Simulation of low-energy HCI-solid interaction

ELSEVIER

Nuclear Instruments and Methods in Physics Research B 98 (1995) 400-406

Beam Interactions with Materials A Atoms

Simuiation of low-energy Xi-solid interaction

Yasunori Yamamura a, * , Sachiko T. Nakagawa a, Hiro Tawara b

a Okayama University of Science, Ridai-rho, Okoyama 700, Japan ’ National institute for Fusion Science, Furou-cho, Chigusa-ku, Nagoya 464-01, Japan

Abstract The interaction of low-energy highly charged Xeq+ ions (q = l-44) with a diamond crystal has been investigated, using

the time-evolution binary collision simulation code DYACOCT. The nuclear interaction between a charged particle and a

neutral atom is calculated by the binary collision approximation, and the Coulomb interaction between charged particles is calculated by the molecular dynamics technique.

It is found that the screening shift is very important in the decay dynamics of electrons captured into highly exited states

in an early stage of the collision process. Some of the captured electrons are stripped off due to the peeling-off process hefnre the ;ntrr,_A,,nor ,br~,, h,mnm,x rlrrm;n,,nt whom Ifl GnI(l Yn4+ (n \ 36 :,v.m o+.nw.nc.h 0 A:nm-...-I .-...A.,.- Ths ml-... “IlYl” LIAU lllll” 1 X” 6”L UV’“, “lr”llllU ““llllll”lll *.llrll A” Rb . LLL. \y L J”, l”llJ appL”aL,, a uIaIII”II” JUllaLG. 111-z >,“W

highly charged Xeq+ ions are almost neutralized before entering diamond. The sputtering yield due to a 10 keV Xe@

(q 2 18) ion is about ten times larger than that due to a singly charged XeC ion and the charge fraction of sputtered particles is about 1.5%.

1. Introduction

Recently, theoretical and experimental investigations of the interaction of a low-energy highly-charged ion (HCI)

with a solid have been one of the most interesting prob-

lems in the field of particle-solid interactions [1,2]. This interaction includes multielectron capture, Auger cascade

processes occurring during ion neutralization, and the di- rect interaction of orbital electrons captured into high Rydberg states with a solid surface, which is the so-called “peeling-off” process (PO) [3]. These studies also provide information required for the understanding of basic collision processes as well as plasma-wall interaction phenom-

ena in fusion research and plasma processing, and for possible nanometer scale lithographic applications [4] due to ion-induced surface modifications.

It is presently understood that when a slow HCI captures a number of electrons from a solid into very high n

states of the ion at relatively large distances from the surface, depending on the ionic charge, this electron trans- fer mechanism can be predicted by the classical over-the- barrier model (COBM) [5-71. That is, the HCI forms multiple excitation states, where many electrons occupy high Rydberg levels while most inner shells are virtually empty, which is often called the “hollow” atom [1,2,3,8]. Studies of the dvnamics of the dp.r.av nrocens nf &&fins -, --------- -- , r------ -- in these Rydberg states as the HCI approaches and enters

* Corresponding author.

the surface are present subjects of an intensive research

effort and are aimed at obtaining increased knowledge of the decay mechanisms and rates. It is recognized that the decay of sufficiently slow hollow atoms (u < 0.1 a.u.) can

occur predominantly above the surface via Auger deexcitation [9], in addition to X-ray cascade [lo] transitions ending in filling the inner atomic shells.

The surface of a conductor provides an essentially limitless source of electrons for approaching HCI. The

limited mobility of electrons in insulators, on the other hand, allows us to study defects and sputtering caused by target ions in insulators via strong electrostatic interactions induced by their presence in the bulk. About twenty years ago, Arifov et al. [ll] reported that sputtering yields of ZnS increase as the projectile charge increases. On the contrary, about ten years ago, de Zwart et al. [12] reported that the sputtering yield of Si semiconducting materials showed practically no dependence on the charge, where

they used 20 keV Ar q’ (q = l-9) ions. For the past

several years, some interesting results from a series of experiments aiming at studying the interaction of a slow HCI with an insulator as well as conductor surface have been reported [13,14]. Microscopic studies by AFM re- vealed that nano-size surface defects were formed on a Mica surface by the incidence of individual HCIs.

!n this nPrW=r n&lo the time-evolution simulation rnrlP r-r-‘? ----‘0 WV..” DYACOCT [15], we investigate the formation and decay of a hollow atom and the sputtering induced by slow 10 keV (u _ 0.05 a.u.) HCI of Xeq+ (q = l-44) incident normally on the (100) surface of a diamond crystal.

