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Image potential effect on the specular reflection coefficient of alkali ions scattered from a nickel surface at low energy
Nuclear Instruments and Methods in Physics Research B 193 (2002) 396–402 www.elsevier.com/locate/nimb
Image potential effect on the specular reflection coefficient of alkali ions scattered from a nickel surface at low energy R. Zemih a, M. Boudjema a
a,*
, C. Benazeth b, Y. Boudouma a, A.C. Chami
a
Laboratoire Interactions Rayonnement-Mati ere, BP 32 El Alia, USTHB Bab Ezzouar, Algiers, Algeria b LCAR, UMR 572 UPS-CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France
Abstract The resonant charge exchange in the incoming path of alkali ions scattered at low energy from a polycrystalline nickel surface is studied by using the image effect occurring at glancing incidence (2–10° from the surface plane) and for specular reflection. The part of the experimental artefacts (geometrical factor, surface roughness. . .) is extracted from the reflection coefficient of almost completely neutralised projectiles (Heþ or Neþ ) compared with the coefficient obtained from numerical simulations (TRIM and MARLOWE codes). The present model explains very well the lowering of the reflection coefficient measured at grazing incidence (below 4°). Furthermore, the optimised values of the charge fraction in the incoming path and the image potential are in agreement with the theoretical calculations in the case of Naþ /Ni at 4 keV. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Among the most interesting features of the low energy ion scattering technique for material analysis under grazing incidence, one can mention its strong sensitivity to the topmost layer and its nondestructive character due to the weak fluence used. These qualities are obviously linked to the scattering yield or reflection coefficient, i.e. the ratio of the number of scattered projectiles to the incident ones. The reflection coefficient of particles by solid surfaces is an important property in some topical studies of materials under irradiation (plasma confining, ion implantation,. . .). Many works have shown the enhancement of the angular selectivity of the glancing beam reflection, which becomes *
Corresponding author. E-mail address: [email protected] (M. Boudjema).
quasi-specular for the smaller incidence angles a [1,2]. Actually, the maximum of the reflection occurs below the specular position. The shift seems dependent upon the target species and upon the collision energy [3]. At 4 keV particularly and for many projectiles (Hþ to Arþ ) colliding onto a polycrystalline nickel surface, we found the scattering angle h corresponding to the maximum of reflection, at 1.65a in accordance with expected values of transport theory [4] and numerical simulation [5]. On the other hand, it is well known that the scattering yield increases continuously as the incidence angle a (measured from the surface plane) decreases. However, our measurements performed for many kinds of projectile show a clear lowering of the specular reflection coefficient at very small incidence angles (below 6°) with regard to the expected behaviour. This apparent disagreement is assumed to be a result of experimental artefacts added to the so-called image effect
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 8 1 1 - X
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
on the ion trajectories near the surface. We focus the present study on these discrepancies aiming to bring out some characteristics of the charge exchange in the incoming path and the image potential between alkali ions (Naþ ) and a metallic surface (Ni). The investigation is performed by comparing the results with those obtained under the same experimental conditions for noble gas ions (Heþ , Neþ ) and with the predictions of numerical simulations.
2. The experiment 2.1. Apparatus The ions are extracted from a discharge source (Colutron type) for the noble gases or from a solid source for the alkali atoms by a 4 kV voltage. After sorting in a Wien filter, the beam is pulsed leading to a pulse width less than 15 ns. Beyond the pulser, the ions can be post-accelerated or decelerated (practically between 1 and 12 keV) and then, penetrate the collision chamber in which the residual pressure is about 4 1010 Torr. The target surface of polycrystalline nickel is mechanically polished and chemically cleaned. Cycles of Arþ and Neþ bombardments at 4 keV and glancing angle of about 15° follow this preparation in situ. In order to avoid a too rapid deposit of hydrogen on the surface, the target is electrically heated up to 200 °C during the whole experiment. The Ni sample is a square of 12 12 mm2 mounted on a precise manipulator enabling lateral, longitudinal and vertical displacements together with polar and azimuthal rotations. The polar rotation, associated to the variation of the incidence angle a, is motorised leading to an aaccuracy better than 0.2°. Just before the target, an Einzel lens collimates the ion beam leading to a beam width equal to 0.82 mm. The scattered particles are analysed by time-of-flight (TOF) technique through a flight tube (619 mm length) in which a pair of slits define an acceptance angle of 1.3° and a solid angle of detection of 1:7 104 sr. The particles may be discriminated in charge state by electrostatic deflection. Thus, three microchannel plates are used to detect simultaneously
397
positive, neutral and negative ions allowing of the charge fraction measurements. The TOF tube can rotate around the target so that the scattering angle h is able to vary continuously from 0° up to 165°. Measurements of the absolute reflection coefficient require the knowledge of the beam intensity, which is not directly measurable with the present set-up. However, for the angular distribution, it is sufficient to insure that this intensity remains constant during the experiments. At least, the possible variations are checked by periodic registration of reference spectra. By this way, normalised count of reflected particles can be given allowing comparison between different orientations of the beam-target surface-TOF spectrometer system i.e. for different sets of incidence and scattering angles (a; h). 2.2. Experimental results Fig. 1 shows the experimental results of the reflection coefficient obtained at 4 keV for specular scattering from polycrystalline Ni, together with the corresponding simulations performed by using a modified TRIM code [6]. The experimental distributions have been normalised to the simulated ones at the biggest angle a (typically 10° except for Liþ on Ni normalised at 6°). The comparison shows a clear lowering of the measured reflection coefficient below 5–6°. The first reason (usually found in scattering experiments) of this discrepancy, is the geometrical factor (G-factor) arising from the beam width (defining the ‘‘irradiated target area’’) and the acceptance angle of the detection system (defining the ‘‘seen target area’’). Indeed, below a ¼ 4°, the irradiated area is larger than the sample surface resulting in a drop of the effective intensity hitting the target. However, in the present work, the irradiated area remains smaller than the seen target area over the whole range of a, so, actually, the acceptance angle does not play a role. The G-factor is not sufficient to explain entirely the departure between experimental and simulated distributions. A slight difference between the target rotation axis and the TOF-tube rotation axis may be also a cause of count loss especially when a varies towards the lower values. Lastly, we can add the role of the
398
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
Fig. 1. Angular distributions of the specular reflection yield for Heþ , Neþ , Naþ and Liþ scattered from polycrystalline nickel surface. The collision energy is 4 keV. The experimental values (solid circles) are normalised at a ¼ 10° for He, Ne and Na and a ¼ 6° for Li, to those obtained by TRIM simulation (solid line).
