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Stopping of low energy protons during grazing scattering from a LiF(001) surface
Nuclear Instruments and Methods in Physics Research B 164±165 (2000) 559±565
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Stopping of low energy protons during grazing scattering from a LiF(001) surface H. Winter *, C. Auth, A. Mertens Humboldt-Universit atzu Berlin, Institut fur Physik, Invalidenstr. 110, D-10115 Berlin, Germany
Abstract Protons with energies ranging from 300 eV to 25 keV are scattered under glancing angles of incidence from a ¯at and clean LiF(001) surface. We have recorded energy spectra for specularly re¯ected projectiles and analyze the data in terms of stopping cross-sections. From our analysis we deduce a threshold behaviour for electronic stopping at the low energy end. We ®nd pronounced eects on energy loss owing to charge exchange and excitation of valence band electrons. At energies below 1 keV energy dissipation proceeds predominantly via excitation of optical phonons. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction When atomic particles interact with solid matter, energy transferred to the medium gives rise to a stopping of the projectiles. For slow ions traversing metal targets inelastic collisions accompanied with electronic excitations (`electronic stopping') and, to a lesser extent, elastic collisions with target atoms (`nuclear stopping') are the dominant energy dissipation processes [1]. The electronic stopping in this regime of projectile energy/velocity can be understood by the excitation of conduction electrons, described by an electron scattering process in the eective potential of the projectile ion [2]. Since the projectile is embedded in an electron gas of atomic densities, the projectile potential is modi®ed by electronic screening. In
*
Corresponding author. Fax: +49-1-588-01-5710. E-mail address: [email protected] (H. Winter).
this model energy dissipation is understood by weak excitations of Fermi-electrons to unoccupied conduction band states [3]. Speci®c features for the stopping of slow ions in metals, as e.g., the linear dependence of stopping powers, dE=dx with projectile velocity or `Z1 -oscillations' (oscillatory variation of stopping power with projectile atomic number), can be described in a consistent manner [4]. In this respect, the observation of a linear dependence of the stopping power with velocity in a wide-band-gap insulator target by Eder et al. [5] came somewhat surprising, since low energy excitations of electrons within the solid are suppressed by the presence of the band-gap. Instead of ®nding evidence for a threshold of electronic excitations and, as a consequence, of electronic stopping, a linear velocity dependence of stopping powers and stopping cross-sections is measured down to projectile energies of about 2.5 keV. Below those energies, transmission experiments of ions through
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H. Winter et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 559±565
solid matter turn out to be a dicult task and have not been carried out so far. On the other hand, it is possible to study electronic stopping of ions in the low energy regime by ion-surface collisions, in particular under glancing angles of incidence. Recently, we performed those ion scattering experiments with a LiF(001) surface and observed a threshold behaviour of stopping for low projectile energies that could not be investigated in transmission so far [6]. In this paper we present a detailed analysis of data from those studies and discuss recent progress achieved in our experimental and theoretical investigations.
studies considerable interest came up to reduce this energy spread, however, we did not succeed to achieve a better energy resolution with our ECR ion source setup. We therefore made use of another small accelerator available in our laboratory with a hollow cathode type of ion source (SO55, HVEE, Amersfoort/NL) and obtained an overall energy resolution in our TOF measurements which was clearly improved in comparison to the other setup (typically dE 2 eV). This high energy resolution turned out to be crucial for detailed studies on the energy dissipation processes in front of a LiF surface.
2. Experiment
3. Results and analysis of data
The energy loss studies were performed by means of an electrostatic energy analyzer (radius of 90 cylindrical segment 0.5 m; energy resolution dE=E < 10ÿ3 ) and a time-of-¯ight (TOF) setup. The well collimated H beam is scattered at a base pressure in the 10ÿ10 mbar domain from a LiF(001) surface under a grazing angle of incidence Uin of typically 1 . The target is prepared by cycles of sputtering with 25 keV Ar ion under grazing incidence Uin 2 and subsequent annealing at T 400 C. In order to a avoid a macroscopic charging of the insulator surface, the target is held during sputtering and the actual experiments on a temperature of about 300 C. In TOF measurements scattered projectiles are recorded by a microchannel plate at a distance of 1 m behind the target. Pulses from the channel plate serve as start of a time-to-amplitude-converter (TAC) which is stopped by the delayed signal from a puls generator that is used to chop the incident beam by means of electric ®eld plates mounted about 0.6 m in front of the target. The beam was chopped with a frequency of about 200 kHz, and the overall time resolution of our setup was better than 1 ns. The experiments were performed with two dierent small accelerators with dierent types of ion sources. The dominant part of our studies were performed with a ECR ion source on a high voltage terminal, where an overall energy width of about 10 eV was achieved for projectile energies in the keV domain, i.e., dE=E 10ÿ2 . During our
In Fig. 1 we show an energy spectrum obtained with the electrostatic analyzer for the scattering of 5.5 keV H ions under grazing incidence along the low index h100i (®lled circles) and a high index (`random') direction (empty circles). The spectra for both azimuthal orientations match closely, only in the low energy tail the losses for scattering along h100i are somewhat larger. This we attribute to a closer approach of a fraction of projectiles between axial strings of atoms in the surface plane for axial surface channeling. In particular for random azimuthal orientation, the spectra for
Fig. 1. Energy spectra for 5.5 keV H ions scattered from a LiF(001) surface under Uin 0:6 for azimuthal settings of the target along h100i (®lled circles) and along a high index direction, `random' (empty circles). The dashed vertical line indicates the energy of the projectile beam.
