- Email: [email protected]
Energy loss and electron emission during grazing scattering of fast noble gas atoms from an Al(1 1 1) surface
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 258 (2007) 87–90 www.elsevier.com/locate/nimb
Energy loss and electron emission during grazing scattering of fast noble gas atoms from an Al(1 1 1) surface S. Lederer a, H. Winter b
a,*
, HP. Winter
b
a Institut fu¨r Physik der Humboldt-Universita¨t, Newtonstr. 15, D-12489 Berlin-Adlershof, Germany Institut fu¨r Allgemeine Physik, Technische Universita¨t Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
Available online 22 December 2006
Abstract Electron loss and electron emission for grazing impact of noble gas atoms with energies in the keV domain are investigated via timeof-flight spectra recorded in coincidence with the number of emitted electrons. The data is analyzed in terms of computer simulations concerning the interaction of the fast atoms with the electron gas in the selvedge of the Al(1 1 1) surface. The interaction is approximated by binary collisions of the fast atoms with Fermi electrons of the conduction band and differential cross sections obtained for electron scattering from free atoms. For an effective number of collisions of about 50 the energy loss spectra are fairly well reproduced by our calculations. We show that for our conditions the shift of the energy spectra for the emission of an additional electron from the surface is close to the work function of the target. Ó 2007 Elsevier B.V. All rights reserved. PACS: 79.20.Rf Keywords: Ion scattering; Electron emission; Surface channeling
1. Introduction Electron emission phenomena induced by energetic atomic projectiles play an important role in a variety of technological applications and are a matter of intensive basic research [1,2]. A special regime of electronic excitation is achieved for impact of fast atoms or ions under a grazing angle of incidence with respect to a solid surface. For sufficiently small angles of incidence, below the so called ‘‘critical angle’’, projectiles are reflected specularly from the topmost surface layer (‘‘surface channeling’’ [3– 5]) and interact with electrons of the selvedge of the target. It turns out that basic features concerning the emission of electrons can be understood by a model of electronic excitations via binary encounter of atomic projectiles with conduction electrons [6]. In such collisions kinetic energy of
*
Corresponding author. Fax: +49 30 2093 7899. E-mail address: [email protected] (H. Winter).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.095
projectiles is transferred to conduction electrons which results in their excitation and emission into the vacuum. For metal electrons described in the approximation of a free-electron gas, the velocities/momenta of electrons are given by the Fermi–Dirac distribution. Based on this distribution for the initial electronic momenta, it is straightforward to calculate the energy distribution of excited electrons and to estimate yields for emission of electrons. Within such a simple classical model the threshold velocity vth for the onset of projectile induced emission of electrons (‘‘kinetic emission’’, KE) [6,7] and the behaviour of the total electron yield with projectile velocity (threshold law) can be deduced [6]. In recent experiments we found evidence for the predicted (v vth)2-dependence of the total electron yield in the near threshold region [8]. We also observed that the classical threshold for the velocity is in good accord with experimental data, if reduced electron densities in front of the surface are taken into account. In the latter case information on Fermi momenta in front of the surface of metals can be derived [9].
S. Lederer et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 87–90
The experimental studies were performed by the coincident detection of the projectile energy loss via a time-offlight (TOF) method with the number of emitted electrons recorded using a surface barrier detector (SBD) biased at a high voltage [10]. It turns out that this mode of detection is particularly suited for measurements of accurate total electron yields as low as 104, since the ‘‘noise’’ of the SBD is eliminated by the coincident detection with a scattered projectile [11]. Whereas the resulting total electron yields have been evaluated and described in terms of the classical model for electron excitation mentioned above, no detailed analysis of the TOF spectra has been performed so far. In the present paper we discuss simulations of TOF spectra obtained for the scattering of noble gas atoms with a velocity slightly above the classical kinetic threshold. Making use of a classical binary encounter model, we describe in a consistent manner the energy dissipation for projectiles via collisions with conduction electrons and discuss also the effect of the emission of an electron on the energy loss spectra.
