Neutralization and excitation in low-energy ion-surface collisions

214

Surface

Science 159 (1985) 214-232 North-Holland, Amsterdam

NEUTRALIZATION AND EXCITATION IN LOW-ENERGY ION-SURFACE COLLISIONS Hai-Woong Department

LEE of Physics, Oakland

Umaersi~v, Rochester,

Michrgun

48063,

USA

and Thomas

F. GEORGE

Department of Chemistr)‘, Received

5 November

(lniuersi!y

1984; accepted

of Rochester,

Rochester.

for publication

New York 14~7,

20 February

,_iSA

1985

A model is presented which describes neutralization and excitatton occurring in low-energy ion-surface collisions. Important processes that determine experimentally measurable quantities such as the charged fraction .f’ and photon yield y are assumed to be Auger neutralization, electronic excitation and radiationless deexcitation. The model yields /’ and y in good agreement with experiment data, although log f’ and log y are found to exhibit nonlinear dependences on the inverse velocity of the incident ion beam.

1. Introduction In low energy (2 5 keV) ion-surface collisions [l-4], a large fraction of incident ions is neutralized via a direct resonance or Auger process. For the case of Ht or rare gas ions incident on a metal surface, a dominant mechanism for neutralization is often believed to be Auger neutralization, in which the transfer of an electron from the metal to the ion is accompanied by an ejection of an Auger electron. hagstrum [5-S] has shown that the probability for Auger neutralization is very high ( - 1) when rare gas ions of low energy (10 eV to 1 keV) interact with a metal surface. Theoretically, the Auger process is commonly described by a model which assumes an exponential dependence of the neutralization rate F upon the ion-surface separation z [7,9], F(z)=A

exp(-uz).

The probability

that the ion remains

(1) ionized

is then given by

where vi I and vr i are, respectively, the normal components of the initial and final velocity of the ion assumed to be constant, and the characteristic velocity 0039-6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V

H.-W. Lee, T F. George / Low-energy ion-surface collisions

215

u, is defined as u, = (A/a)

exp( - uzO).

(3)

In eq. (3), z0 is the distance of closest approach. For a complete description of the ion-surface interactions, however, one must consider other processes that may also occur during the collision. For example, a nonlinear dependence of the logarithm of the ion yield upon the inverse of the initial (or final) velocity has been observed [lo-131, in apparent contrast to eq. (2). This is generally believed to be an indication that the ion is subject to more than one neutralization mechanism. (We, however, show in this paper that Auger neutralization alone can account for the nonlinear behavior.) Theoretical studies in the past have shown that reasonable agreement between theory and experimental data can be obtained if one considers, in addition to Auger neutralization, neutralization and ionization resulting from atomic collision between the incident ion and a surface atom. In their study of 60-90 keV Ar+-Cu collisions, Van der Weg and Bierman [14] assumed that the collision process occurs in two phases: violent atomic collision between a projectile and a target atom leading to ion formation, followed by neutralization of ions (Auger or resonance neutralization) as they recede from the surface. Brongersma et al. [15] and Verhey et al. [16,17] have suggested a model in which the trajectory is divided into three parts: the incoming trajectory, the region of violent atomic collision and the outgoing trajectory. Along the incoming and outgoing trajectories Auger neutralization may occur, while collisional neutralization and ionization of the atomic type take place in the region of violent collision. Based on their H+-graphite data, Overbury et al. [13] estimated the probability for collisional neutralization to be high (over 90%) and that for collisional ionization low (below 10%) at the incident energy 600 eV < Ei < 2.4 keV. MacDonald et al. [18-201, in an analysis of their He+(Ne+)-Ni(Ag) data, suggested that collisional neutralization contributes significantly to the total neutralization probability. Woodruff [21], on the other hand, showed that their He+-Ni data [18] can be understood with a simple model of Auger neutralization and do not require the assumption of a collisional contribution. In addition to surface and atomic neutralization processes discussed above, there may also occur an excitation process leading to the formation of excited atoms. This is clearly indicated by observation of optical radiation produced during ion-surface collisions [22,23]. Experimental studies [24-261 have revealed a rather low photon yield (low3 to lo-’ photons per incident ion), indicating a relatively low excitation probability. Nevertheless, the study of the emitted photon and the excitation process should yield some useful information on ion-surface interactions. Unfortunately, the exact excitation mechanism has not been fully understood theoretically, except that the excitation is generally thought to occur during the stage of violent atomic collision. It is also established from experimental studies [26-291 that the atoms excited at or near