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scattered projectiles are very symmetric, so that within the limits of uncertainty of our measurements mean and most probable energy loss are the same. In detailed studies we investigated how the energy loss depends on the angle of incidence Uin , and measured under specular re¯ection conditions (Uin Uout , image charge eects compensate on incident and outgoing part of trajectory [7]) energy spectra for dierent Uin . In Fig. 2 we display results from those studies for projectile energies of 5.4 and 6 keV. We observe within the uncertainties of data practically no dependence of the energy loss on the settings of the polar angles. This ®nding is important for the analysis of data outlined below. The dependence of the energy loss DE as a function of the projectile energy E is shown in Fig. 3. The data are recorded for a ®xed angle of incidence Uin 0:6 . The dashed line in Fig. 3 represents a linear dependence of the energy loss with energy. We see that the data for E 6 15 keV follow this line quite closely. For energies of some keV a systematic deviation from this linearity seems to be present. This energy domain was studied in more details with our TOF setup. In passing we note that on the basis of the analysis of energy losses in grazing ion surface collisions given by Kimura et al. [8] one concludes for DE Uin const and DE E E that the stopping power is proportional to projectile velocity v, i.e., ÿdE=dx v.
This is the same behaviour as observed by Eder et al. [5] for stopping in thin LiF ®lms and which is well established for metal targets. In order to ®nd a presumably present threshold for the stopping at low energies we performed TOF studies. Since at the low energy end the ion fractions are low (H fractions <1%, Hÿ fractions 1±2%), a TOF technique is needed to analyze the energy of neutralized beams. In Fig. 4 we present TOF spectra transformed to a projectile energy scale for 600 eV H scattered under Uin 1 from the LiF(001) surface. The energy resolution for the projectile beam amounts to about 12 eV and is, as we have said, primarily owing to the energy spread of ECR ion source and accelerator. In the upper panel data for outgoing neutral H0 atoms and in the lower panel for Hÿ ions are shown. Owing to the small ion fractions after scattering from LiF at low energies, the intensity of the Hÿ beam is small and leads to lower statistics and a higher background of data. For H0 atoms the energy loss amounts to some eV, whereas for Hÿ ions we ®nd a clearly larger energy loss of about 18±20 eV. Note that in the low energy tail of the prominent peaks a further discrete peak can be identi®ed, however, the energy spread achieved with the ECR ion source was not sucient to resolve this structure. In experiments with a SO55 ion-source the experimental energy resolution was improved and the discrete energy loss structures are clearly seen in the spectra (see below).
Fig. 2. Energy loss as function of scattering angle for specular scattering of 5.4 (®lled squares) and 6 keV H ions (®lled circles) from a LiF(001) surface.
Fig. 3. Energy loss DE as function of projectile energy E0 for specular scattering of H ions from a LiF(001) surface under Uin Uout 0:6 . The dashed line indicates the proportionality DE E.
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Fig. 5. Energy loss as function of projectile energy E0 for H ions scattered under Uin 0:8 from a LiF(001) surface: ®lled circles: H0 atoms; empty circles: Hÿ ions. The dashed line represents the proportionality DE E as shown in Fig. 3.
Fig. 4. 600 eV surface. circles). beam.
