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Ionization by ion impact at grazing incidence on insulator surface
Nuclear Instruments and Methods in Physics Research B 203 (2003) 62–68 www.elsevier.com/locate/nimb
Ionization by ion impact at grazing incidence on insulator surface M.L. Martiarena *, V.H. Ponce
1
Division Colisiones Atomics, Centro At omico Bariloche, Comisi on Nacional de Energıa, At omica, Instituto Balseiro, Universidad Nacional de Cuyo, 8400 San Carlos de Bariloche, Rıo Negro, Bariloche, Argentina
Abstract We have calculated the energy distribution of electrons produced by ionization of the ionic crystal electrons in grazing fast ion–insulator surface collision. The ionized electrons originate in the 2p F orbital. We observe that the binary peak appears as a double change in the slope of the spectra, in the high energy region. The form of the peak is determined by the initial electron distribution and its position will be affected by the binding energy of the 2p F electron in the crystal. This BEP in insulator surfaces will appear slightly shifted to the low energy side with respect the ion–atom one. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 34.50.Dy; 79.20.Rf; 79.60.Dp; 68.49.)h Keywords: Ion–surface interaction; Electron emission; Insulator
1. Introduction The energy distribution of electrons emitted during the scattering of fast grazing ions from surfaces has been the subject of intense research activity during the last years. Recently, a rapidly increasing number of works consider the electron emission during the bombardment by fast particles of the surface of insulators showing a number of interesting features. Therefore, it will be of importance to understand the detailed interaction
* Corresponding author. Tel.: +54-2944-445220; fax: +542944-445299. E-mail address: [email protected] (M.L. Martiarena). 1 CNEA.
mechanism [1]. However, there is still a lack of detailed experimental information and theoretical understanding of the energy and angle distribution of electrons ejected from insulator surfaces. The scarcity of experimental data and the complexity of the physical processes involved have prevented the development of a comprehensive theoretical picture. This prompted our current studies aimed at identifying some physical mechanisms acting on electron emission in ion-insulators collisions which are well known for metal surfaces. In this case, the electron spectra have different characteristics depending on the electron energy and observation angles and on the type and roughness of the metal surfaces. In the low energy region the energy distribution presents a maximum around 3–9 eV (see Fig. 1(e)) which increases and
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)02175-4
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
suffers a small displacement to lower energies for larger observation angles [2–5]. For energies close to ECE ¼ v2p =2 (vp is projectile velocity) and observation angles around the direction of the ion specular reflection other structures appear whose shape and energy position depend on surface topography [6–10]. For rough surfaces the known convoy electron peak (CEP) is observed at ECE , while for less rough surfaces a broader and shifted structure is also observed at higher energies [11] (see Fig. 1(c)). When the metal surface is smooth enough, this last structure becomes the principal characteristic of the electron spectra, since the CEP becomes unobservable (see Fig. 1(b)). A similar structure has been observed during the 60– 100 keV Hþ grazing bombardment of LiF surface (see Fig. 1(d)), where now a peak appears with the maximum at an energy EM lower than ECE [12].
63
This result was discussed in terms of the attractive (track of positive charges from ionized F ions) and the repulsive surface-induced potential. At higher energies, a broad peak is observed and identified as a binary peak (BEP) [13], well known for ion–gas collisions [14,15]. The BEP arises from hard collisions between the impinging ion and target electrons. From energy and momentum conservation for the projectile-electron subsystem it is possible to estimate the position of the binary peak as kf ¼ 2vp cosðhÞ (kf is the final electron momentum, vp the ion velocity and h the electron emission angle). For grazing collisions on metals surfaces, the maximum of the binary structure for observation angles close to the direction of the ion specular reflection, appears at an energy lower than 2v2p , the value of the maximum in the ion–gas case [7–9].
Fig. 1. Electron spectra for different types and roughness of the surfaces versus ðve =vi Þ2 (ve;i electron and ion velocity): (a) hi , 0.34° and ho , 5.7° [9]; (b) hi , 1.0° and ho , 1.0° [4]; (c) hi , 1.0° and ho , 1.0° [11]; (d) hi , 1.0° and ho , 1.0° [12]; (e) hi , 1.3° and ho , 10.0° [10]. The vertical line show the position of the convoy electron peak (CEP); the position of the classic BEP would be ðve =vi Þ2 ¼ 4 (see text).