1.2 o
1.25 keV He - Al(111) Φin = 2.2 deg
1.0
Normalized intensity
88
0.8 0.6 0.4 0.2 0.0 0
10
20
30
40
Energy loss (eV) Fig. 1. Energy loss spectra for 1.25 keV He atoms scattered under Uin = 2.2° from Al(1 1 1). Full circles: experimental data. Curves: results from computer simulations (dotted curve: nuclear energy loss, dashed curve: electronic energy loss, solid curve: convolution of nuclear and electronic energy loss).
2. Experiment 1.2
3. Results and analysis of data
o
6 keV Ne - Al(111) Φin = 2.2 deg
Normalized intensity
1.0
0.8
0.6
0.4
0.2
0.0 -20
20
40
60
80
Fig. 2. Same as Fig. 1, but for 6 keV Ne atoms.
1.2
12 keV Ar 0 - Al(111) 1.0
0.8
0.6
0.4
0.2
0.0 0
In Figs. 1–3 we display energy loss spectra for 1.25 keV He, 6 keV Ne and 12 keV Ar atoms scattered from Al(1 1 1)
0
Energy loss (eV)
Intensity
In our experiments we have scattered neutral He, Ne, and Ar atoms with a velocity of v = 0.11 a.u., i.e. projectile energies of 1.25 keV, 6 keV and 12 keV, respectively, from a clean and flat Al(1 1 1) target under a grazing angle of incidence Uin = 2.2°. The experiments were performed in a UHV chamber at a base pressure of some 1011 mbar. The surface of the target was prepared by cycles of sputtering with 25 keV Ar+ ions under a grazing angle of incidence of typically 2° and subsequent annealing at temperatures of about 500 °C. The projectile ion beam is chopped via a pair of field plates biased with voltage pulses with ns rise time and neutralized in a gas target operated with the atoms of the same sort as the projectile. Specularly reflected projectiles are recorded by a channelplate detector located 116 cm behind the target which provides the start pulse for a time-of-flight (TOF) setup. The number of electrons emitted during impact of atoms on the target is derived from the pulse height of a SBD operated at a high voltage of 25 kV. The pulse height of the detector is proportional to the number of electrons emitted in the collision of a single atom with the surface [10] and is recorded in coincidence with the output of a time-to-amplitude converter (TAC) from the TOF setup. With this setup TOF spectra can be assigned to a specific number of emitted electrons [11]. Since this also holds for the emission of no electron (noise signal of SBD), the probability for zero electron emission events can be derived with good accuracy which constitutes the basis for the reliable determination of total electron yields of 104 and lower.
50
100
150
Energy loss (eV) Fig. 3. Same as Fig. 2, but for 12 keV Ar atoms.
200
S. Lederer et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 87–90
under Uin = 2.2°. The data show a mean energy loss DE/ E 0.01 and an energy straggling of similar size. The total electron yields c are largest for impact of Ar atoms (c = 0.07) and amount to c = 0.01 for Ne and c 104 for He. In the following we make use of a simple binary encounter model for the description of the experimental data. A detailed microscopic treatment is an elaborate task, since the projectiles interact in the electron gas of the selvedge of the surface. Here important interaction parameters, such as, e.g. electron density or electron momentum distribution, vary with the distance from the surface which has to be taken into account in the description of the interaction mechanisms. Because such a treatment is beyond the scope of the present paper, we analyze our energy loss spectra and electron emission in terms of computer simulations based on effective parameters for the interaction with an electron gas following classical trajectories. An effective trajectory length for the interaction with the surface enters into our computer simulation code via an effective number of collision events N. Atoms interact with an electron gas of constant density and with maximum momenta in terms of elastic binary encounters. The differential cross sections for these atom–electron collisions are obtained from work on electron–noble gas collisions. In Fig. 4 we show differential cross sections dr/dX obtained from phase shift calculations for collisions of electrons of momentum k = 0.95 a.u. with Ar atoms (thick solid curve) [12], of k = 0.9 a.u. with Ne atoms (thick dashed dotted curve) [13], and of k = 0.62 a.u. with He atoms (thick dashed curve) [14]. This choice of electron momenta follows from the planar potential for projectile scattering from the Al(1 1 1) surface and the electron density (Fermi momenta) at the resulting distance of closest approach to the surface plane. Note that, in particular, the scattering of electrons with Ar atoms reveals preferential forward
10
1
10 0.1
o
-
Ar - e (k F = 0.95 a.u.) o
-
o
-
Ne - e (k F = 0.9 a.u.) He - e (k F = 0.62 a.u.)
