Al A1 390 NFGA lyE-ION FORMATION FROM SURFACE SCATTERING AND IIANDERSON CORRELAT I. (U) ROCHESTER UNIV NY OEP OFCHEM STRY CK S LAM El AL FEB 84 UROCHESTER/DC/84/ R 49NI ; l ED N D 48 07 F/G 74 N
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Contract N00014-80-C-0472
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TECHNICAL REPORT No. 49
Neqative-lon Formation from Surface Scatteringand the Anderson Correlation Enerqy U
by
Kai-Shue Lam, K. C. Liu and Thomas F. George
Prepared for Publication
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Physics Letters A
Department of ChemistryUniversity of RochesterRochester, New York 14627
February 1984
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Negative-Ion Formation from Surface Scatterinqand the Anderson Correlation Energy U PERFORMING ORG. REPORT NUMBER
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Prepared for publication Physics Letters A ..
I@. KEY WORDS (Ceaeminme aln vree aide II neeary and Identify by block mInmbe)NEGATIVE-ION FORMATION CORRELATION ENERGYPOSITIVE-ION-SURFACE SCATTERING H+ + CESIATED W(100)TWO-ELECTRON TRANSFER GOOD AGREEMENT WITH EXPERIMENTTIME-DEPENDENT ANDERSON-NEWNS MODEL %
20. ASTRACT fCmlhaa mveee 5 enca mai pIowers by Ak - eorl~eica; I i1nve0igoior(negative-ion formation from positive-ion-surface scatteri g is p esened froma unified point of view. Based on the time-dependent And son-N ns "del, thecorrelation energy U is seen to play an important role' n e two ele trontransfer process. Calculations of the probability of n e-ti o~tion ariin good agreement with experiments on the conversion o to (D ) byscattering from a cesiated W(100) surface.
DO ,JAN 8 1473 UnclassifiedECURITY CLAS111FICATION OF THlS PAGE (39. Data Et orod)
J__l_- _
Physics Letters A, in press
NEGATIVE-ION FORMATION FROM SURFACE SCATTERING
AND THE ANDERSON CORRELATION ENERGY U
Kai-Shue Lam*, K. C. Liu and Thomas F. GeorgeDepartment of ChemistryUniversity of RochesterRochester, New York 14627
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*Present address: Departmnt of PhysicsCalifornia Polytechnic State University3801 West Temple AvenuePcmona, California 917E8
V _n__ _l__Nm__
Abstract
A theoretical investigation of negative-ion formation from positive-
ion-surface scattering is presented from a unified point of view. Based
on the time-dependent Anderson-Newns model, the correlation energy U is
seen to play an important role in the two-electron transfer process.
Calculations of the probability of negative-ion formation are in good
agreement with experiments on the conversion of H+(D + ) to H'(D-) by
scattering from a cesiated W(100) surface.
A
I
JF- -I
Ii
Charge-exchange processes arising from monoenergetic ion beams scattered
from solid surfaces have recently been the subject of much experimental 1-5
and theoretical6-10 interest. Most of these studies focus on the process
of ion neutralization, involving the transfer of a single electron from the
surface to the singly-charged ion. I1 3'6 "10 However, owing to the increase
of applications involving the transfer of two electrons in a variety of
11,12situations, such as plasma fusion and the generation of high-energy
neutral beams, attention has also been directed to processes of negative-ion formation.4'5'13
For ion neutralization, the majority of theoretical work has been based
14on the Anderson-Newns model, originally proposed for the explanation of local-ized magnetization in transition metal alloys and subsequently applied to various
other problems such as chemisorption on metals15 and mixed valence in solids. 16'17
In these applications of this model, the correlation energy U, arising from the
Coulomb repulsion between the two electrons of opposite spin in the same discrete
level, plays a crucial role. However, in studies of ion netrualization (or the
reverse process of atom ionization), this important quantity is either implicitly
assumed to be infinite or completely ignored. Such approaches are thus
incapable of accounting for negative ion formation: U - - completely supresses
the transfer of a second electron, while if only single-electron transfer is
considered, U is irrelevant.
