Calculations of reneutralization effects in ESDIAD

Surface Science 169 (1986) 405-413 North-Holland, A m s t e r d a m

405

C A L C U L A T I O N S OF R E N E U T R A L I Z A T I O N EFFECTS IN E S D I A D

Z. MISKOVIC and J. V U K A N I C Boris Kidri~ Institute of Nuclear Sciences, 11001 Beograd, Yugoslavia

and T.E. MADEY Surface Science Division, National Bureau of Standards, Gaithei'sburg, Maryland 20899, USA Received 4 November 1985; accepted for publication 28 November 1985

Calculations are presented which describe the influence of ion reneutralization processes on measured electron stimulated desorption ion angular distributions (ESDIAD). The results indicate that reneutralization effects generally act in an opposite sense to the image field in affecting ion angular distributions, and that these counterbalancing effects tend to cancel one another partially over a wide range of polar angles.

1. Introduction

The quantitative interpretation of ESDIAD [1] (electron stimulated desorption ion angular distributions) requires a knowledge of the factors which influence the trajectories of desorbing ions. In ESDIAD, ions ejected from a surface layer following electronic excitation by a focused electron beam desorb in discrete cones of emission, in directions determined by the orientation of the bonds which are ruptured by the excitation. It is believed that the initial repulsive forces propelling ESD ions from surfaces originate mainly from 2 hole repulsive states which act along the original chemical bond direction (CBD) [2-4]. However, final state effects, including neutralization and image field effects, can influence the measured ion desorption angles by distorting the ion trajectories and thus, the angular distributions. Several recent papers based on classical trajectory calculations have addressed theoretically the influence of the image force on ESDIAD [1,5,6]. The present paper is intended to provide information about the influence of reneutralization processes on the measured ion angular distributions in electron and photon stimulated desorption ( E S D / P S D ) . The model we use is a simple classical picture: a quasi-impulsive central force ejects an ion along the CBD, the surface is an ideal planar conductor, and the reneutralization rate depends only on the distance z above the surface. 0039-6028/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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Z. Migkovib et al. / Reneutralization effects in E S D I A D

The previous calculations of the influence of image fields on ESD ion trajectories generated several main conclusions. First, the image potential invariably causes an increase in the polar desorption angle 0 (measured with respect to the surface normal) for an ion leaving a metal surface; the amount of the trajectory distortion depends on the "strength" of the image potential. The image potential does not influence the azimuthal angle 4). Second, for monoenergetic ions there is a critical angle for desorption, 0c. For initial desorption angles 0o < 0c, the image potential will bend the ions back to the surface and escape is impossible. The present results indicate that ion reneutralization effects generally act in an opposite sense to the image field in affecting measured ion angular distributions, and that they tend to cancel one another partially for desorption angles less than 0c. In section 2 we calculate the influence of reneutralization on ESDIAD for a finite range repulsive force acting on the desorbing ions, with the image force completely ignored. In section 3 we treat the effects of the image force and reneutralization simultaneously, assuming an infinitely-steep repulsive potential and monoenergetic ions. Our conclusions are given in section 4.

2. Distortion of E S D I A D due to reneutralization with finite repulsion

It has been recognized for many years that ESD ion yields are strongly reduced due to reneutralization processes [7,8], but there are few calculations which treat the influence of reneutralization on ESD ion angular distributions [9,10]. For example, Tully [9] has shown that reneutralization can distort a thermal distribution of ESD ions. For the present case we assume, following Clinton [11], that an ESD excitation probability I 0 is a Gaussian, strongly peaked along the CBD of the ground state surface molecule according to 0° - 0° ]2 - ( sin 0° ]2(4)0 - ~0)a ] 1°(0°'4)°)°c e x p [ - \ - - - ~ w ] \ 4)w ]

(1)

where ¢c denotes proportionality. Here, 00 and 4)o are the initial ion polar and azimuthal angles, and the direction (0 0, 4)o) is the CBD. The half-widths of the distribution /0, 0w and 4)w, are determined by the ground state vibrational normal modes. We adopt here the Hagstrum non-local type of reneutralization, i.e. we assume that the electron which participates in the hopping process is delocalized within the substrate conduction band. This model implies that the reneutralization rate R depends only on the ion-surface separation z, and this dependence is usually modelled by

R ( z ) = A e "~.

