Fortschritte der Physik / Progress of Physics: Band 16, Heft 8 1968 [Reprint 2021 ed.] 9783112500545, 9783112500538

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FORTSCHRITTE DER PHYSIK III K U X . H . I BEN IM Al I TKACI. DEH PHYSIKALISCHEN (.1 H.I.I.Si HAI I IN ])K1< DEUTSCHEN I) K M 0 K R ATI SC II E N R E P U B L I K VON ) . KASCHLI IIN, A.LÜSCHE, K. K1TSCHL L.NU R. ROMPE

B A N D 16 • H E F T 8 • 1 9 6 8

A K A D E M I E

-

V E R L A G

B

E

R

L

I

N

Prof. Dr. G E R H A R D H E B E R

Mathematische Hilfsmittel der Physik 2. A u f l a g e 1968 (Wissenschaftliche T a s c h e n b ü c h e r , Reihe M a t h e m a t i k u n d P h y s i k ) Band I -

162 Seiten -

25 Abbildungen -

8° -

8,- M

B a n d I I — 152 Seiten — 4 Abbildungen — 2 Tabellen — 8° -

8,- M

I n beiden B ä n d e n werden einige in der P h y s i k h ä u f i g b e n u t z t e m a t h e m a t i s c h e Methoden, Sätze u n d F o r m e l n aus d e n Bereichen Differential- u n d I n t e g r a l r e c h n u n g ; Vektoralgebra, Vektoranalysis, Tensorenanalysis; R e i h e n e n t w i c k l u n g e n ; Ausgleichsrechnung; Matrizen, D e t e r m i n a n t e n , O p e r a t o r e n sowie F u n k t i o n s t h e o r i e k u r z dargestellt bzw. z u s a m m e n g e f a ß t . Der Verfasser h a t im allgemeinen die Beweise der b e h a n d e l t e n Methoden, Sätze u n d F o r m e l n fortgelassen, so d a ß der B a n d im Stil einem R e p e t i t o r i u m f ü r S t u d e n t e n der P h y s i k u n d f ü r in der P r a x i s tätige P h y s i k e r ä h n e l t , die einfache physikalische R e c h n u n g e n a u s z u f ü h r e n haben. Bestellungen

durch eine Buchhandlung

AKADEMIE-VERLAG PERGAMON FRIEDRICH

erbeten

• BERLIN

PRESS • OXFORD VIEWEG & SOHN

•

BRAUNSCHWEIG

BEZUGSMÖGLICHKEITEN Sämtliche Veröffentlichungen unseres Verlages sind d u r c h j e d e B u c h h a n d l u n g im In- u n d Ausland zu beziehen. Falls keine Bezugsmöglichkeit v o r h a n d e n ist, wende m a n sich in der D e u t s c h e n D e m o k r a t i s c h e n R e p u b l i k an den A K A D E M I E - V E R L A G , G m b H , 108 Berlin, Leipziger S t r a ß e 3 - 4 i n der D e u t s c h e n B u n d e s r e p u b l i k a n K U N S T U N D W I S S E N , E r i c h Bieber, 7 S t u t t g a r t 1, W i l h e l m s t r a ß e 4 - 6 in Österreich a n den G L O B U S - B u c h v e r t r i e b , W i e n I , Salzgries 16 in N o r d - u n d S ü d a m e r i k a a n Gordon a n d B r e a c h Science Publishers, Inc., 150 F i f t h Avenue, N e w Y o r k , N. Y . 100 11 U.S.A. bei W o h n s i t z im übrigen nichtsozialistischen Ausland a n den D e u t s c h e n B u c h - E x p o r t u n d - I m p o r t G m b H , 701 Leipzig, L e n i n s t r a ß e 16. I m sozialistischen A u s l a n d k ö n n e n Bestellungen ü b e r die B u c h h a n d l u n g e n f ü r f r e m d s p r a c h i g e L i t e r a t u r bzw. den z u s t ä n d i g e n P o s t z e i t u n g s v e r t r i e b erfolgen. Auf W u n s c h sendet der A K A D E M I E - V E R L A G I n t e r e s s e n t e n b e i B e k a n n t g a b e der A n s c h r i f t u n d F a c h g e b i e t e u n v e r b i n d l i c h I n f o r m a t i o n e n ü b e r lieferbare u n d k o m m e n d e V e r ö f f e n t lichungen u n d gibt a u c h Bezugsquellen im I n - u n d Ausland b e k a n n t .

Fortschritte der Physik 16, 419—490 (1968)

Electron Ejection from Solids by Atomic Particles with Kinetic Energy KABL HEINZ K B E B S

Sektion Physik der Humboldt- Universität zu Berlin, Bereich Angewandte Massenspektroskopie

DDR

Contents 1. Introduction

420

1.1 Interaction of Atomic Particles with Solid Surfaces 1.2 Electron Ejection by Atomic Particles 1.2.1 Historical Review 1.2.2 Secondary Electron Ejection 1.2.3 Potential Emission 1.2.4 Kinetic Emission

420 422 422 422 423 423

2. Experimental Arrangements and Methods

424

2.1 Experimental Arrangements 2.1.1 Production of a Defined Atomic Particle Beam 2.1.2 Vacuum System 2.1.3 Target 2.1.3.1. Flash-Filament Technique 2.1.3.2. Surface Cleaning by Ion Bombardment

424 424 425 426 428 429

2.1.4 Detection Arrangements 2.1.4.1 Possible Falsifications of Measurements 2.1.4.2 Arrangements for the Measurement of the Yield y 2.1.4.3 Arrangements for the Measurement of the Energy Distribution of Ejected Electrons 2.1.4.4 Arrangements for the Measurement of the Angular Distribution of Ejected Electrons 2.1.4.5 Arrangements for the Measurement of the Distribution Function Describing the Ejection Process 2.2 Experimental Methods 2.2.1 Remarks Concerning the Quotient Method 2.2.1.1 Metastable Ions in the Bombarding Particle Beam 2.2.1.2. Intensity Measurement of a Neutral Particle Beam 2.2.1.3 Modulation Methods 2.2.1.3.1 Modulation of the Bombarding Particle Current ip, 2.2.1.3.2 Modulation of the Current Target-Collector is 2.2.1.3.3 Double Modulation 30

Zeitschrift „Fortschritte der Physik", Heft 8

430 430 432 437 438 439

439 439 440 440 441 . . . 441 441 443

420

KARL HEINZ K R E B S

2.2.2 Remarks Concerning Measurements by Means of Ion-Electron Converter and Open Multiplier 443 3. Experimental Results

445

3.1 General Data 3.2 Measurement of Yield y 3.2.1. Measurements on Poly crystalline Metal Targets 3.2.1.1 y = f (Energy/Velocity of the Bombarding Ions) 3.2.1.2 y = / (Atomic Number of the Ions) 3.2.1.3 y = f (Ion Mass); Isotopic Effect

445 446 446 446 453 453

3.2.1.4 y = f (Ion Structure)

455

3.2.1.5 3.2.1.6 3.2.1.7 3.2.1.8

457 460 460 461

y y y y

= = = =

/ / f f

(Charge of the Bombarding Particles) (Angle of Incidence) (Mass/Atomic Number of the Target) (Surface Coverage of the Target and Temperature)

3.2.2 Measurements on Monocrystalline Metal Targets 3.2.2.1 y = / (Energy of the Bombarding Ions) 3.2.2.2 y = f (Mass of the Bombarding Ions) 3.2.2.3 y = / (Angle of Incidence)

