ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 21
CONTRT~UTORS TO THIS VOLUME E. V. Bogdanov Z. S. Chernov P. S...
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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 21
CONTRT~UTORS TO THIS VOLUME E. V. Bogdanov Z. S. Chernov P. S. Farago V. Ya. Kislov J. Kistemaker David B. Medved W. C. Nixon C. W. Oatley R. F. W. Pease L. A. Russell C. Snoek Y. E. Strausser
Advances in
Electronics and Electron Physics EDITEDBY L. MARTON National Bureau of Standards, Washington, D.C
Assistant Editor CLAIREMARTON EDITORIAL BOARD E. R. Piore M. Ponte A. Rose L. P. Smith
T. E. Allibone H. B. G. Casimir L. T. DeVore W. G. Dow A. 0. C. Nier
VOLUME 21
1966
ACADEMIC PRESS
New York and London
COPYRIGHT
@ 1965, B Y ACADEMICP R E S S
INC.
ALL RIGHTS RESERVED. NO PART O F T H I S BOOK MAY B E REPRODUCED I N ANY FORM, B Y PHOTOSTAT, MICROFILM, O R ANY OTHER MEANS, W I T H O U T WRITTEN PERMISSION FROM T H E PUBLISHERS.
ACADEMIC PRESS INC. 111 Fifth Avenue, New York, New York 10003
United Kingdom Edition published by ACADEMIC PRESS INC. ( L O N D O N )' LTD. Berkeley Square House, London W.l
LIBRARY OF CONGRESS CATALOG CARDNUMBER:49-7504
P R I N T E D I N T H E UNITED STATES O F AMERICA
CONTRIBUTORS TO VOLUME 21 Numbers in parentheses indicate the pages on which the authors’ contributions begin.
E. V. BOGDANOV (287), Institute of Radiotechnique and Electronics, USSR Academy of Sciences, MOSCOW, Z. S. CHERNOV (287), Institute of Radiotechnique and Electronics, Academy of Sciences, MOSCOW, USSR
P. S. FARAGO (l), Department of Natural Philosophy, University of Edinburgh, Edinburgh, Scotland
V. YA. KISLOV(287) , Institute of Radiotechnique and Electronics, Academy of Sciences, MOSCOW, USSR J. KISTEMAKER (67), F.O. M. Laboratorium voor Massascheiding, Amsterdam, The Netherlands
DAVIDB. MEDVED(101), Electro-Optical Systems, Inc., Pasadena, California
W. C. NJXON (181), Engineering Department, Cambridge University, Cambridge, England
C. W. OATLEY(lgl), Engineering Department, Cambridge University, Cambridge, England
R. F. W. PEASE(181), Engineering Department, Cambridge University, Cambridge, England
L. A. RUSSELL(249), I B M Corporation, Harrison, New York C. SNOER(67), F.O.M. Laboratorium voor Massascheiding, Amsterdam, The Netherlands Y. E. STRAUSSER (lol), N A S A , Lewis Research Center, Cleveland, Ohio
V
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FOREWORD The previous volume contained three papers dealing with plasmas. Continued interest in the subject prompted us to add a fourth paper to the series; the discussion presented here by Dr. Chernov and co-workers has the added attraction of presenting a viewpoint of our colleagues in the USSR. Reviews on related subjects will be presented in future volumes. Interaction of charged particles with solid surfaces is the subject of two reviews in the present volume. A review of the anomalous magnetic monient of the electron is long overdue, and we are-happy to have a very competent reviewer to present this subject. On the more applied side we are presenting here a review of the subject of memory technology, as well as our first review of the scanning electron microscope. As in the past, I would like to list the articles slated for future volumes:
Weak Magnetic Field Measurement by Magnetic Resonances Cryogenic Magnets Semiconductor Circuitry Radioastronomy Progress in Microwave Tubes High Frequency Confinement, Heating, and Accelerating of Plasmas Plasma Experiments with Neutralized Beams Surface Ionization of Cesium Moving Striations and Ionization Waves Dispenser Cathodes Superconductivity Noise in Electron Devices and Bulk Materials Upper Atmosphere Physics Paramagnetic Resonance in Biological Systems Nuclear and Electron Spin Resonance Optimization of Control Reactive Scattering in Molecular Beams Cooperative Phenomena Thermal-Ion Molecule Reaction Rates Radio Sounding of the Ionosphere Vii
P. Grivet and L. Malnar S. H. Autler F. K. Buelow and R. Turnbull 0. E. H. Rydbeck P. R. Guenard H. Motz J. M. Sellen H. Shelton N. L. Olesen A. H. W. Beck F. A. Lynton E. Chenette T. M. Donahue L. A. Blumenfeld E. R. Andrew and S. Clough A. Blaquiere S. Datz J. L. Jackson and L. Klein E. E. Ferguson R. W. Knecht
viii
FOREWORD
Novel High Frequency Solid State Ultrasonic Devices Thermionic Cathodes The Analysis of Dense Electron Beams Progress in Microwave tubes Radio Wave Fading Radio Backscatter Photoelectric Emission from Solids Proceedings of the 3rd Symposium on PhotoElectronic Image Devices
Washington, D. C . October, 1966
N. G. Einspruch P. Zalm K. Amboss 0. Doehler and Kantorovics M. L. Philips M. L. Philips F. G. Allen
J. G. McGee (editor)
L. MARTON
CONTENTS CONTRIBUTORS TO VOLUME 21 .
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V
FOREWORD . .
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vii
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1 3 13 24 45 63
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The Polarization of Electron Beams and the Measurement of the g-Factor Anomaly of Free Electrons P . S. FARAGO I . Introduction . . . . . . . . . . . . . . . I1. Description of Polarized Electron Beams . . . . . . . I11. The Effect of Macroscopic Fields on Polarization . . . . I V . The Production of Polarized Beams . . . . . . . . V . The Measurement of the g-Factor Anomaly of Free Electrons References . . . . . . . . . . . . . . .
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Fast Ion Scattering against Metal Surfaces C . SNOEKA N D J . KISTEMAHER
I . Introduction . . . . . . . . . . . . I1. The Dynamics of Two-Atom Collisions . . . . 111. Scattering Experiments with Solid Targets . . . IV . Light Emission From Ion-Bombarded Metal Targets References . . . . . . . . . . . .
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67 70 78 92 98
Kinetic Ejection of Electrons from Solids DAVIDB . MEDVEDAND Y . E . STRAUSSER
I . Introduction and Background . . I1. Experimental Techniques . . . 111. Experimental Results . . . . IV . Theory . . . . . . . . V . Conclusions and Probable Trends . References . . . . . . .
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165 173 174
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Scanning Electron Microscopy
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C W . OATLEY.W . C . NIXON. AND R . F. W . PEASE
I . Introduction . . . . . . . . . . . . . . . . . I1. Principles of Design of the Scanning Electron Microscope . . . . I11. Techniques and Applications . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . ix
. 186 . 212 . 246
X
CONTENTS
High- Speed Magnetic-Core Memory Technology L . A . RUSSELL
I . Introduction . . . . . . . . . . I1. Coincident-Current Toroidal Core Storage . I11. Two-Dimensional Core Memory . . . . IV . Special Ferrite Storage Devices and Memories References . . . . . . . . . .
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250 273 279 . 283
Physical Foundations of Plasma Applications for Generation and Amplidcation of Microwaves V. Y A. KISLOV,E . V . BOGDANOV, A N D Z . S. CHERNOV
I . Introduction . . . . . . . . . . . . . . . . . . I1. Slow Waves in Plasma . . . . . . . . . . . . . . . I11. Interaction of Slow Waves with Electron Stream . . . . . . . I V . Plasma Traveling Wave Tube . . . . . . . . . . . . . V. Plasma Backward Wave Generator . . . . . . . . . . VI . Interaction on Longitudinal Waves . . . . . . . . . . . VII . Operating-Wavelength Shortening Problems in Plasma Devices . . . VIII . Experiments on Amplification and Generation of Millimeter Band Oscillations by Means of Plasma . . . . . . . . . . . . . I X . Conclusion . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . .
287 291 296 306 314 321 324
AUTHORINDEX . .
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333
SUBJECT INDEX . .
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327 329 329 330
343
The Polarization of Electron Beams and the Measurement of the g-Factor Anomaly of Free Electrons P. S. FARAGO Department of Natural Philosophy, University of Edinburgh, Edinburgh, Scotland Page
1. Introduction. . . . . . . . .......................... 11. Description of Polariz lectron Beams.. . . . . . . . . . . . . . .............. 3 111. The Effect of Macroscopic Fields on Polarization. . . . . . . . . . . . . . . . . . . . . . . . 13 IV. The Production of Polarized Beams.. . . . . . . . A. Polarization by Interaction with Macroscopic Fields. . . . . . . . . . . . . . . . . . . 24 B. Polarization by Scattering Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 C. Removal of Polarized Electrons from Atoms or from Solids . . . . . . . . . . . . 38 V. The Measurement of the 9-Factor Anomaly of Free Electrons. . . . . . . . . . . . . 45 A. Preliminary Remarks. . . . . . . . . . . . . . . . .. . . . . . . . . . 45 B. Dehmelt’s Experiment. . . . . . . . . . . . . . . .................... 48 C. Proposals by Bloch and by Bloom and Erdman.. . . . . . . . . . . . . . . . . . . . . . 51 D. Measurements with Electrons Emitted in Beta Decay.. . . . . . . . . . . . . . . 56 E. Experiments by Crane and Co-workers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 ......................... 63
I. INTRODUCTION Once the existence of the electron had been established (1897), it immediately assumed a role of major importance in physics. Two of its fundamental properties, its charge and charge-to-mass ratio, were measured by various high precision experiments both for free electrons and spectroscopically, i.e., for electrons bound to atoms. The wave nature of the electron, a concept originally introduced for the interpretation of quantized electron states in atoms, was demonstrated experimentally with beams of free electrons and the theoretically postulated relationship between the momentum of the electron and its wavelength was confirmed. The remaining two fundamental properties of the electron, its spin and magnetic moment, remained somewhat of a mystery for quite a while. The concept of the electron spin, an intrinsic angular momentum of the electron, was introduced by Uhlenbeck and Goudsmit (1925) on the basis of spectroscopic evidence and already had proved to be a mostj fruitful hypothesis in the old quantum theory. The formal representation of the experimentally established properties of spin was developed within the framework of nonrelativistic wave mechanics by Pauli (1927). 1
2
P. S. FARAGO
It became perfectly clear that the spin can have no classical analogue, but the explanation of its existence, and of its magnitude, was given in the next stage of the development by Dirac’s relativistic theory (1928). All through this development the spin was always considered as an intrinsic property of the electron itself, but all the experiments that supplied the evidence for this were carried out with electrons bound to individual atoms (spectroscopic measurements, Stern-Gerlach experiment) or solids (magneto-mechanical effects, experiments of Barnett, and of Einstein and de Haas), although attempts to detect the spin and magnetic moment of free electrons were not neglected either. The attitude of the earliest experimenters is probably best characterized by the following quotation (1): “The already classic experiment of Davisson and Germer [on electron diffraction] . . . suggested that it might be of interest to carry out with a beam of electrons experiments analogous to optical experiments in polarization. I t was anticipated that the electron spin . . . recently so happily introduced in the theory of atomic spectra by Uhlenbeck and Goudsmit might appear in such an experiment as the analogue of a transverse vector in optical experiments.” The early experiments, however, gave negative results and theoretical considerations lead to discouraging conclusions also : it was shown that phenomena analogous to the polarization of light by reflection at a mirror are not to be expected. The apparently most straightforward way of separating electrons of a given spin orientation, a Stern-Gerlach type of experiment, with a beam of free electrons, was ruled out by considerations based on the uncertainty principle. The generality of these arguments resulted in a widely spread misconception, namely that it is meaningless to assign a magnetic moment to the free electron. Theoretical investigations by Mott (1928-1932), however, did predict an observable effect depending on the spin of free electrons, and established a method of artificial production of polarized electrons: he found that the elastic scattering of medium energy electrons (0.05-0.4 MeV, say) by heavy nuclei should yield partial polarization. It took, however, a long time before this prediction was confirmed experimentally, the first conclusive experiments were carried out about 10 years later by Shull et al. (1942-1943). ‘LMottscattering” has become the subject of a number of t,heoretical and experimental studies, and it is true to say that it is to date almost the only artificial source of polarized electrons and it is the most extensively used method for the detection of electron polarization. Another, readily available, source of polarized electrons is offered by nature in the shape of radioactive beta decay, where polarization results from parity nonconservation in weak interactions. From a practical point of view both Mott scattering and beta decay have serious limita-
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
3
tions: the available beam intensities are very small, and there is little freedom left in the choice of the energy of the electrons. This explains the renewed efforts made to search for suitable methods by which highly polarized beams of electrons could be produced at controllable energy and at possibly high intensity. Whereas it is true to say that the electron is the most familiar of all the elementary particles, its fundamental properties are still not properly understood. One of the outstanding problems arises from the difficulty of describing a massive point charge in a mathematically consistent way and avoiding the occurrence of infinitely large quantities (divergent integrals) in the formalism. The problem is a very long-standing one; it first appeared in classical electrodynamics and it is present in the quantumtheoretical treatment also. The solution of the problem offered by present day quantum electrodynamics can be tested directly on very few observable phenomena only. One of these is the anomaly of the magnetic moment of the electron. This gives an outstanding importance to the experiments designed to measure the g-factor anomaly of free electrons. In the past eight years or so a number of reviews were published on electron polarization and related subjects. The first of these ( 2 ) discusses both theoretical and experimental problems, with particularly great attention to Coulomb scattering. With the discovery of parity nonconservation, the measurement of the polarization of electrons and positrons emitted in beta decay became of great importance and the requirements of such studies are the prime concern of more recent reviews (3-9). The present paper pays more attention to the problems of producing polarized beams particularly at low energies (Section IV). Experiments with polarized beams carried out for the high precision measurement of the anomalous magnetic moment of free electrons will be described in Section V. From the point of view of the design of experiments with polarized beams, a knowledge of the behavior of electrons in macroscopic electromagnetic fields is indispensable; this is the subject of Section 111. To start with, the general properties and formal description of polarized beams will be outlined. 11. DESCRIPTION OF POLARIZED ELECTRON BEAMS~
Polarization effects arise from some kind of asymmetry in the interaction between spin and electromagnetic fields or matter. Before discussing the concept of polarization it will be helpful to recall some basic ideas of the nonrelativistic quantum theory of spin itself. 1 For fundamental concepts and formulation of nonrelativistic quantum mechanics, including a discussion of density matrices, see Dicke and Wittke (10).The mathematical technique is presented in much greater detail by Rojansky (11).
4
P. S . FARAGO
Electron spin is the name for the intrinsic angular momentum of the electron. The properties of atomic spectra, and the more direct evidence obtained from the experiments of Stern and Gerlach, show that this intrinsic angular momentum has the property that its component parallel to a fixed direction of reference is either +F, or -+h ( h = h/2?r). In quantum mechanics, spin, as all observable physical quantities, may be represented by an Hermitian operator, which is applied to the wave function describing the state of the electron. The possible results of the measurement of the spin appear as the “eigenvalues” of the spin operator. The properties of the operators employed as spin operators are determined by the fact that the physical quantity they describe is angular momentum and that the measurement of its component along a reference direction can have just two values. The first of these requirements fixes the commutation rules to which the components of the spin are subject, and the second requirement shows that the operators are 2 X 2 matrices. Taking the direction of reference as the z axis of a Cartesian coordinate system, parallel to which the spin is f+F,, the spin components are represented by the following operators 0 1
0 -1 The operator d = ( 2 / h ) s is known as the Pauli spin operator. These matrices are Hermitian characterized by the relation a i k = u: (the asterisk signifies the complex conjugate) and it is easy to convince oneself that they “anticommute,” i.e., S,$
=
-sysz
susz = -s2sy
828, = -S,St
(2)
and furthermore
and hence
If the spin component parallel to the z axis is measured, the result of the measurement is one of the two eigenvalues of the operator s,, i.e., +h or -+h as required. The electron state is described by the eigenfunction corresponding to the respective eigenvalue; thus, for example, the state of an electron whose spin component parallel to the z axis is +h or -+h is described by the eigenvector of the operator S, corresponding to the eigenvalue +h or -&h, respectively. The eigenvector of a 2 X 2 matrix is a two component
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
5
vector written in a two element column symbol, and if one denotes the eigenvector of s, corresponding to the eigenvalue +h by a, and that corresponding to the eigenvalue -+h by b, one readily finds that a =
(i)
and
b
@)
=
(3)
Fundamental properties of the spin vector can be derived directly from the commutation relations satisfied by the spin operator. Thus, it is important to note that eigenvectors of S, are not eigenvectors of either S, or s,. According to the fundamental principles of quantum mechanics this means that the three components of the spin cannot be determined simultaneously. It can be shown that if measuring the spin component parallel to the z axis it is found to be, say, i h then the result of a subsequent measurement of the x or y component of the spin is equally likely to yield +h or -+h. On the other hand the operator 82 and any one of the spin component operators have simultaneous eigenstates and hence the absolute value of the total spin, ($)1’2h,and any one of its components can be determined with precision simultaneously. The reference direction, along which a spin component is measured, can be any direction in space, and the essence of the above statements will still be maintained. If the reference direction is that of the unit vector 9, which makes the angles a, p, y with the coordinate axes x, y, x , respectively, then the measurement of the spin component parallel to i? is given by the eigenvalues of the operator S*
8
= +h(d, 00s a
+ d,
COS
-k
d, COS 7)
and it is found that they are i+h, quite independently of the direction of 9. Once the spin component along 9 is measured, the components perpendicular to 8 are, again, equally likely to be +h or -& It is customary to visualize the spin orientation in space with the aid of a vector model. For instance, if the spin component parallel to 9 is +ti, the spin vector of the magnitude ($)WIlies somewhere on the surface of a cone (Fig. l),since it is not possible to specify exactly the components perpendicular to 8. Thus the total spin vector has no precisely specified direction, and only its magnitude and one of its components are determined. In spite of this it is acceptable to characterize this situation by saying that the spin is aligned parallel to the unit vector 8. The justification of this manner of speaking is as follows. If a measurement shows that the spin component parallel to 8 is +h,then the electron state is described by the eigenvector, say J.+ =
(Ei),
of the operator (s 8 ) , as
6
P. S . FARAGO
before, and it is a legitimate question to ask what the aveyage value of the spin is.2 This average, (s), is again a vector defined by its components
and similarly
If u1 and u2 are determined explicitly it is found that ( 8 ) is parallel to the unit vector 8 : (9) = $h8, whatever direction 8 has. Similarly, if the spin component parallel to 2 is found to be -ah, then the average of the spin vector is ( 8 ) = -+ha, and it is antiparallel to 8.
FIG.1. See the discussion in text of spin alignment.
Introducing a 2 X 2 matrix with elements P i k UlUl* @
Note t h a t $+ =
(:>
=
= u1
UlUZ*
(u*ul*UZUZ*
(i) + (y) uz
=
= 'u%uk*, i.e.,
) UIU
+ uzb,i.e.,
the eigenvector,
characterizing an electron with a spin component i h parallel to the unit vector 2,can he expanded in terms of the eigenvectors a and b, describing an electron whose spin component parallel to the z axis is +$fi. It is normalized, i.e., [ ~ + I *= [u1/2 1 ~ ~ 1=2 1, and the expansion coefficients have the following meaning: lull2 is the probability t h a t a measurement on the electron described by $+ will find the z component of its spin equal t o ifi;lull* is the prohahility of finding this spin component to be -@.
+
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
7
This matrix e is called “density matrix,” and its significance will be explained presently. So far we have been concerned with the properties of the spin of a single electron. Let us turn now to the description of an electron beam with respect to the behavior of the spin of its constituent electrons ( l a , 13,l3a,b). From the point of view of quantum-mechanical description two different types of electron beams can be distinguished. The first is said to be in a “pure state,” the other a “mixture.” The electron beam is in a pure state, if each electron in the beam can be characterized by the same value of all of its measurable properties. To obtain such a beam, it has t o be suitably “prepared” in the following manner. (i) Electrons of an arbitrary beam are subjected to all conceivable measurements which are quantum-mechanically compatible, i.e., for each electron one measures all those quantities which can be determined with precision simultaneously. (ii) Only those electrons are retained in the beam for which the respective measurements gave identical results and all others are discarded. The result of this preparation is that each electron is in the same eigenstate of the respective operators which commute with one another, and therefore each electron is described by the same state vector. As a result the beam as a whole can be described in exactly the same way as was done previously for a single electron. The polarization of the beam will be characterized by a vector P, taken-by definition-equal to the average value of the spin operator,
P = (d) For instance if the beam is prepared so that it consists of electrons whose spin parallel to the unit vector 8 is i h , then as seen above (d) = 8 and therefore P = 8, i.e., the beam is polarized in the direction of the unit vector 8. The degree of polarization is given by the absolute value of the polarization vector. We see that in the present case, i.e., when the beam is in a pure state, the degree of polarization P = 1, which means that the beam is totally polarized. In general the polarization vector is determined by three orthogonal
8
P. S. FARAGO
components, for example those parallel to the three axes of a Cartesian coordinate system :
Pz
P,
= (d,)
= (d,)
P,
=
(4)
Since under the present conditions (d,) =
e,
(d,) =
e,
(d,) = e,
where e,, e,, e, are the components of the unit vector 8, the density matrix (2.5) takes the simple form:
@=A( 2
1+e,
e,
+ ie,
1 - e,
(7)
It should be noted that Eqs. ( 5 ) and (7) give the density matrix of a pure state. At this stage it is useful to look at some of the general properties of the density matrix (IS) of a beam in pure state as defined by Eq. (4). (1) The matrix is Hermitian, since P i k = p:, and therefore the diagonal elements must be real numbers. (2) The meaning of the diagonal elements is simple: pl1 = uluI* is the probability that an electron, picked out of the beam arbitrarily, is in a state characterized by the state vector a, and pzz = uzuz*is the probability that an electron in the beam is found in the state characterized by the eigenvector b. (See Eq. (3) and footnote 2.) (3) The sum of the diagonal elements, called the trace of the matrix, is unity: Tr p = ulul* uzuz*= 1 (8)
+
because the wave function describing the beam has been normalized that way. (4) In Eq. (4) the density matrix p is given in terms of the eigenvectors of the operator d,. By a suitable transformation, however, it can be brought to a diagonal form (in which case the off-diagonal matrix elements are zeros). This form is obtained if the density matrix is defined in terms of the eigenvectors of the operator (d a), & being the direction along which the spin of each electron was made to be +Ti by means of the preparation of the beam. The result of this transformation is
-
The density matrix characterizing a totally polarized electron beam can always be brought to this special form. Let us consider again an electron beam, produced in any arbitrary
ELECTRON POLARIZATION A N D g-FACTOR ANOMALY
9
manner, and, as before, let each electron be subjected to all conceivable measurements which are quantum-mechanically compatible. Thus we find several groups of electrons, so-called “representative ensembles,” within which each electron is in the same state. However, the states of electrons in different ensembles are different. Hence each ensemble can be described by one state vector, but different ensembles are described by different state vectors. We recognize that in preparing a beam in a pure state one of these representative ensembles was retained, and all the others were rejected. An electron beam which consists of a number of different ensembles cannot be described by a single wave function, and it is said to be in a mixed state, or more briefly it is a mixture. If an electron beam is in a pure state it can be described by a wave function and the introduction of the density matrix does not lead to any great advantage. If, however, the electron beam is in a mixed state, the density matrix is the most suitable mathematical device for its description that contains all the physically significant information. The fundamental principles of quantum mechanics tell us that, since the classification of the electrons into representative ensembles is based on compatible measurements, the state vector of each ensemble can be expressed in terms of the same set of basic state vectors, which form a complete orthonormal set. For instance, turning our attention to the spin states of the electrons in the beam, we can use as a basis the eigenvectors, a and b, and the state of the different ensembles, labeled by the numbers k = 1, 2, 3, . . . N , is described by
+ Qb + upb . . . . . . . . . = @)a + u p b = u:”a
$‘‘I
== u;”a
$(2)
. . $(W
...........
For each ensemble we can find the mean value of the spin operator as before, for the kth ensemble, for instance, (d)(k)
= ($(k), d$(k))
or, writing it out explicitly for the components, (d,)(k) = ((j)(k)
(Qk)
= =
u(k)U(k)* 1
2
i(u;k’u;k’* u;k)up)*
+ u;k)u;k)*
- u B’u:“*I -
(k) (k)*
(10)
u2 UP
Let us recall that the need for the introduction of a mean value at this stage arises for the same reason that it arises in the case of the pure state -or the case of a single electron, for that matter. Each is a quantum-
10
P. S. FARAGO
mechanical system, and the precise values of the spin-vector components cannot be determined simultaneously. To determine the mean value of the spin vector for the electron beam as a whole, further averaging over all the constituent ensemble is necessary. The average value of the spin vector over all the ensemble will be called, by definition, the polarization of the beam: N
Introducing the density matrix by the definition N
we get from Eq. (11) using Eq. (10)
I t has to be pointed out that one of the significant consequences of the introduction of the density matrix is that it gives a convenient means for evaluating average values. It can be shown quite generally that if an observable quantity is represented by the operator Q,then the average of this quantity over all the representative ensembles of the mixture is given by the trace of the product of the density matrix and the operator in question, 0 = WeQ) (14)
It is easy to convince oneself that Eq. (13) is in agreement with this relation. Just as was done earlier, the density matrix can be written in terms of the components of the polarization vector:
P, - iP, It can be seen that the formal relationship between the polarization vector and the density matrix is the same for a beam in a pure state and one which is a mixture. The properties of the two beams, however, are different and this is well displayed by the differences between the properties of the density matrices in the two cases. Before discussing these differences, it has to be pointed out that two basic properties of the density matrix are maintained even in the present
ELECTRON POLARIZATION AND Q-FACTOR A N O M A L Y
11
more general situation: it8is Hermitian (hence t8hediagonal elements must be real numbers) and its trace is unity. Furthermore, it can be shown (13) that the possible values of the density matrix elements are limited, namely, the sum of their squares cannot be larger than unity: lP&
+
IP1212
+
IPZ112
+
IPZ212
6
1
Inserting the elements of the matrix (15), this relation gives
P,2
+ P,Z + Pz2 =
P2
1
(16)
The equality applies if, and only if, the density matrix represents a pure state, i.e., if the whole beam is described by a single wave function and thus the density matrix defined by Eq. (12) reduces to Eq. (4). If the electron beam is a mixture, relation (16) applies as an inequality, and means that the electron beam cannot be totally polarized. To define the density matrix it was necessary to choose a basic set of eigenvectors, and quite arbitrarily the eigenvectors of the operator d, were chosen. A change in the choice of the bases will change the matrix elements, and just as in the case of a pure state, it is again possible to find a basis that will make the density matrix diagonal. The properties of the density matrix will not be changed, but in the present case of a mixture, as opposed to the case of a pure state, bot,h diagonal elements of the density matrix will be different from zero, and density matrix (15) takes the diagonal form: 1 l + P 0
e=$j
(
1 - p O ) This matrix can be written as the sum of two matxicm:
The matrix
is the densit,y matrix representing an unpolarized beam.3 It was shown earlier that the matrix
(i i)
represents a totally polarized beam.
Thus Eq. (17) shows that, in general, a n electron beam in a mixed state can be decomposed into an unpolarized and a totally polarized beam; the weighting factor P is the degree of polarization. Clearly the extreme values P = 0 and P = 1 correspond to unpolarized and totally To justify this one calculates the polarization, i.e., the average over all ensembles of the spin vector by using this density matrix: P = 5 = Tr ed = & Tr d = 0.
12
P. S. FARAGO
polarized beams, respectively; 0 < P < 1 describes partial polarization. It is good to remember the reverse of the above arguments: if an electron beam is partially polarized or unpolarized it is a mixture in the quantummechanical sense and it cannot be described by a single wave function. If the direction of polarization is parallel to the beam axis, the polarization is said to be longitudinal; if the direction of polarization is perpendicular to the beam axis, the polarization is called transverse. Earlier we talked about preparing an electron beam in a definite state of polarization, a process which involves the use of some filtering device sensit.ive to the state of polarization of the incident particles. A similar device is also used for the detection of polarization. In order to calculate the probability of the response of the filter, i.e., the intensity of the beam transmitted by such a filter, with the incident beam intensity taken as unity, the filter may be considered as a quantum-mechanical system, and represented by a Hermitian operator, say F.The probability of response is given by the mean value of the operator, and if the incident electron beam is described by the density matrix p, one finds
An ideal polarization detector responds completely only to a beam which is totally polarized in a given direction specified by a unit vector, say, 8 with components e,, e,, e,. Such a filter is represented by an operator identical with the density matrix of the beam which is transmitted by it [see Eq. (7)], and hence the probability of response t o a beam of polarization P is
W
=
Tr(pF) = Tr +(1
+ P a 8) = +(1 + P cos e)
(18)
where 8 is the angle made by the unit vector, 8, with the direction of polarization of the incident beam. A beam totally polarized along the direction 8 is completely transmitted, W = 1, since in this case P = 1 and e = 0; a beam totally polarized in the opposite direction (0 = T) is not transmitted at all, W = 0. A real detector deviates from the above described one in detecting total polarization parallel to 8 with a probability wmax < 1, the total polarization antiparallel to 2 with a probability wmin > 0. Such a detector can be described by the operator (12)
F’ = w
+
1 B(Aw/w)e, b(Aw/w>(e, -I- ie,)
+(Aw/w)(e, - ie,) 1 - $(Aw/w)ez
)
where w
=
+(Wmax
+
Wmin)
and
AW
= Wmax
- wmin
(19)
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
13
The probability of response of such a detector is
W = Tr(eF’)
=
w[l
+ +(Aw/w)P. 4
=
w[l
+ +(Aw/w)P cos 01
(20)
A polarization-insensitive detector is clearly characterized by Aw = 0, and in the ideal case it transmit,s the beam without attenuation, i.e., W = w = l . It has to be emphasized that the foregoing treatment is nonrelativistic and therefore it is strictly applicable to beams of slow electrons only. The extension to relativistic electrons requires the generalization of the Pauli spin operator d, and the essential consequence of this is that the polarization measured in the laboratory system of reference can be different from that observed in the rest frame of reference of the electron. More precisely, it can be shown that the longitudinal component of the polarization is the same in both systems of reference, but the transverse polarization in the laboratory frame of reference is smaller than that in the rest frame, the reduction factor being [l (Ek/rncZ)]-’ where Ek is the kinetic energy of the electrons of rest energy mc2. [See Frauenfelder and Rossi (9).]
+
111. THE EFFECTOF MACROSCOPIC FIELDS ON POLARIZATION The motion of electrons in macroscopic electromagnetic fields which are constant in time is described by the classical equations of motion, and electron trajectories are best treated by the methods of geometrical electron optics, provided that beams are defined by apertures with linear dimensions large compared with the de Broglie wavelength of electrons. Otherwise diffraction effects occur and the concept of a trajectory is no longer valid. The fields being “macroscopic” means in this context that the field intensities can be considered constant over regions of space which are large in comparison with the de Broglie wavelength. It goes without saying that if the electrons are fast, i.e., their velocities approach the velocity of light, the equations of motion must be written in a form which is relativistically correct. Now, the following question arises: If a beam of polarized electrons passes through a n electromagnetic field, how will the field affect the polarization vector? In many practical situations fields are designed to deflect the electron beam, by changing the linear momentum of the electrons. It is of particular interest to see how the direction of the polarization vector changes with respect to the direction of the linear momentum; considerations of this kind reveal the possibility of transforming longitudinal polarization into transverse, and vice versa (1%-e) . The problem is greatly simplified by the fact that the effect of a macroscopic electromagnetic field on the polarization can be described
14
P. S . FARAGO
classically. In the nonrelativistic case this claim can be justified as follows (IS). It is well known that if an operator Q representing an observable is not an explicit function of time, its time rate of change is given by the equation ih(aQ/at) = QH - HQ where H is the Hamiltonian operator of the system. It is not difficult to show that (except for the sign) a similar relation applies to the time rate of change of the density matrix e:
ih(ae/dt) = He - pH
(21)
With the aid of this equation and Eq. (14), one can write down the time rate of change of the average of any operator representing an observable; for the polarization vector one has
aP/at
= (a/at)(d)
=
(a/at) Tr(ed)
Since d does not depend explicitly on time, and the time dependence of its average arises from that of e alone, one finds
dP/dt
= =
Tr[(c?e/at)d] = -(i,/h) Tr(Hpd - eHd) - ( i / h ) Tr[p(dH - Hd)] = - (i/h)(dH - Hd)
(22)
(Use has been made of the fact that the trace of the product of two matrices is independent of the order of the factors.) To obtain an explicit equation of motion for the polarization vector the Hamilton operator has to be established. The interaction between spin and electromagnetic fields takes place only by virtue of the magnetic moment of the electron I.1 = (g/4)(e/m)h (in mks units) where the constant factors g is very nearly 2 (see Section V), and the Hamiltonian is
H = -
*
B
-
(e/m)hd Bo
= - (g/4)
if the electron is at rest in magnetic field B,. With this Hamiltonian Eq. (21) yields
dP/dt
=
+i(g/4)(e/m)(d(d
6
-
Bo) - (d B o ) ~ )
Expanding the right-hand side and taking into account the relevant commutation rules [see Eq. (2)], one obtains finally
dP/dt
=
+g(e/m)(d) X Bo = +g(e/m)P X B
= -ao
XP
(23)
ELECTRON POLARIZATION A N D g-FACTOR ANOMALY
15
where 00= + g ( e / m ) B o
is the angular frequency of precession of the polarization vector in the field Bo. Equation (23) is just the classical equation of motion of the angular momentum P, associated with a magnetic moment +g(e/m)P. This theorem remains valid in relativistic generalization also (14), in the sense that averages of dynamical quantities derived from the relativistic quantum mechanics satisfy the corresponding equations of motion of relativistic dynamics. T o determine the behavior of the polarization vector in the laboratory frame of reference one can start by taking Eq. (23), valid in a coordinate system in which the electron is at rest, and then calculate the precession frequency using the transformation rules of the special theory of relativity. For a rigorous treatment of the problem the reader should refer to the papers by Bargman, Michel, and Telegdi (15) and by Meister (16); a somewhat simplified consideration is given below. The transformation of t,he angular frequency 0 0 , measured in the rest frame of reference of the electron, must take into account that the time scale in the laboratory system is different from that in the rest frame by a factor ( l / y ) = (1 - Z P / C ~ ) where ~ / ~ , v is the instantaneous velocity of the electrons and c is the velocity of light. I n addition to the change in time scale, a further correction is necessary. If the electron is not in rectilinear uniform motion, the Lorentz transformation itself does not lead t o the rest system immediately, but to one which itself is precessing with respect to the rest system (“Thomas precession”) (17) with an angular frequency OF
=
-(l/v2)(y - l ) X~( d v l d t )
From the equation of motion, v X ( d v l d t ) = ( l / m r ) v X ( d p l d t ) can be obtained. If the electron of rest mass m is in a n electromagnetic field, E , B, then dp/dt
=
e(E
+ v X B),
(24)
where p = myv is the linear momentum of the electron. If E and B are the field intensities measured in the laboratory frame of reference the magnetic field relevant for the precession of the polarization vector in the rest frame of the electron is given b y the transformation Bo
=
+
v(B v ) / v ~
?[V
X ( B X v ) / ’ v ~-
(V
X E)/c2]
16
P. 5. FARAGO
Therefore the precession frequency in the laboratory system is L
-~ (’
(1 - ?-‘)(a
+ :gY1)]
(25)
C2
where
1 << 1
a=;g-
is the g-factor anomaly of the electron (see Section V, A). In experiments one is usually looking for longitudinal or transverse polarization, and in the present context one is interested in the way one kind of polarization changes into the other when the beam is traversing an electromagnetic field. I n other words, one is primarily interested in the change of the angle 0 between the polarization vector P and the direction of the velocity of the particles. This angle can be defined by the relation cos 0 = ( P * v)/Pv Resolving the polarization vector into components parallel and perpendicular to the velocity of the electrons
P
=
ir cos 0
+ ii sin 0
-
where signifies unit vectors and D A polarization vector gives A
d 0 / d t = fi
= w
*
-
6X
Noting that A ( d t / d t ) = (mvT)-’A (25), one obtains from (26) Q
= (e/m)[aA
(ir X B )
=
A
0, the equation of motion of the
+ A . (dir/dt)
(26)
- (d#/dt), and substituting (24) and
+ (A
*
E)(vr)-’(u - g/2rz)l
(27)
Equation (27) shows that if a polarized electron beam enters a field ( E , B ) such that the direction of the polarization vector makes an angle 0 with the beam axis (direction of electron velocity), this angle will change in the course of the passage through the field. In regard to the magnitude of this effect it should be remembered t,hat a ‘v (see Section V) and hence the term containing this factor is usually negligible. The effect described by Eq. (27) is used in practice for the transformation of longitudinally polarized beams into transversely polarized ones, and vice versa, by means of macroscopic fields. In practice it is of considerable advantage to use field distributions which focus the beam while performing the rotation of polarization. A few examples are given below. (A) Fields are called “longitudinal” if their direction is parallel to
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
17
the velocity of the electrons in the beam, i.e., v X B = v X E = 0. I n this case, Eq. (27) gives Q = 0, i.e., the angle between the polarization vector and the beam axis is constant. The polarization vector, however, does not point in a fixed direction. From Eq. (25) one finds
which is the classical Larmor frequency. Equation (28) shows that if the fields are longitudinal, only the magnetic field affects the motion of the polarization vector making it precess with the Larmor frequency about the direction of the field, which coincides with the beam axis. The effect of the electric field is to accelerate the electrons, and, if they reach I
f
I
FIG.2. See the discussion in text of electron motion in sector fields and its optical description. F represents the foci.
relativistic velocities, the magnitude of the transverse component as observed in the laboratory system will be different from that in the rest frame of reference. (B) It is the case that the properties of most devices using transverse fields to rotate the polarization vector with respect to the beam axis can be derived from a radial electric field maintained between two sectors of coaxial cylindrical electrodes and a superimposed homogeneous magnetic field parallel to the cylinder axis. The basic features of electron motion in such fields can be summarized as follows (Fig. 2). Assuming that the electrodes are at a potential U and - U , respectively, there is a cylindrical equipotential surface of radius R between the electrodes where the potential is zero. Between the electrodes the field can be described in cylindrical coordinates by
E,
=
E,(R/r)
8e
=
E,
=
0
(294
18
P . S. FARAGO
and the magnetic field is
B,
=
Be = 0
B.
=
Bo
It is assumed that both fields vanish abruptly at the plane boundaries of the sector. An electron entering the field at R perpendicularly to the boundary ( u E = u B = 0) will move in a plane perpendicular to the cylinder axis along the equipotential curve of radius R, provided the centrifugal force equals the force due to the fields, 1/R
=
+ (eBdmyv)
(eEdmyv2)
(30)
If the electric or magnetic field were to act alone, then the trajectory of such an electron on its entrance would have a radius of curvature l/pe = eEo/myu2
or
l/pm =
eBo/myv
(31)
The radius R of the “equilibrium orbit” satisfies the relation 1/R
=
(l/Pe)
+ O/Pm)
(32)
In applying Eq. (27) to the present situation, we take A to be in the plane of the electron trajectory4 so that =
a(e/m)Bo
+ (e/mv)Eo(a
- ig/y2)
If the electron spends a period t in the field, the beam undergoes a deflection A+ = vt/R, and the change in the direction of the polarization vector with respect to the beam axis is therefore A+ = Q(A+R/v), which, using relations (11) and (32), takes the following explicit form:
I n a pure magnetic field
pe + a
and therefore
A+ = ayA4
(34)
Were the magnetic moment of the electron exactly equal to 1 Bohr magneton, a = 0, the polarization of the beam would not change a t there is a all. Because of the anomaly in the magnetic moment, a ‘v slow change in polarization, and it can be quite substantial in the extreme relativistic case y >> 1. If the electrons are left in the magnetic field to describe k cyclotron orbits, the change of the direction of orbital momen4 This condition implies that the polarization vector P i s in the z = 0 plane, P , = 0. For the more general situation (16) one can show that P. = const., and the results of the present discussion apply to the behavior of the vector i X P.
ELECTRON POLARIZATION AND 9-FACTOR ANOMALY
19
tum is A+ = 27rk, and the polarization vector rotates with respect to the orbital momentum by A@ = 27rkya
In a pure electric field maintained between coaxial cylindrical condensers, p m m and Eq. (33) reduces to ---f
A@ = A d a - W Y )
(35)
Taking a 0 one finds A@ = -A+/T, i.e., with a cylindrical condenser yielding a fixed beam deflection, the rotation of polarization with respect to the beam axis is a function of the velocity of the particles. For slow electrons y ‘v 1 and A+ N -A@ effectively independent of energy. Cylindrical condensers functioning as described above have been extensively used for the rotation of polarization, particularly to change the longitudinal polarization of a beam into transverse polarization, or vice versa, requiring ]A91 = &r in this case. An important property of a cylindrical field is that it focuses the beam in the plane perpendicular to the cylinder axis, and therefore the design of this type of polarization “transformer” is primarily an electron-optical problem, discussed later. If superimposed electric and magnetic Jields are used, arranged as described before, it is always possible to adjust the fields in such a manner that with a given beam deflection A+o a predetermined spin rotation A% is obtained for any chosen value of the electron energy. This can be seen from Eq. (33). Given Ado, A%, and y one can always choose the fields Eo and Bo in such a manner that the value of pe/Pm =
EO/VBO
satisfies Eq. (33). The “Wien filter,” which consists of crossed homogeneous electric and magnetic fields, is a special example of this case. The two fields are chosen in such a manner that the electric and magnetic deflections compensate one another: p e / p m = -1, and therefore electrons with velocity v = Eo/Bopass through the field undeflected. In this case, A+ = 0 and R --f a,but their product is finite: RA4 = L is the total length of the field measured along the undeflected beam. Taking this into account, one finds from Eq. (33) A@ = (e/m)L(B02/EO)-y-2
(36)
Thus, a given filter of length L will give a prescribed polarization rotation at any kinetic energy E k = m c 2 ( y - 1 ) if the fields satisfy the condition (36) and cBo/Eo= y(y2 - 1)l’z.
20
P. S. FARAGO
Because of the possibility of setting the filter to give a prescribed polarization rotation at any selected value of electron energy it is a very flexible tool for transforming beam polarization and has been used by a number of research workers. I n order to utilize the velocity-selecting property of the filter, its focusing properties have to be known. (C) The field configurations considered in the previous section from the point of view of the rotation of the polarization vector have wellknown focusing properties and it is interesting to see how the two effects are related to one another, since this may influence one’s decision in the choice of the “polarization transformer.” We shall consider a somewhat more general field distribution than previously: the fields are sectors of axially symmetric fields with plane boundaries intersecting in the axis of symmetry and satisfying certain symmetry conditions. Using cylindrical coordinates r, 8, x , we require that in the plane z = 0 the fields be given by
&fdr/R)
E,
=
E g
= E, = 0
Furthermore, if z
=
B, = Bofdr/R) B, = Be = 0
fi(U
=
fdl) =
1
0,
E&) = Er(- 2 ) E*(z) = --E,(-z)
B,(z) = --B,(-x) B,(z) = B , ( - z )
all these relations being valid if 0 6 8 6 Oa and the fields vanish abruptly at the boundaries. A particle entering the field at z = 0, r = R with its velocity perpendicular to both fields and satisfying Eq. (30) will move in the x = 0 plane on a circular trajectory of radius R . Calling this circular arc the “equilibrium orbit” of electrons in the fieId, the focusing properties can be determined by investigating the motion of electrons slightly displaced from this equilibrium orbit (18). The position of an electron can be described by the coordinates s, y, x defined as follows: s is measured along the equilibrium orbit from an arbitrary point of reference, say s = 0 at 8 = 0; y is the radial displacement from the equilibrium orbit, and z is the displacement perpendicular to the equilibrium orbit. If the classical Hamiltonian equations of motion are set up in the relativistically correct form the length of arc s can be introduced as an independent variable instead of time, and thus one obtains differential equations for the trajectory. Considering only the motion of electrons which stay in the vicinity of the equilibrium orbit, an approximation retaining terms up to the second order in y, z, in their conjugate momenta, and in their derivatives is permissible.
21
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
I n this way one obtains for the equations of the trajectory d2y/ds2 = -Xx,'y d2z/ds2 = - A z %
(37)
with
Clearly Eq. (38) describes simple harmonic motion about the equilibrium orbit in its plane and perpendicularly t o it if X,2 > 0 and X,2 > 0, respectively, or in other words one obtains focusing in the plane of the equilibrium orbit if Xu' > 0, and focusing in the axial direction if A,' > 0. The field described acts as an electron lens with cardinal points defined by the following relations (Fig. 2) : Distance of focal points from boundary, g, Distance of principal planes from boundary, h, focal length, .f,
X, ta n X;R9
l/g
=
h 1/.f
=
-AX,tan+X,R9
=
X i sin X,R9
where i = y, z. Thus the electron-optical properties of the lenses are determined by the radius of the equilibrium orbit R, the resulting beam deflection 9, and the parameters Xi. In the design of a polarization transformer one is interested in the electron-optical properties of the transformer with given R and A p = 0 and which gives a predetermined polarization rotation A+ (19.) For the sake of simplicity let us take g = 2, in which case Eq. (33) reduces to A@/A4 = - ~ - ' ( 1 4-pe/pm>-'
+
This approximation is permissible provided y 2 ( l p e / p m ) << 1000, a condition satisfied in mostj cases of practical interest. Using the above approximate expression for A @ / A 4 and taking the relations (31) into account, Eq. (38) can be rewritten6 as follows:
(RX,)
=
(RX,)'
=
( a E r / a ? " ) R- ( a B a / a r ) R ] -p A 4 [I Eo/R Bo/R (A+/A@)' - (RX,)'
(aBs/a?")R
BdR
1
+
(39)
6 The trajectories in the present case are not plane curves. It can be shown, however, t h a t in the "paraxial" approximation considered the effects of the deviation from a plane curve are negligible. It also should be noted t h a t the present treatment is based on the assumption that the degree of polarization is constant. This assumption is examined at the end of this section.
22
P. S. FARAGO
These equations show that if focusing is obtained in the plane of the equilibrium orbit only, A, = 0, A, # 0, the optical properties of the system will be energy independent provided that A@/A4 is energy independent. As was shown earlier, to satisfy this condition a combination of electric and magnetic field is necessary. If double focusing (A, # 0, A, # 0) is achieved by using inhomogeneous fields, the axial focusing will be energy independent if either (A@/A4) = const., or
The former is the case if an electric field is produced between concentric spherical shells in an equatorial plane of the spheres E , = Eo(r/R)-2, E , = Ee = 0. To achieve double focusing with energy independence of the rotation of polarization, an additional magnetic field can be introduced which satisfies Eq. (40). The simplest solution is t,o use a “wedge-shaped” magnetic field, B, = B0(r/R)-l, B , = Be = 0, in addition to the electric field of the spherical condenser. The characteristics of a few arrangement>sare summarized in Table I TABLE I Field in plane z = 0
A@/Alg
B = 0, E cylindrical
Y-’
B = 0, E spherical
Y-’
(z)
1
+
$)-I
B “wedge” E spherical shaped, ? P ( l
+
$)-I
Wien filter: B, E uniform
(Rd2
Remark a
Sl(1
BE uniform, cylindrical
(RZ)Z
A@/L =
6)
1
x 2 .
=
0 :(2)2
20,21
22,23
“double” focus Energy independent, “single” focus Energy independent, “double” focus ... Energy inde- 24-25 pendent, “single” focus
“e)
O
(eBoe)/ ( ~ * E o )
Energy dependent, “single” focus Energy dependent,
Reference
ELECTRON POLARIZATION AND Q-FACTOR ANOMALY
23
(20-26). For the Wien filter, since the beam axis is straight, R = w , the parameters are different from those of the other systems. Details of design and a description of the performance of various systems are given in the references shown. In the previous discussion only the effect of static fields was considered. It should be recalled that the discussion started by establishing the equation of motion (23) of the polarization vector characteristic of an ensemble of electrons at rest in a magnetic field Bo. To deal with an electron beam, the motion of the electrons was taken into account by determining the field “seen” by the electrons with the aid of appropriate transformations. The transformation equations contain the velocity of the electrons, and the application of the results derived imply that all the electrons in the beam have identical velocities. I n the case of a uniform magnetic field or a uniform longitudinal electric field, the velocities of the electrons stay the same throughout the motion if they were initially identical, but in fields of more general distribution the condition mentioned requires that the electrons have identical trajectories. Considering particles moving on an equilibrium orbit this condition is satisfied. In part (C) the electrons considered did not follow identical trajectories but their displacement from the equilibrium orbit was assumed to be small, and that is why it was anticipated that effects arising from this would be negligible. To describe the variation of the polarization vector P in time in complete generality, the solution of Eq. (21) has t o be reexamined. Denoting the density matrix at a time t by e(t), the solution of Eq. (21) can be expressed with the aid of a linear transformation T(t)
e(t) = Te(O)T+
(41)
The condition of “identical trajectories” expressed in quantummechanical terms means that-disregarding spin-all particles in the beam are in the same state, i.e., the spin-independent part of the Hamiltonian is the same for each electron. I t can be shown that in this case the operator T is unitary (TTf = l), i.e., e(t) = Tp(0)T-I. Hence it follows that Tr ez(t) = Tr $(O) and therefore P“t) = P ( 0 ) i.e., the degree of polarization is unchanged in agreement with Eq. (23). In general, however, particles start with different initial conditions, and constitute a beam which cannot be described by a single Hamiltonian. If, accordingly, one takes into account that the beam is in a mixed
24
I?. S. FARAGO
“space state” t o start with, although it is still possible t o relate the density matrices p(t) and p(0) b y Eq. (41), this time T is no longer a unitary transformation. Therefore T r pz(t) # Tr pz(0) and consequently P ( t ) # P2(0), i.e., there is a change in the degree of polarization as well as in the direction of the polarization vector. For details of this consideration the reader has to consult the original papers (ISb,c). The problem of depolarization in a n axially symmetrical magnetic field, in which electrons oscillate about a n equilibrium orbit ( I & ) , is of particular interest from the point of view of the measurement of the g-factor of free electrons, discussed in Section V, E, where the time spent by the electrons in the field is long compared with the period of the Larmor precession. I n situations discussed earlier in this section the change in the degree of polarization is negligible, as anticipated. The effect of fields varying in time is of major interest if they are acting in the presence of a static magnetic field and result in a perturbation of both the orbital motion and the behavior of the spin vector. If the frequency of the perturbing field is in the vicinily of the cyclotron frequency, of the Larmor frequency, or linear combinations of these frequencies a variety of resonance effects can occur depending on the spatial distribution of the perturbing field. Such phenomena will be discussed in Section V with reference to particular schemes suggested for the measurement of the g-factor of free electrons.
IV. THEPRODUCTION OF POLARIZED BEAMS I n the preceding section the behavior of a polarized electron beam was discussed and the magnitude of the polarization was found to remain constant,. I n the present section we shall investigate the possibility of turning a n initially unpolarized electron beam into a polarized one. The methods which have been suggested, in some cases tested experimentally, fall into three categories, which will be discussed in Sections IV, A, IV, B, and IV, C. A . Polarization by rntEruc~ionwith Macroscopic Fields There is a well-known theorem of Bohr, justified in completely general terms by Pauli (27), which states that the spin of a n electron cannot be separated from its orbital momentum b y means of experiments which can be interpreted in terms of classical particle trajectories. This is equivalent t o saying that an unpolarized beam cannot be turned into a totally polarized one by means of a system designed by geometrical electron-optic considerations. It appears, however, th a t the theorem often has been niisunderstood and misquoted, and therefore it seems worthwhile to discuss it in some detail.
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
25
T o obtain a separation of electrons of magnetic moment p in the two spin states one would set up an inhomogeneous magnetic field B, to subject the electrons to a translatory force
F, =
V(p* B)
=
+MVB
opposite in direction for the two possible spin states. There are two cases one would consider: (i) grad B is perpendicular to the direction of the beam, as in the Stern-Gerlach experiment, when the force F , deflects the electrons in a direction depending on their spin states; (ii) grad B is parallel to the direction of the beam and the force F , accelerates or decelerates the electrons depending again on t,heir spin states. Because of the electron charge, el there is, of course, the Lorentz force F, = ev X B acting on the electron and it can easily mask the effect of F,. Therefore in designing such an electron-optical polarizer there are two requirements which have to be satisfied: (a) conditions should be chosen in such a manner that the effect of the Lorentz force is smaller than that of F, and (b) in order that electron trajectories may be described in terms of classical mechanics the smallest linear dimension, d, of beam-defining apertures should be large enough to guarantee that the change of the transverse dimensions of the beam due to diffraction will be small compared with the original beam diameter. (i) There is a well-known argument (28) which shows that in the case of the Stern-Gerlach experiment conditions (a) and (b) are incompatible. Indeed, the Stern-Gerlach experiment is the best known example demonstrating the validity of Bohr's theorem quoted above. Since the difficulty in separating electrons in one spin state from others seems to arise from the presence of the Lorentz force, it is tempting to suggest (29) that it should be compensated by a suitably designed electrostatic field. Consider electrons moving parallel to the x axis of a Cartesian coordinate system v = vi in a magnetic field which is everywhere perpendicular to this direction, B , = 0. Such a field can be derived from a vector potential A = A ( x ,y ) i
If a n electromagnetic field derived from a two-dimensional scalar potential a = @(x, y) is superimposed, the force acting on the electron charge is
F, = e[V@ v
+ v X (V X A)] = e[V((a - v - A ) - (v
*
VIA]
Since for the specified case, ( v ' v ) A = 0, this force vanishes if const. and *(x, v) = vA(2, 9)
=
P.
26
S. FARAGO
and under this condition the elect,ron is subject only to the force on its magnetic moment arising from the inhomogeneity of the magnetic field. Pauli has shown (SO), however, that conditions necessary to separate electrons spatially in the two spin states are not satisfied even in this case. His arguments are reproduced below. If the equations of motion are written in the canonical form, it is readily seen that an integral of these equations is no longer the ordinary momentum mv, but the canonical momentum p = mu - eA; this is also an “adiabatic invariant,” i.e., its value is conserved while slow perturbations take place. Suppose that in a field-free space a monoenergetic beam is produced. If now v = vi, as the fields are developed [always satisfying the relation @(x, y ) = voA(x,y)] p = (mu - eA) will stay constant, and consequently v becomes a function of x and y . Thus it is not possible to produce an electron beam in the field described in such manner that the electron velocity is v = vi and v is independent of the coordinates of the electron across the beam. As a result the Lorentz force will not vanish. To compare the Lorentz force in magnitude with that acting on the magnetic moment, one can consider a beam limited by a circular aperture centered on the origin of the coordinate system and with p = const. For the sake of simplicity let
A
=
-(ax
B
=
-bxE
yielding
+ bzy) + (U + b y ) i
Spin orientation is produced by the field component B ,
=
a and the
y component of the force acting on the magnetic moment is
F, Since p
v
=
+ SV, where
=
&p(aB/ag)
‘U
+pb
const., electron velocities on the periphery of the beam are
Sv,
=
(e/m)SA(e/m)bd2
and the g component of the excess force on the charge is
SF,
=
eSv,B,(d)
=
(e2/m)b2d3
Separation of spin states by deflection can be detected if
SF,/F,
=
(e2/pm)bd3<< 1
(42)
Now, electrons will be diffracted at an angle X/d, where X = h/mv,, and if diffraction effects are t o be negligible it is required that along the
ELECTRON POLARIZATION A N D g-FACTOR ANOMALY
27
length 1 of the beam the spread due to diffraction be smaller than the initial diameter d : l ( X / d ) << d
or
lX/d2
<< I
Multiplying this inequality by (42), and recalling that p one finds
= +(eh/m),
On the left-hand side of inequality (43) we recognize the deflection produced by the force act,ing on the magnetic moment of the electron, and see that it is masked by diffraction described by the right-hand side. Thus the separation of tjhe two spin states cannot be resolved. The method proposed to separate spin states with the aid of an electrostatktically compensated inhomogeneous magnetic field has been revived by van der Spuy (31) as part of a suggested experiment. His considerations referring to this part of his scheme are not sufficiently detailed to draw a conclusion as to whether the effect discussed above had been taken into account. (ii) To separate spin states by the application of the retarding force on the magnetic moment of an electron moving in an inhomogeneous magnetic field essentially parallel to the direction of the field and of its gradient was suggested by Brillouin (32). Consider an axialIy symmetrical magnetic field derived from the vector potential A e = +rB(z), A , = A , = 0 (r, 8, z are cylindrical coordinates), yielding B, = B ( z ) , Br = -+r(aB/az), Be = 0. In such a field the total energy of the electron is given by Hamiltonian
H
=
+ + [ ( p e / r ) + +-BIZ) zk PB
( 1 / 2 m ) { p z n pr2
(44)
where p,, p,, and p e are conjugate momenta. If the electrons enter the field with an initial kinetic energy Ek they will penetrate the field to a depth 2 such that p z 2 = 2mEk - p r 2 -
[(pe/T)
+ +erB]2k p B = 0
(45)
Because the last term may be either plus or minus the depth of penetration 2 for the two states will be different, say 21 and 2 2 > 21, respectively, and there is a region in the field, Z1< z < Z 2 , where only electrons in one spin state can occur. The conclusion, however, is different if one takes into account the fact that a beam of finite cross section has to be used in order to minimize diffraction effects. For the sake of simplicity suppose that the incident beam is parallel to the z axis and is defined by a circular aperture of
28
P. S. FARAGO
radius Aro centered on the axis. By this arrangement the initial radial momentum pro, will be undetermined t o an extent Ap,O; the relationship between the two quantities is given by uncertainty principle ArOAprO > h. In the course of the motion of the electrons in the field the uncertainty of radial position and of the conjugate momentum may change, but the relationship ArAp, > F, remains valid.6 Therefore the energy contribution of the orbital motion about the z axis is spread over a range
> >
3+
+(e/m)ArAp,B
(A/m)(pe/Ar2)
+ + ( e k / m ) B > PB
The consequence of the energy spread A E > p B is that the separation of the spin states predicted by Eq. (45) cannot be observed. Bohr’s theorem, as quoted above, is a negative statement. It can, however, be paraphrased to give guidance in the search for methods of polarizing electron beams: “Production of electron beams in which one spin state is preferentially populated can be achieved by processes which can be described only in quantum-mechanical terms.” One must note that apart from putting Bohr’s theorem in an affirmative form, we are now talking about “preferential population” rather than total “separation” of spin states; this change in terminology reflects the statistical meaning of the results of quantum-mechanical considerations. The case in point can be illustrated by comparing quantuni-mechanical calculations with classical ones with reference t o the same system. Let us take, for example, elect>ronsmoving in a n inhomogeneous magnetic field: in the preceding discussion the problem was whether electrons of different spin states moved on distinguishable trajectories. A quantummechanical discussion poses a different problem: Does a particular component of the polarization vector assume a finite value in the course of the motion of the electrons, even though its initial value is zero? Once the definitions of the polarization vector as a quantum-mechanical mean (expectation value) is adopted, the treatment becomes a quantummechanical one even if the calculations are made by solving equations of motion of the classical form. The longit,udinal polarization arising during the motion of a n initially If the uncertainty of the conjugate coordinates Ar and Apr satisfies the relation ArAp, = a, it means that the particle “fills” a cell of volume a in phase space and according to Liouville’s theorem the volume of the phase cell stays constant while the particle moves according to the laws of classical mechanics.
ELECTRON POLARIZATION AND
9-FACTOR
ANOMALY
29
unpolarized electron beam in a n inhomogeneous magnetic field has been calculated recently by Sannikov (33). The Hamiltonian operator replacing the classical expression (44)is
H
=
(l/2m)[‘x2- +gehdB(r)]
(46)
with the canonical momentum operat.or ’x
=
-ihV
-
eA(r)
(47)
where d is the Pauli matrix [see Eq. (l)].A ( T ) is the vector potential ( T is the position vector), B(r) = V X A , and the conditions v B = 0 and V X B = 0 are set. The momentum operator ‘x and the spin d satisfy the usual equations of motion [see Eq. ( Z l ) ] h / a t = ( i / h ) ( ~ H- Hs) & / a t = - (i/h)(dH - Hd)
If one introduces the unit vector A parallel to the orbital momentum, the mean value of the orbital momentum p = (’x), the polarization vector P = (d), and its component parallel to the orbital momentum P, = (d h), the equation of motion of the longitudinal polarizat,ion vector may be written aP,/dt
=
a(e/m)(BX
A) - P
+ ( p / p ) [ ( P - V) - (A. P)(A - V ) ] ( B P )
Note that the above equation is not linear in P. Before attempting to solve this equation the following observations can be made. The component of the orbital momentuni which is in a plane perpendicular to B precesses with the cyclotron frequency wc = ( e / m ) B , and t,he polarization vector component in this plane precesses at the frequency +gwC. I n time T I = 2n/($g - l ) w c the polarization vector describes a full cycle relative to the momentum and both vectors describe about 1000 turns about B . Disregarding orbital rotation and considering the motion parallel to the field gradient alone, the electrons are acted upon by a force + p V B and if their initial velocity parallel t o tlhe field gradient is v, then those electrons which experience a retarding force will be stopped at a time Tz = mv/(pVB) Taking
p ‘v +(e/m)h,
and introducing the electron wavelength
X = h/mv one finds T z / T 1= (g - 2)(B/XVB)>> 1 in all cases of prac-
tical interest. Thus to average quantities varying in time over periods T I involves averaging over periods long compared with the period of orbital motion but short compared with the time needed to (‘stop” the particles.
30
P. S. FARAGO
For this reason it is justifiable to calculate fj,, the average of P, over a period T I ,rather than P, itself. For this purpose both the orbital momentum vector p and the polarization vector P can be resolved into components parallel to the field B and components perpendicular to it
where 8
= wct,
and Go, B,, and & are orthogonal unit vectors with 20 =
2, X &
=
B/B.
The calculation in t,erms of these quantities gives
and integration over the time t during which the electrons drift along the direction of the field gradient yields p,. The result clearly applies t o a representative ensemble of electrons constituting a pure state. Averaging over all ensembles gives
F, and
-
P , -,
= (p/3)
1
if
(P,2/p3)(& * V ) Bdt' t + (p"/pl")(pVB)-i
Whereas it is interesting t o see that a quantum-mechanical treatment of a problem reveals possibilities not revealed by a classical treatment of the same problem, it is difficult to see how, in this particular case, the theoretical conditions could be met, in the design of a n experiment; in particular, how one would achieve a flight time, t, long enough to produce an appreciable polarization in a feasible magnetic field. An approach, entirely different from the previous ones, is suggested by two schemes put fornard for the measurement of the g-factor of free electrons. Both schemes (34, 36) consist of detecting transitions induced by a radio frequency field between quantized energy states of electrons moving in a homogeneous magnetic field. The transitions are detected by observing electrons whirh are removed from the beam. If these electrons were preferentially in one spin state, the system could be used as a source of polarized electrons. Both suggestions will be described in Section V, C, and it will be seen that their use for electron polarization is not feasible.
B. Polarization by Scattering Processes It was mentioned in Section I that the early search for electron polarization followed lines suggested by optical analogies. It is of interest t o ask, for example, whether a process analogous to optical polarization
31
ELECTRON POLARIZATION AND q-FACTOR ANOMALY
by reflection could take place. I n the optical case, one may consider a n unpolarized beam of light as the incoherent superposition of two linearly polarized beams, polarized in mutually perpendicular directions. If such a beam is reflected from a mirror one finds that one component is preferentially reflected and hence the reflected beam is-in general-partially polarized. Similarly an unpolarized electron beam is described by the incoherent superposition of two plane wave functions representing the opposite spin orientations. I n this case one investigates the reflection from a potential discontinuity. Using methods of relativistic quantum mechanics one can show that (i) the reflection of the wave leaves the spin state of the electron unchanged and (ii) the reflection coefficient for both waves is the same. Hence the reflection process does not polarize the beam. For details of the argument outlined the reader should refer to Sommerfeld’s classic monograph (36). A process, somewhat analogous to x-ray scattering (Barkla’s experiment) which does yield polarized beams is the elastic scattering of fast electrons by the Coulomb field of heavy nuclei. At high electron velocities the electrostatic field of a heavy nucleus, as “seen” b y the electron in its rest frame of reference, consists of both electric and magnetic fields of significant intensity. The Coulomb field in the neighborhood of the nucleus is strongly inhomogeneous and the corresponding inhomogeneous magnetic field in the electron’s rest frame of reference gives rise to a translatory force acting on the magnetic moment of the electron. By virtue of this “spin-orbit coupling” the intensity distribution of the scattered beam about the direction of the incident beam is anisotropic if the incident beam is transversely polarized. Although this phenomenon cannot be described classically, a remarkably simple calculation (37) makes the above statement plausible. Considering a classical point particle of magnetic moment M , moving in a Coulomb field E a r / r 3 , with velocity v = v2, the magnetic field in its rest system is B a v X E a (y& - zQ)r-3, where 2, tj, 2 are ort,hogonal unit vectors. Supposing that M is parallel to the direction of motion, M = M 2 , one finds that M . u x E = 0 and hence the force acting on M is F = V ( M . B ) = 0. Thus the motion of the particle is independent of its magnetic moment. If, however, one considers a particle with a magnetic moment perpendicular to the direction of motion, M = mlg m2& one finds M . B a (m2y- r n l z ) r 3 , and hence the force F = V(M * B ) a (mzy - mlz) V+ (mzi - mi)+
+
+
If the electron approaches t3hescattering center head on, i.e., y the above expression reduces to
F
0:
(M X
= x =
0,
32
P. S. FARAGO
Thus, in t.his case there is a force acting on the magnetic moment perpendicularly to the plane determined by the direction of motion and that of the magnetic moment. Hence it may be expected that the transverse polarization will give rise to a scattering asymmetry: there will be more electrons scattered in the direction of F, than in the opposite direction. The quantum theory of the spin-dependent scattering, based on the relativistic quantum mechanics of the electron, has been established by Mott (98,38, 39)-hence the phenomenon is usually called “Mott scattering’’-and has been further developed b y Tolhoek ( 2 ) and others. The results of the theory can be summarized as follows.
FIG.3. See the discussion in text of Mott scattering asymmetry.
(i) If a beam of particles of incident energy E is scattered elastically by a massive point charge Ze at an angle between 8 and 8 do, then neglecting spin-orbit interaction, the intensity of the scatt,ered beam is
+
I
=
I,f(E, 2, 0) d 0
(ii) If the beam has a transverse polarization P t then scattering in a plane perpendicular to P l leaves this polarization component unchanged. (iii) If one considers the intensity of the scattered beam in the plane perpendicular to P , (see Fig. 3), in directions which make opposite angles 0 and -0 with the directmionof the incident beam, it is found th a t
I ( @ )= f[l and 1(-0) =
+ PtS(E, 2, e)]
1[i- P,S(E, z,e)]
(48)
Thus a wattBeringasymmet,ry 6 is obtained: 6
[ ~ ( -e )1(--0)1/[1(0)+ ~ ( - e ) l= P,S(E, z,0)
(49) (iv) If a n unpolarized beam is scattered, tlhe emergent beam is polarized transversely in a direction perpendicular to the plane of scattering, and the degree of polarization, Pol,is given by =
Pol
=
S ( E , 2, 0)
(50)
33
ELECTRON POLARIZATION A N D g-FACTOR ANOMALY
The intensity distribution after scattering a n unpolarized beam is isotropic, but the polarization produced will make a subsequent scattering anisotropic. If the two successive scattering processes take place in different planes making an angle 4 (Fig. 4), then the intensities aft,er the second scattering are, from Eq. (48), Iz(f02) = L(041
f S ( E , 2, 01)S(E, 2, 0,) cos 41
yielding asymmetry after the second scattering 82 =
S(E, 2, 6 J S ( E ,2, 6,) cos #
where 1, is the intensity aft.er the first scattering and angles of successive scattering.
el and
0 2
are the
FIG.4.See the discussion in text of double scattering.
