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Photon emission from Agn+ clusters: Role of the ionization potential
Nuclear Instruments and Methods in Physics Research B I25 ( 1997)7- 12
Beam lntereetions with Meter&lo 8 Atoms
Photon emission from Ag z clusters: Role of the ionization potential M. Alducin, P. Ape11 Department ofApplied
Physics, Chalmers University of Technology and GGteborg University, S-41296 Giiteborg, Sweden
Abstract Photon emission due to the radiative neutralization of slow Ag: , Ag: and Agl clusters impinging on a silver surface is studied theoretically. The photon spectra and the total photon yield are calculated by using two different sets of experimental data for the ionization potential. The features of the photon spectra such as energy of the emitted photons and frequency at which the emission is maximum strongly depends on the experimental ionization potential chosen as input. Consequently, we propose light emission as a complementary experimental tool to study the electronic properties and, in particular, the ionization potential of such clusters.
1. Introduction
Clusters of metal atoms are the subject of intense basic and applied research because they encompass the evolution of the physical and chemical properties of an atom to those of a solid [l]. Moreover, clusters supported by suitable substrates have attractive catalytic properties or serve as model catalysts [Z]. In this context, the knowledge of electronic properties such as ionization potentials, electron affinities and binding energies are relevant in order to understand the mechanisms involved and next, to find out possible applications. Regarding ionization potentials there are two main techniques to measure them experimentally: photoionization spectroscopy and electron impact ionization studies [3]. Though the latter is easier to use, the phenomena involved in this technique are more complex than those in the photoionization process thus making more difficult the interpretation of the experimental data. In recent years, ionization potentials measured with the photoionization spectroscopy [4] and using the electron impact ionization method [S] have been reported for silver clusters. The values obtained with both techniques show some important discrepancies with no apparent explanation. According to our previous theoretical studies on radiative neutralization of small silver clusters impinging on an Ag surface [6], the photon spectra as well as the total photon yield show a strong dependence on the position of the energy level bound to the cluster. Based on such results, photon emission induced by positively ionized cluster can be considered as a complementary technique to check the validity of the results supplied by the other two. At this point we note that light emission has been provid-
ing valuable information before, in studies of ions impinging on solid surfaces [7-lo]. In present work, photon spectra and total photon yields for slow Agi , Ag: and Ag: clusters impinging on an Ag surface have been calculated using the experimental ionization potentials reported by Alameddin et al. [4] and Jackschath et al. [5]. The ionization potentials for Ag: and Ag: given in both references are in quite good agreement, however for n = 3, 4, 5 they differ significantly. A study on photon emission for such clusters was already made in Ref. [6] using the ionization potentials measured by Jackschath et al. The purpose of this communication is to investigate the sensitivity to the choice of ionization potential.
2. Theory Let us consider a beam of Ag: clusters bombarding an Ag surface. Assuming a beam with a perpendicular kinetic energy of 10 eV, we found in our previous work [6] that most of the Agz clusters are totally neutralized before reaching the surface (3-4 A outside) mainly due to resonant capture. A few are neutralized by radiative capture. The model proposed in Ref. [6] to calculate the photon spectrum and the total photon yield due to the radiative neutralization is now described briefly. The probability of photon emission per unit energy o induced by the radiative neutralization of a cluster at a distance z from the metal surface is denoted l/~~,,(z, w). The fraction of the initial surviving ions at z is n+(z). Hence, the total number of emitted photons per solid angle
0168-583X/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PII SO168-583X(96)00896-8
I. SECONDARY EMISSION - THEORY
M. Alducin. P. Apell /Nucl. Insrr. und Merh. in Phys. Res. B 125 1199717- I2
8
do per impinging cluster and per unit energy w can be obtained by adding all the contributions along the trajectory of the cluster towards the surface, d2N -= dw do
/
dz
n+(z) u.(z)r&