target surface state (roughness) on the reflection yield. This effect becomes important in the very low range of incidence and exit angles. Assuming these three effects independent upon the projectile species, they amount to an effective G-factor, which summarises geometrical features and artefacts of the experiments. On the other hand, charged particles travelling near metallic surfaces experience the so-called image force [7]. As shown elsewhere [8,9], this force essentially acts around the image plane, at few a.u. from the surface. The result is a deviation of the ion trajectories towards the surface. Thus, the effective incidence and exit angles are greater than their nominal values, the departure increasing when a decreases. By nominal angles, we mean the angles defined by the geometrical disposition of the apparatus, i.e. by the beam axis, the target surface plane and the TOF line. Therefore, the image effect also contributes to reducing the scat-
tering yield for glancing incidence. The importance of this phenomenon obviously relies on the ion survival probability around the image plane for both incoming and outgoing paths. Let us consider the positive charge fraction F þ , i.e. the ratio of ion count to the total (neutral plus ion) count, measured for noble gas and alkali ions scattered from Ni. We present in Fig. 2, F þ vs. the incidence angle a at 4 keV and for specular reflection of Neþ , Liþ and Naþ . In all cases, the charge fraction remains constant up to 10°. Contrary to Neþ which is almost completely neutralised by Auger process [10] (F þ ¼ 0:015), strong ion survival probabilities are observed for Naþ (F þ ¼ 0:85) and Liþ (F þ ¼ 0:65) as expected from the resonant neutralisation mechanism [11]. Indeed, by image effect, the ionisation potentials of Na and Li (respectively 5.14 and 5.39 eV far from the surface) become slightly lower than the work function of Ni (5.15 eV) near the surface [12]. In this case, electron transfer to the projectile becomes possible only by dynamical effects (Fermi sphere shift, negligible at 4 keV for Naþ ) [13] and, above all, by broadening of the capture level [14]. This leads to very weak neutralisation probabilities and, consequently, to strong influence of the image force. On the other hand, even at small glancing angles, there is no appreciable image effect on noble gas beam, which is mainly neutral in
Fig. 2. Angular distributions of the positive charge fraction measured in the specular scattering of Ne (up triangle), Li (square), and Na (circle) from polycrystalline nickel surface.
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
both incoming and outgoing paths. Therefore, the yield lowering described above is due only to the effective G-factor. This property can then be used to determine the G-factor by comparison between experimental and simulated reflection coefficients as that will be developed in the next part.