The process described in (iv) makes Coulomb scattering a source of transversely polarized beams, and according to (iii) the same process allows the detection of transverse polarization. The efficiency of the process from both points of view depends on the function S ( E , 2, 0). For low values of the atomic number the asymmetry function S ( 2 ) << 1. Values of this function were calculated by Sherman (40, 41) taking mercury nuclei as scattering centers (2 = 80) a t electron energies E = 128, 205, 304, and 661 kev and for angles 0 in steps of 15” between 45” and 165”. More detailed tables of S ( E , 2, 0), I ( E , 2, 0), and other related functions for 2 = 80 (mercury) and 2 = 79 (gold) have been published recently by Holzwarth and Meister (4.2,4%). As a n example X(E) plotted for 2 = 80 and 0 = 90” is reproduced from Tolhock (a), and S(0) plotted for E = 45, 100, 170, and 204 ltev and 2 = 79 is reproduced from Holzwarth and RIeister (42) (Figs. 5 and 6). It must be made clear that the scattering process is affected by the presence of bound atomic electrons and the calculated values of S depend on how this “shielding” is taken into account (4.2-45). This “shielding” of the nucleus by atomic electrons is one of the complicating factors entering experiments involving Mott scattering. Because of the obvious importance of the function S, a number of experiments have been carried
34
P. S. FARAGO
out to test the theoretical prediction (2, 46-49). The theory refers to single elastic processes whereas in experiments the scattering target, usually a gold foil, is of finite thickness. Therefore correction must be made for plural and multiple scattering, and for an energy-dependent depolarization. For details concerning these problems the reader should
%In (MeJ)
FIG.5. The variation of scattering asymmetry with energy. [Reproduced from Tolhoek (59.1
FIG.6. The variation of scattering asymmetry with scattering angle. [Reproduced from Holzwarth and Meister (@).I
refer to the recent review by Frauenfelder and Rossi (9) and the original papers. I t is sufficient to say here that the experimental values obtained for S for scattering from gold around 90"-120" agree within about 10% with the theoretical value in the energy range between 100 and 250 kev. For the measurement of transverse polarization Mott scattering is the most extensively used method. For this method t o be used to measure longitudinal polarization the beam has to undergo a longitudinal-totransverse polarization transformation before reaching the scatterer. As a source of polarized electrons Mott scattering has two important
ELECTRON POLARIZATION AND
g-FACTOR
ANOMALY
35
limitations. The most important of these is that the scattering cross section is small at angles between 90" and 120°, which yield a relatively high degree of polarization, say 30-40% using beams of 150-200 kev, and therefore the beam intensity is very low. Second, it is difficult to change the electron energies without further loss in intensity. Calculations of the asymmetry function for scattering from gold show high resonance peaks a t low energies (0.6-2 kev). The occurrence of high asymmetry a t such low energies and selected angles can be understood qualitatively as follows. The energy and hence the wavelength of the incident electron in the two different spin states are slightly different from one another because of the interaction between the moving electron and the electric field of the target atom. Therefore, when the electron wave is diffracted by the atom, the maxima and minima of the diffraction pattern have different spacings depending on the spin state of the electron. I n a direction where the intensity is zero in the diffraction pattern for one spin state, only electrons in the other spin state can be observed. To test the theoretical results Deichsel (50) carried out double scattering experiments using a mercury atomic beam as a scattering target, with electron energies in the 1-2 kev energy range at scattering angles 60" < el = e2 < 120". A maximum scattering asymmetry of about 1.5% was found for 2 X 90" scattering at 1.5 kev (corresponding to nearly 40 % polarization in single scattering). Recent calculatioris (42) indicat.e that the asymmetry function has similarly high resonances at, even lower energies (-200 ev). Further experiments by Reichert and Deichsel (5Oa-c) extended over the energy range 900-1500 ev show complete agreement with theory if the calculations take into account the finite resolution in solid angle of the apparat,us. At 10-12A output current over 50% polarization has been obtained. Measurements in the 100-200 ev range are in progress. Polarization effects can also be observed in scattering processes involving interaction between electrons if the target electrons are polarized, i.e., if in the target one spin state is populated preferentially to the opposite one. An example of such a process is the polarization by exchange collision of electrons with oriented atoms. This phenomenon was used by Dehmelt (51,52) for the comparison of the g-factor of free electrons with that of the ground state of Na atoms in an experiment which will be discussed in Section V. It may be noted that, although the polarization of the free electrons is clearly detected in this experiment, it is a n open question whether a significantly polarized beam could be extracted from the system. The possibility of transferring the polarization from a n atomic beam to a cross-fired electron beam through the mechanism of spin
36
I
P. S. FARAGO
exchange collision was investigated recently by Byrne and Farago (52a). Theoretical considerations show that such a scheme is feasible if electrons of low energy (< 1 ev) are trapped in a n interaction region for a few milliseconds. The polarization of the electrons extracted from the trap should be approximately equal to that of the atomic beam. Experiments along these lines are in progress. In a collision between free electrons the scattering cross section depends on the relative orientation of the colliding partners, and the cross section in case of antiparallel spins is larger than that for parallel spins. This follows from the symmetry properties of the wave function describing a system of two electrons obeying Pauli’s exclusion principle. Rather naively, one might say that two electrons with spins parallel, i.e., in the same spin state, cannot occupy the same point in space, and hence cannot collide at all. This situation is approximately true for the scattering by a magnetized foil, because on the one hand in ferromagnetic materials there is a preferential spin orientation along the direction of magnetization, and on the other hand the binding energy of the polarized target electrons is negligible in comparison with the energy of the incident ones. Therefore the intensity of the beam scattered in a given direction depends on the polarization of the incident beam. The spin-dependent properties of electron-electron scattering (“Mgller scattering”) has been the subject of extensive theoretical (53-55) and experimental (56-59) investigations which have led to the development of the most important method for the measurement of longitudinal polarization, particularly of electrons of relativistic energies. For a review of this method the reader should consult Frauenfelder and Rossi (9). The polarization of light by birefringent crystals inspired the experiment of Myers and Cox (60) in search of polarization of electrons transmitted by thin magnetized iron foils. The result was negative. I n view of the qualitative features of Moller scattering theory such an attempt to polarize electrons can be justified as follows. Suppose a thin iron foil is magnetized to saturation in a direction lying in the plane of the foil. An unpolarized electron beam, incident perpendicularly to the foil, can be considered as a mixture of two beams of equal intensity, both with a total transverse polarization, one parallel, the other antiparallel to the direction of the foil’s magnetization. The scattering cross section being different for the two orientations, the transmitted beam consisting of electrons which have suffered no scattering a t all will be polarized to some extent parallel to the magnetization of the foil. One cannot expect a high degree of polarization since even in a foil magnetized t o saturation the degree of polarization of the target electrons amounts to about 8%.
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
37
Raith and Schliepe (6f) have investigated the transverse polarization of 60-kev electrons transmitted by a 500-A thick iron foil magnetized in its plane. The detection method used the asymmetry of Mott scattering of the transmitted beam at 120”, and the polarization was found P < 0.4%. I n a more refined version of the experiment energy analysis of the scattered electrons (with a resolution of about 10 ev) was used to eliminate those inelastically scattered, but the result was the same as before. From this result an upper limit can be set for a “polarization cross section” defined as the sum of the cross section of exchange collision and the spin-dependent part of the total cross section. A quantitative estimate of these quantities supports the result obtained. In a series of almost identical papers (e.g., 6 f a ) Yamaguchi reports the result of electron diffraction experiments carried out with ferromagnetic samples (iron filings on a magnet’s pole face). With a beam at glancing incidence a part of the central region of the diffraction pattern, when examined under considerable optical enlargement, exhibits a splitting which is interpreted as the result of a Stern-Gerlach effect produced by the high magnetic field gradient at the ferromagnetic grain boundaries. In another set of papers (e.g., B l b ) diffraction experiments on NiO-Ni powder are reported and the anomalies in the diffraction pattern are interpreted in terms of electron polarization resulting from a SternGerlach effect caused by the high magnetic field gradient a t the boundaries of the Ni particles within the sample. The brevity of the description prevents a proper assessment of the experiments and in particular leaves doubt as to the justification of the suggested interpretation. Maison ( 6 f c ) has recently suggested that diffraction from a two dimensional lattice of heavy atoms, e.g., the surface of a gold single crystal, could yield a high intensity of a highly polarized beam. Theoretical arguments indicate that coherent scattering from the atoms of the lattice would enhance the intensity of the effect, which has already been observed in the case of target atoms distributed at random, i.e., in scattering by heavy metal vapors (sou). This suggestion seems to contradict the negative predictions of earlier calculations ( B f d ) . It should be recalled however, that, in these calculations, as is usually done, the periodic potential relevant for the scattering from a crystal is approximated by a finite Fourier series. In this way one loses sight of that part of the potential which leads to high field gradients arid which is therefore responsible for polarization effects. The reason why the early experiments of Davisson and Germer ( H e ) failed to detect such an effect is probably that the nickel crystal used consists of atoms of too low an atomic number. It should be mentioned finally that at high energies there are further spin-dependent interactions which-at least in principle-could be
38
P. S. FARAGO
exploited as a source of polarized electrons. For example, Compton electrons produced by circularly polarized gamma rays are longitudinally polarized ( 2 ) as a result of the angular-momentum conservation of the interaction. Whereas phenomena in this category are of great importance in polarization studies as related to nuclear physics, intensity relations rule out their application in the design of a source of polarized electrons of practical interest. For a suggestion relevant a t extremely high energies (several Bev) see Harutyunian et al. (62).
C . Removal of Polarized Electrons from Atoms or from Solids The possibility of producing a polarized beam by removing electrons of a given spin state from atoms or from solids was first discussed by Fues and Hellmann in 1930 and the idea has been revived a t various times. For such a process two requirements must be satisfied. Most-if not all-of the easily removable electrons have to be in one spin state and the method by which the electrons are removed must leave the spin state unchanged. To meet the first condition, atoms with a preferentially populated spin state can be obtained in a Stern-Gerlach experiment and one can select one of the components into which the incident beam is split. This was the approach suggested by Fues and Hellmann (63). An alternative way is offered by the method of optical pumping. In both of these cases the source of electrons is an atomic beam or a sample of a gas. Magnetized ferromagnetic materials offer sources in the form of solid samples. Electrons may be removed from both atoms and solids by photoelectric emission, and it may be expected that the second requirement mentioned above will not be violated in either process. The advantage of using the Stern-Gerlach effect for producing a polarized atomic beam is that it can yield nearly total atomic polarization, provided the atomic electrons have sharply defined spin stat,es. This is the case if in the ground state of the atom there is no spin-orbit coupling and if the electron spin and nuclear spin coupling are negligible. The former condition applies to atoms whose ground state is an s state (1 = 0), and the latter one is satisfied if the external magnetic field is so large that the energy difference of electron spin states is much larger than the hyperfine splitting in the ground state. In addition it is desirable that the beam consist of slow particles to allow possibly large deflection in a reasonably short flight path when the beam is subjected to an inhomogeneous magnetic field. Therefore the source of the atomic beam should have high vapor pressure a t relatively low temperatures. All these requirements indicate that light alkaline atoms (Li, Na, K) can be used with advantage. As mentioned before, photoionization is the most obvious choice for
ELECTRON POLARIZATION A N D $7-FACTOR ANOMALY
39
the removal of electrons from the polarized atoms. The transitions in photoionization are of the same type as those in the Paschen-Back effect, i.e., only the orbital angular momentum is changed.7 Thus the spin states are preserved whatever the polarization state of the incident light. The choice of the actual source of the atomic beam in an experiment is influenced by the efficiency with which photoionization takes place. Lithium has the highest cross section for this process, but in view of the spectral range of commercially available uv lamps potassium is probably the most convenient material. Given an initial atomic beam intensity, the intensity of the separated component can be significantly increased if the inhomogeneous field used for the separation has suitable focusing properties. The inhomogeneous Stern-Gerlach magnet Oven
I
uv light
Wien filter \
Detector
n/
I I
Atomic beam separation
Ionization alignment
B
Polarization rotation
FIG. 7. The basic arrangement of Friedmann’s experiment. [Reproduced from Friedmann (69).]
field can be shaped in such a manner that atoms of one polarization state are subject to an attractive force directed toward an axis or plane of symmetry, and are thus focused, whereas atoms in the opposite polarization state experience a repulsive force, and are thus defocused. Such an effect can be obtained by the field of a six-pole magnet (64-66) acting as a “spherical lens,” or by a restricted region of the field of a dipole magnet (67, 68) acting as a “cylindrical lens.” The considerations outlined above guided Friedmann in the design of his experiment (69), shown schematically in Fig. 7. A t an oven temperature of about 400°C a potassium beam emerges from a 3 X 0.045 mm slit into the inhomogeneous field of a 16-cm long electromagnet with 7 It is recalled t h a t the Paschen-Back effect takes place if atoms are situated in such a high external magnetic field that the Zeeman splitting is larger than the multiplet splitting. In this case the spin-orbit coupling is destroyed, and only the orbital angular momentum changes in a transition. For an atom with a single valency electron the transition in photoionization leads from the ground state (t = 0) t o t h e continuum, where the multiplet separation is zero. Hence the Zeeman splitting, even in a very weak field, is larger than the multiplet splitting.
40
P. S. FARAGO
wedge-shaped pole pieces 2 mm apart. The oven slit is perpendicular to the direction of the field and the passage of atoms in the neighborhood of the plane of symmetry of the system is blocked by a fine wire a few centimeters downstream. The exit aperture is designed to fit the geometrical shadow of the wire so that practically no atoms pass through and out of the system if the magnetic field is off. With the field on, atoms in one polarization state are focused into a line parallel to the exit slit and atoms in the opposite polarization state are focused into a line perpendicular to the slit. With the system appropriately aligned the emergent beam consists predominantly of atoms in one spin state. The output beam intensity was estimated to be about l O I 4 atoms/sec, and the polarization not less than 96%. The direction of polarization, which is at this stage perpendicular to the beam direction, is turned into the beam direction adiabatically while the atoms move into a uniform magnetic field parallel to the beam, and it is in this region that the electrons are detached by photoionization. A beam of uv light is reflected from a mirror into a direction parallel to the atomic beam, and thereby interaction between atoms and light can take place over a long flight path ( ~ 1 cm). 2 Along this interaction section an electrostatic field is maintained to remove the free electrons and accelerate them for further analysis. The electrons thus produced are longitudinally polarized. In order to measure their polarization by ILIott scattering a longitudinal-to-transverse polarization transformation is performed by means of a Wien filter (see Section 111). The maximum output electron current was about A, some three orders of magnitude higher than expected from the available atomic beam intensity, and the polarization of the electron beam was found to be about 84%. Observations made in the course of attempts to reproduce the experiment outlined seem to indicate that the figures quoted above may not be justified. This is shown by an analysis of the method given by Bopp and co-workers (70). Long et al. (70a,b) have recently reported that, using an experimental arrangement very similar to that outlined above, 26 % polarization was obtained with electron currents of 10-13-10-11A. The degree of polarization could be significantly improved by eliminating the formation of potassium molecules in the beam. As soon as the technique of optical pumping was established by Kastler and co-workers (71-74), it was realized that this method can also provide the necessary initial polarization of atoms needed for the production of polarized electron beams by photoionization. As is well known, the method of optical pumping is based on the spectroscopic selection rules for the Zeeman effect, i.e., the laws governing transitions induced by polarized light in atoms situated in a magnetic field. If atoms are illuminated by circularly polarized resonance light incident in a direction
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
41
parallel to the magnetic field, only selected total angular momentum states (magnetic sublevels) are excited and, when the atom returns to its ground state, its different angular momentum states also will be unevenly populated. I n the case of alkaline atoms, the orbital angular momentum of the ground state 1 = 0, one spin state outnumbers the other. Whereas the technique of optical pumping is iii many respects easier than that of a Stern-Gerlach experiment, the latter gives nearly total atomic beam polarization as opposed to less than 50% in a typical optical pumping experiment, and the polarization of the electron beam produced in the next stage of the experiment cannot exceed that of the atomic beam. Boersch and co-workers (75) polarized sodium vapor by optical pumping and ionized it b y ultraviolet light. The polarization of the vapor was 5-15%, and the extracted electron beam of A was polarized to about 2%. The polarization of the atoms in the excited state, produced in the first step of the pumping process, is much higher than that of the ground state. Using photon energies which are sufficient only to ionize atoms in the excited state, one may expect that, the photoelectrons thus obtained will show a very high degree of polarization. I n such a scheme, however, atoms have to absorb two photons in succession, one for pumping, and the other, before the decay of the excited state, for the detachment of the electron. The probability of the sequence of such events is very small, and hence it would yield very low electron-beam intensities. Dicke carried out a n experiment along these lines in which he obtained lo6 electrons/sec with a n estimated, but not directly detected, polarization of about 30% [quoted in Tolhoek (a)]. Undoubtedly the most attractive source of polarized electrons would be a solid cathode emitting polarized electrons. Rozentsveig (76) discussed the possibility of extracting a polarized electron beam by a high electric field, E , from any low work-function cathode situated in a high intensity magnetic field, B, parallel to E. I n the presence of the magnetic field the energy of the conduction electrons is shifted by 5 pB and, therefore, the height of the potential barrier representing the metal surface, as well as the thickness through which electrons are tunneling in field emission, is different for electrons in opposite spin states (Fig. 8). From the theory of field emission one can easily find the ratio of the number of electrons emitted in opposite spin states assuming that the cathode is a t absolute zero temperature:
where
=
4,,
N B is the effective work function for the electrons
42
P. S . FARAGO
in the two opposite spin states. Hence the polarization of the emitted beam is P = [(n+ - n-)/(n+ n-)] = (29h/mc2)”2(cB/E’)
+
One may assume that this expression gives a reasonable approximation at non zero cathode temperatures if the magnetic field is so high that pB >> kT. To satisfy this condition, even at liquid He temperature, fields of 10-100 wb/m2 (106-106 gauss) would be required. The production of such a field is, of course, quite a difficult task, but feasible. I n the above considerations, however, it is apparently overlooked that once the magnetic field is established the electrons in the met,al rapidly return to a
FIG.8. See the discussion in text of the production of polarized electrons by field emission.
state of thermal equilibrium, and electrons in both spin states populate energy states up to the same level, as shown schematically in Fig. 9, for zero absolute temperature. Under these circumstances the polarization of the beam obtained by field emission would reflect only the difference in spin population due to the difference in the average density of states in the energy range from which the emitted electrons originate. Takingfor a typical metal-a quadratic distribution for the density of states, the resulting polarization of the emitted beam would be very small. One might expect that a magnetized ferromagnetic sample would be more suitable source of polarized electrons than a nonmagnetic metal. The suggestion to extract polarized electrons from a magnetized ferromagnetic cathode by field eniission or photoelectric effect was first made over 30 years ago (63), hut the problem has not been analyzed theo-
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
43
retically in detail. Since the ferromagnetic properties are due to the behavior of the 3d electrons, whereas in field emission the conduction electrons (4s) are extracted, the polarization of the emitted beam depends mainly on the direct coupling between t,he 4s and 3d electrons, the effect of the strong internal fields on the conduction electrons is likely to be similar t o that already discussed above. Marshall (77) estimates the polarization of the conduction electrons in cobalt to be a few percent. Others (78) maintain that the interaction between 3d and conduction electrons has a ferromagnetic and an antliferromagnetic effect which cancel one another.
i-i-
1E
-
FIG.9. See the discussion in text of the production of polarized emission by field emission. Von Issendorff and Fleischmann (79) measured the polarization of electrons emitted in a high electric field by the tip of an iron needle magnetized to saturation. Magnetization is achieved by a n external magnetic field parallel to the electric field, and to the axis of the needle. The polarization of the electrons was detected by Mott scattering, after a longitudinal-to-transverse polarization transformation. The scattering asymmetry was determined with an accuracy better than 1: 1000 and the asymmetry found was within the experimental error. Anomalies observed in images obtained with field-emission electron microscopes led Pimbley and Muller (80) to carry out measurements in search of a transverse polarization of electrons emitted by field emission. Single domains of iron and various nonmagnetic emitters were tested, presumably in the absence of an ext,ernal magnetic field, and no polarization was found outside the experimental error estimated at 15% for the measurement with iron and > 3 % in other cases.
44
P. S. FARAGO
Dayhoff (81) considered the removal of electrons from a magnetized ferromagnetic sample by photoelectric effect, and predicted that under favorable experimental conditions the emitted electrons could be polarized to a much higher degree than the polarization of the d electrons in the sample. Considering a t first the d electrons only (Fig. lo), the energy bands available for electrons in opposite spin states are shifted relative to one another by the d-d exchange splitting. If the Fermi level is a t the height A , photons of energy hvd release electrons of one spin state only. With the Fermi level at B , a photon energy h v B will produce a practically unpolarized beam. If the Fermi level is at C, a partially polarized beam of
FIG.10. See the discussion in text of the production of polarized electrons by photoelectronic emission. The distribution of the density of states is schematic and it does not represent any particular metal. [Reproduced from Dayhoff (81).]
photoelectrons could be obtained. The degree of polarization so predicted is decreased by the additional emission of electrons from the bands of the s state. The polarization of s electrons is presumably very small, but the density of s states near the Fermi level is relatively small and therefore no drastic reduction of polarization is expected. In view of the small penetration of the uv light in the metal, photoelectrons are released only from a shallow layer, and, in Dayhoff’s estimate, the depolarization due t o various interactions to which the electron is exposed before leaving the metal is negligible. If the surface itself can be represented by an electric potential barrier without traps, a resulting polarization of 50% or more should be obtainable. Experiments by Fowler and Marton (89)do not confirm the above prediction. Photoelectrons emitted by permanently magnetized thin
ELECTRON POLARIZATION AND $7-FACTOR ANOMALY
45
ferromagnetic films did not show azimuthal asymmetry in Mott scattering in measurements capable of detecting about 5% ’ asymmetry. Similarly, the experiments of Long et al. to detect any polarization of photoelectrons emitted by the (110) face of a single crystal of Ni magnetized along the (111) direction (83a,b) gave negative results. I n view of the negative results of experiments carried out to date a more quantitative reexaminat,ion of Dayhoff’s suggestion seems desirable. This would give more detailed guidance in assessing the feasibility of further experiments along these or similar lines. It has been suggested (84),for example, that some of the difficulties met in the type of experiment discussed might be reduced by using field emission from the sparsely populated conduction band of a semiconductor in which the spin-state separation is produced by a high-value pulsed magnetic field. I n addition one might hope to increase the energy difference between the two spin states in the band b y using a material in which the g-value is very high, for example (86) InSb.
v. THEn/IEASUREMENT OF THE S-FACTOR ANOMALY O F FREEELECTRONS A . Preliminary Remarks The measurement of the g-factor serves as a direct test of the quantum-electrodynamic description of the electron which predicts that its magnetic moment deviates by a small amount from the Bohr magneton. This is the outcome of very complicated mathematical considerations which take account of effects which have been disregarded in Dirac’s relativistic single-particle equation. I n most cases of practical interest a description of electron motion in a n electromagnetic field which considers only the effect of externally applied fields agrees very well with observation. It depends on the nature of the particular problem whether, in describing the interaction, classical methods are applicable or quant,um-mechanical formalism must be used in the description of the motion; in the first case the electromagnetic field can be represented by functions satisfying the classical Maxwell equations, in the second case the electromagnetic field must be considered as a quantized system. It has been known, however, that for a complete treatment one has to consider in addition to the effect of the external fields the effect of the electrical field arising from the charge and the effect of the magnetic field arising from the motion of the electron itself. For example, in applying the laws of energy and momentum conservation one must take into account the energy and momentum carried by the fields produced by the electron.
46
P. S. FARAGO
Considering classically a n electron in uniform motion (86),it is found that the field of the electron has a momentum
where E o is the energy stored in the field of a stationary electron and v is the electron velocity. If the electron is accelerated b y iiv, the impulse applied, 6pl has to cover the change in mechanical momentum M 6 v as well as the change in the momentum of the field +(Eo/c2)iiv: 6p = miiv = [ M
+ +(Eo/cz)]iiv
I n this relation rn signifies the observed mass of the electron which appears t o be made up of two contributions: one is a “bare mass” M and the other is a n “electromagnetic mass” M e = +(E0/c2). If the electron moves under the influence of a n external force it has an acceleration. In this case one has to take into account that, b y virtue of its acceleration, t,he electron emits radiation a t a rate - d W / d t = v2. Therefore the work done by the force must cover the change of the kinetic energy of the electron as well as the energy lost by radiation. Deriving the equation of motion from the energy equation one finds that in addition t,o the external force there is another force proportional to the rate of change of the acceleration (); representing the reaction of the field of the electron on its own motion. The mathematical formalism necessary to express the ideas outlined above in terms of quantum theory is developed by quantum electrodynamics (87). Building, however, a consistent theory along these lines runs into great difficulties-within the framework of classical physics and in quantum theory a l i k e w h e n a n explicit expression of the “self-energy,” Eo, is calculated in terms of the spatial distribution of the electron charge, e. Assuming a uniform distribution over a sphere of radius r, the calculation yields the result
Eo
a
eZ/r+
00
if
r-+ 0
i.e., the self-energy and consequently the electromagnetic mass of a point charge is infinitely large. Any attempt to overcome this difficulty by assuming a finite size is incompatible with the theory of relativity. Furthermore it can be shown that the self-energy cannot account>for the entire observed mass of the electron. This is indicated b y the relation of the self-energy, Eo, and the electromagnetic mass, M e , where the factor contradicts the relativistic energy-mass relationship. I n order to restore the validity of the equivalence of the observed mass and energy, mc2 = Eol a n additional mass M = -i(EO/cZ) is required. This “bare mass” A4
+
47
ELECTRON POLARIZATION AND Q-FACTOR ANOMALY
represents presumably the binding which is needed for assuring the stability of the electron. Although the methods b y which the difficulties arising from divergencies are overcome in quantum electrodynamics are not completely satisfactory, great progress has been made by recognizing th a t all the infinities are caused by the self-energy and electromagnetic mass (also by “self-charge,” a concept which has not entered our qualitative considerations), quantities which themselves are not observable in the case of free electrons; what is observable is the finite sum of the bare mass and the electromagnetic mass. Thus the reaction of the field of the electron on itself remains hidden so long as the electron is free, but it produces observable effects if the electron is situated in a n external field, because in t ha t case the self-energy is modified to some extent and the energy of the interaction changes also. If the electron is in the Coulomb field of a nucleus, the energy levels of the stationary states are slightly different from those predicted by quantum mechanics, and the displacement of the energy levels predicted by quantum electrodynamics is observed in the “Lamb shift.” If the external field is a uniform magnetic field, B , the energy of the electron arising from the interaction between its magnetic moment, p , and the field is slightly different from that which corresponds to 1 Bohr magneton: pB # +(eh/m)B. I n other words a measurement of the magnetic moment, based always on the determination of this interaction energy, is expected t o yield a value p =
+geh/m
with
+g
=
1
+a
where
la/
<< 1
The number a, called the g-factor anomaly, was expressed b y Schwinger (88-91) as a series of radiative correction terms in powers of the fine-structure constant a = +(a/n)
+ b(a/?r)Z +
*
.
.
(51)
The expansion coefficient was determined b y Karplus and Kroll (92) and by Sommerfield (93, 94). The discrepancy between the results of these calculations has been resolved and the accepted value is b = -0.328. With the best value of the fine-structure constant l / a = 137.0391, the theoretical value of the g-factor anomaly is ath
=
0.001159615
(52)
to a fractional error of about 5 x 10-6 arising from the uncertainty in the value of the fine-structure constant itself. The first indication of the fact that the electron has a n anomalous magnetic moment came from the measurement of the hyperfine structure
48
P. S. FARAGO
of hydrogen and deuterium (96) and the first high precision results were obtained by atomic beam measurements carried out by Kusch and co-workers (96-98), determining the g-factor of electrons when bound to atoms. Experiments of Wilkiiison and Crane (99) with free electrons yielded a measured value uexp = 0.001159622 & 0.000000027
(53)
This result of remarkable accuracy means that the coefficient, b, of the second order correction term in the expansion (51) is confirmed to a n accuracy better than 2 %. Circ. polorizer
7
‘No arc
kbsorption bulb
LPhoto cell
FIG. 11. The basic arrangement of Dehmelt’s experiment. [Reproduced from Dehmelt @ I ) . ]
During the 10 years’ development period of Crane’s experiment there have been proposals for alternative methods, some of which have been put into practice, and we shall start with a brief discussion of these.
B. Dehmelt’s Experiment The g-factor of the free electron was compared with that of N a in its ground state in an experiment by Dehmelt (62,52) already mentioned in the previous section. Figure 11 shows scheniatically the experimental arrangement. Saturated sodium vapor and an inert buffer gas7 contained in a sealed bulb, are situated in a uniform magnetic field Bo. The cell is illuminated by circularly polarized resonance radiation from a sodium lamp in a direction parallel to the magnetic field, and the sodium vapor t’hereby undergoes optical pumping as described before. Depending on the intensity of illumination and relaxation times characteristic of processes competing with the pumping, an equilibrium state is reached with a certain excess population of one of the magnetic sublevels of the ground state. The higher the degree reached by this overpopulation, the smaller the absorption of resonance light by the vapor, and therefore the degree
ELECTRON POLARIZATION A N D g-FACTOR ANOMALY
49
of polarization of the atoms can be determined by measuring the intensity of 'the resonance light transmitted by the vapor. If any agency reduces the equilibrium polarization of the atoms, this is detected by observing a decrease in the transmission of the vapor. One process which gives partial depolarization is the excitation of transitions between the magnetic sublevels of the hyperfine structure levels of the ground state. Because of the nuclear spin, I = +,of Na23the ground state is split into two hyperfine levels with F = 1, 2; and in the weak magnetic field (about 20 gauss) these levels are further split as shown in Fig. 12. An rf magnetic field, applied perpendicularly to the field Bo,will excite transitions between the sublevels, and the resonance can be detected by observing the change in
I
mF =
I771mc/s
Blgourrl
10
20
c
FIG12. The Zeeman effect of the ground state 32Sgof NaZ3in weak magnetic fields.
the optical transmission of the vapor as the magnetic field Bo is swept through the resonance value, in a manner generally used in rf spectroscopy. The determination of the resonance frequencies u l , u2, v3, and v4 for the transitions marked (1))(2), (3)) and (4) in Fig. 12 corresponding to a given value of B , is one task of the experiment. The other task, performed simultaneously, is the detection of the spin resonance of free electrons. For this purpose electrons are produced in the bulb by short pulsed discharges; the electrons slow down rapidly as a result of collisions with the buffer gas, and then undergo exchange collisions with the: polarized Na atoms. The result is that the electrons become partially polarized and the polarization of the sodium atoms assumes a reduced equilibrium value. At this stage a rf field of frequency V , satisfying the relation hv = 2 p B 0 , induces spin transitions, and destroys the polarization of free electrons, and subsequent exchange collisions yield a further reduct!ion of the atomic polarization. This resonance process is detected in the same way as the previous one, and using
50
P. S. FARAGO
separate rf fields with suitably chosen frequencies the electron spin resonance and the atomic transitions can be observed simultaneously, as shown by the oscillogram in Fig. 13. (The atomic transition frequencies coincide for very low values of Bo (say 2 gauss) and separate as Bo is increased. It can be shown that the fractional difference (v - 2 ; v i ) / v of the spin resonance frequency and the sum of the atomic resonance
FIG.13. Oscillograms of the magnetic resonance of free electrons and of the ground state of Na. The rf oscillators are adjusted t o induce both resonances when the magnetic field is about 2 gauss. The two curves shown are identical, but they were obtained with higher gain for the free electron resonance signal, the frequency scale of which is marked.
frequencies is independent of the magnetic field Bo, and allows the calculation of the ratio of g-factor of the free electron to the g-factor g.7 of the ground state of the atom, provided the ratio of the latter one to the nuclear g-factor gI is known. Using the value for gJ/gr obtained by Kusch and Taub (97) in atomic beam experiments, Dehmelt concluded that 9/95
=
1.000026
+ 0.00003
ELECTRON POLARIZATION AND
9-FACTOR
ANOMALY
51
At the time of the experiment outlined, measurements were in existence which confirmed the first-order radiative correction for the g-factor of the ground state of Na, and this was the first time that the validity of this correction was experimentally tested on free electrons.
C. Proposals by Bloch and by Bloom and E r d m a n For the direct measurement of the g-factor of free electrons of low (thermal) energy there are two suggestions, one by Bloch (34), the other by Bloom and Erdman (35), which have some features in common, although the first method is designed for measurement of the g-factor itself, the second one to determine the g-factor anomaly directly. In both cases electrons are moving in a homogeneous magnetic field and transi-
FIG.14. See the discussion in text of the angular-momentum relations for a free electron orbiting in a uniform magnetic field.
tions are induced between quantized energy states by a rf field. Before describing these schemes a few general remarks are appropriate. It was pointed out earlier (Section IV) that if r describes the position of an electron moving in a magnetic field, the canonically conjugate momentum is not mi, but p = mi - eA, where A is the vector potential. From this it follows that, in classical description of the motion, whereas the energy of the electron describing a circular orbit in a homogeneous magnetic field B = B i (see Fig. 14) depends only on the radius R of the orbit E = +rnwc2R2 where wo = eB/m the z component of its angular momentum is a function of both the orbital radius R and the radial distance, ro, of the center of the orbit from the origin of the coordinate system: 1, = Qmw,(R2- ro2)
52
P. S. FARAGO
It is seen then that I, > 0 if the orbit encircles the origin of the coordinate system and I, < 0 if the origin is outside the orbit. One can express the coordinates of the center of the orbit, xo, yo (taking z = 0 for the sake of simplicity) in terms of the coordinates x, y and conjugate momenta p,,p, of the electron; considering these quantities as quantum-mechanical operators, one finds a nonvanishing value of the commutator: xoyo- yoxo = -ih/mw, Hence it follows that the center of the electron’s orbit is subject to the following uncertain relation: AxoAy0 3 h/mo,
(54)
If the electron motion is treated quantum-mechanically the appropriate Hamiltonian is given by Eq. (46) and it is found that the energy of the electron can assume one of the following discrete values:
+ +
E = (pZ*/2m> (n
Z81,111
+ + + +gs)hw,
(55)
where n = 0, 1, 2, . . . , Z = 0, f l , f 2 , . . . , the latter being the angular momentum quantum number, s = &+ takes account of the two possible spin states, and 8i.k
=
I
i = k i # k
if if
1 0
is the Kronecker delta symbol. The quantities corresponding to the classical radius of the orbit and the radial distance of the orbit center are quantum-mechanical expectation values: ( R 2 ) = (2h/mwc)(n Z6~,111 $1 (56) and (@) = (2h/mw,)(n - Z ~ - ~ , I L I +) (57)
+
+ +
both independent of spin orientation. The energy levels given by Eq. (55) are shown in Fig. 15. Levels corresponding to the two different spin states are shown side by side and the levels are labeled with values of
k =n
+
~61,(21
Energy differences corresponding to various transitions shown in Fig. 15 are as follows: (a) hw,; (b) &ghw,; (c) ahw,; (d) (69 l)hw,. For the measurement of the g-factor Bloch’s scheme is designed to measure the frequencies which induce transitions (a) and (b), their ratio giving Bg; Bloom and Erdman proposed measuring the frequencies
+
ELECTRON POLARIZATION A N D g-FACTOR ANOMALY
53
inducing the transitions (c) and (a), the ratio of which gives the g-factor anomaly a = (+g - 1) directly. In Bloch’s scheme (34) the motion of the electrons parallel t o the magnetic field is confined to a small region b y means of a n electrostatic trapping field, in which the electrons oscillate back and forth. If in addition t o the homogeneous magnetic field and the electrostatic trapping
I
k+ I
SS!
s=.!
FIQ.15. Energy levels of a free electron orbiting in a uniform magnetic field.
I‘
El. stat.
El. stat.+ rnagn. pot. barrier
FIG.16. See the discussion in text of Bloch’s suggestion for the measurement of the g-factor of free electrons.
field a n inhomogeneous magnetic field, with its gradient parallel to the homogeneous field, is established, the electrons will be accelerated along the direction of the gradient, or in other words the potential barrier will be “tilted” and some of the electrons previously trapped will be able to escape (Fig. 16).* If the inhomogeneous field is switched off, and then on 8 Any complication in the level scheme which may arise from the presence of the electrostatic field, the inhomogeneous field, or processes resulting from their variation in time is here disregarded.
54
P. S. FARAGO
again, no further electrons will escape, unless transitions to the states lying between the extreme positions of the potential barrier have taken place. Such transitions can be induced b y an rf magnetic field of appropriate frequency perpendicular to the homogeneous field producing either the cyclotron orbital transition (a), or the spin flipping transition (b). Thus the experiment would consist of the repetition of the following cycle: (i) Trap electrons by electrostatic field. (ii) Apply inhomogeneous magnetic field to empty top energy levels, and switch off. (iii) Apply rf field, and switch off. (iv) Apply inhomogeneous field and detect escaping electrons, if any. (v) Switch off electrostatic trap. The two resonant frequencies are those at which electrons can be detected i n step (iv). The cycle has t o start always with ‘‘fresh” electrons because the spin flipping takes place between neighboring states only, and-as opposed to the case of cyclotron resonance-electrons will not ‘‘(~limb”monotonically to higher and higher energy levels. Apart from the difficulties arising from the stringent requiremeiits on the precise definition of the height of the electric potential barrier and the intensity and gradient of the inhomogeneous field, it must be realized that the fractional difference between the two resonant frequencies is about 0.1% ’ and the probability of a cyclotron transition is orders of magnitude higher than that of spin flipping. Therefore it is likely that the two resonances cannot be resolved. Probably this is the reason why no experimental results obtained by this method have been reported. Bloom and Erdman (35) suggested using a homogeneous magnetic field B = B o i and an inhomogeneous rf magnetic field, for example, a “quadrupolar” field the components of which can be described in Cartesian coordinates by B, 0: x cos w t , B, c -y cos w t , B, = 0. (Such an rf field could be produced by two pairs of transmission lines driven in phase and situated symmetrically and parallel to the z-axis.) Electrons describing helical trajectories in the uniform magnetic field B , would undergo resonance transitions of the type (c) shown in Fig. 15, if the frequency of the rf excitation was appropriately chosen. The resonance could be detected by observing the change in the electrons’ orbital motion-the increase of orbital radii or the shift of the centers of orbitsresulting from energy absorption. Rastall (loo),however, has shown b y treating the problem quantummechanically that, in the simple field suggested, the required transition cannot take place. In a more detailed analysis of the problem Byrne (101) found that the possibility of inducing the required transition depends on the spatial distribution of the rf field. The angular momentum selection rules operative in the transition in question impose conditions on the angular momentum of the perturbing electromagnetic field and transi-
55
ELECTRON POLARIZATION AND g-FACTOR ANOMALY
tioris cannot take place unless these conditions are satisfied. I n particular it was shown that the transitions required in the proposed experiment can be induced by transverse magnetic modes, TIM,,,, of cylindrical cavity resonators, where the index, u, characterizing the azimuthal periodicity of the field and the change of the total angular momentum A j = A(Z s) characteristic of the transition are related by the equation
+
u = Aj
The frequency uwc a t which transitions are to be detected is only some tens of megacycles in uniform fields of feasible intensity. Therefore the required cavity resonators would be of immense dimensions. If, however, this difficulty is overcome in one way or another (see l o r ) , it still does not mean that the transitions can be detected. The transition involving the absorption of the energy Ah' = uho, takes place with the highest probability if A j = 0, and hence AS = k1,
Al = T 1
(58)
Taking the required energy change, Eq. (55) gives a third selection rule to be satisfied simult,aneously : or Recalling Eq. (56) and using (59) one finds that the transition changes the radius of the electron orbit by
A(R2) = T2h/mw, Since the successive interaction processes which a n electron may undergo involve spin flipping, the orbit radius will alternately increase and decrease. I n other words IA(R*)I is t,he maximum by which the radius of the electron orbit can change in the transition discussed and this cannot be detected on account of the uncertainty principle [see Eq. (54)]. From Eqs. (57) and (60), on the other hand, it follows that A(ro2)= 0; the center of the orbit is not shifted a t all. The same energy change can take place in a very much less probable transition subject to the selection rule A j = - 1 , yielding instead of Eq. (58) -2 As = f l , A1 = (61)
1
and again A(n
+
&,111)
=
T1
56
P. S. FARAGO
with the same consequence regarding the change in orbit radius. The behavior of the center of the orbits, however, is different this time. Since
A(n - Z~-Z,IZI) - A ( n 4-E ~ Z , I Z I ) = -A2 from Eqs. (61) and (59) one gets A ( n - Z6zl,1tl) gives A(ro2)= 2h/mw,
=
1 and hence Eq. (57)
This shift of the center of the electron orbits is always positive and the electron beam will spread monotonically as the result of successive interaction processes of the kind just described. Thus, at least in principle, it should be possible t o detect it. An rf field which induces transitions with with A j = - 1, induces-with the same probability-transitions A j = 1 also. Applying the above arguments to this case one finds that A(ro2) = -2h/mw,, i.e., the shift of the orbit centers is the opposite of that found previously. The two effects, however, do not cancel one another, but the position of the orbit centers changes by a process of “random walk,” and this leads to a net spread of the beam diameter. Experimental results obtained by this approach have not, however, been reported so far. I n Section IV reference was made to the schemes discussed above as possible ways of producing slow polarized electrons. Now it can be seen that Bloch’s method would supply electrons in a selected spin state in step (iv) of the cycle, if spin resonance could be distinguished from cyclotron resonance. The Bloom-Erdman method would not give polarized electrons, since if electrons are removed from the beam, this takes place without preference to spin state.
D . Measurements with Electrons Emitted in Beta Decay
It was seen in Section I11 that if electrons are allowed to describe a large number of cyclotron orbits in a uniform magnetic field, the angle between the direction of orbital momentum and that of the polarization in the plane of the motion changes by a n amount proportional to the g-factor anomaly and to the number of orbital revolutions [see Eq. (34)]. The application of this effect for the measurement of the g-factor anomaly was first suggested b y Crane (102), and led to the experiments described in the next subsection. A straightforward application of essentially the same idea (103, 104), which takes advantage of the longitudinal polarization of electrons emitted in beta decay, is described below. If a beta-active source is situated in crossed homogeneous electric and magnetic fields E = EG, B = Bi,electrons emitted by the source in the (2,y ) plane describe trochoidal orbits. Choosing the electric field so
ELEC T RON POLARIZATION AND g-FACTOR
ANOMALY
57
weak that E’ << cB, its effect can be described &s producing a slow drift along the x axis of the circular orbits described by the electrons in the pure magnetic field B. If the direction of the fields is chosen appropriately, one can arrange that with the use of an additional baffle (Fig. 17), electrons within a limited range of initial velocities reach a scattering target after having performed a predetermined number of cyclotron orbits. Thus the polarization of the beam can be determined as a function of the number of orbital rotations by observing the Rilott scattering asymmetry.
FIG.17. Schematic diagram of the arrangement used in the measurement of t h e g-factor anomaly of electrons emitted in beta decay. The electric field is maintained between the plane parallel plates at the potential ++V; the uniform magnetic field is perpendicular to the plane of the drawing. S, beta source; F, scattering target. Counters (C) are above and below the plane of the drawing.
It is easy to show that in a coordinate system, K’, moving with uniform velocity u = ( E / B ) iwith respect to the laboratory frame of reference, K , the electrons are acted upon by a pure magnetic field B’
=
B/r(u)
where y ( u ) = [l -
(u/c)2]--1’2
I n the moving frame, K’, the electrons describe circular orbits, the period of the orbital motion being
T’ = 27r(m/eB)y(v’) where v‘ is the electron velocity in the moving frame K’. Defining a complete orbital loop in the laboratory system, K , as the path described in a period T after which the orbital velocity reassumes T ) = v ( t ) , one obtains by Lorentz transformation its initial value, v ( t T = y(u)T’, and hence the pitch of the trochoidal orbit is d = uT. If the distance, D, between the source and the scattering target is an integral multiple of the pitch, d, the electrons reach the target after n
+
58
P. S. FARAGO
with the approximation y ( u ) N 1 justified by the fact that in the experiment u/c = E/cB << 1. Since in the moving frame, K‘, the electron is moving in a pure magnetic field, the angle between the orbital momentum and the polarization changes in one complete orbital revolution by A@I =
~ T U ~ ( U ’ )
It can be shown (105) that this quantity is invariant under Lorentz transformation and therefore the same relationship applies in the laboratory frame of reference as well. Hence the number of orbital loops, no, required t o make the direction of polarization complete a full cycle relative t o the direction of the orbital momentum is given by l/no
=
ay(v’)
The initial polarization of the electron beam emitted in beta decay is longitudinal, and therefore the transverse polarization detected by Mott scattering, as a function of the number of orbital loops, varies as P = P o sin (27rn/no).Hence the detected scattering asymmetry can be written in terms of the unknown g-factor anomaly, a, and the relevant experimental parameters as 1
+ SPo sin eDB2 mE ~
where w is a residual instrumental asymmetry and S is the asymmetry function depending on the scatterer, the energy of the electrons, and the scattering angle (see Section IV). At a fixed source-to-target distance, D, and constant magnetic field, B, the scattering asymmetry is measured as a function of the field intensity, El and the g-factor anomaly is evaluated from the length of the period of the curve Y ( E ) plotted against (l/E). Without going into further details, it should be mentioned that there is no restoring force acting on the electrons in the direction parallel to the uniform magnetic field, and electrons emitted with a n initial velocity not perpendicular to the magnetic field drift away from the mid-plane of the system. Since the required number of orbital loops is very large (no‘v lOOO), in order to maintain a reasonable beam intensity a t the scattering target, the field distribution has to be modified to provide the required focusing, without changing significantly the properties of
ELECTRON POLAHIZATION AND g-FACTOR ANOMALY
59
electron trajectories in the mid-plane of the system (106). The modification in the field distribution results in a small amount of drifting of the cyclotron orbits even in the absence of the electric field and as a result the maximum number of orbital loops which permits an unambiguous evaluation of the results without requiring elaborate corrections is limited. The result of Moth scattering asymmetry measurements carried out are pIotted in Fig. 18, and from t,he period of the best fitting sine curve the g-fact,or anomaly was found to be a = 0.001153 i 0.000023, where the error quoted takes into account the statistical error of the counting rates as well as the uncertainties in geometrical parameters and fields.
FIG. 18. Mott scattering asymmetry plotted against the number of orbital loops. (The upper abscissa scale is in terms of the directly measured potential difference across the field plates shown in Fig. 17.)
The result is clearly in agreement with the first-order radiative correction but does not give information about the second-order one. €%. Experiments by Crane and Co-wo&ers
Experiments by Crane and co-workers were developed in three stages, always using electrons polarized by Mott scattering a t 90" from a gold target and detecting the polarization by a second scattering. Between these events the electrons move in an essentially uniform magnetic field which is parallel to the plane of scattering, and as a result the transverse polarization vector precesses about the magnetic field. I n the first experiment (107) electrons of 420-kev energy, scattered into a small solid angle about the axis of a 12-meter long solenoid, undergo a second scattering in a target a t about 10 meters from the first one. I n the appIied field (up to 120 gauss) the time of flight of the electrons between the targets is a few cyclotron periods and the rotation of the transverse polarization is measured by following the rotation of the Mott
60
P. S. FARAGO
scattering asymmetry pattern with a pair of rotatable detectors. The electrons are focused on the second scatterer if the time of flight is a n integral multiple of the cyclotron period. Therefore the rotation of the polarization per cyclotron period can be measured directly as follows: one determines the direction of the maximum scattering asymmetry a t different fields a t which the intensity of sthe beam reaching the second target is a maximum. It was seen in Section 111 that the angular velocity of the precession of the polarization in a longitudinal field is w = +g(e/mr)B [see Eq. (is)],and hence during a cyclotron period, T = 2rmy/eB, the direction of the polarization changes b y A@I = wT = rg. The measurement of the azimuthal asymmetry is not precise enough to allow a highaccuracy determination of the position of maximum asymmetry and the
FIG.19. Schematic diagram of the experimental arrangement used in the second experiment of Crane and co-workers; reproduced from the Ph.D. thesis of A. A. Schupp.
experiment gave the result g = 2.00 k 0.01, without any information about the radiative correction. I n the second experiment (108) 100-kev electrons supplied by a pulsed source and incident on a gold foil parallel to the direction of the magnetic field were scattered at an angle of nearly 90" so that the scattered electrons moved on a low pitch helical trajectory (Fig. 19). The transverse polarization of the beam produced in the scattering process changes during the course of t,he motion, at a rate, ill which is related to the cyclotron frequency, wc, by D = arwc [see Eq. (34)1. To determine a the asymmetry of a second Mott scattering has t o be observed as a function of the time of flight of the electrons. I n order t o follow the variation of the angle between orbital momentum and polarization over a large number of cycles the time of flight of the electrons has to extend over a very large number of cyclotron periods and to achieve this the electrons are trapped for periods up to 300 psec half way between the two scatterers. For this
ELECTRON POLARIZATION AND !?-FACTOR ANOMALY
61
purpose the main magnetic field is reduced by an additional coil in a short axial range so that the resulting field in this area is similar to the field in a betatron. In such a field electrons on a cyclotron orbit with a small momentum component parallel to the direction of the main field oscillate about the symmetry plane of the field, i.e., back and forth in a small axial range. The actual trapping takes place by applying a retarding field for a short period of time when a bunch of electrons injected by the pulsed source reaches the region of the magnetic trap. At the end of the required trapping time the electrons are blown out of the t,rap by a short accelerating pulse. From a plot of the scattering asymmetry against trapping time, the rate of change of the polarization, Q , can be determined. I n addition it is necessary to determine the magnetic field “seen” by the electrons. In view of the rather complicated motion of the electrons in the inhomogeneous region of the field acting as electron trap, a most elaborate field mapping process is required and the effective field is obtained by numerical calculations. Results obtained by measurements at different main field intensities showed a small dependence on the magnetic field, and taking into account likely sources of systematic error the experiment gave u = 0.0011609 k 0.0000024. Writing this result in terms of the radiative corrections,
u
= +(a/r) -
(0.1 f 0.4)(a/~)~
it is seen that the presence of the second-order correction enters as a significant quantity, but the accuracy falls just short of assigning a numerical value to its coefficient. The purpose of the third stage of the development was to improve the accuracy of the determination of this term. The basic principle of the final experiment (99)is essentially the same as that of the previous stage, but there are a number of features in its realization that lead to a significant increase in accuracy. First of all, instrumental asymmetries arising from the use of two counters for the measurement of the scattering asymmetry were eliminated by using one counter and transferring the spatial asymmetry into a temporal one. In an ideal case the counting rates, C , and Cz, given by two identical counters, (1) and (2), situated at azimuthal angles 0 and ?r about the direction of the incident beam are reversed if the polarization vector is rotated by r about the direction of the incident beam, i.e., in the latter case (1) counts Cz and (2) counts C1. The same result is obtained by comparing (instead of C1 and C,) the counting rates of the same counter obtained once with a trapping time t, and then with a trapping time t 4T, where T is the time required to rotate the transverse polarization by 2r. For the determination of the scattering asymmetry the second
+
62
P . S. FARAGO
procedure is a much better approximation to the use of “identical” detectors than the conventional one. Possible sources of systematic errors, discussed in detail in Ref. (log), could be significantly reduced by scaling up some of the geometrical parameters of the apparatus. Using a larger solenoid allowed a more precise field mapping. The modified internal structure allowed the observation of scattering asymmetry with trapping times ranging between 300 psec and nearly 2000 bsec, and this assured that the electrons observed in a pulse showed no properties determined by the injection process, such as undesirable “bunching.” A suspected source of systematic error in the previous experiment arose from charges settled on the electrodes producing the retarding and blow-out fields. The new design of the electrode structure reduced the effect of stray fields from these sources by removing all structural parts from inside the cylinder defined by the electron trajectories. In the evaluation of the observational material, the inhomogeneity of the magnetic field and the finite pitch of the trajectories in the trap were taken into account. The g-factor anomaly, a, is calculated by using the equation
quoted [in Ref. (99)]from unpublished calculations by G. W. Ford, where p = v / c , y = (1 - O2)-k; vE is the axial component of the velocity in the trap, E, is a radial electric field, and f is a possible electric dipole moment of the electron in Bohr magnetons [estimated by earlier measurements The first term on the right-hand side is calculated (109) to f < from directly observed quantities, and so is the second term, which arises from the finite pitch of the trajectories in the trap (using as a n approximate value a = 0.00116). On the right-hand side the term containing the electric dipole moment is negligible, and the factor C ( P ~ ) ~=B1/X , is again obtainable from directly measured quantities. Denoting the calculated values of the right-hand side by A , the above equation takes the form a - XB, = A Figure 20 shows the experimentally obtained values A plotted against, X . The excellent linearit,y is a convincing argument for the assumption that there is a constant stray radial electric field, and t,he correct value of the g-factor anomaly is given by the value of A extrapolated to X = 0. This is the value quoted in Eq. (53), or writ,ing it in terms of the radiative correction, u = + ( L Y / A ) - (0.327 O . O O ~ > ( L Y / T ) ~
ELECTRON POLARIZATION AND g-FACTOR A N O M A L Y
63
Recalling that the theoretical value of the coefficient of the secondorder term is 0.328, the fact, that at present there is no theoretical estimate of the coefficient of the third-order correction, ( ( Y / T )‘v ~ 1.2 and finally that the use of improved experimental data would be precluded by the uncertainty of some of the physical constants involved in the evaluation, it is reasonable to expect that the results of the experiments
f
0-E‘rx
“ t . , . , 0
20
10
X
30
(IO’/Gauss)
FIG.20. Final results of the measurement of the 8-factor anomaly by Crane and co-workers obtained with four different settings of the experimental parameters. The adopted value is the result of the extrapolation for X = 0.
carried out by Crane and co-workers will be the last word for a long time to come as far as anomalous magnetic moment of free electrons is concerned.
ACKNOWLEDGMENTS The author wishes to express his gratitude to Dr. J. Byrne, Dr. P. J. Kennedy, Mr. R. M . Sillitto of the University of Edinburgh, Dr. H. Chr. Siegmann and Mr. D. Maison of the University of Munich for many helpful discussions. Acknowledgment is due to Professor H. R. Crane, Dr. E. S. Dayhoff, Professor H. Dehmelt, Dr. H. J. Meister, and Professor H. A. Tolhoek for permission to reproduce figures from their papers.
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Fast Ion Scattering against Metal Surfaces C. SNOEK
AND
J. KISTEMAKER
F.O.M. Laboraforiunkvoor Massascheiding, Amsterdam, T h e Ketherlands Page I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 11. The Dynamics of Two-Atom Collisions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 A. Elastic Collisions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 B. Inelastic Collisions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 111. Scattering Experiments with Solid Targets. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 80 A. Panin’s Experiment (Moscow). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Walther and Hintenberger’s Experiment (Mainz) . . . . . . . . . . . . . . . . . . . . 83 C. Mashkova and Molchanov’s Experiment (Moscow). . . . . . . . . . . . . . . . . . . 85 D. Fluit and Friedman’s Experiment (Amsterdam).. . . . . . . . . . . . . . . . . . . . . 87 E. Datz and Snoek’s Experiment (Amsterdam) . . . . . . . . . . . . . . . . . 88 IV. Light Emission from Ion-Bombarded Metal Targets. . . . . . . . . . . . . . . . . . . . . 92 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
I. INTRODUCTION One of the phenomena observed during the bombardment of metallic surfaces with ions in the energy range of 10 to 100 kev is the quasi emission of atoms, ions, electrons, and photons b y the target. Most of the atomic particles are ejected by the sputtering mechanism, a rather int,ricate process in which the energy of the primary projectile gives rise to collision cascades in the bulk of the lattice. If a collision chain arrives a t the surface with more momentum than corresponds to the binding energy, then a n atom can leave the surface. Thus one in-coming ion can cause the emission of about 10 neutral target atoms with kinetic energies mostly between 0 and 20 ev, and sometimes up to 200 ev. The yield of sputtered ions from clean metallic targets seems to be quite small. (For review articles about sputt,ering and relat,ed phenomena, see Wehner, 1 , and Behrisch, 1.) Besides the sputtered particles there are some (always less than 5%) neutrals and ions leaving the surface with comparatively high energies (more than 1 kev). The neutrals usually dominate and the ions are mostly positively charged. This paper restricts itself to these fast emitted and reflected particles, being present at ionic bombardment in the energy range of 10 t o 100 kev. Recent investigations have shown that these fast particles are both 67
68
C. SNOEK AND J. KISTEMAKER
projectiles and target atoms, which have, when emitted in a certain direction, a n energy distribution with very pronounced maxima. The energies a t which these maxima occur correspond to the energies that can be calculated assuming single elastic two-body collisions between fast incoming ions and target atoms. Apparently the target atoms a t a surface, in the case of collision with fast projectiles, behave as if they were free. This can be understood by considering the times and energies involved in this kind of collision. The vibration time of the atoms in the lattice is longer by a factor of lo2to lo3 than the collision time, which here is 10-'6 to 10-l6 sec. Thus Mashkova and Molchanov ( 2 ) and Datz and Snoek (3) have indicated the possibility of studying scattering of fast atomic particles from metal atoms a t the surface of a solid target. A related subject has also received attention in the past few years. It deals with the emission of photons from a solid target during bombardment with fast ions. Work was done recently in Amsterdam by Fluit et al. (Q), and Kistemaker and Snoek (5, S), who observed line spectra associated with the impinging ions and the surface atoms. In Pakistan Chaudhri and Khan (7) reported on analogous work. They also observed photons from bombarded surfaces, but their resolution was not high enough t o distinguish line spectra. From Doppler shift measurements of Cu I resonance lines Kistemaker and Snoek could show that photons are emitted by fast neutral atoms (at kiloelectron-volt energies) leaving the surface. Apparently the light emission originates from the fast reffected and ejected particles. It is due to excited states in the collision products after a violent two-body collision. The wide-band photon emission due to the excitation of plasma vibrations in the metal conduction bands, as observed by Steinmann (8), has nothing to do with these line spectra. Wide-band photon emission seems to arise only from thin metal foils by bombardment with high-energy electrons. Our 10- to 100-kev ions are too slow. I n this connection the experiments done by Jopson et al. (8a) might also be mentioned. They used very high-velocity protons (above 100 kev) and heavier particles to bombard solid targets. Characteristic X-rays were observed. The emission of secondary electrons under fast ion bombardment is currently of great interest. At first sight the work done by Molchanov (Q),by Fert (lo),and by Magnusson (11) shows analogies with sputter phenomena (energy and directional dependence). As this paper deals with t,he energetic state and behavior of fast particles after a violent collision with one or more surface atoms, secondary electron emission is not directly reIevant here. The picture which we think to have of superexcit,ed states (12, 13) in which fast particles can be after a violent collision, includes that such
FAST ION SCATTERING AGAINST METAL SURFACES
69
superexcited particles will emit electrons by autoionization within lO-'4 sec after collision. Where Kistemaker and Snoek (5, 6 ) have observed many fast neutrals being in an excited state, such autoionization processes can happen in principle at distances of the order of 10 A from the surface. This very special type of electron emission, giving a misleading impression of normal secondary electron emission, has not yet been investigated. Berry's (14) work on gaseous targets points in this direction, however. More direct knowledge about the repulsive potential between lattice atoms and injected projectiles is of clear interest for radiation damage research. The agreement of the calculations of Robinson and Oen (16) about the slowing down of particles in solids with the experimental results obtained by Piercy et al. (16) was only a qualitative one. This was partially attributed t o the lack of knowledge about the real interatomic potentials in the energy range below 50 kev. This potential can be obtained from the angular distribution of scattered particles originating from two-body collisions. Such determinations have been done on atoms in the gas phase. (For review article about ion-atom scattering, see Fedorenko, l Y ; see also Everhart, 18-20, and Fedorenko, 21, 22.) By bombarding metallic surfaces, an important extension of the number of possible target atoms could be obtained. At first sight the study of atomic scattering might seem difficult, as the interference with other lattice atoms seems to be quite unavoidable, and therefore the study of two-body collisions at the surface of the target looks quite complex. Datz and Snoek (3) pointed out, however, that things become very simple if a single crystalline target is used. It should be oriented in such a way that a low-index crystal axis is exactly parallel with the primary beam. Then only scattering against the very top atoms of such crystal rows will he observed. The angular region in which the scattered particles can be observed is limited by the target geometry. It is impossible to detect small-angle scattering in the laboratory system, as the target is in the way. Largeangle scattering can always be made accessible, however. I t is helpful to use target and projectile particles with different masses, as ions scattered in the same direction can be separated owing to mass and energy differences. Thus, almost all scattering angles in the center-of-mass system are open for investigation. In the following section we will first of all consider the basic rules governing two-atom collisions. Then, in Section I11 a review will be given of the papers dealing with the experiments concerning ionic scattering at solid targets, while Section
70
C. SNOEK A N D J . KISTEMAKER
I V will treat a related subject, the emission of light by ionically bombarded metallic targets. 11. THE D Y N A M I C S
OF
TWO-ATOMCOLLISIONS
A collision between two atoms can be elastic or not. I n the latter case kinetic energy is transformed into potential energy, in a n irreversible way. Usually, this leads to emission of electrons or photons. The probability that a collision process is inelastic is determined by the initial relative kinetic energy of the particles, by the impact parameter, and b y the atomic structures. Particle scattering at a metal surface has strong analogies with ion-atom scattering in the gaseous phase. Several experiments have been done on gaseous phase scattering, by Fedorenko et al. (21, 229, as well as by Everhart et al. (18, 20). Theories more or less confirming the experiments originate from Firsov (23-26) and from Russek (26, 27). I n this section we will mainly try to demonstrate the dynamics of collision processes, using some self-explanatory figures to reduce the length of the text. A . Elastic Collisions The final description of a two-body elastic collision process ran be given in the following simple way: Let the projectile particle have a mass ml, and a kinetic energy in the laboratory system Eo;the target atom may have m2 and no kinetic energy. After the rollision, these data become: ml, m2,
El, scat,tering angle Ez, scattering angle
el; e2.
From the laws of conservation of energy and momentum, one can show that
Ei E,-
(1
1 A ) 2 [COS
+
el f d ~ 2 - sin2 ell2
where A = ( m z / m l ) .The scattering angles are demonstrated in Fig. 1, in which they refer to the initial vector, vo. If one observes a scattering process, and can measure Eo,El, and el, whereas A is given, then Eq. (1) should be satisfied to be sure that the collision was really elastic. The same holds, of course, for E2, O z . I n the same figure we also see the center-of-mass (c.m.) velocity vect,ors, as well as the c.m. scattering angle # relative t o vO. We can calcu-
FAST ION SCATTERING AGAINST METAL SURFACES
late
71
9 in the following way: sin
el
=
A sin (+ - 0,) - 2e2
(3) (4) While all c.m. scattering angles are possible, it can be seen from Eqs. (3)
+=
?r
FIG.1. Velocity diagram for an elastic collision of a projectile with mass m , and incident velocity uo with a target particle in rest in the laboratory system with mass m2.The ratio of the radii equals the mass ratio.
and (4),or from Fig. 1, that in the laboratory system the possible angles of observation are for m1
el 6 arcsin A el 6
if if
e2 < -T
for all m z / m l
m2 m.2
6 ml > m1
for m2 2
The angular distribution of the scattered particles gives information about the interaction potential V ( r ) , where r is the distance between the two atomic nuclei. The center-of-mass angle of scattering # is determined by V ( r ) , by the energy of the relative motion E,, and by the impact parameter p in the following way :
72
C . SNOEK A N D J. KISTEMAKER
The distance of closest approach ro is given by
A direct result of the measurements is the differential cross section related t o p by
.(el),
The way in which the experimental value V ( r ) finally can be found from the measured u(B), e, and Eo values using Eqs. (3-7) can be read in a paper by Lane and Everhart (19) (see Fig. 4 for u ( 0 ) ) .
1.0
-
100
10
keV
FIG.2. The distance of closest approach T O in units of the Bohr radius U O ,as a function of the incident ion energy Eo for 5" scattering in the laboratory system. For some of the colliding pairs the path of the incident ion is drawn schematically (for Eo = 1, 10, and 100 kev) to show the considerable interpenetration of the electron shells. The dotted circle indicates the radius of the target atom. The Bohr potential is used for the calculation of 70. [From F. P. Ziemba, G. J. Lockwood, G. H. Morgan, and E . Everhart, Phys. Rev. 118, 1552 (1960).]
There are several potential models in use in gas scattering anaIysis as well as in radiation damage and sputtering theories. All of these are repulsive potentials, because of the high energies and scattering angles under consideration. I n Fig. 2 we see a n illustration of the distance of closest approach for different energies and particle combinations, and a
FA ST ION S CAT T E RING AGAINST M ETA L S U R F A C E S
73
fixed scattering angle of 5", for a so-called Bohr potential. (This potential was first proposed by Bohr, 28.) The important thing to be seen is the overlap of the electronic shells of the colliding particles, which is certainly true for all cases in Sections 3 and 4. I n the case of such overlaps it makes sense to consider a statistical Thomas-Fermi atomic model, to calculate the interaction potential. This was done by Firsov (24). I n Fig. 3 a n impressive comparison has been given by Lane and Everhart of the Bohr, the Firsov, and the experimentally determined repulsive potential
1 :
0
,
I
1.0
1
I
--
2.0
I
3.0
I
I
r. t f g c m
FIG.3. The potential energy V ( T )of two Ar atoms, as a function of the internuclear distance T , calculated for the potentials of Bohr ( V B )and Firsov (TIP). The solid lines represent the experimentally determined potential for Ar+ ions with incident energies of 25, 50, and 100 kev scattered a t Ar gas atoms. [From G. H. Lane and E. Everhart, Phys. Rev. 120, 2064 (1960).]
cm, the between two Ar atoms. For distances smaller than 3.5 X cm the Bohr three potentials fit very well together. Above 4 X potential goes completely off, whereas the Firsov one seems to fit up to about 10 X cm. A beautiful agreement between the measured u(@) and the calculated cross sections using the Bohr potential can be seen in Fig. 4.Note from this figure that ~ ( 6 )is quite large for small angles, and decreases by a factor of lo3 for large angles. A fact that is not shown in
74
C. SNOEK A N D J. KJSTEMAKER
this graph is that the angular region in which most of the target particles can be found is close to 90". The reason for this apparent discrepancy is in the center-of-mass system, where small-angle scattering is most probable by far.
ArLAr
n
25 kcV
10-l~ O0
16'
8O
24' __L
e.
32'
60'
FIG.4. The differential cross section u ( 0 ) plotted as a function of the laboratory scattering angle e for Ar+ ions of 25, 50, and 100 kev primary energy scattered at Ar gas atoms. The solid lines show the cross sections computed with the Bohr potential. [From E. N. Fuls, P. R. Jones, F. P. Ziemba, and E. Everhart, Phys. Rev. 107, 704 (1957).]
A survey of the potentials used is as follows: 1. Bohr Potential
V(r) = u
=
Z1Zze2 4?reor exp( - r / a ) ~
valid for r
< 3u
+
u ~ / ( Z ~ 222/3)1/2 ~ / ~
where a. = 5.3 x 10-9 cm, co is the dielectric constant in vacuum, and Zle, Z2e are charges of the nuclei.
2. Firsozr Potential valid for r
< 10 X
cni
FAST I O N SCATTERING AGAINST METAL SURFACES
75
3. Born-Mayer Potential
V ( r ) = A exp(-r/B)
valid for r = 10 X
cm
A and B are constants to fit the Thomas-Fermi potential and the elastic properties of the lattice. The Born-NIayer potential is semiempirical, and shaped to give a reasonable integral in Eq. ( 5 ) . It is especially used in radiation damage calculations (see, for example, Gibson et al., 2.9). For the calculation of the actual particle trajectories in lattice structures,
Art. Ar
900
75 w 50 o 25 #5 12 x 6 I
-
w Y
-
’
l n ln
z
-
I .
*’ ”
.* *’
600 -
a a
-
w z w
-
d
23004
W
s
0
0
w .
0.4
1
r,.A
FIG.5. The mean energy loss as a function of the distance of closest approarh measured for collisions between Ar+ ions of various primary energies, and Ar atoms. The radii of the K and L shells of a single Ar atom are indicated by the arrows. T O is calculated for the Bohr potential. [From G. H. Morgan and E. Everhart, Phys. Rev. 128, 667 (1962).]
Lehmann and Robinson (80) have developed a t,runcated potential with a simple algebraic form matched to one of the three above potentials.
B. Inelastic Collisions If Eqs. (1) and (2) are not satisfied, we are sure that the collision was not elastic. The energy Q dissipated in the atoms themselves can be calculated from either
76
C. S N O E K A N D J. KTSTEMAKER
or
Such Q values as measured by Morgan and Everhart (20) are demonstrated in Fig. 5 . We see that Q is a step function of the distance of closest approach ro, and it seems quite interesting that the middle of the Q =: 700 ev plateau corresponds with the radius of highest density of the L electron shell of an Ar atom. The sharp rise in Q is found in a region where the L shells of the two colliding atoms just begin to overIap. The same effect appears if overlapping of the K shells begins. It is quite striking that & ( T O ) is more or less independent of Eo.The energy necessary to excite an electron from the L shell is about 250 ev. Analogous measurements have been made by Afrosimov et al. (62) in Leningrad. Their recent work using Ar ions or atoms with a kinetic energy of 50 kev showed some very interesting features. With coincidence techniques they were able to study the two particles originating from one collision. They could measure the inelastic energy loss for a collision with a well-defined, known distance of closest approach of the two nuclei, resulting in known collision products of a certain degree of ionization. It turned out that the probability of the excess inelastic energy loss, i.e., the energy loss Q diminished by the energy needed to ionize both particles, had three maxima. The maxima occurred at 37, 270, and 470 ev, independently of the distance of closest approach and the type of reaction. Only their relative height was changing (41). Maxima in the inelastic energy loss have also been observed by Everhart et al. and Kessel et al. (42, 43). Explanations are given by Fano and Lichten (44) and Amusia ( 4 5 ) . The two particles after collision are frequently ionized or excited, even down to primary energies as low as 1 kev. This was demonstrated by Fedorenko et al. (21) and by Everhart et al. (It?), in gas scattering. The same was studied by ionic scattering against solids by Panin (31) and by Data and Snoek (3). Up t o seven times ionized atoms were found in the kinetic energy range of 10 to 100 kev. I n Fig. 6 we see that the relative number of ions with a large number of electrons missing increases for larger scattering angle 0. The same is observed if the kinetic energy rises. This demonstrates that a decrease in r o (see Fig. 5) is accompanied by (1) an increase in the inelastic energy loss, Q ; and (2) an increase in the number of multiply charged ions. Once we have seen the fact that inelastic collisions occur, the question arises how the energy is dissipated. In the energy region considered here, the relative velocities of the colliding particles are smaller than the orbital
FAST ION SCATTERING AGAINST METAL SURFACES
77
speed of the outer-shell electrons, and much smaller than that of the inner-shell ones. The transfer of energy from an Ar+ ion to a target atom (Ar) is, therefore, of another kind than a direct excitation or ionization of the same target atom, say by a single fast elect'ron impact. The energy transfer must have to do with the considerable overlap of the electron shells, as demonstrated in Fig. 2. Theories explaining this phenomenon have been developed independently by Firsov (25) and Smirnov (32), as well as by 0.60
I
n
A r t Ar 50 keV
- 0
Fro. 6. The measured relative abundance5 of the Ar ions of various charged states scattered into a n angle e after single collisions with Ar gas atoms. The primary energy was 50 kev. [From E. N. Fuls, P. R. Jones, F. P. Ziemba, and E. Everhart, Phys. Rev. 107, 704 (1957).]