quence of the interaction between the projectile and the surface (AE( z)). For illustrative purposes three limiting cases of the level shift AE have been included: (i) the energy level does not change with the distance, (ii) the classical image potential
u) ’
1
with vi(z) the velocity component perpendicular to the surface. Since the Agz clusters are very massive, the latter is taken as a constant along the trajectory, v I(z) = u I . The expression for l/r,,&;, w) derived in Ref. [6] from the reciprocity theorem of electrodynamics [ 111is
(2) Here M,, is a form factor
AE(z)
= 2(zZ z,) -
4(1-z,)’
with Z = 1 for each cluster, and (iii) the classical image potential with Z = /E,(m), that is, the effective charge in a hydrogenic model. In the previous equation z, = 0.96 au is the distance of the image plane to the the jellium edge [13]. As mentioned above, in proximity with the surface the cluster levels shift and broaden mainly due to resonant capture. Hence the number of surviving ions at a distance z from the surface are obtained by solving dn+( z) -= dz
n+(z) r,(z)u-
(7)
’
where 1/T,(Z) is the level width of the cluster approximated by the Gadzuk’s expression [14] (3) where the initial and final states of the electron involved in the process are described by the wave functions & and & with energies Ek and E,(z), respectively. r, and e(o) are the transmission coefficient and the dielectric function of the Ag substrate. The latter is approximated by 2
E(W)‘l-%-~ 02
NW= tO2-
2’ Wg
(4)
where or = 8.96 eV, N= 5.44, and wg/wf = 1.37 are fitted values which reproduce the experimental absorption peaks of an Ag substrate, observed with Electron Energy Loss Spectroscopy 1121. Lastly, k, = k sin 0 and pr = /m with k = w/c and 0 being the angle defined from the surface normal at which photons are collected. The wave functions Jlk of the electron in the solid are solutions of the Schriidinger equation in which the Ag surface is described by the Jennings potential corresponding to a Fermi energy E, = 5.56 eV (rs = 3 au) and a work function 4 = 4.3 eV [ 131. Since the Ag clusters are very well described within the ellipsoidal shell model [3], the wave functions of the highest occupied orbital $a are taken as one-electron wave functions approximated with a modified hydrogen model in order to avoid more tedious numerical calculations. The energy of the cluster ground state referred to the bottom of the conduction band is E,(z)=E,++-E,(m)+hE(z).
(5)
where E,(m) is the vertical ionization potential of the cluster in vacuum. The z-dependence of E, is a conse-
1 -=27r rrc( z)
c
I(lbsl &r)12+,-E,(z)).
k
(8) Z being the effective charge of the cluster in the hydrogenie model. Finally, the total photon yield or the total number of emitted photons per impinging cluster and per unit solid angle, is calculated as the area of the photon spectrum d’N/dwdn expressed in Eq. (1).
3. Discussion The two sets of experimental ionization potentials (JR) taken as input to evaluate Eq. (5) are given in Table 1. The values differ about 0.5 eV for each cluster. However, Table 1 Vertical ionization energies of Ag, clusters (n = 1. . .5). In the first row we give the values measured with photoionization spcctroscopy from Ref. [4]. In the second row the values reported in Ref. [5] from impact ionization studies are given. The differences between both data ate of the order of 0.5 eV. Notice that the highest values for IP are for Ag: the corresponding to Ref. [4]. whereas for Agz and Agl it is that of Ref. [5]
E,(m)
E&4
(eV)
(eV)
7.50 7.62 5.69 7.13 5.75
7.57 7.60 6.20 6.65 6.35
M. Alducin. P. Apell/Nucl. Instr. and Meth. in Phys. Res. B 125 (1997) 7-12
9
4.oe-09 /-
2.0
1.5
E (eV) Fig. 1. Photon spectra of Agi cluster as a function of the photon energy (in eV). Thin curves are obtained with the ionization potential of Ref. [5], whereas bold cttrves correspond to the values taken from Ref. (41. In both cases the photon spectrum is calculated using different approximations to the energy shift: in solid lines no energy shift was included, in dotted lines the taken as the classical induced potential of Eq. (6) with Z = 1. Finally, in dot-dashed lines the classical energy shift with Z =
notice that whereas the values given in Ref. [4] for Ag; and Ag: are the smallest ones, the ionization potential given by the same authors for Ag: is the biggest. Therefore, the IP ratios are larger in this case. Photon spectra have been calculated assuming that photons are collected
at different angles f? from the normal to the surface (0 = 30”. 45”, 60”). The photon spectra can change a factor 2 depending of the angle considered. However, this factor does not depend on either the cluster or the ionization potential. Thus, the relative differences between the spec-
/ /
1’ \
i
I
i i
\ I
2.5 Fig. 2. Same as Fig. 1, but for the Ag:
~ 3.0
cluster.
