Position-dependent stopping power of low velocity rare gas atomsat a SnTe(001) surface

Kaoru Nakajima a, Yukihiro Fukusumi a, Kenji Kimura a,*, Michi-hiko Mannami a,M. Yamamoto b, S. Naito b

a Department of Engineering Physics and Mechanics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japanb Institute of Advanced Energy, Kyoto University, Uji 611-0011, Japan

Received 15 June 1998; received in revised form 9 October 1998

Abstract

Energy losses of 15±30 keV Ne�, Ar� and Kr� ions specularly re¯ected from a SnTe(001) surface are measured.

Because more than 98% of the re¯ected ions are neutral, the observed energy loss can be considered as the result of

atom±surface interactions. From the observed energy losses, position-dependent stopping powers of the SnTe(001)

surface for neutral atoms are derived. The obtained stopping powers are compared with the theory of the stopping

power for low velocity ions with help of the local density approximation. While the agreement between the experimental

and theoretical results is excellent for Ar and Kr atoms, the experimental stopping is about twice larger than the

theoretical one for Ne atoms. This discrepancy can be explained in terms of the e�ect of excited atoms on the stopping

power. Ó 1999 Elsevier Science B.V. All rights reserved.

PACS: 34.50.Bw; 34.50.Dy; 79.20.Rf

Keywords: Surface; Stopping power; Ion±surface interaction; Excited state

1. Introduction

When a fast ion is incident onto a ¯at crystalsurface at a glancing angle hi smaller than a criticalangle, the ion does not penetrate into the solid butis re¯ected from the surface at an angle of specularre¯ection. This phenomenon called specular re-¯ection of fast ions is suitable to study ion±surface

interactions [1±4]. The trajectory of the ion is well-de®ned and so the impact parameter of the colli-sion of the ion with surface atoms can be con-trolled by its angle of incidence, which allows us toderive position-dependent probabilities of inelasticprocesses at the surface [5±7]. This was ®rst dem-onstrated in a study on the energy loss of fast lightions specularly re¯ected from single crystal sur-faces, where the position-dependent stoppingpower was derived from the hi-dependence of theobserved energy losses [5]. The obtained stoppingpower was explained in terms of single electron

Nuclear Instruments and Methods in Physics Research B 149 (1999) 31±37

* Corresponding author. Tel.: +81 75 753 5253; fax: +81 75

753 5253; e-mail: kimura@kues.kyoto-u.ac.jp

0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 8 9 2 - 1

excitation as well as the plasmon excitation forions faster than the Fermi velocity of the target.On the contrary, for ion velocity smaller than theFermi velocity, direct excitation of plasmon is notallowed. Actually, the experimental stoppingpower of SnTe(00 1) surface for 12.5±30 keV He�

ions (v/vF� 0.40±0.62) was roughly explained bythe theoretical calculation which took account ofthe single electron excitation process only [8]. Thecalculation was based on the local density ap-proximation and an asymptotic formula valid forv�vF was employed. The research was extendedto lower velocities expecting a better agreementbetween the theory and experiment. In a prelimi-nary measurement with 15±30 keV Ne� ions (v/vF� 0.19±0.28), however, the experimental stop-ping power was found to be almost twice largerthan the theoretical result [9]. This anomaly wasleft for further investigation.

In the present work, we complete the mea-surement with Ne� ions and extend the research tomuch lower velocities, i.e. 15±30 keV Ar� and 15keV Kr� ions. The position-dependent stoppingpowers of SnTe(001) for these ions are derivedfrom the observed energy losses and the results arecompared with the theory. The anomalous be-havior of the stopping power for low energy Neions is discussed in relation to the neutralizationprocess in front of the surface.

2. Experimental procedure

A single crystal of SnTe(001) was prepared byepitaxial growth in situ by vacuum evaporation on acleaved KCl(001) surface (25 mm ´25 mm)mounted on a ®ve-axis precision goniometer in aUHV scattering chamber (base pressure 3´10ÿ10

Torr). The crystal structure of SnTe is a NaCl-typestructure and the (001) surface of SnTe is a bulktruncated surface [10]. It is known that surface de-fects, especially surface steps, a�ect the scatteringevent [11]. In the present work, the growth rate waskept to be less than 0.5 nm/min at 250°C so that thedensity of surface step was small [11]. The temper-ature of the crystal was kept at 250°C during thescattering experiment and the epitaxial growth wasrepeated intermittently to avoid radiation damage.

