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Kinetic electron emission from metal surfaces by slow Na+ ions
Nuclear Instruments and Methods in Physics Research B 267 (2009) 1721–1724
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Kinetic electron emission from metal surfaces by slow Na+ ions M. Pisarra a, M. Commisso a, A. Sindona a, P. Riccardi a,*, Z. Sroubek b a b
Dipartimento di Fisica, Università della Calabria and INFN Gruppo Collegato di Cosenza, 87036 Rende, Cosenza, Italy Czech Academy of Sciences, UFE Chaberska 57, Prague 8, Czech Republic
a r t i c l e
i n f o
Article history: Available online 31 January 2009 PACS: 79.20.Rf 68.49.Sf 34.50.Dy 73.20.Mf
a b s t r a c t Kinetic electron emission caused by the impact of singly charged Na ions upon the metal surfaces is analyzed in terms of the recently developed thermal hot-spot model, that heuristically describes the manyelectron nature of the emission process. The model accounts for the exponential decrease of electron emission yields at projectile velocities below the thresholds of Auger processes. The agreement with experiments indicates that, in spite of its simplicity, the model well describes the basic physics of subthreshold electron emission at lowest impact energies for Al and Au surfaces. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Ion-surface impact Ion scattering from surfaces Secondary electron emission
1. Introduction Kinetic electron emission (KEE) during the interaction of slow atomic particles with metal surfaces, i.e. the emission of electrons at the expense of the kinetic energy of incoming projectiles, has been intensely investigated [1,2] but, despite a considerable effort, the microscopic mechanism of KEE has not been identified in most cases, particularly not at very low impact energies. At higher impact energies, basic mechanisms of KEE from metal surfaces are excitations of solid valence electrons in binary projectile-electron collisions in an idealized Fermi electron gas [3], and electron promotion in close atomic collisions [4]. Both these processes are subject to a threshold impact velocity or energy below which their contribution to the emission decreases rapidly. Nevertheless, even below the thresholds, the magnitude of the observed KEE is usually quite strong [5–8]. Electron emission from metals induced by the impact of alkali ions is particularly suitable for studies of this sub-threshold region because, due to their low ionization potential, these ions lack enough potential energy to give rise to the so called potential electron emission (PEE) [10]. Alkali projectiles are therefore well suited to study KEE but, despite of this distinctive advantage, such studies have been undertaken only recently [5–7,9]. Relevant experimental studies of KEE investigated the emission induced by the impact of Na+ ions on a Ru metal surface [6,7]. * Corresponding author. E-mail address: riccardi@fis.unical.it (P. Riccardi). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.120
These experiments showed that electron emission yields decrease exponentially with the reciprocal of projectile velocity 1/v. An exponential trend with 1/v had been previously reported for the yields induced by non metallic projectiles on Au surfaces [8]. Theoretical interpretations of the exponential behaviour shown by electron yields from metal surfaces have been attempted, considering non-adiabatic one-electron excitations [6–8]. However, the contributions of these processes have been found to be small when realistic particle-substrate parameters are used and, contrary to experiments, the predicted yield decreases with the increasing impact angle with respect to the surface normal. The difficulties in interpreting KEE in terms of one-electron excitation indicate that the electron emission could be a more complex many-electron process where electron–electron interactions play an important