216

H.-W. Lee, T. F. George / Low-energv m-surface

collisions

the surface are subject to radiationless deexcitation as they recede from the surface. Those that survive deexcitation then emit photons. However, the exact deexcitation mechanism has not been fully understood, either. It may be resonance ionization followed by Auger neutralization, Auger deexcitation or autoionization, depending upon the system. Among various proposals concerning the excitation and deexcitation mechanisms, we mention that of Heiland and Taglauer [30]. They suggested, based upon experimental data of Ne+-Ag collisions, that the excitation mechanism consists of Auger neutralization followed by electronic excitation, while the excited Ne atoms can be deexcited via autoionization. In this paper we discuss neutralization and excitation processes occurring in ion-surface collisions with a model which is essentially a combination and modification of the earlier ideas mentioned above. As in the work of Van der Weg and Bierman [14], our working equation is the rate equation for the population of ions and atoms. Following Brongersma et al. [15] and Verhey et al. [16,17], we conveniently divide the trajectory into three parts. As hinted by Heiland and Taglauer [30], we assume the following neutralization and excitation processes to occur in each part of the trajectory: (1) During the incoming trip (t < 0), the incident ions can be neutralized via Auger neutralization. (2) In the region of violent collision (t = 0) where particles are subject to a strong repulsive force, those ions that have been neutralized in (1) can be electronically excited. (3) During the outgoing trip (t > 0), those that still remain as ions can be neutralized via Auger neutralization. Those that have been neutralized in (1) and excited in (2) face radiationless deexcitation. We assume the deexcitation process to be resonance ionization followed by Auger neutralization. In contrast to the analysis of Overbury et al. [13] and MacDonald et al. [18-201, we neglect collisional neutralization of the atomic type and assume that neutralization occurs mainly during the incoming and outgoing trips. Our model is schematically illustrated in table 1 with He+-Mo as an example. Based on this model we can immediately write rate equations that govern the time development of the population of ions and atoms. In section 2 such rate equations are presented along with their solutions. Experimentally measurable quantities can then be derived from the solutions. In section 3 the ion yield and the photon yield are discussed in detail, and comparison with experimental data is presented. Finally, a discussion on our model is given in section 4. 2. Rate equation 2.1. Preliminary

considerations

We consider a beam of ions incident energy Ei and a fixed angle of incidence

on a solid surface at a fixed incident \c, with respect to the surface. Among

H.-W. Lee, T.F. George / Low-energy ion-surface collisions

211

Table 1 Neutralization and excitation in ion-surface (He+-MO) collisions; AN: Auger neutralization, EE: electronic excitation, RI: resonance ionization; t = 0 represents the time at the distance of closest approach

t<

He++Mo AN\

t=o

0

He++Mo -

He++Mo -a--%

t>o

He++Mo He+Mo2++e

L He+Mo2+ +e-He+Mo2'+e-

EE\

He+Mo2++e

He*+Mo2+ +e-He*+Mo2+

+e m+photons

He++Mo++e-

N, incident ions, N, (= RN,, R: reflection coefficient) backscattered. We consider those that are backscattered angle (CX,/I) (see fig. 1). If we let N( (Y,P)dS2 be the scattered at an angle (L-X,/II) in the range d&I = d cos (Yd/3, IV,=

1 d cos L.Y7idP N(a, /0 I -1

The scattering

P).

angle B for these particles

cosB=sinacos(p+#).

He++Mo'+e

atoms and ions are at a particular solid number of particles we have (4)

is given by (5)

Fig. 1. Scattering geometry. The surface lies in the yr plane, and the incident beam is in the xy plane.

H. W. Lee, T. F. George / Low-energy ion-surface

218

collisrcm

Assuming a single binary collision between the incident atom, the velocity of the scattered particles is given by Uf=u,(a,

P)=u(a,

ion and

a surface

P) u,,

(6)

where u,=/m,

(7)

