Multichannel neutralization and reionization in scattering of slow ions

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surface science

: ,.>. Surface Science 316 (1994) 198-204

ELSEVIER

Multichannel

neutralization and reionization in scattering of slow ions

F.I. Dalidchik *, M.V. Grishin, S.A. Kovalevskii, N.N. Kolchenko, B.R. Shub Institute of Chemical Physics, Kosygin 4, II 7977 Moscow, Russian Federation

Received 13 January 1994; accepted for publication 2.5April 1994

Abstract A simple kinetic model is proposed for the multichannel neutralization of slow ions scattered on a metal surface. The “V” shape peculiarities observed recently in scattering of Art, He+, N;, CO+, CO: on Pt(100) are interpreted as classic threshold anomalies arising from crossing of the Fermi level by the ground electron levels of the particles. The model predicts two new types of peculiarities (“h” and “A” types) connected with the competition of multichannel neutralization, reionization and deexcitation. The possibility of spectroscopy of the surface collisional complexes (“spectroscopy of threshold anomalies”) is also pointed out in this report.

Recent experiments carried out by Akazawa and Murata [l-31 demonstrated that Hagstrum’s model [4] is not valid for neutralization of very low energy ions A+ (A = He, Ne, Ar, N, N,, C, CO, CO,) on Pt(100) at E < 400 eV. In most of the investigated cases for E < 40-100 eV the intensity of specular reflected ions J(E, fli, 13,) decreases with increasing ion energy (ei,, denote incidence and reflection angles). The J(E, 0) dependences observed exhibit deep asymmetric “V’‘-shape minima at E = E, which show a break for small angles of incidence. These peculiarities are of the same type for all ions with the exception of CO+. It was shown [l] that the observed V-like shape of the ion yield is not connected with energy

* Corresponding

author.

dependence of the scattering cross section. It reflects the complicated energy dependence of the kinetics of electronic transitions accompanying the particle motion near the surface. One can attempt to explain the low energy decrease of J(E, 0) within Hagstrum’s model [4]. The authors of Ref. [l] assumed that the electron characteristic velocity CJ,is defined as [51 u, = (A/a)

exp( -q(

E)),

(I)

where A and a are the Auger neutralization parameters at distance z [4], r( 2) =A exp( -az),

(2)

z,(E) is a root of the equation U(z) = E and U(z) is an ion-surface interaction potential. Approximating the U(z) potential by the Born-Mayer function 161: U(z) = B exp( -bz)

0039-6028/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(94)00268-E

(3)

F.I. Dalidchik et al. /Surface

the authors of Ref. [l] obtained the dependence v, a E”ib

(4)

which allows one to explain the low energy decrease of the scattered ion current in the assumption of a = b. However, Eq. (1) is not grounded theoretically. Experiments [7] are in contradiction with it. The reasons of the anomalous energy dependence of the survival probability of slow ions scattered from a surface (&T/aE < 0) need a more complete theoretical analysis. The breaks of the function J(E, 0) can be reproduced if one uses sectionally continuous functions to approximate v,(E) [21 or U(z) [81. For example [2] v, =

const E,

ECE,,

const E,,

E>E,.

The accuracy of these approximations is insufficient, the physical meaning of the nonanalyticity of u,(E) and U(z) is not clear. The present paper examines the kinetic model of electron transitions accompanying the interaction of low energy ions with a (metal) surface. The processes of multichannel neutralization, deexcitation, reionization and reneutralization are taken into account. The approximation of constant ion velocity (du/dz = 0) is not used. The model establishes the dependence of J(E) on the main parameters of the interaction and electron transitions and interprets the “Y-shape minima as threshold anomalies connected with the crossing of the Fermi level lF by the levels of the ground electron states of the particles A. The model predicts the existence of two new types of peculiarities: a low energy single maxima (,‘A”type peculiarity) and a small scale combination of breaks and maxima C‘h”-type peculiarity). The “A’‘-type peculiarities appear under proper conditions as a result of competition between Auger and resonant neutralization processes. The “h”type peculiarities should occur due to crossing of the Fermi level by the levels of electronically excited particles. The ion energies at which “A”, “h” and “V’‘-types peculiarities appear follow the sequence EA
Science 316 (1994) 198-204

199

irreversible. Therefore we can use master equations to describe the electron subsystem evolution dn,/dt

= c wk( nk - ni).