461 461 462 462

3.2.3 Measurements on Semiconductor and Insulator Targets

463

3.3 Measurement of the Energy Distribution of Ejected Electrons 3.4 Measurement of the Angular Distribution of Ejected Electrons 3.5 Investigations of the Distribution Function of the Electron Ejection 4. Theories of Kinetic Emission

465 466 467 468

4.1 General Data

468

4.2 Theories for Low-Energy Bombarding Particles (EK < 1 0 0 keV) 4.2.1 Theory by v. Roos

469 469

4 . 2 . 2 T h e o r y b y PARILIS a n d KISHINEVSKI

4.3 Theories for High-Energy Bombarding Particles (EK > 100 keV)

471

476

4.3.1 Theory b y STERNGLASS

476

4 . 3 . 2 T h e o r y b y GHOSH a n d KHARE

478

4.4 Theories for the Emission from Monocrystalline Targets

479

4 . 4 . 1 T h e o r y b y HARRISON, CARLSTON a n d MAGNUSON

479

4.4.2 Theory by DRENTJE

482

5. Conclusion

483

6. Literature

484 1. Introduction 1.1 Interaction of Atomic Particles with Solid Surfaces

The process of the interaction of atomic particles with solid surfaces is very manifold. This applies on the one hand to kind of interaction, on the other hand to the number of occurring secondary processes. Fig. 1.1 gives a schematic representation of this fact. A bombarding particle, which is impinging on the solid surface (1), can be a positive or negative charged atomic or molecular ion or a neutral or metastable atom

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

421

or molecule. I t can be scattered elastically or inelastically as a positive, negative, metastable or neutral particle (2). In these processes charge exchange or neutralization is possible. In the case of an impact on adsorption layers these processes are also possible. (Reflexion; see SNOEK and K I S T E M A K E R [ 2 / 7 ] ) .

Another possibility is that the impinging particle is adsorbed on the target surface (1 3) or that it penetrates into the target (4), where it tranfers its energy to target atoms by collisions. After this process it diffuses back to the surface, where it is adsorbed (4-^-3). I t is also possible that the target atoms which are participate in these collisions (5) diffuse to the surface where they are adsorbed (5 - > 3). The atoms of the bombarding beam, the target material and the surface coverage (already present before the interaction), which are adsorbed on the surface (3), can evaporate as positive, negative or neutral particles (6) in case there is sufficient temperature. (Thermic emission of adsorbed atoms; thermic emission of target atoms and glow emission of electrons will not be taken in account). In another case it is possible that the bombarding particle penetrates into the target, sputters atoms of the solid (7), which leave the target as positive, negative, metastable or neutral particles (8). The same process takes place, if the bombarding particle penetrates into adsorbed layers. (Sputtering; see B E H R I S C H [39]). Another occurring secondary process is the ejection of electrons (9), which can originate either from the impinging particles (1), the target (7) or from the adsorbed layers (3). These electrons are frequently and not quite correctly termed as „secondary electrons", because of the close relationship between this process and the process due to primary electrons. I t seems that the term „atomic particle induced electrons" will describe this process more correctly (e.g. ion induced electrons in the case of ion-electron ejection). 30*

422

KARL HEINZ KREBS

Finally, one must consider the emission of electromagnetic radiation (10) as a secondary process possible taking place during the interaction of bombarding particles with the solid surface (see S N O E K and K I S T E M A K E R [217]). During the last years the interaction processes occurring between atomic particles and solid surfaces have been obtained a growing significance. These processes play an important part in many fields of physics, mainly in gas-discharge and plasma physics. They also have a technical significance in experimental atomic physics, e.g. in the construction of particle accelerators, ion sources or detection systems for smallest particle beams, but also in the field of high and ultra-high vacuum technique. 1.2 Electron Ejection by Atomic Particles Among the interaction processes considered the ejection of electrons receives a specific position because a yield > 1 is obtained very frequently, i.e. there are ejected more electrons than bombarding particles impinge. For this reason for many years the study of electron ejection has been the object of many papers. 1.2.1 Historical Review The first investigations concerning the emission of electrons from ion bombarded metal surfaces were carried out at the time where A U S T I N and S T A R K E [26] published their paper. I n general, the discovery of the secondary electron ejection due to primary electrons is ascribed to these two authors. After a first work by V I L L A R D [230] published in 1 8 9 9 , who demonstrated the origin of cathode rays if a cathode is being bombarded with positive ions, THOMSON [228] observed the emission of ,,8-rays" occurring during the bombardment of metals with a-particles. The first aimed work with regard to electron ejection was that by FUCHTBATTER [93], who used canal rays. R U C H A R D T and B A E R W A L D [203] and G E I G E R [94] gave reviews on the works published up to 1925, which now have only a historical value. A detailed compilation of the works which appeared up to 1 9 4 1 was given by M A S S E Y and B U R H O P [163]. This book describes investigations with neutrals and metastables for the first time. In addition to these works further reviews were given (in the order of their publication) by I N G H R A M , H A Y D E N and H E S S [119]; I N G H R A M and H A Y D E N [118];

L I T T L E [149];

M C D A N I E L [165]; a n d GOMOJUNOVA

A R I F O V [15];

H O P M A N [117];

M E D V E D a n d S T R A U S S E R [169];

H A Y M A N N [111]; K A M I N S K Y [124]

AKISHIN

[10];

a n d DOBREZOV

[69],

I t may be stated in this place, however, that in the present work, with a few exceptions, only those investigations will be considered which were carried out after 1950. 1.2.2 Secondary Electron Ejection The ejection of electrons from solid surfaces due to primary electrons as well as to atomic particles have a common description of the external emission process. The investigations of the distribution function as described in chapter 3.5 support this assumption. However, a principal difference lies in the height of energy transfer. Because of their small mass, electrons must possess a certain quantity of kinetic energy, if they will eject secondary electrons from a solid surface. For t h a t

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

423

reason there is exclusively a „kinetic" electron emission due to primary electrons. Reviews on this process are given by M C K A Y [ 1 6 6 ] \ BRTTINING [52]; K O L L A T H [130]; D E K K E B [66] and H A C H E N B E R G and B R A U E R [103]. 1.2.3 Potential Emission There are two mechanisms which can produce the ejection of electrons in the case of an interaction of atomic particles with solid surfaces: the potential and the kinetic emission. Potential emission was investigated extensively on metallic surfaces. This kind of emission occurs if the potential energy of the bombarding particle is higher than the work function of the metal. In this case the electron ejection is exclusively a consequence of the potential energy transfer of the bombarding particle to the metal. If a metastable atom strikes a metal surface there are the following possibilities of electron ejection: the Auger de-excitation (one-step process) or the resonance ionization followed by a Auger neutralization (two-step process). Two processes have to be distinguished, too, if an ion strikes a metal surface, emitting an electron: the Auger neutralization (one-step process) and the resonance neutralization followed by an Auger de-excitation (two-step process). Finally, in case a metastable ion strikes the surface, the electron ejection is produced by a two-step process: at first the return to the normal ionization state by an Auger process, followed by an Auger neutralization. I t has been said already, that potential emission is only possible, if the potential energy Ep of the bombarding particles is higher than the work function

2

2 (Eg + EA), where E0 = width of the forbidden zone and EA = electron affinity. There are no conceptions for undefined semiconductor surfaces. The phenomenon of potential emission was essentially investigated experimentally and theoretically by H A G S T B U M and collaborators and by P B O P S T and collaborators. A review with references is given by K A M I N S K Y [124]. The phenomenon of potential emission is not the topic of the present paper. 1.2.4 Kinetic Emission The other mechanism which can produce an ejection of electrons is the kinetic emission. In this case a part of the kinetic energy Ek of the bombarding particle is transferred to target electrons of which a fraction can leave the solid. The kinetic emission is setting in at energies Ek of several hundred eV, in which case