0.01
Energy (eV)
2
d σ / d Ω (10 -16 cm )
15
5
energy transfer electron energy 1E-3 0
30
60
90
120
150
0 180
Angle of scattering (deg) Fig. 4. Differential cross sections as function of scattering angle for collisions of electrons with momentum kF from Ar (solid curve), Ne (dashed dotted curve), He atoms (short dashed curve). Dotted curve: energy transfer in binary collisions to electrons with initial momentum kF = 0.95 a.u., dashed curve: final electron energy. For details see text.
89
and backward scattering, with a pronounced minimum at intermediate angles owing to quantum mechanical effects. For scattering into extreme angle the cross sections for scattering from Ar exceed those for the other two systems by about an order of magnitude. Since the trajectories of Ar and Ne atoms are comparable for our scattering conditions, we can explain with the difference in cross sections for the two atoms the substantially different total electron yields. In our simulation procedure the probability for electron scattering under an angle H is derived from the differential cross sections shown in Fig. 4 and the corresponding transfer of energy to an electron with initial velocity ve by a heavy projectile of mass M (me/M 1) and velocity vp (atomic units) 1 pffiffiffi2 1 DEtr ¼ ð vp cos2 H þ 2vp ve þ v2e vp cos HÞ2 v2e 2 2
ð1Þ
This energy transfer (dotted curve) as well as the final electron energy (thin long dashed curve) are plotted for electrons with Fermi velocity vF (Fermi momentum kF = 0.95 a.u.) in Fig. 4. From the plots shown in Fig. 4 it is evident that the scattering is dominated by small angle scattering with negligible energy transfer to conduction electrons. However, a substantial probability is also found for backscattering accompanied by an energy transfer of some eV. In passing we note that only for backscattered electrons the energy transfer and the final electron energy is sufficiently large to overcome the solid-vacuum barrier, which is for Fermi electrons the work function W. In the simulations the energy transfer (projectile energy loss) in N events is summed up where the outcome of single collision events is obtained in a Monte Carlo procedure for randomly distributed angles of scattering weighted with the probability resulting from the differential cross sections. The energy loss spectra are represented by the dashed curves in Figs. 1–3. Aside from a smaller width the agreement for scattering of He atoms (Fig. 1) reproduces the experimental spectra fairly well, if a number of N = 45– 50 collisions is assumed. For Ne and Ar projectiles a systematic shift towards smaller energy loss compared to the measurements is observed. Since grazing scattering of atoms from surface proceeds in the regime of channeling [4,5], the energy transfer from projectiles to lattice atoms of the target (‘‘nuclear energy loss’’) is small owing to individual collisions with large impact parameters and small angular deflections [15]. However, in view of the relatively small total energy loss of some 10 eV, contributions of this process cannot be neglected for massive projectiles as Ne and Ar. In additional computer trajectory calculations [16] based on a Moliere potential with modified screening [17] we have calculated energy loss spectra for nuclear stopping (dotted curves in Figs. 1–3) which reveal for Ne and Ar atoms noticeable effects. For scattering of He atoms, the transfer of projectile energy to target atoms is negligible here, i.e. less than 1 eV. Convolution of the spectra for nuclear
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S. Lederer et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 87–90
o
1.0
Ar (no e-) o Ne (no e-)
0.8
Ar (one e-) o Ne (one e-)
0.08
o
0.06
v = 0.11 a.u. 0.6
0.04
0.4 0.02 0.2
Normalized intensity (one electron)
Normalized intensity (no electron)
1.2
0.00
0.0 0
20
40
60
80
100
120
140
Energy loss (eV) Fig. 5. Simulated energy loss spectra for collisions of Ne (circles) and Ar atoms (squares) with electron gas of momentum kF = 0.95 a.u. at v = 0.11 a.u. Full symbols: spectra coincident with emission of no electron, open symbols: spectra coincident with emission of one electron. Solid curve: spectrum for Ar atom coincident with emission of no electron shifted by energy of work function W. For details see text.