3. Model and results Let Vim the variation of the image potential V ðzÞ of incident particle travelling from the infinity into the solid. Far from the target surface, V ðzÞ tends to the classical form (in atomic units, h ¼ me ¼ e ¼ 1), V ðzÞ ¼
1 ; 4ðz dÞ
ð1Þ
where d is the position of the image plane [15] and z the distance of the particle from the surface. Near the surface, the image potential is calculated in the frame of Thomas–Fermi approximation [16] for a given electron density defined by the Wigner– Seitz radius rS . The exact value of rS may be questioned. For polycrystalline nickel, using the effective value rS ¼ 1:8 deduced from plasmon excitation experiments [17], we obtain Vim ¼ 15:8 eV. The electron density can be also calculated from work function measurements [18] giving rS ¼ 2:1 and Vim ¼ 14:7 eV. Lastly, one can use the number of valence electrons of Ni to get rS ¼ 2 and then, Vim ¼ 15 eV. Recently, we showed that the effective value 1:8 is the best to account for the inelastic energy loss in the case of He on polycrystalline Ni [9]. As previously mentioned, the image force is important only around the image plane, i.e. for z d. Therefore, we assume that only the surviving ions at z d are deviated towards the surface plane enabling us to consider that there are two straight trajectories. The first one, beyond the image plane (z > d), defines the nominal angle of incidence an (or of exit bn ). The second trajectory, (z < d), defines an effective angle of incidence ae (or of exit be ) for the part of the incident (or the scattered) particles which remain charged at z ¼ d. The following relation gives the effective angle [16]:
tan ae ðresp:be Þ ¼ tan an ðresp:bn Þ " #12 Vim 1þ ; E sin2 an ðresp:bn Þ
399
ð2Þ
where E is the particle energy around the image plane. The shift between effective and nominal values is very important in the low part of incidence or exit angles and becomes negligible at higher values. At E ¼ 4 keV for instance, the calculated values are ae ¼ 3:7° for an ¼ 1° and ae ¼ 7° for an ¼ 6°. The exact value of E in the outgoing path is not crucial. Indeed, the scattered particle spectra spread out only between 4 and 3.5 keV even for the worst case studied here, i.e. for a ¼ b ¼ 10°. There is no significant difference between the values obtained from the relation (2) for these two energies. It is then reasonable to use the incident energy for the calculation of the trajectory deviation even in the outgoing path. The reflection coefficient Rða; bÞ is defined as the ratio of the number of particles scattered from the surface at h ¼ a þ b to the number of incident particles, a and b being the incidence and the exit angles respectively. As shown elsewhere [5], Rða; bÞ presents a maximum at h ¼ hmax . The angle hmax is found proportional to a up to h ¼ 20°. We can write then hmax ¼ ga. The experimental value of g is equal to 1.65 whatever the projectile used. It is the same as obtained from MARLOWE simulations [19] and close to the value 1.85 deduced from TRIM code [20]. The reflection coefficient is correctly described by the following expression [5], which will be useful for parameter optimisations: v A p ðða þ bÞ gaÞ Rða; bÞ ¼ cos a 2ðg 1Þa for
ð3Þ
a 6 h 6 hmax ;
Rða; bÞ ¼
Ag aþb
v for
h P hmax :
ð4Þ
The parameter v is equal to 1.9 and 3 for TRIM and MARLOWE calculations respectively whereas the constant A depends upon the interacting system. For instance, the appropriate values of A fitting TRIM results are 0.78° for He, 1.1° for
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Li, 1.4° for Ne and 2.1° for Na reflected by Ni surface. In order to consider the image effect, we need the charge fractions, i.e. the survival probabilities þ around the image plane. Let Pinþ ðaÞ and Pout ða; bÞ these charge fractions respectively in the incoming path for an incidence angle a and in the outgoing path after scattering at h ¼ a þ b. The reflection coefficient R ðan ; bn Þ modified by image effect is then given by þ R ðan ; bn Þ ¼ Pinþ ðan Þ Rðae ; be ÞPout ðae ; be Þ þ þ Rðae ; bn Þð1 Pout ðae ; bn ÞÞ þ ðan ; be Þ þ ð1 Pinþ ðan ÞÞ Rðan ; be ÞPout þ þ Rðan ; bn Þð1 Pout ðan ; bn ÞÞ : ð5Þ Another charge transfer mechanism contributing to the ion fraction can be invoked beside Auger and resonant processes. Several works, indeed, underline the key role of the electron promotion on the neutralisation and re-ionisation occurring in violent collisions. In fact, the charge fraction þ Pout ða; bÞ is also the result of such a process and, consequently, cannot be considered rigorously as representative of the charge exchange outside the bulk only. This increases the interest of the Pinþ ðaÞ estimation models for the resonant neutralisation studies. However, for 4 keV-He, Ne and Ar reflected from Ni at small scattering angle h, we found the distance of closest approach higher than the overlap distance [21] confirming previous results [22]. Therefore, we assume that the charge exchange in close collisions is no significant in the present work. The relation (5) has been applied to Heþ /Ni system by using the relation (4) with the Auger neutralisation probability (s1 ¼ 0:014 a.u.) and the image plane position (d ¼ 1:24 a.u.) reported by Narmann et al. [23,24]. The survival probability Pinþ ðaÞ is calculated in the frame of þ Hagstrum model [10] while Pout ða; bÞ is assumed very close to the measured charge fraction (Fig. 2). The angular distribution of the modified reflection coefficient R ðan ; bn Þ (relation 5) is found identical to the direct one, Rðan ; bn Þ (relation 4), confirming the negligible influence of image effect in this case. Consequently, the lowering of the reflection yield proceeds from artefacts only. These considerations
