Statistics of kinetic secondary electron emission due to ion-atom collisions in solids

Nuclear Instruments & Methods in Physics Ftesearch

Nuclear Instruments and Methods in Physics Research B67 (1992) 628-631 North-Holland

Sectqon B

Statistics of kinetic secondary electron emission due to ion-atom collisions in solids K. O h y a a n d I. M o r i Faculty of Engineering, The University of Tokushima, Tokushima 770, Japan

Electron emission statistics of ion-induced kinetic secondary electron emission from solids in the energy range 1-40 keV are studied using a Monte Carlo simulation of the transport of the incident ion and recoiling target atoms and a semiempirical model of the kinetic emission. The emission statistics calculated for H + incident on Au are in good agreement with the experimental data obtained recently by Lakits et al. [Rev. Sci. Instr. 60 (1989) 3151]; they show a larger width of the frequency distribution of emission than that of the Poisson statistics. The simulated calculations not only for H + on Au but also for noble gas ions (He +, Ne +, Ar +, Kr + and Xe + ) on Mo show that large-angle elastic scattering which causes backscattering of the incident ion and the recoil of the target atoms broadens the distribution.

1. Introduction Energetic ions bombarding solid surfaces can cause secondary ~electron emission primarily through two formally distinguishable mechanisms. At low ion kinetic energies only potential electron emission can occur through the transfer of potential energy to an electron upon nemralisation and de-excitation of the incident ion. For swift ions one can envisage kinetic electron emission processes similar to those occurring in energetic gas-phase ionisatifa collisions, suitably modified to take into account differences in electronic states. The secondary electron emission is a stochastic process, which is based on a random series of elastic and inelastic collisions in solids. There is thus a great variety in~ the collision sequences and, consequently, a wide spread in the number of emitted electrons from one projectile impact to the other. The use of high energy-resolution detectors for electrons in ion-electron converters permits a measurement of the emission statistics, viz. the frequency distribution of emission of 1, 2, 3, . - . electrons per incident projectile. However, there is still the unsettled question o.~ the na:urc of the deviations of the measured 0istributions from Poisson statistics, the experimentally determined frequency distribution being of greater width [1]. In the present work the emission statistics are studied using a Monte Carlo simulation of the kinetic electron emission in the energy range 1-40 keV.

2. Calculation procedure Theoretically, the emission statistics are caused both by the collision process of the projectile and by that of

the internal secondary electrons in the solid. For projectiles of high atomic number, there is also the collision processes of the recoiling target atoms which are accompanied by the elastic collisions of the projectile and these excite a considerable number of electrons which are not negligible. For the simulation of the kinetic emission of electrons, a semiempirical model developed by Baragiola et al. [2] is applied to the well known TRIM85 program (transport of ion and matter - version 1985) [3], which simulates a trajectory of the incident ion (recoil atom) in solids. The model is based on the assumption that the number of electrons excited by the incident ion (or recoil atom) in unit length along a free flight path is proportional to the electronic stopping power S e ( = - d E / d x ) , viz. N = ( - d E / d x ) / ~ ; e is the average energy deposited to excite an electron. The transport of the excited electrons (internal secondary electrons) to the solid surface is represented by an exponential attenuation function e x p ( - x / L s) with the excitation depth x and the characteristic length L s. With .to being the prcbability for an electron to overcome the surface potential barrier, one obtains for the total number of electrons emitted from the surface per ion (recoil atom) with incident (starting) energy E o,

n(E°) =

~-"

flight paths

fo fnisht

~ "o

pathse(E ) e x p [ - x / L ~ l

d~.

(1) Statistical fluctuation in the transport of the internal secondary electrons is expressed by a Poisson distribu. tion (pro~m!) e x p ( - p ) ; m is the number of electrons emitted from the surface and p is the electron escape probability evaluated by f0 e x p ( - x / L s ) .

0168-583X/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

K. Ohya, L Mori / Electron emissionstatistics In the present calculation, the characteristic length L s is evaluated by using the Ono-Kanaya formula [4], which is in good agreement with Seiler's experimental data [5]; L s is taken as 13.7 A in Au and 14.6 A in Mo. The factor fo/E is evaluated as a function of E o by fitting an average value of n(E o) calculated with 10 4 ions to the experimental electron yields, are measured for H + - A u (Lakits et al. [6] and Baragiola et al. [2]), and He+-Mo, Ne+-Mo, Ar+-Mo, Kr+-Mo and Xe +Mo (Ferron et al. [7]). For the incidence of noble gas ions the potential emission yields obtained by Hagstrum [8] are deduced from the yields, and for heavy ion incidence the fo/e of the recoil atoms is evaluated separately from that of the incident ion.

