Surface photoelectric effect induced by small clusters impinging on solid surfaces

Nuclear Instruments and Methods in Physics Research B 164±165 (2000) 662±670

www.elsevier.nl/locate/nimb

Surface photoelectric e€ect induced by small clusters impinging on solid surfaces M. Alducin a

a,*

, S.P. Apell

b,c,d

Departamento de Ingenierõa El ectrica, E.T.S. de Ingenieros Industriales y de Ingenieros de Telecomunicaci on, Universidad del Paõs Vasco, Alda. de Urquijo s/n, S-48013 Bilbao, Spain b Department of Applied Physics, Chalmers University of Technology, and G oteborg University, S-41296 G oteborg, Sweden c Departamento Fõsica de Materiales, Facultad de Quõmica, Universidad del Paõs Vasco, Apdo. 1072, 20080 San Sebasti an, Spain d Donostia International Physics Center, San Sebasti an, Spain

Abstract The contribution of the surface photoelectric e€ect to the emission of light is calculated within a free electron model assuming that small ionized Ag‡ n clusters (n ˆ 1; . . . ; 5) bombard a silver surface. The model proposed describes the creation of metal holes in the conduction band as a consequence of the resonant capture to the unoccupied ground state of the ionized cluster. Next, another metal electron ®lls the hole left and the excess energy is emitted as a photon, while the surface accounts for the di€erence in momentum. The photon spectra and, in particular, the trend of the photon yield vs the cluster size are very sensitive both to the ionization potential and to the energy shift of the cluster ground state. Photon spectra due to this process are compared to our previous calculations of photon spectra originated by a radiative capture process directly to the cluster ground state. We ®nd that emission of photons is mainly due to this later process. Ó 2000 Elsevier Science B.V. All rights reserved.

1. Introduction The interaction of particles with surfaces is a complex problem due to the di€erent processes taking place. The relevance of each process is ruled by the di€erent properties of the surface such as electronic structure, work function or position of the Fermi energy and the particle like charge state, energy levels or trajectory. Furthermore, as an additional complication all these properties are modi®ed by the interaction between the surface and the particle. On the other hand, this variety of *

Corresponding author. E-mail address: [email protected] (M. Alducin).

processes gave rise to a wide number of complementary techniques which provide information about the di€erent properties of the system [1±3]. The physical properties of clusters have attracted a lot of interest recently. The knowledge of their electronic structure to explain the abundance of certain sizes and the evolution from the atom to solid matter justify the di€erent investigations of the last years [4±12]. In many experiments, the measurements of the photon spectra due to the interaction of clusters with surfaces supply interesting information about both the cluster and the surface. In some of these techniques clusters are directly grown on the substrate [8±10], whereas in other cases clusters are deposited on the surface [11,12].

0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 1 1 8 5 - 4

M. Alducin, S.P. Apell / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 662±670

Analyzing the di€erent sources which could contribute to the emission of photons during the deposition or collision between ionized clusters and metal surfaces, the so called surface photoelectric e€ect is one of several possible mechanisms to compete with the direct radiative capture we studied previously [13]. It is of particular interest since the cluster neutralization is really a surface e€ect. This mechanism has a long history. In the early studies of photoemission, matter was treated as a free electron gas. Since a free electron cannot absorb a photon, it was necessary to ®nd a third body accounting for the conservation of energy and momentum. The surface as a momentum source was the third body ®rst proposed in [14±20], whereas the lattice contribution would be included later [21]. The ®rst case is known as the surface photoelectric e€ect. A review on this mechanism can be found in [22]. Our purpose is to analyze the relevance of the surface photoelectric e€ect when a beam of ionized silver clusters is impinging on metal substrates by comparing it to the radiative neutralization mechanism of Ref. [13]. The energetic representations of both processes are depicted in Fig. 1(a) (surface photoemission) and Fig. 1(b) (radiative neutralization). In the surface photoelectric e€ect a hole is created in the metal conduction band during the resonant neutralization of the Ag‡ n clusters. The hole left can be ®lled by another metal electron with higher energy. The energy liberated is mainly transferred to a second electron in an Auger event but could also be emitted as a photon; the surface being responsible for the conservation of momentum since we neglect the lattice contribution to the interaction potential. In radiative neutralization, a metal electron is captured to the cluster bound state and the excess energy is emitted as a photon. The theoretical model proposed to calculate the surface photoelectric e€ect is explained in Section 2. 2. Theory We assume a beam of ionized Ag clusters up to 5 atoms in size impinging perpendicular to an Ag substrate with a kinetic energy of 10 eV. The total radiated power per unit photon energy and unit