TOF spectra transformed to projectile energies for H ions scattered under Uin 0:8 from a LiF(001) Upper panel: H0 atoms; lower panel: Hÿ ions (®lled The empty circles represent data for the projectile
The energy loss deduced from the maximum of the prominent peak is plotted in Fig. 5 over the projectile energy for H projectiles emerging after scattering from the LiF surface as H0 atoms (®lled circles) and Hÿ ions (empty circles). The data shown in Fig. 5 are obtained in the low energy regime of our studies from 300 eV to 2 keV. For energies larger than about 1.3 keV we observe a linear dependence of DE with energy, however, shifted from the dependence extrapolated to zero in Fig. 3 (dashed line), i.e., the energy losses are clearly smaller than expected for a proportionality with projectile energy. The linear dependence observed for the data in Fig. 5 extrapolates to a vanishing energy loss at about 1 keV. The experi-
mental data below about 1.3 keV level o and reach constant values of about 3±5 eV for H0 atoms and about 18±20 eV for Hÿ ions. Note that the H0 fractions amount to about 99% here so that the energy loss averaged over the charge states of scattered projectiles follows closely the H0 data. For a comparison with the stopping cross-sections reported by Eder et al. [5] we described the planar potential for H projectiles in front of a LiF(001) surface by a single exponential term U z a1 exp ÿa2 z. The constants a1 13:85 eV 0.509 a.u. and a2 0:881 a.u. are deduced from a best ®t to UZBL z obtained from interatomic ZBL potentials [1]. According to Kimura et al. [8] the position dependent stopping power ÿdE=dx z S z is given for DE Uin const by a 2 S z S0 exp ÿ z 2 1=2
with S0 DEa2 a1 =E =2p. Then S z is integrated between two atomic planes separated by a spacing l in order to obtain the stopping crosssection per LiF molecule rmol s
8S0 l2 ÿ 1 ÿ eÿ a2 =2l a2
1
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with the nearest neighbour separation in a LiF crystal l 3:81 a.u. The stopping cross-sections as function of projectile energy are given in the log±log-plot of Fig. 6. Data for H0 atoms are presented by ®lled circles and for Hÿ ions by open symbols (empty circles: measurements with electrostatic analyzer, open triangles: TOF measurements). For comparison we have plotted also the transmission data by Eder et al. [5] (®lled squares). From the ®gure can be seen that the cross-sections follow closely a linear v-dependence down to energies of about 2 keV as indicated by the solid line with slope 1/2 in the log rs ÿ log E-plot. Below 2.5 keV (no data available in transmission) the cross-sections level o and show a pronounced decay which may serve as an indication for a threshold behaviour for stopping. At energies lower than about 1 keV the cross-sections saturate to about 5±6 10ÿ16 eV cm2 which corresponds to projectile energy losses of about 3±5 eV (see Fig. 5). In more re®ned measurements we succeeded to improve the energy resolution of our setup significantly by making use of (1) a hollow cathode ion source with about 1 eV energy width and (2) a stable digital delay in the ls regime for the stop signal. As representative results from these studies we show in Figs. 7 and 8 energy spectra for 700
563
Fig. 7. TOF energy spectrum for 700 eV H ions scattered from a LiF(001) surface under Uin 0:8 (empty circles: projectile beam, ®lled circles: scattered beam).
Fig. 8. Same as Fig. 7, but for 900 eV H ions.
Fig. 6. Stopping cross-sections as function of projectile energy derived from surface scattering (®lled circles: H0 atoms, open symbols: Hÿ ions) and from foil transmission (®lled squares, data by Eder et al. [5]). The solid line represents a linear dependence with v, i.e., slope `1/2' in the log±log-plot.
and 900 eV H ions obtained with the TOF setup. The spectra (empty circles: projectile beam, ®lled circles: scattered beam) show a clear improvement with respect to energy resolution over our former data displayed in Fig. 4. The resolution is suciently high to clearly identify a number of discrete peaks in the spectra. A comparison of the two spectra shows that an enhanced mean energy loss with energy can be ascribed to an enhanced probability for further discrete energy losses. In these studies we found a slight variation of the spectra with angle of incidence which aects the mean energy loss. This would also slightly shift
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the cross-sections at energies around 1 keV, but this is not considered here. 4. Discussion In recent studies by Roncin et al. [9] similar spectra were recorded in coincidence with electrons emitted during the scattering of H from Li(001). These studies showed that at 600 eV about 60% of the second peak is related to processes without the emission of an electron. The authors proposed the excitation of surface excitons. The other 40% of the second peak is related to processes with the emission of an electron, i.e., the excitation of an electron from the LiF valence band (binding energy 12 eV, width 4 eV) to vacuum. This excitation feature is nicely demonstrated also by the enhanced energy loss for the prominent peak for Hÿ ions revealed in Fig. 4. Whereas H ions are resonantly neutralized by valence band electrons with an negligible energy defect, the formation of Hÿ ions makes necessary the excitation of valence electrons to the anity level with binding energy ÿ0:75 eV. This excitation energy is taken from the kinetic energy of the projectiles. Probabilities for this capture and excitation process can be derived from studies as presented here, which can be considered as a type of `translation spectroscopy' applied here to the scattering of ions from insulator surfaces. Since Roncin et al. [9] have concentrated their analysis of data on these excitation phenomena, we will discuss here the dissipation of energy that is presumably not related to electronic excitations, i.e., the small energy loss of some eV found for the ®rst peak. In a recent study [10] we could demonstrate with Ne ions that excitation of optical phonons in LiF (hxT 38 meV) play a dominant role for stopping in grazing surface collisions with keV energies. With the improved energy resolution (cf. Figs. 7 and 8) we studied the energy loss of the ®rst peak as function of angle and projectile energy. In Fig. 9 we display results for H ions with energies ranging from 600 to 1300 eV scattered from LiF(001) under 0:75 (empty circles) and 1:2 (®lled circles). Note that the energy loss is smaller for a larger angle and does not increase with en-
Fig. 9. Energy loss as function of projectile energy for H ions scattered from a LiF surface under Uin 0:75 (empty circles) and 1:2 (®lled circles). The dashed and solid curves represent calculations on energy loss via excitations of transverse optical phonons (see text).