64
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
It is very interesting to note that for special conditions on the ion energy, the projectile incidence and electron observation angles and the surface roughness, it is possible to observe in metals the convoy electron peak, the shifted convoy and the binary peak coexisting in the same spectra (Fig. 1(a)). In this work, starting from concepts of atomic collisions in the gas phase, we study the binary electron production due to single electron excitation by the direct Coulomb interaction between the incident ion and anions (F ) of the ionic crystal. The fact that F belongs to an LiF surface is accounted for through the shift of the 2p electron binding to fit with the 2p valence band of the insulator.
2. Theory The time dependent Hamiltonian for grazing collisions of a bare charge Zp with an ionic crystal surface is H ðtÞ ¼ Hi þ Vi ðtÞ: In the entry channel the electron bound to the surface is described by Hi ¼
p2 þ Vs ðrÞ; 2
ð1Þ
while the projectile–electron interaction is Vi ðr; tÞ ¼ VC ðr RðtÞÞ þ VPeI ðr; tÞ þ Vlocal ðr; tÞ;
ð2Þ
where r and RðtÞ are the electron and projectile position, respectively (see Fig. 2). We assume that the ion moves parallel to the surface along a classical trajectory and we describe the collision in the impact parameter approximation ~ðtÞ ¼ q^ vp ; R ez þ t~ ex and q is the distance of closest with ~ vp ¼ vk~ approach, equal in this case to the impact parameter. The origin of the coordinate system is chosen at a halide ion on the surface with the zaxis normal to the surface and the x-axis along the ion direction of motion.
Fig. 2. Reference frame for the description of projectile interaction with halide surface.
VPeI ðr; tÞ is the interaction between the electron and the image of the projectile while VC ðr 1 RðtÞÞ ¼ jrRðtÞj is the Coulomb interaction between the electron and the projectile itself. In contrast to metal surfaces the typical decay times for excess surface charges on insulators are far too long to compensate local charge accumulations at the collision time-scale. As a consequence the ion is followed by a trail of surface charges. This excess of surface charges produces the Vlocal ðr; tÞ potential. In this work, we will study the high energy region of electrons ionized by fast beams from ionic crystals. In a first approach, we consider only the Coulomb interaction in the perturbed potential Vi ðr; tÞ, and calculate the energy distribution of the emitted electrons. Considering a time-dependent perturbation X Wðr; tÞ ¼ an ðtÞuin ðrÞeii t ; ð3Þ n
where dak ðtÞ X ¼ i an ðtÞ < ufk ðrÞjVC jun ðrÞ > eiðf i Þt : dt n ð4Þ In first-order Born approximation the transition amplitude is Z 1 ak ð1Þ ¼ i dthufk ðrÞjVC ðr RðtÞÞj 1
uinlm ðrÞieiðf i Þt
ð5Þ
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
with hufk ðrÞjVC ðr ¼
Zp 2p2
Z
Then Zp ak ð1Þ ¼ i p
F2p1;k ðqÞ ¼
RðtÞÞjuinlm ðrÞi
dq iq q e dðDE q vÞFnlm;k ðqÞ q2
65 ci r
dreiQ r rY1;1
ðh; /Þ1 F1 ðig; 1; iðk r þ krÞÞ rffiffiffiffiffiffi X i 3 i ¼ 3 N ðgÞ iai ½Ix iIyi ; 2p 8p i
dq3 iq ðqþvtÞ e Fnlm;k ðqÞ: q2
Z
X 1 N ðgÞ ai 2p3 i
Z
ð6Þ
with form factor, Fnlm;k ðqÞ ¼ hufk ðrÞjeiq r juinlm ðrÞi. We describe the initial bound state considering the Roothaan–Hartree–Fock atomic wave function uinlm ðrÞ [16] for F and the initial energy i corresponding to the mean value of the 2p valence band for the fluoride crystal X ap rnp 1 ecp r Ylm ðh; /Þ: ð7Þ uinlm ðrÞ ¼