(6)

k

Here ni is the ith state population of the particle (i = 0, 1, 2,. . . ; i = 0 corresponds to the ion state, i = 1 to the ground state, i > 1 to the excited state of particle A). We assume that l i(z) > l k(z) if i > k > 1, where e&r) are one electron levels of particle A(i), Cini = 1. The functions FJ$,(t) are the rates of electron transitions: neutralization or reneutralization (A(0) + A(i > O)), deexcitation (A(i > k > 0) + A(k)) and reionization (A(i > 0) + A(O)). Particle A is assumed to be heavy enough and therefore the functions Wik(t) depend on its trajectory R = R(E, Bi, e,) parametrically. The scattered ion current J(E, ei, e,) is proportional to the probability of ion scattering P(E,

ei, e,) =

1 - c ni(t + m). i>l

consider a one-dimensional model, which is sufficient to analyse the reasons of appearance of the P(E, ei, e,) peculiarities connected with the kinetics of electron transitions. In the common trajectory approximation we take into account the relations: Let

us

dz = U( E, z) dt, u(E,

z) =

[2(E - U(z))&“,

(7)

where M is the ion mass, and U(z) is the repulsive potential approximated above by Eq. (3). This is correct if we consider multielectron ions and the condition E c0s2ei,f B

l/42,.

(8) For the values of E, ei, 8, for which the peculiarities were observed in Refs. [l-3] the condition (8) is true (E I > 30 eV, l/42, = 3 eV). For light ions (especially for He+) if the repulsive potential is sufficiently changed due to charge exchange processes or for rather low ion energies or for rather large angles the general trajectory approximation is not correct. These cases are not considered in this article. To approximate the coordinate dependence of W,,(z) we take into account the fact that neutral-

200

F.I. Dalidchik et al. /Surface

ization occurs only when or > ei z i(z). Therefore W,,(z) can be written as: Woi( 2) =A,i exp( -U,iZ)77(Er

-

l;( Z)),

v(x) = 1 for x > 0; 77(x) = 0 for x < 0. It is necessary to underline that the assumption that Auger neutralization is switched off at some distance zi was made in Ref. [2]. As it is shown lately, approximation (5) proposed in Ref. [2] does not follow from Eq. (7). The correct expression for the ion survival probability has the square root peculiarity not at E = 0, but at the point E, = U(zI) (zl is the root of the equation E&Z) = ~~1. Since reionization is possible only if or < E,(Z) we get: =Ai, exp( -aioz)77(~J

i 2 1.

z) -or),

(IO) The densities of the initial and final electron states and the electron wave functions are different for neutralization and reionization processes. So one can expect that aai = ai = ai, Aoi >Aio, (i 2 1). The form of the deexcitation rate function is not important in this work. We take Wik =Ai, exp(-uikz>, uik = (a, + u,)/2. Let us consider the dependence P(E) using Eqs. (6), (7), (9). If E < U,,,, U, = min(U(z,>>, zi are the roots of the equations E,(Z) = or, then only neutralization and deexcitation processes take place. In this case:

,

(11)

where W,&Z>= Ci,lAoi exp(-uiz) is the rate of neutralization for all energetically open channels. It is easy to transform Eq. (11) to P(E)

= exp( -2%(E)/u),

(12)

where a,/b

ue(E)=$Aai l>_l

. = Max(i > 1, under conditions E,(Z > z,) < ~~1, :m= (2E/M)“2,

i 2 1, (9)

yO(z)

Science 316 (1994) 198-204

C(a,,b)=L’y”-‘(l-y)-i”dy,

x=u,/b.

The values a, = b = 1 [1,6], the value of ai,, must be smaller. The resonant neutralization is more important for states near the Fermi level and the corresponding values of ui are minimal. Therefore in Eq. (13) u,/b I 1. The corresponding integrals C(x) are uniformly collected over the whole range of integration and there are no reasons to pick out the contribution of the turning point ( y = l), but in spite of that relation (4) remains valid c’,,~a ~‘~1’~. According to Eqs. (12)-(13), if E < ZJ,,,then the function P(E) is determined by the parameter a, = Min(u,, i I i,). If a, > b/2 then d(u,/u)/d E > 0 and d P/d E < 0. In this case the ion scattering probability monotonically decreases with increasing energy [l-3]. Generally the decrease is more sharp as particle A has more energy levels under the Fermi level for z = (l/u) ln(A/uu>. When a, b/2, i # m, then the function P(E) has a single maximum, E,, which position and halfwidth is determined by the well known interaction parameters (B, 6) [61 and parameters of neutralization (Aai, ai) which can be evaluated from experiment. A low energy maximum appeared in the scattering of CO: ions on Pt(100) [3]. Using the position (E, = 40 eV) and halfwidth (SE, = 40 eV) of the maximum it is possible to estimate the ratio of the rates of resonant and Auger neutralization for this system. Having assumed u2 < 1, a, = b 111, b = 2 [6] we obtained = 0.01. (A low energy peak (E, = 10 eV, Ao2/4H ZiEp = 5 eV) was also observed in scattering of NC ions on Si(100) covered by carbon [9].) Let us consider now the function P(E) near the threshold (E = U,,,(z)). According to Eqs. (6), (71, (9)

i>l

(13)

P(E)

=PO(E)

+pP,,i,,O(E).