are extended to the other noble gas, Neþ , colliding Ni. Thus, we can define the effective G-factor Cðan ; bn Þ as Cðan ; bn Þ ¼
Rðan ; bn Þ ; Rexp ðan ; bn Þ
ð6Þ
where Rexp ðan ; bn Þ is the experimental reflection coefficient of noble gases, normalised to the simulated coefficient Rðan ; bn Þ at 10° of incidence. Table 1 summarises the values of Cðan ; bn Þ deduced from Neþ over the range of interest. Finally, the effective reflection coefficient Reff ðan ; bn Þ taking both image effect and G-factor into account, can be written as Reff ðan ; bn Þ ¼
1 R ðan ; bn Þ: Cðan ; bn Þ
ð7Þ
Now, let us consider the Naþ /Ni case. Owing to the unlikely resonant exchange process, most of the incoming particles remain charged around the image plane and then, Pinþ ðaÞ must be expected to be very close to 1. In the outgoing path, as previously noted, we assume that the measured charge fraction (85%) represents the ion survival probaþ bility Pout ða; bÞ at the image plane. The relation (7) serves to fit the experimental distribution by simultaneous optimisation of two parameters, Pinþ ðaÞ and Vim . Fig. 3 shows the result found after adjustment with TRIM code. The model agrees very well with the experiment for the optimised values Pinþ ðaÞ ¼ 0:96 and Vim ¼ 16:2 eV, in good accordance with the values 1 and 15.8 eV expected from the theoretical models. Similar agreement is found with the MARLOWE code. Thus, the reduction of the specular reflection coefficient at low incidence angles is correctly accounted for by the present model. It is worth noting the time saving fulfilled by using an empirical form as given in relation (3) and (4), compared with the Monte-Carlo simulation codes. This is particularly interesting in the optimisation procedure applied to the relation (5). Table 1 G-factor Cðan ; bn Þ at specular reflection obtained by comparison between the experimental scattering yield of 4 keV-Ne from Ni and the TRIM calculation (relation 6) a
1°
2°
3°
4°
5°
6°
8°
10°
C
36
15.1
5.6
2.8
1.8
1.5
1.2
1
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
Fig. 3. Comparison between the experimental reflection yield (solid circles) and the TRIM simulation (solid line), TRIM simulation (relation 4, see text) with the image effect correction (relation 5), (dashed line), TRIM simulation corrected by the effective G-factor (dashed-dotted line) and TRIM simulation with image effect and G-factor corrections (relation (7)), (dotted line). The measured and the simulated values are normalised at a ¼ 10°.
to the image effect, the reflection yield drop observed at grazing incidence is then fully explained. Furthermore, using Pinþ ðaÞ and the image potential Vim as simultaneous fitting parameters, we obtain results in satisfactory agreement with the theoretical predictions. The interest of this method is enhanced by the use of empirical form (relation (3) and (4)) in place of numerical codes saving lot of time during the adjustment process. This may be considered as a great advantage in studies of dynamical effects on the resonant charge transfer. Thus, it becomes easy to measure quickly the variation of the survival probability in the entry path as the collision energy increases. However, the applicability of the present method is limited to systems with small neutralisation yield as alkalimetal systems. The method require also to perform measurements with noble gas projectiles under the same experimental conditions in order to conserve a common effective G-factor.
The sensitivity of the present model rely on the image effect magnitude and mainly, on the importance of the survival probabilities. This restricts its applicability to the systems with small neutralisation yields.
Acknowledgements
4. Conclusion
References
The influence of the image force on the specular reflection coefficient has been investigated for noble gas and alkali ions scattered from polycrystalline nickel surface. Negligible for noble gases, the image effect contributes to a strong reduction of the alkali reflection coefficient at very low incidence angles. The lowering involved in this way is used to estimate the survival probability of alkali ions Pinþ ðaÞ near the image plane in the incoming path. It is necessary for that, to know the part of the geometrical features together with the influence of set-up defects and surface roughness. This has been made by comparison between experimental angular distribution of the reflection coefficient of noble gases (He and Ne) and the corresponding simulated distribution, resulting in a determination of an effective G-factor. Adding the G-factor
401
We would thank P. Reynes for his appreciable technical assistance on the experimental apparatus and N. Lorente for the helpful reading of the manuscript.
[1] E.S. Mashkova, V.A. Molchanov, Medium energy reflection from solids, Modern problems in condensed matter sciences, North Holland, Vol. 11, 1985. [2] W. Eckstein, Computer simulation of ion–solid interactions, Materials Sciences Series, Springer Berlin, Vol. 10, 1991. [3] Vu Ngoc Tuan, Surf. Sci. 371 (1997) 111. [4] V.S. Remizovich, M.I. Ryazanov, I.S. Tilinin, Zh. Sov. Phys. JETP 25 (1980) 225. [5] R. Zemih, Thesis, USTHB Algiers, 2001. [6] K. Khalal-Kouache, B. Arezki, M. Boudjema, Y. Boudouma, A.C. Chami, C. Benazeth, P. Benoit-Cattin, Lebanese Scientic Research Reports 2N (3) (1997) 846. [7] H. Winter, J. Phys.: Cond. Matter 8 (1996) 10149. [8] B. Arezki, Y. Boudouma, P. Benoit-Cattin, A.C. Chami, C. Benazeth, K. Khalal, M. Boudjema, J. Phys.: Cond. Matter 10 (1998) 741. [9] M. Boudjema, N.D. D’Bichi, Y. Boudouma, A.C. Chami, B. Arezki, K. Khalal, C. Benazeth, P. Benoit-Cattin, Nucl. Instr. and Meth. B 164–165 (2000) 588.