role. Because there is a lack of any comprehensive many-electron theory of the excitation induced by an atomic particle passing through the electron gas, recently a simplified thermal ‘‘hot-spot” model has been used to discuss experimental yield in the case of Na ions impact on Ru [7]. The interpretation of electron emission yields is further complicated by the difficulty to disentangle contributions arising from different KEE processes as testified by the recent debate [5–9,11] about the competition of electron promotion and the other subthreshold processes. In previous research [5], we measured energy distribution and yields of electron emission in the interaction of Na+ ions with Al surface, showing that electron emission is dominated by electron-promotion processes. Here, we compare electron emission yields induced by Na ions impact on Al with previously
M. Pisarra et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1721–1724
2. Experiments The experimental set up has been discussed previously [13]. The measurements were performed in a UHV chamber with a base pressure of 4 1010 mbar. Na+ ions were produced with a Kimball Physics ion gun. The ion beam current was of the order of 109 A and had a Gaussian spatial distribution in both horizontal and vertical directions, as measured with a movable Faraday cup situated in the target position. The polycrystalline Al samples (purity 99.999%) was cleaned by sputtering with 6 keV Ar+. Sample cleanness was assured by the absence of oxygen, carbon and sodium signals in electron induced Auger spectroscopy performed right before and after the acquisition of each electron energy spectrum and by the constancy of the energy position of sodium Auger lines during each spectral scan. Emitted electrons were collected by a hemispherical energy analyzer lying in the incidence plane and operated at a constant pass-energy (DE = 50 eV) and therefore a constant transmission over the measured energy range. 3. Results and discussion Mechanisms for kinetic electron emission have been recently studied by plotting the electron emission yield C as a function of 1/v, the inverse of the velocity of incoming projectiles [5–8]. Fig. 1 reports C versus 1/v for the impact of Na+ ions on Al surfaces. These yields have been obtained in [16] by measuring the current on the sample under positive and negative bias. Further-
+
Na →Al Θi= 60°
0
+
Na →Au Θi= 45° -1
log10 Γ
-2
-3
-4
-5
-6 10
20
30
40
50
60
1/v (atomic units) Fig. 1. The electron yield C as a function of the inverse velocity of Na+ impinging upon Al (circles) and Au [12] (triangles) surfaces. The yields for the gold surfaces predicted from the hot-spot model are marked by the solid and the dashed lines for two choices of the coefficient A.
1.5 +
Na → Al
Intensity (arb.units)
reported [12] yields induced by Na ions on gold surfaces, where promotion effects can be excluded. At the lowest impact velocities, the yields for the two substrates approach very similar values, indicating similar emission mechanisms. Application of the hot-spot model to the yields for the gold surface shows good agreement with experiments, despite the approximations used. This indicates that the hot-spot model may indeed closely describe the manyparticle nature of KEE from bombarded metals.
Intensity (arb. units)
1722
Θ i = 60°
1.0
0.010
0.001
20
25
30
35
Kinetic Energy (eV)
Ei = 400 eV 350 eV 300 eV 250 eV 200 eV
0.5
0.0 2
4
6
7
9
11
13
15
Kinetic Energy (eV) Fig. 2. Energy spectra of electrons emitted from the Al surfaces under the impact of Na+ ions at varying incident ion energy for fixed incidence Hi = 60°. The spectra have been acquired with the sample biased at a negative voltage Vb = 5 V and have been arbitrarily displaced on the vertical scale for clarity. The weak signal below the emission threshold is due to low energy electrons mainly arising from the grounded entrance grid of the analyzer [18].