I. SECONDARY EMISSION - THEORY
10
M. Alducin. P. Apell/Nucl.
Instr. und Meth. in Phys. Res. B 125 (1997) 7-12
E (ev) Fig. 3. Same as Fig. I but for the A& cluster.
tra obtained
with the two sets of experimental IF’ are not sensitive to the angle 0 chosen. Hence, we only show below the results corresponding to 8 = 60” at which the intensities are slighly higher. Figs. I, 2 and 3 show the photon spectra corresponding to Ag:, Ag:, and Ag:, respectively. In bold lines the
photon spectrum of Eq. (1) is calculated using as input the ionization potentials measured by Alameddin et al. [4], whereas the results obtained with the ionization potentials of Jackschath et al. [s] are plotted as thin lines. As mentioned in the previous section, we have considered different approximations for the energy shift: in solid lines
Fig. 4. Total photon yield as a function of the cluster size obtained with the ionization potentials of Ref. 141(in bold lines) and with the values given in Ref. [5] (in thiti lines). In solid lines the energy shift is neglected, in dot-dashed lines the results correspond to the classical energy shift with Z = dm and in dotted lines the classical energy shift with Z = 1. Notice that the differences data (see Table 1) account for the different ratios Agh : Ag: and Agf; : Ag; obtained in each case.
between both sets of
M. Alducin, P. Apell/Nucl.
Instr. mdhfeth.
(A,?,) the energy level E,< z) does not change along the trajectory, in dotted lines (AE,) the energy shift is described by the classical image potential with Z = 1, and in dot-dashed lines (A&) the latter approximation but with Z = \/m. Briefly the features of the photon spectra shown in Figs. l-3 are the following. The energy range of the emitted photons, 0 < w 5 w,, is given by the difference between the Fermi level and the position of the cluster bound state at a distance close enough to the surface to allow the overlapping between the two states involved in the process. When the energy shift is neglected (AE = 0) the energy cutoff is obviously wc = E,(m) - 4, but it shifts to lower energies when a finite AE is included. There is a frequency o, at which the emission of photons is maximum. The value of o, for each cluster and for each approximation to the energy shift is closely related to the neutralization distance z, derived from Eq. (7). In fact, w, is equal to the maximum allowed energy of emitted photons, when the cluster is at a distance z, from the surface (w,,, N E, - E,( z,)). Finally, in the range of small frequencies (w < o,,,), the photon spectrum of Eq. (1) is linear in w:
g-_(*+o($)+...].