629

measurement for the probability for emission of no electrons. The quantity W~ is the probability for emission of a given number n = 0, l, 2, • • • of electrons per incident ion, and the relation between the secondary electron yield "y and IV. is given by

7=~".nW,, n=O

,~__,W,, = 1.

(2)

n=0

The calculated statistics are in good agreement with the experimental data, while the Poisson statistics gives a smaller probability than those for high-n emission: e.g., at E 0 = 5 keV, 0.0169 (calculation), 0.0184 (experiment) and 0.0103 (Poisson) for n = 4. This agreement of the calculation with the experiment leads to the supposition that the larger width of the experimental distribution than predicted by the Poisson distribution is due to the collision processes of the incident ion in Au, because the statistical behavior of the internal secondary electrons is assumed to obey the Poisson distribution. Some of the ions incident on the solid surface are backscattered from it after large-angle elastic scatter-

3. Results and discussion

The calculated emission statistics of Au with H + impact are shown in fig. la for keV energies; in this case, the recoil effect to the statistics is negligible. Fig. lb shows the experimental results obtained by Lakits et al. [6], which were combined with the standard current

• Eo=lkeV [ ] Eo=2keVlTIEo=3keV IT~lEo=4keV [-IEo=5keV 1.0

i

i

i

i

i

H+- Au

0.8

Present calculation

0.6 ..,c

0.4 0.2

,~,_~,

0.0 n=O

n=I

_~, n=2

_~,

n=3

_,

n=4

(a)

n=6

n=5

I Eo=IkeV l~Eo=2keV IZ3 Eo=3keV[ ] Eo=4keVl-IEo=SkeV

1.0

i

i

i

i

I

i

H+- Au 0.8

Lakits et a l . (experiment)

0.6

~=

0.4 0.2 0.0

,

,

.=.~.,::,

,

,

~

,

~

,

_ _

,

(bl

n=O n=1 n=2 n=3 n=4 n=5 n=6 Fig. 1. Electron emission statistics of Au with H + for keV energies: (a) present calculation and (b) Lakits et al. (experiment).

IX. SECONDARY EMISSION

630

K. Ohya, L Mori / Electron emission statistics ¢ =

~

I

-.,.~..I

I

I

I II

II

H+-

I

~'*~. n-O ~ '

I

I

Au

i

I

J i m backscattered ion OA n trapped ion . -.. onian

-

3

00

.;2/

=0.1

•" "" ,"l

0.01

~, I

I i IIIIJ

0.1

i'".". I

I

"".. i

(a) .

illill

1

10

30

"Yb ' Yt ¢ 1

_.

"

~ i

i

n -- 2

...'*

0.1

H+-

I

,

"'~

.""

~0.1

0.01

= 80 °

* liillJ

I

t

llltij

Au i

.................. o i m backscattered ion " ' - ~ . OZ~EItrapped ion

:(

,

• ~ "~'~,.~'"" "-~

'

,,,~i~ n=5

1

10

30

Yb ' ¥ t

Fig. 2. The relations of the electron emission probabilities Wn (n = 0, 2, 5) by backscattered and trapped ions with their average electron yields for H ~ incident on Au. The incident angles ¢ are (a) 0 ° (normal to the surface) and (b) 80°; dotted lines are the Poisson distribution.

emission probabilities by the trapped electrons also deviate from the Poisson distribution because of the large influence of the electron excitation near the end of the ion trajectory, which is dominated by the largeangle elastic scattering, to the total electron emission. For the discussion of the recoil effects on the emission statistics, the emission statistics due to the recoil atoms are distinguished from those due to the incident ion, as shown in fig. 3 for Kr + incident on Mo. The mass ratio of ~he incidet,t ion ( M I = 83.9) to the target atom ( M 2 = 95.5) is approximately unity and the energy transfer from the ion to the target atom due to the elastic collision is the largest of all of the ion-atom combinations in the present calculation. From the figure, it is found that the recoil atoms produce a deviation of the emission statistics from the Poisson distribution even for the case of small electron yield in which the statistics due to the incident ion (or the backscattered ion) approximately obey the Poisson distribution. Finally, figs. 4a and 4b show the variations of the emission statistics due to the incident ion and due to the recoil atoms, respectively, with the mass of the incident ion for an energy of 10 keV. There is a complete antithesis between the variation due to the recoil atoms and that of the incident ion: In the case of the recoil atoms (incident ion), the emission probability IV, for no electron emission decreases (increases) with increasing mass of the ion and the W,, for one electron also increases (decreases). This leads us to an important fact that, in spite of the increase of the electronic stopping power with the increasing mass of the projectile, the energy transfer to the target atoms through the elastic collisions results in a large reduction of the ability to excite electrons by the projectile. On the other hand, the energy transfer also results in the