424

K A B L HEINZ K R E B S

there exists a well-defined threshold for each system bombarding particletarget material. The yield y, i.e. the mean number of ejected electrons per incident particle, shows a distinct shift with the energy Ek . On the whole, the mechanism of kinetic emission has not yet been clarified. Therefore, the present paper has the aim to summarize the already existing experimental investigations and theoretical considerations under common aspects and to find out the general regularities which can lead to a description of the kinetic emission. The following informations can be obtained from investigations of kinetic emission : the yield y — mean number of ejected electrons per incident particle ; the energy distribution of the ejected electrons; the angular distribution of the ejected electrons and the distribution function that describes the ejection process. These informations depend on a large number of parameters. I n order to get defined and reproducible results precise arrangements and methods must be applied. Therefore, the following description will begin with a consideration of the experimental arrangements and methods. 2. Experimental Arrangements and Methods 2.1 Experimental Arrangements The construction of an equipment used for the investigation of electron ejection from solids due to atomic particles with kinetic energy mainly depends on the information which are wanted. However, all equipments have the following four functions in common: the production of a defined beam of atomic particles; the maintenance of the necessary vacuum; the bombardment of the solid target, and the detection of the ejected electrons. The equipments which execute these actions are considered in the following. 2.1.1 Production of a Defined Beam of Atomic Particles The purpose of this part of the equipment is the production of an ionic or atomic beam which is defined according to its intensity, energy and energy width, charge, atomic number (element) or mass (isotope; atom or molecule), and which is striking a specific area of the target. At first, we will consider the use of ions as bombarding particles. I n this case, the ion source is the primary part of the assembly. The selection from the large number of source types described in the literature depends on the characteristics desired from the ion beam, e.g. polarity, intensity, energy width. This is, however, not the problem discussed here. We will rather refer to summaries on ion sources (e.g. K A M K E [125]). After this, the produced ions must obtain the energy with which they are to strike the target. This happens by means of an electric field which simultaneously focusses the ion beam. The kind of the applied assembly extends from a simple acceleration distance between two plane sheets to a complex particle accelerator, because the energy range considered is very large (some eV to several MeV). I n this connection we also refer to the special literature.

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

425

Isotopic pure ion beams are necessary for special investigations. For this purpose the accelerated ion beam must be separated according to energy and mass by means of special electric and magnetic fields. In case of very high ion energies it is recommendable to carry out the particle acceleration in two stages. The energy or mass separation takes place after the first (smaller) acceleration. So the necessary expenditure, e.g. with regard to a deflection magnet, can be reduced substantially. These separation methods are the topic of mass spectrometry. That is why mass spectrometric devices are used in many investigations. Summaries on mass spectrometry were given, e.g. by E W A L D and H I N T E N B E R G E R [80] and BRTTNNEE a n d VOSHAGE

[53].

If atoms or molecules are to be used as bombarding particles one has to lead, in general, a beam of accelerated positive ions of an element or a compound through a collision chamber in which there are atoms or molecules of the same substance, and where a beam of relative energy-homogeneous neutrals is produced by various collision processes. This beam can liberated from charged particles by means of the subsequent action of an electric or magnetic field. Ross [202] reports in detail on the possibilities of producing atom or molecule beams.

2.1.2 Vacuum System The final result of the manipulations decribed in the previous chapter was the fact that a beam of atomic particles defined according to intensity, energy, charge state and species will be focussed on a circular or rectangular slit, passes it and strikes the target. This means that the room of particle production and the target chamber are connected by this slit only. I t is not necessary to say, of course, that all manipulations must be executed in vacuo to avoid the scattering of bombarding particles against residual gas particles. The mean free path of the produced particles must be larger than their total path from production to impingement on the target. If we assume that the total path has a length of 1 to 5 meters according to the well-known estimation X = 5 • 10 - s • — [cm]

(A = mean free path; p = pressure in torr)

(2.1)

a vacuum in the order of 10~6 torr is sufficient in the room of particle production. To produce this vacuum one makes use of pumping equipments known in the high vacuum technique (see, e.g. MONCH [173]). In some cases it is necessary to use a differential pumping system, e.g. there are certain demands as to the intensity of the produced ion or atomic beam which necessitate a higher pressure in the ion source or collision chamber. The vacuum conditions mentioned, however, do not suffice for the target chamber. It is well-known that the time necessary to cover a solid surface by a monoatomic or monomolecular layer depends on the vacuum conditions and that it is relatively brief. I t is given (see, e.g. L E W I N [147]) by

02-s-

}/M • T 3,5- 1 0 2 2 - p

M

(2.2)

426

K a r l Heinz

Kbebs

with M T 0 s

— molecular weight; — temperature in ° K ; — gas-kinetic diameter of the adsorbed particle in cm; — sticking probability (s = 1 means that all stricking particles remain sticking);

. / / . / / \

r.\\\v\\\M i.¿/y.¿/././/.\ Faraday

r.wwwxvi

cage.

r.vwlwwi r.Nwíwwi

zy / s . / / s / / . \

rAwlwsxi [\\\\.>\vw 1

M

i U

- h ..1 -U V

'p

1

!

/

F i g . 2.13 A r r a n g e m e n t f o r t h e m e a s u r e m e n t of g a i n of a n o p e n m u l t i p l i e r u s e d b y SCHRÄM, BOERBOOM, KLEINE a n d KISTE, MAKER [208]

F i g . 2.14 A r r a n g e m e n t f o r t h e m e a s u r e m e n t of y u s e d b y WATERS [232]

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

437

are accelerated by means of a two-electrode system and focussed to the first dynode of an open multiplier. I t is possible to separate the negative ions ejected on the target from the electrons by means of a low magnetic field arranged normal to the beam is. 2.1.4.3 Arrangements for the Measurement of the Energy Distribution of Ejected Electrons Some of the arrangements described in the previous chapter make it also possible to measure the energy distribution dyldE e of the ejected electrons with different accuracy. This is effected by a variation of the collector voltage from positive

at target T used by WEHNER [233]

distribution oF the ejected electrons used by KRONENBERG, NILSON a n d BASSO

[140]

values via zero to negative values (retarding potential method). In this case the current i, is plotted as a function of the collector voltage UK at a constant current ip. After this we differentiate di,ldUK = dy/dEe. This measuring methode is applicable in the arrangements sketched in figs. 2.8 and 2.9. Most of the energy distributions described in chapter 3.2 were measured by means of these arrangements. W E H N E R [233] has described an arrangement for the precise measurement of the energy distribution (fig. 2.15). A part of electrons ejected at target T by bombarding particles traverses a diaphragm system. After a subsequent acceleration to 10 eV they enter a 127°-cylindric capacitor where they are energy-selected and 31*

438

K A R L HEINZ K R E B S

focussed on the slit B 3 . After this they are accelerated to 350 V and counted by means of a multiplier. The graph of energy distribution is received by a variation of the capacitor voltage. K R O N E N B E R G et al. [140] used the arrangement sketched in fig. 2 . 1 6 for measuring the high energetic component in the energy distribution of electrons ejected on a target by energy-rich protons («¿1 MeV). Electrons leaving the target in a defined solid angle range enter diaphragm B 1 ; pass diaphragms B 2 and B 3 and are collected in a Faraday cage. A magnetic field is installed vertically to the electron path between B x and B 2 by the aid of which an energy analysis of the electron beam is practicable. I t is also possible to measure the angular distribution of the high energetic component of electron ejection within fixed limits. G O R O D E T Z K Y et al. [99] used a similar arrangement with a magnetic lens spectrometer for the measurement of the high energetic component of electron ejection. In this case the electrons were counted by means of an open multiplier. 2.1.4.4