402 [10] [11] [12] [13] [14] [15] [16]
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H.D. Hagstrum, Phys. Rev. 94 (1954) 336. J.W. Gadzuk, Surf. Sci. 6 (1967) 133. M. Aono, R. Souda, Nucl. Instr. and Meth. B 27 (1987) 55. R. Bracko, D.M. Newns, Rep. Prog. Phys. 52 (1989) 655. J. Los, J.J.C. Geerlings, Phys. Rep. 190 (3) (1990) 133. N.D. Lang, W. Kohn, Phys. Rev. B 7 (1973) 3541. M. Kato, R.S. William, M. Aono, Nucl. Instr. and Meth. B 33 (1988) 462. [17] D. Isaacsson, NAPS Document (1975) 02698. [18] S.T. Halas, T. Durakiewicz, J. Phys.: Cond. Matter 10 (1998). [19] M.T. Robinson, I.M. Torrens, Phys. Rev. B 9 (1974) 5008.
[20] J.F. Ziegler, J.P. Biersack, U. Littmark, The stopping and ranges of ions in solids, Pergamon Press, New York, 1985. [21] M. Belgroune, M. Boudjema, A.C. Chami, Y. Boudouma, Proceedings of 4th CNPA, Algiers, 2001. [22] Ting Li, R.J. MacDonald, Nucl. Instr. and Meth. B 132 (1997) 395. [23] A. Narmann, W. Heiland, R. Monreal, F. Flores, P.M. Echenique, Phys. Rev. B 44 (1991) 2003. [24] A. Narmann, K. Schmidt, W. Heiland, R. Monreal, F. Flores, P.M. Echenique, Nucl. Instr. and Meth. B 48 (1990) 378.
Image potential effect on the specular reflection coefficient of alkali ions scattered from a nickel surface at low energy R. Zemih a, M. Boudjema a
a,*
, C. Benazeth b, Y. Boudouma a, A.C. Chami
a
Laboratoire Interactions Rayonnement-Mati ere, BP 32 El Alia, USTHB Bab Ezzouar, Algiers, Algeria b LCAR, UMR 572 UPS-CNRS, 118 route de Narbonne, 31062 Toulouse Cedex, France
Abstract The resonant charge exchange in the incoming path of alkali ions scattered at low energy from a polycrystalline nickel surface is studied by using the image effect occurring at glancing incidence (2–10° from the surface plane) and for specular reflection. The part of the experimental artefacts (geometrical factor, surface roughness. . .) is extracted from the reflection coefficient of almost completely neutralised projectiles (Heþ or Neþ ) compared with the coefficient obtained from numerical simulations (TRIM and MARLOWE codes). The present model explains very well the lowering of the reflection coefficient measured at grazing incidence (below 4°). Furthermore, the optimised values of the charge fraction in the incoming path and the image potential are in agreement with the theoretical calculations in the case of Naþ /Ni at 4 keV. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Among the most interesting features of the low energy ion scattering technique for material analysis under grazing incidence, one can mention its strong sensitivity to the topmost layer and its nondestructive character due to the weak fluence used. These qualities are obviously linked to the scattering yield or reflection coefficient, i.e. the ratio of the number of scattered projectiles to the incident ones. The reflection coefficient of particles by solid surfaces is an important property in some topical studies of materials under irradiation (plasma confining, ion implantation,. . .). Many works have shown the enhancement of the angular selectivity of the glancing beam reflection, which becomes *
Corresponding author. E-mail address: [email protected] (M. Boudjema).
quasi-specular for the smaller incidence angles a [1,2]. Actually, the maximum of the reflection occurs below the specular position. The shift seems dependent upon the target species and upon the collision energy [3]. At 4 keV particularly and for many projectiles (Hþ to Arþ ) colliding onto a polycrystalline nickel surface, we found the scattering angle h corresponding to the maximum of reflection, at 1.65a in accordance with expected values of transport theory [4] and numerical simulation [5]. On the other hand, it is well known that the scattering yield increases continuously as the incidence angle a (measured from the surface plane) decreases. However, our measurements performed for many kinds of projectile show a clear lowering of the specular reflection coefficient at very small incidence angles (below 6°) with regard to the expected behaviour. This apparent disagreement is assumed to be a result of experimental artefacts added to the so-called image effect
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 8 1 1 - X
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
on the ion trajectories near the surface. We focus the present study on these discrepancies aiming to bring out some characteristics of the charge exchange in the incoming path and the image potential between alkali ions (Naþ ) and a metallic surface (Ni). The investigation is performed by comparing the results with those obtained under the same experimental conditions for noble gas ions (Heþ , Neþ ) and with the predictions of numerical simulations.