Russek (26, 27). The fact that the collision time (10-16-10-1ssec) is long in comparison with the inverse characteristic electron frequencies in the atoms gives rise to a complex formation with a changing internuclear distance. The energy levels in this particle complex will change continuously during the collision, so that statistical models may be used to find the distribution of the electrons over the energy levels involved. Firsov uses the Thomas-Fermi model. Each individual electron is assumed to interact only with the nearest atomic core. Because of the relative velocity of the atoms, the electron has to change momentum when it comes into the vicinity of the other atom. The excitation energy is picked up from the kinetic energy of the relative motion by momentum transfer of electrons jumping from one particle to another. This process is a function of vrelative and of ro. The energy is available to all outer elec-
78
C. SNOEK A N D J. KISTEMAKER
trons, and will usually lead to autoionization rather than to photon emission. Sometimes, t,his energy can be quite large in comparison with what a single ionization requires. We then have a superexcited state. A comparison of a theory based upon these assumptions with measurements of inelastic energy losses, as well as with measurements of total ionization cross sections, shows agreement within a factor of 2 (26). Russek's theory also supposes an energy transfer mechanism between the electrons of the penetrating shells, and by autoionization multiply charged ions can arise. With a self-consistent ionization theory (2'7) the ionization probabilities for a specified collision could be calculated, as well as the inelastic energy losses as a function of the collision parameter. The ionization probability for n,-fold ionization is defined by
'
=
Number of ions with charge Total number of particles
?z
Russek (2'7) found good agreement with experiments of Everhart et al. There are strong indications that bombardment of solid surfaces gives information quite analogous to that, gained from the bombardment of gaseous targets. This will be discussed in the two following sections.
111. SCATTERING EXPERIMENTS WITH SOLID TARGETS The general subject of sputtering has received much attention in the past 10 years and general reviews have been published by Wehner ( 1 ) and Behrisch ( 1 ) . A special aspect of this research dealing with fast, scattered ions and atoms has gotten more attention in the past 5 years. It was observed that fast particles could completely distort mean energy and angular distribution measurements. The result of this research, to be treated in Sections I11 and IV is that most of the fast scattered particles observed came from events occurring in the first two or three atom layers of the target. We might mention fast particles of another type escaping from a crystalline target. They are created b y violent collisions inside of the target, and escape by means of the channeling mechanism. These particles have a strong preference for directions coinciding with low-index crystal axes, and can be found in the sputtering spots observed by Kamirisky (33). However, they have not been included in the following discussion, although the number of fast channeled ions and that of fast scattered ions are both of the order of 1% of the primary beam (34). Fast particle scattering against solid targets has been done mainly in MOSCOW, Mainz, and Amsterdam. These experiments more or less automatically arise in those groups which do high-intensity mass spectrography or electromagnetic mass separation.
F A S T ION SCATTERING AGAINST METAL S U R F A C E S
79
I n all the experiments described here, a flat solid target is bombarded with a n ion beam with small angular spread. I n most cases the beam is supplied by an accelerator followed by magnetic separation. A monoenergetic, isotopically pure ion beam is obtained. Only Walther and Hinterberger did not use separation. The particles emitted by the target surface mostly travel through a n analyzer, which selects (1) momentum, with a magnet, or (2) energy, with an electrostatic condenser, or (3) velocity, with a time-of-flight method. The target surface must be kept clean during the experiment. Contaminated or oxidized surfaces can give a higher yield of sputtered ions and completely different relative abundances of the charged particles. Mass-spectrometric measurements have proved that from such a surface there can be detected ions not only of the material the target has been made of, but also of whatever adsorbed impurities there are, water, fragments of diffusion pump oil, etc. (Behrisch, Walther; see also Fig. 10). Contamination of the target can influence the energy distribution of the scattered particles as is shown b y Panin and Datz. This can be avoided by using a bakeable target, performing the experiment in a very good vacuum, or working with such a high beam current density that the removal of target atoms by sputtering is much faster than the contamination of the target surface by the ambient gas a t operating pressure. For example, in the experiments of Datz, a t a residual air pressure of about Torr and an Ar+ ion beam with a current density of 200 pamp/cm2, clean surfaces could be maintained because then the sputtering rate (about 10l6 atoms/cm2 sec) is much higher than the flux of incoming gas molecules (10'4 mol/cmf sec). If the current density was lowered to 10 pamp/cm2 the presence of the adsorbed impurities could be proved. Also Mashkova, working with a highintensity ion beam (1 mamp/cm2) could easily maintain a clean target. The other experiments employ targets that can be heated to about 1000"1300"K, and lower gas pressures, because of their lower current densities. Panin used a current density of 10-s-10-3 amp/cm2, a gas pressure of 2 x 10-7 Torr, and a maximum target temperature of 1300°K. I n Walther and Hintenberger's experiments these data were amp/cm2, Torr, and 900"K, respectively. The analysis of the scattered particles can be performed with sectortype instruments, employing either electrostatic (Panin) or magnetic (Datz) deflecting systems, or a combination of both, as used in the parabola mass spectrograph (Hintenberger). With all these methods one can only study ions. Fast neutrals can be analyzed by using pulsed beams, and measuring the time of flight over a known distance (Fluit). Because of the high energies of the particles (10-100 kev), particle multipliers or simple secondary electron emission detectors can be used. Hintenberger used photographic registration.
80
C. SNOEK AND J. KISTEMAKER
Some investigators have used only one observation position relative to target and beam direction (mostly 45'). This is sufficient, if one is merely interested in the kind of particles escaping from the target, and in their energies. However, if one wants t o study real particle scattering, then it is necessary t o measure the angular distribution. If the angle is varied, then using Eq. (5) one can determine the repulsive force between the particles. That the orientation of a single crystalline target with respect to the beam was of high importance to get clean (mlne) spectra was shown by Datz and Snoek. They showed how to get rid of the interference by the lattice (see Section E).
A . Panin's Experiment (Moscow) (31) Panin was the first to demonstrate that the interaction of atomic particles with energies in the kiloelectron-volt range with atoms in a solid
FIQ.7. Schematic view of the apparatus used by Panin for the study of the secondary ions. The in-coming ion beam (1)hits the target (2), and creates secondary ions which, after passing through the electrostatic analyzer (3), are detected with the Faraday cage (4). [From B. V. Panin, Soviet Phys. JETP (EnglishTransl.) 16, 215 (1962).
takes place as if the latter were free particles, and that beam ions scattered through this mechanism can be highly charged after the collision process. In his experiments beams of a great variety of ions (H+, Hz+, He+, N+, Nz+, O+, 02+, CO+, Ar+, and Arzf) with energies of from 7.5 kev up to 80 kev were directed on targets of Mo or Be. The angle of incidence, as well as the exit angle, was 45") in such a way that ions were detected escaping from the target in the direction perpendicular to the in-coming beam direction. The aperture of his analyzing system was 20°, and the
FAST ION SCATTERING AGAINST METAL SURFACES
81
resolving power was about 80. The target area was shielded from magnetic and electrostatic fields. (See Fig. 7.) Secondary ions with positive and negative charges were observed; only the latter to a considerable amount, in case of primary particles with 0.06
6,
1
0.05
a04
M3
i
0.02
0.01
1. 1. t
t
Ar4+Ar3* Ar2+
Ar+
.
0
I
0.2
01
I
0.6
I
8
+O
FIQ.8. Energy distribution of the ions scattered from a Mo surface bombarded by Ar+ ions of two different energies (10 and 80 kev); The yield 6, is given in units of 7.14 X 10-1s ampplamp ev. [From B. V. Panin, Soviet Phys. J E T P (English Trand.) 16, 215 (1962).]
high electron affinity (oxygen). In the energy region O.1Ea < E < Ea, the spectra of the secondary ions showed various aspects depending on the atomic mass ratio of the projectile and the target atom. 1 . ml 6 m 2 (For Example Ar+ on a Mo Target). A very interesting and easily understandable spectrum is demonstrated in Fig. 8. It consists of distinct peaks superimposed on a background. The ( E / E o )values at
82
C . S N O E K A N D J. KISTEMAKER
which the peaks occur are independent of Eo. Each peak corresponds with an Ar ion of a charge ne (n = 1, . . . , 5 ) . They originate from single Ar-Mo scattering events into the acceptance angle of the analyzer. The intensity of peaks with highly charged Ar ions increases strongly with E o increasing.
0025 69
1
PO2 -
0.015
-
M1-
a005
-
-
i
E/EO
FIG.9. Energy distribution of the ions scattered from a Mo surface bombarded by a mixture of CO+ and N2+ ions with Eo = 30 kev. The yield 6, is given in units of 7.14 X 1 0 - 1 3 amp/ramp ev. [From B. V. Panin, Soviet Phys. J E T P (English Transl.) 16, 215 (1962).]
If molecular ions were used (02+, Nz+, and CO+), the spectra were a combination of spectra for each component of the molecular ion. Each component of it behaves as if it were an independent projectile with a kinetic energy corresponding to the velocity of the parent molecule. Typical energy spectra from ml < m2 are given in Figs. 8 and 9. 2. ml << m2 (For Example, H+ on a Mo Target). I n this special case only a very small part of the primary energy E o can be transferred to the target particle, as demonstrated in Eqs. (1) and (2). Therefore, Panin’s energy spect,rurn showed H+ ion energies close to E,.
FAST ION SCATTERING AGAINST METAL S U R F A C E S
83
3. ml > m2 (For Example, Arf on Be Target). I n this case hardly any emitted ion had a n energy higher than O.lEo,and mostly Be ions were released through more or less large-impact parameter collisions. The energetic Ar ions are scattered forward over small angles and disappear in the target. The explanation of Panin’s large background is given by multiple collisions with atoms in his polycrystalline t,argets. Impurities on the target surface can influence the transferred energy strongly, as was demonst,rated b y the differences between energy spectra obtained with hot and cold targets. Especially the low-energy secondary ions were very sensitive to target contamination. When Mo was bombarded by Hf, a heated clean target did not yield any slow ions. The transferred energy was too small to release a Mo ion from the surface. A cold Mo target produced many slow ions, however.
B. Walther and Hintenberger’s Experiment (Mainx) (35) Their work can be divided into two parts: (1) Observation of ions being sputtered in a direction normal to the target. These were present, but not analyzed.
(2) Observation of ions leaving the target in a direction about perpendicular t o the beam. These ions, which were “reflect,ed” ions as well a s “sputtered” ones, were analyzed with a parabola mass spectrograph. Here also the angle of incidence of the primary noble gas ion beam on the polycrystalline targets was 45’. Detection was done with a phot,ographic plate. The schematic representation of the results can be seen in Fig. 10.
To understand this figure, it is necessary to know that all ions leaving the target got an extra acceleration energy of 15 kev. This was done to be sure that also very slow ions (a few electron-volts) leaving the target area would not escape detection. Each point, of a n indicated parabola corresponds with a particle of a certain (mlne) value, and with a certain kinetic energy. The spread in energy can be explained by the different numbers of collisions which projectiles have experienced in the surface of the polycrystalline target. This also causes t,he background in Panin’s experiments (Figs. 8 and 9). Yet, from Hintenberger’s experiments it is clear that there are t,wo types of ions dominating. There are many particles with nearly initial zero energy, and there are fast projectiles being reflected with an energy of the same order of magnitude they originally had. These two types can be recognized in Fig. 10, from the black dotasindicating the maxima in the spectra. The Xef, Kr+,
84
C. SNOEK AND J. KISTEMAKER
Arf, and Ne+ ions that have passed through an elastic collision with an atom of the Au target can cause these maxima. From the position of the dots one clearly sees that Xe has dissipated more energy to the Au atom than has the light Ne atom [Eqs. (1) and (2)]. The projectiles used were He, Ne, Ar, Kr, and Xe, and the target materials were C, Al, Fe, Cu, Ag, Ta, W, Pt, and Au. The primary energies were 5 , 10, and 15 keV.
X,
I
I 15
20
30
60 electric deflection
keV
FIG. 10. Simplified spectrogram of the parabola mass spectrometer as used by Walther and Hintenberger. Shown is a combination of spectra obtained when a AU target is bombarded with 15-kev noble gas ions. At the left side the ions of the target material and the impurities appear with an energy corresponding with the re-acceleration voltage, 15 kv. The heavy solid lines represent the parts of the parabola blackened by the scattered noble gas ions. The dots indicate the maxima in the energy distribution. [From V. Walther and H. Hintenberger, 2.AvutuTforseh.18a, 843 (1963).1
Still, in Fig. 10 one sees COf and COz+, apparently originating from target impurities. Their energy is small, because they are ejected in a direction nearly perpendicular to the beam. Their intensity increased if the bombardment was done with heavier particles. As in:Panin’s experiments, no scattered beam ions were observed if they were heavier than the target atoms. The same holds for neutralized
FAST I O N SCATTERING AGAINST METAL SURFACES
85
beam particles, which are not deflected by the electric and magnetic fields, and which blacken the vertex of the parabola. It was shown that a considerable fraction of the scattered primary beam particles was neutralized during their interaction with the surface. Multiply charged ions were not found. Perhaps the primary energies were too low. There is good agreement between Panin’s and Hintenberger’s results.
C. Mashkova and Molchanov’s Experiment (Moscow) (2) Unlike the former experimentors, Mashkova and Molchanov determined the angular distribution of the scattered primary particles.
FIG. 11. Schematic view of the apparatus used by Mashkova and Molchanov. beam current; I, = current of scattered ions; I t = current of scattered neutrals. [From E. S. Mashkova and V. A. Molchanov, Soviet Phys. “Doklady” (English Transl.) 7, 829 (1963).] I0
= primary
A schematic view of their experimental setup is given in Fig. 11. The angle of incidence on the target can be varied and for each angle cp the secondary electron detector can be scanned through angles e < 35”. Targets of W, Cu, and C were bombarded with 30-kev Ar+ ions, a t almost grazing incidence (cp = 74” to 86”). The emitted particles were detected a t small angles of scattering ( 0 < 30”), as demonst)rated in Fig. 12. For these small angles e most of the detected part,icles were scattered beam particles. It has been known for a long time that a large fraction of the primary ions is neutralized when a beam of ions strikes a metallic surface at glancing incidence (36). With Mashkova’s secondary electron detector arrangement, as demon-
86
C. SNOEK A N D J. KISTEMAKER
strated in Fig. 11: reflected neutrals and ions could be separated. They found many more neutrals than ions for B decreasing from 30" downward. This trend is demonstrated clearly by the curves in Fig. 12. There is a second effect to be seen in this figure, viz. that reflected particles have a very small chance to pass in directions nearly parallel to the surface
FA
N
I
1.0
-
08
-
c
I
o'6:
a-
02 -
0'
;'-'6
tb'
;Io
;ao
d2'
2)6'
30°
- 0
FIG.12. Angular distribution of the beam particles, scattered at a Cu surface; Ar+ with Eo = 30 kev. In 1-7, l2 (the yield of neutral particles) ie plotted for different angles of incidence p. l o= 100 pamp. (1) p = 86", (2) p = 84", (3) p = 82", (4) p = 80°, (5) p = 78", (6) p = 76", (7) p = 74". (8) represents 1 1 (the scattered ions) when l o = 250 Camp, p = 82". [From E. S. Mashkova and V. A. Molchanov, Soviet Phys. "Doklady" (English Transl.) 7, 829 (1963).] (a nearly 90";see Fig. 11).At a values of about 78" each of the curves in Fig. 12 reaches the envelope, which probably corresponds to the undisturbed scattering value. The reason for this effect was supposed to be found in surface irregularities. The decrease with increasing B is in qualitative agreement with the angular distribution for a bi-particle collision with a screened Coulomb potential (dashed curve in Fig. 11). A special aspect was observed a t large B angles, where too many particles were detected. If Ar+ is scattered against a C target, the mathe-
FAST ION SCATTERING AGAINST METAL SURFACES
87
matics of Section I1 do not predict scattered projectiles at 0 angles larger than 17". The opposite experimental experience was, therefore, explained by Mashkova and Molchanov, assuming multiple collisions at the surface of the C target.
D. Fluit and Friedman's Experiment (Amsterdam) (4, 37') Bombarding Cu polycryst-alline targets with Ar+ ions (10, 15, and 20 kev), Fluit studied the fast particles being "reflected" and measured their velocity with an arrangement like the one in Fig. 13. Knowing the distance
FIQ.13. Experimental arrangement used by Fluit for the determination of the velocity of the scattered particles. The in-coming beam is interrupted and on a double beam oscilloscope the time difference between the step in the two signals is measured; p = 70°, 0 = 40°, (I = 70". A is a pulsated condenser, to deflect the beam from the target. B is a deflection condenser, to discriminate ions from neutrals. [See J. M. Fluit, J. Kistemaker, and C. Snoek, Physica 30, 870 (1964).]
between target and secondary electron particle detector (70 em), and using a pulsed beam technique with a cutoff time of 0.1 psec, he could measure the time of flight of the "reflected" particles. Moreover, he could distinguish fast scattered neutrals and fast scattered ions, using a deflecting condenser as indicated in Fig. 13. The results of Fluit's work can be summarized as follows: (1) Curves analogous to those in Fig. 12 were found for Ar+, 15 kev, on Cu. Fluit used cp = 0" to 60") a = 0' to 90"; Molchanov used cp = 74" to 86") a = 60" to 90". Probably because of the more favorable cp region, Molchanov's curves in Fig. 12 seem to be more meaningful. Their envelopes fit better to the theoretical model.
88
C. S N O E K .4ND J. K I S T E M A K E R
( 2 ) The times of flight, measured over a path length of 70 cm, changed from 3.5 to 2.5 psec for cp = 70", a = 70", and, therefore, 0 = 40°, if E0 was varied from 10 to 20 kev. This meant that the energies involved were 80-90% of the primary energy, if the particles were reflected Ar atoms. The scattered particles observed must have been Ar particles, as their energies would have been larger than the primary energies if they had been Cu ones. The experimentally found energy loss of the Ar particles must be compared with that of an Ar atom after a single elastic collision with a Cu atom at a scattering angle of 40" [Eqs. (1) and ( 2 ) ] (about 25%). The discrepancy can be entirely due to experimental errors. The measured ratio between Ar+ ions and Ar neutral atoms was about 1:7 in this case.
E. Datz and Xnoelc's Experiment (Amsterdam) (3) Quite precise work on fast ion scattering against solid surfaces was done recently in Amsterdam, by Datz and Snoek. In the energy range of 40 to 80 kev, they bombarded Cu targets, polycrystalline as well as oriented single crystals, with Ar+ ion beams (beam divergence, 1"). The background pressure around the target was kept a t about 10P Torr, the beam intensity usuaIly was 200 pamp/cm2, and the angle of incidence was kept at 45". By using a big rotatable table, the analyzing mass spectrometer equipment could be turned around the central target. I n this way the angle of observation could be varied between -10" and +110" with respect to the in-coming beam direction. The angular spread accepted by the analyzer was only 0.6",and the resolving power about 100. The current sensitivity was quite high, as a particle multiplier was used for detection. All measurements were done on a dc basis. The spectra measured are shown in Fig. 14. We see the spectrum variation for the scattering angles e = 70", 80", and 90". One can see Cu+ up to CuS+and also Ar+ up to Ar5+. When a gold target was used, even Ar7+was observed. Usually the target had a potential of a few volts with respect to earth. No other extra acceleration of ions in the mass spectrometer was applied. The observed width of the peaks in Fig. 14 corresponds t o the energy spread among the ions with a certain (mlne) value. This width is much larger than corresponds with the resolution. The position of the peaks was independent of the angle of incidence of the primary ions on the target, but depended only on the angle of scattering. If a polycrystalline target was used, a fairly high background was observed, and the peaks had a broad shoulder on the high-energy side. (See Fig. 15.) Also, here the energies a t which the peaks occur correspond t o the energies calculated from two-body-collisions [Eqs. (1) to (4)]. The reason for the high-energy shoulder of the peaks is to be found in multiple scattering. A certain scattering angle, 6, can be reached in a
89
F A S T ION S C A T T E R I N G AQA41NST M E T A L S U R F A C E S
single violent collision, with one certain small collision parameter, p . However, it can be reached also via two or three and perhaps more collisions. The soft collisions with large impact parameters are the most probable in this mult,iple scattering process. A calculation shows t,hat in CU(IDOI
*r+(Arbitrary units I
0
1000
zoo0
3000
iooa
5000
6000
FIG.14. Magnetic analysis of the scattered ions obtained a t e = 70", 80", and 90" from a Cu (100) single crystalline surface bombarded in the [110] direction by 60-kev Ar+ ions. [From S. Datz and C. Snoek, P h p . Rev. 134, A347 (1964).]
the first case (small p ) more energy is transferred by the Ar to the target atom than the total in the latter cases with large collision parameters. This leads to the mentioned shoulders and background in the case of a polycrystalline target. So, in the case of more than one collision, remarka-
300
200
100
0
-.-
Ar, Ag (poly) E,~BOkN Q s L 5 ' 0.70.
600
I+
i
-
L bl
c
2
2 400 .c z
Ag"
K
Ar"
a
Ag"
z
e
Ar"
200
Ar"
31"'"
0
200 1001
500
0 0
4000
2000 Magnetic field
-
6WO
B(GauSS)
Fig. 15. For descriptive legend see opposite page. 90
FAST ION SCATTERING AGAINST METAL SURFACES
91
bly enough, the primary particle has more energy left than when it were scattered through the same angle in one collision. I n order to diminish the effect of multiple collisions, Datz and Snoek have used a Cu single crystal bombarded on a (100) surface under 45' wit,h the normal. Thus, the direction of impact was exactly along a [110] axis. In that case all Cu atoms lying below the top layer are shielded by the very surface atoms [see Fig. 16 (b)]. An Ar+ ion will either collide with a surface atom or graze along it. In the latter case, it is deflected only through small angles and will penetrate too deeply into the Iattice to be
3000
iiw
,200 B IQauu)
(a)
3100
3ioo
[ b)
FIG.16. (a) Line shape of the ArZ+peak (Eo= 60 kev, 0 = 70") scattered from a (100) Cu crystal, for ion beam incidence a t 8 = 45" (110) and e = 37", corresponding with the cases A and B in (b) of this figure. This illustrates the shadowing effect of the surface atoms in the case of beam incidence along a [110] direction. [From S. Datz and C. Snoek, Phys. Rev. 134, A347 (1964).]
seen again as a reflected particle. The improvement is obvious. The background nearly disappears, and the peaks of Fig. 14 are sharp. In Fig. 14 one can even observe that each Ar"+ peak becomes double, with relative intensities of about 2 : 1, caused by the single scattering of the Ar ion against the CuB3or isotope, respectively. Also the Cu ion peaks in Fig. 14 should be split. The fact that they are not is due to the insufficient parallelity of the primary beam and the angular spread of the particles entering the analyzer. The energy of the relatively slow Gun+ ions is very sensitive to minor changes at small scattering angles in the center of mass system. The fact that the improvement was really due to the correct orientation of the crystal is shown in Fig. 16(a), where the influence FIG. 15. Magnetic analysis of the scattered ions for the following systems: (top) Ar+ (60 kev) on Cu (8 = 70"), (middle) Ar+ (80 kev) on Ag (0 = 70"), and (bottom) Ar+ (80 kev) on Au (8 = 80"). The targets in these cases were polycrystalline. Cu, Ag, and Au are in the same column of the periodic table. [Experimental results obtained by S. Dats and C. Snoek, Phys. Rev. 134, A347 (1964).]
92
C . SNOEK AND J. KISTEMAKER
of the angle of incidence is experimentally demonstrated. I n this way multiple collision effects with the second to the fifth layer become visible. They result in an apparent Ioss of resolution with broadening on the high-energy side. No satisfactory data could be obtained about the absolute number of scattered particles for each direction. Datz could only indicate that more Cu+ ions were observed if the angle of scattering e was enlarged. If this angle grew over 75", Datz estimated that the number of neutral Cu atoms took over and became larger than the number of Cu+ ions. These large angles in the laboratory system correspond with a small scattering angle in the center-of-mass system [see Eq. (4)]. Moreover, Datz could measure the ratio of the ionization probabilities, P,. Comparison with the results of 50-kev Ar+ ions on Ar gas obtained by Fuls et al. (18) gave interesting analogies. Fuls found that the relative abundance of the Ar ions changed rapidly if the observational scattering angle was slightly changed at small scattering angles of the primary projectiles. This corresponds with Date's observation on Cu ions (small in the center-of-mass system). Fuls also found that the ionization probabilities P, in the region of large scattering angles were quite insensitive to angular variation such as Datz and Snoek found for the ratio of the Arn+peaks a t 0 values between 70" and 90". The last effect is apparently a consequeiice of the small variation of the distance of closest approach with varying angle. It is due to the steepness of the repulsive potent,ial, if both nuclei approach each other to about 0.1 A. On the other hand, Datz did not find as many multiply charged ions as Fuls did, which might have two reasons:
+
+
( 1 ) The influence of the work function at the target surface. This was examined by comparing the ( m l n e ) spectra obtained with a polycrystalline Cu target with those obtained from a CuzO target. The ratio between the various peaks did not alter. If the electrons are emitted "long" after the collision by an ejected high-speed superexcited atomic or ionic particle, no influence of the work function should be expected. ( 2 ) Charge exchange, or discriminative electric or magnetic stray fields. Although no indications for such effects could be found, they can not be completely excluded.
IV. LIGHTEMISSION FROM ION-BOMBARDED METALTARGETS There are several possibilities for the origin of the photons observed when metals are bombarded with fast ions. If only the near-ultraviolet and visible spectral regions are considered, according to Chaudhri (7) the
FAST I O N SCATTERING AGAINST METAL SURFACES
93
radiation can be caused by plasma oscillations of the electron gas, as is observed when thin foils are irradiated with electrons of some tens of kiloelectron-volts (8). Chaudhri found a spectral distribut,ion consisting of a continuum with several broad maxima when thick targets were used. Moreover, the experiments were performed with optical filters of considerable bandwidth. So, an eventual line spectrum, as observed by the following authors, could not be found by Chaudhri, because of lack of resolution. Another possibility is indicated by Kistemaker (6) and Snoek et al. (6). From their experimental results, which will be discussed later on, they concluded that most of the photons are emitted by atomic particles leaving the surface with energies of a few kiloelectron-volts. They suppose the following mechanism: Atoms or ions coming from the target in an excited state originate from two-body collisions in the surface layer; they belong to the group of particles discussed in the preceding chapter. The deexcitation can take place at some distance from the surface, by emission of a photon. The fact that the inelasticity of the collisions can lead to excitation as well as to ionization was observed earlier in gas scattering experiments by de Heer and Kistemaker (38). Because of the observed high velocities of the emitting atoms, they cannot be normally sputtered particles which have energies of 0 to 100 ev. This is in agreement with the results of experiments by Oliphant and Moon (36,39) and with theoretical considerations by Hagstrum (&I), which predict that only fast particles can leave clean metallic surfaces in an excited or ionized state. I n the experiments of Kistemaker and Snoek, the spectra were examined with the help of a monochromator provided with a photomultiplier. Cu targets were bombarded with Ar+ or Ne+ ions with energies of from 10 kev up to 60 kev. In the early experimental arrangement only the target could be rotated around a vertical axis through the central spot on the target, where the ion beam hits. The in-coming ions could have energies up to 20 kev, and had a fixed, horizontal direction perpendicular to the direction of observation of the monochromator. The experiments with 60-kev Ar+ ions were done with an apparatus in which the monochromator also could be rotated around the same axis as the target (see Fig. 17). The observed spectra were line spect,ra of Cu I and Cu 11,and Ar I1 or Ne 11. A continuous background could not be detected. Until now, all phenomena observed can be understood with the above-mentioned twobody collision process. (a) The angular distribution of the emitted light was found to be isotropic, at least in the region of 20" to 80" with respect to the normal on
94
C . S N O E K A N D J. KISTEMAKER
the target surface. This indicates a light-emitting volume, a thin layer in front of the surface: the particles have left the surface before de-excita,tion. (b) As has been proved by Datz (S), also collisions in layers deeper than the ultimate top layer can contribute to the emission of fast particIes. Fluit et al. (37) and Kistemaker and Snoek (5) have shown that the number of these particles “reflected” in a certain direction with respect to the target surface was strongly dependent on the angle of incidence of f
FIG.17. Schematic view of the apparatus used by Snoek and co-workers for the study of the angular dependence and the angular distribution of the light produced by ion impact on surfa.ces (not to scale). [From C. Snoek, W. F. van der Weg, and P. K. Rol, Phystka SO, 34 1 (1964).J
the ion beam. If a single crystal was used as a target, a minimum in the yield of fast particles was found if the incoming beam was directed along a low-index crystallographic axis. [See Fig. 181 The fact that the photon production exhibited an analogous behavior [see Fig. 191, as found by Kistemaker and Snoek ( 5 ) ,indicates that their origin could be the same. (c) The velocity of the light-emitting Cu atoms has been measured in two different ways: (1) The velocity in t,he direction of the spectrograph can be estimated from the line broadening, due to Doppler shift. This has been
F A S T I O N S C A T T E R I N G AGAINST M E T A L S U R F A C E S
95
studied a t the strongest line, the Cu I resonance line, X = 3247 A, with 60 kev Ar+ ions incident on a polycrystalline Cu target. One observes a broadening of several angstroms at the highfrequency side of the spectral line (Fig. 20) if the monochromator and the target are situated in such a way that the scattered Cu atoms are directed to the monochromator. (See Fig. 17.)
Angle of incidence (‘P)
FIG. 18. Dector current corresponding to the yield of the scattered projectiles. [From J. Kistemaker and C. Snoek, “Le bombardement ionique,” p. 52. C.N.R.S., Paris, 1961.1
The corresponding velocity of the emitting Cu atoms is a few times 107 cm/sec. This must be compared with the velocity of the bulk of the sputtered atoms, which is about 1 X lo6 cm/sec (20 ev), and with the velocity of a 10-kev Cu atom, 2 X 107 cm/sec. Also in agreement with the assumed picture is the increase of the line broadening, if the angle of incidence, cp, is increased, while the position of the monochromator with respect to the target is kept constant. I n the case of higher cp more fast particIes can leave the
I
Cu I 3 2 4 7 1 A r L C u (100)
C
Ar4
$ 8
2 X ? L
a
0 6
C
.-
.-z
5
Ar+
E
8 4 .k 3
-
:2
c n 1
0 angle
of
incidence
9
FIG.19. Intensity of the Cu I line, X = 3247 A, as a function of the angle of incidence. [From J. Kistemaker and C. Snoek, "Le bombardement ionique," p. 52. C.N.R.S., Paris, 1961.1
FIQ.20. Profile of the Cu line, X = 3247 A. Full curve, p = 15", @ = 5"; dashed curve, cp = 40", @ = 5 ; dotted curve, profile of the Hg line, X = 3341 A, to demon' strate the resolution of the monochromator. [From C. Snoek, W. F. van der Weg, and P. K. Rol, Phl~sica30, 341 (19641.1 96
FAST I O N SCATTERING AGAINST METAL SURFACES
97
surface and they will have higher velocities, because then more Cu atoms scattered into low scattering angles can escape from the target. (2) The mean velocity in the direction perpendicular to the target surface was measured by determining the thickness of the lightemitting layer. The target position was kept constant with respect to the beam, while the monochromator was rotated close to
2. c .-
a c
0 c
-c
*lo
OD
I
I
-lo
-2O
p
FIG.21. Intensity of the Cu line (A = 3247 A) as a function of fl for small values of fl. One degree in p corresponds to a distance of 0.52 mm from the target surface. [From C. Snoek, W. F. van der Weg, and P. K. Rol, Physiea 30, 341 (1964).]
the plane of the target surface. (See Fig. 17.) The monochromator was moved from just in front of the plane through the target surface to just behind it, between the limits p1 and pz. After passing the plane in the pz direction a gradually smaller growing portion of the light-emitting volume in front of the bombarded spot on the target could be observed (See Fig. 21). One can see this from simple geonietric reasoning. The distance from the surface a t which the intensity had dropped to l / e of the intensity measured in front of the target plane
98
C. S N O E K A N D J . KISTEMAKER
turned out to be 0.25-0.35 mm. Since the mean lifetime of an undisturbed Cu atom in the resonance level is 0.5 X lo-* sec, the mean velocity in the direction normal to the target surface is about 0.6 X lo7 cm/sec. This is also the order of magnitude of the velocity of the scattered Cu atoms; it is large as compared with the velocity of Cu atoms released by the sputtering process.
REFERENCES R.Behrisch, Ergeb. Exakt. Naturw. 36, 295 (1964). 2. E. 8. Mashkova and V. A. Molchanov, Dokl. Akad. N a u k S S S R 146,585 (1962); see Soviet Phys. ‘‘Doklady” (English Transl.) 7, 829 (1963). 3. S. Date and C. Snoek, Phys. Rev. 134, A347 (1964). 4. J. M. Fluit, L. Friedman, J. van Eck, C. Snoek, and J. Kistemaker, Proc. 6th Inlern. Conf. Ionization Phenomena Gases, Munich, 1961 Vol. I, p. 131. NorthHolland Publ., Amsterdam, 1962. 5. J. Kistemaker and C. Snoek, “Le bombardement ionique,” p. 51. C.N.R.S., Paris, (1962). 6. C. Snoek, W. F. van der Weg, and P. K. Rol, Physica 30, 341 (1964). 7. R. M. Chaudhri and M. Y.Khan, Nature 189,996 (1961); 193,646 (1961); Phys. Rev. 104,1492 (1956);Proc. 5th Intern. Conf. Ionization Phenomena Gases, Munich, 1961. Vol. 11, p. 1195. North-Holland Publ., Amsterdam, 1962; Proc. 6th Intern. Conf. Ionization Phenomena Gases, Paris, 1963 Vol. VI, p. 21. North-Holland Publ., Amsterdam, 1964. 8. W. Steinmann, Phys. Rev. Letters 6, 470 (1960); Z. Physik 163, 92 (1961). 8a. R. C. Jopson, H. Mark, and C. D. Swift, Phys. Rev. 127, 1612 (1962). 9. V. A. Molchanov, V. G. Tel’kovskii, and V. M. Chicherov, Dokl. -4kad. N a u k S S S R 137,58 (1961); see Soviet Phys. “DokEady” (English Transl.) 6,222 (1961); E. S. Mashkova, V. A. Molchanov, and D. D. Odintsov, Dokl. A k a d . N a u k S S S R 161, 1074 (1963); see Soviet Phys. “Doklady” (English Transl.) 8,806 (1964). 10. B. Fagot and C. Fert, Compt. Rend. 268, 1180 and 4670 (1964). 11. G. D. Magnuson and C. E. Carlston, Phys. Rev. 129, 2403 and 2409 (1963). 12. U. Fano, Phys. Rev. 96, 1198 (1954). 13. W. F. Miller and R. L. Platzman, Proc. Phys. SOC.(London) A70, 299 (1957). 14. H. W. Berry, Phys. Rev. 127, 1634 (1962). 16. M. T. Robinson and 0. S. Oen, Phys. Rev. 132, 2385 (1964). 16. G. R. Piercy, J. A. Davies, M. McCargo, and F. Brown, Phys. Rev. Letters 10, 399 (1963). 17. N. V. Fedorenko, U s p . Fiz. N a u k 68,481 (1959); see Soviet Phys.-Usp. (English Transl.) 2, 526 (1959). 18. E. N. Fuls, P. R. Jones, F. P. Ziemba, and E. Everhart, Phys. Rev. 107, 704 (1957); P. R. Jones, F. P. Ziemba, H. A. Moses, and E. Everhart, ibid. 113, 182 (1959); F. P. Ziemba, G. J. Lockwood, G. H. Morgan, and E. Everhart, ibid. 118, 1552 (1960). 19. G. H. Lane and E. Everhart, Phys. Rev. 120, 2064 (1960). 20. G. H. Morgan and E. Everhart, Phys. Rev. 128, 667 (1962). 21. N. V. Fedorenko, Zh. Tekhn. Fiz. 24, 784 (1954); D.M. Kaminker and N. V. Fedorenko, ibid. 26, 2239 (1955); V. V. Afrosimov and N. V. Fedorenko, ibid. 27, 2573 (1957); see Soviet Phys.-Tech. Phys. (English Transl.) 2, 2391 (1957); 1. G. K. Wehner, Advan. Electron. Electron Phys. 7, 239 (1955);
FAST ION SCATTERING AGAINST METAL SURFACES
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N. V. Fedorenko, L. G. Filippenko, and I . P. Flaks, Zh. Tekhn. Fiz. 30,49 (1960); see Soviet Phys.-Tech. Phys. (English Transl.) 6, 45 (1960). 22. V. V. Afrosimov and N. V. Fedorenko, Z h . Tekhn. Fiz. 27, 2557 (1957); see Soviet Phys.-Tech. Phys. (English Transl.) 2, 2378 (1957); V. V. Afrosimov, Yu. S. Gordeev, M. N. Panov, and N. V. Fedorenko, Proc. 6th Intern. Conf. Ionization Phenomena Gases, Paris, 1963 Vol. I, p. 111. North-Holland Publ., Amsterdam, 1964. 23. 0. B. Firsov, Zh. Eksperim. i Teor. Fiz. 34, 447 (1958); see Soviet Phys.-JETP (English Transl.) 7, 308 (1958). 24. 0. B. Firsov, Zh. Eksperim. i Teor. Fiz. 32, 1464 (1957); see Soviet Phys.-JETP (English Transl.) 6, 1192 (1957); Zh. Eksperim. i Teor. Fiz. 33, 696 (1957); see Soviet Phys.-JETP (English Transl.) 6, 534 (1958). 26. 0. B. Firsov, Zh. Eksperim. i Teor. Fiz. 36, 1517 (1959); see Soviet Phys.-JETP (English Transl.) 9, 1076 (1959). 26. A. Russek and M. T. Thomas, Phys. Rev. 109, 2015 (1958); 114, 1538 (1959); J. B. Bulman and A. Russek, ibid. 122, 506 (1961). 27. A. Russek, Phys. Rev, 132, 246 (1963). 28. N. Bohr, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 18, 8 (1948). 29. J. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, Phys. Rev. 120, 1229 (1960). 30. C. Lehmann and M. T. Robinson, Phys. Rev. 134, A37 (1964). S l . B. V. Panin, Zh. Eksperim. i Teor. Fiz. 42, 313 (1962); see Soviet Phys.-JETP (English Transl.) 16, 215 (1962). 32. B. M. Smirnov, Zh. Eksperim. i Teor. Fiz. 46, 155 (1963); see Soviet Phys.-JETP (English Transl.) 18, 111 (1964). 33. M. Kaminsky, Advan. Mass Spectrometry, Proc. Conf., Paris, 1964 Vol. 3. To be
34. 36. 36. 37. 38. 39. 40.
41.
42. 43.
44. 46.
published; M. Kaminsky, “Atomic and Ionic Impact Phenomena on Metal Surfaces,” p. 186. Springer-Verlag, Germany, 1965. M. W. Thompson, At. Energy Res. Establ. (Harwell) Rept. No. M-1262 (1963) (unclassified). V. Walther and H. Hintenberger, 2. Naturforseh. 18a, 843 (1963). M. L. E. Oliphant, Proc. Roy. SOC.A124, 228 (1929). J. M. Fluit, J. Kistemaker, and C. Snoek, Physica 30,870 (1964). J. van Eck, F. J. de Heer, and J. Kistemaker, Physica 30, 1171 (1964). M. L. E. Oliphant and B. P. Moon, Proc. Roy. SOC.A127, 373 and 388 (1930). H. Hagstrum, Phys. Rev. 96, 336 (1954). V. V. Afrosimov, Yu. S. Gordeev, M. N. Panov, and N. V. Fedorenko, Zh. Tekhn. Fiz. 34,1613, 1624, and 1637 (1964); see Soviet Phys.-Tech. Phys. (English Trans2.) 9, 1248, 1256, and 1265 (1965). E. Everhart and Q. C. Kessel, Phys. Rev. Letters 14, 247 (1965). Q. C. Kessel, A. Russek, and E. Everhart, Phys. Rev. Letters 14,484 (1965). U. Fano and W. Lichten, Phys. Rev. Letters 14, 627 (1965). M. Ya. Amusia, Phys. Letters 14, 36 (1965).
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Kinetic Ejection of Electrons from Solids DAVID B. MEDVED* Electro-Optical Systems, Inc., Pasadena, California AND
Y. E. STRAUSSER NASA, Lewis Research Center, Cleveland, Ohio Page 101 101
I. Introduction and Background.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Definitions of Secondary Processe ............ B. Gross Characteristics of Potential C. Historical Review.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Experimental Techniques. ......... ......... [A. Species, Sources, and Detectors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Target Preparation and Control (“Atomically Clean” Surfaces). . . . . . . C. Collector Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Double Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Experimental Results. ..... .... ... A. Polycrystalline Met ..................................... B. Single-Crystal Meta ....................................... C. Insulators and Sem ....................... D. Energy and Angular Distributions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Other Secondary Processes. ........ IV. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Introductory Comments. . . . . . . . . . B. “High-Energy” Theories. . . . . . . . . . C. Medium-Energy and Threshold Th ....................... V. Conclusions and Probable Trends . . . . . . . . . . . . . . . . . . . . . . . . Iteferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
108 110 110 119 126 129 131 131 152 157 161 165
169 174
I. INTRODUCTION AND BACKGROUND A . DeJinitions of Secondary Processes
The interaction of energetic beams of ions, atoms, and molecules with solids results in a variety of secondary processes. In this article we are primarily concerned with the secondary emission of electrons resulting from such interactions, and more specifically with the case where the *Also, Visiting Lecturer on the faculty of the College of Engineering, UCLA, 1963-1964. 101
102
DAVID B. MEDVED A N D Y. E. STRAUSSER
kinetic energy of the impacting particle is a significant variable of the problem. Figure 1 serves to illustrate some of the rich complex of secondary processes. In this case the incident particles are assumed to be ions with flux Ji. Each of the secondary processes may be quantitatively characterized by a yield coefficient. This yield coefficient may depend for its interpretation on the specific measurement techniques (see below for an example). The following definitions are those in general usage but may vary with particular authors: 1. Rejtected Particle Yield, K . That part of the outgoing flux which consists of the incident particle species we arbitrarily designate as
rrJ'
Jsb
I I
Y"
0
I
I
'. '.
: TARGET SURFACE
0 0
INCIDENT PARTICLES (assumed ?a be ions in this achematic) ATOMS OR IONS OF TARGET ATOMS OR IONS OF ADSORBED SPECIES ELECTRONS
FIG.1. Secondary processes under energetic particle impact.
reflected particles J , with the yield coefficient K defined as
K
=
J,/Js
(1)
These "reflected" particles may be neutrals in the ground state, metastable neutrals, positive ions, or negative ions of the incident species. 2. Sputtering Yield. The sputtered flux J , are those particles emitted from the solid that are species of the target material, J B ( t )of, the adsorbed ambient gases, or of impurities in the target. The sputtering yield, S, is defined as S = J8(t)/Ji (2)
where J,(t) is the flux of the sputtered t'arget atoms.
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
103
The “classic1’ method of determining the sputtering yield by weighing the sample before and after a given exposure ignores that part of the incident flux that remains in the target. This may be a factor of some significance, particularly when the atomic masses of the incident beams are of the same order or greater than the target atomic mass. The entrapment of the incident beam species in the target has been treated in recent work by Alm6n and Bruce (1) and by Kornelsen (2). Thus, most values of sputtering yields reported in the literature represent accurate values of net mass loss per incident ion current. These are not, however, necessarily good values of the sputtering yield, according to the definition of Eq. (2). Alternative methods of measuring the sputtering yield such as mass analysis (S), emission spectra of the sputtered atoms (4), and neutron activation analysis (6) more closely approach the definition of Eq. (2). 3. Secondary Electron Yield. I n Fig. 1, J e represents the flux of ejected electrons. The secondary electron yield coefficient y is then defined as Y =
Je/Ji
(3)
In this definition, the various mechanisms responsible for the external electron emission are not distinguished. One might take the operational view in an alternative approach to gross classification of the secondary processes resulting from atomic particle impact on solids. In such a view, the complex of atomic particles and electrons emitted from the surface are not distinguished except in terms of their charge. The various secondary processes may then be classified as secondary positive ion emission, secondary negative particle emission, and sputtering of neutrals. It is important to distinguish between these two approaches, since measurements of so-called secondary electron yields under certain conditions have included an appreciable contribution of secondary negative ions (see Sections 11, C and 111, A, 1).
B. Gross Characteristics of Potential and Kinetic Ejection There are two distinct types of secondary electron emission from solids produced by ions and atoms. These are potential and kinetic ejection of electrons. For those familiar with the language of atomic collisions, kinetic ejection and potential ejection may be considered as particlesolid analogs to “collisions of the first kind” and collisions of the second kind,” respectively. A potential ejection is a consequence of the relative energy level structure (density of states) of the interacting systems. For the case of kinetic ejection, the electron is emitted as a result of an inelastic collision of the incident particle with the atoms of the solid.
104
DAVID B. MEDVED AND Y. E. STRAUSSER
The terms “potential ejection” and “kinetic ejection” may be used also to distinguish the energy ranges of relevance, as well as fundamental differences in mechanism. Figure 2 shows typical variations of the secondary eIectron yield for argon ions and potassium ions incident on molybdenum polycrystals, according to the data of Petrov (8). It also serves to delineate the regions of interest. It turns out that for neutral noble gas atoms and alkali ions only kinetic ejection is possible, whereas with noble gas ions, both processes may occur. H. D. Hagstrum has studied t h e mechanism of potential ejection by noble gas ions in a series of researches spanning the past 15 years (7-9). Some of his data illustrating typical characteristics for t,he region of potential ejection are shown in Fig. 3. I
0.3I
h
02-
I
2
3
4
5
6
ION ENERGY Ek , kev
FIG.2. Petrov’s data illustrating the variation of and potential ejection ( 6 ) .
y
under conditions of kinetic
The gross features of kinetic ejection are illustrated b y the data of Large (10) in Fig. 4. The general features of the two processes contributing to electron emission are clearly exhibited in the typical data of Figs. 2-4. For potential ejection (the curves of Fig. 3), it is found that, in general, (I) y is constant and relatively independent of the kinetic energy Ek of the incident particle. (2) y increases with the ionization potential Ei of the incident species. (3) There is no apparent low-energy threshold observed for the process.
The characteristics of kinetic ejection are discussed with reference to Figs. 2 and 4. For kinetic ejection it is found that
KINETIC E J E C T I O N O F E L E CT RONS FROM S O L I D S
105
1
0.32, 0.28 0.24 0.20 y 0.16
0.12
I
+80 O o 04
xe' 0
0
I
200
1
I
400
600
I
800
1000
E,,eV
FIG.3. Typical data of Hagstrum illustrating potential ejection ( 7 ) .
6.05.04.0Y
3.0-
2.0-
t
k
,nev
FIG.4.Variation of y with ion mass and energy for various ions bombarding tungsten (10).
106
DAVID B . MEDVED A N D Y . E. STRAUSSER
(1) There appears to be a well-defined threshold, as shown b y the data of Fig. 2 for potassium ion on tungsten. (2) The values of y increase with E k until a saturation point is reached at sufficiently high values of incident ion energy. They may then begin to decrease (see the curves for hydrogen in Fig. 4). (3) I n cases where both processes may occur (such as A+ - W of Fig. 2), kinetic and potential ejection may be considered to first order as independent and superposable: = yr
+
(4)
Yk
where y r is a potential ejection contribution and yk is a kinetic ejection contribution t o the total secondary electron yield coefficient. Figure 5 illustrates a simple view of the potential ejection process. An electron, 1, in the metal may undergo a tunneling transition to the empty ground state of the in-coming atom. If the condition
is fulfilled, then a second electron, 2, will have some probability of emission from the solid. The tunneling transitions can take place in either of two equivalent mechanisms, as shown in Fig. 5. A one-step process ( A ) , known as Auger neutralization, is effectively equivalent (insofar as the energetics are concerned) to a two-step process (3 C ) consisting of resonance neutralization ( B ) and Auger de-excitation ( C ) . The electron yields and velocity distributions for the emitted secondaries will not profoundly depend on the kinetic energy of the incident particles. Also on the basis of this model the value of y should increase with the ionization potential of t he ions as is observed in the data of Fig. 3. It should be noted that the interaction and emission processes for potential ejection are essentially localized a t the surface of the solid (see Section 11, B). Figure 6 illustrates a heuristic model, which can be used in interpreting results of experiments in kinetic ejection. There are effectively two ways of viewing this interaction. In Fig. 6(b), the solid is viewed as an array of atoms penetrated by the incident particles. There is a mean depth of penetration determined by a relative cross section a t which a n inelastic atom-atom collision will take place which may result in production of internal electrons. The electrons produced in such a collision may have sufficient energy to escape from the solid. The fraction emitted from the solid will depend on the initial distribution function in velocity of internal secondaries produced in such inelastic collisions and the transport properties of these “hot” electrons. I n such a picture for kinetic ejection, the interaction leading to energy transfer and the subsequent electron trans-
+
107
KINETIC EJECTION OF ELECTRONS FROM SOLIDS EMITTED
- - - - - - * ELECTRON f
--
I
FIG.5. Potential ejection mechanisms.
i
SURFACE O f TARQET
FIG.6. Schematic representations of kinetic ejection.
108
DAVID B. MEDVED AND Y.
E.
STRAUSSER
port are characteristic of bulk processes in the solid. One would thus expect that, compared with potential emission processes, the surface conditions might be less important. At high ion energies it is expected that the relative collision cross sections will decrease and that, with correspondingly deeper penetrations, the secondary electron yield may saturate and eventually decrease. On the basis of this simple model, the position of y saturation will depend on the rate of increase of the ionization cross section (or internal electron production efficiency per particle) with incident kinetic energy or velocity compared with the rate of the increase of the penetration depth. Figure 6(a) is drawn from the viewpoint of band theory. An electron is promoted from one of the filled bands either directly or perhaps by phonons excited by the primary “knock-on.” If the energy loss is less than AE the electron can be emitted.
C . Historical Review A complete and thorough treatment of the early historical development of ion secondary electron emission and of kinetic ejection is neither necessary nor desirable. There already exists an extensive review in the work of Arifov ( l l ) ,which contains a complete historical development and treatment of both theory and experiment. This review is now available in English translation ( l l a ) . Almost all of the work in the first half of the 20th century was carried out under relatively poor vacuum conditions, with consequent illdefined surface properties and contamination effects. Most of the targets were polycrystalline with little or no attention paid to their relative impurity content. Complicating secondary and tertiary processes such as ion reflection, negative ion ejection, and electron reflection from the collector were not considered. The orders-of-magnitude discrepancies in early values of y between the same ion-target pairs in part was due to neglect of these other secondary and tertiary processes. I n writing with the hindsight of the present and all of the advantages of modern technology, we are quite acutely aware of the debt owed to the early investigators and pioneers of the field. On the other hand, papers still appear in the contemporary literature consisting of uninspired cornpilations of data for y vs. Ek on multiplicities of polycrystalline targets for the cases of kinetic ejection. We believe that such pedestrian work, particularly for undefined surface conditions, does little to advance our fundamental understanding beyond the primitive stages outlined in the previous section. This “understanding” eventually evolved as a result of the early work, in spite of the inconsistencies and difficulties in obtaining reproducible data.
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
109
Secondary processes connected with ion/atom impact on solids have been studied since the earliest days of gaseous electronics. For example, Villard ( l a ) ,in 1899, proposed ion-induced secondary electron emission from metal cathodes as a mechanism for the production of cathode rays in discharges. The first reported measurement of y was that of Fuchtbauer (IS) in 1905, who studied the secondary electron yields resulting from proton impact on aluminum and platinum targets. I n their studies of alpha-particle impingement on metals, both Rutherford (14) and J. J. Thomson (15) were plagued by a difficulty which is quite familiar t o modern workers in sputtering by ions. The secondary electrons emitted by their targets interfered with an explicit determination of impinging current. Thus, the alpha-particle charge itself could not be determined directly. The first investigations of y using alkali ions were carried out by Campbell (16) in 1915 on undegassed copper targets bombarded with sodium and aluminum ions with kinetic energies u p to 50 kev. H e observed a linear increase in y with energy, and then a decrease for energies in excess of 40 kev. He proposed th a t the observed decrease a t the higher energies resulted from deeper penetration of these highenergy ions into the target. The general outlines of the theory have not much improved in the intervening half century. Campbell also measured reflection coefficients in this very early work and found the yield of reflected ions was relatively independent of the kinetic energy. I n 1928, Penning (I?'), using extraction from discharges, was the first to report values of y for the noble gases. For the case of neon ions incident on copper under gas discharge conditions, he found that y was 0.03 for a kinetic energy of 1000 ev. These experiments on the noble gases were followed in subsequent investigations, also b y Penning (18), using directed ion beams on molybdenum targets in the energy range up to 1000 ev. A detailed description of specific investigations of more recent vintage will be given in the section on experimental results. I n Section 11, we review the experiniental procedures used in measuring secondary electron emission; emphasis is given to the generation and measurement of alkali ion and neutral beams and the various collection techniques and methods. I n addition to the extensive treatment in the yuasi-textbook of Arifov, other short reviews of the field have recently appeared. Among the more notable are reviews by Haymann (19) and Hopman (20). Hayinann has tried to present a general comparative treatment of ion-secondary electron and electron-secondary electron emission ; Hopman's review is a good literature and data survey (in Dutch). The interested reader is also referred t o the Proceedings of the All-Union Conferences on Cathode Electronics, which are published biannually (21). An extensive review of
110
DAVID B. M E D V E D A N D Y.
E.
STRAUSSER
the earlier work (up to 1952) can be found in Electronic and Ionic Impact Phenomena (Massey and Burhop, 22, Chapter 9). Current research in this field appears to be concentrated in the Soviet Union. Of the several laboratories that can be identified as very active in kinetic ejection studies, three are in the USSR. These include Arifov’s group at the Academy of Sciences of the Uzbek SSR (Tashkent), the staff of the M. V. Lomonosov Moscow State University (single-crystal metals), and the group at the R4. I. Kalinin Leningrad Polytechnic Institute (semiconductors and insulator targets). In France, M. Devienne heads a group at the Laboratoire Mediterraneen de Recherches Thermodynamiques (Nice), which is carrying out investigations using fast neutral beams, and single-crystal work is being carried out by Fert et al. at the University of Toulouse. There are no comparable groups in the United States; the Solid State Group of the Convair Physics Section is no longer active.
11. EXPERIMENTAL TECHNIQUES
A . Species, Sources, and Detectors 1. The Use of Alkali Ions. For most alkali ion target combinations there will be no potential emission and, thus, the use of alkali ions as TABLE I IONIZATION ENERGIES AND ATOMIC MASSESOF
THE
ALKALIS
Element
Ei (ev)
EJ2
Atomic masses
Li Na K Rb
5.39 5.14 4.34 4.18 3.89
2.7 2.57 2.17 2.09 1.95
23 39 85 133
cs
7
a bombarding species is of particular interest. As discussed in Section I, B, potential emission will occur only when the ionization potential of the bombarding atom exceeds twice the work function of the target material [Eq. ( 5 ) ] . In Table I are listed the ionization potentials and atomic masses of the alkali metals. In order for potential emission to occur when the bombarding ion is an alkali, the work function of the target would have to be less than 2.7 ev for the case of lithium. The number of clean targets for which such a condition would be met is quite small. However, for alkali ion beams, small coverages of adsorbed species may significantly lower the work function, well below that of a clean
KINETIC EJECTION OF ELECTRONS FROM GOLIDS
111
surface. For example, coverage of a monolayer of cesium on a slightly oxygen-contaminated tungsten surface has been shown t o reduce the gross work function from 4.52 ev for clean tungsten to about 1.1 ev for the contaminated case. With sufficient care and under appropriately controlled conditions, the use of alkali ions is eminently suited for a fundamental study of the kinetic ejection process. There are several techniques for production of alkali ion beams. The technique of surface contact ionization was pioneered by I . Langmuir (23) and is currently one of the two methods in use for production of ion
FIG.7. Energy diagram for contact ionization.
species in the ion engine electrostatic propulsion program. Electron bombardment ionization (24) is also utilized for generation of alkali ions. The principle of surface ionization can be described in terms of the model shown in Fig. 7. To some extent the process can be considered as the inverse analog of the potential emission diagram of Fig. 5 . For surface ionization to occur, it is necessary that the work funct,ion of the surface be greater than the ionization potential, Ei, of the atom which is to be surface ionized. It is thus clear why species for which ions can be produced readily in this manner will also be species for which potential emission cannot occur. Particle fluxes leaving the surface will contain a given percentage of ions and atoms under conditions of thermal equilibrium as determined by the Saha-Langmuir equation
112
DAVID R . WIEDVED .4NI) Y.
where Ji
E.
STRAUSSER
desorption flux of ions desorption flux of atoms. A typical surface-ionization source is shown in Fig. 8. By applying an electric field of appropriate sign a t the surface, the ions evaporated from it can be accelerated and focused to produce ion beams having the desired properties in energy, spot size, and current density. Refractory metals have certain distinct advantages as substrates for surface-ionization sources. These include (1) low vapor pressure a t the elevated temperatures (-1200°C) required for production of useful ion fluxes and low neutral fraction, (2) their resistjarice to corrosion by
J,
= =
IONIZER HEATER ,TOR
FIG.8. Schematic diagram of contact ionization ion source.
the alkali metals, (3) their relatively high work functions. In ion engines, tungsten is nearly always used. There are two approaches to the problem of supplying the adsorbed gas layer onto the evaporated surface. The first and simplest is t o direct an atomic beam of the alkali element of interest onto the hot surface. The two main problems herein are (1) the accommodation coefficient of the beam and (2) the fact that the neutral beam travels a certain distance through the ion beam, which leads t o charge exchange interactions in the beam. The charge exchange ions then tend to spread the energy distribution of the ion beam and, owing to sputtering, erode the ion accelerator electrode. The other approach, illustrated in the system of Fig. 8, employs a porous plug as the metal evaporator. The alkali atoms are supplied in the vapor phase from a reservoir at the back of the evaporator. Porous
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
113
tungsten evaporators or ionizers are now readily available as a result of the ion engine development program. When operated at about 125OOC with Cs these yield about 98% ionization efficiency a t ion beam current densities up t o about 30 ma/cm2 (25). Of the authors who have reported using alkali ion beams, Arifov and Rakhimov (26), Abroyan (27), and Waters (28) have used the first approach to the feed system problem while Bosch and Kuskevics (29) have used the second method. The problems which are encountered in the use of alkali ion beams include (1) the corrosive nature of alkali metal vapors, (2) leakage across high-voltage insulators when they become coated with thin films of the alkali metals, and (3) photoelectric currents caused by radiation from the high-temperature ionizer. The proper choice of materials and a good apparatus design (using shadow shields over insulators and beam deflection) will solve these problems with a reasonable amount of effort. A particular advantage in using the contact ionization source is in the high purity of the resultant ion heam. 2. Noble Gas Ions. The use of noble gas ions presents no unique problems in generation and intensity measurement of incident particles. The most widely used ion source for noble gas ions, as well as nearly all other ions, is the electron-bombardment ion source. This type of ion source has taken on many forms but they all have certain characteristics in common. The important ones are (1) a gas feed system, (2) a discharge chamber, (3) a magnetic field, and (4) an ion extraction system. The material from which the ion beam is to be formed is fed in gaseous form from a reservoir into the discharge chamber at a rate corresponding to the desired ion beam current. In the discharge chamber an arc is struck between an electron source and an anode. The electrons in the arc, through ionizing collisions with the gas atoms, form a plasma in the discharge chamber. In order to increase the probability of collision of the electrons with the gas atoms, an axial magnetic field is placed between the electron source and the anode. The ions are then extracted from the plasma that has been thus formed by applying a potent.ia1 between two plates, the first of which is at the potential of the electron source, the second being at a more negative potential which corresponds to the desired ion energy. Special problems (which can be avoided with a reasonable amount of care) in handling noble gas ion beams include: (1) Production of multiply charged and metastable ions and atoms. This problem is particularly serious in measuring potential ejection. It may be eliminated or minimized either by (a) electrostatic or mag-
114
DAVID B. MEDVED AND Y. E . STRAUSSER
netic deflection, or (b) use of sufficiently low voltages and pressures in the ion source (2) Presence of fast neutrals in the beam, resulting from charge transfer with residual gas in the ion source or vacuum chamber (3) Photoemission of electrons from the target produced by photons from the ion source in cases where source aperture and target are collinear.
It is clear that a deflection and mass analysis of the incident ion beam between source and target is highly desirable and serves to solve all three sources of error listed. However, available beam current density is reduced by such a procedure. Thus, Magnuson and Carlston, in order to utilize “bombardment cleaning” of the target (30) surface, maintained a direct in-line system between source and target (See Section 11, B, 1). These authors assure the reader that, “Energetic neutrals or metastable ions formed in the source or along the beam trajectory were measured by retarding potential methods and were estimated to comprise less than 0.01% of total ion beam current.” I t is our opinion that this statement was based more on fond hopes than on a careful consideration of the error factors listed above. 3. Neutrals and Metastables. Most of the early work using neutral atoms probably involved investigation of potential ejection rather than kinetic ejection processes, inasmuch as the neutrals were in metastable excited states. The first investigations were reported by Webb (31) in 1924, who studied bombardment of nickel targets by metastable mercury atoms. This work was followed by the studies of Franck and Einsporn (Sd), Messenger (SS), Coulliette ( 3 4 , and Sonkin (35),all of whom used Hg*. The use of metastable atoms of the noble gases was introduced by Uyterhoeven (36) and Oliphant (37) in 1928, followed by Found (38). Subsequent publications of these authors and their colleagues are devoted to further description of secondary processes induced by metastable noble gas atoms (39,40). In 1950 Greene (41) studied bombardment of Mo by noble gas metastables up to 1 kev, and, more recently, Hasted (42) in 1959 investigated the interaction of noble gas metastables with W, Mo, and Pt. The most recent investigation of this type was that of Hagstrum (43) in 1960. Up to the time of Oliphant’s work, most experiments were carried out with the target immersed in a discharge plasma and the surface and bombardment conditions were ill-defined. Beams of metastable atoms are produced by two techniques. The classic technique used by Greene, Oliphant, and others is resonance neutralization of the ion in a glancing collision with a surface. If source and target are collinear, then metastables pro-
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
115
duced by the source can be incident on the target, as in the work of Hasted (42) and Hasted and Mahadevan (44). Greene showed th at metastables were produced by glancing collisions between the ions and the walls of a canal placed between source and target. By using a tube with a long neck, he was able to apply a local magnetic field in this canal region without perturbing the source. Under conditions where only neutral particles could reach the target, he obtained a plot, shown in Fig. 9, which exhibits the variation in total secondary current from the target with applied magnetic field perpendicular to the canal. The results are interpreted as follows: The initial increase in secondary electron current (region a) is due to an increase in the number of wall collisions as the ions are more effectively
M
FIG.9. Effect of magnetic field on secondary electron current emitted by target (Greene's apparatus, 41). deflected to the walls. The decrease to zero (region b) following the maximum results from the drop-off in metastable production efficiency with decreasing angle of ion incidence (see Oliphant, 37). From the data displayed it appears that metastable fluxes equivalent to currents on the order of amp for Ne, Ar, and He were achieved in this work. No attempt was made to measure absolute neutral fluxes in this and the earlier work cited. The first rough estimate of metastable fluxes was carried out b y Dorrestein in 1938 in his studies on electron impact excitation of 2 3 S and 2 ' S states of helium ( 4 5 ) .Subsequently, a Iarge number of investigators in the fields of gaseous electronics and atomic collisions used Augeremitted electrons for detection of metastables. Dorrestein (469, Schulz and Fox (47)?Lamb and Retherford (48),and Novick and Commins (49) all used the metastable-induced secondary electron emission for flux measurements. These measurements of metastable flux were obtained
116
DAVID B. MEDVED AND Y. E. STRAUSSER
under nonreproducible and ill-defined surface conditions of the detector and thus cannot be considered as absolute flux measurements. I n 1957 Stebbings (50) measured the flux of He metastables by means of their ionizing effects on argon gas atoms as a function of pressure. Using the flux thus determined, he was able to obtain absolute data on y for He* on gold surfaces. This work was followed by the research of Hasted (42) and Hasted and Mahadevan (44).I n this work the metastables were produced in the source and the flux determined by measuring the beam attentuation and ionization current in passing through a collision chamber where the Penning ionization process A*
+B
+
Bf
+e +A
(7)
can take place. Energetic beams of neutral particles in the ground state for the study of kinetic ejection have not been extensively used. The essential difficulty in working with neutral particles in the ground state is similar to what is encountered with metastables. It is a relatively straightforward procedure to generate intense monoenergetic neutral particle beams; an accurate determination of neutral particle fluxes is another matter. Secondary electron ejection as a detection mechanism has been attempted, but again we encounter the bootstrap problem of detector surface conditions, properties, and how was its y determined in the first place. There is the additional complication with neutrals in the ground state that the yields from a secondary electron detector are relatively low a t energies below 1000 ev. This limitation does not apply to metastables where the electrons originate via an Auger process. Researchers who have attempted to use secondary electrons as neutral flux detectors include Devienne (51), Utterback and Miller (52), and Berry (65)in his early work. Monoenergetic neytral noble gas particle beams are obtained by resonance charge trarisfer of ion beams accelerated to the required energy : Ar&st
+ Arkmnal
Arzhermal
+ Ar:a>t
(8)
Typical geometry is shown in Fig. 10. The charge transfer cross sections are typically to cm2. The residual thermal ions are swept out by the deflection plates mounted a t the exit of the charge transfer chamber. Some of the earliest work on charge transfer and kinetic ejection was carried out by Rostagni (54) in 1934. Berry investigated electron ejection from Ta targets by atoms and ions of He, Ne, and Ar produced by resonance charge transfer in an energy range of from 500 to 4000 ev (53). He also reported on measurements using Heo on W under improved
117
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
vacuum conditions in 1958 (5 5 ). More recently, in the laboratories of Arifov (56), Medved (57), and Devienne (58) reasonably intense monoenergetic neutral beams have been generated and used for study of kinetic ejection. Investigations with neutral atoms of species other than the noble gases appear to have been limited to the work of Chaudhri and Khan (69) in 1948, and Arifov el al. (60). Chaudhri and Khan used fast atoms of HgO and KO incident to Ni and hilo, and Arifov’s group has studied the neutral alkalis KO and NaO, incident on Ta. Arifov and colleagues have measured the neutral flux by monitoring the ion beam currents at, the entrance and exit apertures of the charge transfer chamber (the method of current differences). Medved and colleagues (57, 61) measured their neutral particle fluxes by means of a Ar0 GAS I N (THERMAL)
ION SOLRCE
CAST A?0
-
4
T - -I ~FLECTION PLATES
i
CHARGE TRANSFER CHAMEER
MONITOR
LOEFLECTION MAGNET
FIG.10. Geometry for neutral beam generation by charge transfer.
thermocouple probe. The probe consists of a platinum disk, 1 mil thick, and fine wire thermocouple assembly mounted as shown in Fig. 11. Motion into the neutral beam is accomplished by means of a pivot bearing connected to a stainless steel bellows. The position of the probe relative to collector and target geometry is shown in Fig. 12. By proper aperture design the flux of neutrals a t the probe is that incident on the target when the probe is removed from the beam. Amdur’s group a t MIT had previously used thermocouple nieasuremeritjs for many years in their research programs in particle-particle interactions (6.2, 63).The thermocouple probes of Comeaux et al. (57, 61) were used in a dc mode, i.e., the beam was not chopped and synchronous detection techniques were not employed. Calibration consisted of measuring the thermal emf produced by a known ion current and assuming that energy transfer characteristics of ions and neutrals of the same species a t the same energy are identical. Subsequent work has shown that this assumption is not valid, particularly a t energies below 1000 ev, as a result of different reflection
118
DAVID B. MEDVED AND Y. E. STRAUSSER COLLIMATING Mo
SPHERICAL COLLECTOR7
I
TAR~BTTO.OO1m
niw ".--
A
---
OR Ar'
TD "FLASHING" WWER SUPPLY OR ELECTROMETER TO GROUND
TO MICROVOLTMETER OR ELECTROMETER (SHIELD NOT S W N )
FIG.11. Thermocouple probe used by Medved et al. (67, 61).
DOUBLE KNIFE EDGE FLANGE
IBACUGROUND
-
5 Xld'mm) FLEXIBLE CONNECTOR
AD H
THERMOCOUPL
PIVOT BEARING
SHIELD CONNECTION\
FIG.12. Thermocouple probe (67) motion as viewed along beam axis.
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
119
characteristics for the ions and atoms of the same species (57, 64). (See Section 111, C.) Devienne has employed the “black-body” concept-in construction of a detector designed to eliminate reflection of neutrals as a source of error in the flux measurements (166). I t consists of a hollow cavity with the entrance aperture at the apex end of a truncated cone which is terminated by a cone of larger angle. The energy transfer of the incident neutrals is converted to an electrical signal by means of a thermopile; sensitivities of 5 X 1O’O neutrals per cm2 per sec at 3000 ev are cited.