where for Z cir F0;k ðqÞ ¼ dreiQ r F1 ðig; 1; iðk r þ krÞÞ; 1
i d F0;k ðqÞ Qj dQj
i8pc 4Qj C g c ik ¼ 2 i Aig þi Cþ i Mj ; D A cA D
Iji ¼
ð13Þ
The final hydrogenic continuum state is
1 d F ðqÞ 2s 0;k c2s i dci
2s 8pc2s 4ci g 1 ig i B A C ¼ þ E ; þ i A D2 D c2s i
Ji ¼
1 ð2pÞ
3
N ðgÞeik r 1 F1 ðig; 1; iðk r þ krÞÞ;
N ðgÞ ¼ epg=2 C½1 ig; g ¼
Zt : k
ð8Þ
Using the Nordsieck integral [17] we obtain Fnlm ðqÞ analytically " 5 X 1 N ðgÞ a2s F2s;k ðqÞ ¼ i Y0;0 ðh; /Þ ð2pÞ3 i¼3 Z 2s dreiQ rci r r1 F1 ðig; 1; iðk r þ krÞÞ
K i ¼ F0;k ðqÞ ¼ A¼1þ2
2 X
dre
iQ rc2s r i
F1 ðig; 1; iðk r þ krÞÞ ; ð9Þ
F2p0;k ðqÞ ¼
ð2pÞ
N ðgÞ 3
X
Z ai
dreiQ rci r rY1;0 ðh; /Þ
i
1 F1 ðig; 1; iðk r þ krÞÞ rffiffiffiffiffiffi X i 3 i Iz N ðgÞ ai ¼ 3 4p ð2pÞ i and
D ¼ Q2 þ c2i ;
S ¼ Q k ici k;
ici þ k i ; cA
Mj ¼
2 ½ð1 AÞQj þ kj ; D ð17Þ
#
Z
1
ð15Þ
a2s i Y0;0 ðh; /Þ
i¼1
S ; D
8pci ig A C D2
ð14Þ
ð16Þ C ¼1þg
þ
ð12Þ
with Q ¼ q k is
p
ufk ðrÞ ¼
ð11Þ
ð10Þ
2 ½ik þ ci ðA 1Þ; D g E ¼ 2 2 ½kðBci þ AÞ þ iBc2i : ci A B¼
We calculate the distance of closest approach q considering the universal ZBL (Ziegler–Biersack– Littmark) [19] screening function , with a screening length aiZBL ¼ 0:8854=ðZp0:23 þ Zi0:23 Þ. For an ionic crystal the planar average potential is produced by two different ion species, so it is necessary to consider the different lattices of anions i ¼ a and cations i ¼ c:
66
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
UZBL ¼ 2pZp
X aj bj j a
c
ðZa nas aaZBL ebj z=aZBL þ Zc nas acZBL ebj z=aZBL Þ:
3. Results and discussion For the collision of Hþ on LiF we use a single exponential expression U ðzÞ ¼ aebz with a ¼ 0:509 a.u. b ¼ 0:88 a.u.1 [18]. In Fig. 3, we present the results obtained for 300 keV Hþ impinging on an LiF surface at an incidence angle (hi ) of 0.34° and an observation angle (ho ) of 5.7°. We consider the ionization of the F 2p and 2s electrons with a binding energy of 15 and 34 eV, respectively. We observe that the binary peak only appears as a double change in the slope of the
spectra. The maximum of this binary peak is observed in a logarithmic graphic at EBLiF 500 eV. Together with that result we plot the experimental data [9] and the theoretical [4] binary electron distribution for a SnTe surface bombarded with 300 keV protons, that peaks at 530 eV. It is seen that the differences between metal and insulator targets affect not only the position but also the form of the binary peak. These effects are associated to the contribution of the 2p0 states. In particular there is a dip on the binary sphere for electrons ionized from the 2p0 initial state. We observe that the maximum of the binary peak in ion–LiF surface collisions appears shifted to lower energies with respect to the ion–atom 2 BEP EBc ¼ ð2vi Þ =2 ¼ 653:42 eV, and in this first Born approximation it has a smooth structure resembling the 2p character of the peak (Fig. 4).
Fig. 3. Emission probability versus electron energy for 300 keV Hþ scattering from different surfaces: LiF (––); and SnTe (– –) [4] hi , 0.34° and electron observation angle ho , 6.3°. The dots correspond to the experimental data for the SnTe surface [9].
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
67
Fig. 4. Emission probability and its first derivative versus electron energy for 300 keV Hþ scattering from LiF hi , 0.34° and electron observation angle ho , 5.7°.