ergy. This excludes prominent contributions owing to elastic binary collisions with surface atoms (`nuclear stopping') which are expected for planar channeling to amount to sub-eV energies only. Support for our interpretation of data comes from a theoretical description of the process. We make use of an analytical expression derived by Echenique and Howie [11] which reads for the position dependent stopping power of a particle of charge e 1 a.u. and velocity v in front of a surface owing to excitations of transverse optical phonons dE 2 e0 ÿ e1 x21 2x1 z ÿ z K0 2 dx e1 1 e0 1 v2 v with x1 e0 1= e1 11=2 xT and the dielectric constants e0 at x 0 and e1 at optical frequencies, eo 9; and e1 1:93 [12]. The energy loss of scattered projectiles is obtained from an integration over the complete trajectory Z dE z dx; 3 DE trajectory dx where the trajectory is derived from the planar potential with ZBL-screening. Comparison with the experimental data (dashed and solid curve) shows fair agreement and supports our interpretation.
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5. Conclusion
Acknowledgements
In studies on stopping of H ions in grazing collisions with a LiF(001) surface at low projectile energies we observed down to E 2 keV that stopping powers and cross-sections follow a proportionality with v. For E < 2 keV a threshold behaviour is observed with a pronounced decrease of stopping. At the low energy end stopping is dominated by excitations of optical phonons leading to an about constant energy loss for surface scattering of some eV. From high resolution TOF studies we conclude that stopping proceeds by excitations of valence electrons with a minimum in excitation energy of about 12 eV. With higher projectile energy the probabilities for these excitation processes increase leading to enhanced mean energy losses. In comparing stopping crosssections for surface scattering and transmission through thin ®lms, we ®nd the same size for bulk and an extrapolation of surface stopping to the regime between two planes within the bulk of the crystal. The question to what extend this ®nding means that the mechanisms for stopping are identical or at least similar in bulk and at the surface has to be left open for future studies on this interesting problem concerning atomic collisions in solids.
This work is supported by the Deutsche Forschungsgemeinschaft under contract Wi 1336. References [1] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. [2] P.M. Echenique, R.M. Nieminen, R.H. Ritchie, Solid State Commun. 37 (1981) 779. [3] M.J. Puska, R.M. Nieminen, Phys. Rev. B 27 (1983) 6121. [4] P.M. Echenique, R.M. Nieminen, J.C. Ashley, R.H. Ritchie, Phys. Rev. A 33 (1986) 897. [5] K. Eder, D. Semrad, P. Bauer, R. Golser, P. MaierKomor, F. Aumayr, M. Penalta, A. Arnau, J.M. Ugalde, P.M. Echenique, Phys. Rev. Lett. 79 (1997) 4112. [6] C. Auth, A. Mertens, H. Winter, A.G. Borisov, Phys. Rev. Lett. 81 (1998) 4831. [7] H. Winter, J. Phys. Cond. Matter 8 (1996) 10149. [8] K. Kimura, M. Hasegawa, M. Mannami, Phys. Rev. B 36 (1987) 7. [9] P. Roncin, J. Villette, J.P. Atanas, H. Khemliche, Phys. Rev. Lett. 83 (1999) 864. [10] A.G. Borisov, A. Mertens, H. Winter, A.K. Kazansky, Phys. Rev. Lett. 83 (1999) 5378. [11] P.M. Echenique, A. Howie, Ultramicroscopy 16 (1985) 269. [12] R.P. Lowndes, D.H. Martin, Proc. R. Soc. A 308 (1969) 473.