(14)

F.I. Dalidchik et al. /Surface

The contribution P,,(E) takes into account the ions which do not participate in neutralization. It has the form

201

Science 316 (1994) 198-204

pO,i,,O(

E 1g

i

$ Ip?pz”p,“~,O(‘rn) 0

xmq(E-U) Jum

x [cwb) XC(~,/~,

xi(E))]

where C(a,/b, xi(E)

x,(E))

-4d

-4&y@

I

= j-;-~~‘+i(l

(15)

3

It follows from Eq. (18) that if E is close to U, the ion scattering probability increases with a very large derivative. The break of the function P(E) at E = U, has the form: dP/dE

-y)-“*

dy,

z -const

The contribution Po,im,,(E) takes into account the ions created in the sequence of transitions A(0) + A( i,) -+ A(0). (16) pCl,i,,O

dz “:;pj;) z,(E) dz’

* ~~+Gi,o-G,)/ r,(E) (

xv(E - q.,),

- 1/2)Aoi( E/B)0”b-3’2

x C(

q/b)

co,

ECU,,

dP/dE=const(E-U,,.,)“*>O,

(19)

E>U,. (20)

It has the form

x ch

g (aJB irl

= Q/E.

= 2P,P,P,(“”

(18)

m*

u(z’)

(17)

where P,(E) is the probability of reaching point zi, by particle A(i,); P,(E) is the survival probability of ions moving from zi, to infinity; P,(E) is the probability of the absence of electronic transitions in the interval (z,(E), zim); Wi, = Cimti ~ IWi i is the total rate of deexcitation of particle A&J; r,, = Ci,,iZIP,,i is the total rate of neutralization of an ion in the interval (z,(E), zim). Analytical expressions for P,, P2 and P3 are known but are rather complicated. It is important that at E = U, all these probabilities are not equal to zero. It is easy to show that if E is close to U, then the function P,(E) and Po,im,O(E) have the square root peculiarity

With increasing energy the probability of neutralization for the A(0) --t A(i decreases also with increasing energy. (The probability of creation of particles A(&,) at (03, zim) decreases. The probability of deexcitation of particles A&,) at (z,, zi,) increases, the number of particles which are able to take place in reionization decreases.) Therefore the function P(E) has its maximum in some point Ei followed by a slump. The singularities having the typical square root break and nearly localized maxima (c‘h”-type peculiarities) are formed by this mechanism. The scale of the “h’‘-type peculiarities depends on the parameters of the rate of neutralization, deexcitation and reionization of the electronically excited particles. This dependence can be used for spectroscopic purposes [lo]. The “h”-type peculiarities are seen in the results of Refs. [l-3]. (See, for example, Figs. 3, 4 in Ref. [l], and Fig. 9 and Fig. 10 in Ref. [3]). The scales of these peculiarities are small enough. In the case of insufficient energy resolution they can be identified by mistake as experimental errors. A clear “h’‘-type peculiarity is seen in Fig. 9 in Ref. [3] (system C+/Pt(lOO), 8 = 60”, E, = 40 eV).

202

F.I. Dalidchik et al. /Surface

As follows from the above, “h”-type peculiarities must be seen in each threshold E = q ~ 2. The number of peculiarities increases with increasing number of excited states levels crossing the Fermi level. The threshold described by Eqs. (19) and (20) must be seen also at the point of crossing of the Fermi level by the ground level: Ed = Ed, but the absence of competitive processes which decrease the ions yield with the increase of energy excludes the formation of a closely located maximum. When E > U, the function P(E) monotonically increases with increasing energy. For E xCJ, this growth can be approximated by Hagstrum’s formula (with v, = const). The threshold break and monotonic energy increase form the deep single “V”-type minimum seen in the ion spectra for incidence and scattering angles close to normal [l-3]. The meaning of the square root peculiarities which form the breaks of the function P(E) in the points E = U,,, is clear. Near the threshold, where the kinetics of the electronic transitions changes, variation of all parameters, in our case the currents of scattered ions, is proportional to the residence time of the system in the configuration when EJZ) > Ed

Science 316 (1994) 198-204

Ln P oj \

\

-l-1\,

40 80 Energy

120 160 (eV)

Fig. 1. Function I’(E) for the model of two-channel neutralIzation: a,,* > b/2 (Parameter values are presented in Table I). The threshold peculiarities arising from crossing of the Fermi-level by ground and excited terms are marked with symbols “V” and “h” correspondingly.