0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDf 0168-583X(95)00155-7

Y. Yamamura et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (I995) 400-406 401

2. Model of simulation

As an HCI approaches the surface of a diamond crystal,

electrons are transferred resonantly from its valence band to the HCI. At the same time, as the number of captured electrons increases, the intra-atomic Auger deexcitation

process sets in, In a conductor the reverse resonant ionization process becomes possible due to the image shift and

the screening shift (SS) of the binding energies of electrons already transferred if the final state is not forbidden by the Pauli principle [1,2], but in a diamond crystal the band gap is about 5.8 eV [16], and thus the reverse resonance ionization process cannot occur even if the

already captured electrons shift their energy levels upward. In the present case there are two possible ionization pro-

cesses of the hollow atom above the surface, i.e. PO process and Auger ionization (AI) process. The dynamical

change of the energy levels in the neutralizing and ionizing HCI approaching a diamond surface is shown schemati-

cally in Fig. 1. The coupled rate equation for the population, P,(R), of

the nth shell of an HCI including the possible elementary

processes is [17]:

-&R) =I,” -I,PP(R) + f c A,,,J’,<(R)2 n’> n

-f’,s(R)2 c A,,, (1) “> Ii

where R is the distance from the surface, I,’ is the current of captured electrons, I,’ is the decay constant due to the

PO process and A,,, is the Auger rate of a projectile. In

the present simulation this coupled rate equation is solved

in a stochastic manner. We apply the COBM for an electron bound initially

with binding energy I in an ion of core charge z being transferred into an HCI of charge q. It is assumed that for z I 2 an HCI captures an electron from the valence band

peeling off m k?

7

I diamond - approaching HCI

Fig. 1. States of a neutralizing HCI approaching a diamond

surface. Electrons captured via resonance neutralization (RN) can be remitted via Auger ionization (AI). Al and “peeling-off” are

enhanced by the screening shift (SS).

of a diamond crystal, whereas for z 2 3 from the atomic

state of a carbon atom. If the distance r between Xeq+

and a target carbon atom satisfies the condition Rmin < r

<R max, the projectile Xeq+ can capture an electron in the valence band of a diamond, where R,, = [2(qz>‘/’ +

zI/I” and Rmin = [2(qz) ‘1’ + z]/I, [6]. The ionization

potentials 1, and 1, correspond to the upper and the bottom edge of the valence band, respectively. The corresponding quantum number n is easily obtained by

where the square bracket [x] is the Gauss symbol, and

I = [2(q.?)“2 + zl/r.

Regarding the Auger deexcitation rates for the n -+ n‘ transition (An = n - n’) of hydrogen-like atoms we use the

following simple scaling rule [ 171:

2.1 x 1ol4 A,,, = cAnj3.46 ‘-I’

For the Auger electron emission, the energy difference between n and n’ states should be larger than the binding energy of n state, i.e.,

%ff,nz < %f,(n-An)2 4eff.n’ --

2nz 2(n-ArQ2 2n2 ’ (4)

where the SS effect illustrated in Fig. 1 is essentially included through the effective charge qeE,n which changes dynamically due to the number of electrons inside the

shell, and has the form n-l

9&f,” =Z, - c P,(R), k

and Z, is the atomic number of a projectile. The PO process can be considered as the scattering of

an orbital electron in a high II state with a carbon nucleus and its core electrons [3,18]. If R < rn the electron in the nth state can be peeled off, where r, is the mean radius of the orbital electron of the nth shell which is given as

rn = n2ao/4eff,n (a, = Bohr radius). Then the PO rate I,’

is given as

where N is the number density of a target material, r, is the period of Coulomb orbits and is given as

2Ta, n3 7 =-- n

uo qeff.02 ’ (6)

and u. is the Bohr velocity. a,,, n is the total scattering cross section of an electron, which is expressed by the Rutherford scattering formula,

u ,.,.=nz,(z2+l)( -$)2~cota(+), (7)

4. SURFACES/CLUSTERS/SOLIDS

402 Y. Yamamura et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (1995) 400-406

0 1 2 3 4 5

r (A)

Fig. 2. Interaction potential between Xeq+ and C’+.

and 0 = cos-‘(r,/R). The distance R becomes negative inside the bulk, and m, is the electron mass at rest. The

minimum scattering angle emi,, of Eq. (7) cannot be defined sharply, but it is set to be 5” in this paper. 2, is the atomic number of a target atom and /3, = u,/c.