Arrangements for the Measurement of the Angular Distribution of Ejected Electrons

Up to now only a few measurements of the angular distribution of electrons ejected on solid surfaces by atomic particles were executed. A detailed description of an arrangement for measurement of the angular distribution was given by K L E I N [129] (fig. 2 . 1 7 ) . Electrons leaving the target T in a solid angle range determined by the entrance slit of the Faraday cage F K are acquired in the collector Ko and subsequently measured. Collector and Faraday cage are holdered by a glass tube which is metallized on the outer side up to the shielding plate S and grounded, and both are rotatable magnetically from outside about a soft-iron core reposed in copper rings around an axis vertical to their direction of motion. The test line operates from collector trough the interior of the glass tube about the soft-iron core and a coil spring to the measuring amplifier. Fig. 2.18 shows the geometry of this arrangement. The angular distribution is measurable in a range ^ 87° related to the target normal with the exception of the

ment of the angular distribution of the electrons ejected at target T used by KLEIN [12V]

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

439

angular range limited by the aperture of ion entrance. The angle of incidence 6 of the ions is variable by rotation of the target. I t is not necessary to measure the current ip because the measurement of i, = f(0) is only a relative one. However, one must provide for the constancy of ip . 2.1.4.5 Arrangements for the Measurement of the Distribution Function Describing the Ejection Process Measurements concerning the statistics of the electron ejection were executed sporadically because of the experimental difficulties. These difficulties originate in the fact that during these investigations the "electron stacks" ejected on the target due to individual atomic particles must be detected and registered. The conventional (also the highly sensitive) current measurement is not applicable. Chapter 2.2.2 deals with special measuring methods. The arrangements used up to now depend on the principle of the ion-electron converter as already described in chapter 2.1.4.2. Fig. 2.19 shows the arrangement used by K R E B S \134\. An electron stack ejected by a single ion which strikes the target emits its energy obtained by subsequent acceleration to the scintillator, where it geneFig. 2.19 Arrangement for the measurement of the distribution rates a energy-proportional function used by KREBS [13t] number of photons. These photons produce a voltage pulse in a i2C-link coupled to the photomultiplier output. This pulse, which is proportional to the number of electrons in the "stack", is amplified and then processed in the corresponding channel of a pulse-height analyser and then registered. Thus, this arrangement consists of an ion-electron converter with a following pulse electronic which is also used in the (3-scintillation spectrometry. In the arrangement used by SIMON et al. [225] and SCHACKERT [205], as described already in chapter 2.1.4.2, the scintillator is replaced by a proportional counter tube, the pulses of which are conducted by way of an amplifier to a multichannel pulse analyser. 2.2 Experimental Methods 2.2.1 Remarks Concerning the Quotient Method During the consideration of the detection assemblies in the previous chapter it was stated that most of the determinations of the y-value have been undertaken by formation of the quotient is (negative current from target to collector) to i (bombarding particle beam to the target). In this case some corrections are neces-

440

K A E L HEINZ K R E B S

sary because of the falsifications described in chapter 2.1.4.1. This trivial method must not be illustrated. The production of a defined beam of bombarding particles has been dealt with already in chapter 2.1.1. I t seems necessary, however, to make some comments on two problems: 2.2.1.1 Metastable Ions in the Bombarding Particle Beam The selection methods mentioned in chapter 2.1.1 do not exclude that metastable ions existing in the ion beam reach the target. These metastable ions cause a higher y-value than unexcited ions because of the effect of potential emission described in chapter 1.2.3. Therefore, they falsify the measurement.

0,086 0,082

0,078

0,074

0,070

0,066 20

25

30

35

40

45

50

55'

60

EQ

CeVl

r i g . 2.20 y — HEq) IN case of bombardment of a Mo target by 500 eV Ar+ ions (MAHADEVAN, LAYTON and MEDVED [153])

et al. [153] could demonstrate the existence of metastable ions in an Ar + beam as follows: They varied the electron energy Eq in the electron impact source used for the ion production, in analogy to mass spectr'ometric measurements of appearance potential (see, e.g. [53]), and determined y = f(Eq) under constant test conditions in the case of Ar+ ions, which were directed with an energy of 500 eV on a molybdenium target (fig. 2.20). They stated a notable jump in the otherwise constant y-graph at i? e -values of ^ 3 3 eV. This fact means that this values is evidently a threshold for the formation of metastable Ar ions. The change in y amounted to approximately 5 % . I t is possible to prevent such a falsification, if the electron energy is kept below the formation threshold of metastable ions of the used element when an electron impact source is applied. MAHADEVAN

2.2.1.2 Intensity Measurement of a Neutral Particle Beam There arises a difficulty in the measurement of ip, if one uses the quotient method in the application of a neutral particle beam. Only a few atomic beam detectors described in the literature (see, e.g. A L L I S O N and G A R C I A - M U N O Z [13]) are applicable to the problems treated in this paper.

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

441

FUANTS et al. [89] measure the ion current in front of and behind the collision chamber. They can estimate the neutral flux by the difference of the currents measured. MEDVED et al. [265] direct the neutral particle beam against a thin platinum foil, which can be inserted into the beam path, whereas CHAMBERS [57, 55] uses the target foil. The heating of the foil by the impinging neutrals is determined by means of a high sensitive thermocouple and is taken as a criterion of the particle flux. The calibration of this arrangement is carried out by means of defined ion beams of the same species and energy. This method presupposes that there is the same energy transfer of neutrals and of charged particles of the same energy. This assumption is not permitted for energies below 1 keV, as measurements by MAHADEVAN et al. [154] have shown. This is caused by the different reflexion behaviour of charged and neutral particles of the same energy. DEVTENNE [67, 65] attempts to eliminate the error produced by different reflexion behaviours, and for this purpose he measures the heating of a funnel-chaped detector, into which the bombarding particle beam has entered (black body).

2.2.1.3 Modulation Methods 2.2.1.3.1 Modulation of the Bombarding Particle Current ip I t has been explained in detail in chapter 2.1.3 that definite measurements can be executed at pure targets only. The principal disadvantages of the two cleaning methods mentioned, flash-filament technique and ion bombardment, were discussed, too. N o w it was attempted to avoid these disadvantages by means of measurements on hot targets, in which case the target temperature was so high that a complete desorption was guaranteed (see estimation (2.4), chapter 2.1.3.1). This method has the disadvantage that a remarkable thermic emission of ions and electrons from the glowing target occurs, which falsifies the measurement. Moreover, it is possible that a thermic ionization at the target surface takes place during the bombardment by neutral particles. I n the investigations considered in this paper the thermic emission of electrons mentioned would falsify the current is directed to the collector. If one wants to work with hot targets, a separation of the glow electrons from the electrons ejected by bombarding particles must be accomplished. This separation was executed by PETROV [/55] by means of a modulation of the bombarding particle beam originating in the ion source with a sinusoidal alternating voltage of 600 cps. The electrons ejected on the target by this pulsed current ip also form a pulsed electron current is to the collector, whereas the glow electrons arrive at the collector as a direct current. The true electron current is can be disengaged, amplified and measured by insertion of the system target — collector into a resonance circle. This method does not allow to investigate secondary effects which are a function of target temperature. 2.2.1.3.2 Modulation of the Current Target-Collector ia The formation time of the first monolayer on a previously clean target surface may be drawn from fig. 2.1 as a function of total pressure p of the target chamber.