2. The experiment 2.1. Apparatus The ions are extracted from a discharge source (Colutron type) for the noble gases or from a solid source for the alkali atoms by a 4 kV voltage. After sorting in a Wien filter, the beam is pulsed leading to a pulse width less than 15 ns. Beyond the pulser, the ions can be post-accelerated or decelerated (practically between 1 and 12 keV) and then, penetrate the collision chamber in which the residual pressure is about 4 1010 Torr. The target surface of polycrystalline nickel is mechanically polished and chemically cleaned. Cycles of Arþ and Neþ bombardments at 4 keV and glancing angle of about 15° follow this preparation in situ. In order to avoid a too rapid deposit of hydrogen on the surface, the target is electrically heated up to 200 °C during the whole experiment. The Ni sample is a square of 12 12 mm2 mounted on a precise manipulator enabling lateral, longitudinal and vertical displacements together with polar and azimuthal rotations. The polar rotation, associated to the variation of the incidence angle a, is motorised leading to an aaccuracy better than 0.2°. Just before the target, an Einzel lens collimates the ion beam leading to a beam width equal to 0.82 mm. The scattered particles are analysed by time-of-flight (TOF) technique through a flight tube (619 mm length) in which a pair of slits define an acceptance angle of 1.3° and a solid angle of detection of 1:7 104 sr. The particles may be discriminated in charge state by electrostatic deflection. Thus, three microchannel plates are used to detect simultaneously
397
positive, neutral and negative ions allowing of the charge fraction measurements. The TOF tube can rotate around the target so that the scattering angle h is able to vary continuously from 0° up to 165°. Measurements of the absolute reflection coefficient require the knowledge of the beam intensity, which is not directly measurable with the present set-up. However, for the angular distribution, it is sufficient to insure that this intensity remains constant during the experiments. At least, the possible variations are checked by periodic registration of reference spectra. By this way, normalised count of reflected particles can be given allowing comparison between different orientations of the beam-target surface-TOF spectrometer system i.e. for different sets of incidence and scattering angles (a; h). 2.2. Experimental results Fig. 1 shows the experimental results of the reflection coefficient obtained at 4 keV for specular scattering from polycrystalline Ni, together with the corresponding simulations performed by using a modified TRIM code [6]. The experimental distributions have been normalised to the simulated ones at the biggest angle a (typically 10° except for Liþ on Ni normalised at 6°). The comparison shows a clear lowering of the measured reflection coefficient below 5–6°. The first reason (usually found in scattering experiments) of this discrepancy, is the geometrical factor (G-factor) arising from the beam width (defining the ‘‘irradiated target area’’) and the acceptance angle of the detection system (defining the ‘‘seen target area’’). Indeed, below a ¼ 4°, the irradiated area is larger than the sample surface resulting in a drop of the effective intensity hitting the target. However, in the present work, the irradiated area remains smaller than the seen target area over the whole range of a, so, actually, the acceptance angle does not play a role. The G-factor is not sufficient to explain entirely the departure between experimental and simulated distributions. A slight difference between the target rotation axis and the TOF-tube rotation axis may be also a cause of count loss especially when a varies towards the lower values. Lastly, we can add the role of the
398
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
Fig. 1. Angular distributions of the specular reflection yield for Heþ , Neþ , Naþ and Liþ scattered from polycrystalline nickel surface. The collision energy is 4 keV. The experimental values (solid circles) are normalised at a ¼ 10° for He, Ne and Na and a ¼ 6° for Li, to those obtained by TRIM simulation (solid line).
target surface state (roughness) on the reflection yield. This effect becomes important in the very low range of incidence and exit angles. Assuming these three effects independent upon the projectile species, they amount to an effective G-factor, which summarises geometrical features and artefacts of the experiments. On the other hand, charged particles travelling near metallic surfaces experience the so-called image force [7]. As shown elsewhere [8,9], this force essentially acts around the image plane, at few a.u. from the surface. The result is a deviation of the ion trajectories towards the surface. Thus, the effective incidence and exit angles are greater than their nominal values, the departure increasing when a decreases. By nominal angles, we mean the angles defined by the geometrical disposition of the apparatus, i.e. by the beam axis, the target surface plane and the TOF line. Therefore, the image effect also contributes to reducing the scat-
tering yield for glancing incidence. The importance of this phenomenon obviously relies on the ion survival probability around the image plane for both incoming and outgoing paths. Let us consider the positive charge fraction F þ , i.e. the ratio of ion count to the total (neutral plus ion) count, measured for noble gas and alkali ions scattered from Ni. We present in Fig. 2, F þ vs. the incidence angle a at 4 keV and for specular reflection of Neþ , Liþ and Naþ . In all cases, the charge fraction remains constant up to 10°. Contrary to Neþ which is almost completely neutralised by Auger process [10] (F þ ¼ 0:015), strong ion survival probabilities are observed for Naþ (F þ ¼ 0:85) and Liþ (F þ ¼ 0:65) as expected from the resonant neutralisation mechanism [11]. Indeed, by image effect, the ionisation potentials of Na and Li (respectively 5.14 and 5.39 eV far from the surface) become slightly lower than the work function of Ni (5.15 eV) near the surface [12]. In this case, electron transfer to the projectile becomes possible only by dynamical effects (Fermi sphere shift, negligible at 4 keV for Naþ ) [13] and, above all, by broadening of the capture level [14]. This leads to very weak neutralisation probabilities and, consequently, to strong influence of the image force. On the other hand, even at small glancing angles, there is no appreciable image effect on noble gas beam, which is mainly neutral in
Fig. 2. Angular distributions of the positive charge fraction measured in the specular scattering of Ne (up triangle), Li (square), and Na (circle) from polycrystalline nickel surface.