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Fig. 1. The Ag substrate is in the halfspace z < 0 and the cluster in the halfspace z > 0. The curve Ea …z† indicates the evolution of the cluster level when approaching to the surface. (a) Energy representation of the surface photoelectric e€ect studied in the present work. An electron from the substrate tunnels to the ground state of the cluster. The hole in the solid is ®lled by another electron in the metal, whereas the energy released during this transition is emitted as a photon of energy hx ˆ Ei ÿ Ea …z†. (b) Energy representation of the radiative  neutralization mechanism. A metal electron is directly captured to the cluster bound state and the excess energy is emitted as a photon of energy  hx ˆ Ei ÿ Ea …z† [13].

solid angle caused by the surface photoelectric effect, at the point r0 far away from the surface can be calculated from X d2 P 2 ˆ 20 c r2 jE…r0 ; x†j d…Ef ÿ Ei ÿ hx†; d…hx†dX i;f …1† where E…r0 ; x† is the radiated electric ®eld associated with the transition of one electron of the conduction band from the initial state jii to the unoccupied state jf i (the hole left in the substrate after cluster neutralization). In what follows we assume a p-polarized electric ®eld, since the current density is mainly induced in the direction perpendicular to the surface. In our previous study

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of the radiative capture process [13] the expression for p-polarized E…r0 ; x† was derived by using the reciprocity theorem of electrodynamics [23] Z 1 d3 r0 E ind …r0 ; r0 ; x† h^
E…r0 ; x† ˆ j0
j …i;j† …r0 ; x†;

…2†

where E ind …r0 ; r0 ; x† is the ®eld set up at r0 by a ^ placed at ®ctitious d-like current, j 0 ˆ j0 d…r ÿ r0 †h, the photodetector site r0 . The current density j …i;j† …r0 ; x† in Eq. (2),  eh  wi …r0 †rwf …r0 † ÿ wf …r0 †rwi …r0 † ; j …i;j† …r0 ; x† ˆ 2 i me …3† is due to the electron transition between the states jii and jf i of the conduction band. From electrodynamics [24] we get within the dipolar approximation that the induced electric ®eld E ind …r0 ; r0 ; x† created by j 0 is E ind …r0 ; r0 ; x† ˆ E0 tx cos h x^ ‡ E0

tx k0 cos h^z pt

…4†

inside the metal (z < 0) and E ind …r0 ; r0 ; x† ˆ E0 …1 ‡ rx † cos h x^ ‡ E0 …1 ÿ rx † sin h ^z

…5†

in the vacuum region (z > 0), where E0 ˆ

iqr0

i q j0 e 4p0 c r0

…6†

and the re¯ection and transmission coecients are rx ˆ

pt ÿ …x†p0 ; pt ‡ …x†p0

t x ˆ 1 ‡ rx ˆ

2pt : pt ‡ …x†p0

x2p N x2p ÿ ; x2 x2 ÿ x2o

eh3 i E0 kzi kzf Mjz …x; kzi ; kzf † h^
E…r0 ; x† ˆ 2 me j0 V0 Z ei …kki ÿkkf †
R ;  d2 R V