442

KARL HEINZ K R E B S

According to the assumption of a necessary measuring time of about 10 min in one series it results a necessary working pressure of 10~9 torr. If it is not possible to produce a vacuum of this order a reduction of the measuring time after annealing and cooling of the target by orders of magnitude is equal to a corresponding improvement of vacuum. This opinion has been used by A R I F O V et al. [16] in the case of modulation of the current target-collector is. The principle of this method is seen in fig. 2.21. Between target (2) and collector (3) is applied a sawtooth voltage with a frequency of 25 cps produced by a generator (1). The secondary particle current is ejected at the target by the bombarding particle current ip causes a voltage drop on B v which is amplified by means of the linearamplifier (4) and furnished to the vertical deflection of an oscilloscope (5). The generator (1) synchronized simultaneously the horizontal deflection of the oscilloscope regulated with R 2 . So a standing picture of the volt-ampere characteristics Fig. 2.21 Sketch of the detection arrangement using modulation of the current target — collector (ARIFOV [Z5])

^a

=

/(^target-collector)

is to be seen on the screen. The generator writes the x-axis (zero line), if the current ip is switched off. The absolute value of the current ip is measured in d. c. operation over R 1 by means of the galvanometer (6). Fig. 2.22 shows a volt-ampere characteristics and the zero line photographed from the oscilloscope screen in the case of bombarding a tantalum target (T — -60 0 +60 U [V] = 300 °K) by Rb+ions of energy o o. Oscillogram n I* »v. 400 eV. If there are negative t • e lvi g . 2.22 ofe a volt-ampere characteristics using the modulation of i, (ARIFOV [1~>\) values of (/target-collector the yamplitude will be a criterion for the secondary ion current ig, in case of positive values it is a criterion for the electron current ij. The advantage of this arrangement is that the measurement of a volt-ampere characteristics after cooling of the target needs only fractions of seconds. The disadvantage is the separate receiving of volt-ampere characteristics and zero line.

443

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

2.2.1.3.3 Double Modulation The called disadvantage is avoided by apply of the method of simultaneous modulation of bombarding particle current ip and target-collector current is described by ARIFOV [15]. The principle of this methode is shown in fig. 2.23. A square pulse generator of frequency 250 cps (6) is used to modulate the current ip. The current is emerging from the target with this frequency is scanned by means of a sawtooth voltage produced in (8) with an frequency which is then times smaller than that of the square pulse generator. This signal is given on the vertical deflection of the oscilloscope (9) the horizontal deflection of which is synchronized by generator (8), too. So, a standing picture similar to fig. 2.22 is resulting on the screen, but now it is interrup- Fig. 2.23 Sketch of the detection arrangement using double modul a t i o n (ARIFOV [ / S ] ) ted periodically because the 1 — thermic ion source, 2 — target, 3 — collector, 4 — shielding, 5 - cylindric capacitor, 6 — square pulse generaprimary current is switched tor, 7 — commutator, 8 — sawtooth generator, 9 — oson and off regularly by the cilloscope, 10 and 11 — commutator square pulse generator. Pig. 2.24 shows a photographed rrrrrrf oscillogram of the same measurement like fig. 2.22, but 's produced by means of double r r r y U u u i u u u modulation. In addition to the •f frrrr' possibility of simultaneous receiving of volt-ampere characteristics and zero line this method has the advantage of reduction the bombarding time of the target. Therefore, the adsorption of bombarding parI J I L ticles on the target (see chap-

±

ter

2.1.3.2)

strongly.

is

diminished

-40

0

+40

U [V]

Fig. 2.24 Oscillogram of the same volt-ampere characteristics like fig. 2.22 using double modulation (ARIFOV [15])

2.2.2 Remarks Concerning Measurements by Means of Ion-Electron Converter and Open Multiplier It was already said in chapter 2.1.4.2 that arrangements for measurement of electron yield based on the principle of ion-electron converter are characterized by the fact that y is not determined by direct measurement of ratio igjip, but by

444

KARL HEINZ R R E B S

measurement of the energy transfer of the ejected and subsequently accelerated electrons to a scintillator or a proportional counter tube. This measuring method depends on two presumptions: a) The y electrons ejected on the target by a single ion must leave the target at an approximately same time. So the energy sum they emit after acceleration to the scintillator or the counter tube appears as originated by a particle of corresponding higher energy. G R E E N B L A T T [100] has shown that the time difference between impinging of primary electrons and emerging of secondary electrons ejected by the primaries is smaller than 7 • 10 -11 s. Compared with the time resolution of a counter tube or the phosphorescence time of a scintillator (e.g. 0,55 ¡AS in the case of CsJ(Tl)) this difference is so small t h a t the presumption called above also is fulfilled in the case of primary ions. b) The bombarding particle current ip on the target, i.e. the number of particles per second has to be so small that every process produced on the target by a single particle is separable from the next by scintillator or counter tube. On the other hand it should be possible to measure so many ion processes that the number of nonresoluted pulses does not exceed 1%. These requirements indicate a limitation of the bombarding particle current ip, which is discussed in detail by K R E B S [134, 135] in the case of application of a CsJ-scintillator. The total measuring procedure consists of a series of individual processes, which can collect in two groups. The processes on the target belong to the first group. The impinging bombarding particles effect, always in the single case, the ejection of an fixed number y of electrons. This statistical process is describing by a distribution function (see chapter 3.5). To the second group belongs the large number of processes which begins with the impingement of the "electron stacks" ejected per bombarding particle at the target on the scintillator respectively with their entrance into the counter tube, and which ends with the registration of the pulse height spectrum by means of a multichannel analyser or singlechannel analyser with following recorder. These processes effect a broadening of the pulse height distribution. Therefore the form of the pulse height distribution recorded at the end of registration is a superposition of the distribution of electrons ejected at the target (group 1) and of the distributions of the discrete energy values of the y electrons (y = 0, 1, 2, ...) of the group 2. Pulse height distributions measured in the described manner are shown in fig. 2.25 (scintillation arrangement) and fig. 2.26 (counter tube arrangement). I t is possible to determine the value of yield y with certain corrections out of the maximum of this distribution. The methode of pulse height determination applied to the measurement of yield y does not need the knowness of the absolute value of the bombarding particle current ip. I t is possible obviously to use the anode current as a criterion of is in converter arrangements utilizing a multiplier system for amplification. In this case the multiplier system is coupled as a preamplifier. If ip is known (the bombarding particle current is measured separately) the yield determination is referred to the quotient method ( H E R O L D [112], H A N U S and K R E B S [109]). I t is remarked that in arrangements with an open multiplier described in chapter 2.1.4.2, by means of a suitable electronic also a receiving of pulse height distribution is possible, out of the maximum of which one can determine y. Up to now this method was used by B A R N E T T et al. [29] and S T A N T O N et al. [220].