(9)
where wp is the plasmon frequency of the substrate. Next, let us compare the photon spectra obtained with the two sets of experimental JP. The smaller JP given by Alameddin et al. for the Ag: and Ag: clusters as compared to those by Jackschath et al. implies a shorter energy range of emitted photons. More precisely, the differences between the energy cutoff o, obtained in each case equal the differences in the JP, independently of the energy shift used. Furthermore, w, is shifted _ -0.4 eV in Ag: and - -0.5 eV in Ag: when the IP from Alameddin et al. instead of the JP from Jackschath et al. are used. Regarding the Ag: cluster, similar changes in o, and in w, are observed. Notice, however, that now the JP given by Alameddin et al. is bigger than that measured by Jackschath et al., and consequently,o, and w, shift towards higher energies with the first JP value. The total photon yield as a function of the cluster size is represented in Fig. 4. The different calculations are represented in the same kind of curves than those of Figs. 1-3. As can be expected from the large differences in the JP of Ag,, the shapes of the curves change strongly depending on the values chosen for JP. For instance, the ratio Agi : Ag: obtained with the data from Alameddin et al. varies either a factor 11 when the energy shift AE, is included or a factor 5 in the two other approximations. In contrast, the same ratio changes to a factor 2 and to a factor which is almost 1 if one takes the values given by Jackschath et al. A final remark to bring forward is the surprising dependence of the ratio Ag,’ : Agz on the approximation to the energy shift. Notice that whereas the
in Phys. Res. B I25 1199717-12
II
level shift in the AE, approximation is independent of the cluster, in the AE, approximation it depends on the IP of the cluster considered. As a consequence w, for Agd as compared to that for Ag c is a factor of 3 bigger in the first approximation and a factor of 2 in the latter. Hence, a crude estimation of the total photon yield from Eq. (9) (N a 0’) gives us a ratio 9: 4 in agreement with the ratio I 1 : 5 mentioned above. Finally, we point out that the total photon yields calculated for Agf and Ag: are a factor 2-3 larger in case of using the values from Jackschath et al.; whereas the photon yield for Ag: is a factor 2 larger with the JP given by Alameddin et al. These differences can be useful to decide which value of IP is more realistic for each cluster.
4. Conclusions We have studied the radiative neutralization of Ag:, Ag,’ and Agl clusters impinging in an Ag surface. To perform this calculation the ionization potentials measured experimentally with two different techniques are used. The differences between them are reflected in the photon spectra and in the total photon yield. First, the energy at which the emission of photons is maximum is shifted 0.4-0.5 eV. As a consequence the total number of photons collected can change by a factor 2-3 depending on the cluster studied. Furthetmom, the difference between the ionization potentials are reproduced almost directly in the range of energies when it is possible to induce emission of photons. The sensitivity to ionization potential energies is of the same order as the energy shift of the level. Hence both the ionization potential and the energy shift have to be considered in analyzing the photon spectra. Finally, the profile of the total photon yield versus the cluster size changes dramatically depending on the values of ionization potential used as input. For instance, in one case the ratios Ag: :Ag: and Agi :Agl are 10: 1, whereas in the other case they are 2: 1. All these features indicate that measurements of photon emission could be considered as a complementary technique in order to study different electronic properties of clusters and also in studies on the interaction of clusters with surfaces to understand how cluster properties are modified due to the surface.
Acknowledgments We thank Prof. R. Berndt for stimulating and suggestions. This work was supported by Natural Science Research Council. One of (M.A.) gratefully acknowledge a grant from Government (Eusko JaurIaritza).
discussions the Swedish the authors the Basque
I. SECONDARY EMISSION - THEORY
12
M. Akducin, P. Apell/Nucl.
Insfr. and Meih. in Phys. Res. B 125 ((9971
References [l] See the Pro. Int. Symp. on Small Particles and Inorganic Clusters, ISSPIC-1, J. Phys. (Orsay) 38 (1977) C2; ISSPIC-2, Surf. Sci. 106 (1981); ISSPIC-3, Surf. Sci. 156 (1985); ISSPIC-4, Z. Phys. D 12 (1989); ISSPIC-5, Z. Phys. D 19 (1991) 20; ISSPIC-6, Z. Phys. D 26 ( 1993); ISSPIC-7, Surf. Rev. Lett. (19961. to be published. [2] U. Heiz, R. Sherwood, D.M. Cox, A. Kaldor and J.T. Yates. J. Phys. Chem. 99 (1995) 8730. [3] W.A. de Heer, Rev. Mod. Phys. 65 (19931 611. [4] G. Alameddin, J. Hunter, D. Cameron and M.M. Kappes, Chem. Phys. Lett. 192 (1992) 122. [5] C. Jackschath, 1. Rabin and W. Schulze, Z. Phys. D 22 (1992) 517.