R. Zemih et al. / Nucl. Instr. and Meth. in Phys. Res. B 193 (2002) 396–402
both incoming and outgoing paths. Therefore, the yield lowering described above is due only to the effective G-factor. This property can then be used to determine the G-factor by comparison between experimental and simulated reflection coefficients as that will be developed in the next part.
3. Model and results Let Vim the variation of the image potential V ðzÞ of incident particle travelling from the infinity into the solid. Far from the target surface, V ðzÞ tends to the classical form (in atomic units, h ¼ me ¼ e ¼ 1), V ðzÞ ¼
1 ; 4ðz dÞ
ð1Þ
where d is the position of the image plane [15] and z the distance of the particle from the surface. Near the surface, the image potential is calculated in the frame of Thomas–Fermi approximation [16] for a given electron density defined by the Wigner– Seitz radius rS . The exact value of rS may be questioned. For polycrystalline nickel, using the effective value rS ¼ 1:8 deduced from plasmon excitation experiments [17], we obtain Vim ¼ 15:8 eV. The electron density can be also calculated from work function measurements [18] giving rS ¼ 2:1 and Vim ¼ 14:7 eV. Lastly, one can use the number of valence electrons of Ni to get rS ¼ 2 and then, Vim ¼ 15 eV. Recently, we showed that the effective value 1:8 is the best to account for the inelastic energy loss in the case of He on polycrystalline Ni [9]. As previously mentioned, the image force is important only around the image plane, i.e. for z d. Therefore, we assume that only the surviving ions at z d are deviated towards the surface plane enabling us to consider that there are two straight trajectories. The first one, beyond the image plane (z > d), defines the nominal angle of incidence an (or of exit bn ). The second trajectory, (z < d), defines an effective angle of incidence ae (or of exit be ) for the part of the incident (or the scattered) particles which remain charged at z ¼ d. The following relation gives the effective angle [16]:
tan ae ðresp:be Þ ¼ tan an ðresp:bn Þ " #12 Vim 1þ ; E sin2 an ðresp:bn Þ
399
ð2Þ
where E is the particle energy around the image plane. The shift between effective and nominal values is very important in the low part of incidence or exit angles and becomes negligible at higher values. At E ¼ 4 keV for instance, the calculated values are ae ¼ 3:7° for an ¼ 1° and ae ¼ 7° for an ¼ 6°. The exact value of E in the outgoing path is not crucial. Indeed, the scattered particle spectra spread out only between 4 and 3.5 keV even for the worst case studied here, i.e. for a ¼ b ¼ 10°. There is no significant difference between the values obtained from the relation (2) for these two energies. It is then reasonable to use the incident energy for the calculation of the trajectory deviation even in the outgoing path. The reflection coefficient Rða; bÞ is defined as the ratio of the number of particles scattered from the surface at h ¼ a þ b to the number of incident particles, a and b being the incidence and the exit angles respectively. As shown elsewhere [5], Rða; bÞ presents a maximum at h ¼ hmax . The angle hmax is found proportional to a up to h ¼ 20°. We can write then hmax ¼ ga. The experimental value of g is equal to 1.65 whatever the projectile used. It is the same as obtained from MARLOWE simulations [19] and close to the value 1.85 deduced from TRIM code [20]. The reflection coefficient is correctly described by the following expression [5], which will be useful for parameter optimisations: v A p ðða þ bÞ gaÞ Rða; bÞ ¼ cos a 2ðg 1Þa for
ð3Þ
a 6 h 6 hmax ;
Rða; bÞ ¼
Ag aþb
v for
h P hmax :
ð4Þ
The parameter v is equal to 1.9 and 3 for TRIM and MARLOWE calculations respectively whereas the constant A depends upon the interacting system. For instance, the appropriate values of A fitting TRIM results are 0.78° for He, 1.1° for
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Li, 1.4° for Ne and 2.1° for Na reflected by Ni surface. In order to consider the image effect, we need the charge fractions, i.e. the survival probabilities þ around the image plane. Let Pinþ ðaÞ and Pout ða; bÞ these charge fractions respectively in the incoming path for an incidence angle a and in the outgoing path after scattering at h ¼ a þ b. The reflection coefficient R ðan ; bn Þ modified by image effect is then given by þ R ðan ; bn Þ ¼ Pinþ ðan Þ Rðae ; be ÞPout ðae ; be Þ þ þ Rðae ; bn Þð1 Pout ðae ; bn ÞÞ þ ðan ; be Þ þ ð1 Pinþ ðan ÞÞ Rðan ; be ÞPout þ þ Rðan ; bn Þð1 Pout ðan ; bn ÞÞ : ð5Þ Another charge transfer mechanism contributing to the ion fraction can be invoked beside Auger and resonant processes. Several works, indeed, underline the key role of the electron promotion on the neutralisation and re-ionisation occurring in violent collisions. In fact, the charge fraction þ Pout ða; bÞ is also the result of such a process and, consequently, cannot be considered rigorously as representative of the charge exchange outside the bulk only. This increases the interest of the Pinþ ðaÞ estimation models for the resonant neutralisation studies. However, for 4 keV-He, Ne and Ar reflected from Ni at small scattering angle h, we found the distance of closest approach higher than the overlap distance [21] confirming previous results [22]. Therefore, we assume that the charge exchange in close collisions is no significant in the present work. The relation (5) has been applied to Heþ /Ni system by using the relation (4) with the Auger neutralisation probability (s1 ¼ 0:014 a.u.) and the image plane position (d ¼ 1:24 a.u.) reported by Narmann et al. [23,24]. The survival probability Pinþ ðaÞ is calculated in the frame of þ Hagstrum model [10] while Pout ða; bÞ is assumed very close to the measured charge fraction (Fig. 2). The angular distribution of the modified reflection coefficient R ðan ; bn Þ (relation 5) is found identical to the direct one, Rðan ; bn Þ (relation 4), confirming the negligible influence of image effect in this case. Consequently, the lowering of the reflection yield proceeds from artefacts only. These considerations