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

2

3

h

5

6

7

8

9

10 11 12 13 Vt

15 16 17 18 19 20 21 22

445

j

F i g . 2 . 2 5 P u l s e h e i g h t d i s t r i b u t i o n of e l e c t r o n s e j e c t e d b y C 0 2 4 i o n s w i t h e n e r g y 2 2 , 5 k e V f r o m N i , r e c e i v e d b y m e a n s of a s c i n t i l l a t i o n a r r a n g e m e n t ( K R E B S [134])

pulse channel hOOO

XN

3000

2000 1000 r>

• j I

_L_

100

200

300 channel

WO number

F i g . 2 . 2 6 P u l s e h e i g h t d i s t r i b u t i o n of e l e c t r o n s e j e c t e d b y A r + i o n s w i t h e n e r g y 18 k e V f r o m B e , r e c e i v e d b y c o u n t e r t u b e a r r a n g e m e n t (SIMON, HERRMANN a n d SCHACKEKT [ 2 i 5 ] )

3. Experimental Results 3.1 General Data It was shown in the previous chapter that many influences must be regarded in the case of unambiguous and reproducible measurements of atomic particle induced electron emission. In this chapter it is attempted to present the results up

446

KABL HEINZ KBEBS

to now described on uniform aspects in the same sequence stated in chapter 1.2.4. A difficulty in this presentation is the comparison of the results with each other. The reason is that there were differential test conditions, which exclude partially a comparison absolutely (especially differential vacuum conditions). On the other hand there are many individual measurements which often are by-products of other investigations. These facts explain the great number of cited papers. Only some works aimed to the investigation of a defined area of electron ejection. We will refer on this point that a true comparison is possible of such results only, which were performed at the same test conditions. 3.2 Measurement of Yield y 3.2.1 Measurements on Polycrystalline Metal Targets The predominant number of present measurements were undertaken on polycrystalline metal targets, therefore they shall be considered at first. Positive ions were used as bombarding particles in the most cases, because the technique of their production and acceleration is develoved very good. Now the parameters affecting the yield y are presented separately. 3.2.1.1 y = f (Energy/Velocity of the Bombarding Ions) It was shown in chapter 1.2.3 that a potential emission from metallic surfaces is. possible if the potential (ionization) energy of the impinging ion is higher than the twofold work function of the target material, i. e. E

p

>

2 W (Petrov [«»])

r 0,5 He*—Mo

OA 0,3 A

o—o— —

0,2

0,1

Ar*~— Mo

—O—

OO£LO_o_O_O—O—O—

0

100

I

I

I

I

500

900

1300

1700

1 2100

* Ek [eV]

Fig. 3.2 y = /(Ek), He+ and Ar+ -» Mo (Mahadevan, Layton and Medved [113])

particle-target, in which potential emission does not appear. I n this starting range one can recognize a quadratic dependence y = f{Ek). An energy range is following, differential in extent at the different particle-target combinations, in which y increases approximately linear with energy Ek. This is shown in fig. 3.4 in the case of bombardment of molybdenium by different noble gas ions and in fig. 3.5 for Cs+ on tungsten. The dependence will be weakener with increasing kinetic energy. The function y = f(Ek) approachs a flat maximum, the position of which dislocates to higher energies with increasing mass of the bombarding particles. This range is seen in fig. 3.6. After this a weak drop is stated.

448

KARL HEINZ

KREBS

o

0,006

C s

OflOi

+

- ~

W

/

•

0,002-

0

^

,

,

400

800

1200

CS+ - > W

F i g . 3.3 y = /(EK),

(WATERS

E

k

[eV]

[231])

t ySa 0,8

-

0,6

•

Ne

, A r

0,4 •

•

/

/ BT

0,2o

V

Xrt.

0

I 0

F i g . 3.4 y =

r

2

4

I

I

6

8

10

Ek[ke

/ ( E K ) , r a r e g a s i o n s - * M o (MAGNDSON a n d CARLSTON [ 1 5 1 ] )

l 0,8C s

0,4

+

- ~

W

-

— 0

1

^ 4

F i g . 3.5 y =

I(EK),

I

1

1

8

12

16

1 20

E

CS+ - > W (BOSCH a n d KUSKEVICS

k

f r e V ] [48])

V]

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

449

Modern measurements for proton bombardment are collected in fig. 3.7 to give a survey about the shape of function y = f(Ek) for a wide energy range. The test values disperse substantially, because of the differential surface conditions of the targets. However, the general shape of the dependence is seen obviously. Other bombarding particles than protons were not used in such a wide energy range.

W-

7,0 •

target

6,0

5,0

4,0 3.0

2,0

7,0 0

1 0

20

1 40

1 60

1 80

Kig. 3.6 Y = / ( & ) , various ions

1

1

ISO

120

1 KO

" EK

[keVl

W (LARGE [145])

H,+—-Mo

i

\

\

\ 5

H / —

Mo

.... 0,1

0,5

1

1 10

50

1 100

500

1000

Ek

m

[keV]

F i g . 3." y — I(Ek), protons in various energy ranges, taken from the following papers: 1 — [155], 2 — [ 9 i ] , 3 - [146], 4 - [SI], 5 - [1], 6 - [171]

In a number of papers y was measured as a function of the ion velocity as shown in fig. 3.8. I n this case corresponding dependences are valid, discussed in detail in chapter 4.2.2. Fig. 3.9 shows the values of fig. 3.6 converted to velocity. The energy resp. velocity dependence of y was investigated in many papers. The publications since 1950 which was available to the author are collected in the tables 3.1 to 3.3 (with addition of two formerly papers in the high energy range). The measurements are arranged in this tables with regard to the energy ranges. The classification in three groups is arbitrary. I t is drawing from this tables that

450

KARL HEINZ KREBS

T a b l e 3.1 y = f (Energy of Bombarding Ions), Poly crystalline Metals I. Low Energy Bange up to 25 keV Energy Bange [keV] 0 , 0 5 - 0,8 0 , 1 5 - 1,0 0,3 - 1,0 0 - 1,4 0,2 - 1,4 0 , 6 - 1,4 0 , 2 - 1,6 0,3 - 1,6 0 - 1,8 0,2 - 2 1 - 2 0 , 0 4 - 2,4 -

2,5 2,5 2,6 3 3

0,8 0,3 0,250,3 1 — 0,2 0,4 0,5 1,2 0 1 2 -

3 3,5 4 4 4 5 5 5 5 6 6 6

0,1 0,1 0,3 0 0,3

Bombarding Ions

Target Material

Author

H 2 , N 2 , He, Ne, Ar, Kr, X e Li, Na, K , Cs, Pb Cd H, He, Ne, Ar K, Cs Ne, Ar Cs Zn He, Ne, Ar, Xe Ar Ar, C0 2 H, H 2 , H 3 , N, N2, 0 , 0 2 He, Ar He He, Ne He He, Ne, Ar, Kr, Xe, K , N 2 , COa Ar, Hg He He, Ar He, Ne, Ar Li, Na, K , Bb, Cs Ar, K Ne He, Ne, Ar He, Ne, Ar, Kr, X e Ar, K Li, K He, Ne, Ar, Kr, X e

brass

GHOSH e t a l .

1 1,2 1 3 2 0,1 0,2 0,5

- 7 - 7 - 7,5 - 7,5 - 8 - 10 - 10 - 10

Cs Ne, Na, Ar, K , B b Li, Na, K, Bb, Cs Ar

0,5 3 3 1

- 10 - 10 - 10 - 13

Ne, Ar, Kr, X e Li He, Ne, Ar, Kr, X e Li

1

- 18

He, Ne, Ar, N, N 2 , Ca

Li, Na, K Cd, Hg Ar K

Mo, Ta, W Ni, Mo, W Mo Mo, Ta, W CuBe W

ARIFOV e t a l . PETROV GREENE PETROV SUGIURA e t a l . WATERS

Ni, Mo, W Na, K Mo Mo Mo

PETROV

Mo Mo Sb Ta CuBe

MAHADEVAN e t a l .

Mo, W W Ta W Mo Mo Mo Mo CuBe W Mo, Ta AgMg, CuBe NiCr

DOROSHKIN e t a l .

B e , Cu, Mo, P t

Cd, Hg Ta CuBe Mo Mo, Ta, W AgMg AI, Ni, Cu, Zr, Mo, Ta Cu, Mo AgMg CuBe jU-metal, dural, V2A W

BRADLEY ARIFOV e t a l . PHILBERT MAHADEVAN e t a l .