13Previous theoretical work on negative-ion formation has centered on
the time-dependent width and shift of the valence level of the impact ion,
where the time dependence is due to the motion of the ion. It was assumed
that first neutralization occurs via a nonresonant Auger process, while the
I m
2'
nuclear motion of the ion can subsequently bring the valence level into
resonance with a band state and thus effect the transfer of the second
electron. The quantity U again does not play an important role in this
theory.
In the present work, we use the Anderson-Newns model to examine the
effects of U on the two-electron transfer process in relation to the dynamics
of the nuclear motion of the impact ion. This represents the first time
that charge-exchange processes in surface scattering have been considered
from a unified point of view. We shall see that the negative-ion formation
depends crucially on the finite value of U, and in fact, recent experimental
results 5 can be explained in terms of our theory.
The time-dependent Anderson-Newns Hamiltonian including the correlation
energy term is given as
H(t) = H0 + V(t),
where
Ho t Undnd
0 = lcdcdoCdo k kck0kk + dond (2)
V(t) t kc. -[vkd(t)c ck + Vkd(t)c d.
The indicles d and k denote the valence state of the impact ion and the
conduction band states of the solid, respectively, a is the spin index and
nd Cd+Cd. The interaction Hamiltonian, V(t), responsible for the electron
transfer between the band and valence states, is the only explicitly time-
dependent part. The motion of the projectile ion can be phenomenologically
3
taken into account by using the specific form6
Vkd(t) = Vkde- (4'
where X, the sole dynamical parameter in our model, is directly proportional
to the normal impact velocity. Hence x controls the duration of the bound-
continuum interaction, while Vkd (time-independent) determines its strength.
To lowest order, the perturbative solution for the time-evolution
operator T in the interaction picture, which contributes to the S-matrix
for negative-ion formation, is given ast - t
i(2) = (-i) 2 f dt'V(t')f dt"V(t"), (5)
where
". V(t) = eiHOtv(t) eiHot (6)
is V(t) expressed in the interaction picture. At t = -®, the ion is taken
to be infinitely far from the surface, and t = 0 is the instant of impact.
It is apparent from Eq. (3) that, since negative-ion formation involves
ultimately the transfer of two electrons, only terms of even powers in
in the expansion of T contribute to the S-matrix.
Figure 1 illustrates schematically the electron-transfer process to
lowest, i.e., second, order as contained in Eq. (5). Physically, every
factor of V(t) corresponds to the transfer of one electron from the band
level ek to the Cd level of the ion, or the conjugate process of electron
transfer from Ed to Ek. Therefore, the contribution to the S-matrix from
4
4
higher-order terms of T can be diagrammatically generated in a straight-
forward manner. Such terms (neglected in this work), however, may involve
those final states i-i which the solid becomes electronically excited, with
levels higher than the Fermi level occupied. In general, low-ordered pro-
cesses are favored by high impact velocities (large x).
To lowest order, the time-dependent probability for negative-ion
formation is then given as
C C
F F()2P(t) = f de f dC'p(e)ci')<k IT 2(t,-w)II>l 2 , (7)
L CL
where _F and CL are the Fermi energy and conduction band edge of the solid,
respectively, P(E) is the density of states of the band, and the initial
and final states, II1 and lk k,k> respectively, are described in Fig. 1.
The matrix element in Eq. (7) can be evaluated by using Eqs. (2)-(6) to give
the result
<k k+' i(2 ) V2 1+(U-c 7c')/2 e[2x+i(U 'c-c')]t (X_ C) .IT J<~ ~ k(k C-()(T(!1_t,-+.l = -
t S 0 (8a)
1, (12~1 1
T )~l(U--c')2Xi(U-c-e')]t AI(--'/X (-A+-r + -XAr c)e[x1 -)t
+ 2V2A. 2 [--(-cn i
+ le fe1(U1 t > 0 (8b)
+IE +€~iU_
...,..........
5
wher £ t
- d an 0 Eki- C wit Cdset as the zero of energy, and
V = V is assumed to be independent of energy. As a first approximation, we
have also assumed that U and Ed are constant within the collision region. This
latter assumption is not expected to affect the results qualitatively.