(2)

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One can see that this model of reneutralization affects only the polar angle dependence of E S D I A D ; the azimuthal dependence is unaffected. The ion survival probability P, i.e. the probability that the ion desorbs without reneutralization is given by

where z(t) is the time-dependent ion-surface separation in the classical trajectory approach. It is reasonable to assume that ion desorption is caused mainly by a strong repulsive central force [2,4,11] acting between the ion and a surface atom. The repulsive potential is of the B o r n - M a y e r type

V ( r ) = B e -b', (4) where r is the distance between the ion and a surface atom. We neglect here the image potential and assume the ion to move in the potential given by eq. (4). For the ions desorbing in (0 0, ~0) direction with zero initial radial velocity and zero angular momentum, the classical equation of motion gives for the trajectory r(t) the expression

where E is the ion kinetic energy far away from the surface and m is the ion mass. Since the direction of ion desorption does not change, the final polar angle 8 and azimuthal angle 0 are equal to 00 and q~0, respectively. The ion-surface separation during desorption is simply

z ( t ) = r ( t ) cos 0. By combining eqs. (2)-(6), one obtains P=exp

-

V Z/~

--

(6)

F cos0,

,

(7)

with F (cos0, b)=

Ya F ( ( a / b ) cosO)

¢70 r((o/b) cos

0 +

(s)

where F ( z ) is the g a m m a function. Expression (7) with (8) for the ion survival probability is a simple generalization of the calculations performed in ref. [13] for ion desorption along the surface normal (00 = 0). Assuming a monoenergetic ion energy distribution [6] we put E = B. In the case of an infinitely-steep repulsive potential (b + oo in eq. (4)), one has a/b---, O. This gives the well-known result (see for instance ref. [10]) for the ion survival probability

(.)

P == exp - - -av± ,

vs =

(,. m

cos 0.

(9)

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Z. Mi~kovib et al. /

Reneutralization effects in E S D I A D

(Note that one may have a/b ~ 0 also for finite b and small a; in this case, neutralization occurs over a wide range of distances from the surface. For large a/b, neutralization occurs close to the surface.) Finally, the resultant E S D I A D is 1(/9, q~)= 10(/9 , q)) P ( 0 ) ,

(10)

with I 0 given by eq. (1) and P ( 8 ) given by eqs. (7) and (8) with E = B. In order to test the above expression with realistic values of the various parameters, we have chosen the well-studied system oxygen on tungsten [12]. From measurements of ESD ion energy and angular distributions we can deduce the following to be reasonable values: 8w = 10 °, B = 8.8 eV, b = 3.5 ~ - 1 . In addition, P = 4 × 10 4 for 00 = q)0 = 0°. In order to fit this value of P using eq. (11) above, one has to select appropriate values for two parameters, A / a and a/b. However, the value of a/b is not uniquely defined, and we have chosen a range of typical values as a/b = 0, 0.5, 2; the corresponding values of A / a are 8.0, 5.1 and 3.0 ( N 1 0 4) m / s . In fig. 1, we plot a number of ion-angular distributions (solid curves) according to eq. (10), using the parameters described above. Several angles of the C B D are chosen: 00 = 0°, 15°, 30°, 45° and 60 °. Several conclusions can be drawn from these results. (a) The peak position of the ion angular distribution is shifted to lower values a

A

A / r-

a b

/

"~

m

_>, ee-

.o 3. 3

//a

..;~/// .../,,// .'f///

1/)

b

/ a /#//-

-2//,, I ii /

\

¢)

\

O t--

=

2

'

A a

=0.5

'

Aa =

51.1o'

=

,

A ~-=

8.0.10

0

=

3.0.104

m/s

4

m/s m/s

o = 30°

\\... \'... \

\ ..