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Stopping of low energy protons during grazing scattering from a LiF(001) surface H. Winter *, C. Auth, A. Mertens Humboldt-Universit atzu Berlin, Institut fur Physik, Invalidenstr. 110, D-10115 Berlin, Germany
Abstract Protons with energies ranging from 300 eV to 25 keV are scattered under glancing angles of incidence from a ¯at and clean LiF(001) surface. We have recorded energy spectra for specularly re¯ected projectiles and analyze the data in terms of stopping cross-sections. From our analysis we deduce a threshold behaviour for electronic stopping at the low energy end. We ®nd pronounced eects on energy loss owing to charge exchange and excitation of valence band electrons. At energies below 1 keV energy dissipation proceeds predominantly via excitation of optical phonons. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction When atomic particles interact with solid matter, energy transferred to the medium gives rise to a stopping of the projectiles. For slow ions traversing metal targets inelastic collisions accompanied with electronic excitations (`electronic stopping') and, to a lesser extent, elastic collisions with target atoms (`nuclear stopping') are the dominant energy dissipation processes [1]. The electronic stopping in this regime of projectile energy/velocity can be understood by the excitation of conduction electrons, described by an electron scattering process in the eective potential of the projectile ion [2]. Since the projectile is embedded in an electron gas of atomic densities, the projectile potential is modi®ed by electronic screening. In
*
Corresponding author. Fax: +49-1-588-01-5710. E-mail address: [email protected] (H. Winter).
this model energy dissipation is understood by weak excitations of Fermi-electrons to unoccupied conduction band states [3]. Speci®c features for the stopping of slow ions in metals, as e.g., the linear dependence of stopping powers, dE=dx with projectile velocity or `Z1 -oscillations' (oscillatory variation of stopping power with projectile atomic number), can be described in a consistent manner [4]. In this respect, the observation of a linear dependence of the stopping power with velocity in a wide-band-gap insulator target by Eder et al. [5] came somewhat surprising, since low energy excitations of electrons within the solid are suppressed by the presence of the band-gap. Instead of ®nding evidence for a threshold of electronic excitations and, as a consequence, of electronic stopping, a linear velocity dependence of stopping powers and stopping cross-sections is measured down to projectile energies of about 2.5 keV. Below those energies, transmission experiments of ions through
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 1 4 3 - X
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H. Winter et al. / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 559±565
solid matter turn out to be a dicult task and have not been carried out so far. On the other hand, it is possible to study electronic stopping of ions in the low energy regime by ion-surface collisions, in particular under glancing angles of incidence. Recently, we performed those ion scattering experiments with a LiF(001) surface and observed a threshold behaviour of stopping for low projectile energies that could not be investigated in transmission so far [6]. In this paper we present a detailed analysis of data from those studies and discuss recent progress achieved in our experimental and theoretical investigations.
studies considerable interest came up to reduce this energy spread, however, we did not succeed to achieve a better energy resolution with our ECR ion source setup. We therefore made use of another small accelerator available in our laboratory with a hollow cathode type of ion source (SO55, HVEE, Amersfoort/NL) and obtained an overall energy resolution in our TOF measurements which was clearly improved in comparison to the other setup (typically dE 2 eV). This high energy resolution turned out to be crucial for detailed studies on the energy dissipation processes in front of a LiF surface.
2. Experiment
3. Results and analysis of data
The energy loss studies were performed by means of an electrostatic energy analyzer (radius of 90 cylindrical segment 0.5 m; energy resolution dE=E < 10ÿ3 ) and a time-of-¯ight (TOF) setup. The well collimated H beam is scattered at a base pressure in the 10ÿ10 mbar domain from a LiF(001) surface under a grazing angle of incidence Uin of typically 1 . The target is prepared by cycles of sputtering with 25 keV Ar ion under grazing incidence Uin 2 and subsequent annealing at T 400 C. In order to a avoid a macroscopic charging of the insulator surface, the target is held during sputtering and the actual experiments on a temperature of about 300 C. In TOF measurements scattered projectiles are recorded by a microchannel plate at a distance of 1 m behind the target. Pulses from the channel plate serve as start of a time-to-amplitude-converter (TAC) which is stopped by the delayed signal from a puls generator that is used to chop the incident beam by means of electric ®eld plates mounted about 0.6 m in front of the target. The beam was chopped with a frequency of about 200 kHz, and the overall time resolution of our setup was better than 1 ns. The experiments were performed with two dierent small accelerators with dierent types of ion sources. The dominant part of our studies were performed with a ECR ion source on a high voltage terminal, where an overall energy width of about 10 eV was achieved for projectile energies in the keV domain, i.e., dE=E 10ÿ2 . During our
In Fig. 1 we show an energy spectrum obtained with the electrostatic analyzer for the scattering of 5.5 keV H ions under grazing incidence along the low index h100i (®lled circles) and a high index (`random') direction (empty circles). The spectra for both azimuthal orientations match closely, only in the low energy tail the losses for scattering along h100i are somewhat larger. This we attribute to a closer approach of a fraction of projectiles between axial strings of atoms in the surface plane for axial surface channeling. In particular for random azimuthal orientation, the spectra for
Fig. 1. Energy spectra for 5.5 keV H ions scattered from a LiF(001) surface under Uin 0:6 for azimuthal settings of the target along h100i (®lled circles) and along a high index direction, `random' (empty circles). The dashed vertical line indicates the energy of the projectile beam.