4. Other I o n Types. In addition to the extensive use of alkali and noble gas ions, a variety of other species have been employed for the study of electron ejection. A tabular summary of the various ion types used by investigators in the field is presented in Section 111, A, 4, where we list the author, ion type, and target material investigated. I t appears that of the miscellaneous species employed in secondary electron investigations, hydrogen and nitrogen are most often used. These ions are produced either in an electron bombardment source or in a radio frequency discharge. Preference appears to have been in the direction of the electron bombardment source, which has been employed by such workers as Arifov et al. (65),Batanov (66), Healea (67), Higatsburger et al. (68), Hill, et al. (69),Petrov (70), and Schwartz and Copeland (71).The radio frequency ion source has been used by Fogel et al. (72), by Large and Whitlock (73), and by Large (10, 7 4 ) . The radio frequency ion source is described thoroughly in t,he literature (75). There has been one study of kinetic secondary electron emission using negative ions. Arifov and Khashiinov (76) used negative chlorine ions which they obtained by bombarding an NaCl target with Nz+ ions and extracting the secondary C1- ions that were produced. The C1- were then accelerated and focused onto the target in the same manner as a positive ion beam would be except for the use of the opposite potentials. B. Target Preparation and Control (“Atomically Clean” Xurfaces) In this section, the effects of surface contamination on the magnitude and functional dependence of the electron yield with energy will be described. A discussion of techniques for controlling and monitoring the degree of surface contamination is also presented. Knowledge and control of the degree of surface contamination is essential in all surface-particle investigations if scientifically reliable and reproducible results are to be obtained. The secondary electron yields are particularly and uniquely sensitive to the degree and type of surface coverage. It appears that the effects of surface coverage are more pronounced for emission processes involving potential ejection rather than
120
DAVID B . MEDVED AND Y . E. STRAUSSER
kinetic ejection. Also, the effects of surface contamination appear to decrease with increasing energy in the region of kinetic ejection (see below). There does not appear to be a satisfactory theory or model which will describe the emission of electrons from contaminated surfaces. I t turns out the functional dependence of the secondary electron yield with
ION KINETIC ENERGY I N
ev
FIQ.13. Yield of electrons ejected by He+ ions from tungsten in various conditions during cleaning by heating (78).
energy exhibits a kinetic ejection character in the potential ejection region if the surfaces are heavily contaminated. This has been strikingly demonstrated in a series of studies by Hagstrum (77, 78). Figure 13 shows his data for the variation of electron yield with energy using helium ions incident on tungsten atoms with surface coverage as a parameter. The data presented in this figure exhibit the variation of the electron yield obtained by taking the target through a heating sequence under
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
121
high-vacuum conditions (background pressures on the order of 10-lo mm were achieved in Hagstrum’s apparatus). Curve 1 is data for variation of the secondary electron yield with energy for a heavily contaminated target surface as it was installed in the experimental tube and without any baking or heating applied; data for curve 2 were obtained after heating the target to 800°K; curve 3 is the data obtained by outgassing the target at 1330’K; and curve 4 (which is similar to the data given in Fig. 3) was obtained by outgassing at 1500°K followed by a flash to 2200°K. Hagstrum states that contamination of the tungsten surface by adsorption of the monolayer of gas can be monitored by its effect on the Auger characteristics and that the method is sensitive enough to detect changes in surface concentrations of less than 5% of a monolayer. There are, effectively, three techniques that have been utilized to obtain “clean surfaces,” for secondary emission studies. These techniques include the outgassing and flashing procedure under ultrahigh-vacuum conditions (as illustrated in the data of Fig. 13), bombardment cleaning, and a “roasting” technique, which has been applied by the Soviet school with some degree of success. Here, the target is maintained over long periods of time a t high temperature in high vacuum. “Roasting” must be employed in conjunction with pulse beam or other techniques, such as double modulation, in order to avoid confusion in the data resulting from the large quantity of thermionic electrons emitted at the “roasting” temperature. Ion bombardment cleaning was first quantiatively used by Farnsworth (79) and his colleagues in studying surface contamination on metals and semiconductors. They utilized low-energy electron diffraction ‘as a tool for monitoring the degree of surface contamination. A direct comparison of surfaces that have been “cleaned” by sputtering with the same surfaces cleaned by flashing a t high temperatures was carried out by Farnsworth and his colleagues on semiconductor surfaces. Hagstrum has attempted to utilize the variation of the secondary electron yield with degree of surface contamination as a monitoring technique of the relative efficacy of flashing and sputtering. In Fig. 14, we present a sequence of the secondary electron yield characteristics before, during, and after a series of sputtering experiments. There appears a continuous variation from the completely contaminated (curve 1) to the “atomically clean” condition (curve 7). There are essentially two ways in which the degree of surface coritamiriation is monitored by the secondary electron yield coefficient or, conversely, by its effect on the secondary electron yield coefficient. The first way is to consider the functional dependence of y with kinetic energy, surface contamination being a parameter (as in Fig. 13). The
122
DAVID €3. MEDVED AND Y. E. STRAUSSER
second consists of monitoring the secondary electron current for given bombardment conditions (constant ion energy and current density) following a flash as a function of time. Figure 15 shows the variation of y with time following a flash in ultrahigh vacuum to the “atomically
ION K I N E T I C ENERGY I N
ev
FIG.14. Sequence of y characteristics taken before, during, and after cleaning by ion bombardment (He+ on W, 7 8 ) .
clean condition.” The data are taken for argon ions incident on molybdenum in the region of potential ejection (80). Not shown on the time scale in this plot is the large rise in secondary electron yield, at times in excess of the monolayer formation time, which in this apparatus was of
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
123
the order of 4 t o 5 minutes. It appears from this and other data that secondary yields from potential ejection are lower under surface coverage conditions between a fraction of a monolayer and one monolayer than they are for the “atomically clean” condition; once a monolayer or more has been formed, the yields increase beyond the “atomically clean” values. It is the latter condition that is characteristic of the data points exhibited in curves 1 of both Figs. 13 and 14. Large has investigated the influence of sorption as well as adsorbed species in his study of hydrogen on T i (74). I n a private communication, Large has stated: “When targets of Mo, Pt, Au and Ag were measured after chemical etching followed by washing in distilled water the value of y obtained was always slightly higher than that for the same targets that had been ‘flashed’ during 0.10
0.00
0 ~ 0 7 1 1
0.06
0
05
10 15
20 2 5 30 35 40 45 50 55 Time after flash (min)
FIG. 15. Variation of y for Mo bombarded by Ar+ with time after flash. Ar+ beam energy 600 ev (80).
the experiments then removed from the vac system and allowed to stand in lab air for several months. The differences in y were only of the order of 10-200/,, but nevertheless they were pretty general and consistent. The effect can be expressed for Mo by reference to figure 5 of Ref. 74. The curve for y versus energy for a chemically etched Mo target peaks at y = 4.8.The same target was removed from the vacuum system after the measurements of y for an atomically clean RiIo surface. It was left, in lab air for six months after which time ymaxwas less than 4.0. Reductions have been observed in y values of five times when outgassing targets. I n the energy range 20-150 kev, the effect of outgassing targets is always to reduce 7.” A working model for the variations of the secondary electron yield coefficients with surface coverage can then be stated essentially as follows: I n those cases for which potential ejection may take place, kinetic ejection is observed when the surface becomes completely contaminated.
124
DAVID B. M E D V E D AND Y. E. STRAUSSER
When the surface is “atomically clean” immediately after a flash under ultrahigh-vacuum conditions, the yield that is measured may be close to the “true” value of y. With increasing cold interval time, potential ejection yield is diminished as a monolayer is formed. Once a complete monolayer has been formed, the secondary yield coefficient appears to remain relatively insensitive during the buildup of further adsorbed layers. At some point, as yet undetermined, a kinetic ejection characteristic appears wit,h a correspondingly large increase in the secondary yield coefficient beyond the value of the clean surface.
Qg
-
90 200
-
150
-
rt
r;
0 CLEAN SURFACE-I
0 CONTAYINATED SURFACE-2 X VARIATION OF YIQWI-YICMIT~I~ICLEAM-1
100
[
-
50
I
0 10
20
3 0 4 0
EI ,keV
FIG. 16. Variation of the kinetic electron emission coefficient. y as a function of Ar+ energy with contamination as a parameter (81).
The influence of surface coverage on kinetic ejection secondary electron yields appears to diminish with increasing energy i n this region. A quantitative study of the problem has recently been reported by Arifov and colleagues (81).Results are exhibited in Fig. 16. Curves 1 and 2 represent the variation of the kinetic ejection yield coefficient with a so-called clean surface and contaminated surface condition, respectively. Curve 3, which shows a monotonically decreasing variat,ion with increasing kinetic energy, is the difference between the clean and contaminated conditions. Unfortunately, the authors did not mention whether they maintained constant current densities over the energy range of interest,.
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
125
It is quite possible, for example, that at higher energies with higher currents, bombardment cleaning of the surface may have had something to do with the nature of the difference curve. The basic idea i n the approach of bombardment cleaning is that the sputtering rate of the target material exceeds the arrival rate of the background gasses a t the target surface. An elementary quantitative statement of the problem in terms of beam current densities and ambient background pressures has been carried out by Yonts and Harrison (82). Essentially, the sputtering or removal rate of atoms from the target should exceed the arrival rate of background “reactive” gases. Experimenters in the field were well aware of such criteria long before this particular publication (cf. Wehner, 83). Bombardment cleaning on targets maintained near room temperature has been utilized by Magnuson arid
Ar’ --Cu
(IIO),Normalincidence
~0 ‘ton Background pressure = 3 . 0 1 1.24
1.08
\
0.92 1001
,
0
2
L 1
4
6 8 10 12 14 16 I8 2 0 22 tC. Beam flag closed time(rnin)
FIQ. 17. Monolayer formation time curve of y vs. beam flag closed time for Ar+ normally incident on a copper (110) crystal. 500-ev beam energy (SO).
Carlston in their studies of y from polycrystalline (SO) and single-crystal metal targets. A similar procedure appears to have been used by Cousinik and colleagues (84).In the Magnuson and Carlston paper (Ref. 30) there appears a n extensive discussion of their procedures in attainment and monitoring of “clean” surface conditions. Consider, for example, their plot of monolayer formation time, shown in Fig. 17. I n this figure, the variation of elect,ron current tJo the collectjor is shown as a function of “beam flag closed time.” It seems strange that, with the background gas pressures cited in this work ( 1 O V mm or higher), apparent monolayer formation times on the order of 8 minutes were obtained. Also, if the authors were working principally in the region of kinetic ejection, it would have been more pertinent to present a curve showing behavior in this region rather than for a copper single-crystal target exposed to FiOO-ev argon ions. Problems associated with a direct in-line target configurat>ionhave already mentioned in the discussion of Section 111, A .
126
DAVID B, MEDVED AND Y. E . STRAUSSER
Finally, these authors neglect the effect of the working gas in considering contamination of the surface. In all work of this nature, working gas pressures in the vicinity of the target are usually orders of magnitude in excess of the cited background pressures. However, in setting u p the bombardment cleaning criteria, experimentalists ignore this feature and utilize the background pressure. In our opinion, it still remains to be conclusively shown that it is indeed the background pressure monolayer formation time that is the significant variable in studying kinetic ejection. Doubts have also been expressed concerning the nature (topography) of the surface that results during the bombardment cleaning procedure. Using low-energy diffraction, Farnsworth and colleagues (85) have shown that important changes in the surface structure result under intense sputtering conditions. T o attain reliable results from single-crystal specimens, Tibbetts and Propst (86) have attempted to develop single-crystal tungsten ribbons that can be flashed t o overcome this difficulty. There are no data available yet on whether they have succeeded in obtaining secondary electron yields on such targets. At this writing, it appears that a combination of techniques, such as the double modulation method applied to highly purified single-crystal specimens maintained at reasonably high temperatures under ultrahigh vacuum conditions, with a monitoring procedure such as low-energy electron diffraction, will serve to resolve the many questions which have been left unanswered in this discussion. On the other hand, if one is willing to settle for accuracies in the data for polycrystalhe specimens in the neighborhood of 10% to 20% there appears to be fairly good agreement between the various contemporary authors. (See Section 111.)
C. Collector Methods There are a t least six different kinds of current collectors described in the literature which have been used in measuring secondary electron yields and energy distributions. Of these the one that was used first and which is the simplest is simply a metal sphere surrounding the target which has a hole in it for admitting the ion beam and another hole for the target support. This sphere is then connected to the target through a current-measuring meter and a biasing power supply. This type of collector has been used in roughly 70% of the experiments reported thus far. The possible sources of error in an arrangement of this type include: (1) Collection of ions of the incident beam which have missed t,he target or which strike the edge of the entrance aperture on their way in. (2) Tertiary electrons which are ejected from the collector by the
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
127
secondary electrons, the secondary ions, or the reflected ions and metastable neutrals. (3) Collection of ions reflected from the target. (4) Collection of secondary ions ejected from the target. (5) Loss of secondary electrons which travel up the ion beam and out the hole in the collector. With a collector arrangement as shown in Fig. 11, problems (1) and (2) can be eliminated or minimized. The two slits, with relative aperture sizes as shown which precede the collector, serve three purposes. First, they limit the beam size so that it does not strike the collector when it goes through the entrance aperture of the collector [part of error (1) above]. Second, they provide a barrier for electrons from the target which would otherwise travel up the beam and out of the collector [error ( 5 ) above]. And third, they collect some of the secondary electrons which are produced outside of the collector. By biasing the collector sufficiently positive with respect to the target, most of the remaining problems could be overcome. This, however, is not possible when making energy distribution measurements by varying the target-to-collector bias. Waters used a spherical grid inside the spherical collector which was biased positive so that electrons were collected on the grid and the secondary and reflected ions were collected on the collector. This arrangement solves problems (3) and (4)but it does not allow discrimination of the tertiary electrons. A variation of this arrangement described by Abroyan (87) and by Batanov (66) uses the inclusion of a spherical grid between the target and the collector which is biased negatively with respect to the collector. This grid will return the tertiary electrons to the collector and possibly collect some of the secondary and reflected ions. Some authors have described the use of a split-sphere collector, the split corresponding to the intersection of the target plane with the sphere (88). The original intent was to use such an arrangement with the hemisphere in front of the target biased negatively and the one behind the target biased positively. With this arrangement it was expected that the secondary and reflected ions would be collected on the front hemisphere and that the secondary electrons could be collected a t the rear hemisphere. According to Abroyan (87),it is possible to collect 80% of the secondary electrons on the rear hemisphere with the optimum potential distribution. Abroyan did, however, use this arrangement with the opposite potential distribution to insure that the entire primary ion beam was focused on the target. Fogel, Slabospitskii, and Rastrepin (72) measured the coefficients of
128
DAVID B. MEDVED AND Y. E. STRAUSSER
secondary positive ion emission, secondary negative ion emission, ion reflection, and secondary electron emission, all in one apparatus and one measurement. To do this they used a system comprised of two plane electrodes, a grid, and a magnetic field parallel to the target face. The secondary electron current was determined by the difference between the target current with the magnetic field on and with it off. The electric field a t the target corresponded to the “electron-collecting mode,” i.e., electrons were accelerated away from the target. Waters (89) used a collector system consisting of two accelerating electrodes and an electron multiplier to increase the sensitivity. In order to subtract out the secondary and reflected ion contribution, he placed
n
Collector segments
h
FIG. 18. Segmented collector system designed for making angular distribution measurements (91).
in front of the electron multiplier an electromagnet that, when on, was just strong enough to stop the secondary electrons. The ratio of the size of the target to the diameter of the collector is a n important factor in angular distribution measurements. If the target is too large, the nonuniform field produced at the target surface will disturb the angular distribution of the secondary electrons. I n the measurement of angular distributions, two different approaches have been used. The first, used by Abbott and Berry, consisted of a +-inch long, +-inch wide, and 5-mil thick piece of nickel ribbon which could be rotated through an angle of 108” with respect to the target and which was connected through a biasing power supply and an electrometer to the target (90).The target-to-collector bias was only about 4 volts but might well have affected the angular distribution of the electrons because of the nonuniform field produced about the target.
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
129
The second system to be used for angular distribution measurements has been described by Propst and Luscher (91). This collector system (shown in Fig. 18) consists of a sphere which has been cut int,o rings, the cuts being in planes that are parallel to the target plane. Concentric with this sphere and inside it there are two spherical grids. The innermost of these grids assures that the electrons travel in a field-free region so that the angular distribution measurements are accurate. The outer grid is used to suppress tertiary electrons, which are emitted from the collector.
D. Double Modulation I n Section 11, B, the techniques most often applied toward the attainment of an “atomically clean” surface during a secondary electron emission experiment have been discussed and described. These are recapitulated as follows: (1) Flashing a target (polycrystalline) under ambient pressure conditions of very high vacuum (on the order of mm, or better) so that monolayer formation time of ambient gases is considerably longer than the time required for an experiment. (2) Utilization of ion bombardment cleaning in which sputtering of the target is greater than the arrival rate of contaminant atoms from the background. (3) Maintain target temperatures that are sufficiently high to keep the target surface clean under moderately high-vacuum conditions (say, on the order of lo-’ mm). However, under such a condition, large quantities of thermionic electrons and ions may be produced, and static techniques cannot be used under such conditions. Also, it may be necessary to determine the variation of the secondary electron yield and the electron distribution functions with target temperature.
Keeping the target a t high temperature may cause more surface contamination than it removes, as a result of diffusion of contaminants from the bulk of the target to its surface a t a rate in excess of their evaporation rate. For example, flashing a tungsten ribbon to a temperature near melting has been an accepted method for production of “atomically dean” surfaces (Section 11, B). However, there appears to be a current opinion that such a procedure creates a surface th a t is contaminated with carbon that has diffused from the bulk. The carbon accumulates a t the surface until the supply in the bulk is depleted, a t which time evaporation from the surface will finally overcome the diffusion from the bulk. Alternatively, one might provide a sufficiently high partial pressure of oxygen in the ambient, which will produce carbon monoxide that will evaporate from the surface.
130
DAVID B. M E D V E D AND Y. E. S T R A U S S E R
An additional problem, particularly with alkali ions, in maintaining a clean target surface is the contamination of the surface by the incident ion beam. I n order to keep this contribution to surface contamination a t a minimum, one should minimize the product of the incident ion beam current and the exposure time. The measurement technique known as the double modulation method was introduced by Arifov to solve these problems (see page 97, Chapter I11 of Arifov, 2 l a ) . A standard target-inside-a-spherical-collector arrangement is used with or without a grid. The target-to-collector voltage is controlled by a sawtooth generator so th a t the voltage is swept from the minimum to the maximum linearly and periodically. T h e usual frequency is about 25 cps. This same generator is used to drive the x-axis A
FIG. 19. Electric schematic diagram of apparatus for the study of secondary processes by the method of double modulation: l-heating coil, 2-target, 3-collector, &protective cylinder, 5-capacitor, 6-square pulse generator, ’?-switches, 8-sawtooth generator, 9-CRO, l(tcommutator, 1l-switches.
deflection plates of an oscilloscope whose y axis measures the current in the target-to-collector circuit. In this way, the oscilloscope is automatically synchronized with the signal. A diagram of the electrical arrangement is shown in Fig. 19. This circuit produces in a fraction of a second a current-voltage curve for a particular operating point of the system. These I-V curves give the yields and energy distributions of the secondary charged particles if the zero current line can be determined. It, is obtained by switching the ion beam on and off, which is the function of the square pulse generator in Fig. 19. This is most efficiently done a t a frequency much higher than that of the sawtooth generator. If possible, the “beam-off” time is much longer than the “beam-on” time. The envelope of the curve th at then results on the oscilloscope screen is the I-V curve on one side and the zero-current line on the other side. An example of such a curve is shown in Fig. 20. This was obtained during the bombardment of Ta by 170-ev Rb+.
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
131
This second pulsing of the signal, hence the term double modulation, has two advantages in addition to giving the zero current line. First, with the beam pulsing on and off a t a low duty cycle, the product of beam current and the time the beam is on the target is reduced even further. Second, this allows one to separate the so-called “inertial” and the “inertialess” components of the secondary particle currents. The inertial components are those which occur with a time distribution such as evaporation of ions of the primary beam while the inertialess components occur immediately, e.g., sputtered ions. With these high-sweep times, the inertial components tend to trail off on the oscilloscope trace. Thus, with the double modulation method of measurement, probability of contamination from the ambient gas is minimized since the measurement at each operating point takes only a fraction of a second. Also, this technique permits the measurement of the secondary currents
“1”
io
b 2b
i o Qo
v, .V
FIG.20. Oscillogram of volt-ampere characteristic of secondary ion characteristic from clean cold tantalum (300”K), bombarded with Rb+ ions of energy 170 ev.
while the target is held a t a high temperature despite the resulting background of thermionic electrons, in those cases where this will help to maintain the surface cleanliness. Third, there is less probability of contamination from the primary ion beam since the total number of particles delivered to the target surface is reduced; and, finally, this method gives more insight into the source of the secondary currents th a t are being measured.
111. EXPERIMENTAL RESULTS A. Polycrystalline Metal Targets 1. Alkali Ion Results. The numerous results obtained using alkali ions to bombard polycrystalline met)al targets have in general borne out the gross characteristics of kinetic ejection as discussed in Section I, B. Table I1 is a compilation, of authors, and ion-target combinations for the alkali ion-secondary electron emission data that are available at this writing.
132
DAVID B. MEDVED AND Y. E. STRAUSSER
Certain of these results, with molybdenum and tungsten targets, will be briefly discussed and compared in the following paragraphs in order to demonstrate the important trends in the data. a. Lithium ion results. The system Li+ bombarding W has been studied by Eremeev and Shestukhina (92) and by Waters (28). As the ion energy ranges studied were different (Fig. 21), there is no possibility of a direct comparison other than the fact that the two curves do not TABLE I1 ION-TARGET COMBINATIONS FOR WHICH MEASUREMENTS HAVEBEEN REPORTEDUSING ALKALI IONS Li+ Paetow and Walcher (96) Koch (176) Eremeev and Shestukhina (92) W Couchet (176) Mumetal Duraluminum Acierinos Ploch (93) Mo Be cu Pt Moroz and Ayukhanov (129) Brunnee (88) Mo Arifov and Rakhimov (26) Waters (28) W Ge Abroyan (27) Petrov (95) Batanov (66) Akishin and Vasil’ev (IT?) Arifov and Ayukhanov (97) Bosch and Kuskevics (29)
KCI NaCl CuBe
Na+
K+
Cs+
Rb+
W Ni
Mo
NaCI Mo Mo
Mo Mo Ge Ta W KC1
NaCl Mo
NaCl Mo Mo
W Ge Mo
Ta
W
seem to fit together through a smooth extrapolation between them. The yield obtained by Eremeev and Shestukhina is higher than the extrapolation of Waters’ data. This type of effect is generally a result of using a target that is not atomically clean in the measurement which yields the higher values of y. Since there is no possibility of potential emission, the yield below about 1 kev is so small th at it is difficult to measure. From this threshold the i n c w s e of yield with energy is essentially linear. The Lif bombarding 110 system was studied by Ploch (93) and by Brunnee (88). Their results are shown in Fig. 22. These investigations
133
KINETIC EJECTION O F ELECTRONS FROM SOLIDS 0
I.05
I
I
I
I
I
l
I
I
I
0
.90-
-
0 0
-
.75-
0 0
t
x
0
.45.30
-
0
0
0-EREYEEV B SHESTUKHINAlRE92 A - WWERS (REF. 89)
-
-
w
Lit-
-
.15-
A 0
I
0
I
I
2
I
3
I
I
4
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I 8
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6
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7
9
10
EK,kev-
FIQ.21. Comparative data, Li+ + W
-
.7
.6
I
I
I
I
-
T
b
1
I
I
0
.5-
h
I
-
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-
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-
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.2 O
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-
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-
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3
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4
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5
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6
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7
8
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9
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0
134
DAVID B . MEDVED AND Y. E . STRAUSSER
cover a similar energy range and, while the slopes of the curves are similar, the higher values were obtained by Ploch. b. Sodium ion results. The Na+ bombarding Mo combination has been studied by Brunnee (88) and by Arifov and Rakhimov (94). These curves are reproduced in Fig. 23. The agreement in the area of overlap is quite good. c. Potassium ion results. The K+ bombarding W system has been studied by Petrov (95).This curve is shown in Fig. 24. Also shown in this figure are the results for the K+ on Mo system obtained by Brunnee (88) and by Arifov and Rakhimov (94).The results reported by Ploch are for a
0
i,_ 0-ARIFOV 8 RAKHIMOV (REF. 9 4 ) A-BRUNNEE (REF.BB)
.I
N.+-hlO
0
I
A
02
3
4
5
6
7
8
9
1
0
EK,kW+
FIG.23. Comparative data, Na+ -+ Mo.
target that had not been cleaned and are typical of the increase in y that will occur for a gas-covered target. His values of y ranged from 0.4 to 2.5 in the energy range from 1 to 6 kev. d. Cesium ion results. The Cs+ bombarding W system was investigated by Paetow and Walcher (96),Waters (28),and Bosch and Kuskevics (29). The indication here again, as can be seen in Fig. 25, is that the surface of the target studied by Paetow and Walcher was not “atomically clean.’’ However, the comparison of the data of Waters with that of Bosch and Kuskevics is somewhat more puzzling. It is possible that the Bosch and Kuskevics curve is just t8helinear portion of the curve and the Waters data show only the initial part of the whole curve. Both investigat,ors apparently were careful with their surface preparation. A possible cause
135
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
0
A
0
0
A 0
.04
2
I
3
4
5
6
7
8
9
1
0
EK,~w-
FIG.24. Comparative data for K+ -+ W and K+ --+ Mo.
~-
A
.04 -
020
-
0 - WllTERS fREF.28)
A
A
A A 0
- ct-w
~ S C a H KUSKEVICS ( REF
0
*
8 WALCHER(RELS6)
A-PAETOW
A
o I
I
I
1
I
I
zs) I
-
136
DAVID B. MEDVED A N D Y. E. STRAUSSER
of the variation may have been the polycrystalline targets of different preferred orientations. The electron emission due to Cs ions bombarding Mo surfaces was studied by Brunnee and by Petrov. Their results are shown in Fig. 26. These results are in quite good agreement and are representative of what would be expected in a good yield determination over this energy range. e. Rubidium ion results. The only measurements of secondary electron emission using Rb+ bombarding metal surfaces were reported by Brunnee (88) and by Arifov and Rakhimov (.26) both using a Mo target, and by Arifov and Ayukhanov (97) on a Na-covered Ta target. The first two of these results are in excellent agreement as is shown in Fig. 27.
-
.060
.04
-
02
-
0
0 - BRUNNEE (REF. 88
-
I
A -PETROV (REF. 9 5 I cf- YO
0
-
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I
I
The study of Arifov and Ayukhanov was actually a study of the secondary negatively charged particle emission from Ta and W surfaces, which were covered with various amounts of the alkali metals. Their results indicated that the negative currents that are emitted from these targets go through a maximum for smaIl coverages of the alkali metal and then level off to a steady-state value for all higher coverages. These currents, they have determined, are primarily secondary negative ions plus a small steady (with changes in coverage) component of secondary electrons (about 10% of the total current). Arifov and Ryukhanov postulate that the alkali metal film serves only to lower the work function
137
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
of the target to the point where it is below the electron affinities of the contaminants from the ambient gases (they worked in -1OW Torr pressures) such as oxygen that have rather large electron affinities. Thus, the sputtering of the oxygen results in the production of large amounts of 0- in addition to neutral 0. The maximum in the negative ion emission at low coverages would then indicate a minimum in the work functions at these coverages. Measurements of the work function of alkali metal-covered W surfaces indicate that, for Cs, the work function decreases steadily from 0 to 0.7 monolayers then increases from 0.7 to about 1 monolayer, and finally becomes essentially constant for further
.e -
f
x
.I6
-
A - BRU "NEE 0-ARIFOV Rb*e
(REF.881
a
RAKHINCV(REF.S~)
Mo 0
.120
.08 -
.w 'A 00
I I
2
A
A
s
I
I
3
4
5
6
7
8
9
10
EK,kev--
FIG.27. Comparative data of Itb+ on Mo (Brunnee and Arifov and Rakhiniov).
increases in coverage. This is just as predicted by the results of Arifov and Ayukhanov. f. Comparison of results. In Fig. 28 the results for all five of the aIkali ions bombarding a Mo surface are plotted as a function of incident ion energy. I n Fig. 29 these same curves are shown as a function of ion velocity. 2. Noble Gas Ions. There exists a vast amount of data on the behavior of y with Ek in the region of kinetic ejection for noble gas ions incident on polycrystalline metal targets. It is our opinion th a t a careful attempt to collate these data would serve no useful purpose; there now exists sufficient agreement of these data with the general theoretical outlines as
138
DAVID B. MEDVED AND Y. E. STRAUSSER
0.7-
x Li+-Mo Q
0.60.5-
t
NO+-MO
K+-Mo Mo MO
o Rb+A CS'-
0
0
X
0.41 0.3
a
0
X X
0.21
X
0
0.1
-
0
0
X
0
X
a
0
FIG,28. Comparison of the secondary electron yields of the different alkali metal ions bombarding Mo, plotted vs. incident ion energy.
0.51 x Li'--Mo
0.4-
a No-i Mo a K+ -MO o Rb" hlo
A Cf-
0
Mo X
tx
a X
0'3-
X
-
0.2
X 0
0
-
0.1
1
0
.
0
A$
x
m
X X
.
a
x
&O"O, 05
10
15 2.0 v,.cm.persecxlO'-
2.5
3.0
FIG.29. Comparison of the secondary electron yields of the different alkali metal ions bombarding Mo, plotted vs. incident ion velocity.
139
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
sketched in Section I, B. Any attempt to extend these working models to a more quantitative theory should be based not on a correlation of existent results with polycrystalline targets, but on results to be obtained from careful measurements with high-purity oriented single-crystals (see Section 111, B). There are probably several hundred target-noble gas ion investigations (y vs. Ek) described in the published literature. Table I11 attempts to summarize these studies in a condensed manner; we consider the following comparison of results as representative rather than particularly significant. The transition from potential to kinetic ejection characteristics has been studied in detail by Petrov (70) and b y Mahadevan et al. (80). Their data are shown in Figs. 30 and 31, for He+ and A r t incident on W and Mo, respectively. It is noted that the kinetic emission threshold for He+ is about 500 ev (1.5 X lo7 cni/sec) and for Ar+ it is about 1000 ev. The slope ( d y / d E ) for He+ is greater than for Ar+. TABLE I11 ION-TARGET COMBINATIONS FOR WHICH MEASUREMENTS HAVEBEEN REPOR.TED USINGNOBLEGAS IONS ~
Ar Cousini6 et al. (84)
+
Ne+
Be At Zr
Colombie and Van Chuong (178)
Guntherschulze and Betz (179) Guntherschulze and Bar (180)
Zn Mn co Pb Fe Ni cu Au W Pt Mo Ag co Ni cu Mg
Mg Fe Ag cu K
He+
~~
Kr+
Xe+
140
DAVID B. MEDVED A N D Y . E . STRAUSSER
TABLE I11 (Continued) Ar
+
Ploch (93) Mashkova et al. (109) Magnuson and Carlston (30)
Mahadevan et al. (80) Parker (181) Takeishi (130) Timoshenko (182) Healea (67) Higatsburger et al. (68)
Large (10) Berry (63) Bradley (183) Ghosh and Sheridan (184) Arifov and Rakhimov (26) Arifov et al. (107) Batanov (194) Batanov and Petrov (185) Fogel et al. (72) Petrov (70)
Ne+
Kr+
Xe+
Mo cu
Mo cu
Be Pt cu Mo cu Ni cu A1 Mo Zr Ta Mo Ta Pt BaO BaO A1 Mo Ni Ni CuBe AgMg AgMg Nichrome V W W Ta Na Brass Mo Ta W Mo Glass Glass Mo Ta
Na Brass Mo Ta W Mo Mo
Hill et al. (69) Bourne et al. (186)
Petrov and Dorozkhin (98) Arifov et aE. (81)
He+
W Mo
W Mo
Mo
BaO Ni AgMg
W W Ta Na Brass
Mo Glass Glass Mo Ta Ni Mo A1 Au Pb Mg cu Steel W W Mo Ni
BaO
AgMg
AgMg
W
Brass Mo Ta W
Na Brass
Mo
A1 Au
141
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
We now turn to the data of Magnuson and Carlston (50) for 1 kev < Ek < 10 kev as shown in Fig. 32 for the ions Ne+, Ar+, Kr+, and Xef incident on polycrystalline Mo. The slope dy/dE again appears to increase with decreasing atomic mass. These data are quite similar to the results of Arifov and Ralthimov and the work of these authors serves to bridge the results of Arifov and Rakhimov and those of Large. The data of
0
I
2
3
4
5
6
7
8
Ek.keV
FIG.30. Data of Petrov (70) for Ar+ (1) and He+ (2) incident on W showing the transition from potential to kinetic ejection. 0.6
-
0.5
z
2 0.4
a
2
y
0.3
0
a
! i 0.2
-
W W -I
&O.I I
100
500
900
1300 ENERGY (rVl
I700
2100
25do
FIG.31. Data of Mahadevan et al. (80) for He+ (1) and Ar+ (2) incident on Mo showing the transition from potential to kinetic ejection.
Large (10)for y as a function of Ek with tungsten as target have been shown in the “typical” kinetic ejection example of Fig. 4. We focus our attention on the curves for He+, Arf, and Ne+, and note that there is a crossover between He+ and Arf in the vicinity of 60 kev, i.e., dy/dE was not constant as in the restricted energy range of Petrov and Mahadevan et al. I t turns out that y is quite linear if plotted as a function of ion velocity. The results are shown in Figs. 33-35. Figure 34 is the data of
142
DAVID B. M E D V E D AND Y. E. STRAUSSER
Tel 'kovskii (99,100) for Art-, Ne+, and He+ on Mo. Figure 33 is the Large data of these species from Fig. 4 plotted on velocity scale and Fig. 35 is data lor Arifov et al. (81). In Fig. 36 the effect of different targets on y as a
20
'0
40
60
80
IOC
Ek,keV
FIG.32. Data of Magnuson and Carlston for noble gas ions incident on Mo (SO). ?.Or
I
I
I
1
-
6.0-
5.0
-
-
-
4.0
h
-
2 .o
nz*
3 ' 0 !
-
1.0 0-
1
I
1
I
INCIDENT ION VELOCITY, cm sec-'
FIG.33. Data of Large for
yi
of noble gases as a function of incident ion velocity
(10).
function of energy is showri, indicating th at Mo and W data are approximately comparable. Most of the data among these three sets of investigators appears t o be within 20% agreement except for Tel 'kovskii's result,s on Ar+, which appear to be about 70 to 90% higher a t 50 kev. Arifov et al. hypothesize t ha t this large discrepancy is probably the result of enhanced
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
143
kinetic emission from Tel ’kovskii’s targets, which (‘were not atomically clean.” However, this does not appear to be a well-founded argument, particularly if Fig. 16 is considered. At *50 kev, surface contamination 4
I
I
I
I
3 -
Y
2 -
I -
0
5.10’
140’
1,5~10’
v(cm / sec)
FIG.34. Data of Tel’kovskii (99) for ion velocity.
yi
of noble gases as a function of incident
FIG.35. Data of Arifov et al. (81) for ion velocity.
yi
of noble gases as a function of incident
effects should be reduced according to this result. Also, the data for He+ appear to be in excellent agreement. On the other hand, data of Large (74) for hydrogen on titanium show a threefold increase of y for contaminated targets above 100 kev. For this system, however, considerable absorption
144
DAVID B. MEDVED AND Y. E. STRAUSSER
of gases in the target could influence the result. There is very little quantitative information and understanding of the effects of adsorbed and absorbed species, oxide layers, etc. on y in the kinetic ejection region (see Section 11, B). Thus, one should not glibly dismiss discrepancies in experimental data by vague references to the other fellow’s poor surface conditions. 3. Results with Neutral Atoms. The earliest results on electron ejection by ground-state neutral atoms were reported by Kallman and Rostagni (101) for ArO, NeO, and Heo incident on copper targets in the energy range 20 to 600 ev. In a series of remarkable and pioneering investigations,
I
I
I
I
10
20
90
40
I
EkkrV
FIG.36. Variation of
y
with Ek for He+ incident on Ni, W, Mo (Ref. 81).
Rostagni obtained results for yn and yi as shown in Fig. 37. Here, y n represents the secondary electron yield per incident neutral and yi is the yield per ion. Although the vacuum conditions were only fair mm), Rostagni (64) was able to observe a quasi-potential ejection character for the yi and he properly interpreted the limiting values for Ek-+ 0 as showing a clear dependence on the ionization potentials Ei of the noble gas ions. The results for y are quite striking since he observes kinetic ejection well below currentIy accepted thresholds for this process. However, since “the measurements were made on collectors of copper and brass without particular precaution for the elimination of the enclosed gases,” we can expect some considerable influence of surface contamination. In this connection we can mention unpublished work of Medved
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
145
and Comeaux where measurable electron ejection was observed from contaminated molybdenum surfaces at energies as low as 100 ev; with the same apparatus kinetic ejection threshold for noble gas neutrals on “the clean surface” was greater than 500 ev. Rostagni refers to work of Kallman et al. (102) in which a decrease of y was not observed until 30 ev. This work is dismissed as “erroneous perhaps because of diffusion of particles.” Rostagni measured his neutral particle fluxes by a difference
r
10,000
I
It
16 202s 30
100
50
,
200
I
,
400 600
V
FIG.37. Rostagni’s data (64)for
yi
and
y,,
of noble gases and hydrogen molecules.
2000 2500 3000 ENERGY OF PARTICLES, volts
I500
FIG 38. Results of Chaudhri and Khan (69) for Ni targets.
K O
and Hg” incident on degassed
technique similar in principle to the method of Arifov et al. (Section 11, A, 3). Chaudhri and Khan in 1948 studied the emission of secondary electrons ejected by nickel and molybdenum targets by neutral atoms of mercury and potassium (69). The HgO were produced by grazing incidence of Hg+ on the walls of a canal, the KO were produced by charge transfer. No attempts to measure absolute neutral particle fluxes were reported. By using a constant flux of incident ions at all energies, the yield curves shown in Fig. 38 were obtained for a degassed Ni target. The secondary
146
DAVID B. MEDVED AND Y. E. STRAUSSER
emission from a dirty target always exceeded that from a clean one. The electron distribution function in energy was measured by a retarding potential method and was found to be Maxwellian, with the effective temperature greater for contaminated surfaces. It was also found th a t dirty surfaces scattered more Hgn than the clean surface, whereas with Kn atoms, the reverse was true. The greater scattering or reflecting ability of clean surfaces for noble gas atoms and alkali ions has been discussed recently in the literature (103). An early investigation, where superposition of kinetic ejection on a potential ejection mechanism was explicitly recognized as such, was that of Greene, who in 1950 studied electron emission from Mo resulting from metastable noble gas atom impact and hydrogen neutrals over an energy interval from 300 to 1100 ev (41). His technique and apparatus have been discussed previously (Section 11, A, 3). He did not directly monitor the incident, fluxes of neutrals to obtain quantitative values of y. He measured the energy distribution functions of the emitted electrons. These results agreed with those of Oliphant for He*, i.e., potential ejection. H e also found that “the proportion of high-energy electrons liberated by argon metastable atoms increased with their kinetic energy.” The contribution of kinetic ejection for Ne* and He* was negligible; this contradicts current notions. However, it was probably masked by the much higher potential ejection values of y for these species. Berry obtained neutral atoms of the noble gases by charge transfer over an energy range from 500 to 4000 ev and investigated kinetic ejection of electrons from tantalum by ions and atoms of He, Ne, and Ar at 30” angle of incidence (53).He subsequently reported on the results of a study of He+ and Heo incident on degassed and contaminated tungsten targets (55).The results are shown in Fig. 39 for y as a function of Ek for ions and neutrals of helium. A threshold, somewhat>ill-defined, appears to occur a t -300 ev for the Henkinetic ejection from the degassed surface. As noted previously, both y n and yi are considerably enhanced for the contaminated surface, with both exhibiting a kinetic ejection charact,eristic in this case. The effect of surface contamination is more pronounced at the lower energies. The value of dy,/dE N 0.14/Ikev, which can be compared with a value of O.ll/kev found by Comeaux and Medved (57) (assuming a linear variation of y n with E in the restricted energy range under discussion). Comparative measurements of He+ and Hen and Nz+ and N2 incident on a tantalum target have been reported by Tel ’kovskii (99) in an energy range from 15 to 30 kev. In this range 4 3 to 5 and thus the potential ejection contribution for the ions is negligible. In Tel ’kovskii’s data the curves for ions and neutrals are essentially similar and are separated by a small constant value.
-
147
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
Devienne and his staff have carried out a series of preliminary investigations using neutral beams of argon over the energy range from 500 to 3000 ev (61, 104-106). A variety of targets are being studied with particular attention given to the influence of the angle of incidence and adsorbed gases on the values of yn. They have recently reported that yn varies linearly from 0.15 at 500 ev to 0.91 at 2850 ev for argon atoms incident on polycrystalline aluminum targets (189). Studies of y n are now being carried out using fast neutral beams of Ho and Hzo between 20004000 ev.
0
W
/
+
-1
0
+'
5
I- 0.6-
0
HE IONS H E NEUTRAL ATOMS
I -
//
a \
+/+-+
cn z
g
/ 1
0.4-
I-
0 W
J
/
1
-
/'
+'/
4 '
)
ENERGY, kev
FIG.39. Berry's data (66) for undegassed tungsten targets.
y
and yn of He+ and He" incident on degassed and
The most extensive investigations of neutral atom ejection of electrons have been carried out by Arifov and colleagues (60,107). They used the method of current differences to determine neutral fluxes with results for ArO, NeO, and Heo incident on Mo shown in Fig. 40.According to this work, if one writes Ti = Y r Yk (9)
+
then yk:for the ion and y n are considered to be identical, i.e., the kinetic ejection yield can be directly superposed on the potential ejection and no effect of velocity on yr is discerned up to 3500 ev. On the other hand, Medved et al. (57, B l ) , using the thermocouple probe (Section 11, A, 3), attempted a direct measurement of the neutral flux, in, for determination of yn of flashed Mo ribbons. These workers carried out a careful comparison of yi and y n which showed up some divergence in the region of kinetic
148
DAVID B. MEDVED AND Y. E. STRAUSSER
r
2ow 3ot/ 10
-
"i:=: :E 0
s
1
2 3 Eh,keV
4
s
30
i
5
40
i30
20
20
100
10
0
1
2 3 4 Eh,keV
1
2
3
4
5
5
Ek ,keV
FIQ.40. Data of Arifov et al. (60) for Mo targets.
y,, and yi
of noble gases incident on flashed
y.yield I
Curve I -0. fa Ar' 0 . ~ 5 -CurveN *** yn for Aro . Curve S 0 0 0 Computed curve From yr+ yn choosing
:
EkveV
FIQ.41. Data of Medved et al. (61) showing divergence between y, and and Ar" incident on flashed Mo targets.
ejection as shown in Fig. 41. Here, dri/dE dy,/dE
=
=
Y~
for Ar+
O.Ob/kev whereas
0.04/kev.
Several hypotheses were considered in an attempt to explain this apparent divergence for Yk of the ions and 7, of the neutrals of argon. It was shown in subsequent work of this group that there is an energy transfer dis-
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
149
crepancy between neutrals and ions of the noble gases, which was interpreted in terms of a preferential reflection of the neutrals. A qualitative explanation for apparent lack of agreement between -yn and Yk can then be carried out along the following lines: Let ii and inrepresent incident fluxes of ions and neutrals, respectively, with p i and p n that fraction of these beams “reflected” from the target. These fractions are then not available for participation in the intimate collisions or interactions in the bulk leading t o kinetic ejection, i.e., the beam fluxes available for such intimate interactions are
ii’ = ii(1 - pi) in’ = in(l- p n ) and the measured values of the yield coefficients will then be in the ratio
As determined for flashed surfaces of Mo, p,, > pi (for argon) and hence Y~ < Yk = yi - T ~ A . more quantitative correction to the data of Fig. 41 cannot be carried out since it turns out that the preferential reflection condition p n > pi also holds for the unflashed platinum targets of the thermocouple probes used in this work1 and thus the calibration procedure of neutral fluxes was in error. The magnitude of the error in measuring the neutral fluxes by the thermocouple probe method is not clearly determined, but it is in a direction so that the -yn determined in Fig. 41 are upper limits, and any correction applied to these data would only serve to increase the observed discrepancy. Further attempts to resolve the discrepancy should be carried out employing better techniques for measuring neutral fluxes (such as those described in Ref. 166) and using defined and controlled surface conditions for the targets (as in Ref. 67). Incidentally, it should be noted that such careful measurements (in comparing y n and ~ k could ) clarify the dependence (if any) of Y~ on ion kinetic energy. 4. Results Obtained Using Other T y p e s of Ions. Of the miscellaneous types of ions that have been used in studies of kinetic secondary electron emission, certainly H I + and Hz+ have been used most often. This can be seen in Table IV, in which are listed the remaining ions that have been used, the investigators, and the t,argets that were studied. Figure 42 shows a composite curve of the results which have been obtained for HI+ bombarding Rlo. This curve is representative of the type of data which have been obtained for the kinetic secondary electron 1 However, the discrepancy appears to be more pronounced for clean than for contaminated surfaces.
TABLE IV ION-TARGET COMBINATION FOR WHICH MEASUREMENTS HAVEBEEN REPORTEDUSINGTHE MISCELLANEOUS IONTYPES ~~
HI+ Higatsburger et al. (68) Healea (67) Mo Hill et al. (69) cu Al Pb Large (10) W Au Large and Whitlock (73) Ag Ni Zr C Pt cu Ti Mo A1 Aarset et al. (136) Ni Au Mg Fe Pb Berry (63) Bourne et al. (186)
H2+
Ha+
AgMg Ni Mo cu A1 Pb Au Ag Ni Zr C
Pt cu Ti Mo A1 Ni Au
A1 Au
D+
Dz+ DH+ O+
O2+
N+
N2+
ZU+ C1- Hg+
B+
Cd+
Ni
w
W
E
Au Ag Ni
U
4 M U
Zr C Pt cu Ti
Ta
A1 Au
Al Au
TABLE XV (Continued) HIf
Ghosh and Sheridan (184) Abroyan (87) Batanov (124) Fogel et al. (78) Murdoch and Miller (187)
H2+
Brass Ge Glass Glass Mo cu cu Au Au
c
c
Ha+
D+ Dt+ DH+ O+
Ot+
N+
Ns+
Zn+ C1-
Hg+
B+
Cd+
Brass Glass MO
cu Au C
Mo Akishin and Vasil’ev (177) Petrov and Doroskhin (98) Schwarts and Copeland (71) Arifov and Khashimov (76) Arifov et al. (66) Chambers (138) Cousine6 et al. (84)
CuBe
CuBe
w
w Cd
Mo Mo CuBe CuBe A1 Pb
Mo cu Guntherschulze and Bar (180)
Mironov and
W
Mo Ni
Ta
Petrov (70)
Al
Pt Fe Ag cu K
Mo CuBe
Mo
Mo
152
DAVID B . MEDVED AND Y. E. STRAUSSER
yield. This figure is indicative of the wide range in values of the yield which can be obtained when polycrystalline targets are used and when the cleanliness of the target surface is not assured. From this figure it is, however, possible to see the general trend in the dependence of the yield on ion energy. Specifically, the yield initially increases linearly with the ion energy, then levels off a t the peak, and then declines with further increase in the ion energy. 4.2 4.0-
3.5-
3.0-
I
' '
d
I , !
I
I [
0 HILL. BEUCHNER. CLARK 8 FISK 1REF.691 0 LARGE 8 WHITLOCK I R E F 7 3 )
1
,
1
I
1
I
I I I I
1
I
1
0
A FOGEL. SLABOSPlTSKll 8 RASTREPIN IREF.72) MURDOCH 8 MILLER (REF.187) ARIFOV, RAKHIMOV, ABDUIAEVA 8 GAIPOV IREEbS I A COUSINlh, COLOMBIE, FERT 8 SIMON IREE 8 4 )
A A
I.o
A
4
y:: .5
01 I
I
I
1
I
.
A: A m m
I l l ,
.
0
0
I
I
1
1
1
10
1
1
1
I00
I
I
1000
ION ENERGY, krv
FIG.42. Compilation of data for HI+ bombarding Mo.
B. Single-Crystal Metals The study of electron emission as a function of crystallographic orientation is one of the most interesting and recent developments in the field of kinetic ejection. Th e most extensive and definitive work has been carried out by groups at the A$. V. Lomonosov A/Ioscow State University and at the University of Toulouse. The first observations of the anisotropy of secondary elect,ron emission from copper as a function of crystal orientation with respect to the incident ions were reported by Molchanov et al. in the 1962 Doklady (108) and by Fagot and Santouil (119). I n a subsequent publication, Mashkova et al. (109) measured y for Ar+ incident on the (100) face of a copper single crystal as a function of
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
153
angle of incidence, cp. The results are shown in Fig. 43 for Ar+ energies of 20 and 30 kev. The solid curves represent a theoretical computation based on a method of Odintsov (110) using several parameters obtained from selected experimental curves. The oscillations in y with incidence angle cp are strongly suggestive of2the crystalline transparency model proposed by Rol et al. to describe observed anisotropy in sputtering of single crystals (111-113). According to these models, the minima of the sputtering yield, S, occur at orientations corresponding to maximum crystalline transparency, i.e., where the collision depth of the incident particle is greatest. Conversely, the maxima of S(cp)occur for positions of
-10
0
10
20
30
40
50
60°
Q-
FIG. 43. Results of Mashkova et a2. (109) on the variation of y with crystalline orientation for Ar+ on Cu. (1) Calculated single crystal a t 30 kev. (2) Calculated single crystal at 20 kev. (3) Calculated polycrystal at 20 kev. (a) Experimental points for single crystal. (b) Experimental points for polycrystal. Dashed line is from data of Tel’kovskii dissertation.
maximum opacity, Le., where collision depth is nearest to the surface. Although these ideas provide a correct qualitative interpretation of the angular positions of maxima and minima of the sputtering yield and of the secondary electron emission coefficient, the magnitude of the anisotropy for sputtering cannot be predicted in a straightforward manner without invoking a cumbersome number of adjustable parameters. Balarin et al. (114, 115) have proposed focused collisions into the crystal as a means of further pronounced reduction of the sputtering coefficient for particular incidence angles. Simultaneous measurement of S and y on oriented Cu single crystals have recently been reported by Mashkova et al. (116). Bombardment cleaning was used to maintain a surface with minimum contamination.
154
DAVID B . MEDVED AND Y. E. STRAUSSER
The dependence of y on time of bombardment was quite similar to the curve of Magnuson and Carlston previously cited (see Fig. 17). The results obtained for 30-kev Ar+ incident on the (110) face of a Cu single crystal as a function of angular rotation about the (110) direction are shown in Fig. 44. It is noted that the relative positions of the maxima and minima for both are in agreement and can be qualitatively described by the simple “transparency model.” The disagreement between “computed” curves (solid lines) and experimental points (particularly for 13” < cp < Z O O ) was assumed by
o
10 XI
M
40
+
5060
ma0
FIG.44. Dependence of y and S on crystallographic orientation for 30-kev Ar+ on Cu (116). (1) Theoretical curve for y. (2) Theoretical curve for S. (3) Experimental points for y. (4) Experimental points for S.
these authors to result from contributions to the yield coefficients from “deep” atomic layers (i.e., deeper than the 10th layer) which for larger incidence angles are “shielded by the overlying layers.” The effect of crystal temperature on the angular dependence of y has been strikingly demonstrated in a recent investigation of V. A. Molchanov (117). The results for target temperatures of loo’, 450” and 900°C are shown in Fig. 45 for 30-kev Ar+ incident on the (100) face of Cu rotated about the (110) axis. The pronounced minimum at 55’ has effectively disappeared at 9OO”C, and the over-all behavior of y(p) approaches the polycrystalline case.
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
155
The dependence of y on crystal orientation was studied in a more qualitative manner by Fert et al. (118-120). Using ion emission microscopy and a copper single-crystal target, Fagot and Fert have measured relative values of y for a variety of incidence angles as parameter on the three low-index planes of copper during a complete 360' azimuthal rotation. The Ar+ beam energy was usually 50 kev.
FIG.45. Temperature dependence of the anisotropy of y for 30-kev Ar+ incident on Cu (117).
Correspondence between the minima of the recorder traces of y over 360' azimuth scan and a stereographic projection of the fcc lattice was carried out by Fagot and Fert (120). More recently, Fagot, Colombie, and Fert (121) have reported some int)eresting quantitative results on absolute measurements of y for 40-kev Ar+ incident on various faces of monocrystalline Cu. A family of curves for y as a function of incidence angle with the plane of incidence as parameter has been presented in Fagot et al. (1.21). The positions of the maxima and minima for the case
156
DAVID B. MEDVED AND Y. E. STRAUSSER
where the plane of incidence is [I101 appear to be in excellent agreement with the data of Mashkova et al. (109). The absolute values of y are also quite close although measurements of Mashkova et al. (109) are given for 30 kev compared with the 40 kev used by the French workers. The anisotropy of secondary electron emission with crystalline orientation has been studied by Magnuson and Carlston (122) in the energy range from 1-10 kev, for noble gas ions incident on copper single crystals. They have measured y as a function of ion bombardment energy with argon ions normally incident on the three low index planes (110), (loo), and (111). The results are shown in Fig. 46. The single crystal surface conditions were maintained by means of bombardment cleaning. It is seen that the relative anisotropy between the three faces increases with increasing kinetic energy.
0
1
2
3
4
5
6
7
8
9
1
0
Ek.keV
Fro. 46. Secondary electron ejection (S.E.E.) coefficient, y, from the three lowindex planes of copper due to Ar+ ion bombardment (122).
In a recent communication, Zscheile (123) has reported measurement of y and ion and neutral reflection from an oriented copper single crystal bombarded by ions and neutrals of the nitrogen molecule (Nz)a t 28 kev. The target was maintained a t “a few hundred “C” in a vacuum of 10-6 Torr and with an ion beam current density of 10 pa/cmz so that the bombardment cleaning criterion was marginal at best. A contour plot of the electron emission current for polar and azimuthal coordinates is presented. In spite of the dubious surface conditions, marked anisotropy in y both for neutral and ion bombardment is observed. The structure of the y anisotropy has similarities to the observations shown in Figs. 4 3 4 5 . The values of ion current emitted under bombardment also follow the same anisotropy as the electron emission. For the case of incident neutrals Zscheile has interpreted the positive component measured by the
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
157
collector as electrons ejected from it by reflected neutrals (a similar interpretation was used by Comeaux and Medved (67) in their measurements of neutral reflection from polycrystals). Finally, he indicates th a t use of Ar+, HI+, or Hz+ at the same energy may increase the depth or width of the minima but that their angular position is invariant with species used.
C. Insulators and Semiconductors Most of the research on kinetic ejection from dielectrics and semiconductors has been carried out in the Soviet Union, particularly by
02
0 4 06 08
10
12 -14
Fro. 47. Ratanov’s results (66)for Li+ incident on NaCl showing effects of target temperature and exposure history.
Batanov and Abroyan and colleagues at Leningrad Polytechnic Institute (66?87, 124-128). Amorphous glasses and films, polycrystals, and singlecrystal targets of the alkali halides and group IV semiconductors bombarded by alkali and noble gas ions have been investigated. Batanov used a pulse technique in order to minimize charging effects, damage, and compositional changes in the target which resulted from prolonged ion beam bombardment. The results for alkali ions incident on alkali halide single crystals are summarized in Fig. 47. The effects of target temperature and exposure history are shown in Fig. 47 for Li+ incident on NaCl single crystal (67).
158
DAVID B. M E DVE D AND Y . E. STRAUSSER
The curves labeled 2 and 1 represent the data for a newly cleaved crystal with 2 corresponding to an energy range of from 200 ev to 1.4 kev and 1 for the range to 6 kev. Curve 3 is a composite of results obtained at different substrate temperatures on a crystal exposed to atmosphere for 2 days, and curve 4 represents a partial “activation” or “recovery” resulting from ion bombardment at 2 kev. Several prominent features also characteristic of other data on insulators to be discussed shortly can be clearly distinguished: (1) Values of y are almost an order of magnitude greater than for metal targets, clean or contaminated. Thus, for Li+ on NaCl a t 5.5 kev, y N 9.0.
E,, keV
FIG. 48. Batanov’s results (126) for Kf incident on alkali halides. (1) KCI, (2) KBr, (3) NaC1, (4) NaF, ( 5 ) NaF (before ion bombardment).
(2) Threshold energies for yk are considerably lower ( ~ 1 ~ ev) 5 0 than for metals. (3) The slope d-y/dE 2.0/kev.
-
Both Batanov and Abroyaii studied electron emission from alkali halides bombarded by potassium ions. The data for y are shown in Figs. 48 arid 49. At a given energy values for y increase as the target band gap, E g ,decreases (see page 2,%5 of Abroyan and Lavrov, 128, for discussion). Secondary negative ion emission and positive ion emission were observed concomitant with the large values of y; threshold energies down to 10 ev and values for K of the order of 0.1 were typical for these processes. Comparative data for silicon and germanium as target materials are presented in Figs. 50 and 51. The values of y and threshold energies appear to be more t>ypical of metal targets, especially for the “clean” silicon case (curve 4 of Fig. 50).
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
159
As far as we can determine, there do not appear to be any studies describing orientation effects on y with single-crystal dielectrics similar t o the investigations on m e h l single crystals discussed in Section 111, B. Moroz and Ayukhanov (129) have reported some very interesting
Ek,keV
FIG.49. Abroyan and Lavrov’s results (128)for K+ incident on alkali halides. (1) KBr, (2) NaCl, (3) CsC1, (4) NaF, (5) LiF.
0
1
2
3
4
5
6
E p V
FIG. 50. Results of Abroyan and Lavrov (128) for K+ incident on silicon under various surface treatments. (1) Washed with distilled H20 after etching. (2) Heated to 800°C. (3) Heated to 1000°C. (4) Heated to 1300°C. results on the influence of target thickness on y and K-. Deposition of NaCl films on Rlo substrates a t a nominal rate of 20 monolayers per second was carried out during measurement and results as shown in Fig. 52 obtained. The values for y and K - are for the case of Cs+ bombardment a t 1500 ev. The bulk nature of kinetic ejection vs. the surface character of negative ion emission is graphically demonstrated in these data. The
160
DAVID B. MEDVED AND Y . E. STRAUSSER
authors also observe that at low energies (<400 ev) the saturat>ionvalues of K- exceed the saturation values of y. In an experiment aimed at separating “emergence depth” of the secondary electrons from “penetration depth” of in-coming ions, Moroz and Ayukhanov measured the
0.6 0.4 0.2 0
2
4
6
8
10
12
14
16
18
20
E,.keV
FIG.51. Ahroyan’s results for alkali ions and Hz+incident on germanium (87).
eo60
-
-
z
-
0
10
20
30
40
50
60
TO
t , sec
FIQ.52. Data of Moroz and Ayukhanov (15’9) on variation of yi and K with deposition time of NaCl films of Mo substrates (Cs+ ions at 1500 ev).
variation of y and (r (the electron-electron emission coefficient) with primary energy as a parameter. It turns out that the saturation thickness is independent of Ek above 1000 ev for Na+ incident on NaC1. Typical results are shown in Fig. 53 for electrons at 680 ev and Na+ at 1120 ev.
K I N E T I C EJECTION O F ELECTRONS FROM SOLIDS
161
The fact that the curves u/u8 and y/y8 exhibit saturation a t equivalent film thicknesses leads to a conclusion that the emergence depth of the electrons is independent of the primary process. Very few data on oxides are available. Takeishi (130) has measured yi for He+, Ar+, Xef, and Ne+ incident on BaO crystals and finds th a t ya is of order 0.5 at 500 ev. In his analysis, he appears to rule out a kinetic ejection mechanism as contributing to results observed, citing Brunnee's data for alkali ions on metals. Apparently, he was not aware of the work of Abroyan and Batanov.
FIG.53. Results of Moroz and Ayukhanov on variation of ion-electron and electron-electron secondary emission yields with deposition times of nNaCl films ( N a i ions at E k = 1120 ev).
D. Energy and Angular Distributions Two areas of investigation related to kinetic secondary electron emission that should produce profitable results in terms of a theory are the determinations of the energy and angular distributions of the secondary electrons. However, as yet there have been only a few measurements of these parameters reported. Qualitative measurement.s of the energy distribution of kinetic secondary electrons have been reported by Brunnee (88),Chaudhri and Khan (59), and Kronenberg, Nilson, and Basso (131). Quantitative results are reported by Chambers (Is%'),Philbert (133), and Waters. Figure 54 shows the results of Waters for 1-kev Li+ bombarding tungsten. These results are typical of the data that have been reported with a large peak at very low energies (-2 ev) and a long tail a t higher energies. For 1-Mev protons, the tail does not drop to zero until about 2000 ev (131).
162
DAVID R . MEDVED AND Y. E. STRAUSSER
For higher bombarding ion energies the peak moves up, although it is only at about 6 ev for 10-kev Hzo (132). Pradal and Simon (134) measured the energy distribution of the secondary electrons and then fit the data to curves of the form
I
= Ioe-uV/kT
(12)
tJhus arriving at an “equivalent temperature of emission” (i.e., the distributions are essentially Maxwellian). These measurements were made with argon ions whose energies were varied between 35 and 46 kev. The targets were ten different polycrystalline metal samples. The “equivalent,
0 Y
E (bv)
FIG.54. Plot of the number of electrons with energy E per incident ion per electron-volt for 1000-ev Li+ incident on clean tungst,en (89).
temperatures” ranged from 31,500” to 89,500°1<. Chaudhri and Khan (59) show the energy distributions from degassed Ni targets bombarded by HgO. The equivalent temperatures of emission were of the order of 30,000”K. There did not appear to be a significant shift in the peak of the emission with incident ion energy. The equivalent temperatures for degassed targets were generally less than those for the contaminated surfaces. There are two different types of angular measurements that are made. First, there is the variation of the total yield as the angle of incidence of the ion beam is varied. This type of measurement has been reported by Aarset, Cloud, and Trump (135), Allen (I%?), and Mashkova, Mol-
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
163
chanov, and Odiritsov (109, 116). The results of Aarset, Cloud, and Trump for 1.G-RIev protons bombarding polycrystalline A1 are nearly reproduced by a curve of the form y =
0.825 csc e
(13)
where y is the secondary electron yield and 0 the angle between target surface and incident ion beam. Allen’s results give a curve of the form y =
3 csc e
(14)
for 120-kev protons bombarding a polycrystalline Ni target. The results of Mashkova et al. are for 30-kev Ar+ bombarding single-crystal targets of Cu. While these data show peaks and valleys, rather than monotonically decreasing with e as the polycrystalline results do, a curve of the form y = k csc e does roughly fit the points. (Note that p and e are cornplementary angles.) These results are discussed more thoroughly in Section 111, B. The other type of angular measurements that have been reported give the dependence of the yield on the angle of secondary electron emission. Abbot and Berry (137) reported on the angular distribution function using He+ of 40 to 825-ev energies bombarding 3OO0I< and 1100°K polycrystalline W targets. The distribution was, in all cases measured, of the form y = lc sin a where a is the angle between target surface and a straight line from the point of impact of the ion beam OII the target to the electron collector. Kronenberg, Nilson, and Basso (131)measured the energy distribution of the secondary electrons as a function of the electron emission angle, a. They used N l - Mev protons bombarding Be, Al, Cu, and Au targets. These results indicate the same general form for the variation of yield with a, but the energy distributions reported are too coarse to integrate for obtaining a graph of y vs. Q for coniparisori with the results of Abbot and Berry. An interesting apparatus for the measurement of angular distribution has been constructed by Propst and Luscher (91) and was described briefly in Section 11, C. However, it appears that a t the present time it has been used only for measurements in potential ejection.
E. Other Secondary Processes The other secondary processes which are of interest in secondary electron emission are (1) secondary positive ion emission, (2) secondary negative ion emission, and (3) ion reflection. These processes contribute
164
DAVID B. MEDVED AND Y. E. STRAUSSER
to the errors in the measurement of the secondary electron current. Such errors have been discussed in Section 11, C. In this section we shall briefly discuss the results which have been obtained in investigations of the yields of these processes since such information is very relevant to a fundamental understanding of secondary electron emission. I n studies of secondary ion emission, it has generally been found that the majority of the ion types th at are emitted are negatively charged. These ions are predominantly ions of the electronegative gases which were adsorbed on the target surface. R!IitJropanand Gumeniuk (138) have measured yields of the order of 10-2 for C-, 0-, OH-, C2-, and C*H, during the bombardment of Cu by protons in the energy range from 0.2 to 1 &/lev.They also measured yields of 10-6 for the emission of H-. Fogel, Slabospitskii, and Karnaukhov (139) have studied the secondary positive and negative ion emission from a Mo surface bombarded by 5- to 40-kev Ne+, A+, and K+. The secondary ions which they observed included H-, C-, CH-, 0-, OH-, C2-, C2H1-, CZHZ-, 0 2 - , C1-, MoOZ-, MoOs-, Mo203-,H1+, and Mo+. The greatest yields, of the order of were observed in the case of 0-, OH-, H-, and Mo+. Arifov and Ayukhanov (97) and Tashkhanova, Rakhiniov, and Arifov (140) have investigated the yields of negative ions from targets which were covered with thin films of the alkali metals. They observed yields of negative ions, which they assumed to be 0-, of the order of 0.25 ions/ion for 840-ev Rb+ bombarding Na-covered Ta and of 0.12 ions/ion for 540-ev Ne+ bombarding Na-covered Ta. The yields were a strong function of Na coverage, which they explain b y the variation of the work function of the target with change in coverage. Their theory is discussed in Section 111, A, 1, e. A comparison of reflection coefficient of noble gas neutrals and alkali ions has been carried out in a communication of hledved (103). Using the data of Brunnee (88) and Comeaux and Medved (57), it is pointed out that the energy dependence of the reflection for these species is quite similar, showing a monotonic decrease in the energy range from 500 ev to 4 kev. On the other hand, data of Hagstrum (141) for reflection of noble gas ions (where both R,, and R,, are considered as the reflected components) show that K = Rim Rti is a monotonically increasing function of incident ion energy. Here Rii is the ion reflection and R,, is the metastable reflection component resulting from noble gas ions incident on clean tungsten, The hypothesis is advanced in Medved (103) th a t the Auger processes accompanying the interaction of the noble gas ion with the target in some manner will influence the reflection process. Arifov and his colleagues (146, 143) have reported on scattering coefficients of alkali ions from tungsten and nickel a t low energies. Veksler
+
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
165
has reported a series of studies on the interactions of low- and mediumenergy alkali ions with molybdenum t,argets (144-147). These studies show that the increase in K with decreasing Ek reported by Brunnee extends to a maximum in the vicinit,y of 50 ev (where it is of the order of 90%) and then decreases to values of 50% at 10-20 ev. Emission of fast secondary atoms froin copper polycrystals and single crystals bombarded by Ar+ in an energy range of 5-15 kev has been studied by Fluit el aE. (148).Th e “fast” secondaries (which were identified as Ar atoms) are detected by means of their kinetic ejection of electrons from a Cu detector (57, 123). A pulsed beam technique was used to determine the velocity of the detected fast particles. Variation of detector current, with angle of incidence for polycrystal targets showed a monotonic increase. Structure was observed for the monocrystal with a peak in the vicinity of 40’-45’ and a minimum a t about 50” for a (100) surface rotated about a [OOl] direction. The anisotropy in reflection is much smaller than for sputtering or secondary electron emission. Angular distribution of ejected particles with incidence angle as parameter was also measured. The influence of surface roughness resulting from the ion bombardment in these distribution functions is discussed. IV. THEORY
A . Introductory Comments Theoretical treatments of the secondary electron emission problem have been carried out by a large number of authors. Some attempts have been made to compute, in considerable detail, the yield values for specific cases. We shall riot give an extensive discussion of these theories here. Arifov has presented a short summary of the theories on kinetic ejection and ion-ion emission in reference ( l l a ) (pages 62-73), and in pages 255303 he discusses in considerable detail the theoretical work carried out by the staff a t the Institute of Nuclear Physics of the Academy of Sciences of the Uzbek SSR. Potential ejection theories have been given b y Oliphant and Moon (39), Shekhter (149), Cobas and Lamb (150), Varnerin (151), and Hagstrum (152).Theoretical treatments of the problem of kinetic ejection have been presented by Kapitza (153),Sommermeyer (154),Ghosh and Khare (155), Frenkel (156), Morgulis (157), Gurtovoi (158), Izmailov (159, I f i O ) , von Roos (161), Parilis and Kishinevskii (162), and Sternglass (163). Kapitza’s theory considered the electron ejection to thermionically originate from microscopic zones of high temperature produced by the impacting particle. Similar ideas were used by von Hippel in developing an early theory of sputtering. The use of a model which
166
DAVID B . M E D V E D A N D Y . E. STRAUSSER
employed thermodynamic equilibrium conditions to treat the interaction of energetic particles with solids was recognized by Kapitza himself as highly doubtful. It was subsequently recognized that there was no significant dependerwe of -yn on either work function or thermal constants of the target. Frenkel proposed that the emitted electrons resulted from a “shaking off” from the bombarding ion as a consequence of its collision with the metal surface. Ihlorgulis and Gurtovoi first point out the analogy between kinetic ejection and ionization processes resulting from ion-atom and atom-atom collisions at medium and high energies. The theories of Sternglass and Ghosh and Khare are essentially highenergy theories, and are applicable to Ek > 100 kev, whereas those of von Roos and Parilis and Kishinevskii are structured for the description of the kinetic ejection process near threshold and a t medium energy (1 kev < Ek < 100 kev).