obtained results are presented in Figs. l-4. The values of the used parameters are given in the Table 1. The calculations were carried out with

Ln P -3 1 From the results mentioned above the appearance of the square root singularities of the function J(E, 8,, 19,) is not connected with the concrete functions U(z) and M$Jz). The existence of “h” and “V” peculiarities for scattered ion current seems to us to be rather general. These peculiarities arise from the sharp change of the electron transition kinetics in surface impact complexes formed during the ion overcoming the energetical barrier. To illustrate all the types of discussed peculiarities and to estimate the influence of different electron transitions on the relative scale of peculiarities we performed a numerical integration of Eq. (6) under conditions for which the existence of “A”, “h” and “V” peculiarities can be expected according to the above consideration. The

A i^\

I

‘;

I

r.

\

-4-

\

i(

h

Fig. 2. Function P(E) in the case a2 5 b/2 (parameter values are presented in Table 1). The low energy maximum forming as a result of competition of processes A(O) + A(1) and A(O) + A(2) is marked by “A’‘-symbol.

F.I. Dalidchik et al. /Surface

Science 316 (1994) 198-204

Ln P

Ln

-

Energy

P

‘3

-3,

140

6’0

203

2‘0

(eV)

I

60

100

Energy

Fig. 3. Influence of deexcitation processes: (1) solid line deexcitation is absent; (2) dashed line - deexcitation is present.

M= 40 am., B = 110 au., b = 2 a.u., U, = 100 eV, U, = 40 eV or U, = 30 eV (Fig. 2). It should be noted that the threshold peculiarities are more sharp for lower values of Bi,r [l-31, when the residence time is in the range where ~~(2) > or is maximal, and the number of trajectories leading to scattering in the appropriate direction is minimal. The simple one-dimensional model considered can be used only for a semiquantative explanation of the reasons of the formation of the observed peculiarities. The variable z(t) may be identified with the curvilinear coordinate f(t) calculated along the trajectory deterrnining the scattering of particles in the selected

140

(eV)

Fig. 4. Influence of reionization processes: (1) solid line reionization is absent; (2) dashed line - reionization is taken into account only for A(1) particles; (3) dotted line - reionization is taken into account for A(1) and A(2) particles.

direction. For a quantitative interpretation of the experimental results [l-3] one needs to perform trajectory calculations taking into account not only the kinetics of electronic transitions but also the scattering of particles A by the Pt(100) surface.

Acknowledgement

This work was supported by the Russian Fundamental Research Foundation (RFRF, Grant 93-03-18519).

Table 1 Parameters used to calculate the ion survival probabilities in figs. l-4 (e = h = m = 1) Number of plot

A,,

A 02

A,2

A 10

A 20

aI

a2

Fig. Fig. Fig. Fig. Fig. Fig. Fig.

1 2 1 1 1 1 1

0.1 0.03 0.15 0.15 0.15 0.15 0.15

1 1 0 2 0 0 0

0.01 0.01 0.01 0.01 0.01 0.01 0.2

0.01 0.01 0.1 0.1 0.01 0.1 0.1

2.5 2.7 2.5 2.5 2.5 2.5 2.5

1.7 0.85 1.7 1.7 1.7 1.7 1.7

1 2 3.1 3.2 4.1 4.2 4.3

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F.I. Dalidchik et al. /Surface

References [l] H. Akazawa and Y. Murata, Phys. Rev. Lett. 61 1218. (21 H. Akazawa and Y. Murata, Phys. Rev. B 39 (1989) [3] H. Akazawa and Y. Murata, .I. Chem. Phys. 92 5551. [4] H.D. Hagstrum, in: Inelastic Ion-Surface Collisions, N.H. Tolk, J.C. Tully, W. Heiland and C.W. (Plenum, New York, 1977).

(1988) 3449. (1990) Eds. White

Science 316 (1994) 198-204 [5] H.W. Lee and T.F. George, Surf. Sci. 159 (1985) 214. [6] A.A. Abrahamson, Phys. Rev. 178 (1969) 76. [7] D.J. O’Connor, Y.G. Shenn, J.W. Wilson and R.J. MacDonald, Surf. Sci. 197 (1988) 277. [8] H. Kaji, K. Makoshi and A. Yoshimori, Surf. Sci. 279 (19921 165. [9] F.I. Dalidchik, M.V. Grishin, S.A. Kovalevskii, N.N. Kolchenko and B.R. Shub, Izv. Acad. Nauk (19941, in press. [lo] F.I. Dalidchik, S.A. Kovalevskii, N.N. Kolchenko and B.R. Shub, Pis’ma ZETF, 58 (1993) 511.