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scattered projectiles are very symmetric, so that within the limits of uncertainty of our measurements mean and most probable energy loss are the same. In detailed studies we investigated how the energy loss depends on the angle of incidence Uin , and measured under specular re¯ection conditions (Uin Uout , image charge eects compensate on incident and outgoing part of trajectory [7]) energy spectra for dierent Uin . In Fig. 2 we display results from those studies for projectile energies of 5.4 and 6 keV. We observe within the uncertainties of data practically no dependence of the energy loss on the settings of the polar angles. This ®nding is important for the analysis of data outlined below. The dependence of the energy loss DE as a function of the projectile energy E is shown in Fig. 3. The data are recorded for a ®xed angle of incidence Uin 0:6 . The dashed line in Fig. 3 represents a linear dependence of the energy loss with energy. We see that the data for E 6 15 keV follow this line quite closely. For energies of some keV a systematic deviation from this linearity seems to be present. This energy domain was studied in more details with our TOF setup. In passing we note that on the basis of the analysis of energy losses in grazing ion surface collisions given by Kimura et al. [8] one concludes for DE Uin const and DE E E that the stopping power is proportional to projectile velocity v, i.e., ÿdE=dx v.
This is the same behaviour as observed by Eder et al. [5] for stopping in thin LiF ®lms and which is well established for metal targets. In order to ®nd a presumably present threshold for the stopping at low energies we performed TOF studies. Since at the low energy end the ion fractions are low (H fractions <1%, Hÿ fractions 1±2%), a TOF technique is needed to analyze the energy of neutralized beams. In Fig. 4 we present TOF spectra transformed to a projectile energy scale for 600 eV H scattered under Uin 1 from the LiF(001) surface. The energy resolution for the projectile beam amounts to about 12 eV and is, as we have said, primarily owing to the energy spread of ECR ion source and accelerator. In the upper panel data for outgoing neutral H0 atoms and in the lower panel for Hÿ ions are shown. Owing to the small ion fractions after scattering from LiF at low energies, the intensity of the Hÿ beam is small and leads to lower statistics and a higher background of data. For H0 atoms the energy loss amounts to some eV, whereas for Hÿ ions we ®nd a clearly larger energy loss of about 18±20 eV. Note that in the low energy tail of the prominent peaks a further discrete peak can be identi®ed, however, the energy spread achieved with the ECR ion source was not sucient to resolve this structure. In experiments with a SO55 ion-source the experimental energy resolution was improved and the discrete energy loss structures are clearly seen in the spectra (see below).
Fig. 2. Energy loss as function of scattering angle for specular scattering of 5.4 (®lled squares) and 6 keV H ions (®lled circles) from a LiF(001) surface.
Fig. 3. Energy loss DE as function of projectile energy E0 for specular scattering of H ions from a LiF(001) surface under Uin Uout 0:6 . The dashed line indicates the proportionality DE E.
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Fig. 5. Energy loss as function of projectile energy E0 for H ions scattered under Uin 0:8 from a LiF(001) surface: ®lled circles: H0 atoms; empty circles: Hÿ ions. The dashed line represents the proportionality DE E as shown in Fig. 3.
Fig. 4. 600 eV surface. circles). beam.
