom Collisions, Derrick S. F. Crothers and Louis J. Dubk
Positron and Positronium Scattering at Low Energies, J. W. Humberston
Volume 31
Adiabatic Expansions and Nonadiabatic Effects, R. McCarroll and D. S. F. Crothers
Energies and Asymptotic Analysis for Helium Rydberg States, G. W. F. Drake Spectroscopy of Trapped Ions, R. C. Thompson Phase Transitions of Stored Laser-Cooled Ions, H. Walther Selection of Electronic States in Atomic Beams with Lasers, Jacques Baudon, Rudolf Diiren, and Jacques Robert Atomic Physics and Non-Maxwellian Plasmas, Michkle Lamoureux
Volume 32
How Perfect are Complete Atomic Collision Experiments?, H. Kleinpoppen and H. Handy
Electron Capture to the Continuum, B. L Moiseiwitsch How Opaque Is a Star? M. J. Seaton Studies of Electron Attachment at Thermal Energies Using the Flowing AfterglowLangmuir Technique, David Smith and Patrik Spangl Exact and Approximate Rate Equations in Atom-Field Interactions, S. Swain Atoms in Cavities and Traps, H. Walther Some Recent Advances in Electron-Impact Excitation of n = 3 States of Atomic Hydrogen and Helium, J. F. Williams and J. B. Wang
Photoionization of Atomic Oxygen and Atomic Nitrogen, K. L. Bell and A. E. Kingston
Volume 33
Positronium Formation by Positron Impact on Atoms at Intermediate Energies, B. H. Bransden and C. J. Noble
Principles and Methods for Measurement of Electron Impact Excitation Cross Sections for Atoms and Molecules by Optical
C O N T E N T S OF V O L U M E S IN THIS SERIAL Techniques, A. R. Filippelli, Chun C. Lin, L. W. Andersen, and J. W. McConkey Benchmark Measurements of Cross Sections for Electron Collisions: Analysis of Scattered Electrons, S. Trajmar and J. W. McConkey Benchmark Measurements of Cross Sections for Electron Collisions: Electron Swarm Methods, R. W. Crompton Some Benchmark Measurements of Cross Sections for Collisions of Simple Heavy Particles, H. B. Gilbody
313
Polarization and Orientation Phenomena in Photoionization of Molecules, N. A. Cherepkov Role of Two-Center Electron-Electron Interaction in Projectile Electron Excitation and Loss, E. C. Montenegro, W. E. Meyerhof and J. H. McGuire Indirect Processes in Electron Impact Ionization of Positive Ions, D. L. Moores and K. J. Reed Dissociative Recombination: Crossing and Tunneling Modes, David R. Bates
The Role of Theory in the Evaluation and Interpretation of Cross-Section Data, Barry I. Schneider
Volume 35
Analytic Representation of Cross-Section Data, Mitio Inokuti, Mineo Kimura, M. A. Dillon, and Isao Shimamura
Laser Manipulation of Atoms, K. Sengstock and W. Ertmer
Electron Collisions with N z, O 2 and O: What We Do and Do Not Know, Yukikazu Itikawa
Advances in Ultracold Collisions: Experiment and Theory, J. Weiner Ionization Dynamics in Strong Laser Fields, L. F. DiMauro and P. Agostini
Need for Cross Sections in Fusion Plasma Research, Hugh P. Summers Need for Cross Sections in Plasma Chemistry, M. Capitelli, R. Celiberto, and M. Cacciatore
Infrared Spectroscopy of Size Selected Molecular Clusters, U. Buck Femtosecond Spectroscopy of Molecules and Clusters, T. Baumer and G. Gerber
Guide for Users of Data Resources, Jean W. Gallagher
Calculation of Electron Scattering on Hydrogenic Targets, I. Bray and A. T. Stelbovics
Guide to Bibliographies, Books, Reviews, and Compendia of Data on Atomic Collisions, E. W. McDaniel and E. J. Mansky
Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence, W. R. Johnson, D. R. Plante, and J. Sapirstein
Volume 34
Atom Interferometry, C. S. Adams, O. Carnal, and J. Mlynek
Rotational Energy Transfer in Small Polyatomic Molecules, H. O. Everitt and F. C. De Lucia
Optical Tests of Quantum Mechanics, R. Y. Chiao, P G. Kwiat, and A. M. Steinberg
Volume 36
Classical and Quantum Chaos in Atomic Systems, Dominique Delande and Andreas Buchleitner
Complete Experiments in Electron-Atom Collisions, Nils Overgaard Andersen and Klaus Bartschat
Measurements of Collisions between LaserCooled Atoms, Thad Walker and Paul Feng
Stimulated Rayleigh Resonances and RecoilInduced Effects, J.-Y. Courtois and G. Grynberg
The Measurement and Analysis of Electric Fields in Glow Discharge Plasmas, J. E. Lawler and D. A. Doughty
Precision Laser Spectroscopy Using AcoustoOptic Modulators, W. A. van Wijngaarden
314
C O N T E N T S O F V O L U M E S IN THIS SERIAL
Highly Parallel Computational Techniques for Electron-Molecule Collisions, Carl Winstead and Vincent McKoy
Quantum Field Theory of Atoms and Photons, Maciej Lewenstein and Li You Volume 37
Evanescent Light-Wave Atom Mirrors, Resonators, Waveguides, and Traps, Jonathan P. Dowling and Julio GeaBanacloche
Optical Lattices, P. S. Jessen and I. H. Deutsch