We now turn to calculations of the probability P(t) of negative-ion
formation and its limiting value at t - P(-o), for various choices of
the parameters U and X. PHac represents the experimental observation of
outgoing negative ions after the scattering event is complete, and P(t)
reflects the behavior of the transient states. The following fixed2
numerical values were adopted: c L = 10 eV, c F = 0.06 eV and L = zV
0.43 eV, where we have assumed the band to have no important structure
so that the density of states p can be taken as constant in the integra-
* tion over the band in Eq. (7). Although the last two numbers have been
used previously in a study of charge transfer in the Na/W(100) system,8
they have no special significance in our present work, which is to
* investigate in general the effects of the variation of x and U, especially
the latter.
Intuitively, we expect the probability P(-~) to be small when the
repulsive correlation energy U is large. However, P(-o) also depends on
x, i.e., on the velocity of the impact ion. As shown in Fig. 2, there is
a peak for P(-) at a small value of X for each U. The explanation for this
is that since small x implies a long duration of interaction whereby from
the uncertainty principle the resonance requirement is stringent, it is
*impossible for the second electron in the solid to overcome the barrier U.
* On the other hand, large x can ease the resonance requirement -- energy
* conservation can be violated for short-duration processes -- but it also
limits the actual time available for electron transfer, resulting in a
small P(-). As a consequence, for each U there exists an optimal value of
6" '
M for which the probability attains a maximum. Moreover, m
increases as U is increased, due to the fact that a shorter inter-
action time is favorable for the second electron to transfer non-
resonantly as U becomes larger.
The close relationship between resonant electron transfer and the
ion velocity becomes obvious when we look at the time evolution of the
probability of negative-ion formation. Figure 3 displays P(t) for various
values of U with fixed x. Each probability curve has a peak at very short
time t m (- 0.2 femtoseconds). We see that tm is smaller for larger U, in
accordance with the arguments given above. In addition, the degree of
transient negative-ion formation, measured by the ratio P(t )/P(..), is morempronounced for larger U. Figure 4 provides yet another manifestation of
the striking transient behavior; namely, although there is an optimal m
at each U for the limiting value of the probability, P(-), this is not
necessarily the case in the transient region.
To test our theory, we shall compare it with measurements on the
conversion of H+(D) to H (D') by scattering from a cesiated W(1O0)
surface at different grazing angles e.5 For this purpose, we identify
x as vcose, where v is the magnitude of the velocity, and phenomeno-
logically introduce a velocity-dependent interaction, a - 0.43 exp(-O.Olv)
(in the unit of eV), to account for the loss of particles due to penetra-
tion into the surface. The variation of e is thus equivalent to the
variation of the normal impact velocity x. Our results, given in
Fig. 5, are in qualitative agreement vOith the experimental ones,5
where for all incident enerC ' th .. nversion probability goes
7
through a maximum. Quantitative comparisons have not been attempted since
precise information on critical parameters, especially A, is still lacking.
For the cesiated W(100) surface, among other complications leading to
unreliable data for parameters is the theoretical evidence of a lowering
of the work function by multiple dipole formation. 18 "9
In this work we have demonstrated, through varying the dynamical
conditions of the impact ion, the significance of the correlation energy U
in negative-ion formation from positive-ion-surface scattering. Though U
in general decreases the probability for rf-ative-ion formation, one can
always exploit the experimentally controllable dynamical conditions (varying
v and e) to achieve an optimal result for a given system. Moreover, there
may even be the possibility of exploiting the characteristic transient behavior
of P(t), since for finite U, P(tm ) is always larger than (-) except for very
large x. For very small x, on the other hand, our perturbation approach may
not yield correct results, since the long interaction times then allowed may
require higher-order processes than the second-order one be considered. Our
results have been shown to be in good qualitative agreement with experiments.
A more elaborate calculation is needed which takes Into account the lowering of the
valence level of the ion near the surface18'19 is needed for quantitative
Jcomparision with experiments.