TOF spectra transformed to projectile energies for H ions scattered under Uin 0:8 from a LiF(001) Upper panel: H0 atoms; lower panel: Hÿ ions (®lled The empty circles represent data for the projectile
The energy loss deduced from the maximum of the prominent peak is plotted in Fig. 5 over the projectile energy for H projectiles emerging after scattering from the LiF surface as H0 atoms (®lled circles) and Hÿ ions (empty circles). The data shown in Fig. 5 are obtained in the low energy regime of our studies from 300 eV to 2 keV. For energies larger than about 1.3 keV we observe a linear dependence of DE with energy, however, shifted from the dependence extrapolated to zero in Fig. 3 (dashed line), i.e., the energy losses are clearly smaller than expected for a proportionality with projectile energy. The linear dependence observed for the data in Fig. 5 extrapolates to a vanishing energy loss at about 1 keV. The experi-
mental data below about 1.3 keV level o and reach constant values of about 3±5 eV for H0 atoms and about 18±20 eV for Hÿ ions. Note that the H0 fractions amount to about 99% here so that the energy loss averaged over the charge states of scattered projectiles follows closely the H0 data. For a comparison with the stopping cross-sections reported by Eder et al. [5] we described the planar potential for H projectiles in front of a LiF(001) surface by a single exponential term U z a1 exp ÿa2 z. The constants a1 13:85 eV 0.509 a.u. and a2 0:881 a.u. are deduced from a best ®t to UZBL z obtained from interatomic ZBL potentials [1]. According to Kimura et al. [8] the position dependent stopping power ÿdE=dx z S z is given for DE Uin const by a 2 S z S0 exp ÿ z 2 1=2
with S0 DEa2 a1 =E =2p. Then S z is integrated between two atomic planes separated by a spacing l in order to obtain the stopping crosssection per LiF molecule rmol s
8S0 l2 ÿ 1 ÿ eÿ a2 =2l a2
1
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with the nearest neighbour separation in a LiF crystal l 3:81 a.u. The stopping cross-sections as function of projectile energy are given in the log±log-plot of Fig. 6. Data for H0 atoms are presented by ®lled circles and for Hÿ ions by open symbols (empty circles: measurements with electrostatic analyzer, open triangles: TOF measurements). For comparison we have plotted also the transmission data by Eder et al. [5] (®lled squares). From the ®gure can be seen that the cross-sections follow closely a linear v-dependence down to energies of about 2 keV as indicated by the solid line with slope 1/2 in the log rs ÿ log E-plot. Below 2.5 keV (no data available in transmission) the cross-sections level o and show a pronounced decay which may serve as an indication for a threshold behaviour for stopping. At energies lower than about 1 keV the cross-sections saturate to about 5±6 10ÿ16 eV cm2 which corresponds to projectile energy losses of about 3±5 eV (see Fig. 5). In more re®ned measurements we succeeded to improve the energy resolution of our setup significantly by making use of (1) a hollow cathode ion source with about 1 eV energy width and (2) a stable digital delay in the ls regime for the stop signal. As representative results from these studies we show in Figs. 7 and 8 energy spectra for 700
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Fig. 7. TOF energy spectrum for 700 eV H ions scattered from a LiF(001) surface under Uin 0:8 (empty circles: projectile beam, ®lled circles: scattered beam).
Fig. 8. Same as Fig. 7, but for 900 eV H ions.
Fig. 6. Stopping cross-sections as function of projectile energy derived from surface scattering (®lled circles: H0 atoms, open symbols: Hÿ ions) and from foil transmission (®lled squares, data by Eder et al. [5]). The solid line represents a linear dependence with v, i.e., slope `1/2' in the log±log-plot.
and 900 eV H ions obtained with the TOF setup. The spectra (empty circles: projectile beam, ®lled circles: scattered beam) show a clear improvement with respect to energy resolution over our former data displayed in Fig. 4. The resolution is suciently high to clearly identify a number of discrete peaks in the spectra. A comparison of the two spectra shows that an enhanced mean energy loss with energy can be ascribed to an enhanced probability for further discrete energy losses. In these studies we found a slight variation of the spectra with angle of incidence which aects the mean energy loss. This would also slightly shift
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the cross-sections at energies around 1 keV, but this is not considered here. 4. Discussion In recent studies by Roncin et al. [9] similar spectra were recorded in coincidence with electrons emitted during the scattering of H from Li(001). These studies showed that at 600 eV about 60% of the second peak is related to processes without the emission of an electron. The authors proposed the excitation of surface excitons. The other 40% of the second peak is related to processes with the emission of an electron, i.e., the excitation of an electron from the LiF valence band (binding energy 12 eV, width 4 eV) to vacuum. This excitation feature is nicely demonstrated also by the enhanced energy loss for the prominent peak for Hÿ ions revealed in Fig. 4. Whereas H ions are resonantly neutralized by valence band electrons with an negligible energy defect, the formation of Hÿ ions makes necessary the excitation of valence electrons to the anity level with binding energy ÿ0:75 eV. This excitation energy is taken from the kinetic energy of the projectiles. Probabilities for this capture and excitation process can be derived from studies as presented here, which can be considered as a type of `translation spectroscopy' applied here to the scattering of ions from insulator surfaces. Since Roncin et al. [9] have concentrated their analysis of data on these excitation phenomena, we will discuss here the dissipation of energy that is presumably not related to electronic excitations, i.e., the small energy loss of some eV found for the ®rst peak. In a recent study [10] we could demonstrate with Ne ions that excitation of optical phonons in LiF (hxT 38 meV) play a dominant role for stopping in grazing surface collisions with keV energies. With the improved energy resolution (cf. Figs. 7 and 8) we studied the energy loss of the ®rst peak as function of angle and projectile energy. In Fig. 9 we display results for H ions with energies ranging from 600 to 1300 eV scattered from LiF(001) under 0:75 (empty circles) and 1:2 (®lled circles). Note that the energy loss is smaller for a larger angle and does not increase with en-
Fig. 9. Energy loss as function of projectile energy for H ions scattered from a LiF surface under Uin 0:75 (empty circles) and 1:2 (®lled circles). The dashed and solid curves represent calculations on energy loss via excitations of transverse optical phonons (see text).