more we verified that the areas of the experimental spectra [5,11] followed the same growing trend with ion energy as the total yields measured by biasing the sample. The yields for Na+ impact on Al are compared with those reported in [12] for the case of Na+ ions impinging on Au surfaces. In the case of Al target the intensity of the emission increases sharply by more than one order of magnitude above a threshold impact energy of about 450 eV (v1 35 a.u.), being correlated with the Auger decay of L-shell excitations produced by the promotion in Al atoms [5]. At impact velocities below the Al-Auger threshold, electron emission is determined by electronic excitations described by the hot-spot model discussed below and by excitations resulting from binary collisions leading to the creation of vacancies in the 2p level of the Na projectiles. This is also shown in Fig. 2, which reports the spectra of electrons emitted by the impact of 200– 400 eV Na+ ions on Al surface. The spectra show the onset of electron-promotion effects, which are manifested by the peak due to Auger decay of sodium atoms excited in the 2p53s2 state [17] during collisions with target atoms, with a threshold impact energy slightly above 200 eV (see the inset in Fig. 2). Below this threshold energy (corresponding in Fig. 1 to a value of v1 50 a.u.), the yield is not vanishing, indicating the existence of other emission process, in agreement with the experimental observations reported for Na impact on Ru surfaces [6]. On the other hand, the yields for Na ions on gold surfaces, where promotion effects can be excluded, are lower than those for the Al substrate. The yields for the gold surface show the exponential decrease with 1/v and, at the lowest impact energies, approach values similar to that for Al surfaces. The interpretation of the exponential behaviour of electron emission yields is still a matter of debate. A promising possibility is offered by a semi-classical ‘‘energy deposition model”, proposed in [7] and based on the idea that target electrons are excited, or ejected, by the ‘‘frictional force” that the many-electron system offers to the projectile moving through the solid. This effect was quantitatively estimated for projectiles with velocities v much larger than the classical threshold for direct projectile-electron collision and gives the electron yield which is proportional to v [3]. However, in the sub-threshold regime only those electrons are emitted which have kinetic energies enhanced above the work
1723
M. Pisarra et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1721–1724
kT e ¼ Bm;
8
x 500 7
6 0
10
20
30
40
50
60
Θ i (degrees)
ð1Þ
where k is the Boltzmann constant and B is a constant independent of v for a classical electron gas but dependent on the size of the impact zone, its heat capacity and on Se. The dependence can be deduced from simple dimensional arguments. The size of the impact zone is actually the only adjustable parameter of the model. Why the excitations can get localized is not yet clarified but a partial localization can be facilitated by multiple scattering between the projectile and nearest atoms of the substrate. Using (1) the yield C of electrons emitted above the vacuum level in the upper half of the space is [7]:
C ¼ A expðU=kT e Þ ¼ A expðU=BmÞ;
E i = 300 eV E i = 1 keV
9
Intensity (arb.units)
function U by the electron–electron interaction with other excited electrons and by ensuing valence electron Auger processes (the hot-spot model) or possibly by multiple collisions with the moving atom [14]. In the hot-spot model the electronic energy deposited in the substrate per unit length of the particle trajectory is given by the electronic stopping power Se. In an ideal electron gas the energy distribution of excited electrons is very narrow, equal to (in a.u.) kf v. To obtain broader distributions it is assumed [7] that the excited electrons are localized for a sufficiently long time in the impact zone to reach quasi-equilibrium by electron–electron interaction and by ensuing valence electron Auger processes. The electron system is then characterized by an effective electron temperature Te and the energy distribution of excited electrons is correspondingly broadened. As discussed in [7], The value of Te can be calculated from equating the deposited electronic energy with the energy content of the electronic excitation in substrate impact zone. The result is
ð2Þ
where U is the substrate work function and A is a constant depending on the escape depth of excited electrons. As mentioned above the coefficient B depends upon the electron concentration in the substrate through the electron heat capacity, upon atomic numbers of the projectile and of the substrate atoms through Se and upon the size of the excited zone [7]. The best fit can be obtained for the zone with the radius of 8 a.u. for substrates with one electron per atom and with smaller radii for substrates with a higher electron concentration. The increase of the heat capacity and the decrease of the spot size partially compensate each other rendering Te less sensitive to the substrate composition. Indeed very similar yield is found for Na–Au and for Na–Al. On the other hand for the same substrate but different projectiles the value of C depends mainly on Se and can vary by an order of magnitude. The previous discussion allows us to set the parameter A and B of equation (2) equal to the value used in [7] (A = 2.6 a.u. and B = 1.08 a.u.) for the system Na–Ru, to draw the solid line in Fig. 1. This line represents the prediction of the total electron yield for Na ions on gold surface (work function U = 5.1 eV), that can be directly compared with the available experimental yields for this projectile-target combination, because promotion effects can be safely excluded in the whole range of projectile velocities. The dashed line in Fig. 1 shows that the agreement with experimental yields can be further improved by halving the value of A, that may still be a reasonable choice for this parameter [7]. It should be stressed that the foregoing discussion neglects the dependence of the electron emission yields on ion incidence angle, whereas the experimental data reported in Fig. 1 are for two different incidence angles. In the case of Na+ impinging on Al we measured the variation of the intensity of the emission as a function of the ion incidence angle for the impact energies of 300 eV [5] and 1 keV for an observation angle of 0°. This is reported in Fig. 3. We observe that the variation of intensity between 45° and 60° is within the experimental errors. Furthermore, the intensity varies by less than a factor of 2 when going from Hi = 0° to
Fig. 3. Intensities of electron emission versus Hi for fixed impact energies Ei = 300 eV and Ei = 1000 eV and He = 0°.