(8) m, and m2 are the masses of the incident ion an the surface atom, respectively. Eq. (6) provides a good estimate of the velocity of scattered ions for the case of He+ incidence [31-331, but scattered He atoms may contain those neutralized inside the solid [34,35]. For heavier rare gas ions such as Ne+, multiple collisions may complicate the matter [32,33]. If incident ions are not rare gas ions, e.g., H+, scattered particles at fixed incident and scattering angles show rather a broad energy distribution peaked at a velocity lower than that given by eq. (6) [13,36-391. For such a case, our analysis to be given in this section applies only to those particles scattered with velocity given by eq. (6). In other words, we deal with those particles only that are “kinematically” scattered. Earlier, Overbury et al. [13] considered such particles only in their study of H+-graphite collisions. The result of our analysis therefore can be extensively compared with the data of Overbury et al. From this point we drop the labels 4~and j3 unless we feel necessary to use them. Thus, N = N( (Y, fl) denotes the number of particles scattered at an angle (a, /3), and ur = ur( a, j?) is the velocity of those particles given by eq. (6). 2.2. Rate equations and solutions The neutralization r=Aexp(-az,)

rate r, given by eq. (I), can be rearranged exp[-a(z-z,)]

au, exp( aUi I t >,

zxz

to yield

1 au,. exp( -auf1

t),

t co, t > 0,

where UiL

=

u,

sin J/,

VII = ut sin (Ysin p = MU,sin (Ysin fi.

(Ioa) (lob)

u, is defined by eq. (3) and t = 0 represents the time at the distance of closest approach. At t c 0, i.e., during the incoming trip, the incident ions can be

H. - W. Lee, T.F. George / Law-energy ion-surface collisions

219

neutralized through Auger neutralization. If we let Ni be the number of ions and N2 the number of neutralized ions (i.e., neutral atoms), the rate equation for Ni and N2 takes the form

W(d --..-= dt

--au, exp(au,,t)

N,(t)=

W(f)

- dt,

subject to the initial condition N,(-oc)=N,

N,(-oo)=O.

(12)

The solution to eq. (11) can be immediately obtained as

The number of ions and that of atoms just before the distance of closest approach are then given by N,(O-)=Nexp(-u,/ui.),

(I4a)

Nz(O-)=N

(14b)

[l-exp(-u,/u~~)].

For low-energy collisions that we consider here, most incident ions are expected to be neutralized, and thus N,(O-) represents only a small fraction of N. At t = 0, some of the neutral atoms are excited to various excited states, j 2 2. Denoting the excitation probability into the jth state by P,, we have N,(O) = N,(O-),

N,(O)=N,(O-)

(Isa)

(l- j=2c 8)’

(15b)

N3j(0) = N,(O-)p,.

(15c)

Here N3, represents the number of atoms in the jth state (j > 2). The excitation probabilities P, are not accurately known, but previous investigations [26-291 suggest that p, may be independent of or vary slowly with the incident energy. As a function of j, P, was observed to be inversely proportional to j6 [29]. For our analysis, however, we do not need to specify the j-dependence of P,. Eq. (15) now provide the initial condition for the outgoing trip, t > 0, for which the rate equations read as

d&(t)

p=

dt

-au,exp(-aufLt)

N,(t)=

-7,

W(t)

@a)

H. - W. Lee, T. F. George / Low-energ); Ion-surfuce colhsions

220

dN&) -= dt

--au, exp(-au,,t)

d&(r) -=

(16b)

N,,(t),

C au,exd -auf f) K,(t) -au, ev-ao,.t) I

dt

&(t),

(16~)

j=2

d&(t)

---=au,exp(-av,.r) N,(t), (led) dt where N4 is the number of ions produced via resonance ionization, and N, is the number of atoms neutralized from those ions via Auger neutralization. We have assumed that the rate r, of resonance ionization from the jth excited state is given by the same exponential form, exp( - az), as the rate of Auger neutralization, but with a different preexponential factor B,, T,(z)

= B, exp( -az).

(17)

This assumption made for mathematical convenience does not seem to severely restrict our analysis because it is often the ratio B,/a, not the separate values of l3, and a, that is important. The characteristic velocity u, (also called the survival coefficient) for resonance ionization from the jth excited state is defined as 0, =

3exp(

-azO).

a

(18)

We mention that B, and thus r_, were observed to be independent of j for the H+-MO system [29]. We however keep the subscript j in B, and c’, for generality of discussion. Eq. (16) can be solved without much difficulty. Here we only show the solution at t = co: N,(cc)=Nexp(-2)

exp[-ej,

(19a)

(19b) N,,(co)=NI’,

N,(m)

[l-exp[--2)]

= N c, &[I

exP[-$-l,

- exp[-

,Il,b)=NL&1

1 - exp

‘

-“,‘[I

-e:p[-2)

$j][exp[-

(19c) 2)

-exp[-

511.