and electronic stopping (solid curves in Figs. 1–3) reproduces the experimental spectra fairly well. The slightly smaller widths of the theoretical spectra are attributed to simplifying assumptions as, e.g. constant electron density without gradient, restriction to Fermi momenta, or the effective number of collisions. A more realistic description is beyond the scope of the present work. Information on the electron emission process can be obtained from our simulations by inspection of the energy transfer and the final electron energy. Only electrons with final energy Efin > W + EF can overcome the solid-vacuum boundary. A detailed description of emission of electrons is an intricate problem which comprises electron transport in bulk and selvedge as well as crossing the solid-vacuum interface [18]. Based on the experimental results we estimate that only one electron out of about 50 electrons (about 2%) fulfilling the threshold energy condition is eventually emitted to vacuum. Then the total electron yields are consistent with the measurements. The very low c for scattering of He atoms originates from the low projectile energy and the resulting distance of closest approach to the surface plane of about 3 a.u. where the electron density and, in particular, electron momenta are too small for a sufficient energy transfer to vacuum energies. An interesting aspect of our simulations concerning electron emission is the resulting shift of the energy loss spectra. The open symbols in Fig. 5 show the simulated
spectra related to the emission of one electron. Compared to the spectra coincident with the emission of no electron (full symbols) a defined shift is evident which is close to the work function of the Al(1 1 1) target (W = 4.3 eV) as also observed for the experimental spectra [8]. In this respect our simulations provide support for the feature that the rather unlikely process of the final emission of an electron compared to the overall number of electronic excitation events involves a shift of energy loss spectra given by the additional energy to reach vacuum, i.e. the work function W. Only electrons which fulfil this latter condition can be subject to an emission event. Note that the data are normalized to the same peak height for the spectra related to the emission of no electron and, furthermore, to the peak height of one electron events for scattering of Ar atoms. Then the data reveals the clearly less probable yield for electron emission induced by impact of Ne atoms. Acknowledgements This work is supported by the Deutsche Forschungsgemeinschaft under contract Wi 1336. We thank K. Maass for his assistance in the preparation of the experiments. HPW is grateful to the Alexander-von-Humboldt-foundation for generous financial support. References [1] D. Hasselkamp, Particle Induced Electron Emission II (Springer, Heidelberg 1992), Springer Tracts Mod. Phys., Vol. 123, p. 1. [2] R.A. Baragiola, in: J.W. Rabalais (Ed.), Low Energy Ion–Surface Interactions, Wiley, New York, 1994. [3] H. Niehus, W. Heiland, E. Taglauer, Surf. Sci. Rep. 17 (1993) 213. [4] D. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [5] H. Winter, Phys. Rep. 367 (2002) 387. [6] H. Winter, HP. Winter, Europhys. Lett. 62 (2003) 739. [7] R.A. Baragiola, E.V. Alonso, A. Oliva Florio, Phys. Rev. B 19 (1979) 121. [8] S. Lederer, K. Maass, D. Blauth, H. Winter, HP. Winter, F. Aumayr, Phys. Rev. B 67 (2003) 121405(R). [9] H. Winter, S. Lederer, HP. Winter, Europhys. Lett. 75 (2006) 964. [10] F. Aumayr, G. Lakits, HP. Winter, Appl. Surf. Sci. 63 (1991) 17. [11] A. Mertens, K. Maass, S. Lederer, H. Winter, H. Eder, J. Sto¨ckl, HP. Winter, F. Aumayr, J. Viefhaus, U. Becker, Nucl. Instr. and Meth. B 182 (2001) 23. [12] A. Dasgupta, A. Bathia, Phys. Rev. A 32 (1985) 3335. [13] A. Dasgupta, A. Bathia, Phys. Rev. A 30 (1984) 1241. [14] P. Hoeper, W. Franzen, R. Gupta, Phys. Rev. 168 (1968) 50. [15] A. Mertens, H. Winter, Phys. Rev. Lett. 85 (2000) 52901. [16] Y. Matulevich, S. Lederer, H. Winter, Phys. Rev. B 71 (2005) 033405. [17] D.J. O’Connor, J.P. Biersack, Nucl. Instr. and Meth. B 15 (1986) 14. [18] M. Ro¨sler, W. Brauer, in: G. Ho¨hler (Ed.), Particle Induced Electron Emission I, Vol. 123, Springer, Heidelberg, 1992, p. 1.