Beams of 15±30 keV Ne�, Ar� and 15 keV Kr�

ions from a RF ion source were momentum-ana-lyzed and collimated by a series of apertures to adiameter less than 0.2 mm and to a divergenceangle less than 0.5 mrad. The beams were im-pinged into the surface of SnTe(0 01) at glancingangles less than 50 mrad. The azimuth angle of thecrystal was carefully chosen to avoid surface axialchanneling. The ions scattered from the surfacewere energy-analyzed by a 120°-cylindrical elec-trostatic spectrometer which was rotatable aroundthe target crystal. The acceptance angle of thespectrometer was �1 mrad and the energy resolu-tion was DE/E� 3´10ÿ3. Removing the spec-trometer from the beam line, the ions scattered atspecular angle were selected by an aperture (ac-ceptance half angle� 1.3 mrad) and the chargestate distribution of these ions was measured bymeans of a magnetic analyzer.

3. Experimental results

Fig. 1 displays an example of the observed Ar�

yield as a function of the scattering angle when 15keV Ar� ions were incident on the SnTe (001) athi� 16.7 mrad, where hi is measured from thesurface plane. The ion yield shows a peak at ascattering angle hs�34 mrad, which is very closeto the specular angle. The peak angles were mea-

Fig. 1. Angular distribution of scattered ions when 15 keV Ar�

ions are incident on a SnTe(001) at hi� 16.7 mrad. The ion

yield has a peak at the specular angle.

32 K. Nakajima et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 31±37

sured at various incident angles and the result isshown in Fig. 2. The observed peak angle agreeswith the specular angle which is shown by a solidline, indicating that the specular re¯ection tookplace up to hi� 50 mrad. The similar results wereobtained for all ions used in the present work.

The energy spectrum of the scattered ions wasmeasured at the specular angle. Fig. 3 shows anexample of the observed energy spectra of specu-larly re¯ected 30 keV Ne� ions at hi� 21.6 mrad.The energy spectrum of the incident 30 keV Ne�

ions is also shown for comparison. Both spectracan be ®tted by Gaussians very well. The mostprobable energy loss DE was determined by thedi�erence between the peak energies of the spectra.Because the observed neutral fraction for scattered30 keV Ne� ions was larger than 98%, it is rea-sonable to assume that the incident ions wereneutralized completely on their incoming trajec-tories and the observed ions were the result of re-ionization of neutral atoms on the outgoingtrajectories. Therefore the observed energy losscan be attributed to the result of the atom±surfaceinteraction and the position-dependent stoppingpower for neutral atom can be derived by ana-lyzing the observed energy loss.

Figs. 4±6 show the most probable energy lossesof Ne�, Ar� and Kr� ions observed at the specularangle as a function of hi. The observed energy

Fig. 2. Peak angle of the scattered ion distribution for 15 keV

Ar� as a function of the angle of incidence. Good agreement

between the observed peak angle and the specular angle indi-

cates that the specular re¯ection occurs up to hi� 50 mrad.

Fig. 3. Energy spectra of incident and scattered ions for 30 keV

Ne� at hi� 21.6 mrad on a SnTe (001). The most probable

energy loss is determined by the di�erence between the peak

energies.

Fig. 4. Energy losses of 15 and 30 keV Ne� ions specularly

re¯ected from a SnTe (001) as a function of hi. Results of ®tting

with various polynomials are shown by curves.

K. Nakajima et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 31±37 33

losses increase with hi. As was mentioned before,from the hi-dependence of the observed energyloss, the position-dependent stopping power S(x)can be derived as a function of the distance x fromthe surface. The details of the procedure were de-scribed elsewhere [5,12]. Here, the procedure isbrie¯y summarized. The energy loss of the specu-larly re¯ected ion can be given by integration ofS(x) along the ion trajectory which lies on the xz-plane:

DE�hi� �Z

traj:

S�x� dz

� 2����Ep Z 1

xm

S�x����������������������������V �xm� ÿ V �x�p dx; �1�

where E is the ion energy, xm the closest approachto the surface and V(x) the continuum surfacepotential. Eq. (1) is an integral equation of Abeltype and the solution is written as

S�x� � ÿ 1

2pEdV �x�

dxDE�0�

����������E

V �x�

s0@�Z p=2

0

dDE�hi�dhi hi�

�����V �x�

E

psin �u�

du

�����!: �2�

The observed energy losses were ®tted by severalpolynomials of hi:

DE�hi� �Xn�N

n�0

anhni ; �3�

and the results are shown by various curves inFigs. 4±6 (dashed, solid and dotted curves corres-pond to N� 1, 2 and 3, respectively). The obtainedpolynomials were substituted into Eq. (2) to getthe position-dependent stopping power. In thecalculation, Moli�ele potential was employed forV(x) and the image potential was neglected be-

Fig. 5. Energy losses of 15 and 30 keV Ar� ions specularly

re¯ected from a SnTe(001) as a function of hi. Results of ®tting

with various polynomials are shown by curves.