--

= 450

o

°

I

-150

I

00

I

I

I

I

I

15 0

300

45 o

600

75 o

Desorption A n g l e 9

Fig. 1. Calculated effects of reneutralization on electron stimulated desorption ion angular distribution ( E S D I A D ) using parameters appropriate for ESD of O ÷ from oxygen on tungsten. The dashed lines show the angular dependence of the survival probability P for different values of a / b , assuming isotropic initial ion angular distributions. The set of solid curves for various chemical bond directions 0o and various a / b is enveloped by the corresponding curve for P. The dotted curve represents the angular dependence of P for a / b ---, ~c.

z. Migkovibet al. / Reneutralizationeffectsin ESDIAD

409

of polar angle 0 when the CBD polar angle 00 is greater than 0 °. The amount of the peak shift increases as a function of 00 and decreases as a function of

a/b. (b) The peak width of an ion angular distribution increases slightly with a/b and is nearly independent of 00. (c) The peak intensity decreases with increasing 00, but this rate of decrease depends on the values of a/b. For small values of a/b (0, 0.5), the peak intensity decreases faster with 00. The dashed curves in fig. 1 show the /)-dependence of the ion survival probability P according to eqs. (7) and (8) for a/b = 0, 0.5 and 2 and with E = B. These curves represent the isotropic initial ion angular distribution (0 w ~ oo) distorted by reneutralization processes for various values of a/b. The widths of these distorted distributions increase with increasing a/b. Note that the set of solid curves for various 00 and a/b is enveloped by the corresponding curve for P. In addition, in fig. 1 we have plotted a dotted curve representing the isotropic initial ion angular distribution for a/b ~ oo (short ranged neutralization). In that case, the /)-dependence of P (eqs. (7) and (8)) can be expressed in terms of the asymptotic form of the F function, giving P=exp [

-a

A~BB

( a ) ,/2[

b,

~__~,/2]

kcos0J

]'

9 <½~r.

In order to fit P(O = 0 °) = 4 X 10 -4, one has to put A / a ~ O. We note that the variation of the width of the initially isotropic distribution is bounded between the widths of the dashed curve with a/b = 0 and the dotted curve (a/b ~ oo). We note also that the angular dependence of the quantity In P is (x --(cos 0) -1 for a / b = O and cc - ( c o s 0) -1/2 for a/b--* oo.

3. Comparison between the image interaction and reneutralization effects in ESDIAD Let us compare quantitatively the effects of the ESDIAD peak shifts, X = 0 p - 00, for both the image interaction and surface reneutralization as a function of the CBD polar angle 00- For the image interaction we use the model presented in our previous paper [6]. We limit ourselves here to the case of an infinitely-steep repulsive potential (b---, oo in eq. (4)) and use the Hagstrum type of reneutralization. It should be noted that both the image interaction and surface reneutralization do not influence the azimuthal motion of an ion. Let the ion be formed at the initial separation s o from the surface image plane and starts its motion with kinetic energy E o and polar angle 0o. The ion moves in the image potential Vi(z ) defined by eq. (6) from ref. [6], and escapes to infinity with kinetic energy E and polar angle 0. In the present calculations

410

Z. Mi.~kovi~ et al. / Reneutralization effects in E S D I A D

we use the monoenergetic approximation [6] and put E 0 = E0 = B and E = = E o - I VI [, where VI is the image potential at the initial ion position. The normal component of ion velocity can be obtained from eq. (8) in ref. [6], d~zc-°[s22(0 m +dt

]V'lz~°)] o

(11)

where the z-coordinate is directed along the surface normal and measures the ion separation from the initial ion position, while z 0 = s o + k ~ with k 1 being the F e r m i - T h o m a s screening length [6]. The ion survival probability can be written in the form

~R(z)dz] P = exp - f0

~-z/Td-~ ]"

(12)

The final ESDIAD, distorted due to both the image interaction and surface reneutralization, can be written in the following form

I(0) = Io(Oo(O)) J(O) P(O), with Io(0o(0)) and J(O) being

(13) derived in ref. [6],

Io(Oo(O)) = e x p { - O w 2 [arcsin(lffl sin O) - 0/,]2},

(14)

J(O) = fl cos 0 / ( 1 - fl sin20) 1/2, while P(O) follows from eqs. (11)

(15) and (12),

P(O)=exp[-a~ofo~(ficos20+~3~)

1/2e Cd~l.