Fig. 5. Emission probability versus electron energy for 300 keV Hþ scattering from LiF hi , 0.34 and different observation angles: (- - -) 2s; (. . .) 2p0 ; (- - -) 2p1 ; (-
-
-) total 2p; (––) total 2p þ 2s.
68
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
SnTe LiFðVlocal ¼ 0Þ
EB (eV) 530 590
DE ¼ EBc EB (eV) 123.42 63.42
In Fig. 5 we show for Hþ (300 keV) impinging on LiF the dependence of the binary electron distribution with the observation angle. As in ion– atom collisions the angular distribution of the binary peak results in a binary sphere, so if the observation angle increases, the BEP is shifted to lower energies. We show in Fig. 5 the contribution of each initial state and observe the different intensities between them. The shift of the BEP peak with respect to the classical result DE ¼ EBc EB gives information on the target characteristics in the ionization process. A characteristic of the ion-insulator crystal collision, that should be of interest to incorporate in future studies, is the excess of surface charges produced by the projectile along its glancing trajectory which give rise to the potential Vlocal ðr; tÞ. The intensity of this potential will increase the binding energy of the target electron that will shift the peak position with respect the value calculated here. The presence of the track of surface charges could also affect the low energy part of the double differential electron distribution. The track will shift the bottom of the LiF conduction band and change the minimum energy of the allowed electron emission together with the position of the low energy maximum observed in metals. To analyze these effects it will be necessary to consider a more realistic perturbation potential and distorted final state wave function. Nevertheless the ionic character of the crystal will produce a higher electron distribution in the low energy region of the spectra than that observed in ion–metal collision. It will be of interest to have experimental results for both the high and low energy regions of electrons emitted in ion-insulator surface collisions, in
order to test the reliability of initial target electron states and the effect of the track on these initial states and in the outgoing ionized electrons.
Acknowledgements We acknowledge financial support from ANPCyT (PICT 03-6325) and Fundaci on Antorchas.
References [1] H. Winter, Prog. Surf. Sci. 63 (2000) 177. [2] C. Rau, K. Walters, N. Chen, Phys. Rev. Lett. 64 (1990) 342. [3] H. Winter, NATO Advanced Research Workshop, Italy, 1992. [4] M.L. Martiarena, E.A. Sanchez, O. Grizzi, V.H. Ponce, Phys. Rev. A 53 (1996) 895. [5] F.J Garcia de Abajo, Nucl. Instr. and Meth. B 79 (1993) 15. [6] G. Gomez, E. Sanchez, O. Grizzi, M. Martiarena, V.H. Ponce, Nucl. Instr. and Meth. B 122 (1997) 171. [7] A. Koyama et al., Phys. Rev. Lett. 65 (1990) 3156. [8] A. Koyama, Nucl. Instr. and Meth. B 67 (1992) 103. [9] K. Kimura, M. Tsuji, M. Mannami, Phys. Rev. A 46 (1992) 2618. [10] A. Hegmann, R. Zimny, H.W. Ortjahann, H. Winter, Z.L. Miskovic, Europhys. Lett. 26 (1994) 383. [11] E. Sanchez, O. Grizzi, M.L. Martiarena, V.H. Ponce, Phys. Rev. Lett. 71 (1993) 801. [12] G.R. Gomez, E. Sanchez, O. Grizzi, V.H. Ponce, Phys. Rev. B 58 (1998) 7403. [13] M.L. Martiarena, E. Sanchez, O. Grizzi, V.H. Ponce, Nucl. Instr. and Meth. B 90 (1994) 300. [14] P.D. Faintein, V.H. Ponce, R.D. Rivarola, Phys. Rev. A 45 (1992) 6416. [15] M. Landolt, R. Allenspach, D. Mauri, J. Appl. Phys. 57 (1985) 3626. [16] E. Clementi, C. Roetti, At. Data Nucl. Data Tables 14 (1974) 177. [17] A. Nordsieck, Phys. Rev. 93 (1954) 785. [18] C. Auth, H. Winter, Phys. Rev. A 62 (2000) 12903. [19] J.F. Ziegler, J.P. Biersack, U. Littmark, in: The Stopping and Range of Ions in Solids, Vol. 1, Pergamon Press, New York, 1985.