MEDVED e t a l . BATJMHAKEL LAPONSKY BATJMHAKEL

BERRY CATONI e t a l . KLEIN BRUNNEE ARIPOV e t a l . BAKHIMOV e t a l . ARIFOV e t a l . HOFFERT e t al. PETROV EREMEEV e t al. HIGATSBERGER

et al.

PLOCH SCHWARTZ e t a l . PETROV AKISHIN e t a l . BOSCH ARIFOV e t a l . INGHRAM e t a l . MAGNUSON e t a l .

Beference [95] im US8] [101] [188] [223] [231] [188] [50] [20] [191] [155] [153] [168] [36, 38] [143] [37] [71] [42] [56] [129] [52] [19] [198] [23] [116] [189] [75, 76] [114] [193] [210] [188] [12] [47] [19] [118] [151]

COUCHET

[151] [44] [208] [60]

PETROV e t a l .

[190]

MAGNTTSON e t a l . BETHGE SCHRÄM e t a h

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

451

T a b l e 3.1 (Continued) Energy Range [keV] 2

- 1 8

0

- 2 0

3

-20

0,4 -20,4 1

- 2 1

7,5 -22,5 17 - 2 5

Bombarding Ions

' Target Material

Na, Ca, Sb, Te, Ba, Bi H, H 2 , H 3 H, He, N, Ne, Ar, Mo He, Ne, Ar, Kr, X e Cs X e , Hg Kr

Author

Reference

[74]

Ni, Sb, T e , B i

DUNAYEV e t .

Be, Al, Cu, CuBe Zr, Mo

SCHACKERT

[205]

TELKOVSKI

[226]

LACHMANN

[141] [48] m [135]

W W Ni Ni

BOSCH e t a l . BERNHARD e t a l . KREBS

? 2,72,1 1,5 Fig. 3.8 Y = / ( » ) , rare gas ions -S- Mo (ARIFOV, RAKHIMOV and KHOSHINSKI [21])

QQ

0,3 T

I 3

I

I 6

I

P 9 v [l0?cm

W- target

.-He*

0

1,0

2,0

Fig. 3.9 y = /(w), various ions 32

Zeitschrift „Fortschritte der Physik". Heft 8

e-—

T

T

T

.3,0

¿,0

5,0

W (conversion of the values of fig. 3.6

v [ 70® cm [li5])

s'1]

452

KARL HEINZ KREBS

noble gas and alkaliions predominantly were used as bombarding particles, a fact the reasons which are of purely technical nature. The same applies t o t h e predominant high-melting target materials. T a b l e 3.2 y = / (Energy of Bombarding Ions), Polycrystalline Metals II. Medium Energy Range up to 250 keV Energy Range [keV]

Bombarding Ions

Target Material

1 -1 -10 -0,4-1 -5 --

H 2 , He H,H 2 , H 3 H, H 2 H, D, H 2 , HD, He K, Zn, Hg, Tl, Pb H, Ar

Ta Cu, Mo, W dural Mo Pt

30 30 30 40 40 40

10

-- 40

1 2 10 20 15 10 15 20

-- 50 -- 60 -- 60 -- 60 -- 75 --100 --100 --120

35 10

--130 --140

1 0 - 140 1 0 - 140 5 0 - 225 5 240

Author

Reference

PETROV

[ISS] [70] [218] [22]

DOROSHKIN e t al. SOMMERIA ARIFOV e t al.

[S7, SS]

FLAKS

B e , A l , M N , F e , COTJSINÉE e t a l .

Co, Ni, Cu, Zn, Mo, W, P t H, He, Ne, Ar, Kr, 0 F E , Cu, Mo, Ta, W He, Ne, Ar Ni, Mo, W CuBe H, H 2 , H 3 H, H 2 , H j CuBe Li V2A D, D 2 steel Ar Cu, Ag, Au Ar Co, Ni, Cu, Ag H, H 2 , H 3 , He, Ne Zr, Mo Ar, Ti H, H 2 H, H 2 , H 3 C, Ti, Ni, Cu, Pt, Zr, Mo, Ag, Au H, H 2 , He, N, 0 , W Ne, Ar, Kr, N 2 , 0 2 H, He, Ne, Xe, Hg Mg, Al, F E , Cu H W H, He, N, Ne, Ar, N 2 CuBe

[61]

FOGEL e t al.

[90]

ARIFOV e t al.

[21]

CHAMBERS SCHWIRZKE SEILER MCCLURE SIMON e t al. COLOMBIE e t a l . TELKOVSKI

[58] [211] [212] [164] [214] [59] [227]

LARGE e t al.

[144] [146]

LARQE

[145]

LABOE

BOURNE e t al. EWING BARNETT e t al.

[49] [81] [29]

T a b l e 3.3 y = / (Energy of Bombarding Ions), Polycrystalline Metals III. High Energy Range above 250 keV Energy Range [keV]

Bombarding Ions

Target Material

Author

Referei

43-- 426 700--2000

H 1( H 2 , H 3 H 1( H 2

Al, Cu, Mo, Pb Mg, Al, Fe, Ni, Au, Pb

HILL e t al.

[215]

700--2300

Hg

N a , Mg, Al, Ni, Cu,

LINFORD

1000--4000 1500--6000

AARSET e t al.

m

[148]

Ag, Cd, Sn, Mo, W

D

Be, Ni, Cu, BeO,

AKISHIN e t al.

HJ

CuBe, CuMg Al, Ni

MIRONOV e t a l .

m [171]

Electron Ejection from Solids by Atomic Particles with. Kinetic Energy

453

3.2.1.2 y = / (Atomic Number of Ions) Measurements of yield y as a function of atomic number or atomic weight of the bombarding particles have been carried out by OKANO [2 100 keV) 4.3.1

Theory by

STERNGLASS

The theory by STERNGLASS [221], which is joining to the energy range of the two theories previously discussed, originates from the experimental finding that the f value reachs a maximum at higher energies and decreases subsequently. Sternglass uses the following simplifying assumptions: a) Electron capture and electron loss effects are neglected because of the high ion energies. b) The penetration depth x of the bombarding particles is in the order 10~4 to 10~3 cm within the considered energy range. This is essentially more than the depth from which excited electrons are able to leave the metal (10~7 to 10 6 cm). Therefore, with a good approximation it is allowed to consider as a constant value the amount energy loss per unit path length dEJdx, which is necessary for the electron excitation. Sternglass distinguishs between two processes, by means of which the ions transfer energy to bound electrons: a) "Distance collisions" with a small energy transfer per collision (slow electrons). b) Quasi-free collisions with large energy transfer, which cause the production of energy-rich electrons (")dx•

( 4 - 2 °)

With regard to the assumption t h a t dEf/dx is constant, and by means of the function calculated by Ste'rnglass f(vh x) = 1 - exp [— x/LsiVi)] where Lt(v() (4.20)

is the effective penetration depth of the d-rays, one obtains from

with F(v,) = (1 + Lb\Ls)-\ If we substitute dEijdx by a value approximated by =

^

-

, ^ T

BOHR

[46~[

(4.22) m

0 p

where are n* = number of atoms per unit volume, m0 Zj Mi Ei Z J0

= = = = = =

electron mass, charge 1 mass > of the incident ion, energy J atomic number of the target atom, Rydberg energy,

we obtain _

=

• A • Lt [1 +

F(Vi)]

or approximated y = k • E^'1' • Ml1' • zf • Zl>> • Ls.