Hi = 60°. This variation is negligible in view of the large variation of the analyzed emission yields with v. The increase of the intensity of emission with incidence angle can be explained by assuming that electron excitation occurs mainly in the bulk of the solid. This means that the intensity of the emission depends on the depth where the excitation occurred. At small incidence angles, ions excite electrons in larger depths and the excited electrons will be more attenuated by collisions on their way to the surface than those excited at the shallower depths accessible at smaller glancing angles. As the incidence angle of the ion beam moves away from the surface normal, electrons are excited closer to the surface so that the electron effective escape length increases. In conclusion, the comparison of the yields due to Na ions impact on Al surfaces with that due to Na impact on gold surfaces allows to establish the role of different processes. In the case of Na–Al system, electron emission is mainly determined by electron-promotion effects, resulting in emission yields that are significantly higher than those observed in the case of gold target, where electron promotion can be excluded. At impact energies below the promotion thresholds, electron emission yields for Na+–Al appear to be very similar to that for the Na+–Au system. We have shown that the ‘‘hot-spot model” proposed in [7] gives a good account of the experimental data. In particular, the model reproduces quantitatively the exponential decrease of the yields with the inverse of the velocity of incoming projectiles. The other models of the sub-threshold KEE, which are based on the effect of one-electron dynamical scattering in the substrate atomic lattices [14,15], would be also interesting to compare with experiments but the comparison is still practically very difficult because they have not been formulated in an analytical form. The behaviour of the yields as a function of the ion beam incidence direction needs to be clarified from both the theoretical and the experimental point of view. The model assumes that this dependence is included in the pre-factor A [7], because the effective electron escape length should depend on the penetration of the ion beam inside the bulk of the solid target, resulting in an increase of the intensity of emission as the ion beam direction is moved away from the surface normal. References [1] HP. Winter, J. Burgdorfer (Eds.), Slow Heavy-Particle Induced Electron Emission from Solid Surfaces, Springer Tracts in Modern Physics, Vol. 225, 2007.
1724
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[2] R.A. Baragiola, P. Riccardi, in: D. Depla, S. Mahieu (Eds.), Reactive Sputter Deposition, Springer Series in Material Science, Vol. 109, 2008 (Chapter 2). [3] R.A. Baragiola, E. Alonso, A. Oliva Florio, Phys. Rev. B 19 (1979) 121. [4] M. Barat, W. Lichten, Phys. Rev. A 6 (1972) 211. [5] M. Minniti, M. Commisso, A. Sindona, E. Sicilia, A. Bonanno, P. Barone, R.A. Baragiola, P. Riccardi, Phys. Rev. B 75 (2007) 045424. [6] J.A. Yarmoff, H.T. Than, Z. Sroubek, Phys. Rev. B 65 (2002) 205412. [7] Z. Sroubek, X. Chen, J.A. Yarmoff, Phys. Rev. B 73 (2006) 045427. [8] J. Lorincik, Z. Sroubek, H. Eder, F. Aumayr, HP. Winter, Phys. Rev. B 62 (23) (2000) 16116. [9] N. Bajales, S. Montoro, E.C. Goldberg, R.A. Baragiola, J. Ferron, Surf. Sci. 579 (2004) L97. [10] R.A. Baragiola, in: J.W. Rabalais (Ed.), Low Energy Ion–Surface Interaction, Wiley, New York, 1994 (Chapter 4).