Ionization by ion impact at grazing incidence on insulator surface M.L. Martiarena *, V.H. Ponce
1
Division Colisiones Atomics, Centro At omico Bariloche, Comisi on Nacional de Energıa, At omica, Instituto Balseiro, Universidad Nacional de Cuyo, 8400 San Carlos de Bariloche, Rıo Negro, Bariloche, Argentina
Abstract We have calculated the energy distribution of electrons produced by ionization of the ionic crystal electrons in grazing fast ion–insulator surface collision. The ionized electrons originate in the 2p F orbital. We observe that the binary peak appears as a double change in the slope of the spectra, in the high energy region. The form of the peak is determined by the initial electron distribution and its position will be affected by the binding energy of the 2p F electron in the crystal. This BEP in insulator surfaces will appear slightly shifted to the low energy side with respect the ion–atom one. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 34.50.Dy; 79.20.Rf; 79.60.Dp; 68.49.)h Keywords: Ion–surface interaction; Electron emission; Insulator
1. Introduction The energy distribution of electrons emitted during the scattering of fast grazing ions from surfaces has been the subject of intense research activity during the last years. Recently, a rapidly increasing number of works consider the electron emission during the bombardment by fast particles of the surface of insulators showing a number of interesting features. Therefore, it will be of importance to understand the detailed interaction
* Corresponding author. Tel.: +54-2944-445220; fax: +542944-445299. E-mail address: [email protected] (M.L. Martiarena). 1 CNEA.
mechanism [1]. However, there is still a lack of detailed experimental information and theoretical understanding of the energy and angle distribution of electrons ejected from insulator surfaces. The scarcity of experimental data and the complexity of the physical processes involved have prevented the development of a comprehensive theoretical picture. This prompted our current studies aimed at identifying some physical mechanisms acting on electron emission in ion-insulators collisions which are well known for metal surfaces. In this case, the electron spectra have different characteristics depending on the electron energy and observation angles and on the type and roughness of the metal surfaces. In the low energy region the energy distribution presents a maximum around 3–9 eV (see Fig. 1(e)) which increases and
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)02175-4
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
suffers a small displacement to lower energies for larger observation angles [2–5]. For energies close to ECE ¼ v2p =2 (vp is projectile velocity) and observation angles around the direction of the ion specular reflection other structures appear whose shape and energy position depend on surface topography [6–10]. For rough surfaces the known convoy electron peak (CEP) is observed at ECE , while for less rough surfaces a broader and shifted structure is also observed at higher energies [11] (see Fig. 1(c)). When the metal surface is smooth enough, this last structure becomes the principal characteristic of the electron spectra, since the CEP becomes unobservable (see Fig. 1(b)). A similar structure has been observed during the 60– 100 keV Hþ grazing bombardment of LiF surface (see Fig. 1(d)), where now a peak appears with the maximum at an energy EM lower than ECE [12].
63
This result was discussed in terms of the attractive (track of positive charges from ionized F ions) and the repulsive surface-induced potential. At higher energies, a broad peak is observed and identified as a binary peak (BEP) [13], well known for ion–gas collisions [14,15]. The BEP arises from hard collisions between the impinging ion and target electrons. From energy and momentum conservation for the projectile-electron subsystem it is possible to estimate the position of the binary peak as kf ¼ 2vp cosðhÞ (kf is the final electron momentum, vp the ion velocity and h the electron emission angle). For grazing collisions on metals surfaces, the maximum of the binary structure for observation angles close to the direction of the ion specular reflection, appears at an energy lower than 2v2p , the value of the maximum in the ion–gas case [7–9].
Fig. 1. Electron spectra for different types and roughness of the surfaces versus ðve =vi Þ2 (ve;i electron and ion velocity): (a) hi , 0.34° and ho , 5.7° [9]; (b) hi , 1.0° and ho , 1.0° [4]; (c) hi , 1.0° and ho , 1.0° [11]; (d) hi , 1.0° and ho , 1.0° [12]; (e) hi , 1.3° and ho , 10.0° [10]. The vertical line show the position of the convoy electron peak (CEP); the position of the classic BEP would be ðve =vi Þ2 ¼ 4 (see text).