(4.24)

One can obtain the following statements from (4.24): a) y ~ E f ' 1 ' within the considered energy range, b) f — f{Mi, Z), i.e., dependent on the ion mass and the atomic number of the target material,

KARL HEINZ KREBS

478

c) y ~ zf, i.e., charge dependence, d) y ~ La, because Ls = f(T), it means a temperature dependence, e) the energy distribution of the ejected electrons. The lacks of the theory by Sternglass are situated firstly in the usual limitations; moreover, in the simplifying assumptions initially mentioned, the neglect of electron capture and electron loss effects as well as the constancy of dEijdx, and finally in the charge and temperature dependences, which are not verified by experiment. Sternglass has compared the function y = f{EK), computed by means of his theory, with experimental results obtained by AARSET et al. [ 1 ] and H I L L et al. [115] (see fig. 4 . 6 ) .

5 l> -

x Mg 12 Aarset • Al 13 Aarset 1 Al 13 Hilt

0,1

0,2

0,4

0,6 0,8 7

2

3

Ek [Me V]

Tig. 4.6 Comparison of the function y = 1(EK) computed by STERNGLASS [221] with the experimental values o b t a i n e d b y A A R S E T , CLOUD a n d TRUMP [ 1 ] a n d b y H I L L , BUECHNER, CLARK a n d F I S K

4.3.2.

[11S]

Theory by GHOSH and K H A R E

GHOSH and K H A R E [96] have attempt to eliminate some lacks of the Sternglass theory by means of the replacement of the stopping power dEildx by an ionization cross section Q„i, which regards also electron capture and electron loss effects. They express y BETHE'S

=

[43] expression for Q„i is used

where are E„i = ionization energy of the nl-shell of the target atom, Znl = number of electrons in this shell, Cnl

=

cnl

=

(Et -

Enl)

and

{Zlsln*.al)j\xnl!k\*dlc

(4.25)

Electron Ejection from Solids by Atomic Particles with Kinetic Energy

479

The value of the absorption coefficient « is obtained from (4.25) by means of fitting the experimental value y = 1,08 obtained by A A B S E T et al. [ 2 ] (1 Mev protons -> Al). The validity range of (4.25) was strongly restricted by Ghosh and Khare and comparisons iyere made only with experiments, in which light bombarding particles (H+, D+, HJ, H°) were used in the energy range 0,2—2 MeV. In a later paper [97] G H O S H and K H A B E have extended their conceptions to the energy range 0,02—2 MeV, and corrected (4.25) to 0,25 • n* '

«

Qnt £

(1 +

(4.26)

PIEt,

where (} = constant = 0,0745 MeV. It is possible to obtain statements from (4.26) analogous those from equation (4.24) computed by Sternglass. Doubtless, a lack of the theory by Ghosh and Khare is situated in the determination of the constants « and /?.

7 6-

5-11 4)

E(p,Etel)

= K

J

a,

HEM

V(B)

p2

(4.28)

481

E l e c t r o n E j e c t i o n f r o m Solids b y A t o m i c P a r t i c l e s w i t h K i n e t i c E n e r g y

The limit i i E M of the second integral is less important, because 2(q)Iq becomes very small for R > R 0 . R E M is approximately equalized to the smallest value o f -Kmax-

The determination of R m a x is given by the corresponding position of the particle trajectory related to the lattice atoms. I t means that a considered impact must be closed before the consideration of the next is beginning. Therefore, one considers always double collisions, in which case all those lattice atoms are regarded as collision partners, which are "seen" by the normally incident beam of bom? barding particles, corresponding to the orientation (h, k, I) of the crystal system. 1,0 (in h The geometric parameters in case of nor0,9 mal incidence on the (100) plane of a fee lattice is shown in fig. 4.8. We must re0,8 mark that in this figure R j does not indicate the distance of the lattice pla0,7 nes. 0,6

0,5 OA 0,3

TTi

0,2 0,1

0 Fig. 4.8 Geometric parameters in the case of normal incidence on the (100) plane o( a fee lattice (HARRISON, CARISTON a n d MAGNUSON

[110])

2

6

8

10

Ek

CkeVl

Fig. 4.9 Comparison of the function yCEx) in the case of bombardment of the (111), (100) and (110) plane of a Cu crystal by Ar+ ions computed by HARRISON,

CARISTON a n d

MAGNUSON

{110}

MAHADEVAN

and

with the experimental values obtained by CARISTON, MAGNUSON, HARRISON [55]

Moreover, fig. 4.8 shows that R j and the impact parameter p determine the amount ofi? m a x , and with that the integration limits of ( 4 . 2 8 ) . However, the lattice influences the distribution of the possible p values for every orientation. This fact is expressed in ( 4 . 2 7 ) by the probability density This probability density is mechanically computed by Harrison et al. in the cases of every orientation of the considered crystal systems, just as the function ne (p, Ev) in ( 4 . 2 7 ) . Because of the previously mentioned conceptions of the authors about the impact mechanism, it is not possible to use this function in the simple form (4.8) given by Parilis and Kishinevski. The mechanically computed values are fitted in ( 4 . 2 7 ) , and by means of an adaption to the experimentally found values the adjustable parameters are determined, which are included in the factor K. In fig. 4.9 is shown a comparison of the function y = j {K k ) computed by means of ( 4 . 2 7 ) with the experimental values given by CARLSTON et al. [ 5 5 ] in the case of

482

KAHL HEINZ KREBS

bombardment of the three low-indicated planes of Cu by Ar+ ions (normal incidence, EK = 1 ... lOkeV).

4.4.2.

Theory by

DRENTJE

Because of the assumed simplifications, the theory by Harrison, Carlston and Magnuson does not satisfy, a fact which is remarked by the authors themselves. They attempt to explain the anisotropy of the electron ejection by variation of the orientation of the bombarded plane at constant angle of incidence. The influence of the crystal lattice is determined in this manner, and is joined as a correction into the function y(Ex) given by Parilis and Kishinevski. The anisotropy of yield y occuring in the case of variation of the angle of incidence during the bombardment of an orientated surface is not explicit included in the theory given by Harrison et al. D R E N T J E [73] attempts to describe theoretically this effect and to join into the theory given by Parilis and Kishinevski. The basic principle consists in the fact to vary the angle of incidence at constant orientation, in opposition to the basic principle used by Harrison et al. Drentje's conception is the following: A parallel beam of bombarding particles is normally impinging on a metal surface orientated in a certain manner. If we consider the scattering of impinging particles on a surface atom, it is possible to state the intensity distribution I0 = f(r) of the scattered bombarding particle beam on a plane, which is situated parallel behind the surface in a distance d. I n this case the zero point of t h e abszissa is situated in the center of the vertical projection of the the considered surface atom on the «¿-plane. This atom flings a shadow on the ¿-plane, the border of which is situated at a value r = re. Therefore, it is valid I0 = f(r) = 0 for r < re. The value of re is dependent on the scattering angle. The scattering angle is dependent on p and EK. I n the case of scattering on Cu atoms Drentje has found re ~ E~°,2S in good agreement with re ~ E'1!' given by MASHKOVA et al. [ 1 5 5 , 159]. Now, in the center of the ¿-plane m a y situated an additional lattice atom (i.e., in direction of view of the normal incident beam exactly behind the considered surface atom at the distance d). An energy transfer b y normal impinging particles to this atom is not possible, because it is situated in the shadow of the surface atom. If one changes the angle of incidence of the bombarding particle beam and regards the mean energy transfer E(p) (equation 4.7 in chapter 4.2.2) on the considered atom in the ¿-plane as a function of the angle of incidence