are extended to the other noble gas, Neþ , colliding Ni. Thus, we can define the effective G-factor Cðan ; bn Þ as Cðan ; bn Þ ¼
Rðan ; bn Þ ; Rexp ðan ; bn Þ
ð6Þ
where Rexp ðan ; bn Þ is the experimental reflection coefficient of noble gases, normalised to the simulated coefficient Rðan ; bn Þ at 10° of incidence. Table 1 summarises the values of Cðan ; bn Þ deduced from Neþ over the range of interest. Finally, the effective reflection coefficient Reff ðan ; bn Þ taking both image effect and G-factor into account, can be written as Reff ðan ; bn Þ ¼
1 R ðan ; bn Þ: Cðan ; bn Þ
ð7Þ
Now, let us consider the Naþ /Ni case. Owing to the unlikely resonant exchange process, most of the incoming particles remain charged around the image plane and then, Pinþ ðaÞ must be expected to be very close to 1. In the outgoing path, as previously noted, we assume that the measured charge fraction (85%) represents the ion survival probaþ bility Pout ða; bÞ at the image plane. The relation (7) serves to fit the experimental distribution by simultaneous optimisation of two parameters, Pinþ ðaÞ and Vim . Fig. 3 shows the result found after adjustment with TRIM code. The model agrees very well with the experiment for the optimised values Pinþ ðaÞ ¼ 0:96 and Vim ¼ 16:2 eV, in good accordance with the values 1 and 15.8 eV expected from the theoretical models. Similar agreement is found with the MARLOWE code. Thus, the reduction of the specular reflection coefficient at low incidence angles is correctly accounted for by the present model. It is worth noting the time saving fulfilled by using an empirical form as given in relation (3) and (4), compared with the Monte-Carlo simulation codes. This is particularly interesting in the optimisation procedure applied to the relation (5). Table 1 G-factor Cðan ; bn Þ at specular reflection obtained by comparison between the experimental scattering yield of 4 keV-Ne from Ni and the TRIM calculation (relation 6) a
1°
2°
3°
4°
5°
6°
8°
10°
C
36
15.1
5.6
2.8
1.8
1.5
1.2
1
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Fig. 3. Comparison between the experimental reflection yield (solid circles) and the TRIM simulation (solid line), TRIM simulation (relation 4, see text) with the image effect correction (relation 5), (dashed line), TRIM simulation corrected by the effective G-factor (dashed-dotted line) and TRIM simulation with image effect and G-factor corrections (relation (7)), (dotted line). The measured and the simulated values are normalised at a ¼ 10°.
to the image effect, the reflection yield drop observed at grazing incidence is then fully explained. Furthermore, using Pinþ ðaÞ and the image potential Vim as simultaneous fitting parameters, we obtain results in satisfactory agreement with the theoretical predictions. The interest of this method is enhanced by the use of empirical form (relation (3) and (4)) in place of numerical codes saving lot of time during the adjustment process. This may be considered as a great advantage in studies of dynamical effects on the resonant charge transfer. Thus, it becomes easy to measure quickly the variation of the survival probability in the entry path as the collision energy increases. However, the applicability of the present method is limited to systems with small neutralisation yield as alkalimetal systems. The method require also to perform measurements with noble gas projectiles under the same experimental conditions in order to conserve a common effective G-factor.
The sensitivity of the present model rely on the image effect magnitude and mainly, on the importance of the survival probabilities. This restricts its applicability to the systems with small neutralisation yields.
Acknowledgements
4. Conclusion
References
The influence of the image force on the specular reflection coefficient has been investigated for noble gas and alkali ions scattered from polycrystalline nickel surface. Negligible for noble gases, the image effect contributes to a strong reduction of the alkali reflection coefficient at very low incidence angles. The lowering involved in this way is used to estimate the survival probability of alkali ions Pinþ ðaÞ near the image plane in the incoming path. It is necessary for that, to know the part of the geometrical features together with the influence of set-up defects and surface roughness. This has been made by comparison between experimental angular distribution of the reflection coefficient of noble gases (He and Ne) and the corresponding simulated distribution, resulting in a determination of an effective G-factor. Adding the G-factor
401
We would thank P. Reynes for his appreciable technical assistance on the experimental apparatus and N. Lorente for the helpful reading of the manuscript.
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