(19d)

i (19e)

H. - W Lee, T. F. George / Low-energv ion-surface collisions

221

Eqs. (19) represent the main result of this section. Experimentally measurable quantities such as the ion yield and the photon yield can be derived from these equations, as discussed in detail in the next section.

3. Theoretical analysis and comparison with experimental 3.1. Charged fraction

data

f+

Among N particles scattered at an angle ((Y,p), N+= N,(a) + N4(co) remain as ions. Since the excitation probabilities Pj are generally very low, N+ is given approximately as N+z N,(a). Thus, the charged fraction F is

f+z v=exp[

-( $-+-$-)uC].

(20)

Eq. (20) indicates that the charged fraction is determined mainly by Auger neutralization along the incoming and outgoing trajectories, in accordance with our neglect of atomic neutralization in the region of violent collision. Here we note that, if we had chosen the radiationless deexcitation process to be Auger deexcitation instead of resonance ionization plus Auger neutralization, N+= N,(m) and eq. (20) would have been arrived at regardless of whether the excitation probabilities are small or not. It would seem that eq. (2) is in disagreement with the nonlinear behavior of log f+ with respect to l/u, or l/Ui observed by several groups in the past [lo-131. It however is important to note that the characteristic velocity o, is not independent of the incident energy Ei due to the dependence of .zOon Ei (see eq. (3)). We show below that the observed nonlinear behavior can indeed by explained by taking the energy dependence of u, into account. Let us limit our consideration to specularly reflected particles for which 0 = 24 (see fig. 2). Since the variation of the parallel component I,,, of the ion velocity is oscillatory in nature, we assume that u,, at the distance of closest approach is the same as its initial value, u,, = Ui cos 1c/. We further assume that,

Fig. 2. Specular

reflection.

222

H.-W. Lee. T.F. George / Low-energy ion-surfuce

at the distance of closest approach, the repulsive potential of the form

the ion-surface

V(z)=Bexp(-hz). From

Solving

interaction

is governed

by

(21)

energy conservation,

$miu f = im,uf

collisions

we then have

cos21i, + B exp( -hz,,).

(22)

eq. (22) for zO, we obtain

z0 = - klog(gsin2$).

(23)

and therefore (24) It is clear from eq.(24) that u, is an increasing function of energy at a given angle of incidence, consistent with the observation of Verhey et al. [17] and MacDonald et al. [19,20], and also an increasing function of 4 (and of 0) at a given incident energy, consistent with the observation of Bertrand et al. [ll] and Overbury et al. [13]. From eqs. (20) and (24) we obtain log f’=

- $($jU’”

(1 +i)

[L&1”*.

(25)

should exhibit a linear dependence on According to eq. (25) log f’ not on l/Ui. Eq. (25) also indicates that at a given incident (1/U,)‘-2a’b, energy log f’ varies linearly with (l/sin 4)’ P2U’h as the angle Ic/ is changed. The angular distribution of scattered ions therefore should provide a good test of our model. In the following, we give a quantitative analysis of our model using the data of Overbury et al. [13]. From their experimental data for H+-graphite collisions, Overbury et al. calculated f of kinematically backscattered hydrogen using a screened Coulomb potential for different values of + and incident energy Ei. Shown in table 2 are their data for specularly scattered particles for the case Ei = 1 keV (i.e., u, = 4.38 x 10’ cm/s). Their values of f’ are listed for different values of of1 , i.e., for different values of $. (Recall url = or sin 8/2 = ur sin # for specular conditions - see fig. 2.) From these values we have calculated 4. u, i and u,_, which are also shown in table 2. The angle rl/ was calculated using eq. (6) and the relation sin \c,= ur./ur. The characteristic velocity uc was calculated from the relation u, = _ (log f+)uiLUrI ‘ U,L +ur1 which was obtained

(26) by solving eq. (20) for uc. It can be seen from table 2 that

H. - W.Lee,

T.F. George / Low-energy ion-surface coltisions

223

Table 2 H+-graphite data for specular conditions and for Ei = 1 keV; f’ and url values are taken from Overbury et al. (111 and 4, ui i, ucand za are calculated using our model described in this paper

r 0.008 0.0085 0.0115 0.0105 0.012 0.0135 0.017 0.0205 0.0235 0.025 0.0245

“IL

4

(lO’cm/s)

(deg)

“I I (lO’cm/s)

:O’cm/s)

;I)