…9†

where …7†

p In these expressions, q ˆ x=c, pt ˆ …x†q2 ÿ k02 , p0 ˆ q cos h, and k0 ˆ q sin h; with h the angle of incidence de®ned from the normal to the surface and …x† the dielectric function of the substrate, which for Ag we model as …x† ˆ 1 ÿ

where xp ˆ 9:07 eV (corresponding to rs =a0 ˆ 3). N ˆ 5:44 and x2o =x2p ˆ 1:37 are ®tted values to reproduce the main loss peaks in an electron energy loss spectrum for an Ag substrate [25]. Since we are interested in a frequency range, where …x† is negative and we are below the interband threshold (4 eV) it is enough to consider a real …x†. Considering the range of energies involved in this particular problem (up to 3.3 eV below the d-band onset), the Ag substrate is well-described within the free metal electron model in which the lattice contribution is neglected. Notice that if we were studying a bulk problem, the radiated ®eld E…r0 ; x† of Eq. (2) would be zero within this approximation, as can be easily obtained after replacing j …i;j† …r0 ; x† by Eq. (3) and integrating. However, the surface can provide momentum, making possible the existence of a ®nite current density even if the lattice is not included. The question now is how to mimic the surface potential. Since our purpose is to bring out the main features of the surface photoelectric e€ect taking place during the interaction of clusters with metal surfaces, we use the step potential model as a ®rst approximation to this problem. Describing the Ag surface by a step potential barrier model of height V0 ˆ EF ‡ / with a Fermi energy EF ˆ 5:49 eV and a work function / ˆ 4:30 eV, the radiative ®eld E…r0 ; x† in Eq. (2) becomes

…8†

Mjz …x; kzi ; kzf † ˆ

kzi2 ‡ kzf2 ‡ 2 kzi0 kzf0 kzi2 ÿ kzf2 ! kzf0 ÿ kzi0 tx k0 …x† cos h: ‡ 0 kzi ‡ kzf0 pt

…10†

The subscripts i and f indicate initial and ®nal component of the wave states. kk is the parallel  p vector. kz and kz0 ˆ 2 V0 ÿ kz2 are the perpendicular components of the wave vector inside (z < 0) and outside (z > 0) the metal. V is the normalization volume of the free electron wave functions.

M. Alducin, S.P. Apell / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 662±670

Now, the thing left to calculate of the radiated power in Eq. (1) is the states involved in the process. The initial state should verify: ®rst, the condition of being an occupied state of the conduction band, i.e., ki 6 kF and secondly, the conservation of the energy during the radiative hx. Regarding the ®nal decay, hence Ei ÿ Ef ˆ  state, the hole created in the substrate as a consequence of the neutralization of the ionized clusters can decay via Auger process or photon emission. Therefore, the unoccupied states jf i ®lled by photon emission are only a fraction of the holes created. The way to proceed is to solve the corresponding rate equation system. However, for slow velocities and since the hole ®lling rate is faster than the hole production rate under normal experimental conditions, the hole created in the substrate is occupied before the cluster moves closer to the surface. Hence, the adiabatic regime appears as a good approximation to our problem (dnh =dt ' 0). In fact, we checked that even for our worst case (Ag‡ 3 ) the error is less than 10%. Based on these results and for the sake of simplicity, the problem is henceforth formulated assuming adiabatic conditions. Thus, following the method of Mahan [26], one obtains that the fraction of holes available is nh …z† ˆ n‡ …z†

1=s…z† : 1=sA …z† ‡ 1=ss …x; z†

…11†

In this expression n‡ …z† is the density of available ionized clusters. s…z† is the mean lifetime of the empty ground state in the cluster. sA …z† and ss …x; z† are the mean lifetimes of the substrate hole due to Auger and photon emission (surface photoelectric e€ect), respectively. Both n‡ …z† and 1=s…z† were already calculated in [13] assuming resonant capture as the main process accounting for the neutralization of the Ag‡ n clusters. Such an assumption appeared as a good approximation in the particular system under study. Thus, 1=s…z† is taken as the resonant capture rate 1=src …z†. Finally, ss …x; z†  sA …z† at distances where nh …z† is di€erent from zero. Thus, the expression to evaluate the total number of photons emitted per unit photon energy and unit solid angle is