64
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
It is very interesting to note that for special conditions on the ion energy, the projectile incidence and electron observation angles and the surface roughness, it is possible to observe in metals the convoy electron peak, the shifted convoy and the binary peak coexisting in the same spectra (Fig. 1(a)). In this work, starting from concepts of atomic collisions in the gas phase, we study the binary electron production due to single electron excitation by the direct Coulomb interaction between the incident ion and anions (F ) of the ionic crystal. The fact that F belongs to an LiF surface is accounted for through the shift of the 2p electron binding to fit with the 2p valence band of the insulator.
2. Theory The time dependent Hamiltonian for grazing collisions of a bare charge Zp with an ionic crystal surface is H ðtÞ ¼ Hi þ Vi ðtÞ: In the entry channel the electron bound to the surface is described by Hi ¼
p2 þ Vs ðrÞ; 2
ð1Þ
while the projectile–electron interaction is Vi ðr; tÞ ¼ VC ðr RðtÞÞ þ VPeI ðr; tÞ þ Vlocal ðr; tÞ;
ð2Þ
where r and RðtÞ are the electron and projectile position, respectively (see Fig. 2). We assume that the ion moves parallel to the surface along a classical trajectory and we describe the collision in the impact parameter approximation ~ðtÞ ¼ q^ vp ; R ez þ t~ ex and q is the distance of closest with ~ vp ¼ vk~ approach, equal in this case to the impact parameter. The origin of the coordinate system is chosen at a halide ion on the surface with the zaxis normal to the surface and the x-axis along the ion direction of motion.
Fig. 2. Reference frame for the description of projectile interaction with halide surface.
VPeI ðr; tÞ is the interaction between the electron and the image of the projectile while VC ðr 1 RðtÞÞ ¼ jrRðtÞj is the Coulomb interaction between the electron and the projectile itself. In contrast to metal surfaces the typical decay times for excess surface charges on insulators are far too long to compensate local charge accumulations at the collision time-scale. As a consequence the ion is followed by a trail of surface charges. This excess of surface charges produces the Vlocal ðr; tÞ potential. In this work, we will study the high energy region of electrons ionized by fast beams from ionic crystals. In a first approach, we consider only the Coulomb interaction in the perturbed potential Vi ðr; tÞ, and calculate the energy distribution of the emitted electrons. Considering a time-dependent perturbation X Wðr; tÞ ¼ an ðtÞuin ðrÞeii t ; ð3Þ n
where dak ðtÞ X ¼ i an ðtÞ < ufk ðrÞjVC jun ðrÞ > eiðf i Þt : dt n ð4Þ In first-order Born approximation the transition amplitude is Z 1 ak ð1Þ ¼ i dthufk ðrÞjVC ðr RðtÞÞj 1
uinlm ðrÞieiðf i Þt
ð5Þ
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
with hufk ðrÞjVC ðr ¼
Zp 2p2
Z
Then Zp ak ð1Þ ¼ i p
F2p1;k ðqÞ ¼
RðtÞÞjuinlm ðrÞi
dq iq q e dðDE q vÞFnlm;k ðqÞ q2
65 ci r
dreiQ r rY1;1
ðh; /Þ1 F1 ðig; 1; iðk r þ krÞÞ rffiffiffiffiffiffi X i 3 i ¼ 3 N ðgÞ iai ½Ix iIyi ; 2p 8p i
dq3 iq ðqþvtÞ e Fnlm;k ðqÞ: q2
Z
X 1 N ðgÞ ai 2p3 i
Z
ð6Þ
with form factor, Fnlm;k ðqÞ ¼ hufk ðrÞjeiq r juinlm ðrÞi. We describe the initial bound state considering the Roothaan–Hartree–Fock atomic wave function uinlm ðrÞ [16] for F and the initial energy i corresponding to the mean value of the 2p valence band for the fluoride crystal X ap rnp 1 ecp r Ylm ðh; /Þ: ð7Þ uinlm ðrÞ ¼
where for Z cir F0;k ðqÞ ¼ dreiQ r F1 ðig; 1; iðk r þ krÞÞ; 1