Nuclear Instruments and Methods in Physics Research B 258 (2007) 87–90 www.elsevier.com/locate/nimb
Energy loss and electron emission during grazing scattering of fast noble gas atoms from an Al(1 1 1) surface S. Lederer a, H. Winter b
a,*
, HP. Winter
b
a Institut fu¨r Physik der Humboldt-Universita¨t, Newtonstr. 15, D-12489 Berlin-Adlershof, Germany Institut fu¨r Allgemeine Physik, Technische Universita¨t Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria
Available online 22 December 2006
Abstract Electron loss and electron emission for grazing impact of noble gas atoms with energies in the keV domain are investigated via timeof-flight spectra recorded in coincidence with the number of emitted electrons. The data is analyzed in terms of computer simulations concerning the interaction of the fast atoms with the electron gas in the selvedge of the Al(1 1 1) surface. The interaction is approximated by binary collisions of the fast atoms with Fermi electrons of the conduction band and differential cross sections obtained for electron scattering from free atoms. For an effective number of collisions of about 50 the energy loss spectra are fairly well reproduced by our calculations. We show that for our conditions the shift of the energy spectra for the emission of an additional electron from the surface is close to the work function of the target. Ó 2007 Elsevier B.V. All rights reserved. PACS: 79.20.Rf Keywords: Ion scattering; Electron emission; Surface channeling
1. Introduction Electron emission phenomena induced by energetic atomic projectiles play an important role in a variety of technological applications and are a matter of intensive basic research [1,2]. A special regime of electronic excitation is achieved for impact of fast atoms or ions under a grazing angle of incidence with respect to a solid surface. For sufficiently small angles of incidence, below the so called ‘‘critical angle’’, projectiles are reflected specularly from the topmost surface layer (‘‘surface channeling’’ [3– 5]) and interact with electrons of the selvedge of the target. It turns out that basic features concerning the emission of electrons can be understood by a model of electronic excitations via binary encounter of atomic projectiles with conduction electrons [6]. In such collisions kinetic energy of
*
Corresponding author. Fax: +49 30 2093 7899. E-mail address: [email protected] (H. Winter).
0168-583X/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.095
projectiles is transferred to conduction electrons which results in their excitation and emission into the vacuum. For metal electrons described in the approximation of a free-electron gas, the velocities/momenta of electrons are given by the Fermi–Dirac distribution. Based on this distribution for the initial electronic momenta, it is straightforward to calculate the energy distribution of excited electrons and to estimate yields for emission of electrons. Within such a simple classical model the threshold velocity vth for the onset of projectile induced emission of electrons (‘‘kinetic emission’’, KE) [6,7] and the behaviour of the total electron yield with projectile velocity (threshold law) can be deduced [6]. In recent experiments we found evidence for the predicted (v vth)2-dependence of the total electron yield in the near threshold region [8]. We also observed that the classical threshold for the velocity is in good accord with experimental data, if reduced electron densities in front of the surface are taken into account. In the latter case information on Fermi momenta in front of the surface of metals can be derived [9].
S. Lederer et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 87–90
The experimental studies were performed by the coincident detection of the projectile energy loss via a time-offlight (TOF) method with the number of emitted electrons recorded using a surface barrier detector (SBD) biased at a high voltage [10]. It turns out that this mode of detection is particularly suited for measurements of accurate total electron yields as low as 104, since the ‘‘noise’’ of the SBD is eliminated by the coincident detection with a scattered projectile [11]. Whereas the resulting total electron yields have been evaluated and described in terms of the classical model for electron excitation mentioned above, no detailed analysis of the TOF spectra has been performed so far. In the present paper we discuss simulations of TOF spectra obtained for the scattering of noble gas atoms with a velocity slightly above the classical kinetic threshold. Making use of a classical binary encounter model, we describe in a consistent manner the energy dissipation for projectiles via collisions with conduction electrons and discuss also the effect of the emission of an electron on the energy loss spectra.
1.2 o
1.25 keV He - Al(111) Φin = 2.2 deg
1.0
Normalized intensity
88
0.8 0.6 0.4 0.2 0.0 0
10
20
30
40
Energy loss (eV) Fig. 1. Energy loss spectra for 1.25 keV He atoms scattered under Uin = 2.2° from Al(1 1 1). Full circles: experimental data. Curves: results from computer simulations (dotted curve: nuclear energy loss, dashed curve: electronic energy loss, solid curve: convolution of nuclear and electronic energy loss).