Here, fl = 1 - I VI I/k2o, vo = (2F.o/m) I/z, and 8 = the peak angle 0p of the distorted ESDIAD is arcsin y = 0 o -

0~

A

__1 -fl

2-~ [ (/~--Y2)(I

72) 1/2

(azo) 1. The

+~Vo(1--y2)l/2K(y;

(16) equation for

]

fi, 8) , (17)

where y = V/fl sin 0p and

K(Y;e'8)=fo°C( fl-y2+

1~]1-'8t

3/2e Cd~.

(18)

It should be noted that for A = 0 (reneutralization absent) eq. (17) is reduced to eq. (28a) from ref. [6]. In the opposite case, when VI = 0 (image interaction absent), eq. (17) is reduced to arcsin y = 00

0~ A

y

2 avo 1 _y2"

(19)

z. Migkovib et al. / Reneutralization effects in ESD1AD

411

W e note also that parameter 6 = (az o) 1 compares the slope of the reneutralization rate R ( z ) with the slope of the image potential V~(z) at the initial ion position. One can conclude that usually [5,10] a >> z o 1, so that 6 < 1 or/~ << 1. We note that, since 6 is usually << 1, one can expand the integral K, eq. (17), in powers of 6. In order to solve eq. (17), we use the following values of parameters [12]: I VI I/ff~0 = 0.25, 0w = 10 °, E 0 = B = 8.8 eV and A / a = 8 × 10 4 m / s (corresponding to a / b = 0). F r o m refs. [5,10] we estimate z 0 -- 1.6 ,~ and a = 3 ~ , - l, hence 6 = 0.2. In fig. 2, we have plotted curve (1) as solution of eq. (28a) from ref. [6]. This curve presents the peak shift of E S D I A D due to the image interaction only (A = 0). Curve (2) is the solution of eq. (19) and presents the peak shift due to surface reneutralization only (V I = 0). Curve (3) in fig. 2 is the exact solution of eq. (17) with the parameters above. This curve presents the resultant peak shift of E S D I A D distorted by both the image interaction and surface reneutralization, treated simultaneously. In order to test the influence of the variation of the parameter 6 = (az o ) on the resultant peak shift, we have plotted in fig. 2 dashed curves (4) and (5) representing the resultant peak shifts for/~ --* 0 and 8 --* oo, respectively; these curves represent the lower and upper limits of the peak shifts. In addition, we have plotted a dash-dotted curve (6) as the sum (with different signs) of the curves (1) and (2) in fig. 2 in order to obtain a simple estimation of the counteracting effects of the image force and neutralization. I

o i

10 ° -~

,",

5o

II ,,<

0o

,-

.5 o

I

I

I

~ ~

(

1

(/)

•

I

I

~ )

12)

-10 °

<~ -150 -20°

k 10°

I 20 o

i 300

i 400

i 50 o

i 600

, 70 o

80 o

Chemical Bond Direction 8o Fig. 2. Influence of the image potential (curve 1) and reneutralization processes (curve 2) on the shift of the E S D I A D peak, ?, = 0p - 00, as a function of 00. The peak shift ~ is defined as the difference between the measured peak position 0p and the ground state chemical b o n d direction 0o, i.e., ~, = Or, - 0o. Curve (3) is the resultant shift with reneutralization and image interaction effects calculated simultaneously for 8 = 0.2. The shaded area represents the region of the resultant peak shifts w h e n ~ varies from 0 (curve 4) to infinity (curve 5). Curve (6) is the s u m of the curves (1) and (2).

412

z. Mi~kovi~ et al. / Reneutralization effects in ESDIAD

N o t e that the effects of the i m a g e i n t e r a c t i o n a n d surface r e n e u t r a l i z a t i o n on the p e a k p o s i t i o n 0p of the final ( m e a s u r e d ) ion a n g u l a r d i s t r i b u t i o n tend to c o m p e n s a t e one a n o t h e r over a wide range of CBDs, 00 < 50°. F o r values of 00 > 50°, the p e a k of the a n g u l a r d i s t r i b u t i o n is strongly b e n t t o w a r d the surface normal.