d2 N ˆ d…hx†dX

Z

665

dz n‡ …z† sA …z† Ns …x; z†; v? …z† src …z†

…12†

where v? …z† is the velocity component perpendicular to the surface. Since the projectiles are very massive, the acceleration due to the image potential can be neglected, and the velocity is taken as a constant along the important part of the trajectory, v? …z† ˆ v? . Ns …x; z† is the number of emitted photons per substrate hole, unit photon energy, time, and solid angle. Ns …x; z† is obtained by inserting Eq. (9) into Eq. (1) and dividing the radiated power by the photon energy hx, Ns …x; z† 1 ˆ 4p0



e h me

2

h A x m e 2 p 2 c3

Z

dkkf …2p†

2

Z

2 dkzf kzf2 kzi0 Mjz …x; kzi0 ; kzf † 2p V02 ! 2 h2 kF2 h kzf2 h ÿ hx ÿ 2me 2me 



h2 kF2 h ÿ …Ea …z† ‡ hx† 2me   2 2 h kF h ÿ Ea …z† : 2me



…13†

In this equation A isq the quantization area of the  2 substrate and kzi0 ˆ kzf ‡ 2me x=h. Ea …z† is the energy level of the cluster bound state wa referred to the bottom of the conduction band, Ea …z† ˆ V0 ÿ Ea …1† ‡ DE…z†. We take the values for the vertical ionization potential Ea …1† from the experimental values of [27]. The dependence on z expressed in the term DE…z† is due to the interaction of the cluster with the surface. Here DE…z† is described by the classical image potential   1 Z e2 e2 ÿ …14† DE…z† ˆ 4p0 2…z ÿ zI † 4…z ÿ zI † with a core charge Z ˆ 1. This approximation to the level shift is referred to as DE1 in [13]. zI ˆ 0.96 a.u. is the distance of the image plane to the jellium edge [30].

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The integral over ®nal states (dkkf ; dkzf ) is calculated including that the cluster bound state has a ®nite width. In particular, we use the mean lifetime h=2src …z†. In the due to resonant capture, Ea …z†   limit Ea …z†  h=src …z†, the surface emission rate shows a linear dependence on the resonant capture rate, Ns …x; z†  f …x†

1 src …z†

…15†

where f …x† ˆ

 2 Z ka2 1 A e h x dy 4p0 …2p†4 me c3 0 V02 r 2me x y ‡ y2  h ! 2 1=2  2me x 1=2 ‡y ;y  Mjz x h 

…16†

is a function with only a weak dependence on z as compared to the exponential decay of 1=src …z†. In this expression ka is the wave number associated with the energy Ea …1†. Finally, the decay of the hole due to an Auger process is estimated in the free electron model as [28]: 1 ˆ sA …z†

p 2 3 p xp …EF ÿ Ea …z††2 : 128 EF2

…17†

This expression is a good approximation even for a non-free electron metal as Ag, provided the energies involved in the process are below the d-band onset of 4 eV. The inclusion of improvements such as d-states screening and density of states increases, the lifetime of the hole about 30% [29]. According to Eq. (17) the closer a hole is to the Fermi level, the smaller is the probability to decay by an Auger process. Hence, the Auger decay should be faster when the holes are created by those clusters with larger ionization potentials (Ag‡ 1;2 ). In particular, 1=sA …z† is of the order 100± 340 meV for Ag‡ 1;2 (we take Ea …1† ˆ 7:57; 7:60 eV, respectively) and 10±150 meV for Ag‡ 3;4;5 (we take Ea …1† ˆ 6:20; 6:65; 6:35 eV).