1.1 1.5 1.8 2.15 2.2 2.4 2.6 3.0 3.2 3.3 3.45

14.7 20.5 25.0 30.7 31.7 35.3 39.1 47.9 53.0 56.0 60.9

1.11 1.53 1.85 2.24 2.30 2.52 2.16 3.25 3.50 3.63 3.83

2.67 3.61 4.08 4.99 4.97 5.29 5.45 6.06 6.27 6.38 6.73

0.77 0.64 0.56 0.49 0.48 0.44 0.40 0.34 0.31 0.29 0.27

the characteristic velocity u, is an increasing function of 4, in accordance with eq. (24). In fig. 3 we show a plot of log u, versus log(sin2$). According to eq. (24) a linear relationship is expected, which is approximately indicated by the figure. The slope of the line yields the parameter a/b. From the graph we estimate a/b z 0.37. A similar analysis of the 2 keV specular data of Overbury et al. also gave a/b G 0.37 (although not shown here). A rough estimate of parameters for the H+-graphite system is now possible. Following Hagstrum [7], we take B = 3 keV and b = 5 A-‘, and thus a = 0.37b = 1.85 A-‘. The distance of closest approach z,, for kinematically and specularly reflected hydrogen can be estimated from eq. (23). In the last column in table 2 we show values of z0 for different angles of incidence 11/for

Fig. 3. log U, versus log(sin*$) at E, = 1 keV for the H+-graphite best linear fit to the data points.

system. The line represents

the

224

H. - W. Lee, T F. George / Low-energy

ion-surface

collisions

Ei = 1 keV, where z,, is seen to range from 0.27 to 0.77 A for 4 = 60.9” to 14.7”. The parameter A/a can now be estimated using the relation A/a = u, exp(az,). This parameter of course is characteristic of the system being considered, and therefore its values calculated at different J/ should be the same within calculational uncertainties. We indeed obtain A/a z 1.1 x 10’ cm/s within _+5% for all different $ listed in table 2. We mention that we have also made the same analysis on the 2 keV specular data of Overbury et al. and obtained the same value of A/u within A 5%. From A/u = 1.1 x 10’ cm/s and a = 1.85 A-‘, we obtain 2.0 X 1016/s for A, the rate of Auger neutralization at z = 0 [see eq. (l)]. In table 3 we show nonspecular data (f’ versus uI .) of Overbury et al. for E, = 1 keV and a fixed scattering angle 8 = 90”, along with our calculated velocity Us is seen to decrease as J, values of 4, ui I and u,. The characteristic moves from the specular angle 45”, indicating that the incident ion approaches closer to the surface as the scattering condition moves toward specular reflection. The decrease of u, as $ approaches a grazing angle at constant 0 has also been observed by Bertrand et al. [ll] in the analysis of their He’-Cu scattering data.

Table 3 H+-graphite data for B = 90” and E, = 1 keV; f’ and t!rL values are taken from Overbury [ll], and 4, a, L and uC are calculated using our model described in this paper f+

Ufi (lO’cm/s)

4 (de@

(‘1i (107cm/s)

CC (lO’cm/s)

0.025 0.0225 0.021 0.0215 0.0215 0.019 0.020 0.0185 0.0175 0.0195 0.018 0.020 0.019 0.0185 0.0195 0.018 0.0195 0.0175 0.016 0.0165 0.0155

3.9 3.8 3.15 3.1 3.5 3.3 3.25 3.2 3.0 2.85 2.85 2.75 2.65 2.4 2.35 2.05 2.05 1.7 1.55 1.4 1.05

14.4 19.3 21.3 23.2 29.6 34.9 36.2 37.4 41.8 45 .o 45.0 46.9 48.8 53.4 54.3 59.4 59.4 65.0 67.4 69.7 74.9

1.09 1.45 1.59 1.72 2.16 2.50 2.58 2.66 2.92 3.09 3.09 3.20 3.29 3.51 3.55 3.77 3.77 3.97 4.04 4.10 4.22

3.14 3.98 4.31 4.51 5.13 5.64 5.63 5.80 5.99 5.84 5.96 5.79 5.82 5.69 5.57 5.33 5.22 4.82 4.63 4.28 3.50

et al.