[11] M. Commisso, M. Minniti, A. Sindona, A. Bonanno, A. Oliva, R.A. Baragiola, P. Riccardi, Phys. Rev. B 72 (2005) 165419. [12] G. Lakitis, F. Aumayr, M. Heim, HP. Winter, Phys. Rev. A 42 (1990) 5780. [13] P. Riccardi, P. Barone, A. Bonanno, A. Oliva, R.A. Baragiola, Phys. Rev. Lett. 84 (2000) 378. [14] G. Falcone, Z. Sroubek, Phys. Rev. B 39 (1989) 1999. [15] HP. Winter, S. Lederer, H. Winter, C. Lemell, J. Burgdorfer, Phys. Rev. B 72 (2005) 161402. [16] M. Minniti, M. Commisso, A. Sindona, P. Barone, A. Bonanno, A. Oliva, P. Riccardi, Nucl. Instr. and Meth. B 257 (2007) 618. [17] M. Commisso, A. Bonanno, A. Oliva, M. Camarca, F. Xu, P. Riccardi, R.A. Baragiola, Nucl. Instr. and Meth. B 230 (2005) 438. [18] A. Sindona, R.A. Baragiola, G. Falcone, A. Oliva, P. Riccardi, Phys. Rev. A 71 (2005) 052903.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Kinetic electron emission from metal surfaces by slow Na+ ions M. Pisarra a, M. Commisso a, A. Sindona a, P. Riccardi a,*, Z. Sroubek b a b
Dipartimento di Fisica, Università della Calabria and INFN Gruppo Collegato di Cosenza, 87036 Rende, Cosenza, Italy Czech Academy of Sciences, UFE Chaberska 57, Prague 8, Czech Republic
a r t i c l e
i n f o
Article history: Available online 31 January 2009 PACS: 79.20.Rf 68.49.Sf 34.50.Dy 73.20.Mf
a b s t r a c t Kinetic electron emission caused by the impact of singly charged Na ions upon the metal surfaces is analyzed in terms of the recently developed thermal hot-spot model, that heuristically describes the manyelectron nature of the emission process. The model accounts for the exponential decrease of electron emission yields at projectile velocities below the thresholds of Auger processes. The agreement with experiments indicates that, in spite of its simplicity, the model well describes the basic physics of subthreshold electron emission at lowest impact energies for Al and Au surfaces. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Ion-surface impact Ion scattering from surfaces Secondary electron emission
1. Introduction Kinetic electron emission (KEE) during the interaction of slow atomic particles with metal surfaces, i.e. the emission of electrons at the expense of the kinetic energy of incoming projectiles, has been intensely investigated [1,2] but, despite a considerable effort, the microscopic mechanism of KEE has not been identified in most cases, particularly not at very low impact energies. At higher impact energies, basic mechanisms of KEE from metal surfaces are excitations of solid valence electrons in binary projectile-electron collisions in an idealized Fermi electron gas [3], and electron promotion in close atomic collisions [4]. Both these processes are subject to a threshold impact velocity or energy below which their contribution to the emission decreases rapidly. Nevertheless, even below the thresholds, the magnitude of the observed KEE is usually quite strong [5–8]. Electron emission from metals induced by the impact of alkali ions is particularly suitable for studies of this sub-threshold region because, due to their low ionization potential, these ions lack enough potential energy to give rise to the so called potential electron emission (PEE) [10]. Alkali projectiles are therefore well suited to study KEE but, despite of this distinctive advantage, such studies have been undertaken only recently [5–7,9]. Relevant experimental studies of KEE investigated the emission induced by the impact of Na+ ions on a Ru metal surface [6,7]. * Corresponding author. E-mail address: riccardi@fis.unical.it (P. Riccardi). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.120