3. Discussion The photon spectra and the photon yield are calculated for a photodetector located at h ˆ 60° from the normal to the surface. Fig. 2 shows the photon spectra, i.e., the number of photons per cluster, unit photon energy, solid angle, and area due to the surface photoelectric e€ect for Ag‡ n (n ˆ 1; . . . ; 5 atoms). The spectra show some similarities to those obtained in the radiative capture problem. First, due to the conservation of energy during the process there is an energy hxc for each cluster above which no photons are emitted. At any distance to the surface, the maximum energy of the emitted photons corresponds to the transition of an electron from the Fermi level to the substrate hole left after cluster neutralization, hx ˆ EF ÿ Ea …z†. Since the energy level is shifted upwards as the cluster approaches to the surface (see Fig. 2), this maximum energy decreases as z decreases. Thus, hxc corresponds to the maximum energy released when the cluster is close enough to create the ®rst holes in the substrate. Secondly, for each cluster the emission of photons is maximum at an energy hxm di€erent from the energy cuto€ hxc . This is a consequence of the level shift DEa …z†. Despite Ns …x; z† increasing with x, the total number of photons emitted with an energy x is according to Eq. (12), the result of weighting for this particular x the contribution of Ns …x; z† along the trajectory. And as explained above, the most energetic photons can only be emitted when the cluster is far away from the surface; but here nh …z† is almost zero and as a consequence the photon emission is maximum at xm < xc . We see that as in the radiative neutralization process, hxc and hxm are ruled by the ionization potential (IP). Hence, both Ag‡ 1 (Ea …1† ˆ 7:57 eV) and Ag‡ 2 (Ea …1† ˆ 7:60 eV) are responsible for photon emission in a larger range of energies (up to 2.6 eV), whereas for Ag‡ 3 (Ea …1† ˆ 6:20 eV), only photons up to 1.2 eV can be emitted. xm can be roughly estimated by analyzing the z dependence of both nh …z† and Ns …x; z†. From Eq. (15), the latter is mainly ruled by the exponential decay of 1=src …z†. Taking into account that nh …z† shows a well de®ned maximum at the

M. Alducin, S.P. Apell / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 662±670

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Fig. 2. Photon spectra of the di€erent Ag‡ n clusters as a function of the emitted photon energy (eV). The range of energies at which there is emission of photons is ruled by the ionization potential of each cluster, 0 <  hx 6 EF ÿ Ea …z† (see Fig.1). Hence, photon ‡ ‡ ‡ emission at the highest energies is induced by those clusters with larger ionization potential (Ag‡ 1;2 ), followed by Ag4 , Ag5 and Ag3 . ‡ The dotted line corresponds to the shape of the photon spectrum of Ag1 calculated in [13] assuming radiative neutralization process. The di€erent nature of the two mechanisms is essentially re¯ected in the di€erent x-dependence at small energies.

neutralization distance zn , de®ned as the point at which dn‡ =dz ˆ 0, Eq. (12) can be estimated as d2 N ˆ d…hx†dX

Z

dz nh …z† Ns …x; z† v?

 nh …zn † Ns …x; zn †

…18†

and is thus a direct measure of the number of holes at zn . Next, let us compare the contribution of the surface photoelectric e€ect and the radiative neutralization process to the emission of photons. With this purpose, a dotted line reproduces in Fig. 2 the shape of the photon spectrum due to the radiative neutralization of Ag‡ 1 , previously calculated in Ref. [13]. The kinetic energy, position of the photodetector and energy shift are the same in both mechanisms. We remark that a quantitative comparison between both spectra is not possible before correlating them with details of the cluster beam cross-section. The di€erent nature of the two photon emission mechanisms is directly re¯ected in the di€erent behaviour of each spectrum with the emitted photon energy. This is most easily seen

at low energies, hx  hxm . In the surface photoelectric e€ect, the asymptotic behaviour of the photon spectrum is mainly ruled by the square modulus of Mjz …x; kzi0 ; kzf † which appears in Ns …x; z†. In the limit x ! 0, the second term (see 0 Eq. (10)) is negligible since kzi0 ! kzf0 , and only the current density inside the metal contributes, that is, 2 2 tx k0 h…kzf2 ‡ kzf02 † Mj …x; kzi0 ; kzf †  z pt me x ! ! x2 x2  2 1‡O ‡


: xp x2p …19† Neglecting the x dependence of the square root in the integral of Eq. (16) one gets ! ! d2 N x3 x2  1‡O ‡


d…hx†dX x3p x2p for hx ! 0 ;

…20†

whereas in Ref. [13], we found that the photon spectrum in the direct radiative process behaves as

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d2 N x  d… hx†dX xp

x2 1‡O x2p

for hx ! 0:

!