ergy. This excludes prominent contributions owing to elastic binary collisions with surface atoms (`nuclear stopping') which are expected for planar channeling to amount to sub-eV energies only. Support for our interpretation of data comes from a theoretical description of the process. We make use of an analytical expression derived by Echenique and Howie [11] which reads for the position dependent stopping power of a particle of charge e 1 a.u. and velocity v in front of a surface owing to excitations of transverse optical phonons dE 2 e0 ÿ e1 x21 2x1 z ÿ z K0 2 dx e1 1 e0 1 v2 v with x1 e0 1= e1 11=2 xT and the dielectric constants e0 at x 0 and e1 at optical frequencies, eo 9; and e1 1:93 [12]. The energy loss of scattered projectiles is obtained from an integration over the complete trajectory Z dE z dx; 3 DE trajectory dx where the trajectory is derived from the planar potential with ZBL-screening. Comparison with the experimental data (dashed and solid curve) shows fair agreement and supports our interpretation.
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5. Conclusion
Acknowledgements
In studies on stopping of H ions in grazing collisions with a LiF(001) surface at low projectile energies we observed down to E 2 keV that stopping powers and cross-sections follow a proportionality with v. For E < 2 keV a threshold behaviour is observed with a pronounced decrease of stopping. At the low energy end stopping is dominated by excitations of optical phonons leading to an about constant energy loss for surface scattering of some eV. From high resolution TOF studies we conclude that stopping proceeds by excitations of valence electrons with a minimum in excitation energy of about 12 eV. With higher projectile energy the probabilities for these excitation processes increase leading to enhanced mean energy losses. In comparing stopping crosssections for surface scattering and transmission through thin ®lms, we ®nd the same size for bulk and an extrapolation of surface stopping to the regime between two planes within the bulk of the crystal. The question to what extend this ®nding means that the mechanisms for stopping are identical or at least similar in bulk and at the surface has to be left open for future studies on this interesting problem concerning atomic collisions in solids.
This work is supported by the Deutsche Forschungsgemeinschaft under contract Wi 1336. References [1] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. [2] P.M. Echenique, R.M. Nieminen, R.H. Ritchie, Solid State Commun. 37 (1981) 779. [3] M.J. Puska, R.M. Nieminen, Phys. Rev. B 27 (1983) 6121. [4] P.M. Echenique, R.M. Nieminen, J.C. Ashley, R.H. Ritchie, Phys. Rev. A 33 (1986) 897. [5] K. Eder, D. Semrad, P. Bauer, R. Golser, P. MaierKomor, F. Aumayr, M. Penalta, A. Arnau, J.M. Ugalde, P.M. Echenique, Phys. Rev. Lett. 79 (1997) 4112. [6] C. Auth, A. Mertens, H. Winter, A.G. Borisov, Phys. Rev. Lett. 81 (1998) 4831. [7] H. Winter, J. Phys. Cond. Matter 8 (1996) 10149. [8] K. Kimura, M. Hasegawa, M. Mannami, Phys. Rev. B 36 (1987) 7. [9] P. Roncin, J. Villette, J.P. Atanas, H. Khemliche, Phys. Rev. Lett. 83 (1999) 864. [10] A.G. Borisov, A. Mertens, H. Winter, A.K. Kazansky, Phys. Rev. Lett. 83 (1999) 5378. [11] P.M. Echenique, A. Howie, Ultramicroscopy 16 (1985) 269. [12] R.P. Lowndes, D.H. Martin, Proc. R. Soc. A 308 (1969) 473.