H. - K Lee, T. F. George / Low-energy ion-surface collisions

225

3.2. Photon yield The number of photons emitted resulting atom from the jth level to lower levels is

u,=

I 1d cos (YI =ddp N& -1

from the decay of the projectile

P),

0

(27)

where cascade decays are neglected. Substituting obtain, for the photon yield per reflected particle,

eq. (19~) into eq. (27)

we

(28) Since N, U, and u depend on (Yand p in a nontrivial way, eq. (28) cannot be analytically integrated in general. nevertheless, a rough estimate of y, can be made by noting that the most important term in the integrand is sin (Ysin p. Other terms vary relatively smoothly with respect to p and cos CX.The term [ 1 - exp( - uC/ui sin $)I is not much different from 1 at low energies where Auger neutralization occurs with high probability. The factor ~(a, /3) is usually a slowly-varying function of CYand p, especially for the case of light ions (H+, He+) incident on a heavy solid (W, MO, etc.). The dependence of the characteristic velocity uj for radiationless deexcitation on cu and /3 is not known. Judging from the behavior of uC as discussed in the previous subsection, we expect u, to vary by a factor of a few as (Yand /3 change. This certainly is a non-negligible change but is still a slow variation compared with that due to (sin (Ysin p)-‘. The number of scattered particles N also varies with (Y and p in a nontrivial way [39]. Experimental data [28,40] indicate that, as +L increases toward normal incidence, the angular distribution becomes less sharply peaked. The approximation to neglect the angle dependence of N(cY, p) is thus expected to work better for normal or near-normal incidence than for grazing-angle incidence. Eq. (28) can now be written approximately as

%( 77/21 77/Z) ui sin I+ X

n * d cos LX dpexp I -1 J0

i

uj( T/2,

u(m/2,

n/2)ui

m/2)

sin ff sin p

(29)

The double

integral

can be evaluated

if C is large (i.e., energy is low) so that

Iim _2$&exp(-Cxy)-~~~~exp(-Cxy)=Xo(Q).

(30)

X

and &(CV)~

exp(--Cy),

6755

where K,, is the modified integration, 44

Y/ GS

(31)

Bessel function.

n/2,71/2)

We obtain.

“, ( 71/2, v/2) t?i sin 4

“I

after a straightforward

“,(77/2, 47T/2.

n/2) “/2)U, (32)

At low energies,

-2-z

44

a/2,

such that uj < Q. n/2)

“j ( 7r/2, 71/2) Di exp

.N,R

“/

i

4 n/2,

T/2) Lti1 .

(33)

We emphasize that the characteristic velocity “, is not independent of the incident energy Ei, and thus the exact dependence of the photon yield on E, (or u,) can be found only when we determine how “, depends on E,. Within out approximation, we only need to evaluate “, for particles kinematically scattered at uz= /I = n/2. For normal incidence li, = z/2, such particles are specularly reflected ones, and therefore the characteristic velocity u, can be estimated as described in the previous subsection 3.1. From eqs. (18) and (23), we immediately obtain, for normal incidence, u, = (B,/a)(

“,Uf/2B)U’6.

Substituting

eq. (34) into eq. (33), we obtain

P

YJ ~&$2a/h

exp( _Q,+"U,'"),

Q

N,R

(34)

(35)

where

(“‘)O’“.

4

Q=

U(“/2,

a/2)

u

23

(36)

According to eq. (39, yj/Ni R varies as u~-*~/~ exp( - Q/u!-“~““). Thus, our model predicts a somewhat weaker dependence of the photon yield on ion

i .

H.-W. Lee, T.F. George / Low-energv ion-surface collisions

227

Table 4 Photon yield per reflected particle, 7,/N, R (in arbitrary units), for the 388.9 nm line of He emitted during He+-MO collisions l/o, (10-s s/cm)