! ‡


…21†

At higher energies, photon spectra scale as xc with 3 < c < 4 for the surface photoelectric e€ect and 2 < c < 3 for the radiative neutralization event. Furthermore, the energy range of emitted photons is slightly smaller (0.5 eV) in the surface emission e€ect than in the radiative neutralization process. This is due to the smaller number of available holes for the surface photoelectric e€ect. At large distances, the Auger transition rate is faster than the surface emission rate and holes left after cluster neutralization are mainly ®lled by Auger processes. The total photon yield per cluster is calculated by integrating each photon spectrum in Fig. 2 and multiplying it by the appropriate area A in Eq. (13). This area appears since the ®nal state or substrate hole is an extended state parallel to the surface making the probability for the surface photoemission e€ect proportional to the quantization area. However, the resonant neutralization of clusters provides the mechanism of producing the holes in the substrate. In particular, only one hole can be created per cluster. This restricts the possible area to a ®nite value. Neglecting the level broadening of the cluster bound state, the parallel wave number of the hole, kjj , may take values in the interval 0 < h2 kjj2 =…2me † 6 Ea …z†. The number R of states in the parallel direction is Njj ˆ occ A= 2 …2p† dkjj ˆ Aka2 =4p. This allows us to estimate the quantization area for each cluster as A ˆ 4p=ka2 by taking Njj ˆ 1. The total photon yield per cluster as a function of the cluster size using the above is shown in Fig. 3. The solid line corresponds to the total yield obtained when the energy shift of Eq. (14) is included, whereas in the dashed line the energy shift is neglected, DE…z† ˆ 0. The inclusion of the energy shift reduces the total yield by a factor of 2 to 3, but in both cases, the total yield due to the surface photoemission e€ect shows the same odd± even oscillations we got for the radiative capture process. Brie¯y, the dependence of the total yield on the number of atoms in the cluster re¯ects di-

Fig. 3. Total photon yield per cluster as a function of the cluster size: for the solid line the classical energy shift of Eq. (14) is used and for the dashed line the energy shift is neglected (DE…z† ˆ 0). The photon yield decreases by a factor of 2 to 3 when the energy shift is included. Except for the dimer, the odd±even oscillations of the ionization potential are reproduced ‡ in the total yield. The Ag‡ 1 :Ag2 anomaly is a consequence of the Pauli Principle. The dash-dotted line corresponds to the total yield per cluster due to the radiative neutralization process [13]. The contribution of this process to the total photon yield is larger than the contribution of the surface photoelectric e€ect. Nevertheless, the trend of the total photon yield is similar in both mechanisms of photon emission.

rectly the odd±even oscillations of the IP except for the dimer. In this particular case, we ®nd that despite the IP of Ag‡ 1 is slightly smaller than the IP of Ag‡ 2 , the total yield is around a factor of 2 smaller for the dimer. The explanation, as in Ref. [13], is related to the Pauli Principle. Since the ground state in Ag‡ 1 is empty, both electron with spin up and down can be captured. However, since the ground state of Ag‡ 2 is a singlet state, either electrons with spin up or spin down can ®ll the unoccupied hole in the cluster. Thus, the fraction of holes per cluster created in the substrate is a ‡ factor of 2 larger for Ag‡ 1 than for Ag2 . In addition, the cluster level width used to calculate Ns …x; z† is also double for Ag‡ 1 . As a result the di€erence in IP between the atom and the dimer is completely masked by spin considerations. Finally, let us compare the contribution to the total photon yield of the radiative neutralization mechanism and the surface photoelectric e€ect. The photon yield due to radiative neutralization