2. Experiment 1.2
3. Results and analysis of data
o
6 keV Ne - Al(111) Φin = 2.2 deg
Normalized intensity
1.0
0.8
0.6
0.4
0.2
0.0 -20
20
40
60
80
Fig. 2. Same as Fig. 1, but for 6 keV Ne atoms.
1.2
12 keV Ar 0 - Al(111) 1.0
0.8
0.6
0.4
0.2
0.0 0
In Figs. 1–3 we display energy loss spectra for 1.25 keV He, 6 keV Ne and 12 keV Ar atoms scattered from Al(1 1 1)
0
Energy loss (eV)
Intensity
In our experiments we have scattered neutral He, Ne, and Ar atoms with a velocity of v = 0.11 a.u., i.e. projectile energies of 1.25 keV, 6 keV and 12 keV, respectively, from a clean and flat Al(1 1 1) target under a grazing angle of incidence Uin = 2.2°. The experiments were performed in a UHV chamber at a base pressure of some 1011 mbar. The surface of the target was prepared by cycles of sputtering with 25 keV Ar+ ions under a grazing angle of incidence of typically 2° and subsequent annealing at temperatures of about 500 °C. The projectile ion beam is chopped via a pair of field plates biased with voltage pulses with ns rise time and neutralized in a gas target operated with the atoms of the same sort as the projectile. Specularly reflected projectiles are recorded by a channelplate detector located 116 cm behind the target which provides the start pulse for a time-of-flight (TOF) setup. The number of electrons emitted during impact of atoms on the target is derived from the pulse height of a SBD operated at a high voltage of 25 kV. The pulse height of the detector is proportional to the number of electrons emitted in the collision of a single atom with the surface [10] and is recorded in coincidence with the output of a time-to-amplitude converter (TAC) from the TOF setup. With this setup TOF spectra can be assigned to a specific number of emitted electrons [11]. Since this also holds for the emission of no electron (noise signal of SBD), the probability for zero electron emission events can be derived with good accuracy which constitutes the basis for the reliable determination of total electron yields of 104 and lower.
50
100
150
Energy loss (eV) Fig. 3. Same as Fig. 2, but for 12 keV Ar atoms.
200
S. Lederer et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 87–90
under Uin = 2.2°. The data show a mean energy loss DE/ E 0.01 and an energy straggling of similar size. The total electron yields c are largest for impact of Ar atoms (c = 0.07) and amount to c = 0.01 for Ne and c 104 for He. In the following we make use of a simple binary encounter model for the description of the experimental data. A detailed microscopic treatment is an elaborate task, since the projectiles interact in the electron gas of the selvedge of the surface. Here important interaction parameters, such as, e.g. electron density or electron momentum distribution, vary with the distance from the surface which has to be taken into account in the description of the interaction mechanisms. Because such a treatment is beyond the scope of the present paper, we analyze our energy loss spectra and electron emission in terms of computer simulations based on effective parameters for the interaction with an electron gas following classical trajectories. An effective trajectory length for the interaction with the surface enters into our computer simulation code via an effective number of collision events N. Atoms interact with an electron gas of constant density and with maximum momenta in terms of elastic binary encounters. The differential cross sections for these atom–electron collisions are obtained from work on electron–noble gas collisions. In Fig. 4 we show differential cross sections dr/dX obtained from phase shift calculations for collisions of electrons of momentum k = 0.95 a.u. with Ar atoms (thick solid curve) [12], of k = 0.9 a.u. with Ne atoms (thick dashed dotted curve) [13], and of k = 0.62 a.u. with He atoms (thick dashed curve) [14]. This choice of electron momenta follows from the planar potential for projectile scattering from the Al(1 1 1) surface and the electron density (Fermi momenta) at the resulting distance of closest approach to the surface plane. Note that, in particular, the scattering of electrons with Ar atoms reveals preferential forward
10
1
10 0.1
o
-
Ar - e (k F = 0.95 a.u.) o
-
o
-
Ne - e (k F = 0.9 a.u.) He - e (k F = 0.62 a.u.)