Experimental [22] Our model Linear model

2.1

2.3

2.6

2.9

3.3

3.8

4.4

0.7 0.69 0.64

0.52 0.50 0.48

0.28 0.32 0.33

0.22 0.23 0.24

0.15 0.15 0.15

0.095 0.090 0.082

0.049 0.049 0.037

energy (or ion velocity Vi) than the commonly accepted linear model according to which log(y,/N,R) is inversely proportional to ui [28,29]. We show below, however, that our model yields as good an agreement, if not better, with experimental data as the linear model. A large number of experimental data exist in photon emission from ion-surface collisions [22,23]. Since we have assumed a single binary surface collision in our analysis, eq. (35) is expected to work better for the case of He+ incidence. For this reason we take the He+-metal data of Heiland et al. [28]. They have indicated that most of the radiating particles originate from surface collisions. In table 4 we show experimental data for the photon yield for the 388.9 nm line of He emitted during He+-Mo collisions at several different incident velocities. Also shown are values of the photon yield calculated using our model as well as the linear model. For our model, eq. (35) was used with a/b = 0.37 and Q 1’o.26= 5.34 x 10” cm/s, and the calculated photon yield was normalized to the experimental value at l/ui = 3.3 x 1O-8 s/cm. Although normal incidence was assumed in eq. (35), direct comparison with the experimental data is possible because the data was taken at near-normal incidence (J, = 85’). For the linear model, we have assumed the relation yj/Ni R a exp( - uC/ui I) with u, = 1.2 X 10’ cm/s as estimated by Heiland et al. and again the calculated yield was normalized to the experimental value at l/Ui = 3.3 X lo-’ s/cm. it is seen that our model gives the photon yield in excellent agreement with experimental data, with better agreement being produced by our model than the linear model. The data shown in table 4 is also graphically illustrated in fig. 4. It should be noted that, in order to obtain good agreement between our model and experimental data, we need to choose an appropriate value of the parameter Q. For He+-Mo the choice Q 1’o.26= 5.34 X 10” cm/s gives the best fit. Assuming this value of Q, we can then estimate the parameter B,/a for the He+-Mo system using eq. (36) with B = 3 keV as before. We then obtain B,/a = 4.2 X lo8 cm/s and thus, with a = 1.85 A-‘, Bj = 7.8 X 106/s for the rate of radiationless deexcitation at z = 0. In table 5 we show experimental [28] and calculated values of the photon yield for the 587.6 nm line of He emitted during He+-Mg collisions. The

228

H. W. Lee, T. F. George / Lowenergp

ion-surface

collrsions

10 r-

8

8

5

R

3 ;; " 5

2

? P " 2

1

0

8

$_ .5

.3

.2

.l

I

1

I

2

3

4

$(10e8

s/cm)

1

Fig. 4. log(y,/N,R) versus l/u, for the 388.9 nm line of He emitted during He+-MO collisions: (0) experimental data of Heiland et al. [22]; (x) calculated values according to our model; (0) calculated values according to the linear model. All the points should lie on a straight line.

calculated values were normalized to the experimental yield at l/ui = 3.3 x 10-s s/cm. The parameters used for our model calculation are a/b = 0.37, ~‘/“.26 = 5.67 x 10’0 cm/s, and for the linear model we chose u, = 0.78 x 10’

Table 5 Photon yield per reflected particle during He+ -Mg collisions l/u,

Experimental [22] Our model Linear model

y,/N,R

(lo-’

(in arbitrary

units), for the 587.6 nm line of He emitted

s/cm)

2.1

2.6

2.9

3.3

3.8

0.9 0.83 0.85

0.55 0.52 0.55

0.42 0.43 0.45

0.33 0.33 0.33

0.27 0.25 0.23

H. - W. Lee, T E George / Low-energy ion-surface collisions

229

cm/s. Both models give the photon yield in good agreement with experimental data. With Q1’o.26= 5.67 X 10” cm/s and using eq. (36), we estimate B,/a z 1.8 x lO*cm/s and thus Bj z 3.3 x lOu’/s for the rate of radiationless deexcitation at z = 0 for the He+-Mg system. For our comparison with experimental data we have extensively used the data by Heiland et al. [28]. A more recent work by the same group [29] reported the results of H+-MO collisions, in which the linear relationship between y,/N,R and l/U, is more apparent. For this system, however, a more elaborate analysis than presented in this paper may be necessary because backscattered hydrogens show a broad energy distribution in violation of eq. (6). Although a critical evaluation of our model against the linear model or any other model is desirable, the photon yield data of Heiland et al. [28] does not clearly favor one to the other. Both our model and the linear model give good agreement with experiment with an appropriate choice of Q and u,. Finally, we mention that the above analysis of He+-Mo and He+-Mg data is based on the value of a/b (0.37) deduced from H+-graphite data. The good agreement between our model and experimental data indicates that the value of a/b is not significantly different for different systems.