l-12
[6] N. Lorente, R. Monreal, M. Alducin and P. Ape11 (1996) submitted. [7] W. Heiland, Solid State Phenom. 27 (1992) 107. [8] J.K. Nprrskov, D.M. Newns and B.1. Lundqvist, Surf. Sci. 80 (19791 179. [9] B. Kasemo, E. Tijmquist, J.K. N~rskov and B.I. Lundqvist. Surf. Sci. 89 (19791 554. [lo] L. Hellberg, J. Striimquist. B. Kasemo and B.I. Lundqvist, Phys. Rev. Lett. 74 (I 995) 4742. [I 11 L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, London, 1977). [12] C. Wehenkel, Thesis, L’UniversitC Pierre et Marie Curie, Paris ( 1975). [13] P.J. Jennings, R.O. Jones and M. Weinert Phys. Rev. B 37 (19881 6113. [14] J.W. Gadzuk, Surf. Sci. 6 (I%71 133, 159.
Beam lntereetions with Meter&lo 8 Atoms
Photon emission from Ag z clusters: Role of the ionization potential M. Alducin, P. Ape11 Department ofApplied
Physics, Chalmers University of Technology and GGteborg University, S-41296 Giiteborg, Sweden
Abstract Photon emission due to the radiative neutralization of slow Ag: , Ag: and Agl clusters impinging on a silver surface is studied theoretically. The photon spectra and the total photon yield are calculated by using two different sets of experimental data for the ionization potential. The features of the photon spectra such as energy of the emitted photons and frequency at which the emission is maximum strongly depends on the experimental ionization potential chosen as input. Consequently, we propose light emission as a complementary experimental tool to study the electronic properties and, in particular, the ionization potential of such clusters.
1. Introduction
Clusters of metal atoms are the subject of intense basic and applied research because they encompass the evolution of the physical and chemical properties of an atom to those of a solid [l]. Moreover, clusters supported by suitable substrates have attractive catalytic properties or serve as model catalysts [Z]. In this context, the knowledge of electronic properties such as ionization potentials, electron affinities and binding energies are relevant in order to understand the mechanisms involved and next, to find out possible applications. Regarding ionization potentials there are two main techniques to measure them experimentally: photoionization spectroscopy and electron impact ionization studies [3]. Though the latter is easier to use, the phenomena involved in this technique are more complex than those in the photoionization process thus making more difficult the interpretation of the experimental data. In recent years, ionization potentials measured with the photoionization spectroscopy [4] and using the electron impact ionization method [S] have been reported for silver clusters. The values obtained with both techniques show some important discrepancies with no apparent explanation. According to our previous theoretical studies on radiative neutralization of small silver clusters impinging on an Ag surface [6], the photon spectra as well as the total photon yield show a strong dependence on the position of the energy level bound to the cluster. Based on such results, photon emission induced by positively ionized cluster can be considered as a complementary technique to check the validity of the results supplied by the other two. At this point we note that light emission has been provid-
ing valuable information before, in studies of ions impinging on solid surfaces [7-lo]. In present work, photon spectra and total photon yields for slow Agi , Ag: and Ag: clusters impinging on an Ag surface have been calculated using the experimental ionization potentials reported by Alameddin et al. [4] and Jackschath et al. [5]. The ionization potentials for Ag: and Ag: given in both references are in quite good agreement, however for n = 3, 4, 5 they differ significantly. A study on photon emission for such clusters was already made in Ref. [6] using the ionization potentials measured by Jackschath et al. The purpose of this communication is to investigate the sensitivity to the choice of ionization potential.