Channeling Heavy Ions through Crystalline Lattices, Herbert F. Krause and Sheldon Datz
Evaporative Cooling of Trapped Atoms, Wolfgang Ketterle and N. J. van Druten
Nonclassical States of Motion in Ion Traps,
Volume 39
Author and Subject Cumulative Index Volumes 1-38 Author Index Subject Index Appendix: Tables of Contents of Volumes 1-38 and Supplements
Volume 40
Electric Dipole Moments of Leptons, Eugene D. Commins
High-Precision Calculations for the Ground and Excited States of the Lithium Atom, Frederick W. King
Storage Ring Laser Spectroscopy, Thomas U. Kiihl
Laser Cooling of Solids, Carl E. Mungan and Timothy R. Gosnell
Optical Pattern Formation, L. A. Lugiato, M. Brambilla, and A. Gatti
J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller
The Physics of Highly-Charged Heavy Ions Revealed by Storage/Cooler Rings, P. H. Mokler and Th. St6hlker
Volume 38
Electronic Wavepackets, Robert R. Jones and L. D. Noordam
Chiral Effects in Electron Scattering by Molecules, K. Blum and D. G. Thompson Optical and Magneto-Optical Spectroscopy of Point Defects in Condensed Helium, Serguei I. Kanorsky and Antoine Webs
Rydberg Ionization: From Field to Photon, G. M. Lankhuijzen and L. D. Noordam
Volume 41
Two-Photon Entanglement and Quantum Reality, Yanhua Shih Quantum Chaos with Cold Atoms, Mark G. Raizen
Study of the Spatial and Temporal Coherence of High-Order Harmonics, Pascal Salikres, Ann L'Huiller Philippe Antoine, and Maciej Lewenstein
Atom Optics in Quantized Light Fields, Matthias Freyburger, Alois M. Herkommer, Daniel S. Krdhmer, Erwin Mayr, and Wolfgang P. Schleich Atom Waveguides, Victor I. Balykin
Atomic Matter Wave Amplification by Optical Pumping, Ulf Janicke and Martin Wilkens
Studies of Negative Ions in Storage Rings, L. H. Andersen, T. Andersen, and P. Hvelplund
Single-Molecule Spectroscopy and Quantum Optics in Solids, W. E. Moerner, R. M. Dickson, and D. J. Norris
Volume 42
Fundamental Tests of Quantum Mechanics, Edward S. Fry and Thomas Walther
C O N T E N T S O F V O L U M E S IN THIS SERIAL Wave-Particle Duality in an Atom Interferometer, Stephan Diirr and Gerhard Rempe Atom Holography, Fujio Shimizu Optical Dipole Traps for Neutral Atoms, Rudolf Grimm, Matthias Weidemiiller, and Yurii B. Ovchinnikov Formation of Cold (T ~<1K) Molecules, J. T. Bahns, P. L. Gould, and W. C. Stwalley High-Intensity Laser-Atom Physics, C. J. Joachain, M. Dorr, and N. J. Kylstra Coherent Control of Atomic, Molecular, and Electronic Processes, Moshe Shapiro and Paul Brumer Resonant Nonlinear Optics in Phase Coherent Media, M. D. Lukin, P. Hemmer, and M. O. Scully The Characterization of Liquid and Solid Surfaces with Metastable Helium Atoms, H. Morgner Quantum Communication with Entangled Photons, Harald Weinfurter
315
Kinetic Energy Dependence of Ion-Molecule Reactions Related to Plasma Chemistry, P. B. Armentrout Physicochemical Aspects of Atomic and Molecular Processes in Reactive Plasmas, Yoshihiko Hatano Ion-Molecule Reactions, Werner Lindinger, Armin Hansel, and Zdenek Herman Uses of High-Sensitivity White-Light Absorption Spectroscopy in Chemical Vapor Deposition and Plasma Processing, L W. Anderson, A. N. Goyette, and J. E. Lawler Fundamental Processes of Plasma-Surface Interactions, Rainer Hippler Recent Applications of Gaseous Discharges: Dusty Plasmas and Upward-Directed Lightning, Ara Chutjian Opportunities and Challenges for Atomic, Molecular, and Optical Physics in Plasma Chemistry, Kurt Becker, Hans Deutsch, and Mitio Inokuti
Volume 44 Volume 43
Plasma Processing of Materials and Atomic, Molecular, and Optical Physics: An Introduction, Hiroshi Tanaka and Mitio Inokuti The Boltzmann Equation and Transport Coefficients of Electrons in Weakly Ionized Plasmas, R. Winkler Electron Collision Data for Plasma Chemistry Modeling, W. L. Morgan Electron-Molecule Collisions in LowTemperature Plasmas: The Role of Theory, Carl Winstead and Vincent McKoy Electron Impact Ionization of Organic Silicon Compounds, Ralf Basher, Kurt Becket, Hans Deutsch, and Martin Schmidt
Mechanisms of Electron Transport in Electrical Discharges and Electron Collision Cross Sections, Hiroshi Tanaka and Osamu Sueoka Theoretical Consideration of PlasmaProcessing Processes, Mineo Kimura Electron Collision Data for PlasmaProcessing Gases, Loucas G. Christophorou and James K. Olthoff Radical Measurements in Plasma Processing, Toshio Goto Radio-Frequency Plasma Modeling for Low-Temperature Processing, Toshiaki Makabe Electron Interactions with Excited Atoms and Molecules, Loucas G. Christophorou and James K. Olthoff
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