Some of the peeled-off electrons will be recaptured by charged carbon ions in solids, and others emitted into the vacuum. In the present model we employ the following assumption. If an orbital electron in a high n state is

backscattered with more than a 165” angle by a carbon nucleus and its core electrons in the first surface layer of a diamond, it will be emitted into the vacuum. Otherwise,

the electron is recaptured by a charged carbon ion near its orbit if it is stripped-off according to Eq. (5).

The interaction between charged particles is repre- sented by a partially screened Coulomb interaction potential, V(r), which has the long-range force as is shown in Fig. 2. In the DYACOCT code the interactions between charged particles are solved numerically by the molecular dynamics technique. The lattice atom is assumed to be

trapped in the potential well and so a Newtonian equation

of the charged kth lattice atom located at rk is presented in the form:

2

M2$= -;

k ( C ‘Cr!fj) + Hrkl).

j#k

where

En is the bulk binding energy, and rkO is the equilibrium position of the kth lattice atom.

The binary interaction including neutral atom can be treated by the binary collision approximation, because the interaction potential drops rapidly at a large distance, which is known from Fig. 2. We assume the interaction potential to be given as

Z,Z,e’ V(r) = - r 4(r/aTF)7

where 4(x) = Maximum[ &(x), qlq2/Z1Z2], and (bTF(x) is the usual Thomas-Fermi screened potential. q1

and q2 are the net charges of the projectile and the target atom, respectively. The screening length uTF is defined by

0.4685 ‘TF =

/(Z, - q1)2’3 + (Zz - 42y3

(A>. (11)

Concerning the electronic stopping power in solids for charged Xe q+ ions, we employ the ZBL model [19]. For a 10 keV Xeql ion the electronic stopping is not so large,

moreover q is less than 3 just above the surface. Then, we neglect the contribution of electrons produced by inelastic

collisions with lattice carbons, because the band gap of a diamond is sufficiently large.

When the charged carbon atom in solids is released from its original lattice site due to Coulomb explosion or elastic collision with an energetic particle, it will capture an electron in the valence band of a diamond crystal. This

neutralization process is also treated by COBM in the present simulation.

3. Simulated results and discussions

As an HCI approaches a diamond surface, it captures electrons from the valence band of the diamond crystal into a high Rydberg state and forms a hollow atom. After

this, either the intra-atomic Auger deexcitation or the PO process, or both, set in, and therefore the electron population of the nth shell in the projectile dynamically changes with time r and distance R from the surface. For one example, we show in Fig. 3 some snapshots of the interaction of a 10 keV Xe44+ ton with a diamond (100) surface as a function of t and R (t is set to zero at R = 41 A). At R = 11 A the net charge of a projectile is 2, and it increases to 3 at R = 5 f due to the PO process or the AI

process. Fig. 3 shows high potential energy deposition in the first few layers of a diamond crystal due to a 10 keV Xe 44+ ion. As a result, target atoms near the surface are in the atomic state. This strong electrostatic field causes a new type of sputtering and surface defect. At t = 35 fs a

carbon atom is going to leave the surface, although the collision cascade is not yet developed.

The dynamical change of the electron population P,, of the nth shell in the projectile is shown in Fig. 4, where the population P, is averaged over 40 primary XeU+ ions. The present simulation has shown the following features: the first electron is captured into the n = 34 state of Xe ions at R = 37 A, as is expected from COBM, and at the next instant another electron is transferred to a Xe ion from the same position. As a result, this target carbon can no longer be in the solid state, but in the atomic state. Approaching further, a number of electrons are captured into broad n states of an HCI. Before R = 24 A, some electrons still exist at high n states, and the net charge q is

Y. Yamamura et al. /Nucl. Ins&. and Meth. in Phys. Res. B 98 (1995) 400-406 403

about 16, as is shown in Fig. 5(a). This means that, owing

to the SS effect, the orbital radius of electrons at high n

states, which are captured in the early stage, becomes

large, and the PO process becomes possible even if the distance is large. This is why thtre is no electron at the

higher states (n > 18) at R = 14 A, as seen in Fig. 4. The SS effect also affects the Auger process. The

energy levels of high Rydberg states become closer and closer due to the SS effect. In the present simulation model this effect is included in the following manner. When we

estimate the population P,, the population P,,+i is added to P,, if AE”c0.5, where AE,,=IE,,-E,+jl(j= + 1, + 2,. . .>. Since many electrons are transferred al-

ready at R = 14 A where the average net charge of the Xe

ion is less than 5, the energy difference 1 E, - E,+j ( become sufficiently small, and so the effective population P,, is large. As a result, we have a large amount of Auger