2. Theory Let us consider a beam of Ag: clusters bombarding an Ag surface. Assuming a beam with a perpendicular kinetic energy of 10 eV, we found in our previous work [6] that most of the Agz clusters are totally neutralized before reaching the surface (3-4 A outside) mainly due to resonant capture. A few are neutralized by radiative capture. The model proposed in Ref. [6] to calculate the photon spectrum and the total photon yield due to the radiative neutralization is now described briefly. The probability of photon emission per unit energy o induced by the radiative neutralization of a cluster at a distance z from the metal surface is denoted l/~~,,(z, w). The fraction of the initial surviving ions at z is n+(z). Hence, the total number of emitted photons per solid angle
0168-583X/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PII SO168-583X(96)00896-8
I. SECONDARY EMISSION - THEORY
M. Alducin. P. Apell /Nucl. Insrr. und Merh. in Phys. Res. B 125 1199717- I2
8
do per impinging cluster and per unit energy w can be obtained by adding all the contributions along the trajectory of the cluster towards the surface, d2N -= dw do
/
dz
n+(z) u.(z)r&
quence of the interaction between the projectile and the surface (AE( z)). For illustrative purposes three limiting cases of the level shift AE have been included: (i) the energy level does not change with the distance, (ii) the classical image potential
u) ’
1
with vi(z) the velocity component perpendicular to the surface. Since the Agz clusters are very massive, the latter is taken as a constant along the trajectory, v I(z) = u I . The expression for l/r,,&;, w) derived in Ref. [6] from the reciprocity theorem of electrodynamics [ 111is
(2) Here M,, is a form factor
AE(z)
= 2(zZ z,) -
4(1-z,)’
with Z = 1 for each cluster, and (iii) the classical image potential with Z = /E,(m), that is, the effective charge in a hydrogenic model. In the previous equation z, = 0.96 au is the distance of the image plane to the the jellium edge [13]. As mentioned above, in proximity with the surface the cluster levels shift and broaden mainly due to resonant capture. Hence the number of surviving ions at a distance z from the surface are obtained by solving dn+( z) -= dz
n+(z) r,(z)u-
(7)
’
where 1/T,(Z) is the level width of the cluster approximated by the Gadzuk’s expression [14] (3) where the initial and final states of the electron involved in the process are described by the wave functions & and & with energies Ek and E,(z), respectively. r, and e(o) are the transmission coefficient and the dielectric function of the Ag substrate. The latter is approximated by 2
E(W)‘l-%-~ 02
NW= tO2-
2’ Wg
(4)
where or = 8.96 eV, N= 5.44, and wg/wf = 1.37 are fitted values which reproduce the experimental absorption peaks of an Ag substrate, observed with Electron Energy Loss Spectroscopy 1121. Lastly, k, = k sin 0 and pr = /m with k = w/c and 0 being the angle defined from the surface normal at which photons are collected. The wave functions Jlk of the electron in the solid are solutions of the Schriidinger equation in which the Ag surface is described by the Jennings potential corresponding to a Fermi energy E, = 5.56 eV (rs = 3 au) and a work function 4 = 4.3 eV [ 131. Since the Ag clusters are very well described within the ellipsoidal shell model [3], the wave functions of the highest occupied orbital $a are taken as one-electron wave functions approximated with a modified hydrogen model in order to avoid more tedious numerical calculations. The energy of the cluster ground state referred to the bottom of the conduction band is E,(z)=E,++-E,(m)+hE(z).
(5)
where E,(m) is the vertical ionization potential of the cluster in vacuum. The z-dependence of E, is a conse-
1 -=27r rrc( z)
c
I(lbsl &r)12+,-E,(z)).
k
(8) Z being the effective charge of the cluster in the hydrogenie model. Finally, the total photon yield or the total number of emitted photons per impinging cluster and per unit solid angle, is calculated as the area of the photon spectrum d’N/dwdn expressed in Eq. (1).