4. Discussion We have presented a model describing ion-surface collisions in which important processes are assumed to be Auger neutralization, electronic excitation and radiationless deexcitation. The radiationless deexcitation is assumed to consist of resonance ionization followed by Auger neutralization. Some comments on the model are now in order. (1) In general, possible surface neutralization processes include resonance neutralization and quasi-resonant charge transfer as well as Auger neutralization. In our model quasi-resonant charge transfer, which gives rise to an oscillatory behavior of scattered ion yields [41,42], has been neglected. As for resonance neutralization, the process can easily be incorporated into our model because the rate of resonance neutralization is also known to decrease exponentially with respect to the ion-surface separation, i.e., eq. (1) can also be applied to resonance neutralization. Even if the dominant neutralization mechanism is resonance neutralization and not Auger neutralization, the same rate equations and solutions presented in section 2 can still be applied with an understanding that the parameters A and a now refer to resonance neutralization. It should be mentioned here that, although Auger neutralization is generally believed to be a dominant surface neutralization mechanism for many ion-metal systems, the relative importance of resonance neutralization is not yet completely understood [19,43-451. The relative importance of the two neutralization processes is an important issue, for example, in the area of

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H.-W. Lee, T. F. George / Low-energy ion-surface collisrons

laser-induced-surface processes. The rate of resonance neutralization can be greatly enhanced by laser excitation of a surface [46], whereas Auger neutralization is not expected to change significantly when the surface is excited. (2) In general, the electronic excitation of projectile atoms can be achieved directly from incident ions, for example, through electron capture into excited states. We however neglect this because, in the low-energy region considered, a majority of the incident ions have already been neutralized when they arrive at the region of violent collision. In other words, our model is expected to be accurate in the low-energy region where the neutralization probability is substantial. This is the region where the scattering data do not differ much for the cases of ion incidence and neutral-atom incidence. Previous experimental results [38,47] suggest that the model should be valid for the primary ion energy up to a few keV for the case of light ions (Hi, He+) incident on a metal surface. For the H+-graphite system studied in detail in the previous section, the ion fraction at the time of violent collision, given by f’= exp( - uC/ul I), ranges from 0.05 to 0.13 at E, = 1 keV. At this energy, therefore, the neglect of direct charge exchange into excited states does not lead to significant errors. (3) The radiationless deexcitation process assumed to be resonance ionization followed by Auger neutralization could be Auger deexcitation or autoionization depending on the system. This again presents no problem as long as the rate of the dominant deexcitation process decreases exponentially with respect to the ion-surface separation, i.e., as long as eq. (17) can be used for the rate of deexcitation.We note that each of the above deexcitation processes involves emission of a free electron. Excitation and deexcitation of each incident ion is thus associated with emission of an electron. one therefore might expect to see an increase in the electron yield at the threshold energy of electronic excitation. Hagstrum [6-81 has observed a rise in the electron yield curve above 400 eV for the systems He+-Mo and He+-W. It could be that 400 eV represents the threshold energy for electronic excitation of a helium atom at a metal surface. In section 3 we have shown that our model yields charged fraction and photon yields in good agreement with experimental data. The model might be characterized as a nonlinear model, as both the logarithm of the charged fraction and the logarithm of the photon yield are predicted to exhibit nonlinear dependence on the inverse velocity. According to our model, the charged fraction is determined mainly by Auger neutralization. This is in contrast to the view held by Verhey et al. [16,17] and Overbury et al. [13] who introduced atomic neutralization and ionization in addition to Auger neutralization. If the characteristic velocity u, is assumed to be independent of the incident energy, the introduction of the atomic processes is necessary to explain the observed angular and energy dependence of the ion yields. We on the other hand assert that atomic neutralization and ionization are negligible compared with Auger neutralization and that the observed angular and energy dependence of the ion yields can be explained by taking into account the fact

H. _W Lee, T F. George / Low-energ

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231

that u, is not constant but varies with J, and ui according to eq. (24). Considering that the probabilities PJ for electronic excitation were found to be low from photon yield data, it seems reasonable to assume that the probabilities for atomic neutralization and ionization are negligible. On the other hand, if the atomic processes are introduced and u, is considered independent of energy, one is led to a strongly asymmetric result that the probability for atomic neutralization is substantially higher than the probability for atomic ionization [13]. A critical evaluation of our model against other models requires further experimental and theoretical work on the ion and photon yields and possibly the electron yield. In particular, photon yield data over the range of energy wide enough to clearly separate our model from the linear model seem desirable. There exist a large number of photon data at higher incident energies ( Ei 2 10 keV) than considered here, for example, that of Baird et al. [26,27]. However, at such high energies, processes not considered in our model may contribute significantly to ion and photon yields.

Acknowledgments

This research was supported in part by the Air Force Office of Scientific research (AFSC), United States Air Force, under Grant AFOSR-82-0046, the Office of Naval research, and the National Science Foundation under Grant CHE-8320185. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon. Acknowledgment is made by H.W.L. to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. T.F.G. acknowledges the Camille and Henry Dreyfus Foundation for a Teacher-Scholar Award (1975-86).

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