Advances in Atomic, Molecular, and Optical Physics, Volume 44: Electron Collisions with Molecules in Gases: Applications to Plasma Diagnostics and Modeling

Advances in ATOMIC, MOLECULAR, AND OPTICAL PHYSICS VOLUME 44 Editors BENJAMIN BEDERSON New York University New York...

Author: Mineo Kimura

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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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This book is printed on acid-free paper. (~) Copyright

9 2001 by Academic Press

All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. The appearance of code at the bottom of the first page of a chapter in this book indicates the Publisher's consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the U. S. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for chapters are as shown on the title pages; if no fee code appears on the chapter title page, the copy fee is the same for current chapters, 1049-250X/01 $35.00 ACADEMIC PRESS A Harcourt Science and Technology Company 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA http://www.academicpress.com Academic Press Harcourt Place, 32 Jamestown Road, London NW1 7BY U K International Standard Book Number: 0-12-003844-7 International Standard Serial Number: 1049-250X

Printed in the United States of America 00 01 02 03 MB 9 8 7 6 5 4 3 2 1

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


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)


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


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


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.


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


FIG. 4. Electron collision cross-section sets.


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


FIG. 5. Overview of the electron energy loss spectra for 0 2 and

C F 4.


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


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


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


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 +.


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


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.


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


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.


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).


26 2.0

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.

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~

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9 i

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1

!

t

i

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ill

i

,

100 ELECTRON ENERGY (eV)

t

t

_, t

tl

1000

FIG. 10. Cross section for the production of fluoromethyl radicals by neutral dissociation and dissociative ionization from electron impact on fluoromethanes.

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


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

i

%

i

i

llllll

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!

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.

.

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Electron energy (meV) FIG. 12. Relative cross sections for SF6 formation in collisions of free electrons with S F 6 molecules in a collimated supersonic beam over the energy range 0.01-10meV.

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


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.


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


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


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


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 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


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


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.


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 __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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’’’"1

’

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’

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’’’"1

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i

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o

101

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v v

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McCorkle (1984)

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X ....

co

9

x~ %

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(a)

....... QO . ~.~..:.-r.~ - ' "'~---~ ~ . .~'~...."" . _...," ~ ' - . .

E

\

see text

-

Cl 2 ( ~ .... 'o~ .................................... \ e'-.. ....

\

Chantry (1982)

....... Kurepa (1981) \ --McCorkle (1984) + Kurepa (1978)\

100 0.01

i

i

i

i

t

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i

i

i

i

i

"~". . . . . . . . . . .

illl

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’

’

’

I

.

.

.

.

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E o o4

’

(b)

_

10-1 -

b

_

CI a

v _

v

r 1 0 - 2

b

"o

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. . . . .

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10

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


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


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

74 i

101

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I

,

Ill,

I

l

- CF4

E

!

b

i

llll

100

i

..... X

i

v

#

b i

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./

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......

,,I

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o 04

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w-'

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cO ..o .m >

,

,

......

0.1

i

i

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i III

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--

-

ill

'e.

%,~. .,/.~

(ivib, dir, t (ivib, dir, t (iinel, t (Ida, t (ivib, indir, t I

-

o

~

o

o

"%.

-

/ /'"'"',~

....

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/i Ixo) "~,, ,!,l

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P i n h ~ o (I 9 9 5 ) Derived

X,~....

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/~

,

~-' \

/. I

,/

i lil

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.....

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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).


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


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.


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.


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)

20( > 27.1) 9.5) ~ 17.0 (22.7) 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.


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


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.


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


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.


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

10 2

’

’ ’’""I

’

’ ’"’"I

’

’ ’"’"I

’

’ ’"’"I

’

’ ’"’"I

’

’ ’’"]

O4

E .....,.. -

0

--" 9

.i

1, .~.,,,,,.~.. ~ . . . . . #~/~_.,. #.

~.,%

"%.