3. Discussion The two sets of experimental ionization potentials (JR) taken as input to evaluate Eq. (5) are given in Table 1. The values differ about 0.5 eV for each cluster. However, Table 1 Vertical ionization energies of Ag, clusters (n = 1. . .5). In the first row we give the values measured with photoionization spcctroscopy from Ref. [4]. In the second row the values reported in Ref. [5] from impact ionization studies are given. The differences between both data ate of the order of 0.5 eV. Notice that the highest values for IP are for Ag: the corresponding to Ref. [4]. whereas for Agz and Agl it is that of Ref. [5]
E,(m)
E&4
(eV)
(eV)
7.50 7.62 5.69 7.13 5.75
7.57 7.60 6.20 6.65 6.35
M. Alducin. P. Apell/Nucl. Instr. and Meth. in Phys. Res. B 125 (1997) 7-12
9
4.oe-09 /-
2.0
1.5
E (eV) Fig. 1. Photon spectra of Agi cluster as a function of the photon energy (in eV). Thin curves are obtained with the ionization potential of Ref. [5], whereas bold cttrves correspond to the values taken from Ref. (41. In both cases the photon spectrum is calculated using different approximations to the energy shift: in solid lines no energy shift was included, in dotted lines the taken as the classical induced potential of Eq. (6) with Z = 1. Finally, in dot-dashed lines the classical energy shift with Z =
notice that whereas the values given in Ref. [4] for Ag; and Ag: are the smallest ones, the ionization potential given by the same authors for Ag: is the biggest. Therefore, the IP ratios are larger in this case. Photon spectra have been calculated assuming that photons are collected
at different angles f? from the normal to the surface (0 = 30”. 45”, 60”). The photon spectra can change a factor 2 depending of the angle considered. However, this factor does not depend on either the cluster or the ionization potential. Thus, the relative differences between the spec-
/ /
1’ \
i
I
i i
\ I
2.5 Fig. 2. Same as Fig. 1, but for the Ag:
~ 3.0
cluster.
I. SECONDARY EMISSION - THEORY
10
M. Alducin. P. Apell/Nucl.
Instr. und Meth. in Phys. Res. B 125 (1997) 7-12
E (ev) Fig. 3. Same as Fig. I but for the A& cluster.
tra obtained
with the two sets of experimental IF’ are not sensitive to the angle 0 chosen. Hence, we only show below the results corresponding to 8 = 60” at which the intensities are slighly higher. Figs. I, 2 and 3 show the photon spectra corresponding to Ag:, Ag:, and Ag:, respectively. In bold lines the
photon spectrum of Eq. (1) is calculated using as input the ionization potentials measured by Alameddin et al. [4], whereas the results obtained with the ionization potentials of Jackschath et al. [s] are plotted as thin lines. As mentioned in the previous section, we have considered different approximations for the energy shift: in solid lines
Fig. 4. Total photon yield as a function of the cluster size obtained with the ionization potentials of Ref. 141(in bold lines) and with the values given in Ref. [5] (in thiti lines). In solid lines the energy shift is neglected, in dot-dashed lines the results correspond to the classical energy shift with Z = dm and in dotted lines the classical energy shift with Z = 1. Notice that the differences data (see Table 1) account for the different ratios Agh : Ag: and Agf; : Ag; obtained in each case.
between both sets of
M. Alducin, P. Apell/Nucl.
Instr. mdhfeth.
(A,?,) the energy level E,< z) does not change along the trajectory, in dotted lines (AE,) the energy shift is described by the classical image potential with Z = 1, and in dot-dashed lines (A&) the latter approximation but with Z = \/m. Briefly the features of the photon spectra shown in Figs. l-3 are the following. The energy range of the emitted photons, 0 < w 5 w,, is given by the difference between the Fermi level and the position of the cluster bound state at a distance close enough to the surface to allow the overlapping between the two states involved in the process. When the energy shift is neglected (AE = 0) the energy cutoff is obviously wc = E,(m) - 4, but it shifts to lower energies when a finite AE is included. There is a frequency o, at which the emission of photons is maximum. The value of o, for each cluster and for each approximation to the energy shift is closely related to the neutralization distance z, derived from Eq. (7). In fact, w, is equal to the maximum allowed energy of emitted photons, when the cluster is at a distance z, from the surface (w,,, N E, - E,( z,)). Finally, in the range of small frequencies (w < o,,,), the photon spectrum of Eq. (1) is linear in w:
g-_(*+o($)+...].