10 keV Xe+44+ C(100)

R = 238( t=15fs

0

R= l7A t = 20 fs

0

R=ilh t = 25 fs

Q

R=-9/i t=41 fs

Fig. 3. Snapshots of a neutralizing and ionizing HCI approaching a diamond surface and induced positive carbon ions in solids. The concentric circle corresponds to the charge state, and the circle with a cross means an energetic neutral carbon atom.

events aear 10 A, which is shown in Fig. 6(a). Then, at

R = 9 A the level of n = 3 is occupied by several electrons

due to Auger deexcitation.

In Fig. 5 the dynamical change of the net charge q of a Xe ion (Fig. 5(a)) and the integrated charge Q (Fig. 5(b)) induced in solids are shown as a function of distance for Xe44+, Xe36+, Xe”+ and Xesf. Since 10 keV Xe is slow, all these HCIs are nearly neutralized before entering the solid, and their net charges are less than unity just below the surface. The induced integrated charges, Q, of Xe’+, Xe”+, Xe36f and Xe44C are 1.6, 2.0, 2.3 and 2.4 times

larger than the primary net charge of an HCI, respectively. In Fig. 6 the frequencies of the intra-atomic Auger

events (Fig. 6(a)) and that of the PO events (Fig. 6(b)) are shown as a function of distance for 10 keV Xeq+ (q = 8,

18, 36 and 44). Even at large distances (> 20 A> the PO process sets in due to the SS effect before the Auger decay becomes dominant. The contribution of the PO process is slightly larger than the Al process for Xe44+ and Xe36f. But, for Xe”+ and Xesf the contribution of the AI

process is larger than the PO process. Especially for Xe”+ the AI contribution is three times larger than the PO contribution, because the possible highest Rydberg number is less than 16 for Xe”+.

When a projectile enters the solid, it loses its energy with elastic collisions and inelastic collisions with target

atoms. As a result, some target atoms are sputtered and the

surface is eroded. In this case, furthermore, the potential energy of an HCI is deposited in a few surface layers in the early stage, therefore a lot of positively charged lattice

atoms are distributed near the surface. The extremely strong fields induced by these distributed positively charged lattice atoms contribute positively to sputtering. Fig. 7 shows plots of the sputtering yield (atoms/ion/ps) against time for 10 keV Xe qi (q = 1, 4, 8, 18, 36 and 44). In

Table 1 we show the charge dependence of the sputtering yield and the charged fractions of sputtered particles due to

a 10 keV Xeq’ ion bombarding normally on the (100) surface of a diamond crystal, where the numbers of primary HCIs used in the present simulation are 1000, 1000,

100, 40, 40 and 40 for q = 1, 4, 8, 18, 36 and 44, respectively, and the cascade is followed until 6 = 400 fs,

and the thickness of a diamond crystal is 30 A which is sufficiently large for sputtering.

As is seen from Fig. 7 almost all sputtered particles are ejected before 200 fs except for Xe”+. The sputtering by Xe’+ and Xe4+ 1s mainly due to the collision cascade developed in solids which becomes dominant at - 90 fs. The sputtering yields by Xeq’ (q > 8) have strong peaks near t = 60 fs when the collision cascade is not well developed. Therefore, these large sputtering yields can be recognized as “potential ejection”. The collision cascade sputtering or “kinetic” ejection at - 90 fs is also enhanced for Xe qf (q > 8). Even though the present calculated yields include large statistical errors, the sputtering yield of a Xe q+ (q 2 18) ion is about ten times larger than



PO 15 10

5 0

15 10

5 0

15 10

5 0

tt 1;

c 5 .o 0 A 15

1 2 3 4 5 6 7 8 91011121314151617181920212223242526272829303i32333435

n

Fig. 4. Formation of “hollow” atoms near the surface; averaged occupation number of the nth shell at distances R from the surface, where

10 keV XeU+ ions are incident on the (100) surface of diamond.

that of a singly charged XeC ion. The sputtering yield increases with increasing charge q for q < 18, and it seems to be saturated or constant for larger q. The fraction of charged sputtered carbons to the total sputter ed particles

et(4 10 keVXe+q+C(lOO)

100

80

60 a

40

20

0

10 keVXe+q+C(lOO)

40 30 20 10 0

R(A)

Fig. 5. (a) The dynamical net charge q as a function of distance from the surface for 10 keV XeU+, Xe36+, Xe’a+ and Xe*+

ions. (b) Plots of the integrated charge Q induced in diamond by 10 keV Xe#+, Xe36i, Xe”+ and Xe8+ ions as a function of

distance R.