Fig. 6. Energy losses of 15 keV Kr� ions specularly re¯ected

from a SnTe(001) as a function of hi. Results of ®tting with

various polynomials are shown by curves.

34 K. Nakajima et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 31±37

cause the almost all ions were neutralized at thesurface. Figs. 7±9 show the position-dependentstopping powers derived with various ®ttingcurves. Because the present procedure cannot givethe stopping power at x smaller than the closestapproach for the largest hi, the stopping powersare not shown in this region. The obtained stop-ping powers are almost independent of the ®ttingfunctions at x<2.5 �A, showing that the stoppingpower is obtained with a substantial accuracy inthis region. In order to improve the accuracy atx>2.5 �A, the measurement for smaller hi is nec-essary.

4. Discussion

The stopping power of an electron gas for alow-velocity ion has been extensively studied [13±18]. For the ion velocity less than the Fermi ve-locity, the collective response of the valence elec-trons does not contribute to the stopping power.

The stopping power due to the single electron ex-citation can be written by a simple formula forv�vF [18]:

S � n m vvFrtr�vF�; �4�where n is the density of the valence electrons, m isthe electron mass and the transport cross sectionrtr(vF) is de®ned as

rtr�v� �Z�1ÿ cos h� dr�v�

dXdX; �5�

where dr(v)/dX is the di�erential cross section ofthe electron±ion scattering. The position-depen-dent stopping power of the surface can be calcu-lated with Eq. (4) by employing the local densityapproximation, i.e. replacing the constant electrondensity n by the local density n(x) of the valenceelectrons at the surface.

The distribution of the valence electrons n(r) atthe surface was calculated by ab-initio pseudo-potential method with the local density approxi-mation (LDA). The Bloch wave functions are ex-

Fig. 8. Experimental position-dependent stopping powers of

the SnTe(001) for 15 and 30 keV Ar ions derived with the re-

sults of various ®ttings. The theoretical result is shown by a dot-

and-dashed curve.

Fig. 7. Experimental position-dependent stopping powers of

the SnTe(001) for 15 and 30 keV Ne ions derived with the re-

sults of various ®ttings. The theoretical result is shown by a dot-

and-dashed curve.

K. Nakajima et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 31±37 35

panded in a mixed basis with both plane wavesand numerical wave functions centered on atomicsites [19,20]. We have used cuto� radii of 2.2 and2.5 a.u. for the local orbitals of Te and Sn, re-spectively, and plane waves with kinetic energy upto 20 Ry. The obtained distribution n(r) was av-eraged over x-y plane to get n(z). Regarding thetransport cross section, the ions were almostcompletely neutralized in the vicinity of the sur-face. Therefore, the transport cross sections for theelectron±atom collisions should be used. The rec-ommended values for the transport cross sectionare given by Hayashi [21]. The cross sections arertr(vF)� 2.44´10ÿ16, 1.4´10ÿ15, 1.39´10ÿ15 cm2

for Ne, Ar and Kr atoms at vF� 1.95´108 cm/s.The calculated stopping powers (dot-and-da-

shed curves) are compared with the experimentalresults in Figs. 7±9. Although the agreement be-tween the theoretical and experimental results are

reasonably good for Ar and Kr, the experimentalstopping power for Ne is about twice larger thanthe theoretical one irrespective of the ion energy.Because Eq. (3) can be applicable for the ion ve-locity much less than vF, the discrepancy for Neions might be attributed to the relatively high ve-locities of the Ne ions than others. The velocity of15 keV Ne ion is, however, the same as that of 30keV Ar ion (v/vF� 0.20) for which the agreement isreasonably good (see Fig. 8). Moreover, the pre-vious study demonstrated that the agreement be-tween the theoretical and experimental stoppingpowers is also good for 12.5±30 keV He ions (v/vF� 0.40±0.62) [8]. Thus the disagreement for Neions cannot be ascribed to their high velocities.