These experiments showed that electron emission yields decrease exponentially with the reciprocal of projectile velocity 1/v. An exponential trend with 1/v had been previously reported for the yields induced by non metallic projectiles on Au surfaces [8]. Theoretical interpretations of the exponential behaviour shown by electron yields from metal surfaces have been attempted, considering non-adiabatic one-electron excitations [6–8]. However, the contributions of these processes have been found to be small when realistic particle-substrate parameters are used and, contrary to experiments, the predicted yield decreases with the increasing impact angle with respect to the surface normal. The difficulties in interpreting KEE in terms of one-electron excitation indicate that the electron emission could be a more complex many-electron process where electron–electron interactions play an important role. Because there is a lack of any comprehensive many-electron theory of the excitation induced by an atomic particle passing through the electron gas, recently a simplified thermal ‘‘hot-spot” model has been used to discuss experimental yield in the case of Na ions impact on Ru [7]. The interpretation of electron emission yields is further complicated by the difficulty to disentangle contributions arising from different KEE processes as testified by the recent debate [5–9,11] about the competition of electron promotion and the other subthreshold processes. In previous research [5], we measured energy distribution and yields of electron emission in the interaction of Na+ ions with Al surface, showing that electron emission is dominated by electron-promotion processes. Here, we compare electron emission yields induced by Na ions impact on Al with previously
M. Pisarra et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1721–1724
2. Experiments The experimental set up has been discussed previously [13]. The measurements were performed in a UHV chamber with a base pressure of 4 1010 mbar. Na+ ions were produced with a Kimball Physics ion gun. The ion beam current was of the order of 109 A and had a Gaussian spatial distribution in both horizontal and vertical directions, as measured with a movable Faraday cup situated in the target position. The polycrystalline Al samples (purity 99.999%) was cleaned by sputtering with 6 keV Ar+. Sample cleanness was assured by the absence of oxygen, carbon and sodium signals in electron induced Auger spectroscopy performed right before and after the acquisition of each electron energy spectrum and by the constancy of the energy position of sodium Auger lines during each spectral scan. Emitted electrons were collected by a hemispherical energy analyzer lying in the incidence plane and operated at a constant pass-energy (DE = 50 eV) and therefore a constant transmission over the measured energy range. 3. Results and discussion Mechanisms for kinetic electron emission have been recently studied by plotting the electron emission yield C as a function of 1/v, the inverse of the velocity of incoming projectiles [5–8]. Fig. 1 reports C versus 1/v for the impact of Na+ ions on Al surfaces. These yields have been obtained in [16] by measuring the current on the sample under positive and negative bias. Further-
+
Na →Al Θi= 60°
0
+
Na →Au Θi= 45° -1
log10 Γ
-2
-3
-4
-5
-6 10
20
30
40
50
60
1/v (atomic units) Fig. 1. The electron yield C as a function of the inverse velocity of Na+ impinging upon Al (circles) and Au [12] (triangles) surfaces. The yields for the gold surfaces predicted from the hot-spot model are marked by the solid and the dashed lines for two choices of the coefficient A.
1.5 +
Na → Al
Intensity (arb.units)
reported [12] yields induced by Na ions on gold surfaces, where promotion effects can be excluded. At the lowest impact velocities, the yields for the two substrates approach very similar values, indicating similar emission mechanisms. Application of the hot-spot model to the yields for the gold surface shows good agreement with experiments, despite the approximations used. This indicates that the hot-spot model may indeed closely describe the manyparticle nature of KEE from bombarded metals.