B . “High-Energy” Theories There are two theories of kinetic secondary electron emission which are applicable only in the region of high incident ion energy. These are the theories of E. J. Sternglass (163) and of S. N. Ghosh and S. P. Khare (155). The limitation of these theories to the high-energy region results from certain simplifications introduced by the authors. Basically each theory considers first the number of secondary electrons created per unit path length of the ion while traveling into the target and then the fraction of these secondaries which are able to escape from the depth a t which they were created. The simplifying assumptions that limit the theories to the region of high ion energies are, first, that the energy loss per unit path length is a constant in the region near the surface (from which all of the secondary electrons that are able to escape originate), and second, in the case of Sternglass, th at the expression for energy loss in the target, in the vicinity of the surface, is free from the complicating effects of electron capture and loss. I n the high ion energy region in which these theories apply there is a very limited amount of experimental data. Those data which do exist are limited to the use of Hf, HO, D+, and He+ as the primary ion beam. In his development of the theory, Sternglass considers the interactions of the ions with the target that produce secondary electrons to be of two types. The first, which directly produces secondary electrons, is a distant collision of the ion with an atom of the target in which the ion produces only a small perturbation in the atom, thus losing only correspondingly small amounts of energy. The second type of collision involves a close
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
1G7
approach of the incident ion to an atomic electron which transfers a relatively large amount of energy to the electron which then becomes what he calls a 6-ray. These high-energy electrons then produce higher-order secondaries which are the secondary electrons which are observed i n the experiment. The formation of internal electrons is given by the BohrBethe theory of ionization (164, 166) as
where Eois the mean energy loss per secondary formed arid j ( v , , 2) is the fraction of (dEi/dx)avgthat is available for the production of secondaries in higher-order processes a t depth X . The average energy loss per unit distance is assumed to he
where (dE,/dz)A!,)gis the niean energy loss of the ion per unit distance going into distant collisions, (dE7/dx)$$the mean energy loss of the ion per unit distance going into the production of &ray, and (dE,/dx)avgthe total energy loss of the ion per unit length. This condition is true when v p > 2zzvo where 2, is the charge of incident particle, v o the Bohr hydrogen orbital velocity, and up the velocity of incident particle. For protons this means energies above 100 ltev. The diffusion of these internal secondaries to the surface is computed by treating the target as a collection of atoms whose electron-scattering cross sections are essentially similar to those of a gas, and consequently the probability of escape from a depth x is
P(J)= ~ A e - ~ / ~ a where
7
is the surface transmission coefficient. The yield is then
-
1
1 /dE,\
[1
+ f(vi,
X ) ] ~ A ~dx- ~ / ~ S
where for f(vi, x ) he uses f(v,, z)
= 1
- e--z/La
where La is the effective penetration depth of the &rays. Integrating gives
7AL8[I F"\x/,,g
1 1 /dE,\ =
2
+
1
+ La/L,
168
DAVID B. M E D V E D A N D Y . E. STRAUSSER
Using Bohr's approximation for dEi/dxaVggives .rA?re4Zi2~.4Z1I3
y =I E o u g~ I O l / 2 p g
where lo= Rydberg energy, E,, = +moviz = (mo/M)Ek, m o = electronic mass, e = electronic charge, ill = ion mass, Ek = ion energy, Zi= ion charge, ug = geometric area of the outermost filled shells of the target atoms as determined by the covalent radii. By further approximation and substitut,ion of numerical values the expression (16) can be reduced to
for the case T A = 0.5. The comparison of this result with experimental data of Hill et al. (69) and Aarset et aE. (135) is shown in Fig. 55. a Mg 12 Aorset eta/. .A1 13 Aarset eta/. A A1 13 Hill 8 f d . 0 Fe 26 Aarset et a/, Ni 28 Aarset eta!. OCU 29 Hill eta/. 0 Mo 42 Hill et a/. 1 Au 79 Aarset eta1 1Pb 82 Aarset et 01. v Pb 82 Hill et 01.
5
+
I" Curve I
2
Y
1.0 0.8 0.6
0. I
0.2
0.3 0.40.5
1.0
2.0
3.0
Ek,MeV
FIG.55. Comparison of Sternglass theory and experimental data.
The approach t,aken by Ghosh and Khare is very similar t,o th a t of Sternglass except that Ghosh and Khare use an ionization cross section to give the rate of production of secondaries instead of the stopping power expression used by Sternglass. For incident protons the beam is treated
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
1ti9
as a multicomponent beam, i.e., consisting of both HI+ and H1O (whereas Sternglass neglects the effects of electron capture and loss). The expression for y used by Ghosh and Khare is (155, 166) 7 =
2
( 0.5N7 ) Qnl nl
where N = number of metal atoms per cubic centimeter, Qnl = ionization cross section of the metal atom for the nl shell, a ! = absorDtion coefficient. The expressions for Qnl are those used by Bethe (165). The value of a is not known. However, solving this equation in terms of a! for 1-Rlev H1+
7
---Theory of Ghosh md Khore (1551 .Data of Hill ef0/.(69) o Doio of Aarset et 01. (1351
,
01 0 2 04 0 6
08
I
12
1.4
16
18
2.0
Ek.MeV
FIG,56. Comparison of the experimental values of
y for
Hf on A1 with calculated
curve.
bombarding A1 and using for y 21 1.08 from the data of Aarset et al. (135) gives a! = 8.5 X loK cm-l. This then says that the secondary electrons can escape from the target from depths of up to 1/a! or 120 A. Comparisons of experimental values of y for H+ incident on A1 with those computed from Eq. (17) are shown in Fig. 56. It should be noted that when using the appropriate expressions for QSLl (165) y shows a decrease with increasing E k . In comparisons with the available experimental data, the percentage of deviation is only about lo%, well within experimental errors.
C . Medium-E’nergg and Threshold Theories Parilis and Kishinevskii (16%’)of the Uzbek SSR Academy of Sciences have carried out a detailed formulation of kinetic ejection using the
170
DAVID B. MEDVED AND Y. E. STRAUSSER
approach suggested in the earlier work of RIorgulis and Gurtovoi. The eiiergy transfer mechanism from impacting particle to electron is by promotion of the inner shell or valence band electrons to the conduction band. As such, the theory is quite different from that of Izmailov, who considers elect.ron emission as a result of a retardation field set u p b y the subsequent interaction distortions of the impacting particle with the target. This retardation field then acts on the conduction electrons to eject them.
SURFACE
FIG. 57. Model of kinetic ejection according to Parilis and Kishinevskii. (A) Ionization (internal) of inner shells hy in-coming atom. (U) Hole-electron recombination, energy coupled to electron 2. (C) Electron 2 excited to emission level.
In the theory of Parilis and I-iishinevskii the interaction of the incident particle with the lattice is treated as an individual atom-atom collision and the theory of Firsov (167,168) is used to compute the ionization cross section of such a process, ~ ( vwhere ) v is the relative velocity of t'he colliding atoms. A key feature of their theory involves the use of an internal Auger process for production of the secondaries observed. They argue that discrepancies exist bet,ween observed energy distribution functions of the electrons emitted from the solid and the maxima of energy spectra E m observed in ion-atom collisions. A figure of Em < 6 ev is cited as justification for invocation of the Auger mechanism and t,his we consider to bz the most dubious step in their argument. The essence of the idea is showti in Fig. 57. Process A produces a hole-electron pair as the result of the
KINETIC EJECTION O F ELECTRONS FROM SOLIDS
171
inelastic atom-atom collision but electron 1 has insufficient energy to surmount the barrier at the surface. The Auger process corresponds to a coupling of the hole-electron recombination energy (process B) to electron 2, which can then be emitted (process C). Parilis and Kishinevsltii use for the probability of this sequence the empirical relation of Hagstrum
P ( E u )= O.OlG(E, - q+)
(18)
in which E , plays a role analogous to that of E,. The expression for y is then given by y = N ”:/ u(v)P(Eu)e-zlx dc (19) where N is the atom density in the lattice, X is the mean free path of the L‘hot”electron, 2, and 2, is an effectivepenetration depth or the distance a t which the velocity falls to a minimum value for electron production. Apparently it is assumed that X > c, for the low velocities. It is the computation of ~ ( vand ) its variation with x which occupies the major effort of this treatment. Assuming a decrease in velocity with penetration depth according tao vk2
- v2 =
kx
(where v k is the velocity of the incident particle) they obtain =
NP(E,)X[u(vk)- A5(vk)I
where
The term A5(vk) is most iinportarit a t low energies in the region near threshold. Theoretical curves have been computed for a variety of target-ion combinations and compared with experiment. The results are shown in Fig. 58. According to a numerical reduction, the value of y at threshold increases slowly with v k , then varies as v k 2 - $uf,,,, and finally (as A 5 goes to zero) approaches a linear form, Le., u ( v k )N
vk
tan-’ [O.G X 10-7(vk - urnin)]
The theory was limited for those target-ion (2,) combinations ZZ, where < Z2/Zl < 4. Extension to lighter ions has recently been discussed by Kishinevskii and Parilis (169). Von Roos (161, 170) working at the University of Marburg (on the same staff as C. Brunnee), carried out an extensive theoretical treatment of kinetic ejection and ion “reflection,” which he applied specifically to the systems studied by Brunnee (alkali ions of energy 1-4 kev incident, 011
172
DAVID B . MEDVED AND Y. E. STRAUSSER
clean surfaces of molybdenum) (88). He treated these processes as collisions between a stream of ions and the atoms of the lattice in terms of the Boltzmann equation, analogously to discussions of neutron diffusion in solids. The distribution function of the primary ions, N(r, v), is determined by solution of the Boltzmann equation. It is assumed that since ionization cross sections are much less than the scattering cross section, the distribution function N(r, v) is not affected by ioriizatioii events. Thus the results of his calculation for N ( v , r) (270) are applied directly in his expression for electron production, dN,,
dN,
= “(2,
K , e)k dx d K dB] * n* dQi
where dQi is the differential ionization cross section, K = M V / h , n* is the number of “scattering centers” in the solid, and z is in the direction
v , 10’cm.secC
FIG.58. Comparison of theory of Parilis and Kishinevskii with experimental data for various ions bombarding Mo. Experimental points: (1) Ar+, (2) Kr+, (3) K+, (4) Ar+, (5) Mo+.
of the normal to the metal surface with 8, the angle coordinate of the velocity vector with respect to x. At this point von Roos makes a fundamental assumption which probably constitutes the weakest part of his argument. He considers the penetration depth of incident ions to be of the order of 10 A or less so that almost all electrons produced by ionizing collisions within this distance will be emitted (citing Wolf’s work, 171) and consequently the distribution functions of emitted secondaries will be given by the spectrum of internal electrons as follows:
where J o = flux of incident ions, k = wave number of generated electrons n2k2/2m= G , E = energy of the electrons,
KINETIC EJECTION OF ELECTRONS FROM SOLIDS
K,
173
= the minimum ion “velocity” which can lead to emission of
an electron of energy
e
(MV,
=
hK,),
K O = incident ion “velocity” ( M V o = h K o ) , and PI(€) and FZ(c)are those functions of electron energy which describe the angular dependence of electron escape. The ionization cross section is computed in a highly detailed manner using the perturbed stationary state method (22) and an expression for the distribution function 6(c) dc is obtained and compared with Brunnee’s
dN
z
0
5
I5
10 El,
20
ev
FIQ.59. Comparison of theory (161) and experiment (88)for distribution function in velocity of secondary electrons (for Cs+ at 2 keV on Mo). curves a t 2 kev. An example is shown in Fig. Fig. No direct comparison of total yield with experiment is presented.
V. CONCLUSIONS A N D PROBABLE TRENDS All the theories on kinetic ejection suffer from a common defect. They do not take into account the lattice structure of the solid and thus the meaningful results of those investigators who have observed the y anisotropy from single-crystal metal targets cannot be readily fitted within the framework of the existing theories. The experimentalists have attempted to explain their results by simple geometrical models (116, 122).
174
D A V I D B. MEDVED AND Y. E. STRAUSSER
The incorporation of these “crystalline opacity” models into theoretical computations of the type outlined in Section I V is clearly required. Recent experimental and theoretical work on channeling processes in solids may also be of some significance to any comprehensive underst,ariding of the secondary emission process (172, 173). The penetrat,ion of medium-energy atoms along tubes or channels to dist,ances in excess of 1000 A has been established. The ranges of “hot” e1ect)rorisin solids have been measured in excess of 500 A in gold (274). It is interesting to note that accept,ed values of mean penetration of atomic particles in solids and the mean free paths of electrons with energy several electronvolts above the Fernii level have both increa.sed considerably in the past few years. Thus, an appreciable fraction of the emitted secondaries may originate deep i n the latkice rat>herthan coming exclusively from the first few atomic layers. In addition t,o careful measurements of the y anisotropy from metal single crystals, angular arid energy distribution functions need to be determined. Of even more immediate interest is a comparison of yield values bet,ween classes of single-crystal materials such as insulators, semiconductors, and metals. The values of yk for silicon in the range 1-10 kev are more typical of met,al behavior (y 1) than those for the alkali halides ( y 10). The occurrence of kinetic ejection for t3hosecases where there are not conduction band electrons appears to rule out t,he ret,ardation pulse theory of Izniailov and lends credence to the assumption that in all cases the internal primary electron originated from the valence band. For such a model, we might expect that the dependence of angular and velocity distributions of emitt,ed secondaries on incidence angle of the bombarding ions (if the ionizat,iori process is not complet,ely isotropic) would permit one to isolate the contribution of Auger mechanisms t o the kinetic ejection process.
-
N
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176. J . Koch, Z. Physik 100, 685 (1936). 176. C. Couchet, Conipl. Rend. 236, 944 (1952). 177. A. I. Akishin and S. S. Vasil'ev, Soviel Phys.-Solid Slate (English Transl.) 1, 755 (1959). 178. N . Colombie and Phan. Van Chuong, Compt. Rend. 263, 1567 (1961). 179. A. Guntherschulze and H. Betz, Z. Physik 108, 780 (1938). 180. A. Guntherschulze and W. Bar, Z.Physik 109, 121 (1938). 181. J. H. Parker Jr., Phys. Rev. 93, 1148 (1954). 182. G . Timoshenko, J . Appl. Phys. 12, 69 (1941). 185. R. C. Bradley, Phys. Reu. 93, 719 (1954). 184. S. N. Ghosh and W. F. Sheridan, J . Chem. Phys. 26, 480 (1957). 186. C. M. Batanov and N. N. Petrov, Sovief Phys.-Solid Slate (English Transl.) 1, 1701 (1960). 186. H . C. Bourne, Jr., R. W. Cloud, and J. G. Trump, J . Appl. Phys. 26, 596 (1955). 187. J . W. Murdoch and G. H. Miller, USAEC Rept. No. ZSC-662 (1955). 188. E . S. Mironov and L. &I. Nemenov, Soviet Phys.-JETP (English Transl.) 6, 188 (1957). 189. F. M. Devienne, J. C. Roustan, and J. Souquet, Compt. Rend. 260, 4701 (1965).
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Scanning Electron Microscopy C. W. OATLEY, W. C. NIXON,
AND
R. F. W. PEASE
Engineering Department, Canlbridge University, Cambridge, England Page 181 .... .... . . . 181 .......................................... 183 ......................... 184 11. Principles of Design of the Scanning Electron Microscope.. . . . . . A. Schematic Arrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 B. Fundamental Limitations.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 ............................................ 194 trast in the Scanning Electron Microscope.. . . . . . 201 E. The Effects of Penetration of Incident Electrons into the Specimen. . . . 209 F. Practical Limits of Resolution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 111. Techniques and .......................... 212 A. Introduction .......................................... 212 B. Stereoscopic ...................... C. Low-Voltage Operation of the M ..................... 11. The Examination of Insulating Specimens. . . . . . . . . . . . . . . . . . . . . E. The Examination of a Nylon Spinning J e t . . . . . . . . . . . . . . . . . . . . . . . . . . 220 F. Forming Processes in Point-Contact Rectifiers. . . . . . . . . . . G. The Investigation of Potential Variations on the Surface H. The Examination and Fabrication of Integrated Circuits. I. Direct Observation of Chemical Changes.. . . . . . . . . . . . . . . . . . . . . . . . . . . 229 J. The Activation Process in Dispenser Cathodes . . . . . . . . . . . . . . . . 229 K. Investigation of the Sputtering of a Metal Sur Positive I o n s . . . . 232 L. The Examination of Biological Material and of Synthetic Fibers.. . . . . . 234 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
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I. INTRODUCTION A . Principle of the Instrument The principle of the scanning electron microscope is illustrated schematically in Fig. 1. A beam of electrons from a cathode, C, passes through electron lenses L1, Lz, LB and is brought to a focus on the surface of the specimen, S. The lenses are so placed th a t the diameter of the beam a t S is of the order of 100 A. A portion of the electron current leaving S is collected by a plate, P, and conveyed to a n amplifier, A, the output of which controls the potential of the modulating electrode G of a cathoderay tube and thus the brightness of the spot on the face of this tube. 181
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C. W. OATLEY, W. C. N E O N , AND R. F. W. P E A S E
Deflections of the initial electron beam and of the spot on the cathoderay tube are caused by the passage of current from a saw-tooth generator, B, through pairs of coils DIDIand D,D,, respectively. Two systems of this kind are used t o produce deflections in two directions a t right angles, so that both the initiaI beam and the cathode-ray tube spot traverse zig-zag rasters in synchronism. Furthermore, since the current reaching P varies as the electron beam scans the surface of S, the brightness of the cathode-ray tube spot varies in sympathy and a n image of S is built up on the face of this tube. It does not immediately follow that this image will be similar in appearance to one that would be obtained with a n optical microscope but, as we shall see later, this turns out to be the case. The magnification of the image is the ratio of the linear dimensions of C T
I
h-1L2-
I I
-
FIG.1 . Principle of the scanning electron microscope. C, cathode; L1, L,, LB, electron lenses; D,, D?, scanning coils; S, specimen; P, collector; A, amplifier; B, scan generator; G, control grid in the display cathode-ray tube.
the rasters on the cathode-ray tube and on S, respectively, and this, in turn, depends on the currents in the coils D2D2 and DID, and can be varied a t will. I n practice, as in most optical or electron-optical instruments, the useful magnification is limited by the resolution that can be achieved. The above scheme niay be modified in various ways without changing the basic principle. Electrostatic rather than magnetic deflection of the electron beams niay be used; the final image may be built up on a facsimile recorder instead of on a cathode-ray tube and the combination of the collector P and the amplifier A may be replaced in part by a n electron multiplier or by a scintillator and a photomultiplier. Again, instead of deriving the output modulating signal from the electron current passing from S t o the collector P, it may be obtained from variations in the total current flowing through S and returning to the high-voltage source.
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B. Historical The first instrument operating on the above principles was built b y Knoll (1) in 1935, to investigate the charging potential of surfaces under electron bombardment and further investigations of a like nature were reported by Knoll and Theile (2) in 1939. I n this work the electron beam was produced by a conventional electron gun without demagnifying lenses and resolution was limited by the final beam diameter, of the order of 100 p. The first true scanning electron microscope was built by von Ardenne (3) in 1938. A final beam diameter of 100 A was claimed and recording was carried out by allowing the beam to pass through the specimen and then to strike photographic paper which was scanned mechanically in synchronism with the beam. A recording t,ime of 30 minutes was required and, since no provision was made for a visual image, focusing had to be carried out by trial and error for each specimen. I n 1942, Zworykin, Hillier, and Snyder ( 4 ) reported the construction of a scanning electron microscope which achieved a resolution of 500 A with a solid specimen. The final image was obtained on a facsimile recorder, each picture taking 10 minutes to record. Published micrographs show a good deal of background noise, indicating that the collection system was not very efficient. Furthermore, the ancillary electronic equipment used in this instrument was very complicated. This early work has recently been the subject of a review by Mollenstedt and Lenz (6). I t showed that microscopes of the type under consideration could be made to work, but suggested that the new type of instrument had few advantages over conventional electron microscopes to justify the additional complexity which is inherent in the scanning system. After the war, interest in scanning electron microscopes was revived in France and an instrument was constructed under the direction of Leaut6 in 1946. As in earlier microscopes, noise was a serious limiting factor and the resolution was not better than a few microns. I n the same year Brachet (6a) published a theoretical treatment of the scanning electron microscope and showed that, if the electron current leaving the specimen could be collected and amplified without adding noise to th a t already present, a resolution of about 100 A should be possible. I n 1957, Davoine (6) reported the construction of a scanning microscope for the study of the secondary emission from stressed metals. The resolution was about 2 p and the published micrographs suggest that the collection system was not very efficient. This instrument has since been used (7) t o investigate cathodolurninescence in crystals b y
184
C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
picking up the light, emitted under electron probe excitation, with a photomultiplier. Research on the scanning electron microscope was begun in the Engineering Laboratory, University of Cambridge, in 1948 and has been actively pursued since th at date (‘7a,b). The remainder of this article is largely, but not exclusively, concerned with work carried out by members of this group.
C. M c M u l l a n ’ s Scanning Microscope The initial work at Cambridge resulted in the construction of a scaiining electron microscope described by McMullan (8) in 1953. This instrument incorporated a number of novel features which have been retained in more recent models arid it is convenient to enumerate these at this point, The most important were the following: 1. T h e U s e qf an Eficient and Relatively Noise-Free S y s t e m jor Collecting and Amplgfying the Electron Current Srom the Specimen. The problem of noise-free amplification was solved by the use of an electron multiplier. Devices of this sort had, of course, been known for many years but the earlier multipliers had all contained cesium-coated electrodes which could not conveniently be used in demountable vacuum systems. Shortly after the war, however, multipliers with beryllium-copper dynodes (9) became available and it was a detector of this type that AlcMullan used. The second part of the problem was to ensure that a reasonable fraction of the electron current leaving the specimen reached the first dynode of the multiplier. This was achieved by mounting the specimen so that the normal to its surface was inclined a t an angle of about 65” to the incident electron beam. This allowed the multiplier to be placed in such a position that some 20% of the electrons leaving the specimen were collected. Although the above system has since been superseded by one employing a scintillator and photomultiplier, it, represented a great advance on any previously used and has played a large part in the development of the scanning microscope. At the outset it was feared that foreshortening of the final image, brought about by allowing the incident electrons to strike the specimen obliquely, might be objectionable, but this has not proved to be the case. The human eye is accustomed to observing objects at an angle and to making automatic correction for foreshortening, so long as the ratio of maximum to minimum magnification does not exceed 2 or 3. Thus i t has become common practice t o place the specimen surface a t a n angle to
SCANNING ELECTRON MICROSCOPY
185
the incident electron probe and to indicate on the final micrograph the greatest and least values of magnification. 2. Separate Display Channels for Visual Observation and Photographic Recording. It will shortly be shown that with existing types of electron gun, it is inherently impossible to obtain a noise-free micrograph with high resolution unless recording times of the order of minutes are employed. On the other hand a more or less instantaneous visual display is required for focusing the instrument and for selecting the required area of the object. The visual display is conveniently provided by a cathode-ray tube with long-afterglow screen, operated at a frame repetition frequency of the order of one per second. This gives a reasonable compromise between speed of operation and noise integration. To achieve additional noise integration in the photographic record the visual display picture could, of course, be photographed, the exposure being continued for any required length of time. However, this is undesirable on two counts. I n the first place, the spot on a cathode-ray tube with afterglow screen usually exhibits some degree of halation which impairs the definition in a photographic record, Second, it is difficult t o keep conditions absolutely steady for periods of the order of minutes and, if the visual display is photographed with a n exposure extending over msny frame cycles, any drifts, whether electrical or mechanical, will cause blurring in the final micrograph. For these reasons it is better to provide a quite separate display for photographic recording. A cathode-ray tube with very high definition is required and it should therefore have short afterglow. Furthermore the sweep frequencies should be such that a single frame occupies the whole of the required exposure time. Drift will not then cause blurring of the micrograph, though it may produce slight distortion of the image.
3. Double Defiection of the Electron Probe. It is necessary to scan the electron probe over the specimen and it is inconvenient to deflect the electrons after they have passed through the final lens, since very little room is available to accommodate the scanning coils a t this point. It has therefore become customary to mount these coils between the last two lenses or within the box of the final lens and, by using two pairs of coils for each coordinate direction to deflect the beam twice, as shown in Fig. 2. I n this way the center of the beam passes through the center of each lens and maximum deflection is thereby increased.
4. The Formation of Contrast. I n earlier scanning microscopes it had been tacitly assumed that contrast in the final image was caused
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C. W. OATLEY, W. C. NIXON, AND R. F. W. PEA SE
only by variation in secondary-emission coefficient over the surface of the specimen. McMullan was the first to appreciate that contrast could result from other factors such as the variation of high-energy electron current passing from specimen to collector, whether as a result of changes in the composition of the specimen or of variations in the local angle at which the incident beam strikes the specimen surface.
11. PRINCIPLES OF DESIGNOF
THE
SCANNING ELECTRON MICROSCOPE
A . Schematic Arrangement I n accordaiice with what has already been said, a scanning electron microscope will consist of the major components shown diagrammatically
1
- - LENS 2
FIG.2. Double deflection of the electron probe. The same current flows in each set of coils but the set nearer lens 3 has twice the number of turns so t h a t the beam is deflected through twice the angle of deflection of the first coil set. The beam oscillates about the center point of lens 3 and the effect of aberrations is reduced.
in Fig. 3. It is our purpose in this section to discuss general principles underlying the design of these components, but we shall not be concerned with details which could be modified at the discretion of a n individual designer.
B. Fundamental Limitations 1. Shot Noise in the Electron Probe. The brightness of a particular point of the image is determined by the number of electrons passing from specimen to collector while the corresponding point of the specimen is being scanned. But, since the arrival of electrons a t the specimen is a random process, this number is subject to statistical fluctuation which results in noise in the final image. Suppose a square area of the object of side D to be under observation and let this area be scanned by the electron probe in a total time t. We
SCANNING ELECTRON MICROSCOPY
187
shall see later that the distribution of current over the cross section of the probe is subject to some uncertainty but, for our present purpose, it is sufficient to assume the probe spot to be a square of side do, with uniform current density j inside the square and no current outside. If e is the electronic charge, the number n of electrons reaching the square of side do during the time taken t o scan this area is given by
n
= j d o 2*
The rms fluctuation in n will be
do2t/D2e
d;, so that n / v % = .\/n
(1)
represents
LIGHT PIPE
0-M
SCANNING
SECOND LENS
FIG.3. Schematic diagram of the scanning electron microscope. Three lenses are used to demagnify the electron beam. The secondary electrons are collected with a biased scintillator. A long-persistence display tube is used for visual results and a shortpersistence high-definition tube for 2-3-minute single-frame scan photographic recordings.
the basic signal-to-noise ratio of the element being scanned. Subsequent stages in the production of the final image cannot improve this ratio, though they may make it worse. For the moment we suppose that they leave it unchanged. Following Rose ( l o ) ,we may assert that the eye will not, be able to distinguish an area of brightness B in the final image from an adjacent one of brightness B AB unless the ratio of signal to noise is approximateIy five times the ratio of B to AB. We therefore write
4;
> 5B/AB
giving, with Eq. (l),
25(B/AB)26 jdo'?/D2e
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C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
Turning now to the factors which may cause additional noise in the final image, we note that Eq. (2) is based on the assumption that, in a “white” area of the image, each electron striking the specimen results in the production of at least one photon on the cathode-ray tube and this will be so only if each electron gives rise to a recognizably independent “event” at each stage along the chain. Beginning with the secondary emission process itself, the number of independent events will clearly be reduced unless the secondary emission coefficient is greater than unity in the “white” areas. This will generally be the case; even when it is not, the maximum secondary emission coefficient is unlikely to fall appreciably below unity. However, additional noise will be introduced because the production of secondaries is itself a random process. Some primaries produce several secondaries while others produce none so that, even if the total number of secondaries is greater than that of primaries, the number of independent events may be less. The effect will be appreciable unless the over-all secondary emission coefficient is much greater than unity and this will rarely be the case. Everhart (11) has investigated this matter theoretically and has given a formula for the increase of noise t,o be expected from the effect. At the time when he wrote the only experimental data available related to primary electrons with energies up t o 1600 ev. Extrapolating these results to the much higher primary energies used in scanning electron microscopy, Everhart concluded that, in unfavorable circumstances, the noise might be increased by a factor as high as 16. More recent work by Pease ( I d ) suggests that this factor is certainly much too high and that an increase of four times is probably not far from the truth for most specimens. Still further noise may be introduced if the collector does not collect all the secondary electrons or if the number of independent events falls below the number of primary electrons at any stage of the subsequent amplification process. These effects are examined in greater detail below but it may be said that, at the present time, it is possible to keep the factor by which they increase the noise t o a value of about 2. Stmilllower values are likely to be achieved in the future. Taking all these factors into consideration it seems reasonable to amend Eq. (3) empirically to read
<
100(B/AB)2 jdo4t/D2e and we shall adopt t,his as our basic equation for noise limitation.
(4)
2. Current Density in the Probe. It has been shown by Langmuir ( I S ) that when electrons, emitted from a thermionic cathode with a Maxwellian distribution of velocities corresponding to an absolute temperature
SCANNING ELECTRON MICROSCOPY
189
T , are brought to a focus by any electron-optical system, the maximum current density j that can be produced in the image is related to the current density j o a t the cathode surface by the equation j = jo(eV/kT
+ 1) sin2a
(5)
where e is the electronic charge, V the potential difference between the cathode and the point where the image is formed, k is Boltzmann’s constant, and a the semiangIe of the cone of rays which converge to form a point of the image. In the present instance, a is always small and eV is much larger than kT, so Eq. ( 5 ) becomes j = joeVa2/kT
(6)
Measurements made by Haine and Einstein (14) suggest that this limiting current density in the image is closely approached in practical electron guns so long as these are not operating under conditions where space charge is appreciable. I n the scanning electron microscope conventional guns with hairpin tungsten filaments have commonly been used and at the temperatures at which these are generally operated, space charge is not negligible. To allow for this fact we shall assume Eq. ( 5 ) to be correct,, but shall take the rather low value of 2 A/cm2 for j,. 3. Lens Aberrations. The purpose of the electron-lens system is to produce a demagnified image of the crossover of the electron gun. This crossover, considered as the object, is not a sharp circular disk because the initial velocities of the electrons cause the current density at the edge to fall off gradually. If the lens system were perfect, the current density in the image would have a similar distribution and following Smith (16) we shall arbitrarily take the Gaussian diameter, do, of the image to be that diameter within which 80% of the total current would then lie. Because of the lens aberrations and the wave nature of electrons, each point of the Gaussian image is expanded into a circular disk of least confusion in an adjacent plane and, taking the various effects separately, we may write for the diameters of these disks: (a) Spherical aberration. d, = +C8a3 (7)
where C, is the spherical aberration coefficient of the lens and a is the semiangle of the mys converging to form an image point. (b) Chromatic aberration. d, = C,aSV/V
190
C.
W.
OATLEY,
W.
C. NIXON, A N D R. F. W. PEASE
where C , is the chromatic aberration coefficient of the lens and 6V is the voltage spread in the eht,’ voltage V. (c) Diffraction. d f = 1.22X/e (9) where X is the wavelength of the electron waves. Expressing V in volts, Eq. (9) may be written dz =
1.22
1/150/V cm ~
Following a procedure which has commonly been adopted, we write for the over-all diameter d of the image d2 = do2
+ d,’ + + df2 dC2
(11)
This equation oversimplifies the problem of combining the aberrations, but gives a good idea of the effective diameter of the image.
4. The Number of Lines per Picture. From the foregoing it is clear that, to reduce noise and diffraction effects, a should be as large as possible, while to reduce lens aberrations it should be as small as possible. Before we can use Eq. (11) to determine the best value of a, we need some criterion for the Gaussian probe diameter do and this we obtain by working backward from the final display unit. The number of lines, N , in the final picture is determined by the size of this picture, since the line spacing should be roughly equal to the smallest distance that the eye can readily detect, say 0.02 cm. A larger distance than this gives a ragged picture and nothing is to be gained by using a smaller distance. Thus, for direct visual examination of a picture 7.5 X 7.5 cni on the face of a cathode-ray tube, a reasonable value for N would be 400. On the other hand, if it is intended to photograph this picture and afterwards produce an enlarged print, a correspondingly larger value of N would be justified since photographic film can record finer detail than the eye can see. The advantage of enlarging the final print, with an increased number of lines, is that a larger area of the specimen can be photographed without loss of detail. I n general, we may expect N to lie between 300 and 1000 and the cathode-ray tube must be capable of resolving whatever number of lines is chosen. Turning now to the specimen, let the area scanned be a square of side D and suppose, in the first instance, that the scanning probe has square cross section of side d, with uniform current density inside this square and zero outside. Under these conditions it would be appropriate to adjust We shall use the abbreviation eht (for “extra high tension”) as equivalent to “electron gun accelerating voltage.”
SCANNING ELECTRON MICROSCOPY
191
the magnification so that D/d was equal to N . To see this we note th a t a square of side d is the smallest area of the specimen that can be resolved by the scanning beam and that, by our choice of N , this area is represented in the final picture by the smallest area that can readily be resolved by the eye. If we make D/d greater than N , the probe will be too small to fill the raster and parts of the specimen within the raster will not be scanned. We are neglecting these parts in a n attempt to obtain higher resolution (by the use of a smaller probe diameter) in those parts which are scanned. This is clearly unsatisfactory and could, in certain circumstances, lead t o a final picture which was not a true representation of the specimen. If, on the other hand, we make D / d less than N , successive scan lines will overlap and, unless the ratio of N to D/d is a n integer, some parts of the specimen will be scanned more intensively than others. I n any case, the total area of specimen scanned is less than it could have been for the same resolution. I n effect, we are using a higher magnification than is justified and are attempting to show, in the final picture, fine detail which the probe beam is incapable of resolving. Thus the collection and display of information is carried out most satisfactorily when D/d is made equal to N . The above discussion is based on the assumption of a hypothetical beam with square cross section and sharp edges. With a beam of cirular cross section, diameter d, and a sharp boundary, some overlapping of successive scan lines would be desirable to compensate for the fact that fewer electrons fall along the edges of a line than along the center. However, what we have in practice is a beam of approximately circular cross section whose boundary is by no means sharp. A gradual fall-off of the electron density is brought about partly by the initial velocities of the electrons and partly by the lens aberrations. I n these circumstances it seems a reasonable approximation to the truth to take as our criterion for satisfactory scanning N = D/do (12) where d o is to be identified both with the diameter of the Gaussian image in Eq. (11) and with the side of the hypothetical probe, of square cross section, in Eqs. ( l ) , (3), and (4). We may then assume th a t the gradual fall-off of the current density at, the boundary of the beam provides sufficient overlap of scan lines to gives approximately uniform irradiation of the specimen. Any attempt at a more sophisticated treatment is rendered valueless by our ignorance of the exact shape of the crossover of the electron gun and the distribution of current within it. Both of these factors depend quite critically on the geometrical adjustment of the gun.
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C . W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
5 . The Optimum Aperture. We may now combine Eqs. (4),( 6 ) , and (12) to give the minimum Gaussian diameter of the probe as
Using this value of do, we may write Eq. (11) as dZ =
+ &a2+ Rae
(14)
where, from Eqs. (7), (8), and (lo),
2.23 x 10-14 V Q = (C,6V/V)2 R = (C,/2)2 p
=
+
kTN2
(15) (16) (17)
Differentiating Eq. (14) to find the value of a that will make d a minimum, we find 1/Q2 12PR - Q (ffopJ4= 6R
+
and we take the value of d obtained when this value of a is used to be the smallest distance that the microscope can possibly resolve. 6 . Typical Valuesfor the Limit of Resolution. T o get a general idea of the limits set by the above equations, we take the following values for the aberration coefficients of lenses suitable for use in a scanning electron microscope. I n addition, for an electron gun with a hairpin tungsten
Electrostatic Magnetic
5 . 0 cm 0 . 8 cm
10 cm 2 . 0 cm
filament, we niay take T = 2800"K,jO= 2 A/cm2, and 6V = 1.0volt as a result of initial velocities. Setting V = 20 k V and B/AB = 10, we then find the relations shown in Fig. 4 between d and t, between a and t, and between the beam current I and t, for different values of N . Too much attention should not be paid t o the absolute values of the quantities shown in these graphs since the const,ants used are merely typical ones and are not necessarily appropriate t o any given set of conditions. For example, the value of B / A B may well depend on the nature of the specimen; nothing is to be gained by attempting to reproduce a large number of shades if the surface of the object consits entirely of black and white patches. Again, Eq. (2) is based on the ability to
ts
2-
3-
I100,
t
IN
-ELCCTROSTATIC ---- MffiNmC
1 0
SECONDS
100
'1
IN SECONDS
FIG. 4. (a) Probe size d vs. recording time t for various numbers of lines per frame and two types of lens. (b) Semiangular aperture LY vs. t . (c) Electron probe current I vs. t .
t
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C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
discriminate between an area of brightness B and one of brightness B & A B ; it does not ensure a virtually noise-free picture, which may be desirable on other grounds. Finally, we shall shortly see that the diameter of the probe is not the only factor that limits resolution. I t is now clear that, so far as lens aberrations and noise are concerned, the limit of resolution should not be much greater than 100 A, whether we use electrostatic or magnetic lenses. Furthermore, the curves suggest that little is to be gained by using scanning times much in excess of 300 sec. To do so would be very tedious and, moreover, it would not be easy to avoid elect,rical and mechanical drifts for such long periods.
C . Practical Details 1. Electron Lenses. The theory given in Section 11, B shows that, so far as lens aberrations are concerned, it should be possible to obtain resolution less than 100 A using either magnetic or electrostatic lenses of conventional design. We shall see later that factors unconnected with the lens system tend to limit the resolution to about 100 A, so the choice between the two types of lens can be made on grounds of practical convenience although, other things being equal, magnet'ic lenses would be preferred because of their lower aberration coefficients. During the past few years a good deal of experience has been gained of both the magnetic and the electrostatic types of scanning electron microscope. Present practice favors the magnetic, chiefly because of the much greater ease with which magnet.ic lenses can be cleaned. I t is difficult to avoid contamination of the lens surfaces as a result of interact,ion between the electron beam and residual vapors and the cleaning of electrostatic lenses has proved rather troublesome. Magnetic lenses have other advantages. The lenses themselves are more robust and less likely t o go out of alignment than are the component>s of an electrostatic lens. They faci1it)atethe task of the microscope designer since he has fewer high-voltage leads to bring into the column, and they allow him tJoreduce the volume of the evacuated space since the magnet windings can be outside the vacuum. One point, in favor of electrostatic lenses should perhaps be mentioned. As has previously been explained, the specimen is usually mounted so that its surface is inclined to the elect,ron beam. Thus, since the beam is scanned over the surface, it cannot be accurately in focus at, all points. The normal pract.ice is to adjust for the center of the scan and to rely on the depth of focus to avoid trouble at the edges. In general this is satisfactory, but under certain circumstances edge defocusing is appreciable. When electrostatic lenses are used this difficulty can be overcome by applying a portion of the scan voltage to the center electrode of the lens
S C A N N I N G ELECTRON MICROSCOPY
195
in such a way as to keep the beam in focus throughout its travel. Thornley (16) has shown that this scheme can be made to work satisfactorily and that improved micrographs result from its use. It is less easy to devise a comparable arrangement for magnetic lenses, since the high inductance of any modulating winding would militate against rapid changes of focal length. The purpose of the complete lens system is to reduce the diameter of the electron beam from its value at the crossover of the electron gun to the value required a t the specimen. For the former value we take 100 p ; by careful adjustment of the gun a rather smaller crossover can be achieved, but 100 p is probably a good working figure. If the full potentiality of the microscope is to be realized, the final probe diameter should be less than 100 A, say 30 A, to give some latitude. I t thus follows that the total demagnification must be about 30,000 times and, in a column of reasonable length, so large a value cannot be obtained with two lenses. We are thus led to a three-lens system. As is usual in systems of this kind, the aberrations result almost entirely from the final lens which operates with much larger angular aperture than the other two. We shall therefore confine our attention to this final lens; any reasonable design will serve for the earlier ones. To provide adequate working distance the focal length of the final lens can conveniently be 1 to 1.5 cm. For some purposes an even longer focal length may be desirable. We shall assume the lens to be magnetic and, with this relatively long focal length, a rather large structure is needed to reduce spherical aberration to reasonable proportions. The vaIues of the aberration coefficients quoted in Section 11, B, 6 indicate the kind of performance that can be achieved without too much difficulty. Although the resolution that one can hope t o obtain with the scanning electron microscope is much lower than that given by the conventional transmission instrument the permissible mechanical tolerances are about the same in the two cases. This comes about because the scanning microscope operates a t a lower voltage and has a final lens of longer focal length. For the same reasons, shielding from stray magnetic fields must be carried out as carefully as in the transmission instrument. It is important that, so far as possible, the specimen should lie outside the magnetic field of the final lens, since quite a small field a t this point might impair the collection of the slow secondary electrons. It is therefore advantageous to design this lens to have a small final bore and a much larger initial one, rather than two bores of equal radius. In practice this does not substantially increase the aberration coefficients. The limiting aperture of the system will be situated at the final lens and i t is desirable to make provision for a rapid change of aperture size,
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C . W. OATLEY, W. C . NIXON, AND R. F. W. PEASE
since the discussion in Section 11, B, 6 shows that the optimum size depends on the total scan time that can be allowed. Quite apart from this, it is convenient to be able to make a preliminary examination of a specimen with a relatively large aperture and correspondingly large beam current even though, at a later stage, the aperture size is reduced to give the best possible resolution and/or a greater depth of field. In addition to the main limiting aperture, spray apertures are placed at appropriate points along the system to prevent unnecessary beam current from st’riking successive lenses. With well-constructed lenses in clean condition a stigmator is not usually necessary.2 However, it is a wise precaution t o include a device of this kind since operating conditions are not always perfect. The exact design of stigmator is not of any great importance. d. The Deflection System. The deflection of the electron beam needed to scan it over the surface of the specimen is usually carried out in the space between the second and third lenses. As previously mentioned the beam is bent twice in each coordinate direction and the two deflections are so proportioned that a ray which was originally traveling along the axis passes through the center of the final lens. In principle, either electrostatic or magnetic deflection might be used, though the same type should preferably be employed in the column and in the cat,hode-ray tube of the display unit. I n practice, electrostatic deflection appears to have no advantages. I t must be operated from a high-impedance circuit and stray capacitance can easily cause phase shifts between the deflection of the electron probe and that of the cathode-ray tube beam. The deflecting plates must necessarily be placed inside the column (whereas magnetic deflecting coils can be mounted outside) and, if t,hey become contaminated, can give rise to distortion. Finally, it appears to be appreciably more troublesome to design a satisfactory drive unit for electrostatic plates than for magnetic coils, though neither is really difficult. For these reasons magnetic deflection has usually been preferred and this is in accordance with the fact that most commercial high-definition cathode-ray tubes of the type needed for the final display also employ magnetic deflection. Although the specimen will normally be mounted on a carriage which can be moved in two perpendicular directions, it is not easy to arrange really smooth position control at the highest magnifications. It is therefore convenient to provide electrical shifts by the passage of adjustable direct current through the deflecting coils. A single set of coils may carry a For information on stigmators, see, for instance, M. E. Haine, “The Electron Microscope,” Spon, London, 1961.
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197
both the scanning currents and the direct currents or two separate sets, wound on the same formers, may be used. In either case the direct current should be supplied from a high-impedance source, so that the alternating current flowing through this source is negligibly small. At high magnifications the electrical shift should be kept as small as possible to minimize aberrations in the final lens. At low magnifications, where this is less important, the electlrical shift can be calibrated by direct comparison with known mechanical movement of the specimen. The calibration cannot be carried out once and for all, since it depends on the value of the eht2 voltage and on the distance of the specimen from the final lens. It should, however, be independent of magnification for a given set of conditions and for a particular point on the specimen. 3. The Collector and Head Amplifier. The secondary current leaving the specimen has an order of magnitude of A and so small a current cannot be amplified by conventional methods wit houi the introduction of excessive noise. In McMullan’s microscope the difficulty was overcome by the use of an electron multiplier with beryllium-copper dynodes and this arrangement was subsequently used by Smith (15). In more recent scanning microscopes the electron multiplier has been replaced by a scintillator and photomultiplier and this combination has been found to have many advantages over the earlier device. The chief defect of the electron multiplier is that it is necessarily a rather bulky component which cannot conveniently be mounted very close t o the specimen and therefore is not a very efficient collector of the secondary electrons. Furthermore, the secondary emission coefficient of beryllium-copper alloy is not very high and a proportion of the electrons striking the first dynode produces no secondaries. Thus, additional noise is added to the signal. For these reasons we shall not give further consideration to the electron multiplier. A satisfactory detector using a scintillator and photomultiplier has been developed by Everhart and Thornley (17) and the arrangement of the scintillator head for the detection of relatively slow secondary electrons is shown in Fig. 5. The detector consists of a cylindrical metal shield which is closed a t the end facing the specimen by a grid of copper gauze and is biased positively with respect to the specimen to attract the low-energy electrons. Once through the grid these electrons are accelerated toward a hemisphere of plastic scintillator, which is covered with a layer of aluminuni about 700 A thick. This layer is maintained a t a positive potential of 7 to 12 kv with respect to the specimen. The intense electrostatic field, shaped by the focusing ring, causes most of the electrons to strike the
198
C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
hemisphere near its apex. The light generated in the scintillator is guided by a Perspex light pipe to a photomultiplier which converts the light back to an electronic signal and provides most of the required amplification. When necessary the light pipe can be bent to facilitate the mounting of the scintillator head in any desired position, and the photomultiplier can be kept outside the evacuated specimen chamber. The plastic scintillator used was of the type developed commercially for the detection of beta particles and its sensitivity t,o electrons with energies of the order of 10 kv was found to depend critically on surface treatment. Good sensitivity was obtained by water-cooling the plastic while it was being machined and by subsequent polishing with French chalk and water. More efficient scintillators such as zinc sulfide could
ff +200-500v ALUMINIZED
1 \I -
PHOTO CATHODE
SCINTILLATOR
FIG.5. The secondary electron collector using a positive biased plastic scintillator, light pipe, and photomultiplier for low-noise, high-gain, and wide-bandwidth detection (from Smith, 16).
undoubtedly be used, but it would then be less easy to obtain uniform response over a wide area of scintillator and to arrange for efficient transfer of the light from the crystal to the light pipe. Everhart and Thornley (17) carried out a detailed investigation of the efficiency of the light pipe. They found that, although bends did not seriously impair the transmission, considerable loss of light could occur if extreme care was not taken with the surface finish. Loss could also be caused by reflection a t entry to and exit from the light pipe and by absorption at points where the pipe was supported. The final conclusion of these investigators was that, so long as the accelerating voltage applied to the detector was greater than 10 kv, substantially noise-free amplification of the initial electron current could be obtained. They also estimated the bandwidth of the system to be greater
S C A N N I N G ELECTRON MICROSCOPY
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than 10 R/Ic/sec and found that the scintillator showed no sign of saturation until the input current density reached about 1 A/cm2-figures greatly in excess of any likely to be encountered in the scanning electron microscope. With the arrangement described above the detector will collect and amplify the electrons leaving the specimen with relatively low energies, say, less than 50 ev. There is, however, another group of secondary electrons consisting of those primaries which have been reflected with relatively little loss of energy. These will not be appreciably deflected by the potential difference of a few hundred volts applied between specimen and collector and will therefore not enter the collector unless the latter happens to be directly in their path. Thus, with the arrangement of Fig. 5 , the output signal is derived largely from the low-energy secondaries. The high-energy reflected electrons do, however, contribute more to the signal than one might expect because some of them strike the surface of the final lens and there produce secondaries which are drawn into the collector. I n a particular experiment (18) 65% of the output signal was found to result from secondaries produced at the specimen, 5% from reflected electrons entering the collector, and 30% from indirect secondaries liberated at surfaces other than that of the specimen. These proportions would be expected to depend markedly on the precise geometrical arrangement of the specimen and collector and on their potentials with respect to the lens. We shall see later that there are occasions when we wish to obtain a signal from the high-energy reflected electrons while ignoring the lowenergy secondaries. This can readily be done by removing the outer box from the detector and keeping the scintillator at the potential of the specimen or slightly below it. The light output from the slow electrons can then be made negligibly small. Furthermore, with the outer box removed, the scintillator can be placed sufficiently close to the specimen to detect a reasonable proportion of the fast electrons and thus to ensure a satisfactory output ~ i g n a l . ~
4. Magnijication Control. The magnification produced in the scanning electron microscope is determined principally by the ratio of currents flowing in the deflector coils of the microscope coluinn and the cathoderay tube, respectively. It is also affected by the eht voltages applied to microscope and cathode-ray tube, and by the distance from the specimen a The box to be removed is the electrode kept at a positive voltage when collecting secondary electrons as shown in Fig. 5. If only high-energy reflected primary electrons are required, then the positive bias voltage serves no purpose and the solid angle can be increased by removing this box and positive electrode and placing the scintillator much closer to the surface.
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to the final lens. Since the specimen is inclined to the electron beam, this distance depends on the particular area under examination and is not usually known with any precision. For these reasons it is not a simple matter to design a magnification control which can be calibrated once and for all. It is, however, possible to construct an attenuating network by means of which the ratio of the currents in the two sets of deflector coils can be varied in accurately known steps. Then, under any given set of operating conditions, the magnification can be varied in a similar known manner. If, in addition, the specimen is mounted on a carriage actuated by a micrometer head, a direct comparison can be made between the actual size of any convenient feature of the specimen and the size of the corresponding image, when the magnification is sufficiently low. Calibration at any higher magnification then follows from the known properties of the attenuating network. During the preliminary examination of a specimen it is usually convenient to work with a low value of magnification, so that a large area can be covered quickly to select features of interest. Thus the lowest magnification obtainable is of considerable interest. Since the size of the final image is fixed, low magnificat,ion implies large deflection of the electron beam in the microscope and, at sufficiently low values, this beam will strike the edge of the aperture of the final lens. To some extent this difficulty can be overcome by increasing the distance between lens and specimen and hence the focal length of the final lens, though this increases the aberration coefficients and obviously cannot be taken too far. In practice, a lowest magnification of about 30 can be achieved without running into other difficulties. 5 . Miscellaneous. One of the major advantages of the scanning electron microscope over more conventional instruments is that it permits operations to be carried out on the specimen while the latter is under observation. I t is therefore convenient to provide the scanning instrument with a large specimen chamber which can accommodate any ancillary apparatus that may be needed. The chamber should also have as many ports as possible, through which connections to external apparatus may be led. It should be bolted rigidly to the final lens to reduce trouble from mechanical vibration. There is much to be said for designing the microscope with the specimen chamber at the top, since this greatly facilitates setting up auxiliary apparatus. The principal disadvantage of this arrangement is that, unless particular care is taken, dust and dirt may be dropped from the specimen chamber into the lenses. So far as the operation of the microscope itself is concerned, a pressure between 10-4 and 10-6 Torr is low enough, but it is sometimes necessary
SCANNING ELECTRON MICROSCOPY
20 1
to keep tEe specimen in a better vacuum than this. Since the main column is connected to the specimen chamber only through the very small aperture of the final lens, there is no difficulty in providing additional pumping t o keep the pressure in the chamber below that in the column. I n work so far reported pressures down to lo-% Torr have been achieved and there is no reason to doubt that ultrahigh vacuums can be maintained in the specimen chamber when necessary. To obtain micrographs at the highest magnification, exposures as long as 5 minutes may be needed, so power supplies must have adequate stability over such periods. The eht and the lens current supply should be stable to 4 parts and 2 parts in lo6, respectively. For the photomultiplier and cathode-ray tube supplies, a stability of 0.1 % is usually adequate and is easy to provide. Details of the column of a scanning microscope constructed in accordance with the principles explained above are given in Fig. 6, while Fig. 7 shows the external appearance of a commercial microscope manufactured by the Cambridge Instrument Company Ltd.
D. Factors A flecting Contrast in the Scanning Electron Microscope I . Introduction. The strength of the signal which controls the brightness of any point of the final iniage in a scanning electron microscope depends in a complicated manner on a number of factors which have been considered by Everhart,, Wells, and Oatley (18). As we have already seen, the collector can be arranged to give a n output signal resulting principally from slow electrons with energies of a few tens of electronvolts or, alternatively, from fast electrons with energies of the order of 20 kev. We should expect the contrast mechanism to be different in the two cases, which must therefore be considered separately, and it is convenient to refer to the slow group of electrons as secondaries and to the fast group as reflected electrons. The most important difference between the two groups arises from the fact that the paths of the reflected electrons from specimen to collector are substantially straight, while those of the slow secondaries are governed by the applied electric field and are usually sharply curved. It follows that reflected electrons traveling directly to the collector cannot reveal detail of any part of the specimen from which there is not a straight-line path, while secondary electrons are not subject to this limitation. Thus secondary electrons provide far more detail when a rough surface is under examination and it is normally advantageous to set up the collector to detect the secondaries and to ignore, as far as possible, the reflected electrons. Quite apart from the greater amount of informa-
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FIQ.6. A high-resolution scanning electron microscope producing an electron probe size of 5C100 A (Pease a,nd Nixon, ?‘a).
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tion which they furnish, th e secondaries usually give a larger total signal and thus a better signal-to-noise catio. Reference has already been made to indirect secondaries produced b y impact of reflected electrons with surfaces other than that. of- the specimen, The way in which these electrons affect contrast has not been investigated, but we should expect them to behave in much Thhe'Bame way as reflected electrons from the specimen. I n the present discussion they will be ignored.
FIG.7. A commercia.1 scanning electron microscope manufactured by the Cambridge Instrument Co. Ltd., Cambridge, England.
Occasionally it, is desirable t,o oblain the output, signal from reflected electrons. This is particularly the case when the surface of the specimen is subject to electric or magnetic fields which would impair the detection of the slow secondaries. For example, if the specimen were a good insulator, the primary electron beam might cause it to become charged and the amount of such charging that, could be tolerated would clearly be greater with reflected than with secondary electrons.
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A second, less important, difference between the images produced by secondaries and by reflected electrons, respectively, is that greater contrast is usually obtained with the latter. This difference is exhibited in the two micrographs of an etched aluminum surface reproduced in Fig. 8,
FIG.8 (a). An etched aluminum surface using the secondary electrons, showing detail within the pit since the secondaries are attracted to the collector (18).Magnification = 2500X.
which also shows the greater detail obtained from the use of secondary electrons. 2. Contrast Resulting jrom Sugface Topography. Whether one is working with reflected electrons or with secondaries, the most important single cause of change in signal strength from point t o point of the speci-
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men is the variation in the angle between the incident electron beam and the local normal to the surface of the specimen. For reflected electrons this effect was investigated by McMullan (8),using objects consisting of various metals with polished surfaces. He concluded that the effect was
FIG.8 (b). An ctched aluminum surface using reflected primarietl only, with loss of detail except an the flat surface (18). .Magnification = 25OOX.
large enough to account for t,he contrast, which he observed in his scanning microscope. Similar experiments have since been carried out by Everhart el al. ( I @ , using secondary electrons. From these results it appears that a n alteration in surface inclination of only one or two degrees would generally be sufficient to cause a n appreciable change in brightness of the final image.
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With a rougher surface, additional contrast may result from the shadowing of one area by another or by the failure of electrons from a pit to reach the collector. These effects are all displayed in the micrograph of a germanium surface shown in Fig. 9. It will be apparent that there is a close analogy between the above
FIG.9. Surface of a germanium crystal showing contrast from surface topography only (18).Magnification = 650X.
mechanisms of contrast formation and that which operates in the case of an optical image observed by the eye, with or without the interposition of an optical microscope. I n both cases the brightness of a n area of tJhe image is largely determined by the inclination of the corresponding area of the object to the incident beam of light or electrons. This analogy is of the greatest importance because it causes the pictures produced by
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the scanning electron microscope to be very similar in appearance t o those obtained with a low power optical microscope. Since the eye is accustomed to interpret the latter in terms of a three-dimensional object, it can do so equally well with the former and this adds greatly to the value of scanning electron micrographs. 3. Contrast Resulting from the Chemical Nature of the Specimen. When secondary electrons are used to produce the output signal the brightness of any point of the image is proportional to the secondary emission coefficient of the corresponding point of the object, so contrast can result from variation of this coefficient over the surface of the specimen. For most materials the secondary emission coefficient is not very different from unity and the effect that we are considering is not of much importance. It can, however, provide useful information when we wish to examine surfaces with areas where the coefficient is abnormally high. The effect is less valuable than one might expect because of the difficulty of distinguishing between highlights caused by high secondary emission and those resulting from raised portions of the surface-and between holes in the surface and areas of low secondary emission. When the collector is arranged to give an output signal dependent on reflected rather than secondary electrons, the case is different. Palluel (19) and Sternglass (20)have shown that the proportion of electrons reflected increases with the atomic number of the material of the specimen, so, with a specimen containing different materials, we should expect correspondingly different mean levels of brightness in the final image. These average brightness levels would be superimposed on the point-topoint variations resulting from surface topography. The validity of this expectation has been confirmed b y Wells ( I S ) , who used a n artificial specimen made by forcing a brass rod into a duralumin tube, turning the end square, and grinding it with emery. The surface finish was thus approximately the same for the two metals and the additional contrast resulting from the difference of material was plainly visible. When the collector was set to record secondary electrons, the additional contrast was less marked. Hitherto, in scanning electron microscopy little use has been made of‘ contrast obtained in this way. However, if it is desired to identify elements with a resolution better than that which can be obtained with the scanning X-ray microanalyzer (-1 p ) , this type of contrast may be of considerable importance.
4. Contrast Resulting .from Potential Variations on the Surface of the Specimen. When the collector is set to record secondary electrons a high proportion of the output signal comes from electrons which leave the
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specimen with energies of only a few electron-volts. The trajectories of these electrons are sharply curved and depend very markedly 011 the potential of the specimen relative to those of the final lens and the collector. A set of such trajectories obtained with a large-scale model in a n electrolytic tank is shown in Fig. 10; it relates to electrons leaving the specimen along a normal to the surface with initial energies of 4 ev, for various values of specimen potential. From these curves it is clear that, if the entrance aperture of the collector is restricted to a slit, the potential of the point from which an electron leaves the surface will determine whether this electron enters the collector or not. Thus any variations of potential over the surfare of the sperimen will result in corresponding
FOUR VOLT ELECTRON TRAJECTORIES S PEClMEN VOLTAGE VARIABLE
FIG. 10. An electrolytic tank plot of the 4-volt electron trajectories when the specimen voltage is varied as shown (18). The collector is placed between M and N.
areas of light arid shade in the final image and the curves suggest that a potential difference of 0.,5 volt or less should give detectable contrast. The sensitivity will depend on the width of the collector aperture and this cannot be made too small without causing an unacceptable loss of signal strength. Such a loss can be made good by increasing the size of the aperture in the final lens and consequently sacrificing resolution so, in any given case, a compromise must be reached between resolution aiid sensitivity to potential variations. These conclusions are borne out b y practical experience with the microscope, from which i t appears that potential differences considerably less than 1 volt can be detected without appreciable loss of resolution. The location of the collector aperture is of great importance and the best position, for any given arrangement of specimen and collector, must be found by trial.
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The ability to detect potential variations on the specimen surface is one of the most valuable features of the scanning electron microscope. Examples of its use are given later. It is perhaps worthwhile to mention that attempts t o detect contrast resulting from magnetic domain structure in the specimen surface have hitherto proved unsuccessful. Magnetic fields a t the domain boundaries must exist in the region imniediately above the surface and it would be of great interest if the influence of these fields on the secondary electrons could be used to locate the boundaries. The problem has been investigated in considerable detail by Thornley (26), who concluded that the fields are too small to provide detectable contrast.
E. The Effects oJ’ Penetration o j Incident Electrons into the Specimen It has previously been assumed that the resolution in a scanning electron microscope is limited by the diameter of the incident probe beam,
-2
(a)
-I
0
I
2
(b)
FIG. 11. (a) Spreading of the electron beam after entering the specimen surface. (b) Distribution of the secondary electrons over the surface of the specimen as a function of the distance r from the point of entry of the primaries. a is defined in Eq. (19). (From Everhart et al., 18.)
but this would only be true if the incident electrons did not penetrate into the specimen. I n fact, using the results of Terrill ( d l ) , we may estimate the range of a 20-kev electron in an average solid to be of the order of lo4A and we must now consider what effect,s this is likely to cause. The problem has been studied by Everhart, Wells, and Oatley (18) and their conclusions are summarized below. Suppose the incident beam to be of zero cross-sectional area and let it be incident normally on a smooth specimen surface. Suppose also that only slow secondary electrons cont,ribute to the output signal. As the primary electrons enter the solid they will be deflected and will lose energy. Thus the beam will spread and, before the electrons have lost the whole of their initial energy, they will have occupied a roughly pearshaped volume, as shown in Fig. l l (a).
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Along the path of the primary electrons secondaries will be generated and some of these will travel toward the surface. These, also, will lose energy as they go and, following Bruining (22), it is assumed that the number N of those that, after traveling a distance x from their point of origin, retain sufficient energy to penetrate the surface potential barrier is given by an expression of the form
where 01 is a constant. Experimental results obtained by Becker (23) and, more recently, by Sternglass and Wachtel (24) suggest that 01 is almost certainly greater than 0.01 A-I. Thus, although primary electrons may penetrate some lo4A into the specimen, nearly all of the secondaries which escape through the surface will have originated within about 100 A of the surface and, within this distance, the spread of the primary beam is small. Moreover, the primary beam loses only a negligible fraction of its initial energy in traveling through this distance. Using a simple model based on the above ideas it is possible to calculate the distribution of the secondary electrons over the surface of the specimen as a function of the distance r from the point of entry of the primaries. The result,ing curve is shown in Fig. l l ( b ) , from which it appears that rather more than half of the secondaries are emitted within a distance of +a of the point of entry of the primaries, that is, within a distance which is probably less than 50 A. It is not easy to state exactly what effect this distribution will have on contrast and resolution, but the following considerations are relevant. When the primary beam, still assumed to be of negligible cross-sectional area, falls on a point of the specimen, the brightness of the corresponding point of the image depends on the number of secondaries reaching the collector and is independent of the paths by which they travel. I t has already been stated that contrast results largely from variations in the inclination of the surface to the primary beam, so the number of secondaries must also depend strongly on this inclination. However, the number of electrons excited in the solid per unit length of the primary beam must be almost independent of the inclination, so the variation in the number of secondaries results from changes in the distances that excited electrons must travel before reaching the surface. When the surface is plane, or nearly so, these distances are governed by the inclination of the incident beam, and the distribution of the secondaries over an area of dimensions of the order of l / a should not have much effect on contrast or resolution. In practice, the incident beam will have a finite area of cross section and
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21 1
the electron distribution over this area will probably be Gaussian, but the same general principles will apply. When the surface is irregular the situation is much more complicated, for, in this case, any part of the pear-shaped volume depicted in Fig. 11(a) might lie sufficiently near to the surface to contribute secondary electrons. Whether or not it does so depends on the nature of the surface irregularities. We can thus divide the secondary electrons reaching the collector into two groups. Those in the first group are the ones generated in the immediate vicinity of the point of entry of the primary beam; as in the case of a plane surface, their number will depend largely on the local inclination of the surface to the primary beam and they will contribute useful information in the usual way. The second group contains those electrons which, if the surface had been plane, would not have been released at all and their existence depends on the presence of suitable irregularities at point,s more or less remote from the point of entry of the primary beam. In general these electrons can give no useful information about the surface at this point and their contribution to the output must be regarded as noise rather than signal. They are likely to impair resolution and distort contrast. An extreme form of the effects just described may arise when the specimen surface contains asperities which are so thin that the primary beam can pass right through them and emerge with sufficient energy to generate further secondaries at another part of the surface. When this happens the asperities may appear in the final image as though they were partially transparent, with other parts of the surface showing behind them. A further complication is the production of secondary electrons by reflected electrons. The latt,er result from the large deflections which can occur when primary electrons pass near atomic nuclei. In themselves they are of no importance in the present context, since it has been assumed that the collector has been set to ignore them. However, on their way to the surface, they generate secondaries and the number of these that can escape depends on the path of the reflected electron and the form of the surface irregularities. Neither of these factors is directly related to any property of the surface at the point of entry of the primary beam, so these secondaries also contribute to noise rather than to useful signal. At high magnifications, when the diameter of the incident beam is of the order of 100 A, they may account for about half of the total secondary current. At lower magnification, when the escape area of these electrons does not exceed the dimensions of a picture element, they may contribute usefully to the signal.
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F . Practical Limits of Resolution It was shown in Section 11, B, 6 that, so far as lens aberrations are concerned, resolution of features with dimensions less than 100 A should be possible. However, it is clear from Section 11, E that, in this range, penetration of electrons into the specimen may set a limit to what can be achieved. Reasons have been given for expecting that penetration effects will be least serious when the specimen surface is smooth, but such specimens tend not t o be the ones where optimum resolution is required. It is clearly difficult t o arrive a t any simple conclusion which will be of general application. On the experimental side, a careful investigation of the problem has been reported by Pease (18). I n his instrument the electron probe diameter, measured in transmission, was 70 k 15 A a t a beam voltage of 15 kv and 50 _+ 10 A at 30 kv. The finest particle-to-particle resolution achieved was 100 k 20 A and, for a specimen showing normal topographical contrast, the corresponding figure was 150 30 A (Pease and Kixon, 7a). These values are in general agreement with those arrived a t on theoretical grounds and probably represent the best performance to be expected with favorable specimens. A more realistic figure for average specimens might be 200 A. The above statements refer to the use of the scanning electron microscope with electrons collected from the front surface of the specimen. With sufficiently thin specimens it is, of course, possible to use the scanning technique and to collect transmitted electrons. This arrangement has not hitherto been used to any great extent since specimens of this kind can readily be examined, at, higher resolution, with a conventional transmission electron microscope. However, if the scanning technique is used in transmission, with a n energy analyzer (85), a different method of obtaining contrast is brought into play. Preliminary work along these lines, using a field-emission source and quadrapole lenses, has been briefly reported by Crewe (85a). 111.
TECHNIQUES AND
APPLICATIONS
A . Intyoduction Although the scanning electron microscope has already proved its value in the solution of a considerable number of research problems, it is still, in its modern form, a relatively new instrument. I n the following Sections a n account is given of the more important techniques and applications that have so far been established; there is no reason t o doubt,
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that, as more microscopes become available, the range of usefulness of the instrument will be greatly extended. It should perhaps be emphasized that the scanning microscope is in no sense a competitor of the conventional transmission instrument. When the latter can be applied to a problem, its superior resolving power will almost always malie it the preferred instrument. Many cases arise, however, in which the scanning microscope can be used, while the other is ruled out for one reason or another. In several of these, resolving power is of secondary importance; the features of the scanning microscope which make it valuable are (i) Its ability to examine a surface directly with large depth of field. (ii) The easy access to the specimen due to the long working distance and the positioning of the specimen rhamber a t one end of the electron optical column. (iii) The ability to detect potential variations on the specimen surface. Other spccimen properties which can be examined with the scanning electron microscope will also be illustrated in the examples which follow.
B. Stereoscopic Pairs o j Micrographs Mention has previously been made of the “three dimensional” akipearance of scanning electron micrographs, which greatly aids their interpretation. With suitable specimens it is worthwhile to make full use of this property by taking stereoscopic pairs of micrographs, to be examined through a viewer in tEe usual way. A good deal of work on these lines bas been done by Smith (15) in connection with investigations on the fibers in wood pulp, and by Stewart, (26). Before considering how stereo pairs of micrographs may be produced, it is @ellto point out that me are here concerned with a process in which en illusion of three dimensions is created by supplying the observer with information which he interprets in a manner conditioned by his experience in dealing ui t h three-dimensional objects. To secure a good illusion it is therefore important that the informat ion supplied by the micrographs should resemble as closely as possible the information supplied by the observer’s eyes when looking at three-dimensional objects. One important difference between micrographs obtained with the scanning electron microscope and images formed by human eyes arises from the follov,ing facts. In the latter case the object is generally illuminated with light coming from all directions but, of the reflected light, only a narrow cone in a particular direction enters each eye. I n the scanning microscope, on the other hand, the incident electron beam is confined t o a narrow cone, while electrons leaving the specimen are collected over a
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C. W. OATLEY, W. C. NIXON. AND R. F. W. PEASE
much wider angle. As a result, the micrograph represents the view of the specimen that would be seen when looking along the incident electron beam; the direction in which the collector lies is largely irrelevantparticularly so, since electrons travel to it from the specimen in curved paths. It follows that, in making stereo pairs, it is the angle between the incident electron beam and the specimen that must be varied. We now consider various ways of doing this. In Fig. 12, DO is the direction of the incident electron beam. The mean plane of the specimen surface is normal to the plane of the paper, which it intersects in the line AB. As previously explained, it is usually convenient to make 0 about 30" to allow space for the collector, which is not shown in the diagram. Thus the view shown in the micrograph is that D
FIG.12. Stereoscopic diagram: Electron beam, DO; specimen, AB; axis of rotation, 0s.
obtained by looking along DO and there is a foreshortening of all surface distances parallel to the plane of the paper. One common method of making stereo pairs is to vary the angle 0 by from 2" to 15" between successive exposures. When such a pair is placed in a viewer, a good three-dimensional effect is obtained, but the illusion is not perfect, for the following reason: Suppose an observer is asked to look at an approximately plane surface, without the intervention of any optical or electron-optical device, and wit,h the proviso that, the surface must lie at a n angle of about 30" from the vertical plane containing his eyes. The natural way of meeting this proviso is to hold the surface in such a way that it intersects the vertical plane containing the eyes in a horizontal line, with the top of the surface further from the eyes than the bottom. This is a common way of looking at a surface and the eyes have no difficulty in interpreting what they see. However, when a stereo pair is made by the method described above and the two micrographs are placed side by side in a viewer, the result, is as if the surface were inclined so as to intersect the vertical plane containing the observer's eyes in a
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vertical line. One is looking a t a surface sloped sideways and, although the three-dimensional effect is obtained, the result is not quite natural. If the specimen is extremely rough, a mean surface plane does not exist and the above difficulty largely disappears. The arguments just put forward suggest that a better way of making a stereo pair would be to rotate the specimen through a small angle about the axis PQ in Fig. 12, between successive exposures. So far as is known this method has not been used because the specimen stage usually provided does not allow rotattion about this axis. An alternative method which has been used quite extensively is to rotate the specimen through a small angle about the axis 0s in Fig. 12, a movement for which the specimen stage generally makes provision. This can be regarded as a combination of rotations about DO and PQ, respectively, of which the latter is the one that is wanted. At first sight the rotation about DO can be ignored, since it does not change the aspect of the specimen as seen along the incident beam. However, it does change the position of the specimen with respect to the collector and this is likely to alter the appearance of the final image in some way, though it is not easy to say what the change will be. As a result of this unwanted rotation it is sometimes found difficult to secure satisfactory registration of the two micrographs of a pair, when they are placed in a viewer. The effect is not usually serious if the rotation about 0s does not exceed 10". It is occasionally necessary to make quantitative measurements of topographical features on the surface of a specimen. The way in which such information can be extracted from a stereo pair of micrographs, using techniques similar to those employed in aerial photographic mapping, has been considered b y Wells (27'). Tipper, Dagg, and Wells (%'?'a)have shown that the scanning electron microscope, when used in this way, is a most effective instrument for the examination of very rough surfaces such as those which occur when metallic crystals are fractured.