The possible explanation for the disagreementis related to the neutralization process in front ofthe surface. Fig. 10 illustrates the energy levels ofNe, Ar and Kr atoms together with the valenceband of SnTe. The neutralization of Ne� ionsoccurs via resonant neutralization to excited stateswhile this channel is closed for Ar� and Kr� ionsand they are neutralized into the ground state viaAuger neutralization. Half of the Ne atoms cre-ated by the resonance neutralization are in meta-stable states. They have a large chance to interactwith the surface without changing their electronicstates especially at small hi. In the calculation ofthe position-dependent stopping power, we usedthe transport cross section for the ground stateatom. This is appropriate for Ar and Kr but not

Fig. 9. Experimental position-dependent stopping powers of

the SnTe(001) for 15 keV Kr ions derived with the results of

various ®ttings. The theoretical result is shown by a dot-and-

dashed curve.

Fig. 10. Energy level diagram of Ne, Ar and Kr atoms. The

valence band of SnTe(001) is also shown.

36 K. Nakajima et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 31±37

for Ne. The transport cross section for an excitedatom is generally larger than that for the groundstate atom and so the stopping power for the ex-cited atom should be larger than that for theground state atom. Thus the disagreement betweenthe calculation and experiment may be ascribed tothe e�ect of the excited atoms on the stoppingpower.

Acknowledgements

We are grateful to Prof. T. Fujimoto for hisuseful suggestion, and A. Katoh and T. Sugimotofor their assistance in measurements. This workwas partly supported by a Grant-in-Aid for Sci-enti®c Research from the Japanese Ministry ofEducation, Science, Sports and Culture.

References

[1] G.S. Harbinson, B.W. Farmery, H.J. Pabst, M.W.

Thompson, Radiat. E�. 27 (1975) 97.

[2] K. Kimura, M. Hasegawa, Y. Fujii, M. Suzuki, Y. Susuki,

M. Mannami, Nucl. Instr. and Meth. B 33 (1988) 358.

[3] H. Winter, Phys. Scripta T 6 (1983) 136.

[4] H.J. Andr�a, H. Winter, R. Fr�ohling, N. Kirchner, H.J.

Pl�ohn, W. Wittmann, W. Graser, C. Varelas, Nucl. Instr.

and Meth. 170 (1980) 527.

[5] K. Kimura, M. Hasegawa, M. Mannami, Phys. Rev. B 36

(1987) 7.

[6] K. Kimura, H. Kuroda, M. Fritz, M. Mannami, Nucl.

Instr. and Meth. B 100 (1995) 356.

[7] K. Kimura, S. Ooki, G. Andou, K. Nakajima, M.

Mannami, Phys. Rev. A 58 (1998) 1282.

[8] K. Narumi, F. Kato, Y. Fujii, K. Kimura, M. Mannami,

Nucl. Instr. and Meth. B 115 (1996) 51.

[9] M. Mannami, Y. Fukusumi, K. Nakajima, K. Narumi, H.

Katoh, K. Kimura, M. Yamamoto, S. Naito, Scanning

Microscopy, in press.

[10] M. Suzuki, H. Kawauchi, K. Kimura, M. Mannami, Surf.

Sci. 204 (1988) 223.

[11] K. Narumi, Y. Fujii, K. Kimura, M. Mannami, H. Hara,

Surf. Sci. 303 (1994) 187.

[12] Y. Fujii, S. Fujiwara, K. Narumi, K. Kimura, M.

Mannami, Surf. Sci. 277 (1992) 164.

[13] J. Lindhard, K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 28

(8) (1954).

[14] J. Lindhard, A. Winther, K. Dan. Vidensk. Selsk. Mat.-

Fys. Medd. 34 (4) (1964).

[15] E. Fermi, E. Teller, Phys. Rev. 72 (1947) 399.

[16] T.L. Ferrell, R.H. Ritchie, Phys. Rev. B 16 (1977) 115.

[17] P.M. Echenique, R.M. Nieminen, R.H. Ritchie, Solid

State Commun. 37 (1981) 779.

[18] P.M. Echenique, R.M. Nieminen, J.C. Ashley, R.H.

Ritchie, Phys. Rev. A 33 (1986) 897.

[19] C. Els�asser, N. Takeuchi, K.M. Ho, C.T. Chan, P. Braun,

M. F�ahnle, J. Phys.: Condens. Matter 2 (1990) 4371.

[20] M. Yamamoto, C.T. Chan, K.M. Ho, Phys. Rev. B 50

(1994) 7932.

[21] M. Hayashi, Recommended values of transport cross

sections for elastic collision and total collision cross

sections for electrons in atomic and molecular gases,

IPPJ-AM-19.

K. Nakajima et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 31±37 37