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, and
the Office of Naval Research. The United States Government is authorized
to reproduce and distribute reprints for governmental purposes notwith-
standing any copyright notation hereon. TFG acknowledges the Camille
and Henry Dreyfus Foundation for a Teacher-Scholar Award (1975-84) and
the John Simon Guggenheim Foundation for a Fellowship (1983-84).
-a
8
References
1. H. H. Brogersma and T. M. Buck, Surf. Sci. 53, 649 (1975).
2. R. L. Erickson and D. P. Smith, Phys. Rev. Lett. 34, 297 (1975).
3. E. G. Overbosch, B. Rasser, A. D. Tenner and J. Los, Surf. Sci. 92,310 (1980).
4. E. G. Overbosch and J. Los, Surf. Sci. 108, 117 (1981).
5. J. N. M. van Wunnik, B. Rasser and J. Los, Phys. Lett. 87A, 288 (1982);J. Los, E. A. Overbosch and J. N. M. van Wunnik in Proceedings of theSecond International Symposium on the Production and Neutralization ofNegative Hydrogen Ions and Beams (Brookhaven, 1980).
6. W. Bloss and D. Hone, Surf. Sci. 72, 277 (1978).
7. Y. Muda and T. Hanawa, Surf. Sci. 97, 283 (1980).
8. R. Brako and D. M. Newns, Surf. Sci. 108, 253 (1981);Vacuum 32, 39 (1982).
9. K. L. Sebastian, V. C. Jyothi Bhasu and T. B. Grimley, Surf. Sci. 110,L571 (1981).
10. J. C. Tully, Phys. Rev. B 16, 4324 (1977).
11. K. H. Berkner, R. V. Pyle and J. W. Stearns, Nucl. Fusion 15, 249 (1979).
12. K. Wiesemann, K. Prelec and Th. Sluyters, J. Appl. Phys. 48, 2668 (1977).
13. B. Rasser, J. N. M. van Wunnik and J. Los, Surf. Sci. 118, 697 (1982).
14. P. W. Anderson, Phys. Rev. 124, 41 (1961).
15. D. M. Edwards and D. M. Newns, Phys. Lett. 24A, 236 (1967); D. M. Newns,Phys. Rev. 178, 1123 (1969).
16. B. Coqblin and J. R. Schrieffer, Phys. Rev. 185, 847 (1969).
17. J. H. Jefferson and K. W. Stevens, J. Phys. C 9, 2151 (1976).
18. K. H. Klngdon and I. Langmuir, Phys. Rev. 21, 380 (1923).
19. E. Wimmer, A. J. Freeman, N. Welnert, H. Krakauer, J. R. Hiskes andA. M. Karo, Phys. Rev. Lett. 48, 1128 (1982).
- -- - ~ 7
9
Figure Captions
Fig. 1. Schematic diagram of electron transfer in negative-ion formation.
Cis the upper and EL the lower edge of the band. (a) Initial
state LI>: valence state Ed empty, band filled up to the Fermilevel EF. (b) Intermediate states Ik + and 1k;>: states cor-
responding to the neutralized atom; one electron transferred
from the Ekor kilevel to the Cdlevel. The arrows denote
the spin states of the electrons, and the solid and hollow
circles represent electrons and holes, respectively. (c) Final
states Ik~k'>: negative-ion states; two electrons transferred
to the Ed level.
Fig. 2. PHcc vs X for various values of U. Energy is in the unit of eV.
Fig. 3. P(t) vs t for various values of U with fixed X. As U increases,
the characteristic short-time behavior becomes more pronounced.Energy is in the unit of eV, and time is in the unit of 6.59 x
10 6sec fl)
Fig. 4. P(t) vs t for various values of X with fixed U. The units are the
same as in Fig. 3.
Fig. 5. P(-o) vs e, the incident angle of impact. v.<V v2v< V 4.
... 1 . ... ....... .
leEF Ed
Eu Eu
IE
F-+E Ed Ed
IKKF Ed
Fis.1
-C3
C)o
In
Ui,
Lrr1
IIf
-LA-
NQ
LO
Lq 10 10(0lra M t
(I n
ifj
MlH
CID
'MC
LUL)
i-C)
LUCC
A *1I!
(oon
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