0.01
Energy (eV)
2
d σ / d Ω (10 -16 cm )
15
5
energy transfer electron energy 1E-3 0
30
60
90
120
150
0 180
Angle of scattering (deg) Fig. 4. Differential cross sections as function of scattering angle for collisions of electrons with momentum kF from Ar (solid curve), Ne (dashed dotted curve), He atoms (short dashed curve). Dotted curve: energy transfer in binary collisions to electrons with initial momentum kF = 0.95 a.u., dashed curve: final electron energy. For details see text.
89
and backward scattering, with a pronounced minimum at intermediate angles owing to quantum mechanical effects. For scattering into extreme angle the cross sections for scattering from Ar exceed those for the other two systems by about an order of magnitude. Since the trajectories of Ar and Ne atoms are comparable for our scattering conditions, we can explain with the difference in cross sections for the two atoms the substantially different total electron yields. In our simulation procedure the probability for electron scattering under an angle H is derived from the differential cross sections shown in Fig. 4 and the corresponding transfer of energy to an electron with initial velocity ve by a heavy projectile of mass M (me/M 1) and velocity vp (atomic units) 1 pffiffiffi2 1 DEtr ¼ ð vp cos2 H þ 2vp ve þ v2e vp cos HÞ2 v2e 2 2
ð1Þ
This energy transfer (dotted curve) as well as the final electron energy (thin long dashed curve) are plotted for electrons with Fermi velocity vF (Fermi momentum kF = 0.95 a.u.) in Fig. 4. From the plots shown in Fig. 4 it is evident that the scattering is dominated by small angle scattering with negligible energy transfer to conduction electrons. However, a substantial probability is also found for backscattering accompanied by an energy transfer of some eV. In passing we note that only for backscattered electrons the energy transfer and the final electron energy is sufficiently large to overcome the solid-vacuum barrier, which is for Fermi electrons the work function W. In the simulations the energy transfer (projectile energy loss) in N events is summed up where the outcome of single collision events is obtained in a Monte Carlo procedure for randomly distributed angles of scattering weighted with the probability resulting from the differential cross sections. The energy loss spectra are represented by the dashed curves in Figs. 1–3. Aside from a smaller width the agreement for scattering of He atoms (Fig. 1) reproduces the experimental spectra fairly well, if a number of N = 45– 50 collisions is assumed. For Ne and Ar projectiles a systematic shift towards smaller energy loss compared to the measurements is observed. Since grazing scattering of atoms from surface proceeds in the regime of channeling [4,5], the energy transfer from projectiles to lattice atoms of the target (‘‘nuclear energy loss’’) is small owing to individual collisions with large impact parameters and small angular deflections [15]. However, in view of the relatively small total energy loss of some 10 eV, contributions of this process cannot be neglected for massive projectiles as Ne and Ar. In additional computer trajectory calculations [16] based on a Moliere potential with modified screening [17] we have calculated energy loss spectra for nuclear stopping (dotted curves in Figs. 1–3) which reveal for Ne and Ar atoms noticeable effects. For scattering of He atoms, the transfer of projectile energy to target atoms is negligible here, i.e. less than 1 eV. Convolution of the spectra for nuclear
90
S. Lederer et al. / Nucl. Instr. and Meth. in Phys. Res. B 258 (2007) 87–90
o
1.0
Ar (no e-) o Ne (no e-)
0.8
Ar (one e-) o Ne (one e-)
0.08
o
0.06
v = 0.11 a.u. 0.6
0.04
0.4 0.02 0.2
Normalized intensity (one electron)
Normalized intensity (no electron)
1.2
0.00
0.0 0
20
40
60
80
100
120
140
Energy loss (eV) Fig. 5. Simulated energy loss spectra for collisions of Ne (circles) and Ar atoms (squares) with electron gas of momentum kF = 0.95 a.u. at v = 0.11 a.u. Full symbols: spectra coincident with emission of no electron, open symbols: spectra coincident with emission of one electron. Solid curve: spectrum for Ar atom coincident with emission of no electron shifted by energy of work function W. For details see text.