(9)
where wp is the plasmon frequency of the substrate. Next, let us compare the photon spectra obtained with the two sets of experimental JP. The smaller JP given by Alameddin et al. for the Ag: and Ag: clusters as compared to those by Jackschath et al. implies a shorter energy range of emitted photons. More precisely, the differences between the energy cutoff o, obtained in each case equal the differences in the JP, independently of the energy shift used. Furthermore, w, is shifted _ -0.4 eV in Ag: and - -0.5 eV in Ag: when the IP from Alameddin et al. instead of the JP from Jackschath et al. are used. Regarding the Ag: cluster, similar changes in o, and in w, are observed. Notice, however, that now the JP given by Alameddin et al. is bigger than that measured by Jackschath et al., and consequently,o, and w, shift towards higher energies with the first JP value. The total photon yield as a function of the cluster size is represented in Fig. 4. The different calculations are represented in the same kind of curves than those of Figs. 1-3. As can be expected from the large differences in the JP of Ag,, the shapes of the curves change strongly depending on the values chosen for JP. For instance, the ratio Agi : Ag: obtained with the data from Alameddin et al. varies either a factor 11 when the energy shift AE, is included or a factor 5 in the two other approximations. In contrast, the same ratio changes to a factor 2 and to a factor which is almost 1 if one takes the values given by Jackschath et al. A final remark to bring forward is the surprising dependence of the ratio Ag,’ : Agz on the approximation to the energy shift. Notice that whereas the
in Phys. Res. B I25 1199717-12
II
level shift in the AE, approximation is independent of the cluster, in the AE, approximation it depends on the IP of the cluster considered. As a consequence w, for Agd as compared to that for Ag c is a factor of 3 bigger in the first approximation and a factor of 2 in the latter. Hence, a crude estimation of the total photon yield from Eq. (9) (N a 0’) gives us a ratio 9: 4 in agreement with the ratio I 1 : 5 mentioned above. Finally, we point out that the total photon yields calculated for Agf and Ag: are a factor 2-3 larger in case of using the values from Jackschath et al.; whereas the photon yield for Ag: is a factor 2 larger with the JP given by Alameddin et al. These differences can be useful to decide which value of IP is more realistic for each cluster.
4. Conclusions We have studied the radiative neutralization of Ag:, Ag,’ and Agl clusters impinging in an Ag surface. To perform this calculation the ionization potentials measured experimentally with two different techniques are used. The differences between them are reflected in the photon spectra and in the total photon yield. First, the energy at which the emission of photons is maximum is shifted 0.4-0.5 eV. As a consequence the total number of photons collected can change by a factor 2-3 depending on the cluster studied. Furthetmom, the difference between the ionization potentials are reproduced almost directly in the range of energies when it is possible to induce emission of photons. The sensitivity to ionization potential energies is of the same order as the energy shift of the level. Hence both the ionization potential and the energy shift have to be considered in analyzing the photon spectra. Finally, the profile of the total photon yield versus the cluster size changes dramatically depending on the values of ionization potential used as input. For instance, in one case the ratios Ag: :Ag: and Agi :Agl are 10: 1, whereas in the other case they are 2: 1. All these features indicate that measurements of photon emission could be considered as a complementary technique in order to study different electronic properties of clusters and also in studies on the interaction of clusters with surfaces to understand how cluster properties are modified due to the surface.
Acknowledgments We thank Prof. R. Berndt for stimulating and suggestions. This work was supported by Natural Science Research Council. One of (M.A.) gratefully acknowledge a grant from Government (Eusko JaurIaritza).
discussions the Swedish the authors the Basque
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Insfr. and Meih. in Phys. Res. B 125 ((9971
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