C. Low-Voltage Operation of the Microscope I n the description of the scanning electron microscope given earlier it was tacitly assumed that the instrument would be operated a t an eht voltage of 15-30 kv, since this appears to be the optimum value for good resolution. Occasions arise, however, when it is convenient to work a t voltages down t o 1 kv or lower and it is therefore of interest to consider what effect this is likely to have on the performance of the instrument. The problem has been investigated by Thornley (16, 27b) in connection with the examination of insulating specimens and most of the information which follows results from his work. The principal effects of changing from high-voltage to low-voltage
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working may be summarized as follows: (a) The effective wavelength of the electron beam is inversely proportional t o the square root of its voltage and will therefore increase. Diffraction will thus become more important. (b) The different lens aberrations will change in different ways, but the over-all effect of the aberrations will be greater at low voltages, so the resolving power of the microscope will be impaired. (c) The theoretical maximum current density which it is possible to achieve in the electron probe is proportional to the voltage and so will decrease. Practical electron guns fall short of the theoretical performance to a n extent depending on their design and there is no reason that a properly designed low-voltage gun should be significantly worse than one intended for use at high voltages. However, it is not always convenient to fit a new gun when changing the voltage and it may well happen that a gun designed for use at, say, 20 kv is used a t much lower voltages. In such cases a still further reduction in the current density of the probe is to be expected. Moreover, the size of the crossover will be increased. (d) For many materials the secondary emission coefficient (for slow secondaries) reaches a maximum value for a n incident energy of a few hundred electron-volts and falls at higher energies. Thus, if the detector is set to collect slow secondaries, the signal strength for a given incident beam current should increase by a factor of the order of 5 when the eht voltage is reduced from 20 to 1 kv. On the other hand the generation of fast reflected electrons is a less efficient process at low voltages than it is a t high. Thus, with low-voltage operation, it is not profitable to derive the output signal exclusively from these fast electrons. (e) The penetration of the electron beam into the specimen is roughly proportional t o the square of the eht voltage and so will be greatly reduced. At 1 kv it is likely to be of the order of 100 A. This reduction may be important in improving the visibility of surface films on a specimen. (f) When solid specimens are under examination, almost the whole of the energy of the incident beam is dissipated in the specimen and, for a given beam current, this energy is proportional to the eht voltage. (g) With low-voltage operation, disturbances resulting from given stray magnetic fields become correspondingly more serious, so improved shielding is needed. (h) At sufficiently low voltages space charge must cause a broadening of the electron probe. However, a rough calculation shows that this effect is likely to be negligible unless voltages well below 1 kv are used. Consideration of the above factors suggests that a resolution of less
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than 1000 A should be possible even when the eht voltage is reduced to as low as 1 kv. This expectation has not yet been realized in practice, but relatively little work under these conditions has so far been carried out. The best resolution reported by Thornley for 1-kv operation is 2000 A : this, however, was obtained with an instrument which was not designed for low-voltage working and some of the causes of the poor result were well understood.
D. The Examinatzon of Insulating Specimens Although the beam current in a scanning electron microscope is usually of the order of lo-" A, this is sufficient to cause intolerable charging of insulating specimens if no precautions are taken. The onset of charging is characterized by loss of resolution and the appearance in the image of irregular bright patches within which no detail can be distinguished. The simplest way out of the difficulty is t o give the specimen a thin evaporated metal coating, but occasions arise when this does not provide a satisfactory answer. For example, it was desired to study the effects of abrasion on certain synthetic fibers. They were coated with metal in the usual way and mounted in the microscope and it was then found that any attempt t o manipulate them caused the coating to crack and charging t o take place. An attempt was made to neutralize the charge by spraying the specimen with positive ions, but the result was unsatisfactory and the work was discontinued. If the charging is not too severe, fairly satisfactory micrographs may often be obtained by setting the collector to derive the output signal mainly from the fast reflected electrons. For a given degree of charging these are deflected to a much smaller extent than the slow secondaries would be, but the procedure involves a serious loss of signal strength and, moreover, the incident electron probe may be distorted by the field between the specimen and the final lens. A better technique, which has been examined in some detail by Thornley (I@, depends on the fact that, for most, insulators, the secondary emission coefficient is greater than unity over a range of energies of the incident beam in the region of 1-2 kev. The operating voltage of the microscope is therefore reduced to a value for which the coefficient exceeds unity for all points on the specimen surface. This prevents negative charging but, since the surface is not necessarily uniform, there will be some parts of it which tend to charge positively. However, this process cannot go far since, as soon as the potential of a n area rises more than one or two volts above that of its surroundings (e.g., the final lens), the
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C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
slowest secondary electrons will be held back so that the effective coefficient is reduced to unity. Thus the whole surface is stabilized a t a potential not very different from that of its surroundings. The above procedure reduces the number of t,he factors which can contribut)e t,o contrast in the final image. Witjh conducting specimens, tJhe
FIG.13. Freshly fractured insulating ceramic surface observed at 1.5 kv without charging (2%). Magnification = 3700 X.
electron current passing from specimen t o collector may be affected by the chemical nature of a particular area of the specimen or, more especially, by its inclination tto the incident, beam. With insulators, neither of t,hese mechanisms is operative since the effective secondary emission coefficient is unity for every point of the specimen. Thus cont'rast can arise only from variations in the efficiency with which electrons are collected from different areas. This efficiency is unlikely to vary very much over areas
SCANNING ELECTRON MICROSCOPY
219
that are turned away from the collector, so there should be no contrast and therefore no observable detail within these areas. This is found to be the case. The scanning electron microscope used in the way just described has proved to be particularly useful in the study of ceramics, since alternative
Fro. 14. Inside of the 50-p bore of a spinneret used for producing nylon (28). Collector placed below the hole. Magnification = 2500X.
methods are not very satisfactory. Freshly fractured surfaces are too rough for optical examination or for the preparation of replicas for transmission electron microscopy, and polishing is a tedious process which often produces surface conditions which are not characteristic of the bulk material. A scanning electron micrograph obtained by Thornley (27b) is shown in Fig. 13.
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C. W. OATLEY, W. C. NIXON, A N D R . F. W. PEASE
E. The Examination of a Nylon Spinning Jet A typical nylon spinneret consists of a platinum plate about 100 p thick in which are a number of holes perhaps 50 p in diameter. T o check the cleanliness of the spinneret it is necessary to examine the inside surfaces of the bores and this is a problem t o which conventional techniques do not give a satisfactory answer. An optical microscope has not sufficient depth of field and it is difficult. to collect enough light from the surface under examination. The preparation of a replica for transmission electron microscopy would clearly not be easy. The possibilit,y of using a scanning electron microscope for specimens of this kind has been investigated by Wells (28). At first he tried the
FIG. 15 (a). Point-contact rectifier formed by placing an etched tungsten wire against a germanium surface. Wire in contact (7b). Magnification = 2000 X .
SCANNING ELECTRON MICROSCOPY
22 1
normal arrangement of the collector, so that the signal was produced by secondary electrons emerging from a bore on the same side as that through which the incident beam had ent,ered. This gave a good image of the lip of the hole, but provided no detail of the surface further down the bore, since too few of the secondary electrons were then reaching the collector. This difficulty was overcome by placing the collector to record secondary electrons which had passed through the bore and had emerged on the far side-an arrangement which is possible because the final image is independent of the paths by which the electrons pass from specimen to collect or. A micrograph obtained by this technique is shown in Fig. 14.
FIG.15 (b). Point-contact rectifier formed by placing an etched tungsten wire against a germanium surface. Wire removed ( 7 b ) . Magnification = 2000X.
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C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
F. Forming Processes in Point-Contact Rectifiers A point-contact rectifier may be constructed b y mounting a tungsten wire, having tip dimensions of a few microns, so th a t it presses on the surface of a piece of suitably doped germanium with a force of between 5 and 30 gm. The combination is then subjected to a forming process in which a pulse of current is passed through it. Rectifiers of this type have been largely superseded by p-n junction devices, but they were of importance a few years ago and considerable interest then centered on the forming process, which was not completely understood. Smith (29)has shown that the scanning electron microscope can be put to good use in investigations of this kind. He mounted the germanium pellet in the specimen c'iamber of the microscope and constructed a mechanical device by means of which the tungsten wire could be lowered on to the pellet, with known force, b y manipulation of control knobs outside the chamber. Any deformation of the point could be observed with the microscope. Next, the forming current could be passed through the rectifier and the voltage/current characteristic measured. Again any change in the outward appearance of the rectifier could be observed. Finally, the point could be lifted from the germanium to permit examination of the surface of the latter, Micrographs obtained by Smith are reproduced in Fig. 15.
G. The Investigation of Potential Variations on the Surface OJ a Specimen
It was shown in Section 11, D, 4 that contrast is caused by variations in potential on the surface of a specimen and this fact has been used by Oatley and Everhart (SO, 3Oa) in a study of p-n junction diodes. The diode was given a reverse bias of one or two volts and the p and n regions then had quite different brightnesses in the final image. This difference disappeared when the bias was removed. Typical micrographs obtained in this way are reproduced in Fig. 16. A rather different study of a p-n junction has recently been reported by Spivak et al. (31). Reverse voltages of the order of 200 volts were used and conditions of operation were such that the collector output signal was derived chiefly from fast reflected electrons. I n this case the electrons were appreciably deflected only in the high-field region of the depletion layer of the junction and, as shown in Fig. 17 (sou),it was only this region of the final image which showed any change of brightness when the reverse voltage was applied. Even when the output signal is derived from slow secondary electrons,
SCANNING ELECTRON MICROSCOPY
223
the aperture and position of the collector may be so chosen that brightness in the final image depends on the tangential electric field at a point on the specimen surface rather than on the absolute potential of this point. This has been demonstrated by Thornton, Culpin, and Drummond (32), who used a scanning electron microscope to investigate potential variations in a specimen of high-resistivity gallium arsenide. Earlier work had ehown that the electrical properties of this material can be affected by
FIG. 16. Germanium-indium p-n junction showing the black and white voltage contrast across the junction when a bias is applied (18). (a) 3-volt bias, magnification = 1,400X; (b) 1-volt bias, magnification = 9,OOOX. The length of the white rectangle in (a) is lob, (b) 1.5~.
the distribution of dislocations and it was found possible to correlate this distribution with potential-probe measurements and with brightness variations in electron micrographs of the type shown in Fig. 18. These authors concluded that the scanning electron microscope was sufficiently sensitive to detect field differences of about 200 volts/cm in regions with dimensions of the order of 4 x cm.
H . The Examination and Fabrication of Integrated Circuits The scanning electron microscope is an excellent tool for the nondestructive examination of integrated circuits. If voltages are applied
224
C . W. OATLEY, W. C. NIXON, A N D
R. F. W. PEASE
to the elements of the circuit while they are under examination, the resulting potential variation can be explored as explained in Section G and, in this way, short circuits, open circuits, or thin spots in evaporated aluminum leads can be locat,ed and the positions of p-n junctions can be determined with high precision.
FIG.17. Junction diode ( 3 1 ) . Top, 200-volt bias; bottom, zero bias. Arrow shows the junction position. Magnification = 150X.
A second method of locating p-n junctions in a n integrated circuit has been described by Everhart, Wells, and Matta (33). When a n electron beam falls on a semiconducting device, secondary electrons are produced and a n output signal from the collector is obtained in the usual way. I n addition, however, t,he primary beam generates hole-electron pairs which diffuse to the electrodes of the device and if these electrodes are con-
SCANNING ELECTRON MICROSCOPY
225
FIG.18. Gallium arsenide junction relating the junction position to defects in the specimen (32). (a) Zero bias; (b) 300-volt bias. Magnification = 1OOX.
226 C. W, OATLEY, W. C. NIXON, AND R. F. W. PEASE
FIG. 19. An integrated microcircuit with various forms of voltage contrast ( 3 5 ) . (a) Voltsqe betn-ecn B and C only, 16 kv. (b) Signal from specimen current mixed with secondary electron signal, beam voltage lowered, and B now dark with respect to C. 12 kv. (c) As for (b) with beam voltage raised to 16 kv as in (a). (d) As for (b) ~ i t b2am h voltage raised to 20 kv. E a n d B now both dark. Emitter, base, and collectx regions are easily distinguished. N
trl
-a
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C. W. OATLEY, W. C . NIXON, AND R. F.
W.
PEASE
nected to earth through a high resistance, a second output signal becomes available. The strength of this second signal depends on the instantaneous position of the incident beam. If the hole electron pairs are generated in the depletion layer of a junction, all of them will contribute to the output signal. On the other hand, carriers generated a t a point remote from a junction may recombine before they are able to affect the output. Everhart, Wells, and Matta developed a technique in which the second signal is mixed with the ordinary collector signal in such a way as to modulate the brightness of the final image. This procedure is particularly effective in the examination of active devices where the active regions are beneath one or more layers of material (as in passivated integrated circuits). The extent to which the incident beam penetrates these layers depends on the voltage of the beam and, b y varying this, the second signal may be made t o give information about the separate layers. The method is well illustrated by the four micrographs of Fig. 19. I n Fig. 19(a), no second signal is used and the contrast results from the different potentials applied to the layers. I n Fig. 19(b), taken with a beam voltage of 12 kv, there is selective blackening of the base region where this is not covered by other layers, and the blackening is particularly intense near the baseemitter and base-collector junction. I n Fig. 19(c), taken at 16 kv, penetration of the emitter lead causes blackening of the base region beneath. Finally, at 20 kv, [Fig. 19fd)I there is appreciable penetration of the emitter region itself. Wittry arid Kyser (34) have described a third method for examining semiconductors with a scanning electron microscope. An infrared photomultiplier was used instead of the secondary electron collector; in this way radiation due to carrier recombination was detected and used to build up the image. In certain gallium arsenide specimens they were able t o observe dislocations and variations in impurity concentrations. Czaja and Wheatley (35) have reported the use of a scanning electron beam to detect dislocation slip patterns in silicon using electron beaminduced currents to build up the image. The scanning electron beam can also be used in the fabrication of integrated circuits. The orthodox method of forming in-contact masks (needed when selective etching or deposition is required) is to cover the workpiece with a thin film of photo-resist and expose the desired areas to ultraviolet light; on development only the exposed pattern remains. Wells and Matta (36) have demonstrated that the electron beam can also be used to expose the photo-resist. Pattern line widths down to 1 p have been achieved. More recently Broers (37) has demonstrated a line width of 0.25 p and used a flood beam of 5-kv argon ions as a n etchant to form, under the exposed pattern, ridges with a typical height-to-width ratio of 5: 1.
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I . Direct Observation o j Chemical Changes The normal decomposition of silver azide is of considerable interest in the study of explosives and has been investigated by simultaneous transmission electron microscopy and electron diffraction, using the electron beam itself to promote decomposition. The results showed that the decomposed azide had a particle size of the order of 0.1 p, whereas crystals which had suffered pure thermal deconiposition gave a particle size about 10 times as large. Attempts to resolve this discrepancy using a conventional transmission or reflection electron microscope were unsuccessful, but it seemed possible that the scanning instrument, with its very much lower beam current, might give useful results. A small silver hotplate, whose temperature could be measured with a thermocouple, was placed in the specimen chamber. The crystals of silver aside were mounted on it and given a light coating of silver to prevent the accumulation of electrical charge. It was found possible to obtain good micrographs with electron beam currents sufficiently small to have little effect on the crystals and a detailed investigation of the phenomena attending decomposition has been carried out b y McAuslan and Smith (38).Figure 20, which is taken from their paper,-shows a composite micrograph of a partially decomposed crystal, of which only one end is in close contact with theahotplate. Because of the resulting temperature gradient along the crystal, the process of decomposition could be studied without difficulty. Another example of the direct examination of the progress of a chemical surface reaction is provided by the oxidation of iron observed by Pease et al. (39). Samples of pure iron were heated in air in the specimen chamber of a scanning electron microscope. Between successive stages the surface was examined and the occurrence, distribution, and growth of spikes, whose diameter was a few hundred angstroms, was observed. The low power of the incident beam did not appear to affect spike growth (in the conventional electron microscope the spike tips melted). The occurrence of spikes appeared to be due to residual impurities at the surface. The oxide film itself was not flat but had a lumpy appearance; the hump height was about 0.25 p after 5 minutes of oxidation in air at 630°C.
J . T h e Activation Process in Dispenser Cathodes The hot cathodes used in microwave valves and similar thermionic devices are commonly of the dispenser type, in which the active material is enclosed behind, or embedded in, a metallic matrix. Before use, such cathodes must be subjected to a thermal activation process, during which an active layer is formed on the surface from which thermionic emission
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C. W. OATLEY, W. C . N I X O N , AND R. F. W. PEASE
takes place. What happens during the act,ivation process and what is the final emission mechanism are matt,ers still in dispute. Microscopic examintttion of the cathode surface at various stages might be expected to yield valuable information, but conventional techniques are fraught with difficulties. The optical microscope has small
FIG.20. Decomposition of a needle crystal of silver azide by heat from a hot stage and not from the electron beam (38).Magnification = 5000X.
depth of field and provides insufficient resolution; moreover, it is not, convenient to use this instrument when the specimen must be in a high vacuum and may be a t a high temperature. The conventional t,ransmission electron microscope can only be used by way of replicas and these are largely precluded because the cathode must not be exposed to air once it has undergone the activation process. Beck and Ahmed (40) have shown that these difficulties can be over-
SCANNING ELECTRON MICROSCOPY
231
come by the use of a scanning electron microscope. With this instrument it was found possible to keep the cathode in a vacuum of Torr and to observe its surface with a resolution of 200 A a t various stages of activation. The thermionic emission from the cathode could be measured at any stage and it was even found possible to obtsin micrographs of the surface
FIG.21. Tungsten-aluminate-impregnated tion = 2500X.
cathode before processing. Magnifica-
when the latter was at a high t'emperature. To do this it was necessary to prevent passage of light from the cathode to the photomultiplier and this was achieved by placing a n interference filter between the light pipe and the photomultiplier and by coating the light pipe and the scintillator with a thin layer of silver. Micrographs taken during this work are reproduced in Figs. 21 and 22.
232
C. W. OATLEY, W . C. NIXON, AND R. F. W. P E A S E
FIG.22. Tungsten aluminate-impregnated cathode when fully active therniionically (40). Magnification = 10,OOOX.
The microstructure shown in Fig. 22, which appears after thermionic current has been drawn from the activated cathode, had not previously been reported.
K . Investigation o j the Sputtering o j a Metal Surface by Positiue Ions An interesting example of the way in which a scanning electron microscope can be iiicorporated in apparatus for a particular piece of research is afforded by work carried out by Stewart (41) on the sputtering of metals by positive ions. The problem in this case was to observe the metal surface intermittently, during the progress of the sputtering, without exposing it to the atmosphere. The arrangement, of the apparatus is shown in Fig. 23. The positive
233
SCANNING ELECTRON MICROSCOPY
ions were formed in a convent ioiial radio-frequency source, were focused by electrostatic lenses, and projected through a small aperture 011 to the metal specimen which was mounted in the usual way in a scanning microscope. With differential pumping and apertures to separat>ecomponent Cold Trop
ION SOURCE. R. F. CrmlrdCopperSstpe.
To c d d trap
ctron Collection
and pumps.
/ ION FOCUSING
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SCANNING ELECTRON MICROSCOPY
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Scanning Coils.
OF
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Three Electrostatic Ienacs. Working Distance 1cm Lenses Prraligned EHT up to 16 k V
SPECIMEN
Specimen con bemoved in X.y.3.
1
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FIG.23. A combined scanning electron microscope and ion bombardment source for continuous observation of the specimen while it is being sputtered by the ions (41-43).
parts, it was found possible to maintain a reasonably good vacuum in the microscope column, despite the relatively high pressure in the ion source. As a rule, alternate periods of ion bombardment and surface examination were used but, when necessary, it was found possible to carry out
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C. W. OATLEY, W. C. N M O N , A N D R. F. W. PEASE
these two processes simultaneously. To do this it was essential to set the collector to record only high-velocity reflected electrons, because the lowvelocity secondary electron current produced by the incident electron beam was masked by other secondaries and negative ions generated by the impinging positive-ion &ream. Examples of the way in which the sputtering process can be observed are shown in Fig. 24. During the course of this work a totally different use for the apparatus came to light. Ion bombardment is becoming increasingly popular as a means of etching materials for microscopic examination. With certain soft materials t,he degree of etching required is quite critical and, unless the process can be monitored, it is very difficult t o prepare satisfactory specimens. The apparatus shown in Fig. 23 provides an excellent method of controlling the etching and observing its progress. I t has been so used by St,ewart and Boyde (42, 49) for the preparation of dental specimens.
L. The Examination o j Biological Material and of Synthetic Fibers 1. Direct Examination. A number of biological specimens do not suffer any change of appearance when placed in a vacuum because their cell walls remain unbroken. Such specimens may be examined directly with the scanning electron microscope, though it may be desirable to treat them with heavy-metal stains to improve contrast. I t is also usually necessary to evaporate onto them a thin metallic coating to increase surface conductivity and thus avoid charging. For specimens of this kind the scanning electron microscope offers important advantages. I t has much better resolution and a much greater depth of field than an optical microscope and, by comparison with the conventional transmission electron microscope or the reflection instrument, it provides a more readily interpreted “three-dimensional” image while using a very much smaller mean elect,ron-beam current density. The last point is an important one since biological material is easily damaged by the heat from excessive beam current. Examples of specimens which have been directly examined in the scanning electron microscope are shown in Fig. 25 (courtesy of Dr. A. Rezanowich) . A special case which has received considerable attention is the examination of organic fibers and it is convenient to include under this heading synthetic as well as natural fibers. Early micrographs obtained by Dr. Smith are shown in Fig. 26. More recently the Canadian Pulp and Paper Research Institute has carried out extensive investigations of the wood fibers used in paper making and examples of this work are reproduced in Fig. 27 (44, 46).
SCANNING ELECTRON MICROSCOPY
235
FIG. 24. Argon ion-bombarded (V = 5.2 kv; I = 200 pamp/cm*; a = 22'; p = 24') surfaces showing the effect of shielding due t o insulating dust particles (41). Times and magnifications as shown. The magnification of each photograph is given in microns and this length is equal to 5 mm as reproduced here.
23G C . W. OATLEY, W. C. NIXON, AND R. F. W . PEASE
SCANNING ELECTRON MICROSCOPY
237
FIG.25(b) FIG.25 (a) and (b). Biological specimens seen in the scanning electron microscope. (a) The simple eyes (ocelli) a t the vertex of a fly’s head. Magnification = 358X. (b) The compound eye of the common housefly as in (a). Magnification = 686X
238
C.
W. OATLEY, W.
C. NIXON, AND
FIG.25(c)
R. F. W. PEASE
S C A N N I N G ELECTRON MICROSCOPY
239
FIG.25(d)
FIG.25 (c) and (d). Biological specimens seen in the scanning electron microscope. (c) The compound eye of (b) at magnification = 3965 X. (d) Bristle on meaI worm grub (Tenebrio molitor), silver coated (7%). Magnification = 2 0 , 0 0 0 ~ . Micrographs (a-c) by courtesy of Dr. A. Rezanowich, Canadian Pulp and Paper Research Institute, Montreal, using the microscope of K. C. A. Smith (46).
240
C. W. OATLEY, W. C. NIXON, AND R. F. W. PEASE
FIG. 26 (a). Wool fiher shoving scales due t o natural growth (29). Magnification = 4000X.
2. Other Techniques. Where the forcgoing technique of direct examination is not applicable, the conventional transmission electron microscope has been of the greatest value in the investigation of biological specinleiis but its use for this purpose is subject to important limitations. Whether replicas or thin sections of the original specimen are placed in the microscope, dehydration of the specimen is usually necessary and it is difficult to be certain that this causes no changes in structure. Again, biological material is composed largely of the lighter elements and, when thin sections are used, selective heavy-metal positive or negative staining must be employed to give adequate contrast. Thus the preparation of a section involves initial dehydration, embedding, cutting, and staining, and one or other of these processes may well produce artefacts.
SCANNING ELECTRON MICROSCOPY
24 1
FIG.26 (b). Orlon fiber (gold-palladium coated) showing extrusion marks only due to manufacturing process but no lateral ridges corresponding to those on the wool fiber (7b). Magnification = 4000X.
It is natural to inquire whether the scanning electron microscope offers any possibilit,ies of overcoming these limitations which might compensate for the fact that its resolving power is inherently poorer than that of the transmission i n s h m e n t . The question has been examined in some detail by Thornley (16, 27%) following earlier work by Smith (29) and a good deal of experimental work has been carried out. It must be admitted that, the results so far obtained have been disappointing and the future outlook is, perhaps, not very promising. Nevertheless, the case is not hopeless so it may be of interest to record the present position. Thin sections can be examined by transmission scanning electron microscopy, but the difficulty of obtaining sufficient contrast is rather
242
C. W. OATLEY, W. C. N E O N , AND R. F. W. PEASE
FIQ.27 (a). The appearance of spruce fibers a t an early stage in the formation of paper. The sample was freeze-dried to preserve all the structures in their original position. Magnification = 1320 X IPhotograph courtesy of Dr. A. Rezanowich (44), using the microscope of K. C. A. Smith (46).
greater than with the conventional electron microscope and the resolution is worse. The only advantage offered by the scanning instrument appears to be a reduction of specimen heating and this is not normally of great importance with thin sections. The technique of freeze drying has commonly been used for the dehydration of specimens prior to embedding and sectioning for examination in the conventional transmission microscope. When suitable methods are used, there is little damage to the structure of the specimen and shrinkage
SCANNING ELECTRON MICROSCOPY
243
FIG.27 (b). A sample of spruce fibcrs, similar t o that of Fig. 27(a), but now air-dried from the wet state. This micrograph shows the collapse of the pulp fibers into flat ribbons and the bonding of one fiber to another, which occurs in the process of airdrying a wet mass of fibers. Magnification = 1463 X . Photograph courtesy of Dr. A. Rezanowich (44), using the microscope of K. C. A. Smith (46).
is small. The surfaces of freeze-dried specimens can be directly examined in the scanning electron microscope if precautions are taken to avoid charging, and this technique has been used by Thornley in an attempt to locate the cell boundaries on endothelial surface. Although surface detail very much smaller than the cell size was easily resolved, the micrographs gave no indication of the positions of the cell boundaries and revealed no other features of particular interest.
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C. Wr. OATLEY, W. C. NIXON, A N D R . F. W. P E A S E
An alternative technique that can be used with specimens of this kind is t o lower the temperature of tke4specimen to a point where the vapor pressure of water is well below the maximum pressure that can be tolerated in the scanning microscope. For this purpose there is little difficulty in providing a refrigerating specimen holder which can be cooled by pouring liquid nitrogen into a tube which projects through the wall of the specimen chamber. Precautions must be taken to avoid the introduction of artefacts during the freezing process and Meryman (46) has shown that the first essential is to freeze the specimen as rapidly as possible; he recommends a rate not lower than 0.6 cm/minut,e. Once the specimen has been frozen, it must be kept below -130°C. Below this temperature Meryman and Kafig (47) have shown that the ice exists in a vitreous form, while above - 130°C recrystallization sets in, though temperatures up to - 100°C can be allowed for short periods. With specimens prepared in this way, Thornley has shown that it is possible to obtain satisfactory micrographs of the surfaces, using the scanning electron microscope. However, as in the case of freeze-dried specimens, these micrographs have not hitherto yielded information of much interest. The unanswered question with these two techniques is not whether they can be operated satisfactorily, but whether there are any specimens for which they are likely to be particularly useful. Experiments of a quite different kind have been carried out by Smith and by Thornley in an endeavor to examine a biological specimen without subjecting it to either freezing or dehydration. For this purpose the specimen must be surrounded by water vapor a t the saturation pressure, which, a t room temperature, is about 14 Torr. Since this is vastly greater than the maximum pressure that can be tolerated in the body of the microscope, the specimen must be isolatedin a cell to which electrons have access through a suitable window. One possible arrangement is shown diagrammatically in Fig. 28. An ordinary 50-p aperture disk is sealed to the top wall of the cell and is covered with a film of collodion a few hundred angstroms in thickness. Such a film will withstand the pressure difference between the interior of the cell and the body of the microscope, while allowing relatively free entry to the incident electron beam. The specimen is placed on the under side of this film and electrons which pass through it strike the scintillator and produce the output signal in the usual way. The side tube is connected to the pumping system and to the water-vapor reservoir. During the pumping-down process, precautions must be taken to avoid a n excessive pressure difference across the collodion film. So far as the maintenance of a sufficiently low pressure in the body of the microscope is concerned, the presence of the collodion film is unneces-
SCANNING ELECTRON MICROSCOPY
245
sary since the relatively slow passage of water vapor through a 5 0 - p aperture could be dealt with by a fast pump or by a surface cooled with liquid nitrogen. However, without the film, it would not be easy to avoid excessive scattering of the incident electron beam by water molecules. Once the electrons have passed through the specimen they are subject to a great deal of scattering but, so long as they reach the scintillator without undue loss of energy, this does not affect the operation of the scanning electron microscope. In fact, the distance between specimen and scintillator can be increased to several nrillinreters without adverse effect. As an alternative to the above arrangement the scintillator can be mounted outside the cell, adjacent to the incident beam. The output signal then results from electrons reflected by the specimen, which pass a
FIG.28. Water vapor cell using a 5C-p aperture covered by a few hundred Angstroms collodion film to separate the microscope column vacuum from the specimen, which may be living. The transmitted electrons are detected by the scintillator and photomultiplier in the usual way (16).
second time through the collodion film on their way to the scintillator. With both arrangements a major difficulty is the lack of contrast obtained with biological specimens. With transmitted electrons contrast can result only from differences in energy loss since moderate deflection of the electrons does not affect the output signal. When reflected electrons are used, contrast is caused primarily by surface topography and this does not necessarily reveal features of interest to biologists. If contrast has to be enhanced by heavy-metal staining, there seems little point in attempting to examine the specimen in an atmosphere of water vapor and it must regretfully be concluded that, a t the present time, these techniques offer no advantages over conventional electron or optical microscopy. It should also be added that the above methods of maintaining a specimen in a n atmosphere of water vapor offer little hope of making possible the examination of an organism in the living state. Data on the lethal effects of an electron beam are scanty but, from the available information,
246
C. W. OATLEY, W. C. NIXON, AND R . F. W. PEASE
Thornley has concluded that the letkal dose for the most robust bacteria is likely to he exceeded in considerably less than 1 sec when an electron hezm of 10-11 A is scanning a square raster of 1 0 0 - ~side.
ACKNOWLEDGMENTS In writing this article the authors have had most valuable help and comments from former research students who have worked on the scanning electron microscope in the Engineering Department of the University of Cambridge. They wish to express their indebtedness particularly to D. McMullan. K. C. A. Smith, 0. C. Wells, T . E. Everhart, R. F. M. Thornley and A. D. G. Stewart.
REFERENCES 1. M . Knoll, Z . Tech. Physik 16, 467 (1935). 2. M. Knoll and R. Theile, 2. Physik 113, 26!) (1939). 5. M. von Ardenne, 2. Physzk 109,553 (1938). 4. V. K. Zworykin, J. Hillier, and R. L. Snyder, A S T M Bull. 117, 15 (1942). 6. G. Mbllenstedt and F. Lenz, Advan. Electrox Electron Phys. 18, 2.51 (1963). 6a. C. Brachet, Bull. ilssoc. Tech. Maritzme Aeron. 46, 369 (1946). 6. F. Davoine, Dissertation, University of Lyons (1957). 7. F. Davoine, P. Pinard, and M. Martineau, J . Phys. Radium 21, 121 (1960). 7a. R. F. W. Pease and W. C. Nixon, J . Sci. Znslr. 42,81 (1965). 7b. K.C. A. Smith and C. W. Oatley, Brit. J. A p p l . Phys. 6, 391 (1955). 8. D. McMullan, Proc. Inst. Elec. Engrs. (London) B100, 245 (1953). 9. A. S. Baxter, Dissertation, Cambridge University (1949). 10. A. Rose, Advan. Electron. 1, 131 (1948). 12. T . E. Everhart, Dissertation, Cambridge University (1958). 12. R. F. W. Pease, Dissertation, Cambridge University (1964). 13. D. B. Langmuir, Proc. I R E 26,977 (1937). 1.6. M. E . Haine and P. A. Einstein, Brit. J. A p p l . Phys. 3, 40 (1952). 16. K. C. A. Smith, i n “Encyclopedia of Microscopy” G. L. Clark (ed.), p. 241. Reinhold, New York, 1961. 16. R. F . M. Thornley, Dissertation, Cambridge University (1960). 17. T. E . Everhart and R. F. M. Thornley, J. Sci. Inst. 37, 246 (1960). 18. T. E. Everhart, 0. C. Wells, and C. W. Oatley, J . Electron. Control 7, 97 (1959). 19. P. Palluel, Compt. Rend. 224, 1492 and 1551 (1947). 20. E. J. Sternglass, Phys. Rev. 96, 345 (1954). 21. H. M. Terrill, Phys. Rev. 22, 101 (1923); see also M. Davis, i6id. 94,243 (1954); C. Feldman, ibid. 117, 455 (1960). 22. H. Bruining, “Physics and Applications of Secondary Emission.” Pergamon Press, Oxford, 1954. 23. A. Becker, Ann. Physik [5] 2, 249 (1929). 24. E. J. Sternglass and M. M. Wachtel, Phys. Rev. 99, 646 (1955). 25. J. Hillier and R. F. Baker, J . Appl. Phys. 16, 663 (1944). 26a. A. V. Crewe, J . A p p l . Phys. 36, 3075 (1964) Abstract. 26. A. D. G. Stewart, “Stereoscan.” Cambridge Instr. Co. Ltd., Cambridge, England, 1900. 27. 0. C. Wells, Brit. J. App2. Phys. 11, 199 (1960). 27a. C. F. Tipper, D. I. Dagg, and 0. C. Wells, J. Iron Steel Inst. (London) 193, 133 (1959).
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27b. R. F. M. Thornley, Proc. 2nd Reg. Conf. ( E u r . ) Electron Microscopy, Delft, 1960. Vol. 1, p. 173. Almqvist & Wiksell, Uppsala, 1961. 28. 0. C. Wells, J. Electron. Control 7, 373 (1959). 29. K. C. A. Smith, Dissertation, Univ. of Cambridge (1956). 30. C. W. Oatley and T. E. Everhart, -1. Electron. 2, 568 (1957). SOU. T. E. Everhart, K. C. A. Smith, 0. C. Wells, and C. W. Oatley, Proc. 4th Intern. Conf. Electron Microscopy, Berlin, 1958 Vol. 1, p. 269, Springer, Berlin, 1960. 31. G. V. Spivak, G. V. Saparin, B. Massarani, and M. V. Bikov, Proc. 3rd Reg. Conf. (Eur.) Electron Microscopy, Prague, 1964 p. 285. Czech. Acad. Sci., Prague, 1964. 32. P. R. Thornton, M. J. Culpin, and I. W. Drummond, Solid-State Electron. 6, 532 (1963). 3.9. T . E. Everhart, 0. C. Wells, and R. Matta, J. Electrochem. SOC.111, 929 (1964). 34. D. B. Wittry and D. F. Kyser, J. A p p l . Plays. 36, 2439 (1964). 36. W. Czaja and G. H. Wheatley, J . Appl. Phys. 36, 2782 (1964). 36. 0. C. Wells and R. Matta, Eleclrochem. Society Mee!ing, New York. 1,'163. 37. A. N. Broers, Microelectronics and Reliability 4, 103 (1965). 38. J. H. L. McAuslan and K. C. A. Smith, Reg. C'onJ. (Em-.) Electron Microscopy, Stockholm, 1956 p. 343. Academic Press, New York, 1957. 39. R. F. W. Pease, A. N. Broers, and R. Ploc, Proc. 3rd Reg. Conf. (Eur.) Electron. Microscopy, Prague, 1964 p. 389. Czech. Acad. Sci., Prague, 1964. 40. A. H. W. Beck and H. Ahmed, J. Elec!ron. Control 14, 623 (1963). 41. A. D. G . Stewart, Proc. 5th Intern. Co.7J. Electron Microscopy, Philadelphia, 1962 1'01. I, Art. 7 D-12. Academic Press. 1962. 48. A. Boyde and A. I>. G. Stewart, J. Ultrastruct. Res. 7, 159 (1962). 43. A. D. G. Stewart and A. Boyde, A'alure 196, 81 (1962). 44. 0. V. Washburn and J. G. Buchanan, P u l p Paper Mag. Can. 66,T400 (1964). 45. K. C. A. Smith, Proc. 2nd Reg. Conf. (Eur.) Electron Microscopy, Delft, 1960 Vol. 1, p. 177. Almqvist & Wiksell, Uppsala, 1961. 46. H. T. Meryrnan, Naval Med. Res. Inst. Bethesda 63, 3 (1953). 47. H. T. Meryman and E. Kafig, Naval Med. Res. Inst. Bethesda, Project NMooooi8.oi.o9 (1955).
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High- Speed Magnetic-Core Memory Technology L . A . RUSSELL I B M Corporation. Harrison. New York
Page I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 I1. Coincident-Current Toroidal Core Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 A . Background of the Concept., . . . . . . . . . . . . . . . . . . . 250 B. Refinement o f t h e Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 C . Introduction to the Three-Dimensional Core Memory . . . . . . . . . . . . . . . . 251 D . The 3-D Ferrite Core and Storage Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 E . Drive Switches and Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 F. Sense Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 G . 3-D Memory Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 I11. Two-Dimensional Core Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 A . Comparison of 3-D and 2-1> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 B . A 2-D Memory Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 C . 2-D Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 D . Core Properties for 2-D Memories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 E . 2-D Memory Design Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 F. Summary of 2-D Memory Characteristics., . . . . . . . . . . . . . . . . . . . . . . . . . 278 I V . Special Ferrite Storage Devices and Memories . . . . . . . . . . . . . . . . . . . . . . . . . . 279 A . Nondestructive Read Memory . . . . . . ........................ 279 B . Content-Addressable Memories . . . . . ........................ 281 C . Multiaperture Cores .... ...................................... 281 D . Batch-Fabricated Storage Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 ...................................................
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I. INTRODUCTION The use of ferromagnetic devices for information storage is a subject of intense engineering int,erest to those responsible for the design and implementation of digital computer systems . One of the ferromagnetic devices, the ferrite toroidal core, has been found to be excellently suited for the storage of information . This chapter is primarily intended to pruvide the reader with a general understanding of the basic design principles, characteristics, and progress of the technology employing ferrite cores in digital storage or memory units . The technical level and extent of detail presented are, hopefully, of the appropriate amount to be neither too extensive for those not generally familiar with the subject, nor too superficial for those who have been 249
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directly engaged in this area of engineering. It is also hoped that the selection of referenced works, although far from a n exhaustive listing, will be a helpful guide for those desiring detail beyond what was felt to be practical for inclusion in this chapter. The first and major portion of the chapter describes and discusses the coincident-current or three-dimensional core memory. The coincidentcurrent approach is the one that has received greatest engineering attention and application. Following this, the chapter turns attention t o the word-organized or two-dimensional ferrite core memory, which basically provides a speed advantage over the coincident-current approach. Finally, the chapter considers other approaches using ferromagnetic devices and comments on the relationship of those t o the previous approaches, and in addition discusses outstanding variations in functional characteristics that have been accomplished in ferrite core st,orage units. One additional introductory comment is that the chronology of developments in this technology is made reasonably obvious in the text and referenced publications. By doing this, the author has attempted to provide the reader with an appreciation of the impressive extent of progress that has been made by workers in this field. Perhaps it will also permit the reader to make extrapolations of future developments. Although the chapter intentionally does not provide forecasts of future developments, it identifies trends of developments which provide guidelines for forecasts. 11. COINCIDENT-CURRENT TOROIDAL CORESTORAGE
A . Background of the Concept The three-dimensional or coincident-current, toroidal core storage array is undoubtedly the most widely explored and used random-access electronic memory. It achieved this prominent position for the following major reasons : (1) Its invention occurred when a highly reliable, fast, and relatively inexpensive random-access storage was recognized to be an essential part of the stored-program computer ( 1 , 2 ) . (2) The simple physical geometry of the toroidal core permits inexpensive fabrication, testing, and assembly into a three-dimensional array of cores threaded with electrical conductors. (3) The use of two dimensions of access to the group, or word, of storage cells (cores) permits a relatively small number of selection devices and circuits to access a storage of large capacity, thereby reducing cost and improving reliability. (4) The speed that can be achieved with ferrite cores in a three-dimensional array is fast enough to satisfy most random-access storage requirements.
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B. Refinement of the Concept These advantages of the three-dimensional concept in ferrite core stores were recognized even before the design and utilization of the first storage systems employing it. However, much engineering effort has been required t o solve the many problems confronting the designers as they reduced the concept to the first practical products, and then set about refining the technology in order to improve the capacity, speed, reliability, and cost. This section will review the major developments which today give us the highly refined three-dimensional (3-D) core storage systems. These developments involve many aspects of 3-D memories such as ferrite DATA INlOUT STORE / FETCH CONTROL
CONTROL
\
DECODE
DECODE
STATUS SIGNALS MEMORY SELECT
ADDRESS REGISTER
ADDRESS INPUT - - - - - -
FIG.1. Functional diagram of 3-1)memory.
cores, array wiring, drive sources and switches, sense amplifiers, addressdecode and data-flow logic, clocking circuitry, and over-all packaging and supporting hardware. As often occurs in engineering, improvements by something like a factor of 10 in the cost, speed, size, and storage capacity were achieved by refinements on the basic approach that did not require radical departure from the original concept.
C . Introduction to the Three-Dimensional Core Memory I. Basic Description. Figure 1shows a functional or block diagram of a 3-D memory in which the complete memory is represented by a set of
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blocks. Each block represents a different function, and the intercorinecling lines with arrows represent the electrical interconnection of the functional blocks. Some of the functions shown niay be associated with other parts of the using system and omitted in the memory itself. This frequently occurs in the case of the data and address registers and the timing and control functions. 2. Memory Cycles. A brief description of the memory cycle of operation and the associated terminology will be given before the functional diagram is discussed. The 3-D core memory has two basic types of operating cycles-a “store” cycle in which new information is eritered in, and a “fetch” cycle in which information is obtained from a selected address or location of the memory. I n a store cycle it is normally necessary t o first> “clear” the address of previously stored information and then t o “write” the information to be stored. Therefore, a store cycle is composed of a clear and then a write sequence. I n some cases the clear operation may have been accomplished during a previous cycle of operation; this is termed “split-cyc*le” operation. I n a fetch cycle the information is “read” from the memory, and then, because of the “destructive-read” characteristic, a “regenerate” operation is required. In some cases the regenerate operation is omitted and the address is Ieft in the cleared state, which again falls into the split-cycle category. Although no practical approaches for a 3-D toroidal core memory in which the information is not destroyed by a read operation or i n which clearing is not necessary prior t o a write operation are known b y the author, the possibility for obtaining these characteristics does exist. I n summary, there are two memory cycles: a store cycle composed of clear-write operations and a fetch cycle composed of read-regenerate operations. 3. Core Storage Array. The magnetic core storage array is shown in the center of Fig. 1. It has three sets of input lines; two sets, the X and Y drives, are used to specify an address or word location, arid the third set, the 2 drive, is used t o control the information written in the selected address during store or regenerate portions of a memory operating cycle. The storage array has one set of output lines which transmit signals indicating the iriformation stored a t the selected address during thc read portion of a n operating cycle. An address is selected by the coincidence of a current pulse on one of the N I X drive lines with a pulse on one of the N2Y drive lines. Since there are N 1 times N2 X and Y drive combinations, there are N l N 2 unique addresses or words in the storage array. These two sets of lines communicate with two of the three dimensions of the array. The third dimension is used in common for the functions of controlling and sensing the information stored a t a selected address. The
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connection to this dimension is by N 3 lines in an array capable of storing N 3 bits of information at each address or word. I n actual practice the two sets of N 3 lines may physically be one set with appropriate circuitry used to selectively switch the lines to either the Z drive or the sense amplifier blocks. One magnetic core is used to store one bit of information; therefore, the storage array will contain N 1 N 2 N 3cores.
4. Address Register. The address register is used t,o store temporarily the address information while a memory cycle is being executed. In some designs this function may be provided by the address-decode or drive circuitry. Part of the address-register output is connected to the X address-decode block and the remainder to the Y block. The number of lines to each decode block will depend on the number of lines in the corresponding dimension of the array and on the address-information code being used. For example, if N1 equals 64 and a binary address code is used, then 6 address information lines are required from the address register to the X address decode. The address-decode function will depend on the characteristics of the X and Y drive circuitry being used. The net requirement is that the drive circuits must generate or switch current pulses to one of the N 1 and one of the N z address-selection lines. In some cases the drive circuits may provide some or all of the address-decode function. From the above, the function of the X and Y drive blocks is obvious except for one detail. The output current must be in one direction on a given line during the read or clear portion of the cycle and in the opposite direction on the same line during the write or regenerate portion. 6 . Sense AmpliJiers and Z Drive. The function of the sense amplifiers is very simply that of amplifying the signal level emitted by the sense lines to a level sufficient to operate the data-flow control and data-register circuits. In addition, the sense circuits sometimes improve signal-to-noise discrimination by nonlinear gain, time sampling, or time integration techniques. They may also provide polarity inversion and rectification. Generally there are N3 sense amplifiers. The complementary function provided by the 2 drive circuits is to generate during the write or regenerate portion of the memory cycle current pulses which will control the information storage states of each of the cores at a selected address. This is accomplished by generating a current pulse which, in effect, cancels or inhibits the ability of the coincident, X and Y drive currents to switch the cores from one datum state to the other. Contrary to the X and Y drive current requirement, the 2 drive current is required t o be of only one polarity.
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6 . Other Functional Blocks, The data register serves a dual purpose. The first is to temporarily store a data word to be written or regenerated during a memory cycle; the data word is received from the using system or the sense amplifiers, respectively. The second is to temporarily store information read during a fetch cycle while waiting for transmission of the information to t,he using system. The function of the data-flow control block is to provide the appropriate routing of data words between the sense amplifier, data register, and 2 drive blocks. The routing will be controlled by the type of memory cycle, store or fetch, requested. Finally, the function of the timing and control block is to receive operation command signals from the using system, time and control the operation of the various funct,ional circuits in the memory, and provide the using system with signals indicating the operating status of the memory. The diagram in Fig. 1 omits blocks performing functions such as error checking and correction, maintenance aids, power supplies, and environmental controls that are sometimes included in the memory design. Although these functions may be needed in many memories, they are not felt to be essential to the understanding of the 3-D core memory concept. On the basis of the preceding review of the 3-D core memory concept, the immediately following sections will point out and discuss the design and operational details that have been developed by contributors to this technology over the past several years.
D . The S-D Ferrite Core and Storage Array 1. Array History. The primary factor determining the over-all design and operating characteristics of the total 3-D memory is the ferrite core storage array. Publications in 1951 and 1952 described the basic metJhod by which cores assembled in a 3-D array may be selectively addressed in groups or words and how the information contained in the selected word can be controlled and sensed (1-3). These publications were followed by others in 1953 which described the design and operation of experimental memories based on the previously published concepts (4-6). Although the storage array concepts described varied somewhat from what lat,er became essentially the standard approach, they contained many of the fundamentals.
2. Basic Array. The basic storage array design that evolved is shown in Fig. 2. This example shows an array containing five planes with each of the planes containing 16 cores in a 4-by-4 matrix. However, within practical limits, an array could contain any arbitrary number of planes with an arbitrary number of cores in each plane. Figure 2(a) shows that
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the array is composed of two-dimensional planes stacked one upon the other to form a three-dimensional configuration. In Fig. 2(b) a typical configuration for the toroidal cores (short diagonal lines) and the X and Y address-selection lines of a single plane is shown. With the planes assembled to form the solid array configuration, the corresponding X and Y wires are interconnected to form a series circuit, plane to plane, starting in plane 1 and ending in plane 5 . The 2 lines for the inhibit-drive and sense windings are omitted in section b; there is one set for each of the X - Y planes. In section c an individual toroidal core is shown with four associated windings. As previously mentioned, the sense (8)and inhibit
(C)
FIG.2. 3-D core array of five planes of 4 X 4 cores each: (a) 3-D array, (b) X-Y plane, (c) core and wiring.
(I)drive may be combined into one (2)winding since they thread through identical cores. 3. Core Characteristics. Figure 3 shows in some detail the characteristics of ferrite cores and also the applied currents and resultant output or sense-winding signals in a 3-D memory. Figure 3(a) shows a core with an inside diameter I.D. and an outside diameter O.D., and with an n-turn winding for application of drive current resulting in a magnetizing drive of n i ampere-turns. The test winding can also be used to observe the induced rate of change of magnetic flux linkages (v), from which may be determined the flux linkage (n4) which is equal to Jv dt. The hysteresis loop shown in Fig. 3(b) describes the way in which the flux linkage (n4)
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changes as the number of drive ampere-turns (ni)is slowly varied, starting from zero, increasing toward a maximum positive value, decreasing to zero, increasing toward an equal maximum negative value, and then decreasing again to zero drive. The arrows shown on the hysteresis loop indicate the path followed for this sequence of changing drive. If the rate of change of drive current is made arbitrarily small, then the loop traced will be essentially the static (d-c) hysteresis loop. The static loop is an important one in studying the characteristics of cores pertinent to 3-D memories. Typically the drive to the core will be applied at a constant value
v t
(C)
(d)
FIG.3. Core characteristics and operation: (a) core and test winding, (b) hysteresis loop, (c) core with 3-D windings, (d) drive and output waveshapes.
long enough for the flux change to reach a steady-state condition, and then removed for an indefinite period. Examination of the hysteresis loop reveals the following important characteristics: (1) Increasing the drive from zero causes little change in the flux until a drive of nia is applied. (2) Increasing the drive above the niovalue causes the flux to change rapidly and then approach a state of little change with further increase. (3) Relaxing the drive back to zero leaves the flux at essentially the value attained by the maximum drive. (4) When the polarity of the drive is reversed the flux vs. drive characteristics follow an identical pattern in the reverse direction.
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Also shown in Fig. 3(b) is ni,, which is termed the coercive ampereturns or that value of drive required to reduce the flux state to zero. Finally, the stable positive and negative flux states, shown as “1” and “0” on the loop, are the two stable storage states that are used in the storage of a binary bit of information in a core cell. Figure 3(c) shows the four functional windings threading the core. Note that the I , and I , currents pass through the core’s aperture in the same direction (front-to-back) , and therefore cause a drive ampere-turns proportional to the sum of the two. However, the Z winding threads the core in the opposite direction (back-to-front) in order to cause a canceling or inhibiting ampere-turns equal to that caused by I , or I,. The direction of current flow indicated by the I , and I , arrows is for a write or regenerate portion of a memory cycle which is the same interval for application of 2 drive current. During a read or clear portion of a cycle, the direction of I , and I, current flow will be opposite to that shown in Fig. 3(c). Figure 3(d) is a composite drawing of typical waveforms of the various drive and output voltages as a function of time. The drives are current pulses having substantially rectangular wave shapes. The “1” and “0” curves are the output signals of a single core for the cases of reading/writing the two binary states.
4. Operation in the Array. The operation of the storage cell in the array is based on the following simple principles : (1) The amplitude of the individual I,, I,, and I , drives is adjusted to slightly less than nio, the threshold drive for causing a major flux change in switching the core from one state to the other. (2) If two drive currents pass through the core aperture in the same direction, they cause a drive of almost twice nio which is sufficient to cause a substantial change in the flux state of the core. (3) If three drive currents are applied simultaneously but one of the three passes through the core aperture in a direction opposite to the other two, then the net drive is that caused by one of the two in the same direction. (4) If two drives of the same direction are applied but in the direction to switch the core to the state that it was left in by previous drives, then only a minor flux change occurs. When these basic principles are related t o the memory design, it becomes apparent that, for a store cycle, the cores at the selected address are first switched to the cleared or zero state by the coincident application of negative-polarity I , and I , drives. Following this, the same I, and I , drives are coincidently applied but with a positive polarity which will switch the selected cores to the one state only if a counteracting Z or
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inhibit drive is not applied simultaneously. This is the write portion of the cycle during which some cores of a selected address will be switched to the one datum state (no 2 drive applied to planes containing them) and others will remain in the zero state (2 drive applied to their planes). I n a fetch cycle, the exact same sequence of drives occurs, and in addition voltage induced in the output or sense winding of each plane is detected during the first, read portion of the cycle. The voltage pulse will be relatively large in both duration and amplitude if the core has been left in the one state by a previous cycle and small in both if it has been left in the zero state. A last consideration worth emphasis is that the I , and Iv drives individually pass through other cores of the same row and column of each plane and the I , drives pass through all cores of each plane in which they are applied. The cores receiving these partial drives are called half-selected cores. Cores receiving only one of these drives, or I , in addition to I , or I,, will not undergo a major flux change, since the net will be slightly less than nio. However, as will be discussed later, the noise signals collectively induced by the many cores disturbed in each plane require special design attention. It is apparent, then, t,hat the core is a key factor in the design and operating characteristics of the 3-D memory. Consequently this device has been extensively studied in attempts to understand and control its properties. Particular attention has been given to developing mathematical models describing the switching behavior as the cores are driven from one direction of magnetization to the other. Menyuk, Goodenough, Gyorgy, and Haynes made significant contributions in providing these models (7-9). Except for Gyorgy, these contributions favored a model based on the nucleation of domains of reverse magnetization and the growth of these domains by domain-wall motion. Gyorgy’s model proposed that the magnetization was reversed (switched to the opposite state) by a rotation of all the flux vectors in a simultaneous fashion. He projected this to be the flux reversal mechanism in cores responding to large drive fields that result in a fast switching of the flux. Since the drive field is restricted to slightly less than twice nio in the 3-D memory, it is doubtful that this value of drive would be sufficient for the rotational model to be applicable. However, as will be discussed later, there are other core memory concepts that do permit larger drives. Shevel later provided experimental results that indicated transitions from one mode of switching to another as the drive field was increased (10,11). Reports on the development of magnetic cores and measurenients of their properties have been provided by several contributors (12-24). These publications indicate the many variations in material, process, and
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physical size that have been explored and developed and the range of properties that have been obtained. The objectives of these efforts were to obtain the following improvements in primary properties : (1) An increase in the retention of magnetization at a given flux state to which a core has been magnetized. Magnetization must be retained after the removal of drive and, even more difficult to achieve, after the application of an arbitrarily large number of half-select)drives which tend to cause switching to the opposite flux state. Improvements have been obtained through material and process changes and through reductions in the ratio of outside to inside diameters of the cores. (2) A reduction in the amount of current required to switch a core from one state to the other. Part of the improvements in this property have been obtained through materials and processes that reduce H,, the coercive force. The remainder have been through reductions in the diameters of the cores. (3) A reduction in the time required for the cores to be switched from one flux state to the other. The t,, switching time, improvements were obtained through changes in materials and processes which resulted in increases in Ho, threshold field, and decreases in s,, the switching coefficient, of the cores. The switching time is related to these two properties by the following equation: 2, = sw/(Ha - H o ) where Ha is the applied drive field which is proportional to the sum of I , and I,. It is also important that a range of cores with different switching times be available for memories of different cycle time requirements. (4) An increase in the ratio of output signal developed by the reading of cores storing a one-datum state to noise developed by reading cores storing a zero and noise from the half-selected cores. These properties and those following were improved by changes in material and process. (5) A decrease in the dependence of the storage and switching properties on the ambient temperature. (6) A decrease in the switching losses and the attendant heating of the cores. Although perhaps obvious, it should be emphasized that another characteristic which demanded much development and manufacturing attention was that of obtaining cores having uniform and stable magnetic, electrical, and physical properties. Table I indicates typical ranges of values that have been obtained for the core characteristics of importance to the memory designer. I t is not implied that it has been possible to obtain the extreme values of all the parameters given in Table I in the same core. Compromises necessarily exist, e.g., to obtain a switch time approaching 0.4nsec would require a
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TABLE I TYPICAL RANGEOF 3-D CORECHARACTERISTICS Parameter Inside diameter (inches) Outside diameter (inches) Height (inches) Drive current (milliamperes) “One” Signal (millivolts) “One”/”zero” ratio Switch time (microseconds) H, temperature coeff. (%/”C)
Minimum 0.02 0.03 0.006
150 10 2/1 0.4 0.2
Maximum 0.06 0.09
0.030 600 200 10/1
4.0 1.0
drive current approaching 600 ma. With respect to this table, the remark should also be made that improvements past the limits given will occur or have occurred. 5. Plane and Array Design. Once the core has been selected for a particular memory application, probably the most significant problem facing the designer is the design of a satisfactory wiring geometry for the X , Y , inhibit, and sense wires in the storage array. Certainly the most difficult of these four is the sense winding. This winding is most difficult owing to the influence its design will have on noise induced in it by undesired coupling with the driven windings and the disturbance of magnetization in half-selected cores in the array. Another problem which should not be minimized in the selection of wiring geometry is the eventual problem of assembly in a manufacturing operation at reasonable expense. 6 . Sense and Inhibit Windings. The design of the sense-winding geometry or pattern in the core planes has received much attention throughout the evolving development of 3-D core memories (25-29). In earlier designs much attention was directed toward the reduction of noise coupled from drive to sense windings caused by the close spacing between them. The approach was to reduce this coupling by selecting a geometry in which the sense winding passed through the cores of a plane a t a n angle of 45’ to the drive wires. This diagonal pattern for the sense winding, diagonal paths within N 1 x Nz rectangular matrix of cores, resulted in the sense winding being immediately adjacent to the drive windings only a t core locations. By this technique, both the capacitive coupling and that inductive coupling not caused by flux changes in the cores were reduced.
7. Noise Problems. The 45’ or diagonal sense winding provides a reduction in the noise coupling between drive and sense windings; however it
HIGH-SPEED MAGNETIC-CORE MEMORY TECHNOLOGY
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does not reduce it to zero and is difficult to fabricate. A typical pattern for a sense winding of this type together with the inhibit winding is shown in Fig. 4(a). In the drawing the polarity signs to the left of each core indicate the polarity of the signal and noise that will be induced in the sense winding when read pulses are applied. As is shown, there is an equal number of positive and negative signals and noise voltages on each row and column. Therefore the noise caused by I , and I , drives will tend to be canceled. There is one noise problem arising in very high-speed memories that this type of winding does not solve. It relates to the transmission delay of the windings discussed below. The problem is that the noise voltages do not cancel in time because the noise-coupling positions are not located at approximately equal wire lengths from the sensewinding terminals. This problem as well as the one of fabrication difficulty
INHIBIT
(a)
(b)
FIG.4. Sense/inhibit winding geometries: (a) diagonal sense winding, (b) parallel sense winding.
were substantially reduced by the parallel sense winding geometry such as shown in Fig. 4(b). The parallel geometry is felt to be a significant improvement over the previously developed diagonal one. The other major source of noise was from induced voltages in the sense windings due to small flux changes in each half-selected core. These are the cores that are half-selected by the application of I,, I,, or I , drives. Basically the approach taken was to thread the sense winding through half the cores of a plane in one direction and half in the other direction with respect to the direction of current flow of I , and I , drives during a read or write operation. This approach attempted to cancel half the core-induced noise voltages against the remaining half of a given plane. However, an exact cancellation cannot be obtained, because the noise voltage induced by a particular core is a variable dependent on the datum state stored by the core and also on the polarity of the immediately preceding half-select drive. This required that the so called
262
L. A. RUSSELL
“worst-case’1 condition of datum states and disturbance history be identified in the calculation or measurement of core-induced noise. The difference it1 induced voltage due to these factors is usually referred to as the “delta noise,” which is the maximum difference in noise voltage induced in the sense winding by a pair of half-selected cores. Techniques have been developed to reduce the delta noise occurring at read time but none have completely eliminated it. The techniques frequently used are termed “post-write disturb” and “staggered read.” I n the post-write disturb approach, the inhibit drive is applied following the write or regenerate operation (this will not be necessary if it has been applied for the storing of a zero state). The result obtained is that all the cores are half-selected by a drive of the same polarity that will be applied by a subsequent I , and I , read drive. This tends to reduce and equalize the half-select read-flux changes. The disadvantage of this technique is that additional time is required in the memory cycle. Also, although no additional drives are needed, a small amount of logic and timing circuitry must be added. The staggered read technique is one in which either I , or I, is applied slightly sooner than the other. By doing this, the noise contributed by one of the selection drives is made to occur before the application of fullselect drives. The amount of stagger necessary is approximately equal to the rise time of the early drive current, since the half-select flux change occurs primarily during the drive-current transition. As with the postwrite disturb, the disadvant,age of the staggered read technique is a n increase in memory cycle time. Secondary disadvantages are extra logic and timing circuitry and a slight increase in the power requirements on I, or I, drives. Even after the above techniques for reduction of sense-winding noise are incorporated, the amount of noise remaining is larger than can be tolerated if this winding passes through all the cores of very large planes. It is typical to limit the number of cores per sense winding to 4096, whereas the total number of cores per plane may be 16,384 and even larger. Therefore, it is commonplace to design core planes in which the sense winding is segmented into several sections. The outputs of these sections are mixed a t the input to the sense amplifier. I n some designs a preamplifier is provided for each sense segment. Another factor which often requires the segmenting of sense and inhibit windings, and in some cases the I , and I, windings, in larger and very fast memories is that the winding propagation time and attenuation of drive currents and signals can limit the maximum length of the wires. Depending on the core size and spacings and the wire sizes and winding geometries, the delay will usually be in the range of 10 to 30 nsec per
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1000 cores and the attenuation in the range of 5 to 15% per 10,000 cores. For designs where the delay approaches or exceeds the transition time for the drive current or sense signal, the winding must be terminated in its characteristic impedance to avoid reflections. The characteristic impedance usually ranges from 75 to 200 ohms. Thus there is the twofold problem of an increased number of windings to be driven or sensed and of providing the extra power dissipated in the terminating resistors. The drive-power requirement can be so large as to cause the designer to resort to additional segmentation in order to avoid the need for characteristicimpedance termination. I n summary, the design of the core array is one of the most difficult problems confronting the 3-D memory designer. It ranges all the way from selecting wiring geometries that will allow the assembly of millions of cores in a single array at a practical cost to including the transmission properties which can cause serious delay and distortion of the signals and currents in large, very fast memories. The care taken in the design of the core array will have a major influence on the performance and cost of the total memory system.
E . Drive Switches and Circuits 1 . Address Selection. The techniques for supplying the address-selection drives to the X and Y dimensions of the core memory have probably received more attention than any of the circuit groups associated with the storage array (3, 4, 30-41). The problem here is that an economical and reliable means must be devised to selectively apply a drive current of several hundred milliamperes to one of the many windings in each X and Y address-selection group. Further, these drive currents must have short rise and fall times, usually between 50 and 500 nsec, and have an accurately controlled, flat-top pulse amplitude, within about 5 %. Initial techniques used the vacuum tube for an active source and switch. However, in most present designs the transistor has replaced the vacuum tube. The magnetic core has been extensively used for pulse transformers and switch matrices. Also, the semiconductor diode is becoming increasingly popular in the matrix-switch application. Many of the techniques devised for the 3-D core memory are also satisfactory with little or no modification for other magnetic-memory designs. The large current-amplitude requirement imposed by the core characteristics made the use of current step-up transformers attractive. This was particularly true when the designer was restricted to the vacuum tube as an active device since these are suitable for control of tens but not hundreds of milliamperes owing to space and cost factors. Another factor which favored the use of pulse transformers was that the address-selection
264
L. A. RUSSELL
currents had to be bipolar with one polarity of drive current during the first portion of a cycle and the other during the second. The obvious solution was to employ pulse transformers with oppositely polarized primary windings that could be driven alternately during a memory cycle and provide bipolar pulses from a single secondary winding. An early example of the use of pulse transformers in the X - Y drive circuits is given by Papian (33). Other approaches which also use magnetic devices were proposed and developed by several early contributors. These approaches require the use of saturable magnetic cores and are usually called magnetic matrix switches. These cores contain two or more drive windings which are interconnected into a matrix such that each drive source acts on several cores. Each core also contains an output winding which couples an output pulse to an address winding in the storage array. The main advantage of this technique over the straightforward pulse transformer one is that the number of drive sources required is fewer than the number of address lines to be driven. It also retains the pulse transformer advantages of current transformation and unipolar-to-bipolar pulse conversion. Another advantage offered is that the switch can often be designed in a configuration that provides some or all of the address-decode function. The saturable magnetic core is one in which moderate positive or negative drive forces will result in a large change in magnetization toward corresponding positive or negative magnetization. However, an increase in drive above the amount necessary to saturate the magnetization causes only a very small change in magnetic flux. Saturable magnetic cores may also have a pronounced irreversible flux-change characteristic which is used in some matrix-switch designs. Cores having this characteristic retain a high percentage of the flux state caused by the drive field after the drive is removed. A typical B vs. H relationship (d-c hysteresis loop) is shown in Fig. 5(a). Ideally, the tails on the loop should be horizontal, and for some matrix switch applications, the magnetization at zero drive should approach the saturation value. Secondary considerations worth mentioning are that the opening of the loop should be small in order to avoid excessive losses and the sides of the loop should be nearly vertical SO that the output winding current will be constant during the switching operation. On these points, one would also have to consider the dynamicswitching characteristics in addition to the d-c hysteresis loop. However, in a typical design, the secondary ampere-turns is several times larger than the magnetizing ampere-turns which substantially reduces the effect of the magnetizing drive on the secondary current. This follows from the relationship that the secondary ampere-turns is equal to the primary minus the magnetizing ampere-turns.
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2. Matrix Switches. Two basic types of matrix switches received design attention at an early stage in the development of core memories. Raj chman described versions of both of these basic types in his publications (3, 4). One of the techniques uses 2n 1 drivers and provides 2" outputs from 2* switch cores. Each core contains n pairs of drive windings with one of each pair being driven to provide a current pulse to the storage array during a read operation. The n pairs of drive windings are selected by a binary code with the selected winding of each pair corresponding to
+
3 8
7 6
5
OUTPUTS
3 2 1
'
J
Rz
Ri
CI
cz
c3
c4
(C)
Fro. 5. Matrix switch techniques: (a) saturable magnetic core characteristic, (b) binary switch, (c) coincident switch.
the bivalued binary number associatcl with the pair. Figure 5(b) shows a wiring pattern for a switch of this type containing three input pairs and eight cores and outputs. In the drawing the horizontal lines represent the switch cores, the vertical lines represent the windings passing through the cores, and the short diagonal lines indicate the direction in which the winding passes through the core. One thing not indicated in the drawing is that the number of turns for the I,, I b , and I , driven windings are a function of the winding polarities and the size of the switch. The bipolar switches at the bottom represent the selection of a winding of a pair according to the binary-address number of a-b-c bits. The binary-address switch offers the obvious advantages of many
266
L. A. RUSSELL
outputs per drive source for large switch sizes and also the inclusion of the complete address decode function in binary-addressed memories. However, the designer is confronted with the serious disadvantages that the number of windings increases rapidly to the impractical range if the switch is made large. As a result this matrix switch design is seldom used in memory applications. There are variations of the design shown in Fig. 5(b) but they have very similar design characteristics and offer the same general advantages and disadvantages. The other type of matrix switch contributed during the early period of core memory development is the coincident or anticoincident switch. It received widespread acceptance from the start and its use in new memory designs has continued. The switch cores are arranged in a rectangular matrix with rows and columns of drive windings linking cores of a given row or column in series. Output windings placed on the switch cores connect separately to the selection lines in the storage array. I n the coincident version all the cores are continuously driven by a bias current to a negative saturation state. The bias drive is approximately the same as the row or the column drives. To provide an output from a given core, the row and column windings linking it are driven and the specified core receives a net drive equal to the sum of the row and column drives minus the bias drive. Therefore, the selected core receives a net positive drive, the half-selected cores a net zero drive, and the unselected cores remain biased at a saturated negative state of magnetization. After completion of the read operation both row and column drives are removed and the bias reswitches the selected core, which results in an opposite-polarity pulse for the write operation. The coincident matrix switch is shown in Fig. 5(c) for the case of two rows and four columns which provide eight outputs. In this drawing the switch cores are represented by the heavy diagonal lines, the row windings by lines R l and R2, the column windings by lines Cl-C4, and the output windings by OrOs. The bias winding is not shown; it may be eliminated by superimposing the bias current on the row or column windings. The anticoincident switch is very similar to the coincident one. The difference is that the polarity of either the row or the column drive is reversed so as to oppose the other. Instead of using a bias, all but one of the drives of the reverse-polarity group are applied during a read operation. One of the windings of the other group is applied. The result is that the core linked by the one driven winding of a group and the one undriven winding of the other group is selected by a net positive drive. During this operation the net drive to each of the cores is the same as in the coincident switch. For the write operation the one drive that was not driven in the reverse-polarity group is applied, which reswitches the selected core.