%

|

o

I--" v v

101

CO

/

0 O0

(a)

b

100 0.001

i

| ii1,|11

'

' ' '""1

10 3

--

W i

i i|||||l

0.01

i

i illl|ll

|

0.1

~,~

C,F0

..... C~F,, | ||11111

1

~'""1

'

i

10

' ' '""1

'

' ''""1

0 O4

10 2

!

o

'.,

v v

OJ

~

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

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,


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 ~ 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.


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


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


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


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


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


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

I

'

I

'

I

'

I

'

'

I

'

I

'

'

I

'

I

'

_

(a), 30 eV

102

101 100 ~,_ t~ O4

E

10-1

-

'

I

101 \

'

I

(b) 30 eV

0

O4

00

~

10 1

Q.

.~

0-2

"0

-

10 2

'

I

,

'

I

(c) 3 0 e V

1)-*Ba(6s5d 1D2)

101 100 10 -1 10-2

o

10

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


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

12

.

.

.

.

I

’

’

’

’

I

’

’

’

’

I

’

’

’

’

.r'l~ I

10

E

8

t

-, ; \

’o V

]

-

-\ ~

;

I::'.

0 cxi "I[""

He* (21S)

t.

"

c a l - Margreiter (SC, 1990)

~ \

9 \

;i ~. ". ~. \ I: t~i- ~ " ~ \ li ] '~ '.. \ \\

6

9

9 .

-!~i |! II

-Ic

~

\ - ".. \ . ~..,"- ~.

!1

4

\

,~ ",,

~k,, X .~.,

I

",,

........ .........

c a l - Ton-That (BE 1977) c a l - T o n - T h a t (BF, 1977)

.......... 9

cal- Ton-That (BH 1977) e x p - Krishnakumar (1988)

-

"-,

~"-~

I

2

-

cal- Margreiter (CBE, 1990)

"":".:", ~ -

-

"" ""~,,4..'~.. ~

~

~

~

--

He (11S0)

0

i

0

,

_

I

50

100

I

150

I

I

I

I

200

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 .

.

.

.

I

.

.

.

.

I

.

.

.

I

b

- oo

V

-

o

m

o oo 9

o

Ne*(33P2,o) o o

-*

(a)

o o

' ""

0

' ""

i ""

' """

"

. . . .

o 9 o t

. . . .

I

’

’

’

E

v

~

6

. m

~:.

4

,- :-,~, 9

~ ~ . ~

"

.

~,

0

,

,

,

""'---..

" .. :;.:...:..~.~...,

(b)

2

.........

" 'qzv-~ ::: ......

--.. . . .

....

"""""’..................._...

"--’~-.--’~-,,..... o. I

50

,

,

,

,

I

100

. . . .

I

Ton-That (BHR, 1977) T o n - T h a t ( B F R , 1977) M c G u i r e (SBI, 1979) H y m a n (SBE, 1979) M a n n ( D W A , 1996) M a r g r e i t e r (BE, 1990) M a r g r e i t e r (SC, 1990)

...... ----.. ...~ ~'~'-.~ Q.I'I.. ~

’

V r i e n s (BEI, 1964) T o n - T h a t (BEI, 1977)

.....

04

200

150 ......

/-~ i , ~', ~. ' '

b

1

100

I

o

' . . . .

50

10

’1"-

|

’

9o

~

~3

04

’

Krishnakumar (1988)

E

o 04

o

’

J o h n s t o n (1 996) Dixon (1 973)

o

04

.

~

,

o J

9

~

I

150

o ~

,

,

,

200

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


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


12 8

[~:~'..\

10

'~-..

4

_

~ ,,:

2

-

’

! Z-'..""

I ~,:.'

~ , , x

.

Ar

O O4

i'7 ,

10

,"

t/

"4,.:.?.

’~

J i iiii

100

(b) Kr*

'"....