2oIohyxso] I5 : Auger ionization _

.“” “.“,, 2 IO_

q = 44

?i

q=3cj ;

- q=1e r

- q-8 ‘I 5_

Cd

IO keVXe+q+C(lOO)

15 - q = 44

q = 36

- q=18 peeling-off

Fig. 6. Counts of Auger ionization events (Fig. 5(a)) and peeling-

off events (Fig. S(b)) at distance R for 10 keV XeU’, Xe36+, Xe18’ and Xe*+ ions on C(lO0).

Y. Yamamura et al. / Nucl. Instr. and Meth. in Phys. Res. B 98 (1995) 400-406 405

10 keV Xe+q --f C(100)

- q=44

- q=36 ,,x,II/...” q = ,fJ

,, ,,,, - q-8

- q=4

- q=l

1

t (fs)

Fig. 7. Plots of sputtering yields as a function of time for Xe”+,

Xe3”+, Xe”‘, Xe*+, Xe4+ and Xe’+ ions on C(lOO), where the

incident energy is 10 keV, and the unit of the ordinate is atoms/ ion/ps.

is about 15% for a XeqC ion (q 2 18) which is far larger than in metallic targets.

The present calculated features for sputtering yield dependence on the charge of HCI are qualitatively in agreement with the observation by Arifov et al. [ll], who reported that the sputtering yields of ZnS increases as the projectile charge increases, where the band gap of ZnS is

3.8 eV. On the contrary, about ten years ago, de Zwart et al. [12] reported that the sputtering yield of Si semicon-

ducting material showed practically no dependence on the charge. Possible explanations of the discrepancy between the present results and their experiment can be as follows. The electric conductivity of Si is far larger than that of diamond. Thus, the positive ions produced in the bulk tend to be neutralized much quicker in Si than in diamond.

Table 1

The ion charge dependence of sputtering yield and the charge

fraction of sputtered atoms resulting from bombarding a diamond

(100) surface with 10 keV Xe+q ions.

Ion charge 4

1 4 8 18 36 4.4

Yield 0.46 0.50 3.7 7.3 4.5 3.2

(atoms/ion) Charge fraction of 0.0 0.03 0.05 0.12 0.21 0.16

sputtered atoms

Therefore, sputtering due to Coulomb repulsion in Si can

be minimal, compared with that in diamond. The velocity of 20 keV Ar is about 2.6 times larger than that of 10 keV

Xe, and yet the band gap of Si is only 1.08 eV, which is much smaller than those of diamond and ZnS. Therefore, some electrons produced by inelastic collisions of Ar with

Si may be promoted into the conduction band of a Si crystal.

4. Conclusion

Using the time-evolution simulation code DYACOCT, we have investigated the interaction of a slow highly charged Xe 4+ (q = l-44) ion with diamond crystal, i.e. the formation of transient “hollow” atoms above the surface and the synergistic effect between the induced electrostatic field near the surface and the collision cascade. It is found that for the dynamic decay of electrons promoted into highly exited states in an early stage, the peeling-off process is more important than the intra-Auger

decay when 10 keV Xeqf (q > 36) ions approach a diamond surface, and highly charged Xe ions are almost neutralized before entering diamond. The sputtering yield

due to a 10 keV Xe4+ (q > 8) ion is about ten times larger than that of a singly charged ion.

The present simulation code includes possible funda-

mental physical processes in the interaction of highly charged ions with solids. But, some fundamental processes employed in this code included rough approximations. For example, we must include the Slater screening matrix in estimating the screening shift. The peeling-off process is estimated by the Rutherford scattering formula which is for relatively high-energy electron scattering and we use a

phenomenological screening function for nuclear interaction which must be determined from first principles, using

a realistic electron density. Much more reasonable im- provement of this prototype simulation code is now in progress.

Acknowledgements

The authors would like to express their sincere thanks to Prof. L.P. Presnyakov of Lebedev Physical Institute (presently at NIFS Nagoya), Prof. M. Kitagawa of North Shore College, Prof. H. Saito of Okayama University of Science, and Prof. Y. Yamasaki of the University of Tokyo for their valuable discussions.

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Documents

Simulation of low-energy HCI-solid interaction