and electronic stopping (solid curves in Figs. 1–3) reproduces the experimental spectra fairly well. The slightly smaller widths of the theoretical spectra are attributed to simplifying assumptions as, e.g. constant electron density without gradient, restriction to Fermi momenta, or the effective number of collisions. A more realistic description is beyond the scope of the present work. Information on the electron emission process can be obtained from our simulations by inspection of the energy transfer and the final electron energy. Only electrons with final energy Efin > W + EF can overcome the solid-vacuum boundary. A detailed description of emission of electrons is an intricate problem which comprises electron transport in bulk and selvedge as well as crossing the solid-vacuum interface [18]. Based on the experimental results we estimate that only one electron out of about 50 electrons (about 2%) fulfilling the threshold energy condition is eventually emitted to vacuum. Then the total electron yields are consistent with the measurements. The very low c for scattering of He atoms originates from the low projectile energy and the resulting distance of closest approach to the surface plane of about 3 a.u. where the electron density and, in particular, electron momenta are too small for a sufficient energy transfer to vacuum energies. An interesting aspect of our simulations concerning electron emission is the resulting shift of the energy loss spectra. The open symbols in Fig. 5 show the simulated
spectra related to the emission of one electron. Compared to the spectra coincident with the emission of no electron (full symbols) a defined shift is evident which is close to the work function of the Al(1 1 1) target (W = 4.3 eV) as also observed for the experimental spectra [8]. In this respect our simulations provide support for the feature that the rather unlikely process of the final emission of an electron compared to the overall number of electronic excitation events involves a shift of energy loss spectra given by the additional energy to reach vacuum, i.e. the work function W. Only electrons which fulfil this latter condition can be subject to an emission event. Note that the data are normalized to the same peak height for the spectra related to the emission of no electron and, furthermore, to the peak height of one electron events for scattering of Ar atoms. Then the data reveals the clearly less probable yield for electron emission induced by impact of Ne atoms. Acknowledgements This work is supported by the Deutsche Forschungsgemeinschaft under contract Wi 1336. We thank K. Maass for his assistance in the preparation of the experiments. HPW is grateful to the Alexander-von-Humboldt-foundation for generous financial support. References [1] D. Hasselkamp, Particle Induced Electron Emission II (Springer, Heidelberg 1992), Springer Tracts Mod. Phys., Vol. 123, p. 1. [2] R.A. Baragiola, in: J.W. Rabalais (Ed.), Low Energy Ion–Surface Interactions, Wiley, New York, 1994. [3] H. Niehus, W. Heiland, E. Taglauer, Surf. Sci. Rep. 17 (1993) 213. [4] D. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [5] H. Winter, Phys. Rep. 367 (2002) 387. [6] H. Winter, HP. Winter, Europhys. Lett. 62 (2003) 739. [7] R.A. Baragiola, E.V. Alonso, A. Oliva Florio, Phys. Rev. B 19 (1979) 121. [8] S. Lederer, K. Maass, D. Blauth, H. Winter, HP. Winter, F. Aumayr, Phys. Rev. B 67 (2003) 121405(R). [9] H. Winter, S. Lederer, HP. Winter, Europhys. Lett. 75 (2006) 964. [10] F. Aumayr, G. Lakits, HP. Winter, Appl. Surf. Sci. 63 (1991) 17. [11] A. Mertens, K. Maass, S. Lederer, H. Winter, H. Eder, J. Sto¨ckl, HP. Winter, F. Aumayr, J. Viefhaus, U. Becker, Nucl. Instr. and Meth. B 182 (2001) 23. [12] A. Dasgupta, A. Bathia, Phys. Rev. A 32 (1985) 3335. [13] A. Dasgupta, A. Bathia, Phys. Rev. A 30 (1984) 1241. [14] P. Hoeper, W. Franzen, R. Gupta, Phys. Rev. 168 (1968) 50. [15] A. Mertens, H. Winter, Phys. Rev. Lett. 85 (2000) 52901. [16] Y. Matulevich, S. Lederer, H. Winter, Phys. Rev. B 71 (2005) 033405. [17] D.J. O’Connor, J.P. Biersack, Nucl. Instr. and Meth. B 15 (1986) 14. [18] M. Ro¨sler, W. Brauer, in: G. Ho¨hler (Ed.), Particle Induced Electron Emission I, Vol. 123, Springer, Heidelberg, 1992, p. 1.