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MEMORY TECHNOLOGY
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Thus the coincident or anticoincident) switch provides m times n outputs with m plus n drive sources, where m and n are the number of row and column drives. It is relatively simple to construct,, and accomplishes some of the address-decoding function. It requires only three or four windings per core regardless of size, and the geometry of the winding pattern remains the same for all sizes. One of the major design problems is t o keep noise outputs from partially selected cores at a n adequately low level. These noise outputs are the result of coupling between drive and output windings due to air coupling and small flux changes from cores shuttling back and forth along the saturation region of the hysteresis loop. This problem is contained by careful design of the windings and cores. Another problem is that for large switches the series-connect,ed drive windings distort the drive-current wave shape as a result of their nonideal transmission-line properties. However, the limits imposed by these problems have not been severe. The technique has been ext,ensively used. As memory designers continued their push toward larger and faster 3-D core memories, the speed and power requirements on the array drives increased a t a rapid rate. The load-sharing matrix switch described by Constantine is a contribution toward increasing the practical limits of memory size and speed (36). Unlike the coincident matrix switch, the load-sharing switch does not provide a greater number of outputs than drive inputs t o the switch. I n fact, in its basic form as initially described by Constantine the number of input drives was twice the number of outputs, which is the same as for pulse transformer-coupled drives. The primary advantage is that the power obtained from a single output is contributed collectively by half of the input drivers. For example, if each of the 32 input drivers to a 16-output switch can provide 1 watt of power, then the power delivered by an output will be 16 watts, neglecting losses in the switch. Table I1 gives the polarities for the drive windings of a four-output load sharing switch. There are four pairs of drive windings A-D, with each drive winding threading serially through the four cores. Each of the cores has a n output winding which is connected to a selection line of the storage array. I n operation, drives are applied simultaneously to one winding of each drive-winding pair. As to which of the two windings of pairs are to be driven, the combination will determine which output will occur and what the polarity will be. For example, if a positive current is required from output 1, abcd must be driven. If a negative current from output 3 is required, a'bcd' must, be driven. &amination of the table will reveal another important property of the switch, which is that all cores other than the one being selected receive a net drive of zero. This is important
268
L. A. RUSSELL
TABLE I1 DRIVE-OUTPUT COMBINATION FOR LOAD-SHARING MATRIXSWITCH Drives
B
A a
8’
+ + + -
+ -
C
b
b‘
c
+ + -
+ +
+ +
D c’
+ + -
d
d’
Output
t
-
1 2 3
- + + - +
4
since it ideally provides a switch that does not produce noise outputs from unselected cores and does not require cores having a saturation characteristic. In practice, some noise is produced owing to differences in the shapes, amplitudes, and durations of the drive pulses. The requirement for uniformity of drives appears to be the most severe requirement this switch technique imposes on the driver characteristics. As mentioned above, the load-sharing switch requires two drive sources per output. Marcus later showed how the number of drives per out,put could be reduced to a ratio approaching 1:l (37). Although the above does not provide a comprehensive discussion of all magnetic-core matrix-switch techniques, the ones omitted are primarily variations and combinations of the ones discussed. The reader is referred to a comprehensive and analytic publication by Minnick and Haynes for an extensive treatment of the subject (41). The use of semiconductor diodes and transistors for switch matrices did not occur until the development of core memories was well along. The limited availability, high initial cost, and speed and power limitations of the early semiconductor devices did not allow them to compete favorably with magnetic-device switches until recent years. For the most part their initial use was in 2-D or word-organized core memories rather than the 3-D design. Because of this early tie-in with the word-organized memory approach, a discussion of this drive switch technique will be included in Section I11 rather than here.
F. Sense AmpliJers 1 . Design History. Although the sense amplifier may initially appear to be a straightforward circuit-design problem, the designer usually faces many subtle and sophisticated difficulties in reaching a satisfactory solution. As with the storage array and drive circuitry, the problems become
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more difficult to solve as the memory size and speed increase. I n this section the nature of the problems and some of the novel approaches will be discussed. A review of the core memory literature shows that very few contributors have presented works on the design of sense amplifiers as the central subject. Instead, they have tended to include the sense-amplifier design as secondary or supporting sections of publications on complete memories. This has probably occurred with good reason in that the characteristics required from it are so peculiar t o a particular storage-array design. However, a few contributors have centered attention on this portion of the memory in publications (42-44). 2. Functional Requirements. Basically, the function th a t the sense amplifier performs is very simple. It must amplify the information signals received from the sense winding to an energy level suitable for detection of whether a one- or zero-datum state has been read, and must drive tke information control logic. In some designs it is convenient t o separate the amplifier and detector portions of the circuit. However, the term sense amplifier is intended to include bot,h here. Usually, the information is determined by amplitude-discrimination techniques with a one signal being large and a zero signal small in amplitude. Frequently the shorter time durat,ion of the zero signal is used t o enhance the discrimination. There are two techniques that are employed individually or in combination t o take advantage of the time difference. One is to strobe or gate the amplifier into operation after the zero signal occurs. The other is to use an amplifier that has less amplification for the higher predominate frequencies of the zero signals, a low-pass filtering technique. It should also be noted that sense amplifiers which integrate the information signal with respect t o time have been proposed as a method of discrimination. However, few designs use it since it increases the time required to sense the information and the additional discrimination provided is usually not necessary. On looking more critically at the requirements that the sense-winding characteristics and signals impose on the amplifier, one is impressed, or probably depressed, by the considerations tha t must be included in the design. The usual considerations are as follows: (1) Termination of the sense winding in its characteristic impedance: The impedance th at the amplifier presents to the sense winding must match the characteristic impedance in order to avoid reflections if the sense winding passes through many cores and the memory performance is high. This impedance is normally in the range of 100 to 200 ohms. (2) Common-mode rejection: The capacitive coupling between the
270
L. A . RUSSELL
drive and sense windings causes a large noise voltage to appear on the sense winding as a result of change in drive-winding voltage. This can be separated from the information signal if the two sense-winding terminals are sensed for a difference signal. Therefore, the sense amplifier is usually a differential input or is coupled through a common-mode trap t o the sense winding. A common-mode rejection ratio of 1OO:l is often required. (3) Bipolar information signals: The sense winding is required to thread half the cores in one direction and the remaining half in the other t o balance half-select noise. This causes the information signal to be of the opposite polarity for half the addresses. Therefore, the amplifier must be capable of discriminating signals of either polarity. (4) Rapid recovery from large write noise: The inhibit drive induces large noise signals in the sense winding a t write time. Array design can usually reduce the air-coupled difference noise to a negligible amplitude but delta noise cannot be eliminated. The amplitude and polarity of this noise is dependent on the information state of the cores. Amplitude of 100 times the one-signal amplitude is not unusual. The peak amplitude occurs during the rise and fall times of the inhibit driver. Either this noise must be blocked from or within the sense amplifier or the amplifier must recover from its effects before the next read operation. The presence of this large difference-mode noise on the sense winding is the primary reason for terminating the winding in its charact,eristic impedance. I n highperformance memories it often limits the minimum cycle time. (5) Repetitive occurrences of unipolar signals: It is possible to induce iterations of signals having a nonzero volt-time integral over a period of many memory cycles. For example this will occur if a sequence of reading zeros and writing ones occurs in addresses producing the same polarity of sense-signal voltage. This could cause a zero-level shift to occur in a n a-c coupled amplifier. (6) Variable time periods between successive memory cycles: I n the general case the period between successive memory cycles can vary from the minimum cycle for which the memory was designed to a period approaching infinite time. This requires that the voltages and currents of the amplifier be essentially a t quiescent levels and that no resonant conditions occur for periods equal to or longer than the minimum cycle time. Another significant consideration is that the sense-amplifier design must have excellent stability and uniformity characteristics without the need for individual adjustment and must be economical and compact because many are required for long-word-length, large-capacity memories. I n early memory designs vacuum-tube sense amplifiers were generally used. However, the tube was soon replaced by semiconductor devices.
HIGH-SPEED MAGNETIC-CORE MEMORY TECHNOLOGY
27 1
Pulse transformers have been used extensively for common-mode traps and also for interstage coupling. Most of the early designs were a-c coupled, but the recent trend has been to d-c coupling along with progress in stability of d-c-coupled amplifiers. If a-c coupling techniques are used, either time constants are made short with respect to the minimum cycle time or some technique is used to restore the amplifier to a fixed quiescent level prior to read operations. The tunnel diode is often found in recent designs in the detector portion of the amplifier. Push-pull circuits with full-wave rectifier outputs are generally used as a solution to the bipolarsignal requirement.
G. 3-D Memory Examples In this section a few examples of memories that have been described in the literature will be discussed with respect to their major characteristics (46-62). I t is hoped that the ones selected represent a reasonable cross section of what has been accomplished. One criterion in the selection of the examples is that the memory is understood to have been built and employed in a useful computing system. There are naturally many memories that were designed and built primarily for exploratory rather than utility purposes which are not judged to meet this criterion. The memories will be discussed in the order that they are presented in Table 111: 1. This memory was provided by International Telemeter Corp. for the Johnniac computer. I t is one of the first known for actual computer application. As the table indicates, it used larger cores than the rest of the examples given, had a moderately long cycle time, and its capacity was near the low end of the range, if example 6 is omitted. Actually, this memory is of a special 2-D configuration. However, it is included for its TABLE 111 3-D MEMORY EXAMPLES
Cycle time No.
hsec)
15 9 20 12 6 10 4 2.18
Core size 1.D.-O.D. (mils) No. words Bits/wd. 70-100 50-80 50-80 50-80 50-80 50-80 30-50
4,096 4,000 4,096 32,768 65,536 256
io,oao
16,384
40 35 36 36 37 25 60 72
Tot. cap. (bits)
Reference (date)
163,840 140,000 147,456 1,179,648 2,424,832 6,400 600,000 1,179,648
46 (1956) 46(1956) 47(1957) 48(1957) 49(1957) 60(1958) 61(1961) 62(1961)
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L. A. RUSSELL
early accomplishment and the employment of many 3-D principles. For the most part it uses vacuum-tube circuits although some semiconductor diodes are used. I t used a coincident-current switch core-driver matrix with inhibiting inputs to control outputs. The sense winding is transformer coupled to the amplifier and provides a low-pass filter. The X and Y read drive was staggered to reduce noise at read time. 2. IBM Corp. developed this memory for use in the 705 processing system. It is probably one of the first designed for large-scale manufacture. The core size is that used in several later designs. I n addition to the main storage unit it also contained a special 512-word, 7 bits/word characterstorage unit. It was a true 3-D memory as generally described in the preceding sections. The drive was provided through two anticoincident matrix switches of 8 X 10 and 5 X 10 sizes. As in example 1, the circuits used vacuum tubes and semiconductor diodes with pulse-transformer inputs to sense amplifiers. 3. Remington Rand (UNIVAC) developed this memory for the Transac 5-1000 computer. Its total capacity is about the same as examples 1 and 2 and its cycle time the longest of the three. However, ambitious volume and power restrictions were imposed on its design, and it achieved approximately a factor of 10 reduction in these measures as compared with the previous examples. All circuits used semiconductor devices. Except for transformer coupling in four primary current-pulse-generator circuits, the X - Y drive was performed with transistor-matrix switches. 4. This is the IBM Corp. Model 738 memory designed for the 704 and 709 computers. The significant difference between it and the three above examples is the large increase in bit capacity, about a factor of eight. Its circuit design closely resembles that of example 2 with the exception that transistors are used in the sense amplifiers instead of vacuum tubes. The array is divided into two sections of 16,384 words, each with the X-selection lines for the two sections connected in series with common drive switches. However, separate Y drives and windings are used for the two halves. Sense windings and inhibit are divided into four segments of 4096 cores each and mixed by transformer-diode circuits at the input to each amplifier. X-Drive windings pass through 9216 cores and Y windings through 4608. The transmission delay for an X winding is about 0.25 psec. A diagonal sense winding is used. 5 . This memory is an even larger and faster one developed by the MIT Lincoln Laboratory for the TX-2 computer. It clearly is a distinct improvement in both performance and capacity over the preceding exaniples. Semiconductor devices are used except for vacuum-tube current drivers. Core matrices of 16 x 16 cores are used in a coincident-current matrix switch for driving the X and Y windings. A very short pulse
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(80 nsec) strobes the sense amplifier in order to improve signa1:noise discrimination. The 256 X 256 array plane is made up of a matrix of sixteen 64 X 64 subplanes. 6. This example was included to draw attention to the use of 3-D memory in highly specialized applications. The capacity is much smaller than the other examples but the application, space telemetry, imposes special requirements of size, weight, ruggedness, temperature, and reliability. The memory uses transistors throughout the circuits. Ambienttemperature insensitivity is accomplished by heating the storage array to slightly above maximum ambient temperature. The techniques used for driving and sensing, array wiring, etc., are primarily the same as for standard-application memories. 7. The memory in this example is designed for the LARC computer. No details are given in the reference other than those in Table 111. Its performance increases over the previous examples should be noted. 8. This is the IBM Model 7302 memory for use in several high-speed computers: e.g., STRETCH, 7080, and 7090. It provides a performance improvement with the bit capacity at the upper end of the range. Design details worthy of note are that a smaller core is used, the array and terminating resistors are immersed in an oil coolant, the array windings are driven by load-sharing switches and terminated in their characteristic impedance, and a parallel-geometry sense winding is used. The above examples show the increase in maximum performance and capacity that has occurred in the design-evolution process and the variety of techniques and technologies that have been applied in bringing this about. It is obvious from recent marketing announcements of even larger and faster memories, not yet described in technical publications, that this evolving process is continuing. 111. TWO-DIMENSIONAL CORE RIIEMORY The two-dimensional (2-D) core memory is in many ways a simplification of the widely used 3-D approach to high-speed, random-access computer storage. Only one of the dimensions, instead of two, is used for address selection. For this reason the 2-D memory is often called “wordorganized’’ or “linear-select.” The other dimension, equivalent to the 2 dimension in a 3-D memory, is used for controlling and sensing the information stored. There is only one drive winding and current involved in the selection of an address or word, and hence the cores do not have to possess coincident-current switching properties for this function. Address selection is performed in total in circuits external to the core array. However, there is a coincident-current switching technique employed in switching the cores for the storage of information during the write opera-
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tion. As in the 3-D memory, the operations of read or clear and regenerate or write occur in the two halves of the memory cycle. The basic 2-D approach requires one core per bit stored, although two cores per bit have been used in several designs.
A . Comparison of 3- D and 2- D In Fig. 6, a block diagram of tJhat portJion the 2-D memory that is different from the 3-D version is shown. It may be helpful to compare this with the block diagram of the 3-D memory given in Fig. 1. The memory contains N 1 words of N z bits each for a total storage capacity of NI times N z bits. The number of lines connecting to the array are as indicated: N 1 word lines and two times N z bit lines. These are the number of functional lines; the actual numbers of lines may be greater for the word lines and
INF&%I CONTROL LOGIC
DRIVE BIT
LINES
‘-’
s~~~~
U
LINES A & !,SENSE ’!E % O N LOGIC
U NI LINES
’
DRIVE
FROM ADDRESS DECODE
FIQ.6. Partial block diagram of 2-D core memory.
greater or less for the bit-drive and sense. The word-drive function may be performed by the combination of a word-matrix switch and associated drivers and gates.
B. A 2-D Memory Schematic Figure 7 shows a simplified schematic of a typical array, drive, and sense circuits for a 2-D memory of four words of four bits each. Although the 16-bit capacity of this memory is far less than sizes of interest, its expansion to larger sizes is straightforward. The sixteen short, heavy diagonal lines represent the cores of the storage array. The two vertical lines passing through each column of cores are the read and write word windings. The two horizontal lines passing through each row of cores represent the drive and sense-bit windings. The bit windings are equivalent to the 2-dimension windings and the word windings are related to the X and Y address-select windings in the 3-D memory. Although the memory could be designed with separate read and write word drivers for each word of the array, the opportunity was taken to show the frequently
HIGH-SPEED MAGNETIC-CORE MEMORY TECHNOLOGY
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used diode address-selection switch. In effect, the diode switch permits all the addresses in the array to be selected by a number of voltage gates and current drivers similar in functlion and number to X and Y drivers in a direct-driven, 3-D memory. Specifically a memory of N 2 words requires N gates plus N read drivers plus N write drivers. The bit drive and sense technique is fairly obvious with individual circuits for each bit of the words.
t r
qwl..$
FIQ.7'. Schematic diagram for a 4 X 4 2-D memory.
C . 2-D Operation
In operation, a word is read or cleared by the application of a rectangular current pulse to the word-read winding of the selected address. The current is of sufficient amplitude to switch the cores to the zero-datum &ate. As a first approximation, the cores are assumed to have the same characteristics as those for use in a 3-D memory. Bit drivers are not operated during a read or clear operation. If a core is switched from the one t o the zero state by read current it induces a relatively large voltage
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pulse in the sense winding threading it. This signal is amplified and detected by the sense amplifier. Otherwise, if a zero is read, the core induces a smaller signal which is detected as a zero. The writing information is accomplished by simultaneously applying a current drive to the write winding of the selected word and separate current to drive each of the bit windings in which one states are to be stored. Neither of these drives are made large enough to individually switch any cores to the one state. However, cores receiving both word and bit drive will be switched to the one state, i.e., cores of a selected word which also receive bit drives. It is important to note that whereas the cores in the array may be subjected to disturbances or half-select drives from a n arbitrarily large number of bit drivers, they need only withstand the disturbance of one word-write drive between the storing of a datum state and the time that it is subsequently read. For typical core characteristics, this permits the word-write drive to be slightly larger than the bit drive. The advantage of using larger write drive is that the total drive to the cores being switched to the one state will be larger and, hence, the switching faster. I n the interest of faster operation, it should also be noted that the read drive inay be as large as desired since all the cores receiving it are to be switched to the zero or cleared state. No partial-select considerations exist for read or clear operations. These last two comments point up the paramount advantage of 2-D memories over 3-D : faster performance. There are also other advantages and disadvantages which will be indicated later. There are two diode-matrix switches in Fig. 7 : one for the read and the othe? for the write word windings. They are operated by the combined operation of one of the two gate transistors, GI and G z ,and one of the two word read or write transistors, R 1and Rzor W1 and W2. For example, if a read current is desired for word B, gate GI and word-read R, transistors are driven into conduction. This combination causes only the read-winding diode shown at the top of word B t o be placed in conduction. The conduction of gate transistor G1 attempts to forward-bias the four diodes associated with words A and B but since only R2 of R1,It2, W1, and Wz transistors are switched into a conducting state, none but the diode connected to the word B read winding will conduct current. The resistor connected in series with the collector of R2 and the source voltage V will limit the word-read current.
+
D . Core Properties jor 2-D Memories There appear to be more variations in the design of 2-D memories than of 3-D. This seems to be especially true for the characteristics and modes
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of operation of the storage cores. I n addition to the 3-D core properties of switching threshold, retention of flux state at top or bottom of hysteresis loop with zero drive, etc., which are required for operation in the 2-D technique, there are other core properties which are particularly useful in 2-D memories. Newhouse, for example, reported that there is a domain-wall viscosity property which causes the threshold for irreversible flux change to be increased as the duration of the drive is made short even though the drive may cause a significant reversible change (53). This property may be used in connection with the word-write drive to increase its maximum amplitude, and thereby reduce the core-switch time. The additional noise caused by the reversible flux change is permissible since it occurs in only one core per sense winding and at write time only. A faster mode of switching a t large drive fields was also described which is due to a change from domain-wall motion to rotational switching. The switching constant (Sw) is observed to be several times smaller. Later, McMahon and Tancrell described a partial-switching technique which further shortens switch times for the cores (54, 65). The partial-switching technique is a simple one; during the write operation either, or both, the word or bit drive is terminated before the core is fully switched to the upper extreme of the hysteresis loop which normally represents t h e one state. By doing this, the switching time is reduced since there is less flux switched. The above techniques of using special properties of the cores can provide a reduction in cycle time approximately equal to and in addition to that obtained by the use of large read drives mentioned earlier. They are important contributions for the 2-D memory.
E. 2-D Memory Design Variations There have been several contributions to the literature describing 2-D memory designs and operational properties (58-65). Early in the development period McMahon recognized the advantages offered by the 2-D approach over the 3-D one with which it competes (66).The advantages pointed out by him are (1) increased drive power efficiency; (2) inproved core tolerance requirements; (3) low noise ; (4) reduced current-regulation requirements; and (5) increased speed capabilities. Those contributing to 2-D memory development showed designs of many variations. The ones of primary interest are in the areas of coreoperation, array-wiring, and word-switching techniques. Some of the differences in core operation have already been pointed out. Another significant one is that some designs use two cores per bit of storage with the second core threaded by a separate bit winding. The separate bit winding is connected to a second input of a differential sense amplifier in order to
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cancel noise developed in the first bit winding. If bit drive is provided for the secondary core, it is applied in a way causing the second core to store the complementary state of the first. This results in developing equalamplitude, opposite-polarity information signals at the sense-amplifier input. Also it has the advantage that the voltage drop in the word windings is a constant independent of the information being stored or read. If no bit drive is provided, the second core always remains in the zero state, and therefore cancels the zero signal (noise) from the first core at the sense-amplifier input. A basic advantage of the two-core-per-bit technique is that it permits the use of cores having lower 1 : O signal ratios. The major variations in array wiring are separate or common read and write word windings, and the same for bit-drive and sense windings. Some designs also use multiturn windings, particularly for the word-read winding since it must provide the largest drive. There are three approaches to using a common word winding for both read and write currents. One is to use a bipolar-output gate circuit and two diodes connected in opposite directions to the current-drive end of the word winding and with the bipolar gate connected to the other end. This approach also requires that the read and write drivers conduct current in opposite directions. The second approach is to use bipolar gate and drive circuits and a single diode. The diode has to be a special type that has a long reverse-recovery characteristic. Read drive passes current through the diode in the forward direction and write drive in the reverse during the reverse-recovery period. The third approach uses a pulse transformer for each word. This provides directly the bipolar current characteristic. The primary winding or windings of the pulse transformer may be driven in a variety of ways. The common bit-drive and sense winding is usually accomplished by dividing a common winding into two halves and connecting one end of each into a differential amplifier. The ot,her ends are driven in common or separately by pulses of the same polarity. The bit, drives cause a large, common-mode current at the sensed end of the winding segments but this can be blocked by common-mode rejection techniques.
F. Summary of 2-D Memory Characteristics The chief advantage offered by the 2-D core memory over its 3-D competitor is a reduction in cycle time. I t appears that at least a factor of 2 and perhaps a factor of 3 reduction can be obtained. The chief disadvantage is that the words must be individually switched or driven by components and circuits totally external to the storage array. This increases the amount of circuitry and components necessary to select a given number of words as compared with the 3-D memory, which provides some of this selection within the storage array. Therefore a 2-D memory
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tends to be more expensive and probably less reliable for the same capacity. The higher word-selection cost, together with the need for shorter bit windings owing to bit-winding delay and noise factors being more of a limitation at shorter cycle times, tends to make designs having fewer words and more bits per words favorable for a given storage capacity. On this point, it is apparent that, for either a 2-D or 3-D memory of a given storage capacity, there will be a minimum in the cost as a function of the number of words and bits per word to achieve the storage capacity. Naturally, the memory designer must consider the using computer in selecting the word length. However, it is possible to transmit and receive word lengths that are submultiples of the actual word length of the memory by simple logical gating techniques. IV. SPECIAL FERRITE STORAGE DEVICES AND MEMORIES Thus far attention has been confined to a conventional or relatively standard use of the toroidal core in 3-D and 2-D memories. These memories have gained widespread engineering acceptance and computer usage for approximately 10 years. They have been continually improved in performance, capacity, and cost of manufacture during this period as the previously referenced material will substantiate. However, there has naturally been a search for improved approaches and for approaches that provide different functional characteristics for high-speed, digital-computer memories. Some of these searches have resulted in new approaches which certainly deserve mention and comment here. However, the number that have been worked on is exceptionally large and varied and an exhaustive presentation of them is felt to be beyond the scope of this chapter. What will be presented is a short description and discussion of the uniqueness of several popular approaches. For the most part only those using ferrite devices for the storage element will be included. However, this is not meant to imply that devices of other materials such as ferromagnetic metal are not important for memory application. In some cases, these ferrite devices are of the simple toroidal geometry, whereas in others they are of different shapes. This section is subdivided into four topics. The first two concentrate on innovations in the functional characteristics and the last two deal with different geometries for the magnetic-storage devices and planes.
A . Nondestructive Read Memory
In conventional ferrite-core memories the reading of a word of stored information switches all the cores of that word to the zero state. The
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computer frequently requires that the memory restore the same information after this destructive-read operation, and therefore a regenerate operation is provided in the memory-fetch cycle. This results in disadvantages of additional time required and in possible lower reliability owing to the probability of electrical failures during the regenerate operation. High requirements for improving the speed and reliability characteristics of memory resulted in interest in designing memories of a nondestructive read-out (NDRO) type. Several contributors to the magnetic-memory technology accepted this nondestructive read challenge early in the development period and showed how this characteristic could be obtained through basically different ways with square-hysteresis-loop magnetic cores. One used a read-drive field in a direction predominately orthogonal to the direction of magnetization caused by writing fields (66-68). This caused the magnetization in the direction representing the storage state to be reduced, which resulted in readable sense signal. Furthermore, when the read drive was removed, the magnetization would relax sufficiently toward the previous information-storage state to permit the same, orthogonal read operation tto be repeated as many times as desired. The orthogonal-read field was generated in one case by passing a current in the spiral direction of a metallic, tapewound core. In the other case, this current was conducted in a wire which was threaded through a radial hole in a ferrite core. This core device was probably one of the first multiaperture cores for use in memory (see below). A second basic approach was to apply read field in the direction that would ordinarily switch the core to the zero state, but restrict the amplitude to an amount that would cause reversible, but not irreversible, flux changes. Information could be sensed owing to the nonlinear and assymmetric characteristics of the upper and lower, relatively horizontal regions of the hysteresis loop. One of the first contributions using this scheme also made use of the core as a frequency-mixing device where two drive frequencies were mixed by the nonlinear characteristics, and the phase of the difference frequency would be either 0 or 180 degrees depending on the information state of the core (69). A third basic approach which provides NDRO and other functions as well involves again a multiaperture device. In this approach the read winding threads an aperture and carries sufficient field to switch flux in regions adjacent to the aperture, but not along flux paths enclosing other apertures as well (magnetic field is inversely proportional to the length of a flux path). Drives to windings threading the various apertures result in flux-storage states. In the one datum state there is a continuity of some of the flux lines that link only the read-winding aperture. In the zero state, none of the flux lines link this aperture. One of the ferrite mu1t)i-
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aperture devices suitable for this type of NDRO storage is called the Transfluxor’ (70). There have been many contributions to the literature describing and evaluating NDRO devices and memories (71-79). I n general, the device techniques presently available permit a substantial reduction in the time necessary for a fetch cycle as compared with destructive-read approaches. However, the complexity of the memories, and therefore their costs, are relatively high.
B. Content- Addressable Memories This functional type of memory is also called associative memory and nonaddressable memory. There is a major functional difference between this and the conventional types. The difference is that in a fetch operation, information that is presumed to be contained in a portion of one or more of the words is presented to the memory and a comparison is made with all words, and the words having the same information in the specified portion are fetched. Therefore, the memory is interrogated by its information content rather than by an address for each word of storage. It is possible to have a conventional memory simulate this function by addressing its contents and sequentially comparing each stored word with the specified information. However, this sequential operation would require many memory cycles and restrict performance of the computing system. Therefore there have been efforts to implement the function in the basic hardware design of the memory (80, 81). However, only a moderate amount of success has been achieved; the hardware tends to be complex and expensive and the maximum storage capacity small. There are fundamental problems in simultaneously interrogating and comparing many bits in parallel, which must be done in order to achieve fetch cycles of interest.
C. Multiaperture Cores The single-aperture device, the toroid, is a very simple structure which is attractive from the fabrication, assembly, and minimum magneticpath-length aspects. On the ot,her hand its geometrical simplicity imposes practical limits on the sophistication of its magnetic device characteristics and drives to achieve them. These limit,ations caused many workers in the field to consider device shapes with multiple apertures. With multiple apertures, the device contained a variety of paths in which magnetic states and flux changes could be caused by current-conducting wires passing through the plurality of apertures. (Cores of this type are also 1
RCA trade name.
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called multipath cores.) There have been several contributions in the literature describing various types and uses of these devices with the uses including not only memory but logic-circuit applications as well (70,71, 82-88). Most of the earlier work was toward 3-D concepts with a major objective of reduced cycle time. The magnetic devices typically were planar in geometry with two or three holes whose axes were parallel to each other and perpendicular to the major plane of the device. Some windings received continuously flowing bias currents whereas others received excitation pulses or developed voltages from flux changes for sensing. The drive windings in some cases linked more than one path. Also, it was common to have interactions between two or more flux paths. Somewhat later emphasis was placed on devices that are essentially cubic in shape in which one aperture passes through the cube from front to back and the other from side to side. The two apertures are slightly displaced from each other in the vertical dimension with the material in the central region mutually acted on by windings through the two apertures. This mutual region is operated by orthogonal fields. Wanlass and Wanlass, who reported on this device, named it the BIAX (71). In several cases the multiaperture devices provided NDRO operation which enhanced higher-speed capabilities. Also each magnetic device was usually designed to store one binary bit of information. The primary disadvantages of the multiaperture devices typically are greater power consumption due to longer flux-path lengths and greater cost due to complexity of device and array fabrication. As a competitor of the toroidal core, its disadvantages are judged to be serious in view of the limited number of multiaperture memories that have been manufactured.
D. Batch-Fabricated Storage Devices These devices are characterized as having many storage locations within one magnetic device or structure. They are primarily aimed at reducing the process and fabrication cost and time for the storage array. Devices of this type have been developed for both 2-D and 3-D memories but with apparent recent emphasis on the 2-D versions. Most of the approaches provide for including some of the array wiring in the device fabrication. There are several known variations of this approach to storage arrays (89-101). One of the earliest batch-fabricated devices, the aperture plate, consists of a machined or molded sheet of ferrite having an array of holes through the sheet positioned in a row and column matrix. Normally the ferrite around each hole is operated on as a toroidal core. Also, there is usually at least one conductor deposited by chemical or evaporation
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techniques which passes through the holes in the aperture plate thus forming some of the array wiring by batch process. Often the plates are stacked one upon the other and conductors threaded through the holes in the stack so that many plates are wired at once. Another approach, which recently has received a large amount of interest, prints or molds ferrite material in an unfired, slurry form (99-101).Conductors that are printed or preformed in a matrix grid are placed within the ferrite slurry and the entire device with wiring is heat processed to the desired magnetic characteristics. The process is limited to the use of metals for the conductors which can withstand the high temperatures necessary for the heat treatment or sintering of the magnetic material. Storage devices made by this process tend to be of the multiaperture type, with two perpendicular apertures. Batch fabrication shows promise of providing memories with lower cost, higher bit density, and lower power requirement. The device characteristics obtained tend to be better suited to 2-D than to 3-D memory. Therefore, the lower storage cost is a t least partially offset by higher drive and sense-circuit cost when evaluated for the large number of applications in which the 3-D toroidal core memory can be used. The major problem in the development of batch-fabricated devices appears to be one of obtaining uniformity in the characteristics of all storage locations. This may well be the deciding factor determining the use of this approach.
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on Circuit Theory, IEEE Electronic Circuits and Systems Committee. 98. A. H. Bobeck, IEEE Intermag. Conf., Intern Conf. Nonlinear Magnetics, Washington, D.C. Papcr No. 3-2 (1963). 99. R. Shahbender, C. Wentworth, K. Li, S. Hotchkiss, and J. A. Rajchman, AFIPS 24, 77 (1963). ZOO. R. F. Elfant, W. A. Crapo, and K. R. Grebe, IEEE Intermag. Conf., Intern. Conf. Nonlinear Magnetics, Washington, D.C. Paper No. 8.7 (1964). [Paper does not appear in proceedings of conference. See J. M. Brownlow, E. A. Bartkus, W. A. Crapo, R. F. Elfant, K. R. Grebe, and 0. A. Gutwin, ZBM J . Res. DeueEop. 8, 170 (1964).] 101. J. M. Brownlow, E. A. Bartkus, and 0. A. Gutwin, ZEEE Intermag Conj., Intern. Conf. Nonlinear Magnetics, Washington, D.C. Late paper. [Paper does not appear in proceedings of conference. See J. M. Brownlow, E. A. Bartkus, W. A. Crapo, R. F. Elfant, K. R. Grebe, and 0. A. Gutwin, I B M J . Res. Develop. 8, 170 (1964).]
Physical Foundations of Plasma Applications for Generation and Amplification of Microwaves V. YA. KISLOV, E. V. BOGDANOV, AND
Z. S. CHERNOV Institute of Radiotechnique and Electronics, Academy of Sciences, Moscow. U.S.S.R . Page Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 291 Slow Wavesin Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction of Slow Waves with Electron Stream. . . . . . . . . . . . . . Plasma Traveling Wave T u b e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plasma Backward Wave Generator.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 321 Interaction on Longitudinal Waves.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operating-Wavelength Shortening Problems in Plasma Devices. . . . . . . . . 324 Experiments on Amplification and Generation of Millimeter Band Oscillationsby Means of Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 IX. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 List of Symbols. . . ............................................. 329 330 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I. 11. 111. IV. V. VI. VII. VIII.
I. INTRODUCTION Studies of new methods of generation, amplification, and conversion of microwave oscillations as well as advances in plasma investigations connected with the problem of thermonuclear synthesis led to the origination of a new trend in microwave electronics, i.e., plasma microwave electronics. A short-wave radiation of the Sun and stars that occurs as a result of processes taking place in plasma has already been under study for a long time in radioastronomy. This radiation is connected with plasma oscillations which are excited by streams of charged particles (1-4). Plasma has interesting high-frequency properties. First, plasma can transmit and guide electromagnetic waves (5-20). Second, it possesses resonance properties (11-14) , and electron plasma resonance occurs in the microwave range. Third, plasma is permeable for electron streams. This feature is a very important one as far as excitation and amplification of electromagnetic waves are concerned. Fourth, plasma oscillations have strongly pronounced nonlinear properties (16-1 7) which have not been 287
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V. YA.
KISLOV, E.
V.
BOGDANOV, AND Z. S. CHERNOV
sufficiently studied during the experimental investigations but which are of great interest (18, 19). On the other hand, the investigation of plasma properties recently has become one of the main physical problems while plasma application is rapidly spreading in the leading scientific and technical fields, i.e., power engineering (20, 21) and aerodynamics. This, in turn, facilitates the use of plasma and its spread in radiophysics. The investigation of interactions of charged particle beams with plasma is of particular interest. This interaction forms the foundation of a number of physical processes and is of great interest from the point of view of instabilities which may take place in devices for thermonuclear reaction (Z2-24). Recently this interaction has become the base for new methods of charged particle acceleration (25) and new methods of generation of microwave oscillations (65-27, 5 6 ) . The first studies of plasma oscillations were carried out by Langmuir and Tonks ( 1 1 , 28), who investigated the phenomenon of electron plasma resonance and gave a classical formula determining the frequency of electron (Langmuir) oscillations of plasma. At the same time there appeared the so-called Langmuir paradox, which lies in the fact that an electron beam emitted by a cathode is scattered much earlier than would otherwise follow from the theory of scattering of a n electron stream in plasma due to binary collisions. I n subsequent experimental work, investigations of Langniuir oscillations and anomalous scattering of electrons (29) were carried out. Some attempts were made to increase the power and shorten the wavelength of Langmuir oscillations (30-32). However, rather powerful and well-formed monochromatic electron streams were not used during these investigations, though an electron beam played the main role in the interpretation of oscillations. The principle of a continuous interaction of the electron stream with a slow electromagnetic wave was not used or known. Only later was it suggested that Langmuir’s paradox could be explained on the basis of the interpretation of electron beam scattering as an interaction between a traveling wave and plasma (33, 34). The technique of obtaining and forming the electron beams and electron devices with continuous interaction developed much later (35, 36). The theory developed along with these investigations. On the basis of considering ideal plasma with a zero temperature a number of features of propagation of electromagnetic waves in plasma were made clear (37-39). To take into account the finite plasma temperature there was used a hydrodynamic method which later proved to be incorrect but still is sometimes used for a qualitative description of the phenomenon connected with taking into account the finite temperature (40, 41, 42).
GENERATION AND AMPLIFICATION O F MICROWAVES
289
Many features of electromagnetic processes in plasma were made clear only by means of a kinetic consideration. Vlasov suggested a rather strict statistical theory which takes into account the collective properties of a system of many particles ( 4 3 , 4 4 ) .Landau made more precise Vlasov’s results connected with damping and also considered the problem of penetration of an electromagnetic field into plasma (46). Kinetic consideration of plasma oscillations was carried out in works of Bohm and Gross (46). On the basis of these results there was later worked out a strict kinetic theory of electromagnetic processes in plasma. According to this theory, plasma is considered to be a continuous medium with space-time dispersion (47-51 ) . The problem of excitation of plasma waves b y an electron stream was considered by Bohm and Gross (46) and also by Akhiezer and Feinberg (62). These authors derived a dispersion equation connecting the frequency and wave vector of growing pIasma waves, the propagation of which takes place in the plasma-beam system. The regions of amplification described by this equation were investigated by a number of authors (26, 52, 63, 57). For a long time this theory was the only one. Though it showed the existence of growing solution still there was no experimental confirmation. No growing waves were found in experimental work (54).Piddington (55) questioned the correctness of the interpretation of the growing solution of the dispersion equation. Only after the appearance of experimental works (56-62) and discussion, in which stronger substantiation of the “substitution analysis” method was given (63,6 4 ) ,did it become clear th a t plasma was a medium good enough for amplification and generation of microwave oscillations. A number of subsequent works show further progress of this trend (65-80). I n considering plasma as a medium suitable for amplification and generation of microwave oscillations, it is convenient to make a comparison between possible mechanisms in plasma (a part of which are performed experimentally) and mechanisms which are the basis of operation of usual electron microwave devices:
(I) Interaction of slow electromagnetic waves propagating in infinite magnetoactive plasma (the sizes of plasma are much greater than the wavelength of oscillations) at some angle to a constant magnetic field with a n electron stream moving along the magnetic field. There is no similar system in microwave electronics. Interaction of slow traveling waves with an electron stream is a pattern quite close to it. There is some published work on transient instability (81-83).
290
V. YA. KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV
(2) Excitation of longitudinal plasma oscillations by an electron stream (with and without a magnetic field). This mechanism has put into effect experimentally in some work (56-62). Some devices, with so-called resistance or inductive walls, can serve as analogs. (3) Interaction of slow waves in plasma waveguides with a n electron stream penetrating this waveguide. This mechanism is also performed experimentally in some works (69, 66). As a matter of fact, here we have a plasma traveling-wave tube (TWT) and backward wave tube (BWT). The difference here lies only in the fact th at a plasma waveguide with all peculiar properties is used instead of the usual slow-wave structure (helix, interdigital line, etc.). (4) Interaction of an electron stream with space harmonics of densitymodulated plasma (84). This system has not yet been created. Devices in which metal waveguides are loaded with rings can serve here as an analog. (5) Some experiments show that an interaction similar to that occurring in klystron generators is quite possible in plasma (31, 85). ( 6 ) It is also possible to use the interaction between beam and plasma located in crossed electrical and magnetic fields (86). ( 7 ) I n (94) the possibility of creating a plasma parametric amplifier is investigated. Undoubtedly the realization of other systems similar to those used in microwave electronics is also possible. I n connection with the problem of using plasma for generation and amplification of microwave oscillations a number of physical investigations of interaction between beams and plasma were conducted, and some attempts were made to create plasma microwave devices (amplifiers and generators). The “plasma-electron beam” system is the most interesting one as far as generation and amplification of microwave oscillations are concerned, This system is unstable within a wide variation of the parameters of the beam and plasma, i.e., oscillations occurring in this system rise either in time or in space. The energy source of the increasing oscillations is the beam. Space interaction is very peculiar for the plasma-beam system while the interaction between beam and usual slow-wave structure occurs only directly near the structure itself. The two following types of interaction between beam and plasma are known, an interaction with induced charges in plasma and a synchronous interaction between beam and a slow electromagnetic wave propagating in a plasma waveguide. The first type of interaction is not connected with the necessity of creating large magnetic fields and takes place in the case when the characteristic frequency of plasma oscillations slightly exceeds the signal frequency. A specific feature of this case is the absence of propagation of slow waves in plasma without a beam. This fact prevents the system from
GENERATION AND AMPLIFICATION OF MICROWAVES
29 1
self-excitation and permits the realization of great amplification factors. The disadvantage of this type of interaction is the necessity of modulating the beam and removal of high-frequency energy with the help of ordinary slow-wave structures. At the same time the difficulties of shortening the operating wavelength in microwave devices are not practically eliminated. The second type is the interaction with a slow electromagnetic wave propagating in a plasma waveguide. Of great interest is the use of body waves, i.e., waves for which the longitudinal component of the electric field is maximum along the waveguide axis. The structure of fields in a plasma slow-wave structure permits a great increase in the beam diameter and, consequently, the power characteristics of the device. Besides that, the coupling impedance of the plasma slow-wave structure is considerably higher than that of the helix and interdigital line slowwave structures. This fact points to the possibility of decreasing the dimensions of the devices. From the point of view of the future of plasma electronics, Refs.
(57-70)on investigation of interaction between high-current pulse beams and plasma are of great interest. The authors of these works succeeded in obtaining the oscillation power under conditions of amplification and generation up to 10 kw in pulses at the efficiency of 10-20%. The possibility of obtaining great power in plasma-beam systems is shown in Ref. (71). A more detailed analysis of works on pIasma electronics (8'7-90)leads to the conclusion that though plasma microwave devices are not yet ready to compete with the conventional microwave devices, the number of plasma investigations and the participation of leading elctronics firms, companies, and institutes are increasing. At the same time there has been, significant success in this field. The purpose of this paper is to analyze the physical principles and possibilities of designing plasma amplifiers and generators.
11. SLOWWAVESIN PLASMA The oscillatory and waveguiding properties of plasma may be understood if the random thermal mot,ions are not taken into consideration and we assume that plasma is a medium consisting of a mixture of two kinds of charged fluids: electrons and ions. Under the action of electric fields currents are induced in this medium. The currents in turn cause a change of the fields. It is convenient to consider plasma as a dielectric. Taking into consideration the fact that the motion of ions in the microwave frequency range can be disregarded in a constant magnetic field directed along the axis 2,the following tensor of dielectric permeability describes
292
V. YA. KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV
the behavior of a plasma: e ik
0 €0 3)
-ie2
€1
:(O€
where 2)'
€1=1--
€2
1 - u'
v' 4 2 1 - u)
= ___
€3
= 1
- v'
W'
is the signal frequency, wP the electron plasma frequency, W H the gyrofrequency of electrons, and v,ff the effective frequency of electron collisions. The wave equation for a plane monochromatic wave of the exp { i[wt (kr)]}type and a corresponding dispersion equation take the following form:
w
ki(kE)
+
ko2€ikEk
detln26ik- nink -
€ikl
=0 = 0
(2)
(3)
where
Solution of Eq. (3) gives us the well-known expression n = n(u, v, 0) for the refractive index of the ordinary and extraordinary wave, where 0 is the angle between the direction of the wave vector and magnetic field. A characteristic feature of plasma in the microwave range is the presence of two regions of propagation of slow waves dependent on resonance properties of plasma electrons. The regions of their existence are connected with the presence of a singularity in the expression for the refractive index at tan2 e = -e3/e1. The first region is the region of higher frequencies:
while the second one is w
< min
):(
GENERATION AND AMPLIFICATION O F MICROWAVES
293
The use of interaction of slow waves of such a type as well as plasma resonance with an electron stream is one of the main foundations for the design of plasma amplifiers and generators. The finite temperature of electrons should be taken into consideration for the correct description of slow waves in plasma. Under kinetic consideration for the case of oblique propagation and for oscillations having wavelength greatly exceeding the average radius of Larmor orbit of plasma electrons ( I C , . V ~ / W H << l), the tensor of plasma dielectric permeability takes the following form (50).
- vw
Eyy
=
Ezz
c,,
=
1 - uw
k
% ([(a- k*vz)) WH
\-/2VZ2
(5)
\
((w - k2VZ)/
VT'
where
[(x)
=
-i
lo"
eid dt
=
(I/%) - id($)
The term l/s corresponds to the principal value of the integral; VT is the root-mean-square velocity of thermal motion of electrons. The angular brackets denote the averaging according to the Maxwell distribution function. Averaging gives ([(W
Z
=
X(x)
-
iU(x)
- kEVZ))= X(z)
-2
=
1
-
( L T1)
+
222
3 + G2 +
.
I n the cases of interest, when x >> 1 the imaginary part of Z can be neglected. For the interaction with fast beam electrons we shall be interested in the wave with a phase velocity greatly exceeding the thermal one (VT << uf or T = n2Pr2<< 1). After averaging and expanding in powers of
294
V. YA. KISLOV, E. V. BOGDANOV, AND 2. S. CHERNOV
x we obtain xz v’(1
+
324’) 2 (1 - u’)3 2)’ - iv’d2 ____ + ? u’+ -xrz (1 - u’)Z 1- I t 2 (1 - u’)2 i v ’ d u ” I +n“ 1 - u’ 2 (1~ -‘ u’)2 + 3 x, v’(1 3u’) x,. __ u’- 3 0’ I---- iv’ d u ‘ 1 - u’ 2 (1 - u1)3 2 (1 - u’)2 8’ u ‘ 3 - - iv’ 4 2 -x21 (1 - u’)2 2 (1 - u’)2 1 - v’(1 $xz) u’
1 - u’
]
1
+
BZZ
+
where xz = PT2nzz, x,, = PTznZnt,PT = vT/c. The dispersionequation (3) forthewavewith n(n,, 0, nz),n,/n. for slow waves, taking account of (B), is of the following form:
AnZ4- ( B - pis)n,2
[i: +
A = PT~V-
cc = v [ l +
tan2 e
i-(l1
2(15 --u1 4 3
+ &)]
I
=
tan 8,
+C =0
B = (1 - V )
+ (1 - - 1 :J t a n 2 e C
= (1 -
v)(l
-
&)
(7)
The corresponding dispersion curves are shown in Fig. 1. When the thermal motion of electrons at points where tan2 0 = - t 3 / t 1 is taken into account the refractive index takes a finite value. Consider some more properties of plane waves. The solutions of the dispersion equation determine the propagation of the wave phase. The direction of the energy flow vector S and the direction of the wave vector k in a n anisotropic medium do not coincide. In particular for the slowwave vectors S and k are mutually perpendicular and the angle 0’ between S and the direction of the magnetic field is connected with the angle e by the relation tan el = - l / t a n e. This fact should be taken into account in considering the physics of propagation and amplification of electromagnetic waves. The direction of damping or growth of the wave in the presence of dissipation due to collisions or interaction with a beam should coincide with the direction of S vector, i.e., if k = ko Ak and kZo/k> = tan 8, then the ratio ( A I C ) J ( A ~should )~ be equal to tan 8’. Consider, for example, the damping of a slow electromagnetic wave
+
295
GENERATION AND AMPLIFICATION OF MICEtOWAVEB
in an anisotropic medium which is characterized as indicated by the following dispersion equation:
+
=
(8) Expand this equation in powers of s = Y / W . Let koand k = k Ak characterize the wave at s = 0 and s # 0. Assuming the perturbation kZ%3
kzftl
kO2ele3
+
IOOC
100 n
10
jJ W2
w;
FIG. 1. Dispersion dependences for slow waves in nonconfined plasma at 0,
W~*/WH'
#
= 1.6.
introduced by the damping is small, i.e., Ak/lco << 1, and a t the same time taking into consideration that
we may write down the dispersion equation in the following form:
+
ko + (Ak)z12[e3
€1
tan2 8 - pis
+
tan @(tan8' - tan S)] =
ko2w3
(10)
Then we have
We obtain a pure imaginary value Ak which characterizes the damping of an electromagnetic wave in the direction of the power flow. I n the first region of propagation of slow waves (high frequencies) where € 3 > 0 and €1 < 0 the wave damps in the direction of negative values of Z (k,O > 0 ) , which coincides with the direction of the power flow. In
296
V. YA. KISLOV, E.
V.
BOGDANOV, AND 2. S. CHERNOV
the second region where c3 < 0 and c1 > 0, the wave attenuates in the direction of positive values of Z (kzo> 0), which also coincides with the direction of the power flow. As p / l e l ( le3l 1 and s 10-6-10-3, Ak/k s and the damping of electromagnetic waves is small.
+
-
-
-
111. INTERACTION OF SLOW WAVESWITH ELECTRON STREAM Consider the interaction between a n electron stream and electromagnetic wave the phase of which is propagating a t a n angle of 0 to the direct field Ha (the energy flow is propagating respectively a t an angle of 0'). Like plasma, an electron stream the constant component of which is compensated by the ion background may be characterized in the linear approximation by a tensor Eik which corresponds to the linear relation between the density components of the oscillating current and field j , = m z k E k . If such a relation is found, then the pattern of the system of homogeneous Maxwell equations and the dispersion equation of system (7) remain the same. The difference consists only in the fact that the components of tensor czk will include the terms connected with the presence of the electron beam. In the particular, but the most important, case when the electron stream passes along the field H o , this relation can be easily determined from the motion equation, continuity, and the expression for the current density : dv= q E ap - - ai -i j , = pov, vop dt
at
a2
+
Taking into consideration that all the variable values are proportional to exp [ i ( w t - k z ) ] and, what is very easy to prove, th a t v J v Z << 1, we obtain
where q = e / m , lee = w / v o is the electron wave number, and the tensor of dielectric permeability of the beam has the following form:
where be = w i , / w 2 and cope is the plasma frequency of a n electron stream. 'Below in this paper will be given a more general expression of the tensor for a monochromatic beam the electrons of which are moving at a n angle toward the magnetic field.
297
GENERATION AND AMPLIFICATION OF MICROWAVES
Usually the value be is much smaller than unity. As is seen from the expression for the tensor, the beam may considerably affect the propagation of electromagnetic waves only a t (k,/k, - 1) << 1. This resonance condition corresponds to the synchronous velocity of the electron stream and component of the phase velocity of the wave in the direction of the beam motion. I n the presence of the beam, the dispersion equation for the case of plasma with a zero temperature has the form
The presence of the beam is characterized by a term which is the part of the expression € 3 = e30
k,
=
+ (AIC)~
kZo
+
8€3
k , = /cZo
8t3
=
+ (Ak),
kzo = kzotan O (Ak),
=
(Ak), tan 0’
The dispersion equation in the absence of the beam has the form
+ e l tan2 O] = ko2D
(15)
Assuming that the excitation introduced by the beam is sma11, i.e., ( A k ) / k Z o<< 1, and a t the same time taking into consideration that k,/kz = tan 0 (Ak),/kZo(tan8’ - tan O ) , after expansion of the dispersion equation in powers of (Ak)z//r,o, we obtain (later, index 0 is omitted and the new symbols k, = 7, k , = ye, lczo = yo are introduced)
+
I n the first region (lower frequencies) the right-hand part is positive and is equal to
where C is the amplification parameter, while that in the second region is negative and is equal to
- _0, 2
Introducing the symbol id,
(ell
+1
- -C3 ICSI
298
V. YA. KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV
where b is the parameter of bypass while d is the damping parameter (corresponding to a direct wave), in the first case we obtain -62
=
1 -b - i d
+ is
This is the equation for the backward wave tube (93). I n the second case we obtain
which is the Pierce equation for a direct wave. Damping parameter d already has been determined :
The solutions of the equations obtained and the properties of the systems which they describe have been studied extensively. Using, in particular, the equations obtained for a backward wave we may calculate the starting density of the currents for systems with limited length 1 along the direction of the beam mot,ion and nonlimited in the transverse direction. For example, in the case of small damping losses
L
=
0
and
C3 =
0.314 ( 7)
vox where V ois the beam voltage. The amplification factor for direct waves may be calculated in a similar way using the solutions and diagrams for the case when el < 0 and € 1 > 0 known from the traveling wave tube theory. I n case of plasma with a nonzero temperature, the dispersion equation describing the interaction between slow waves and the beam may be written in the following form:
+ (1 - v) (1 + ,",) ~
=
0
(21)
GENERATION AND AMPLIFICATION O F MICROWAVES
299
After the expansion of the dispersion equation in powers of (Alc)z/lc,o we obtain
(y)y?+) =
be --
+
1
2 e3 - el - 2 / 3 ~ ~ n , ~ u ( $[ ( 5 - u)/4(1 - ~ ) ~ ] ( t Ba n ~1)) (22)
-
-
The last term in the denominator takes into account a thermal spread in plasma, As nz2 1/& and leal ell 1, consequently the term
+
FIQ. 2. Critical parameter of amplification depending upon velocity spread of velocities in beam.
connected with the thermal spread is small, but, nevertheless, it may become greater a t u --f 1 and u v -+ 1. Consider the effect of the thermal spread in the electron beam. When electrons are moving from the cathode to collector, a n increase in the electron beam spread is charact>eristicof the plasma amplifier, as the beam scatters at the expense of collisions with plasma ions and neutrals as well. Obviously the spread of the thermal velocities in the beam should decrease the amplification of the system. In the case of a small amplification parameter it is very simpIe tJo take into account the spread of velocities in the beam. Equation (16) with the spread of velocities considered, takes the following form:
+
300
V. YA. KISLOV, E. V. BOGDANOV, AND 2 . S. CHERNOV
where v T / v , is the ratio of the average thermal velocity in the beam to the average velocity of the beam. The solution of the equation shows that the value of the spread affecting the amplification and disturbing the amplification mechanism depends on the amplification parameter. The dependence of the amplification upon the spread of the electron velocities in the beam at the given amplification parameter is shown in Fig. 2. Dependence vT/ve perturbing the amplification upon C is illustrated in Fig. 2. As follows from these curves, the amplification in the system may be perturbed even a t relatively small values of v T / v , . I n a number of cases the thermal spread in the beam may limit the effective length of the system. Now we consider a general case when electrons of the beam are moving at helix trajectory along the magnetic field. On the basis of general expressions obtained in Shafranov's work (50) we can derive an expression for the monochromatic beam tensor with electrons moving a t helix trajectory along the magnetic field. The distribution function of such a beam obviously has the form of
Averaging fo in the general expression for the tensor and leaving only the resonance terms proportional to
and after a number of transformations we obtain the following expression for the beam tensor:
where
30 1
GENERATION AND AMPLIFICATION O F MICROWAVES
where w, = w - nox. At n = 0, v, = 0, Eq. (24) is changed into a simple expression obtained earlier for €;k of a beam. The terms with n # 0 correspond to a resonance interaction of the beam a t the cyclotron waves. At n = 0 there is an interaction with the space charge waves in the beam. Using physics terminology we may say that the case of n = 0 corresponds to the cherenkov interaction while the case of n # 0 corresponds to the Doppler effect interaction. The interaction equation of a slow beam with plasma for a n n resonance takes the following form:
It was assumed that perturbation produced by the beam was rather small. This fact permitted us to take into account the beam terms only in comparison with a small difference, e3 e l tan2 eo. At n = 0 we obtain Eq. (7). The transverse interaction with n # 0 possesses a number of important and interesting features. In the case of the cherenkov interaction, kz = w / v o is always greater than ko. This specifies the impossibility of a wave radiation into free space, while for the Doppler interaction an effective excitation even is possible a t k, = (W - nwfl)/va. This fact is of great interest as, at w nww, k , may become quite small ( k z << ko). I n this case an electromagnetic wave radiation into free space occurs. Now we estimate the value of the argument of Bessel functions: k, = Z T / X , ~ , V ~ / W H = r H ; r H is a Larmor radius. At a magnetic field of Ho 3 X lo3 oe and v I o 2 X lo8 cm/sec, T H 0.3 mm. For X 3 cm, A, may be of some millimeters and even less. Therefore, argument J , may be rather great. In this case the excitation is possible not only of the basic resonance a t w w H , but also a t W H w/n. On the other hand, the case when k , r H << 1 can be carried out with greater ease. It turns out that a resonance with n = 1 is rather significant. And the equation describing the interaction between the beam and plasma takes the following form :
+
--
-
+
AnZ4 nZ2e3-I- nz2€1where w 1
= w
-
WH.
-
=
D
(26)
Or if the thermal spread in plasma is neglected, then:
302
V. YA. KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV
If we compare this case with a case when n = 0, then, as is seen from the equation, the term connected with the presence of the beam at n = 1 may be greater than a t n = 0, if ( V , ~ / V O ) > ~> 1 or tan2 0 >> 1. Thus, the transverse interaction may be rather effective, especially when the transverse motion in the beam prevails and the beam velocity along the field is small. I n this case the conditions of radiation into free space become substantially easier. The direct radiation into free space occurs at v f r > c or at vo/[l - n ( w H / w ) ] > c, i.e., at 1 > n ( w / w ) > 1 - 0 and p = vo/c. The radiation band at 0 10-1 is about 10% wide. But even at vfr c the conditions for taking off high-frequency power are significantly facilitated as the velocity of the exponential decrease of the fields from the plasma boundary into free space decreases with the increase of v,, (or decrease of kz). Thus, the propagation regions of slow waves near the critical frequencies may be used for the design of plasma amplifiers and generators. A kinetic approach should be used for the description of these waves. Taking into consideration the thermal motion of electrons, the refractive index a t the critical point with tan2 e = -e3/el takes t#hefinite value of n l / P T . Landau damping becomes quite significant at greater values of n. These values correspond to plasma wave propagation and this region is not suitable for amplification. Wave damping outside this region is comparatively small. But at w H / w + 1 it can become rather significant. As the phase velocity of waves can be lower than th a t of light, a resonance interaction between waves and the beam in the presence of synchronism of the wave velocities and the beam is possible. The equations describing the interaction between slow waves and the beam can be reduced to Pierce-type equations used in the traveling and backward wave tube theory. This permits one to use the calculated values of the amplificat,ion factor for direct waves and starting currents for backward waves. The influence of the thermal spread in plasma upon the efficiency of the interaction is rather small. But a t u--t 1 and u v -+ 1 it can be rather great. The spread is more significant in the beam. I n some cases the thermal spread in the beam can limit the useful length of the system. Besides the Cherenkov effect resonance, the transverse Doppler effect resonance is also possible. The transverse interaction is most effective a t w W H and also in case the transverse motion in the beam prevails. I n a number of cases the conditions for obtaining high-frequency power become significantly easier at the Doppler effect interaction. I n some practical cases both the beam and plasma usually have finite dimensions, and the influence of boundaries should be taken into consideration in the analysis of propagation of electromagnetic waves and their interaction with the beam. In comparison with the case of infinite
<
-
-
+
-
GENERATION AND AMPLIFICATION O F MICROWAVES
303
medium, the nature of wave propagation as well as that of the interaction with the beam can significantly change. The following two systems are of practical interest: plasma cylinder waveguide and plasma strip-type waveguide pierced through along the axis by the beam. I n the region filled with plasma the solutions in the form of superposition of E and H waves satisfy the Maxwell equations. In a n axially symmetrical case the longitudinal field components of these waves in the internal region are in proportion to J o ( T r )or cos T z , while transverse J 1 ( T r )or sin Tx and radial constant T satisfies the characteristic equation (3) with lc, = T , k, = y. At ( k ~ / y ) ~ / [-l ( WH /W)<< ~ ]1, E and H waves are approximately separated. The dispersion equation for slow E waves takes the following form:
where
K , are modified Bessel functions. If a metal waveguide is filled with plasma the dispersion equation for slow E-waves takes a very simple form of J o ( T a ) = 0 [Eq. (28a)l for a cylinder case and cos Ta = 0 for a strip-type case. As high-frequency fields are basically concentrated in plasma, the solutions of dispersion equations of type (28a) should not differ greatly from the solutions of Eq. (28). The analysis shows that this difference is really small as far as slow waves are concerned and the values of radial constants obtained from Eq. (28) are close to the roots of the J o function. It should be noted that the precise dispersion equation for a metal cylindrical waveguide filled with plasma has the following form :
+
T ( - T 2 - y 2 ko2€i) . -Jo(Ta) -T' ko'e3 Ji(Ta)
+
T( - T ~ -7'
- y2
+
+ k o 2 ~ iK) o ( 7 ~ ) (29)
k02e3
KI(7a)
With an accuracy to terms about ko2/y2we obtain
T2
= -7'(ea/~1)
72
= -y
and
Jo(Ta) = 0
Constant T is not dependent on the values connected with the second wave and the waves are separated. Thus, if a rapidly falling field outside of the plasma waveguide is neglected we shall obtain the following equation for slow E waves:
where
p,
are the roots of Jo(Ta) and the
COB
Ta functions.
304
V. YA. KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV
The following equation is obtained for the phase velocity of a slow wave :
As is seen from this relationship the dispersion for the high modes is more sloping than that of the fundamental one. S urfoce waves 3
2 YO
1
I
2
3 4
5
6
7 8
910
v -1
FIG.3. Dispersion dependence on surface waves for plasma rod in vacuum and dielectric with e = 5.
The influence of the thermal motion on the dispersion of slow waves can easily be taken into account by using the dispersion relationship for infinite plasma obtained in the kinetic approximation with
The equation for det>erminationof n, takes the following form :
where nzz = p , L 2 / ( k o a ) 2 . Far from the critical point the solution of this equation remains the same : n,2 = €1 -n 2 (33) €3 but as opposed to the case when PT = 0, and a t v + 1 and u -+ 1, the phase velocity takes the finite value. For example, a t e3 ---f 0
GENERATION AND AMPLIFICATION O F MICROWAVES
0
0.5
0.25
305
0.75
I-v
FIG.4. Dispersion curves on body backward waves for plasma column in vacuum at various values of u.
0
1
2
I
,
I
I
3
4
5
6
I
7
v- I
FIG.5. Dispersion curves on body wave with normal dispersion.
The dispersion curves for slow waves are shown in Figs. 3-5. Figure 3 corresponds to surface waves propagating a t v > 2 - u, u < 1. Figures 4 and 5 correspond to body waves with anomalous max and normal
(z> w
dispersion.
< w < 1/wH2
< min
+
(z~)
wp2
306
V. YA. KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV
It is very characteristic of volume waves that the fields are distributed in the waveguide cross section. This cannot be obtained in any metal slow-wave structure. The plasma waveguides possess a high interaction efficiency with an electron beam owing to this field distribution and a small group velocity as well. The basic efficiency index of an interaction in microwave devices is
FIQ.6. Dependence of coupling impedance upon constant of propagation for different waves in plasma cylinder.
the value of an electron beam coupling impedance with high-frequency fields of structures. The calculated coupling impedances for various types of waves are given in Fig. 6. The coupling impedances for body waves in plasma are higher than the coupling impedance of the usual helix slowwave structure. IV. PLASMA TRAVELING WAVE TUBE The plasma traveling wave tube is a high-frequency device in which a continuous interaction between an electron stream and a slow electromagnetic wave, spreading in the plasma waveguide, occurs. It should be noted that high-frequency energy is introduced here directly into plasma
GENERATION AND AMPLIFICATION O F MICROWAVES
307
by using the phenomenon of electromagnetic wave propagation in plasma waveguides. The use of plasma as a slow-wave structure results in all the following advantages of this device : the possibility of wide-band electronic tuning of operating frequencies by changing the parameters of a plasma waveguide, the possibility of increasing the amplification per unit length, and consequently the reduction of the length of interaction space and increase of the efficiency a t the expense of the higher values of plasma waveguide coupling impedance in comparison with that of metal slow-wave structures. As far as a n increase of power is concerned the possibility of transmission of high electron currents through plasma and isolation of plasma from the walls of the device with the help of a magnetic field is significant.
FICA7. Schematic diagram of experimental plasma traveling wave tube: (1) electron gun; (2) discharge cathode; (3) discharge anode; (4) plasma; ( 5 ) electron stream penetrating plasma; (6) helic coupling devices; (7) attenuator; (8) collector; (9) envelope.
A schematic diagram of a plasma traveling wave tube suggested in (69)is shown in Fig. 7. A plasma column generated by means of a system of discharge electrodes is penetrated by a fast electron stream. Plasma of a required concentration can be generated also, without the help of a special discharge electrode a t the expense of gas ionization by a more powerful fast electron stream. Electromangetic waves in plasma are excited by matching devices in the form of helix sections. The helix slowing-down corresponds to a slow wave in the plasma waveguide. A cylindrical plasma column in vacuum fully penetrated by an electron stream is considered as a simplified theoretical model of a, plasma traveling wave tube. It leads to the following system equation:
where
308
V.
YA. KISLOV,
E. V.
BOGDANOV, AND Z. S. CHERNOV
I n deriving the equation it was assumed th a t th e signal is rather weak, the waves excited by an electron stream are slow, and plasma has a zero temperature. The extension of Eq. (35) by small perturbations introduced by the electron stream and damping due to the collisions leads to the wellknown characteristic equation of TWT:
S
+
=
(
=
4’ez
+ F’
(37)
J l / J o for a volume wave for a surface wave
F’ and 9’ are the derivatives of the Bessel function argument. From (36) it is clear th at Q does not exceed 0.5.
> 0. Consequently, the parameter of space discharge QC can be neglected in the case of the plasma traveling wave tube with a n electron stream penetrating through all the cross section of the waveguide. The calculated characteristics of an amplifier according to formulas (37) depending on the plasma parameters show that high values of the amplification factor are characteristic of a plasma TWT. The values of the amplification parameter for a plasma traveling wave tube are given in Fig. 8. For comparison, the limiting values of amplification parameter C for the usual TWT with a slow-wave structure in the form of a helix conducting cylinder (solid beam, filling equals to unit) are given in Fig. 8 too. The effect of a magnetic field on the amplification parameter in the regime of plasma T W T surface wave is shown in Fig. 9. The effect of the magnetic field value on the amplification parameter for complete filling of the cylinder is slight. The amplification parameter grows with an increase of ya. A significant dependence of the amplification on the magas #/#’
G E N E R A T I O N A N D AMPLIFICATION O F MICROWAVES Volume wave
309
be = 0.01
0.3
c
0.2
0.1
0
3
2
1
5
4
YO
FIG.8. Dependence of amplification parameter C upon y a for body wave in plasma waveguide and for helix carrying cylinder. Solid line: plasma traveling wave tube. Dashed line: conventional traveling wave tube. 0.3
0.2
C 0.1
0
I
3
2
4
5
Ya
FICA9. Amplification parameter C depending on y a for surface wave in plasma waveguide.
netic field occurs in the case of a narrow axial electron beam. The amplification rises with an increase of the magnetic field. This feature of a surface wave ensures the possibility of operation with large-diameter plasma waveguides. As is seen from Fig. 10 this is also connected with the distribution of fields in the plasma waveguide section. With a n increase of the magnetic field the longitudinal component of the high-frequency field along the axis of the plasma waveguide grow too. With a further increase of the magnetic field a distribution corresponding to a body wave occurs.
310
V. YA. KISLOV, E. V. BOGDANOV, A N D Z. S . CHERNOV
Experimental investigations of slow-wave propagation in plasma waveguides confirm the conclusions of the theory of existence of surface and body waves in plasma waveguides (9,59, 91). Surface waves of a homogeneous plasma column in a vacuum occur only when WH < up in the following frequency band:
< w < d ( U p 2 -k wH2)/2
(39) Volume (body) waves have two transmission regions: forward in the frequency band of 0 < w < min(w, or ~ H ) , a n dbackward in the frequency band of UH
The dependence of signal attenuation passing along a plasma waveguide without magnetic field (a) or with magnetic field (b) is illustrated
Disionce f r o m the oxis of plasrno waveguide
FIG.10. Longitudinal electric field distrihution in cross-section plasma waveguide within body and surface wave conditions for two values of ya.
in Fig. 11. The attenuation is3nsignificant at low frequencies but as the frequency becomes critical the signal attenuation is more and more significant. The vertical dotted lines correspond to the frequencies obtained experimentally and no wave propagation occurs at these frequencies. With an increase of the discharge current (electron concentration) the
GENERATION AND AMPLIFICATION O F MICROWAVES
311
0
I
200
300
I
400
500
I
,
600
I
700
I
800
I
900
f,Mcps ( b)
FIG.11. Experimental dependence of the value of a signal passing along a 15-cmlong plasma waveguide on signal frequency at different discharge currents: (a) H O= 0; (b) Ho = 180 oe.
critical point is shifted toward higher frequencies. With a magnetic field available the critical frequency, corresponding to the same discharge current in the absence of any magnetic field, is shifted toward higher frequencies. This phenomenon is in full accord with the theory. A comparison of the experimental and theoretical relationship of ucrit and ucrit parameters for a critical frequency is given in Fig. 12. A shift of the critical frequency with change of plasma concentration parameter (ucrit) and a magnetic field parameter (uorit) is in full accord with the following ratio: Vcrit
=
Ucrit
1-2
+
+ d(1 -
U,,it)
(41)
312
V.
YA.
KISLOV, E. V.
BOGDANOV,
AND 2. S. CHERNOV
The plasma cylinder is surrounded by a dielectric with dielectric permeability E. Figure 12 shows that with an increase of the magnetic field and in transition from a surface wave to a body one, the value vorit really tends to unity and does not depend on the magnetic field. Experimental investigations of plasma TWT’s were carried out within a wide frequency range of decimeter and centimeter waves (59, 90). Reference (90) is of particular interest; in this work amplification was obtained equivalent to 30 decibels at frequencies of 7-9 Gcps with a n output power of 0.5 watt.
“crit
FIG.12. Dependence of critical valuep, u,, upon uOr.Rated curve compared with experimental values.
A plasma T W T with 9-mm-diameter plasma waveguide (Fig. 7) operates within the frequency range of 200-2000 Rilcps. Real amplification of up to 45 db is obtained with the regime corresponding both to the surface and body waves (See Tables I). The amplification bandwidth for fixed parameters equals about 20-30%. With the magnetic field changed, frequency retuning of the amplifier occurs. The retuning characteristics as well as a corresponding actual amplification are shown in Fig. 13. As is seen, the retuning band amounts to about an octave in this case. It should be noted that the tube length depends significantly upon the inhomogeneity of the magnetic field. When the field inhomogeneity is less than 3%, the length of space interaction amounts to 3-5 cm, while in the case of an inhomogeneous field (-30%), the length of space interaction a t the same signal amplification increases up to 15-20 cm. The
TABLE I(a) SURFACE WAVES
f
H (Mcps) (oe) 620 775
718 740
60 126 160 126 160 126 160
Idiseh
Udisch
Ibeam
Uheam
(ma)
(volts)
(ma)
(volts)
120 50 30
30
200 660 330 610 400 600 400
3 -
700 660 330 610 400 600 400
G G L (elect. (net fp fc (cm) gain) gain) (Mcps) (Mcps) 10 -50
-
15
1800 1200
9
-
18
950
9
-
36
950
11 16.5
170 370 460 370 460 370 460
P u
8.5 2.4 1.8
1.7
u 0.07 0.27 0.36 0.27 0.4 0.25 0.39
ya
(mm Hg)
Q
Gas
1.1 1.25
2 . lo-* Residual gas 8.10-3 Hydrogen
1.25
8 . 1 0 e 3 Hydrogen
1.26
7.