Intensity (arb. units)
1722
Θ i = 60°
1.0
0.010
0.001
20
25
30
35
Kinetic Energy (eV)
Ei = 400 eV 350 eV 300 eV 250 eV 200 eV
0.5
0.0 2
4
6
7
9
11
13
15
Kinetic Energy (eV) Fig. 2. Energy spectra of electrons emitted from the Al surfaces under the impact of Na+ ions at varying incident ion energy for fixed incidence Hi = 60°. The spectra have been acquired with the sample biased at a negative voltage Vb = 5 V and have been arbitrarily displaced on the vertical scale for clarity. The weak signal below the emission threshold is due to low energy electrons mainly arising from the grounded entrance grid of the analyzer [18].
more we verified that the areas of the experimental spectra [5,11] followed the same growing trend with ion energy as the total yields measured by biasing the sample. The yields for Na+ impact on Al are compared with those reported in [12] for the case of Na+ ions impinging on Au surfaces. In the case of Al target the intensity of the emission increases sharply by more than one order of magnitude above a threshold impact energy of about 450 eV (v1 35 a.u.), being correlated with the Auger decay of L-shell excitations produced by the promotion in Al atoms [5]. At impact velocities below the Al-Auger threshold, electron emission is determined by electronic excitations described by the hot-spot model discussed below and by excitations resulting from binary collisions leading to the creation of vacancies in the 2p level of the Na projectiles. This is also shown in Fig. 2, which reports the spectra of electrons emitted by the impact of 200– 400 eV Na+ ions on Al surface. The spectra show the onset of electron-promotion effects, which are manifested by the peak due to Auger decay of sodium atoms excited in the 2p53s2 state [17] during collisions with target atoms, with a threshold impact energy slightly above 200 eV (see the inset in Fig. 2). Below this threshold energy (corresponding in Fig. 1 to a value of v1 50 a.u.), the yield is not vanishing, indicating the existence of other emission process, in agreement with the experimental observations reported for Na impact on Ru surfaces [6]. On the other hand, the yields for Na ions on gold surfaces, where promotion effects can be excluded, are lower than those for the Al substrate. The yields for the gold surface show the exponential decrease with 1/v and, at the lowest impact energies, approach values similar to that for Al surfaces. The interpretation of the exponential behaviour of electron emission yields is still a matter of debate. A promising possibility is offered by a semi-classical ‘‘energy deposition model”, proposed in [7] and based on the idea that target electrons are excited, or ejected, by the ‘‘frictional force” that the many-electron system offers to the projectile moving through the solid. This effect was quantitatively estimated for projectiles with velocities v much larger than the classical threshold for direct projectile-electron collision and gives the electron yield which is proportional to v [3]. However, in the sub-threshold regime only those electrons are emitted which have kinetic energies enhanced above the work
1723
M. Pisarra et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1721–1724
kT e ¼ Bm;
8
x 500 7
6 0
10
20
30
40
50
60
Θ i (degrees)
ð1Þ
where k is the Boltzmann constant and B is a constant independent of v for a classical electron gas but dependent on the size of the impact zone, its heat capacity and on Se. The dependence can be deduced from simple dimensional arguments. The size of the impact zone is actually the only adjustable parameter of the model. Why the excitations can get localized is not yet clarified but a partial localization can be facilitated by multiple scattering between the projectile and nearest atoms of the substrate. Using (1) the yield C of electrons emitted above the vacuum level in the upper half of the space is [7]:
C ¼ A expðU=kT e Þ ¼ A expðU=BmÞ;
E i = 300 eV E i = 1 keV
9
Intensity (arb.units)
function U by the electron–electron interaction with other excited electrons and by ensuing valence electron Auger processes (the hot-spot model) or possibly by multiple collisions with the moving atom [14]. In the hot-spot model the electronic energy deposited in the substrate per unit length of the particle trajectory is given by the electronic stopping power Se. In an ideal electron gas the energy distribution of excited electrons is very narrow, equal to (in a.u.) kf v. To obtain broader distributions it is assumed [7] that the excited electrons are localized for a sufficiently long time in the impact zone to reach quasi-equilibrium by electron–electron interaction and by ensuing valence electron Auger processes. The electron system is then characterized by an effective electron temperature Te and the energy distribution of excited electrons is correspondingly broadened. As discussed in [7], The value of Te can be calculated from equating the deposited electronic energy with the energy content of the electronic excitation in substrate impact zone. The result is