Kr +- Mo

ing from the solid atoms, while the remainder experience some small-angle scattering and penetrate deeply into the region, below the solid surface before ultimately being trapped in the solid. Therefore, the two types of kinetic electron emission are distinguished by using the emission statistics: one type is the statistics due to the backseattered ions and the other is that due to the trapped ions. Figs. 2a and 2b show the emission statistics dlue to the backscattered and trapped ions as a function of each averaged electron yield, for the incident angles ~b = 0 ° and 80 °, respectively. The emission probabilities of electrons by the backscattered ions show slower variations with the secondary electron yield than~ those by the trapped ions which obey the Poisson distribution. The slower changes lead to a larger width of the distribution, and it is enhanced not only for a large yield of secondary electrons but also for oblique incidence. Furthermore, for @ = 80 ° the

1

~

,

~

.

v

~

,

,

,

,

I

,

n=o - - o ~ . • A l l recoi I atoms O z~nincident ion ........ Poissonian

=K=0.i

0.01 0.01

,

~.

n=l

O.i

-.. .~ .......:".:.?'.... ~

.." .'"

~::.:..=' ::,. .... ,

"...

1

Yr ' Yi

Fig. 3. The relations of the electron cmission probabilities IV. ( n = 0 , 1, 2) by incident ion and recoil atoms with their average electron yields for Kr + normally incident on Mo; dotted lines are the Poisson distribution.

K. Ohya, L Mori / Electron emission statistics B He+

[ ] Ne+

[7~Ar+ i

i

l.O

[ ] Kr+

l-]Xe +

F~

the emission statistics due to the incident ion show a large contribution to the higher-n emission.

i

Eo=lOkeV

631

Mo

Incident ion

0.8

4. Conclusions

°I[ii Io 0.2

I

(a)

0.0

•

He +

n=2

n=l

n=O [ ] Ne +

171 Ar +

IT• Kr+

i

1.0

n=3 []

Xe+

l

Eo=lOkeV

Mo

Recoil atoms

0.8

0.6

0.4

The emission statistics of ion-induced secondary electron emission from solids were studied in the energy range 1-40 keV, using a Monte Carlo simulation of the transport of the incident ion and recoiling target atoms and a semiempirical model of the kinetic emission. The emission statistics calculated with H + incident on Au were in good agreement with the experimental data obtained recently by Lakits et al., while the Poisson statistics gave a smaller width of the frequency distribution of emission. In particular, the electron emissions by backscattered ion and recoil atoms produced deviations of statistics from the Poissonian. These results showed that large-angle elastic scattering which cause the backscattering of the incident ions and the recoiling of the target atoms broadens the distribution.

References

0.2

(b)

t

0.0

n=O

t n=l

~ l n=2

_ n=3

Fig. 4. Electron emission statistics of Mo due to (a) incident ions and (b) recoiling Mo atoms. The incident ions are He +, Ne +, Ar +, Kr + and Xe +. rising of the electron-excitation ability by the recoil atoms. In addition, because the the excitation ability of heavy atoms may be small, in analogy to the ion-pair formation in gases [9], there is only a small probability for n >__2 in the statistics due to the recoil atoms, while

[1] W.O. Hofer, Report KFA Jiilieh, no. Jiil-2317 (1989). [2] R.A. Baragiola, E.V. Alonso and A. Oliva-FIorio, Phys. Rev. B19 (1979) 121. [3] J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985) chaps. 4 and 8. [4] S. Ono and K. Kanaya, J. Phys. Di2 (1979) 619. [5] H. Seiler, Z. Angew. Phys. 22 (1967) 249. [6] G. Lakits, F. Aumayr and H. Winter, Rev. Sci. Instr. 60 (1989) 3151. [7] J. Ferr6n, E.V. AIonso, R.A. Baragiola and A. OlivaFlorio, J. Phys. D14 (1981) 1707. [8] H.D. Hagstrum, Phys. Rev. 96 (1954) 336; 104 (1956) 672. [9] J.R. Macdonald and G. Sidenius, Phys. Len. A28 (1969) 543.

IX. SECONDARY EMISSION