M. Alducin, S.P. Apell / Nucl. Instr. and Meth. in Phys. Res. B 164±165 (2000) 662±670

processes is plotted in Fig. 3 with a dash-dotted line. This process dominates the total photon yield. However, the surface photoelectric e€ect will be enhanced by using a more reliable description of the surface potential, as it was already done in the radiative neutralization process. Compared to the step potential barrier, the wave functions given by the Jenning's potential [30] are more extended in the vacuum region [31]. Thus, the contribution of the external ®eld (see Eq. (10)) will be more important than in the present model with the step potential barrier. As a consequence, the photon spectra and the total yield will be probably enhanced. Moreover, the surface photoelectric e€ect is very sensitive to the electric ®eld acting in the vicinity of the surface, de®ned as the jellium edge. Our model uses a classical treatment of the electric ®eld, in which the internal ®eld abruptly increases to the external ®eld. It will be desirable to have a local treatment of the electric ®eld, but for the moment, it is beyond the scope of the present contribution. 4. Summary The surface photoemission e€ect taking place when ionized Ag‡ n clusters up to 5 atoms in size collide with an Ag substrate has been studied theoretically. This mechanism is compared to the radiative neutralization process, we had studied previously in [13]. The trend of the photon spectra shows similarities: the energy at which photon emission is maximum and the energy range of the emitted photons. These features are mainly related to the ionization potential of each cluster. However, the energy cuto€ is slightly shifted to lower energies in the surface emission e€ect (0.5 eV) as a consequence of Auger processes competing in the hole ®lling. Moreover, the di€erent nature of the radiative neutralization event and the surface photoelectric e€ect is re¯ected as a di€erent dependence of the photon spectra on the photon energy, especially at low energies. At energies below the energy at which emission is maximum, photon spectra increase faster in the surface emission e€ect than in the radiative neutralization process.

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Comparing the total photon yield induced by both mechanisms, the radiative neutralization process appears as the main source of photon emission. However, a more reliable description of the surface potential barrier could enhance the surface photoelectric e€ect. Calculations in this direction are in progress. Finally, the surface photoelectric e€ect is very sensitive to the electric ®eld around the surface, providing an experimental technique to measure the local electric ®eld at the surface. Acknowledgements This work is supported by the Swedish Natural Science Research Council and Iberdrola S.A. References [1] H.D. Hagstrum, G.E. Becker, Phys. Rev. B 8 (1973) 107. [2] M. Landolt, R. Allenspach, D. Mauri, J. Appl. Phys. 57 (1985) 3626. [3] C. Rau, K. Waters, N. Chen, Phys. Rev. Lett. 4 (1990) 1441. [4] W.A. de Heer, Rev. Mod. Phys. 65 (1993) 611. [5] U. Hild, G. Dietrich, S. Kruckeberg, M. Lindinger, K. Lutzenkirchen, L. Schweikhard, C. Walther, J. Ziegler, Phys. Rev. A 57 (1998) 2786. [6] J. Lerme, B. Palpant, B. Prevel, M. Pellarin, M. Treilleux, J.L. Vialle, A. Perez, M. Broyer, Phys. Rev. Lett. 80 (1998) 5105. [7] C.M. Grimaud, L. Siller, M. Andersson, R.E. Palmer, Phys. Rev. B 59 (1999) 9874. [8] H. Hovel, B. Grimm, M. Pollmann, B. Reihl, Phys. Rev. Lett. 81 (1998) 4608. [9] D. Martin, J. Jupille, Y. Borensztein, Surf. Sci. 404 (1998) 433. [10] I. Rabin, W. Schulze, G. Ertl, J. Chem. Phys. 108 (1998) 5137. [11] S. Fedrigo, W. Harbich, J. Buttet, Phys. Rev. B 58 (1998) 7428. [12] M. Pattabi, K.M. Rao, S.R. Sainkar, M. Sastry, Thin Solid Films 338 (1999) 40. [13] N. Lorente, R. Monreal, M. Alducin, P. Apell, Z. Phys. D 41 (1997) 143. [14] H. Fr ohlich, Ann. Physik 7 (1930) 103. [15] R. Mitchell, Proc. Roy. Soc. (London) A 146 (1934) 442. [16] R. Mitchell, Proc. Cambridge Phil. Soc. 31 (1935) 416. [17] R. Mitchell, Proc. Roy. Soc. (London) A 153 (1935) 513. [18] R.E.B. Makinson, Phys. Rev. 75 (1949) 1908. [19] M.J. Buckingham, Phys. Rev. 80 (1950) 704. [20] A. Meesen, J. Phys. Radium 22 (1961) 308.

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