ð2Þ
where U is the substrate work function and A is a constant depending on the escape depth of excited electrons. As mentioned above the coefficient B depends upon the electron concentration in the substrate through the electron heat capacity, upon atomic numbers of the projectile and of the substrate atoms through Se and upon the size of the excited zone [7]. The best fit can be obtained for the zone with the radius of 8 a.u. for substrates with one electron per atom and with smaller radii for substrates with a higher electron concentration. The increase of the heat capacity and the decrease of the spot size partially compensate each other rendering Te less sensitive to the substrate composition. Indeed very similar yield is found for Na–Au and for Na–Al. On the other hand for the same substrate but different projectiles the value of C depends mainly on Se and can vary by an order of magnitude. The previous discussion allows us to set the parameter A and B of equation (2) equal to the value used in [7] (A = 2.6 a.u. and B = 1.08 a.u.) for the system Na–Ru, to draw the solid line in Fig. 1. This line represents the prediction of the total electron yield for Na ions on gold surface (work function U = 5.1 eV), that can be directly compared with the available experimental yields for this projectile-target combination, because promotion effects can be safely excluded in the whole range of projectile velocities. The dashed line in Fig. 1 shows that the agreement with experimental yields can be further improved by halving the value of A, that may still be a reasonable choice for this parameter [7]. It should be stressed that the foregoing discussion neglects the dependence of the electron emission yields on ion incidence angle, whereas the experimental data reported in Fig. 1 are for two different incidence angles. In the case of Na+ impinging on Al we measured the variation of the intensity of the emission as a function of the ion incidence angle for the impact energies of 300 eV [5] and 1 keV for an observation angle of 0°. This is reported in Fig. 3. We observe that the variation of intensity between 45° and 60° is within the experimental errors. Furthermore, the intensity varies by less than a factor of 2 when going from Hi = 0° to
Fig. 3. Intensities of electron emission versus Hi for fixed impact energies Ei = 300 eV and Ei = 1000 eV and He = 0°.
Hi = 60°. This variation is negligible in view of the large variation of the analyzed emission yields with v. The increase of the intensity of emission with incidence angle can be explained by assuming that electron excitation occurs mainly in the bulk of the solid. This means that the intensity of the emission depends on the depth where the excitation occurred. At small incidence angles, ions excite electrons in larger depths and the excited electrons will be more attenuated by collisions on their way to the surface than those excited at the shallower depths accessible at smaller glancing angles. As the incidence angle of the ion beam moves away from the surface normal, electrons are excited closer to the surface so that the electron effective escape length increases. In conclusion, the comparison of the yields due to Na ions impact on Al surfaces with that due to Na impact on gold surfaces allows to establish the role of different processes. In the case of Na–Al system, electron emission is mainly determined by electron-promotion effects, resulting in emission yields that are significantly higher than those observed in the case of gold target, where electron promotion can be excluded. At impact energies below the promotion thresholds, electron emission yields for Na+–Al appear to be very similar to that for the Na+–Au system. We have shown that the ‘‘hot-spot model” proposed in [7] gives a good account of the experimental data. In particular, the model reproduces quantitatively the exponential decrease of the yields with the inverse of the velocity of incoming projectiles. The other models of the sub-threshold KEE, which are based on the effect of one-electron dynamical scattering in the substrate atomic lattices [14,15], would be also interesting to compare with experiments but the comparison is still practically very difficult because they have not been formulated in an analytical form. The behaviour of the yields as a function of the ion beam incidence direction needs to be clarified from both the theoretical and the experimental point of view. The model assumes that this dependence is included in the pre-factor A [7], because the effective electron escape length should depend on the penetration of the ion beam inside the bulk of the solid target, resulting in an increase of the intensity of emission as the ion beam direction is moved away from the surface normal. References [1] HP. Winter, J. Burgdorfer (Eds.), Slow Heavy-Particle Induced Electron Emission from Solid Surfaces, Springer Tracts in Modern Physics, Vol. 225, 2007.
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