4. Conclusions T h e plots of figs. 1 a n d 2 are b a s e d on a limited range of p a r a m e t e r s a p p r o p r i a t e to one system, E S D of oxygen on W. However, the results of o u r c a l c u l a t i o n s s u p p o r t the view that q u a n t i t a t i v e conclusions of b o n d angles b a s e d on E S D I A D m e a s u r e m e n t s alone d e p e n d strongly on the m e a s u r e d value of p o l a r angle 0p. I n general, for values of 0p less t h a n 3 0 0 - 4 0 ° or so, o n e can d e t e r m i n e the initial d e s o r p t i o n angle, consistent with the a s s u m p t i o n s of the simple models. F o r m e a s u r e d angles m u c h greater t h a n 50 ° , it is difficult a n d in m o s t cases i m p o s s i b l e to d e t e r m i n e q u a n t i t a t i v e l y the initial d e s o r p t i o n angle. It was f o u n d earlier [6] that the p e a k angle a n d w i d t h of an E S D I A D b e a m can be insensitive to the strength of the i m a g e p o t e n t i a l at large values of 0, a n d the r e n e u t r a l i z a t i o n effects illustrated a b o v e in figs. 1 a n d 2 i n t r o d u c e further c o m p l i c a t i o n s , as d o the presence of steps, defects a n d o t h e r surface t o p o g r a p h i c a l effects. W e c o n c l u d e that at large values of 0p, the m a i n utility of E S D I A D is qualitative, i.e., to identify that the C B D is strongly i n c l i n e d with respect to the surface normal.

Acknowledgement This w o r k was s u p p o r t e d in p a r t b y U S - Y u g o s l a v i a n Joint B o a r d Project N B S (G)-267.

References [1] T.E. Madey, in: Inelastic Particle Surface Collisions, Springer Series in Chemical Physics, Vol. 17, Eds. W. Heiland and E. Taglauer (Springer, Heidelberg, 1981) p. 80; T.E. Madey and J.T. Yates, Jr., Surface Sci. 63 (1977) 203. [2] P.J. Feibelman, in: Desorption Induced by Electronic Transitions, Springer Series in Chemical Physics, Vol. 24, Eds. N.H. Tolk, M.M. Traum, J.C. Tully and T.E. Madey (Springer, Heidelberg, 1983) p. 61. [3] D.E. Ramaker, J.Vacuum Sci. Technol. A1 (1983) 1137. [4] T.E. Madey, D.E. Ramaker and R. Stockbauer, Ann. Rev. Phys. Chem. 35 (1984) 212. [5] W.L. Clinton, Surface Sci. 112 (1981) L791. [6] Z. Mi~kovi6, J. Vukani6 and T.E. Madey, Surface Sci. 141 (1984) 285. [7] D. Menzel and R. Gomer, J. Chem. Phys. 41 (1964) 3311.

Z. Migkovib et a L / Reneutralization effects in E S D I A D

[8] [9] [10] [11] [12]

413

P.A. Redhead, Can. J. Phys. 42 (1964) 886. J.C. Tully, ref. [2], p. 31. D.P. Woodruff, Surface Sci. 124 (1983) 320. W.L. Clinton, Phys. Rev. Letters 39 (1977) 965. See E. Preuss, Surface Sci. 94 (1980) 249, and references therein; also, H. Niehus, in: Proc. 7th Intern. Vacuum Congr. and 3rd Intern. Conf. on Solid Surfaces, Eds. R. Dobrozemsky, F. Rudenauer, F. Viehbock and A. Breth (Berger, Austria, 1977) p. 2051; T.E. Madey, J.T. Yates, Jr., D.A. King and C.J. Uhlaner, J. Chem. Phys. 52 (1970) 5215. [13] M. Nishijima and F.M. Propst, Phys. Rev. B2 (1970) 2368.