,,,,

.~\........ :,, ,

i "/;.~ N2+(A2]Iu)

..." i i I

.............. CO-(a31-I) -> CO+(X2Z +) ,

,

~

i

,

,

i

10

i

_-

I

100

200

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


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


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

E ..c o

~

~"-' d

10 3

.__. rr

] 0e

~

c-

96

0

r

121

100 0.0

10~

'v,

10 1

o

r

o

_~ ~c~

"0

5---~

D2

--. _

101

E

231

AND MOLECULES

-

o ~

101

ATOMS

~

,

,

~

,

I

~

,

,

,

0.5 ,

,

I

~

~

[]

Wadehra (1978)

o

Allan (1978) ,

J

1.0

,

,

,

,

I

~

,

~

1.5

,

I

’

’

,

I

,

!

~

,

I

2.0 ’

’.--.-’.-.L.

’

--=

(b) _:

10 "2 [E

/~'~'

]~ 10 -3 ~/,~/ L ,,~'/

~ ..... ........ ------

Hickman (1991) Wadehra (1978) Gauyacq i1985i MiJndel (1985)

2

3

10 -4

10-5 0

1

4

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

'

'

'

I

'

'

~

I

'

'

~

I

0702

'

'

'

I

'

K

2~ 04

/

E

f

04 04 '11""" v

-0

/,

1

0

0

2

4

6

8

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)


234

2.5

’

9 9 9

2.0 o

1.5

F2 %

2

0

0,0

I

0.0

i

,

t

,

,

,

400

600

I

" ,i,ll i-"

i

I

i

i

i

i

i

0.5 Mean electron energy (eV) ’

I

’

~ , ~ v ,

,

T e m p e r a t u r e (K)

=ill

10

,

i i I .

""""’’"

0.5

’

0

1

200

"0

’

o

E b

9 /i I

1.0

v

’

o

09

(a)

|

0

’

2

m

ffl

E

I

~'~

T = 233 K T = 298 K T = 373 K

~

~

I

’

I

’

I

=1

1.0

’

(b) v=0

F2 _

04

E O 04

b

v "O

t3

0 0.0

0.2

0.4 0.6 0.8 Electron lenergy (eV)

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


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

~
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

O

I

I

’

I

’

-oOo o

~

---.

~ooo~o

Cl 2

~~I~ ~ 0

9

9

E

3

b

2

o

"~

~

4

1

co

0 .... 200

E

0

9

9 9

9

x L,,,,"? . . . . . . . J, 250 300 350 T e m p e r a t u r e (K)

n

0

1

I

-

213K

9

v

A

233 K

o o

o

t I

273 K 9

O

| , II

298 K 323 K

i

0

!!

253 K

9

0

O

I

0.2

I

I

0.4

I

I

0.6

O

O

O

I

0.8

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


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


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


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


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


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


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


0.0

0.0

0.2

0.4


FIG. 46. (a) Total dissociative electron attachment rate constants as a function of the mean electron energy kda,t(~ 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.


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 (~) 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

'

I ,

'

,

ta)

-

.,-~ -

'

I

'

K /" ..... "

I

'

| 1

/"F~\65oK t

//,.-----~\

-1

I-(-Ts~ b ~~

~

L

',

-

r

-

I

-

0

) ,- -

~ 6so K - ~ "

,,;,/ oo< t ,~i,il’l~~176 -4_, ~ 1.o[-r ,il ~-

.

4

I 750

""

0 1 2 3 4 5 Mean electron energy (eV)

0.0

i

0

i

. .

~

-

C’F’

i

flilXitI,I

:-

illl

!lil

i,!il

",,.

:li

, .s,,_u,

_

-

,

,

~

,

"r--~

2 4 6 8 Electron energy (eV)

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( 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 (

Advances in Atomic, Molecular, and Optical Physics, Volume 44: Electron Collisions with Molecules in Gases: Applications to Plasma Diagnostics and Modeling

Advances in Atomic, Molecular, and Optical Physics, Volume 59 (Advances in Atomic, Molecular and Optical Physics)

Advances in Atomic, Molecular, and Optical Physics