Udisch
Ibeam
Ubearn
(ma)
(volts)
(ma)
(volts)
207
210
20
254
110
80
970 1000 1000
900 900 900
10 19 5
640 200 800 300 54 60 30
0.9 2.0 2.0
640 200 800 300 1000 790 450
22 10 13 13
2
Hydrogen
> z u ~
6
E =! d c 2
8
G G L (elect. (net fp fc (cm) gain) gain) (Mcps) (Mcps) 22
+
1:
TABLE I(b) VOLUME WAVES
Idisch
! M
m
U
r
P V
u
ya
(mmHg)
Gas
3 m
-
-40 30 25 -
45
800
570
15
7.6
0.34
3.10-3 Residualgas
15
1350
304
29
1.4
0.37
3.
10 10 23
-
2500 2500 2500
-
7 6.2 6.2
-
-
-
-
-
-
-
-
Residual gas Mercury Mercury Mercury
'?F1 w
314
V. YA. KISLOV, E. V. BOGDANOV, AND 2. S. CHERNOV
inhomogeneity of the magnetic field as well as the inhomogeneity of concentration connected with it should lead to a change of the phase velocity and a synchronous disturbance of the wave with a beam. As is seen from the analysis of the dependence of the longitudinal high-frequency field on the magnetic field value the redistribution of high-frequency field occurs in the plasma waveguide with an increase of the magnetic field, and the longitudinal electric field at the axis of the waveguide grows. This phenomenon occurs both in the region of surface waves and in that of body waves.
600
700
800
900
f,Mcps
FIG.13. Retuning characteristic at magnetic field changed.
The regimes given in Table I(b) can serve as experimental confirmation of this fact. Optimum amplification at a magnetic field of 110 oe (u = 1.5) is 15 db. Increase of magnetic field up to 210 oe (u = 7.6) led to a rise in amplification a t the same length and close frequency u p to 45 db. Trimming of the discharge current and beam voltage for optimum amplification was carried out in both cases. As the operating point is located on a sloping part of the dispersion curve (v 15-30, ya 0.35), the change of the wave attenuation should be slight with the increase of the magnetic field.
-
-
V. PLASMA BACKWARD WAVE GENERATOR As stated above, one of the regions of wave propagation in plasma waveguides corresponds to backward waves. The analysis of interaction between the electron stream and the waves is identical with that for a plasma traveling wave tube carried out above and accordingly results in
GENERATION A N D AMPLIFICATION OF MICROWAVES
315
the following characteristic equation for the plasma backward wave tube: -62
=
1 -b - id
+ is + 4QC
(42)
This equation determines three slow waves (6,) in the given parameters: QC, d, b Isee formulas (37)]. Consideration of interference of these waves leads to the self-excitation of the system (the amplification factor of the system tends to infinity) and permits one to determine such a length of the system when continuous oscillations develop for given QC, d, b, and 6,. Initially C N , in the function, where N is a number of slowdown wavelengths, depends on attenuation parameter d. This dependence is obtained by numerical solution of a self-excitation equation in ref. (93). Consequently, to calculate the starting currents in the system it is enough to determine the attenuation factor of body backward waves depending upon plasma parameters (v, u, s). Since the value vj >> VT is always true for the plasma generators under consideration, wave damping in plasma is basically determined by collisions of plasma electrons with heavy particles. Relations between the attenuation factor Aya/s on the one hand and magnetic field as well as propagation constant ya on the other hand, calculated by means of formula (37) for the backward wave band, are shown in Fig. 14. With an increase of ya and decrease of the magnetic field, wave group velocity is reduced and the damping increases rapidly. Calculating amplification parameter C and coupling impedance K [see formulas (37)] and determining the initial value of CN found from attenuation (d), the following starting currents are obtained:
where U o is electron beam voltage. Starting current value is dependent upon six parameters (if it is remembered that at w H 2 / u 2 << 1 oscillations occur a t a frequency close to Langmuir’s), such as u, u(v), ya, s, N , C/ZJ,, or values which are more convenient in experiments, H o , A, v, U o ,I, a. Using these parameters it is possible, to fix first the geometry of the system (a and Z), and second, v / w , after which the most typical dependence of the starting current upon only three parameters remains, i.e., the signal frequency, beam voltage (slowdown), and magnetic field. Consider this dependence, provided a = 0.2 i 0.5 cm, 1 = 3 +- 4 cm, v / w = 10-4 + The value of the starting currents depending upon y a
316
V. YA. KISLOV, E. V. BOGDANOV, A N D 2. S. CHERNOV
is shown in Fig. 15. It is evident that there are sharply outlined regions of weak starting currents for fixed magnetic field values and concentration of plasma. Elevation of the left-hand part of the curve is due t'o a decrease in number of slowdown wavelengt'hs along the plasma column. The starting current increase in the right-hand part of the curve at significant slowdown is associated with a sharp attenuation increase of slow waves. Dependence of starting currents on magnetic field at a fixed beam voltage and frequency is shown in Fig. 16. Within the region of a short-wave limit
-U
0.033 O.Oi.25
FIG. 14. Damping coefficient depending on magnetic field and propagation constant.
when relative magnetic fields are not large the starting current decreases sharply with an increase of the magnetic field. Within the region of magnetic fields that are close to the cyclotron resonance the starting current increases slowly. With reduction in frequency of collisions the start,ingcurrent decreases and the boundary of the generation region shifts toward extreme short waves. The same variation of the starting current occurs with a decrease of the plasma column diameter. According to the theoretical interpretation, a n interaction between
GENERATION A N D AMPLIFICATION O F MICRO WAVES
317
70
FIG.15. Starting currents in interaction at backward wave and depending upon ya.
HI oersteds
FIG.16. Dependence of starting currents upon magnetic field.
the electron stream and slow waves within the band of anomalous dispersion is notable for its high efficiency. Many authors associate oscillations observed in plasma and generated by a beam of fast electron with backward waves in the plasma waveguide (65, 66, 70). I n ref. (66) is described a n experiment which clearly shows that oscillations in plasma, generated by a beam of electrons, are excited within the band of backward waves.
3 18
V.
YA. KISLOV, E. V. BOGDANOV, AND 2 . 8. CHERNOV
It should be pointed out that passing of the beam through plasma generated by itself is accompanied by the excitation of a great number of modes of oscillations which form the foundation for various physical processes. Among these it is possible to name such modes of oscillation as the excitation of ionic oscillations, oscillations on direct and backward slow waves in plasma waveguides, oscillations excited by gyrating electrons in the magnetic field, etc. To reveal oscillations on a backward wave it is necessary to set up experiments for checking the anomalous character of the dispersion dependence, a correlation between oscillation powers removed from the gun and collector terminals of the system, and determination of the band of generation frequencies upon the magnetic field.
I
'
850
I
870
860
I
880
I
f,Mcps
FIG.17. Experimental dispersive dependences of oscillations at backward wave in plasma cylinder.
Experiments confirm the existence of a backward wave band in the plasma waveguide. The experiments were set up with plasma generated by an electron beam at a gas pressure of 10-2-10-4 mm Hg. Varying the beam voltage within the limits 100 and 2000 volts gave a beam current, up to 100 ma. The diameter of the plasma cord measured 1 cm and the magnetsic fields were of up to 2000 gauss. The studies were carried out in hydrogen, neon, mercury vapor, and residual gases. The dispersion dependence for two values of the magnetic field is illustrated in Fig. 17. I n accordance with present-day theoretical concepts the dispersion is of a n anomalous character and with an increase of the magnetic field the slope of the curve falls while the region of generation expands. To gain differing signs for the phase and group velocity in the field of
GENERATION AND AMPLIFICATION OF MICROWAVES
319
anomalous dispersion the following inequality should be realized :
-
-
According to the diagram, w / q 7, Aw/AvY, 4, and consequently the inequality is true. Direct measurements of the high-frequency power flow along the plasma column were carried out by means of a comparison between power taken off the collector and gun terminals of the system. The measurements show that in the backward wave states the power taken off the gun terminal is 15-20 db more than that taken off the collector terminal. But i t should be noted that in the system of the design given aside from backward wave states there occur generation states for other interaction mechanisms. I n these states there occurred equal powers or a backward relation between powers a t two terminals of the high-frequency energy. The oscillations under consideratmionmay be divided into three characteristic types. First, there are oscillations for which a condition of u > 1 is realized. The frequency of these oscillations changes slightly with magnetic field variation. The oscillation dispersion is of normal character. Propagation and excitation of body waves a t u > 1 and greater ya occur a t frequencies close to Langmuir’s Second, there are oscillations close to an electron cyclotron frequency. And last, there exist generation zones for which the inequality u < 1 is true and with the increase of the magnetic field the zones are shifted to the region of high frequencies. These oscillations associated with backward waves overlap well into the band of wH to 1 / w P z wB* if estimated according to fp 500-700 Mcps. The fact that oscillations within different wavelength ranges are obtainable with a model possessing fixed geometrical dimensions is of particular interest as far as the plasma generators are concerned. For example, using the plasma backward wave tube system described above it was possible to obtain oscillations within 10- and 3-cm bands and passage from one band range to another was achieved by changing two values, i.e., the values of beam current (discharge) and magnetic field (see Table 11).
-
+
TABLE I1 X<3cm
X>10cm
h>10cm
1200 24 2200 100 200
1200 12 2200 100 100
800 28 600 50 300
-
(volts) Z.o~~ectar(ma) Ucolleotar
H (oe) Ugrid
(volts) (Volts)
Uanode
320
V. YA. KISLOV, E. V. BOGDANOV, A N D 2. S. CHERNOV
Oscillations in the system are critical to a gas pressure change. Dependences of the generated power upon hydrogen and residual gas pressure given in relative units are shown in Figs. 18 and 19.
80
.-c 60 u)
a
.-c0 40
0
P .< 20
d
2.2
2.6 3.10-3 P,mm Hg
FIG.18. Dependence of generated power upon gas pressure (hydrogen).
4
FIG.19. Dependence of generated power upon gas pressure (residual gas).
For every type of gas there exists a certain region of an optimum pressure under which the greatest oscillation power occurs. Experiments prove that for the systems under consideration optimum pressures for hydrogen and neon lie within the region of 2 X 10-8 mm Hg, while the optimum pressure for the residual gas equals about 5 x 10-4 mm Hg.
GENERATION AND AMPLIFICATION O F MICROWAVES
32 1
VI. INTERACTION ON LONGITUDINAL WAVES The first theoretical works on interaction of the electron stream with plasma are associated with this kind of interaction. Akhiezer and Feinberg as well as Bohm and Gross proved that the state of a boundless electron stream penetrating into the infinite plasma is unstable. This results in the wave growth of the space-charge density in the electron stream accompanied by an excitation of longitudinal electron waves with increasing amplitude in the plasma. Interaction between an electron stream and plasma also on longitudinal waves was experimentally obtained for the first time (56).An electron beam, modulated within the 10-cm band range, penetrated the gas discharge region and an amplification of the original modulation was obtained. I n the early theoretical works one-dimensional systems were considered though a system with a confined electron stream is nearer to the real conditions of the experiment. Consider an interaction between infinite and homogeneous plasmas which are free from propagation of slow electromagnetic waves along the magnetic field without an electron stream. The dispersion equation for homogeneous plasma in the magnetic field is of the following form:
Analyzing the dispersion equation we take advantage of t,he method given in ref. (92).The first part of the equation is the slowly changing function y. It is possible, therefore, to have y = yein the right-hand side. As a result the right-hand side of the equation turns out to be well-known function yea, 21, u and can be easily calculated. In general it presents a complex value. The left-hand side of Eq. (45) is also constructed throughout the complex plane. Comparing the functions which represent the right- and left-hand sides of the dispersion equation, the dependence of Tla on 710 is derived. On the other hand, according to the determinat,ion Y = ye[l
k
(mpe/W)(p
+ iq)l
(46)
Thus, amplification per unit length is expressed by means of the formula G, = 8.69yP,q db/cm (47)
322
V.
YA. KISLOV, E.
V.
BOGDANOV, A N D Z. S. CHERNOV
Two types of dependence of amplification upon plasma concentration are typical. At small magnetic fields, when W H < w , the dependence is of resonance character and amplification occurs at w < d w P , 0 8 2 . With larger magnetic fields ( w H > w ) amplification begins with u p = w and there is no resonance (see Fig. 20). Increasing the magnetic field results in lowering the resonance peak of the curve and enlargement of the interaction region toward higher frequencies,
+
a
w2 u2
-*
P
FIG.20. Dependence of amplification upon plasma concentration in interaction on longitudinal waves.
Neglecting of thermal spread is justified in the region which is far from resonance. Carrying out a strict kinetic consideration in the resonance region with a three-dimensional spread and dependence of fields upon the radius is rather complicated. Consider a simplified model with plasma having thermal spread in the direction of the magnetic field only. Taking into account a rectangular pulse distribution function, new expressions e,, T,and T are derived. The terms y 2 v T 2 / w zappear in these expressions. The procedure for solving the dispersion equation requires no changes. Diagrams of amplification parameter qresa t resonance point u = 1 at different values of the magnetic field are shown in Fig. 21.
GENERATION AND AMPLIFICATION O F MICROWAVES
323
I n experimental device (27) (see Fig. 22) the electron stream, created with the help of a special gun, passed through the input modulating section of the helix, then through the holes in the cathode and anode into the interaction space, which was filled with plasma, and, at last, into the output section of the helix. Using this experimental const,ruction real amplifications from 20 to 40 d b were obtained within the band of wavelengths from 30 to 3 cm, while the discharge current equalled 100-200 ma
__c
YO
FIG.21. Dependences of maximum values of amplification parameter pre. upon ya; V T / V ~=
1/20.
and the electron beam current was less than 1 ma. The course of amplification depending upon the discharge current density for various wavelengths is shown in Fig. 23. Sharp decrease of amplification for signal frequencies higher than the critical frequency was theoretically predicted and can be observed here. With the increase of plasma concentration the amplification slowly decreases. As stated above, at comparatively weak magnetic fields (u < O.l), in the case of homogeneous plasma, a sharp overswing should occur 011 the amplification curve. Though in the experiments the value of u reached 0.01 of such overswings, nothing occurs either with changes in signal frequency or with variations in discharge current (plasma concentration). This may indicate that, in the experiments inhomogeneous plasma was dealt with.
324
V.
YA.
KISLOV, E. V. BOGDANOV, AND Z. S. CHERNOV Magnetic coils
FIG.22. Schematic diagram of experimental device on which interaction of electron stream was carried out for longitudinal waves.
FIG. 23. Experimental dependences of amplification of longitudinal waves upon discharge current with different wavelength bands.
VII. OPERATING-WAVELENGTH SHORTENING PROBLEMS IN PLASMA DEVICES To make clear the possibility of the use of plasma generation and amplification of millimeter waves, a number of problems should be solved. Among these problems are, first of all, finding out the features of mechanisms for interaction between the beam and plasma, provided the operating wavelength is shortened; second, generation of dense plasma with concentration equaling 1014-1016 ~ m - and, ~ ; last, a solution of problems concerning the output and input of energy directly into plasma (without using any metal wave structures and resonators). Features of plasma beam amplifiers in conformity with the problem of shortening the operating wavelength were estimated in Ref. (95).
GENERATION AND AMPLIFICATION OF MICROWAVES
325
The advantage of plasma beam amplifiers over conventional electron devices like plasma traveling wave tubes is that there is no decrease of high-frequency fields in the direction toward the beam center. In principle this permits one to increase the beam diameter and output power. But it is difficult to make effective use of this advantage before solving the problem of an effective input of energy directly into plasma. Apart from this there are other limitations primarily connected with dissipation of high-frequency power at the expense of electron collisions. This is primarily true for output power limitation owing to scattering of the electron beam itself while passing through the gas in which dense plasma is generated. But these limitations increase with frequency much more slowly than in standard electron devices. This is illustrated in Fig. 24
too Gain >tO db
6 40
u L
a" 20 0 Frequency in Gcps
100 200 300 400 500 Frequency in Gcps
FIQ.24. (Left) Electron beam plasma devices may operate in the triangular area of the power-frequency plane. (Right) Calculated curves f o r plasma amplifier gain as a function of frequency and percentage of plasma ionization.
from Ref. (95). According to Ref. (95) the amplification criterion for a plasma-beam system can be written down as Kl > 1, where K is an amplification constant depending upon the beam diameter, its velocity and density, and upon the signal operating frequency and collision frequency of electrons in plasma. The free path length of the beam, 1, is determined by such parameters as electron beam velocity, collision cross section of fast electrons with gas molecules, and, lastly, density of plasma particles. The mean free path length with ions having fixed density increases with an increase in the ionization ratio. Consider then the problem of the possibility of creating dense plasma. To carry out amplification or generation on a given frequency the concentration of plasma must be in compliance with the plasma resonance of electrons. In most types of discharges, ionization occurs at the expense of
P
TABLE III'.' M lonization Ioniea- Volume paten- tion recombiEle- tial probanation ment (volta) bility coe5cient
H Ar C8 Hg @
b
13.5 15.7 3.9 10.4
1.2 12 15 18
8 mm
Po (mm Hg)
Power (watt)
4 mm
-___ P
sw/w
I
(mm Hg)
Power (watt)
2 mm
__ v.rr/w
Po (mm Hg)
Power (watt)
1 mm
ueff/w
P O (mm Power Hg) (watt)
30 1.04.10-1 1.68 3.28.10-' 1.85 0.105 4.10-5 4.1.10-4 0.006 5.2'10-8 6.5. 10-3 10-11 2.10-10 8.25.10-4 0.156 1.66.10-6 1.31.10-2 2.46 1.32.10-4 2.1.10-1 39.6 1.06.10-3 3.72 700 292 5.0 lo-' 1.78.10-2 1.04 4.5.10-2 2.86.10-1 16.7 3.4.10-10 1.12.10-~0.065 6.10-4 2.85 533 1.87 0.63. 10-9 1.6 10-1 30 10-9 2.3.10-10 6.3.10-4 0.118 8 . 10-5
A l-amp/cmt current. is chosen considering the possibilities of oxide-coated cathode. Po = pressure required for creation of discharge with given concentration.
.
-
4
veff/o
2.9.10-3 0.9*10-'
-
GENERATION AND AMPLIFICATION OF MICROWAVES
327
electron-molecule collisions. On the other hand, losses of particles in dense plasma are associated mainly with radiation recombination (where we are speaking of densities from 1014to 1016 ~ m - pressures ~, equaling mm Hg, and plasma temperatures of about lo4 OK). Table 111 is based upon a balance of these two processes. The adduced data indicate that the millimeter band can be reached by creating dense plasma. But, owing to an increase of volume recombination (-j4), powers for creating plasma, suitable for the submillimeter band, sharply increase. At the same time, the pressure of the system must also be increased and this results in an increase of the collision frequency and disturbance of the operating mechanism of amplification or generation. I n creating dense plasma (where volume recombination serves as the basic deionizing factor), the least energetic expense occurs for hydrogen and cesium. The collision frequency for hydrogen is the least as compared with other gases. Low-temperature plasma with a high degree of ionization can be obtained with the help of cesium. But to use cesium the system should be thermostatic. As compared with hydrogen, cesium has a greater recombination coefficient and collision cross section (Qc.L% 40 Q H ~ ) . A penning arc discharge is an effective discharge for creating dense plasma. Application of heated cathodes and low discharge voltage make such a discharge comparatively stable. VIII. EXPERIMENTS ON AMPLIFICATION A N D GENERATION OF MILLIMETERBANDOSCILLATIONS BY MEANSOF PLASMA The experiments described here were aimed toward obtaining a n amplification effect in the millimeter band (77). I n the experimental devices the beam modulation was carried out with the help of conventional slow-wave structures. The systems with helices made it possible to work with smaller magnetic fields. Modulation efficiency was low but quite sufficient for examination of the amplification. The conventional slow-wave structures and electron detector were modified for beam demodulation. Demodulation with the help of a n electron detector turned out to be the simplest means for demodulation. A schematic diagram of the electron detector is shown in Fig. 25. The experiments were carried out in the residual gas atmosphere or in mercury vapor. The length of the discharge gap was 2-2.5 cm. Penning discharge was applied. I n the system the pressure was equal to 10-2-10-3 mm Hg. The magnetic field varied within the limits of 200 and 2000 gauss. The best results were achieved with small magnetic fields. Some conditions of plasma amplification systems operating on 8-mm wavelength are given in Table IV.
328
V. YA. KISLOV, E. V. BOGDANOV, AND 2. S. CHERNOV
Thus, we succeeded in proving the fact that a plasma-electron beam system operates effectively enough in the 8-mm band. But it should be noted that, in most experiments carried out in the millimeter band, other sorts of instability interfered with the process of obtaining amplification. Under the action of these instabilities generation at frequencies less than that of the amplified signal occurred. This generation resulted in velocity spread within the beam and in suppression of useful beam modulation.
i
f
FIG.25. Electron detector schematic diagram: (1) electron gun; (2) electron beam; (3) plasma; (4) collector.
TABLE IV
MagDisnetic Current charge field, density length (gauss) (amp/cma) (cm)
Gas
Beam voltage (volts)
2.5 2.5
Air Mercury fumes
900 1100
700 200
2.5 5
ColBeam Plasma lector current amplicurrent density fication (ma) (amp/cm2) (db) 1
1
0.1 0 .1
20
25
Identical amplification effects were obtained with cesium plasma at 23-Gc frequency (95) with plasma amplification equal to 40 db on wavelength X = 1.2 cm and real amplification equal to 8 db. Apart from millimeter-wave amplification in plasma, obtaining electromagnetic oscillations in plasma-beam systems is of particular interest. One of the possibilities for obtaining millimeter wave radiation was experimentally illustrated in ref. (80). In a pulsed high-current discharge (-5 psec, I 100 ka, 6 kgs) electromagnetic radiation occurred when runaway electron current reached a certain critical value. As can be seen from the experiments, the radiation is polarized, coherent, and the radiation intensity 10' times exceeds the heat radiat,ion intensity a t a temperature of 10 ev.
-
GENERATION AND AMPLIFICATION OF MICROWAVES
329
IX. CONCLUSION Thus, extensive theoretical and experiment a1 studies show that plasma can be successfully used for amplification and generation of electromagnetic oscillations within a wide range of wavelengths. In plasma devices wide-band electronic tuning of the frequency is available because of the possibility of varying the plasma electrodynamic characteristics electrically. The amplifiers and generators can be rather compact owing to high efficiency of interaction between the electron stream and plasma. The increase of the operating frequency in this case is not associated with the fact that the system sizes should decrease in accordance with the operating wavelength. And the possibility of passing electron streams of high density through plasma as well as of isolating plasma from the metal walls leads to an essential power increase of plasma devices. All these qualities call for further expansion and intensification of examining the plasma-beam systems for solving a number of complicated problems of creating plasma amplifiers and generators of microwave oscillations.
LIST OF SYMBOLS Signal frequency e Velocity of light in space Dielectric permeability of e0 free space x Wavelength in free space = e/m, electron charge-to1) mass ratio wave numko = W/C = ber in free space Wave vector w
Wave vector projections Refractive index = x/n,wavelength in plasma = 2lr/x, =
2iT/h~~
=
kon
Constant components of electron velocity v , v z Variable components of electron velocity ke = yn = w/e,, electron wave number V T Root-mean-square velocity Phase velocity Vt
WH
U
= =
S
= vedw
V
211,
gyrofrequency of electrons Effective frequency of collisions of plasma electrons = poqHo,
v'
op=/w2 WH2/W2
Values of the same quantity with collisions taken into account
Tensor coniponents of dielectric permeability S Energy flow vector e Angle between wave vector k and magnetic field direction €Io 8' Angle between vector direction S and field HO Plasma frequency of electron stream = o;./wa
Amplification parameter, identical with Pierce parameter Q Space charge parameter b By-pass parameter
330
V. YA. KISLOV, E. V. BOGDANOV, AND Z . S . CHERNOV
Group velocity = vT/C = uo/c
=
V//C
Variable and constant current density P , PO Variable and constant charge density E Electric field strength H , Ho Intensity of magnetic field = plasma elecWP tron frequency
d Altenuation parameter 1 System length N = l/hg, number of slow waves along the system K Coupling impedance Vo, uo Constant voltage T H Larmor radius T , 7 Radial constants a Plasma waveguide radius J” Bessel function I,, k‘n Modified Bessel functions
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Author Index Numbers in parentheses are reference numbers and indicate that an author’s work is referred to although his name is not cited in the text. Numbers in italics show the page on which the complete reference is listed.
A
B
Aarset, B., 150, 162, 168, 169, 178 Abbas, S. A., 282(86), 286 Abbott, H. W., 282(85), 286 Abbott, R. C., 128(90), 163, 176, 178 Abdulaeva, 119(65), 151(65), 152, 176 Abroyan, I. A., 113, 127, 132, 151, 157,
Baker, R. F., 212(25), 246 Balarin, M., 153, 177 Baldwin Jr., J. A., 282(87, 88), 286 Bar, W., 139, 151, 179 Bargman, V., 15, 64 Barnes, G. H., 277(57), 284 Bartkus, E. A., 282(100, l O l ) , 283(100,
158, 159, 160, lY6, 176, 177
Afrosimov, V. V., 69(21, 22), 70(21, 22),
lOl), 286 Bartlett, J., 33(43), 66 76(21, 22, 41), 98, 99 Basso, M., 161, 163, 177 Ahmed, H., 230, 232(40), 247 Batanov, G. M., 119, 127, 132, 140, 151, Akhiezer, A. A., 289(52), 331 Akishin, A. I., 132, 151, 179 157, 176, 177, lY9 Bauer, E. W., 282(82), 286 Albers-Schoenberg, E., 254(6), 283 Baxter, A. S., 184(9), 246 Alexander, M. A., 271(45), 284 Beck, A. H. W., 230, 232(40), 247 Alexander, W., 258( 23), 284 Becker, A., 210, 246 Alexeff, I., 289(71), 291(71), 332 Behrisch, R., 67, 78, 98 Alfen, Xh., 288(39), 331 Bennewitz, H. G., 39(65), 66 Allen, C. A., 271(52), 284 Benzer-Koller, N., 36(57), 66 Allen, J. S., 162, 178 Beresina, G. P., 289(67, 68), 291(67, 68), Allen, M. A., 289(60), 290(60), 831 332 AlmBn, O., 103, 174 Berezin, A. K., 289(67, 68, 69), 291(67, Amdur, I., 117(62), 176 68, 69), 332 Amusia M. Ya., 76, 99 Bernashevsky, G. A., 289(77), 332 Angew, Z., 287(5), 330 Arifov, U. A., 108(11a), 113, 117, 119, Berry, H. W., 69, 116, 117(55), 128(90), 140, 146(53, 55), 147, 150, 163, 98, 124, 130, 132, 134, 135, 136, 137, 140, 176, 176, 178 142, 143, 147, 148, 151, 152, 164, Bethe, H. A., 167, 169, 178 165(11a), 176, 176, 177, 178 Bete, H., 139, lY9 Anderson, P. W., 43(78), 66 Beuchner, W. W., 119(69) 140(69), 150 Apalin, V. A., 34(47), 66 (69), 152, 168(69), 176 Arsenault, W. R., 280(68), 286 Bienlein, H., 22( 22), 23( 22), 34(48, 491, Arzimovich, L. A., 288(20), 330 Ashley, A. H., 260(28), 284 64, 66 Ayukhanov, A. Kh., 117(60), 132, 136, Bikov, M. V., 222(31), 224(31), 247 147(60), 148(60), 159( 160), 164( 142), Bincer, A. M., 36(53), 66 Birdsell, C. K., 321(92), 332 1 Y6, 177, 178 333
334
AUTHOR INDEX
Bloch, F., 30(34), 51, 53, 64 Bloom, M., 30(35), 51, 54, 64 Bobeck, A. H., 282(97, 98), 286 Bobona, R., 22(20), 23(20), 64 Boersch, H., 41, 66 Bogdanov, E. V., 288(27), 289(58, 59), 290(58, 59), 307(59), 310(59), 312 (59), 323(27), 331 Bohm, D., 289, 331 Bohr, N., 73, 167, 99, 178 Bolotin, L. I., 289(67, 68), 291(67, 68), 332
Bopp, F., 40, 66 Boseh, S. H., 113, 132, 134, 135, 176 Bourne Jr., H. C., 140, 150, 179 Boyd, G. D., 288(56), 289(56), 290(56), 321(56), 331 Boyde, A., 233(42, 43), 234, 847 Brachet, C., 183, 246 Bradley, R. C., 140, 1Y9 Brillouin, L., 27, 64 Broers, A. N., 228, 229(39), 247 Brosi, A. R., 22(23), 23(23), 64 Brown, I). R., 254(6), 283 Brown, F., 69(16), 174(173), 98, 178 Brown, S. C., 289(54), 331 Brownlow, J. M., 282( 100, 101), 283(100, 101), 286 Bruce, G., 103, 1 ~ 4 Bruce, G. S., 271(52), 284 Bruining, H., 210, 246 Brunnee, C., 127(88), 132, 133, 134, 135, 136, 137, 161, 164, 172(88), 173(88), lY6 Buchanan, J. G., 234(44), 242(44), 243 (44), 247 Buck, 1). A., 280(66), 286 Bulman, J. B., 99 Burger, R. M., 121(79), lY6 Burhop, E. H. S., 110, 173(22), 176 Byrne, J., 36, 54, 55( 101), 66, 66
C Campbell, N., 109, 176 Carassi, L. M., 13(13e), 64 Carlston, C. E., 68(11), 114(30), 125, 140, 141(30), 142, 156, 173(122), 98, 1Y6, 1Y7
Carter, I. P. U., 263(39), 284 Case, K. M., 7(13a), 13(13a, 13c, 13d), 24( 13c), 64 Cavanagh, P. E., 22(24), 23(24), 64 Chambers, E. S., 151, 161, 162(132), lY8 Chaudhri, R. M., 68, 92, 117, 145, 161, 162, 98, lY6 Chernov, Z. C., 289(77), 332 Chernov, Z. S., 289(58), 290(58), 331 Chicherov, V. M., 68(9), 152(108), 98, 1YY Childress, J. D., 260(26), 284 Chorney, P., 287(10), 330 Christopherson, W. A., 263(40), 284 Clapier, R., 147(104, 105), 1YY Clark, J. S., 119(69), 140(69), 150(69), 152, 168(69), 176 Clogston, A. M., 43(78), 66 Cloud, R. W., 140(186), 150(135, 186), 162, 168(135), 169(135), lY8, lY9 Cobas, A., 165, 178 Cohler, E. U., 260(28), 284 Coleman, C. F., 22(24), 23(24), 64 Colombie, N., 125(84), 139(84), 151(84), 152, i55(ii8), I T S , I T Y , im Comeaux, A., 117(57), 118(57), 119(57, 64), 146, 147(57), 157, 164, 165(57), 176 Commins, E. D., 115, lY6, Constantine, Jr., G., 263( 36), 267, 284 Cook, M. H., 258( 15), 283 Cooke, P., 260(29), 284 Copeland, P. L., 119, 151, 176 Couchet, G., 132, 179 Coulliette, H. J., 114, 176 Councill, E. D., 271(52), 284 Courant, E. D., 20( IS), 64 Cousinik, P., 125, 139, 151, 152, lY6 Cox, It. T., 2(1), 36, 63, 66 Crane, H. R., 48, 56(102), 59(107), 60 (108), 61(99), 62(99, 108, log), 66 Crapo, W. A., 282(100, 101), 283(100, l O l ) , 286 Crawford, T. W., 290(85), 332 Crewe, A. V., 212(25a), 246 Critchlow, D. L., 282(86), 286 Culpin, M. J., 223, 225(32), 247 Curtis, P. B., 291(90), 312(90), 332 Caaja, W., 228, 24Y
335
AUTHOR INDEX
D Dagg, D. I., 215, 846 D'Amico, C., 120(78), 122(78), 176 Datz, S., 68, 69, 70, 88, 94, 98 Davies, J. A., 69(16), 174(173), 98, 178 Davis, M., 846 Davisson, C. J., 37, 66 Davoine, F., 183(7), ,946 Dayhoff, E. S., 44, 66 de Heer, F. J., 93, 99 Dehmelt, H., 35, 48, 66 Deichsel, H., 35, 66 DeMichele, D. W., 103(5) 174 Demirkhanov, R. A., 289(62), 290(62), 3S8
Demorest, H. L., 119(68), 140(68), 150 (68), 176 Denisov, N. G., 188(42), 331 De Pasquali, G., 22(20), 23(20), 36(56), 64, 66
Devienne, F. M., 116, 117, 119(166), 147 (51, 104, 105, 106, 189), 149(166), 169(166), 175, 176, 177, 178, 179 Dicke, R. H., 3, 64 DilIiston, D. C., 260(29), 884 Domeij, B., 174(173), 178 Doroekhin, A. A., 139, 140, 141, 151, 177 Dorrestein, R., 115(45), 176 Drummond, I. W., 223, 225(32), 247 Drummond, W. E., 289(73), 332 Dehurakulov, Kh., 117(56), 140(107), 147 (107), 176, 177
E East, L. U., 64 Edwards, D. B. G., 277(60), ,986 Eichbaum, B. R., 258( 16), d83 Einsporn, E., 114, 176 Einstein, P. A., 189, 846 Eisenberg, N., 258(22), ,984 Elfant, R. F., 282(100, 101), 283(100, 101), 886 Erdman, K., 30(35), 51, 54, 64 Eremeer, M. A., 132, 133, 176 Erginsoy, C., 174(172), 178 Everett, R. It., 263(30), 884 Everhart, E., 69, 70, 72, 76, 92( 18), 98, 99
Everhart, T. E., 188, 197, 198, 199(18) 201, 204( 18), 205( 18), 206( 18), 207 (18), 208( 18), 209, 222, 223( 18), 224, 227(33), 846,847
F Fagg, L. W., 3(3), 63 Fagot, B., 68(10), 152, 155(118, 119), 98, 177 Fainberg, Ya. B., 287(7, 8, 16), 288(22, 25), 289(52, 57, 65, 67, 68), 290(57), 291(67, 68), 317(65), 330, 331, 332 Fano, U., 7(12), 12(12), 68(12), 76, 64, 98, 99 Farago, P. S., 21(19), 36, 56(103, 104), 59( 106), 64, 65, 66 Farnsworth, H. E., 121, 126, 176 Fedorenko, N. V., 69, 70, 76(22, 41), 98, 99 Feinstein, I., 287(2), 330 Feldman, C., ,946 Felsner, G., 34(48, 49), 66 Ferrari, R. L., 291(90), 310(9l), 312(90), 338 Fert, C., 68, 125(84), 139(84), 151(84), 152, 155, 98, 176, 177 Field, L. M., 288(56), 289(56), 290(56), 321(56), 331 Filimonov, G. F., 289(64), 33.2 Filippenko, L. G., 70(21), 99 Finch, T. R., 282(97), 286 Firsov, 0. B., 70, 73, 77, 78(25), 170, 99, 178 Fisher, D. G., 281(72), ,985 Fisk, J.B., 119(69), 140(69), 150(69),152, 168(69), 176 Flaks, I. P., 70(21), 99 Fleischmann, R., 34(49), 43, 66, 66 Fluit, J. M., 68, 87, 94, 153(111, 1121, 165,98,99,177, 178 Flyants, N. N., 117(60), 147(60), 148(60, 176 Fogel, Ya. M., 119, 127, 140, 151, 152, 164, 176, 178 Foglia, H. R., 281(77), 886 Foley, H. M., 48(96), 66 Ford, G. W., 36(54), 65 Forrester, J. W., 250( l), 254( I), 883
336
AUTHOR INDEX
Fortin, E. G., 258(24), 284 FOSS,E. D., 271(48), 284 Found, C. C., 114, 176 Fowler, H. A., 44, 66 Fox, R. E., 115, 176 Fradkin, D. M., 15( 14), 64 Franck, J., 114, 175 Frank, W. I., 280(66), 286 Frauenfelder, H. 3(89), 13, 23(20), 34, 36 (56, 58), 63, 64, 66 Freeman, J. R., 258( 14), 283 Frenkel, Ya. I., 165, 178 Fridburg, H., 39(64), 65 Friedman, L., 68(4), 87, 98 Friedmann, H., 39( 67), 65 Fiichtbauer, C., 109, 175 Fues, E., 38, 42(63), 66 Fuls, E. N., 69(18), 70(18), 76(18), 92, 98
G Gabor, L., 288(32), 331 Gabovich, M. D., 287(13), 330 Gaipov, S., 119(65), 151(65), 152, 176 Card, G. A., 22(24), 23(24), 64 Gardiner, B. B., 56( 104), 66 Gelbard, E., 258( 13), 283 George, T. H., 121(79), 176 Germer, L. H., 37, 66 Cershman, B. H., 288(42), 331 Gershman, B. N., 289(49), 331 Gertsenshtcin, M. E., 289(48), 331 Getty, 289(70), 291(70), 317(70), 338 Gevorkov, A. K., 289(62), 290(62), 338 Ghosh, S. N., 140, 151, 165, 166, 169, 178, 179 Gibson, J., 75, 9-9 Ginsburg, V. L., 288(37), 331 Cinzburg, V. L., 287(3, 15), 288(42), 330, 331 Classtone, S., 288(24), 330 Cluckstein, R . L., 22(21), 23(21), 64 Goeler, E. U., 22(20), 23(20), 64 Goland, A. N., 75(29), 99 Golant, V. E., 287(17), 330 Goldstick, C. H., 269(42), 284 Good, T i . H., 15( 14), 64 Good, W. M., 119(75), 176 Goodenough, J. B., 258, 283
Gorbatenko, M. F., 287(7), 289(76), 330, 332 Cordeev, Yu. S., 69(22), 70(22), 76(22, 411, 99 Gould, It. W., 287(9), 288(56), 289(56, 61), 290(56,61), 310(9), 321(56), 330, 331, 332 Grebe, K. R,., 282(100, 101), 283(100, 101), 286 Greenberg, J. S., 22(21), 23(21), 45(83), 64, 66 Creene, D., 114, 115, 146(41), 176 Grodsins, L., 3(7), 63 Gross, E. P., 289, 331 Gruich, D. D., 164(142), 178 Gfinthner, R.,22(22), 23(22), 34(48, 49), 64, 66 Cumeniuk, U. S., 164, 178 Cuntherschulze, A., 139, 151, 179 Curevich, A, V., 287(15), 330 Gurtovoi, A. E., 165, 178 Cutwin, I. A., 281(77), 282(100, 101) 283( 100, 101), 285, 286 Cyorgy, E. M., 258, 883
H Haeff, A. V., 287(1), 330 Hagstrum, H. D., 93, 104(7, 8, 9), 105, 114, 120, 122(78), 164, 165, 99, 174, 176, 176, 178 Haine, M. E., 189, 246 Hamilton, D. It., 39(66), 66 Hammond, J. S., 269(44), 284 Haneman, W. J., 282(92), 885 Hanna, S. S., 3(3), 63 Hanson, A. D., 36(56), 65 Haratyunian, F. R., 38(62), 66 Harmsen, D. M., 36(59), 65 Harrington, M. C., 114(40), 175 Harris, L., 117(63), 176 Harrison Jr., D. E., 125, 176 Harutyunian, V. M., 38, 65 Hasted, J. B., 114, 115, 116, 175 Haymann, P., 109, 175 Haynes, J. L., 263(41), 268, 284 Haynes, M. R., 258, 883 Healea, M., 119, 140, 149(67), 150, 157 (67), 176 Hedvall, P., 289(78), 332
337
AUTHOR INDEX
Heitler, W., 46(87), 66 Helbig, W. A,, 271(50), 284 Hellmann, H., 38, 42(63), 66 Higatsburger, M. J., 119, 140, 150, 176 Hill, A. G., 119, 140, 150, 152, 168, 176 Hillier, J., 183, 212(25), 246 Hintenberger, H., 83, 99 Holm, K., 36(59), 66 Holzwarth, G., 33, 34, 35(42), 66 Honig, R.. E., 103(3), 174 Hopman, H. J., 109, 176 Hopson, I. E., 289(79), 332 Hotchkiss, S., 282(99), 283(99), 286 Hughes, V. W., 22(21), 23(21), 40(70a), 45(83), 64, 66 Hunter, L. P., 282(82), 286
I Issendorff, H. V., 22(22), 23(22), 34(48, 49), 64, 66 Izmailov, S. V., 165, 178
J Jones, P. R., 69(18), 70(18), 76(18), 92( 18), 98 Jonson, H. R., 298(93), 315(93), 332 Jopson, R. C . , 68, 98
Kafig, E., 244, 247 Kallmann, H., 144, 145, 177 Kaminker, D. M., 69(21), 70(21), 76(21), 98
Kaminsky, M., 78, 99 Kapitsa, P. L., 165, 178 Karnaukhov, J. M., 164, 178 Karplus, R., 47, 66 Kastler, A., 40, 66 Kaufman, B. A., 269(44), 284 Kaufman, H. R., 113(25), 176 Kaufman, M. M., 282(91, 93, 94,) 285 Kennedy, P. J., 45(84), 66 Kessel, Q . C., 76, 99 Khadshimukhamedov, Kh. Kh., 164 (143), 178 Khan, A. W., 117, 145, 161, 162,176
Khan, M. Y., 68, 92(7), 98 Kharchenko, I. F., 289(57, 65), 290(57), 317(65), 331, 332 Khare, S. P., 165, 166, 169, 178 Khashimov, N. M., 119, 151, 176 Khozinskii, 0. V., 124(81), 140(81), 142 (81), 143(81), 176 Kilburn, T., 270(60), 286 Kilpatrick, W. D., 111(24), 176 Kino, G. S., 288(18), 289(60), 290(60, 84, 85), 330, 331, 332 Kiseda, J. R., 281(77, 78), 286 Kishinerskii, L. M., 165, 169, 171, 178 Kislov, V. Ya., 288(27), 289(58, 59) 290 (58, 59), 307(59), 310(59), 312(59), 323(27), 331 Kistemaker, J., 68(4), 69, 87(4, 37), 93, 94(37), 153(111, 112), 165(148), 98, 99, 177, 178 Kitsenko, A. B., 289(82), 332 Klein, E. F., 269(42), 284 Klimontovich, Yu. L., 288(34), 331 Knauer, F., 25(29), 64 Knoll, M., 183, 246 Koch, J., 132, 179 Koenig, S.H., 48(98), 66 Kornelsen, E. V., 103, 174(173), 174, 178 Kornfield, N. R., 282(91, 94), 286 Kornilov, E. A,, 289(65), 317(65), 332 Kovner, M. S., 289(81), 332 Krenz, Y. H., 288(18), 330 Kroll, H. M., 47, 66 Kronenberg, S., 161, 163, 177 Kurrelmayer, B., 2( l), 6 3 Kusch, P., 48, 50, 66 Kuskevics, G., 113, 132, 134, 135, 176 Kutikov, I. Y., 34(47), 66 Kworykin, V. K., 246 Kyser, D. F., 228, 247
L Lamb Jr., W. E., 115, 165, 176, 178 Lanipert, M. A., 288(26), 289(26), 330 Landau, L., 289(45), 331 Lane, G . H., 69( 19), 72, 98 Langmuir, I>. B., 188, 246 Langmuir, I., 111, 176 Langmuir, T., 287( 11), 288, 330, 331 Lanigan, M. J., 270(60), 286
338
AUTHOR INDEX
Large, L. N., 104, 105(10), 119, 123, 140, 141, 143, 150, 152, l Y 4 , 176 Lasareff, W., 145(102), 1YY Lavrov, V. P., 157(128), 158, 159, 177 Lawrence Jr., W. W., 282(83), 286 Lax, B., 45(85), 66 Layton, J. K., 117(61), 118(61), 119(64), 122(80), 123(80), 139(80), 140(80), 141(80), 147(61), 148(61), 1Y6 Lear, 280(86), 332 Lehmann, C., 75, 99 Lehmann, J., 282(92), 286 Lemmerick, J., 41(75), 66 Lemonick, A., 39(66), 66 Lenz, F., 183, 246 Lessoff, H., 258(24), 284 Levine, L., 289(66), 290(66), 317(66), 332 Levine, N., 22(20), 23( 20), 36(56), 64, 66 Lewis, H. R., 22(20), 23(20), 64 Li, K., 282(99), 283(99), 286 Lichten, W., 76, 99 Linkhart, T. G., 287( 12), 330 Lipkin, H. J., 36(58), 66 Lo, A. W., 281(70), 282(70, 84), 286 Lochinger, R., 282(96), 286 Lockwood, G. J., 69(18), 70(18), 76(18), 92( 18), 98 Long Jr., R. L., 40, 45(83a,b), 66 Looney, I). H., 282(89), 289(54), 286, 331
Louisell, W. H., 56( l02), 59( 107), 66 Loveberg, R. H., 288(24), 330 Lukashevitch, I. I., 34(47), 66 Luscher, E., 128(91), 129, 163, fY6 Lussier, R. R., 281(81), 285 Lutsenko, E. A., 289(65), 317(65), 332
M McAuslan, J. H. L., 229, 230(38), 247 McCargo, M., 69( 16), 98 McDermid, W. L., 281(80), 286 McIlwraith, C. G., 2(1), 63 McKay, R. W., 258( 18), 284 McMahon, R. E., 277, 284 McMullan, D., 184, 205, 646 McNamara, F., 260(27), 284 Magnuson, G. D., 68, 114(30), 125, 140, 141(30,) 142, 156, 173(122), 98, 176, 1YY
Mahadvan, P., 115, 116, 117(61), 118 (61), 119(64), 122(81), 123(80), 139, 140, 141, 147(61), 148(61), 176, I Y 6 Maison, D., 37, 40(70), 66, 66 Malone, D. P., 22(21), 23(21), 6.4 Marcus, M. P., 263(37), 268, 284 Mark, H., 68(8a), 98 Marshall, W., 43, 66 Martineau, M., 183(7), 246 Marton, L., 44, 66 Mashkova, E. S., 68, 85, 140, 152, 153, 156, 163(109, 116), 173(116), 98, 1YY Massarani, B., 222(31), 224(31), Z4Y Massey, H. S. W., 25(28), 32(28), 33(44), 110, 173(22), 64, 66, 176 Matta, R., 224, 227(33), 228, 647 Maydanov, P., 288(30), 331 Medned, D. B., 117, 118, 119(57, 64), 122(80), 123(80), 139(80), 140(80), 141(80), 146(103), 147, 148, 157, 164, 165(57), lY6, f Y Y Meister, H. J., 15, 33, 34, 35(42), 64, 66 Melan, E. H., 258( 15), 283 Melmed, A., 263(38), 277(58, 62), 284, 286
Mendlowite, H., 7(13a, 13b), 13(13a, 13b, 13c), 24( 13b, 13c), 64 Menyuk, N., 258, 885 Merrill, I., 288(29), 331 Merwin, R. E., 271(46), 284 Meryman, H. T., 244, 2.447 Messenger, H. A., 114, 176 Michel, L., 15, 64 Mickelsen, W. It., 113(25), 176 Mikaelyan, L. A., 34(47), 66 Milgram, M., 75(29), 99 Miller, G. H., 116, 151, 152, 176, 179 Miller, W. F., 68( 13), 98 Minnick, R. C., 263(41), 268, 684 Mironov, E. S., 151, lY9 Mitropan, I. M., 164, 178 Moak, C. D., 119(75), 1Y6 Mollenstedt, G., 183, 246 Moller, C., 15(17), 64 Mohr, C. B. O., 33(44, 45), 66 Molchanov, V. A., 68, 85, 140(109), 152 (log), 153(109, 115, 116), 154, 155 (117), 156(109), 163(109, 116), 173 (116), 98, l Y Y Moon, B. P., 93, 114(39), 165, 99, 176
339
AUTHOR INDEX
Morgan, G. H., 69(18, 20), 70(18, 20), 76( 18), 92( 18), 98 Morgulis, N. P., 165, 178 Moroz, L. P., 132, 159(160), 177 Morris, D. J., 258(23), 284 Moses, H. A., 69( 18), 70( 18), 76( 18), 98 Mott, N. F., 25(28), 32, 64 Movnin, S. M., 157(128), 177 Muir, J., 56( 104), 66 Muller, E. W., 43, 66 Murdoch, J. W., 151, 152, 179 Murray, G., 22(25), 23(25), 64 Mullin, C. J., 36(54), 65 Myers, F. E., 36, 65
N Nafe, J. E., 48(95), 6'6 Neidigh, R. V., 289(71), 291(71), 317(71), 339 Nelson, H. F., 33(41), 34(46), 62(109), 64, 65, 66 Nelson, E. B., 48( 95), 66 Nelson, T., 282(96), 986 Nemenov, L. M., 151, 179 Newhouse, V. L., 277(53), 282(91,93,94), 284, 985 Nier, A. O., 119(68), 140(68), 150(68), 176 Nikolayev, P. M., 289(65), 317(65), 332 Nilson, K., 161, 163, 177 Nixon, W. C., 184(7a), 202, 212, 246 Novick, R., 115, 175
0 Oatley, C. W., 184(7b), 199(18), 201, 204( 18), 205( 18), 206( 18), 207( 18), 208(18), 209( 18), 220(7b), 221(7b), 222, 223( 18), 239(7b), 241(7b), 246, 947 Odintsov, D. D., l25( 110), 140(log), 152 (log), 153(109, 116), 156(109), 163, 173(116), 98, 177 Oen, 0. S., 69, 98 Oliphant, M. L. E., 85(36), 93, 114(3R), 115, 165, $9, 176 Olsen, K. H., 263(31), 284 Olson, N. T . , 103(5), 174 Ornedahl, W., 277(62), 285
P Paetow, H., 132, 134, 135, 177 Page, I,. A., 3(4, 5), 63 Palluel, P., 207, 246 Panin, B. V., 76, 99 Panofsky, W. K. H., 46(86), 66 Panov, M. N., 69(22), 70(22), 76(22, 41), 80(31), 99 Papian, W. N., 250(2), 254(2, 5), 263(33), 264, 271(49), 283, 284 Papoulis, A., 280(67), 285 Parilis, E. S., 165, 169, 171, 178 Parker Jr., J. H., 140, 179 Partridge, R. S., 271(48), 984 Paschke, J., 290(94), 332 Pasechnik, L. L., 287( 13), S30 Paul, W., 39(64, 65), 65 Pauli, W., 24(27), 26, 64 Peacock, It. N., 22(20), 23(20), 64 Pearlman, H., 117(62), 176 Pease, I<. F. W., 184(7a), 188, 202, 212, 220, 246, 247 Pedenko, N. S., 289(65), 317(65), 332 Peeo, W. F., 289(71), 291(71), 3S2 Penn, T. C., 281(72), 285 Penning, F. M., 109, 175 Perry, G. H., 281(74), 285 Petersen, H. E., 281(80), 286 Petrov, N. N., 104, 119, 132, 134, 135, 136, 139, 140, 141, 151, 174, 176, 177, 179 Philbert, G., 161, 178 Phillips, M., 46(86), 66 Pidd, R. W., 34(46), 56( 102), 59(1O7), 60 (108), 62( 108, log), 65, 66 Piddington, J. H., 289(55), 331 Pierce, J. R., 288(35, 36), 331 Pierce, R. I)., 281(79), 285 Piercy, G. R., 69, 174(173), 98, 178 Pimbley, W. T., 43, 66 Pinard, P., 183(7), 246 Pines, D., 289(73), 332 Pipkin, F. M., 39(66), 65 Platzman, It. L., 68( 13), 98 Ploc, R., 229(39), 247 Plock, W., 132, 133, 140, 176 Popov, A. P., 289(62), 290(62), 332 Pradal, F., 162, 178 Prodell, A. G., 48(98), 66
340
AUTHOR INDEX
Propst, F. M., 126, 128(91), 129, 163, 176 Pyatigorsky, L. M., 287(6), 330
Q Quartly, C. J., 277(59), 285
Roys, P. A., 64 Rosentsveig, L. W., 41, 66 Rukhadse, A. A., 289(51), 331 Rumble, W. G., 271(50), 282(95), 984, 285 Russek, A., 70, 76(43), 77, 78(27), 99 Russell, L. A., 277(61), 685 Rutherford, E., 109, 175
R S Rabi, 1. I., 48(95), 66 Rae, A. G. A., 56( 104), 66 Raffel, J. L., 260(25), 263(32), 284 Raith, W., 37, 40(70a), 65, 66 Rajchman, J. A., 254(3, 4), 263(3, 4), 265 (3, 4), 271(51), 281(70), 282(70, 84, 90, 99), 283(99), 283, 284, 286, 286 Rakhimov, R. R., 113, 117(56), 119(65), 124(81), 132, 134, 135, 137, 140(81, 107), 142(81), 143(81), 147(107), 151(65), 152, 164, 175, 176, 1'77, 178 Rappoport, V. O., 289(83), 332 Rastall, P., 54, 66 Rastrepin, A. S., 119(72), 127, 140(72), 151(72), 152, 276 Ratcliffe, J. A., 288(38), 331 Reddish, A., 310(91), 332 Reese Jr., H., 119(75), 176 Regenfus, G., 39(68), 40(70), 65, 66 Reichert, E., 35, 37(50a), 65 Reid, G. R., 111(24), 176 Renwick, W., 263(34), 284 Retherford, R. C., 115, 176 Rhodes, W. H., 277(61), 285 Ridley, B. W., 22(24), 23(24), 64 Robinson, M. T., 69, 75, 153( 113), 98, 99 177 Rogers, J. L., 282(87, 88), 285 Rojansky, V., 3, 64 Rol, P. K., 68(6), 69(6), 93(6), 153, 98, 177 Rose, A., 187, 246 Rosen, B., 145(102), 177 Rosenberg, M., 271(45), 284 Rossi, A., 3(9), 13, 22(20), 23(20), 34, 36( 56, 58), 64, 65 Rostagni, A., 116, 144, 145, 175, 177 Roth, L. M., 45(85), 66 Roustan, J. C., 117(58), 147(104, 106, 189), 176, 177, 179
Sagdeen, R. Q., 288(23), 289(72), 330,332 Sakalay, F. E., 277(61), 286 Sands, E. A., 258( 12), 283 Sannikov, S. S., 29, 64 Santouil, R., 152, 155(119), 177 Saparin, G. V., 222(31), 224(31), 2.47 Scharbeg, J., 281(76), 286 Schliepe, R., 37, 41(75), 66, 66 Schlier, R. E., 121(79), 176 Schneider, R. P., 277(57), 281(81), 284, 286 Schuensel, E. C., 258( 15), 283 Schuls, G. J., 115, 176 Schumann, O., 287(5), 330 Schupp, A. A., 60(108), 62(108, log), 66 Schwarts, M., 119, 151, 176 Schwarsschield, A., 36(57), 65 Schwinger, J., 47, 66 Sferrino, V. J., 277(63), 285 Shafranov, V. D., 289~47,50), 293(50), 300, 391 Shahbender, R., 282(96,99), 283(99), 286 Shapiro, V. D., 289(75), 332 Shekhter, S. S., 165, 178 Sheridan, W. F., 140, 151, 179 Sherman, N., 33, 64 Shestukhina, V. U., 132, 133, 176 Sherel Jr., W. L., 258(10, l l ) , 283 Sherlin, R., 263(38), 277(58, 62), 284,286 Siegmann, H. Chr., 40(7U), 66 Silin, V. P., 289(51), 331 Simon, R., 125(84), 139(84), 151(84), 153, 162, 176, 178 Slabospitskii, R. P., 119(72), 127, 140 (72), 151(72), 152, 164, 176, 178 Slutsky, A., 288(30), 331 Smirnov, B. M., 77, 99 Sniirnov, G. V., 34(47), 65 Sniit, J. A., 115(45), 175
341
AUTHOR INDEX
Smith, H. P., 103(5), 174 Smith, K. C. A,, 184(7b), 189,1197, 198, 213,22O(?b), 221(7b), 222(30a), 229, 230(38), 234(45), 239(7b), 240(29), 241(7b), 242, 243, 846, 247 Smullin, L. D., 289(70), 291(70), 317(70), 332 Smullin, L. J., 287( lo), 330 Snolk, C., 68(4), 69, 76, 87(4, 37), 88, 93, 94(3, 37), 165(148), 98, 99, 178 Snyder, C . L., 258( 17), 284 Snyder, H. S., 20( 18), 64 Snyder, R. L., 183, 246 Sommerfeld, A., 31, 64 Sommerfield, C. M., 47, 66 Sommermeyer, K., 165, 178 Sonkin, S., 114, 176 Sosnowski, R., 22(26), 23(26), 64 Souquet, J., 117(58), 147(105, 106, 189), 176, 177, 179 Southern, A. L., 153(113), 177 Speiser, R. C., 111(24), 176 Spicer, W. E., 174(174), 178 Spitzer, L., 288(41), 331 Spivak, G. V., 222, 224(31), 247 Spivak, P. Y., 34(47), 66 Stebbings, R. F., 116, 176 Stehle, P., 36(55), 66 Steinmann, W., 68, 93(8), 98 Stepanov, K. N., 289(82), 332 Sternglass, E. J., 165, 166, 207, 210, 178, 846 Sternheimer, R. M., 3(6), 6s Stewart, A. D. G., 213, 232, 233(41, 43, 43), 234, 235(41), 846, 247 Stix, T., 287( 14), 330 Stuart, R., 103(4), 174(174), 174, 178 Stuart-Williams, R., 258( 19), 271(45), 284 Stupak, 289(67), 291(67), 338 Sumi, M., 288(33), 289(53), 331 Suprunenko, V. A., 289(80), 328(80), 332 Suran, J. J., 282(85), 286 Swartz, G. A,, 324(95), 325(95), 328(95), 338 Swift, C. D., 68(8a), 98
Tancrell, R. H., 277, 284 Targ, K., 289(66), 290(66), 317(66), 332 Tashkhanova, Dzh. A., 164, 178 Tassie, L. J., 33(45), 66 Taub, H., 48(97), 50, 66 Taylor, J. B., 111(23), 176 Teig, M., 281(78), 286 Telegdi, V. L., 15, 58(105), 64, 66 Tel’kovskii, V. G., 68(9), 142, 143, 146, 152(108), 153(115), 98, 177 ter Haar, D., 7( 13), 8( 13), 11(13), 14(13), 64 Terrill, H. M., 209, 246 Theile, R., 183, 246 Thomas, M. T., 70(26), 77(26), 99 Thompson, M. W., 78(34), 99 Thomson, G. P., 331 Thomson, J. J., 109, 176, 331 Thorensen, R., 280(68), 286 Thornley, R. F. M., 195, 197, 198, 209, 215,217,218(27b), 219,241,245( 16), 246, 247 Thornton, P. It., 223, 225(32), 247 Tibbetts, G., 126, 176 Tillman, R.. M., 281(73, 75), 886 Timoshenko, G., 140, 179 Tipper, C. F., 215, 246 Tolhoek, H. A., 3(2), 32, 33, 34(2), 38(2), 41, 63 Tonks, L., 287(11), 288, 330 Trivelpiece, A. W., 287(9), 289(61), 290 (61), 310(9), 330, 332 Trump, J. G., 140(186), 150(135, 186), 162, 168(135), 169(135), 178, 179 Tsui, F. F., 269(43), 284 Tumanian, V. A., 38(62), 66 Turner, J. F., 22(24), 23(24), 64
T
Valenty, G. E., 271(47), 284 Van Chuong, Phan, 139, 155(118), 177, 179
Takeishi, Y., 140, 161, 177
U Ullman, J. D., 36(58), 66 Utterback, N. G., 116, 176 Uyterhoenen, W., 114(40), 176
V
342
AUTHOR INDEX
van der Spuy, E., 27, 64 van der Weg, W. F., 68(6), 69(6), 93(6), 98 van Eck, J., 68(4), 87(4), 93(38), 98, 99 Varnerin Jr., L. J., 165, 178 Vasil'ev, S. S., 132, 151, 179 Vedenev, A. A., 289(72), 332 Vedenev, A. V., 289( 74), 332 Vedenov, A. N., 288(23), 330 Veksler, V. I., 165(144, 145, 146, 147)' 178 Velikhov, E. P., 288(23), 289(72), 330, 332
Villard, M. P., 109, 175 Vineyard, G. H., 75(29), 99 Vise, J. B., 36(57), 65 VIasov, A. A., 289(43, 44), 331 von Ardenne, M., 183, 246 von Issendorff, H., 43, 66 von Roos, O., 165, 171, 173(161), 178
W Wachtel, M. M., 210, 246 Walcher, W., 132, 134, 135, 177 Walentine, J., 282(96), 286 Walther, V., 83, 99 Wanlass, C. L., 281(71), 282(71), 285 Wanlass, S. D., 281(71), 282(71), $86 Warren, C. S.,271(50), 282(92, 95), 284, 285 Washburn, 0. V., 234(44), 242(44), 243 (44), 247 Waters, P. M., 113, 128, 132, 133, 134, 135, 162(89), 175, 176 Webb, H. W., 114, 175 Webb, W., 288(29), 331 Wegener, H., 22(22), 23(22), 34(48, 49), 64, 66 Wehner, G . K., 67, 78, 98, 103(4), 125, 174, 176, 288(31), 290(31), 381 Weisskupf, V., 37(61d), 65
Weisz, R. S.,258(21), 284 Wells, G., 277(64, 65), 286 Wells, 0. C., 199(18), 201, 204(18), 205 (18), 206( 18), 207, 208( 18), 209( 18), 215,219(28), 220, 222(30a), 2'23(18), 224, 227(33), 228, 846, 247 Welton, T., 33(43), 65 Wentworth, C., 282(99), 283(99), 286 Whalen, R. M., 277(61), 285 Wheatley, G. H., 228, 247 Whinnery, I. K., 321(92), 332 Whitlock, W. S., 119, 150, 152, 176 Whitmer, M., 258(20), 284 Widdows, S. J., 281(74), 285 Widrow, B., 280(69), 686 Wiley, D. L., 281(79), 285 Wilkelmi, Z., 22(26), 23(26), 64 Wilkinson, D. T., 48, 61(99), 62(99), 66 Willis, W. R., 153(113), 177 Winston, R., 58( 105), 66 Wittke, J. P., 3, 64 Wittry, D. B., 228, 247 Wojtokowska, J., 22(26), 23(26), 64 Wolf€, P. A., 172, 178 Wooten, F., 174(174), 178 Wu, C. S., 36(57), 65
Y Yamaguchi, S., 37(61b), 65 Yonts, 0.c., 125, I76 Younker, E. L., 263(35), 284
Z Zheleenyakov, V. V., 287( 3, 4), 330 Ziemba, F. P., 69( 18), 70( 18), 76( 18), 92 (18), 98 Zipffel, 290(86), 332 Zscheile, H., 156, 165(123), 177 Ziverdling, S., 45(85), 66 Zworykin, V. K., 183, 246
Subject Index A Aberrations, electron-lens, 189-190 Address register, 253 selection, 263-264 Amplifiers, sense, 253, 268-271 Aperture, optimum, scanning electron microscope, 192 Atom beam production, neutral and nietastable, 114-119 by charge transfer, 116-117 emission, fast secondary, 165-173
B Beams atom, production, 114-119 polarized electron, 1-66 production of, 24-25
C
magnetic, mnltiaperture, 281-282 memory linear-select, 273-279 three-dimensional, 250-273 two-dimensional, 273-279 word-organized, 273-279 saturable magnetic, 264 storage array, 252-253, 254-263 coincident-current toroidal, 250-273
D Damping of slow wave in a n isotropic medium, 294-296 Deflection system, scanning electron microscope, 196-197 Density matrix, 7, 8, 10 Dispersion equation for plasma, 297-299 for slow E-waves, 303 of slow waves, influence of thermal motion, 304-305 Doppler effect, transverse, resonance, 301, 302 Drive switches and circuits, 263-268
cherenkov effect resonance, 301-302 Cleaning of solid surfaces by heating, 120-121, 129 by ion bombardment, 121, 125 E Collector, scanning electron microscope, 197-199 Ejection, kinetic, of electrons from solids, Collisions, two-atom, dynamics of, 70-78 101-179 elastic, 70-75 Electron(s) inelastic, 75-78 beams, polarized, 1-66 Contrast, scanning electron microscope, “mixed state,” 9-12 201-209 “pure state,” 7-9 resulting from chemical nature of speoiremoval from atoms or solids, 38-45 men, 207 moving a t helix trajectory along magfrom potential variation on surface, netic field, 300-301 207-209 penetration into specimens, 209-21 1 from surface topography, 204-207 probe Core current density in, 188-189 array storage cell, 257-260 Gaussian, diameter of, 190-191 ferrite, characteristics, 255-257 shot noise in, 186-188 343
344
SUBJECT INDEX
Emission fast secondary atom, 1 6 5 1 7 3 light, from ion-bombarded metal targets, 92-98 secondary electron, 119-173 by alkali ions, 131-137 current collector methods, 126-129 double modulation measurement, 130-1 3 1 effect of surface contamination, 119126 energy and angular distribution, 161-163 with hydrogen ions, 149-152 from insulators and semiconductors, 157-161 methods of monitoring, 121-123 with neutral atoms, 144-149 by noble gas ions, 137-144 from single-crystal metals, 152-157 theories, 165-173 secondary ion, 164
F Fields focusing properties, 20-22 longitudinal, 16-17 transverse, 17-19 Filter, Wien, 19-20, 23 Flux, neutral particle, thermocouple probe measurement, 117-119
G g-factor anomaly of free electrons, 45-66 measurement by Dehmelt, 48-51 with electrons emitted in beta decay, 56-59 of free electrons of low energy, 51-56 Ghosh and Khare theory of secondary emission, 168
H Head amplifier, scanning electron microscope, 197-199
I Interaction of electron stream with plasma, 321-324 Ion alkali, production, 110-113 emission, secondary, 164 scattering, fast, against metal surfaces, 67-99 Datz and Snoek’s experiments, 88-92 Fluit and Friedman’s experiments, 87-88 Mushkova and Malchanov’s experiments, 85-87 Panin’s experiments, 80-83 Walther and Hinterberger’s experiments, 83-85 sources, noble gas, 113-114 Ionization, surface, 111-112
L Langmuir paradox, 258 Lenses, electron, 1 9 4 1 9 6 aberrations, 189-190 Light emission from ion-bombarded metal targets, 92-98
M Magnetic-core memory technology, 249286 Magnification control, scanning electron microscope, 199-200 Memory content-addressable, 281 core, three-dimensional, 273-279 memory cycle, 252 noise problems, 260-263 sense and inhibit windings, 260 core, two-dimensional, 273-279 core properties, 276-277 linear-select, 273-279 nondestructive read, 279-281 word-organized, 273-279 Micrographs, stereoscopic pairs of, 213215 Microscopy, scanning electron, 181-247 activation process in dispenser cathodes, 229-232
345
SUBJECT INDEX
examination of insulating materials, 2 17-2 19 of integrated circuits, 223-228 of nylon spinning jet, 220-221 factors affecting contrast, 201-209 forming processes in point-contact rectifiers, 222 investigation of specimen surface potential, 222 low voltage operation, 215-217 McMullan’s, 184-186 observation of chemical changes, 229 principles of design, 186-212 techniques and applications, 212-246 Microwaves, plasma applications for, 287-332
effect of macroscopic fields, 13-24 by optical pumping, 40-41 by scattering, 30-38 transmitted by magnetized foils, 3637 transformer, 20-21 vector in laboratory frame of reference, 15-16 time variation, 23-24 Post-write distribution, 262 Potential Bohr, 74 Born-Mayer, 75 Frisov, 74 Power flow, high-frequency, along plasma column, 319
N
R
Noise problems, 3-D core memory, 260-263 shot, in electron probe, 186-188
0 Oscillations on backward wave, 317-320 Langmuir, 288 millimeter band, 327-328
Read, staggered, 260 Reflection coefficient of alkali ions, 164-165 of noble gas neutrals, 164 Resolution limit, scanning electron microscope, 192-194, 212 Iies_onance Cherenkov effect, 301-302 transverse Doppler effect, 301, 302
P
s
Permeability, plasma dielectric, 293-294 Plasma applications for microwaves, 287-332 backward-wave generator, 314-320 starting current, 315-316 creation, dense, 325-327 devices, operating-wavelength shortening problems, 324-327 -electron beam system, 290-291 slow waves in, 291-296 traveling-wave tube, 306-314 Polarization of electron beams, 1-66 by exchange collision with oriented atoms, 3.536 by field emission, 41-43 by interaction with macroscopic fields, 24-30
Scattering fast ion, against metal surfaces, 67-99 Mott, 2, 32 ff, 59 polarization of electrons by, 30-38 Spin electron, 4 ff Bohr’s theorem, 24-25, 28 vector, 5-6, 10 Sputtering of metal surfaces by positive ions, 232-234 Sternglass theory of secondary emission, 16e-168 Storage devices, batch-fabricated, 282283 Switches, drive, 263-268 coincident or anticoincident, 266-267 load-sharing matrix, 267-268 magnetic matrix, 264-268
346
SUBJECT INDEX
T Traveling-wave tube, plasma, 306-314
W Wave@) backward, oscillations in, 317-320 slow damping in an isotropic medium, 294-296 dispersion, influence of thermal motion, 304-305 interaction with electron stream, 296-306 phase velocity, 304 thermal spread, 299-300
Waveguides, plasma, 303 signal attenuation passing along, 310311 surface and body waves in, 310
Y Yield reflected particle, 102 secondary electron, 103 sputtering, 102-103
Z Z drive, 253