i d F0;k ðqÞ Qj dQj
i8pc 4Qj C g c ik ¼ 2 i Aig þi Cþ i Mj ; D A cA D
Iji ¼
ð13Þ
The final hydrogenic continuum state is
1 d F ðqÞ 2s 0;k c2s i dci
2s 8pc2s 4ci g 1 ig i B A C ¼ þ E ; þ i A D2 D c2s i
Ji ¼
1 ð2pÞ
3
N ðgÞeik r 1 F1 ðig; 1; iðk r þ krÞÞ;
N ðgÞ ¼ epg=2 C½1 ig; g ¼
Zt : k
ð8Þ
Using the Nordsieck integral [17] we obtain Fnlm ðqÞ analytically " 5 X 1 N ðgÞ a2s F2s;k ðqÞ ¼ i Y0;0 ðh; /Þ ð2pÞ3 i¼3 Z 2s dreiQ rci r r1 F1 ðig; 1; iðk r þ krÞÞ
K i ¼ F0;k ðqÞ ¼ A¼1þ2
2 X
dre
iQ rc2s r i
F1 ðig; 1; iðk r þ krÞÞ ; ð9Þ
F2p0;k ðqÞ ¼
ð2pÞ
N ðgÞ 3
X
Z ai
dreiQ rci r rY1;0 ðh; /Þ
i
1 F1 ðig; 1; iðk r þ krÞÞ rffiffiffiffiffiffi X i 3 i Iz N ðgÞ ai ¼ 3 4p ð2pÞ i and
D ¼ Q2 þ c2i ;
S ¼ Q k ici k;
ici þ k i ; cA
Mj ¼
2 ½ð1 AÞQj þ kj ; D ð17Þ
#
Z
1
ð15Þ
a2s i Y0;0 ðh; /Þ
i¼1
S ; D
8pci ig A C D2
ð14Þ
ð16Þ C ¼1þg
þ
ð12Þ
with Q ¼ q k is
p
ufk ðrÞ ¼
ð11Þ
ð10Þ
2 ½ik þ ci ðA 1Þ; D g E ¼ 2 2 ½kðBci þ AÞ þ iBc2i : ci A B¼
We calculate the distance of closest approach q considering the universal ZBL (Ziegler–Biersack– Littmark) [19] screening function , with a screening length aiZBL ¼ 0:8854=ðZp0:23 þ Zi0:23 Þ. For an ionic crystal the planar average potential is produced by two different ion species, so it is necessary to consider the different lattices of anions i ¼ a and cations i ¼ c:
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UZBL ¼ 2pZp
X aj bj j a
c
ðZa nas aaZBL ebj z=aZBL þ Zc nas acZBL ebj z=aZBL Þ:
3. Results and discussion For the collision of Hþ on LiF we use a single exponential expression U ðzÞ ¼ aebz with a ¼ 0:509 a.u. b ¼ 0:88 a.u.1 [18]. In Fig. 3, we present the results obtained for 300 keV Hþ impinging on an LiF surface at an incidence angle (hi ) of 0.34° and an observation angle (ho ) of 5.7°. We consider the ionization of the F 2p and 2s electrons with a binding energy of 15 and 34 eV, respectively. We observe that the binary peak only appears as a double change in the slope of the
spectra. The maximum of this binary peak is observed in a logarithmic graphic at EBLiF 500 eV. Together with that result we plot the experimental data [9] and the theoretical [4] binary electron distribution for a SnTe surface bombarded with 300 keV protons, that peaks at 530 eV. It is seen that the differences between metal and insulator targets affect not only the position but also the form of the binary peak. These effects are associated to the contribution of the 2p0 states. In particular there is a dip on the binary sphere for electrons ionized from the 2p0 initial state. We observe that the maximum of the binary peak in ion–LiF surface collisions appears shifted to lower energies with respect to the ion–atom 2 BEP EBc ¼ ð2vi Þ =2 ¼ 653:42 eV, and in this first Born approximation it has a smooth structure resembling the 2p character of the peak (Fig. 4).
Fig. 3. Emission probability versus electron energy for 300 keV Hþ scattering from different surfaces: LiF (––); and SnTe (– –) [4] hi , 0.34° and electron observation angle ho , 6.3°. The dots correspond to the experimental data for the SnTe surface [9].
M.L. Martiarena, V.H. Ponce / Nucl. Instr. and Meth. in Phys. Res. B 203 (2003) 62–68
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Fig. 4. Emission probability and its first derivative versus electron energy for 300 keV Hþ scattering from LiF hi , 0.34° and electron observation angle ho , 5.7°.
Fig. 5. Emission probability versus electron energy for 300 keV Hþ scattering from LiF hi , 0.34 and different observation angles: (- - -) 2s; (. . .) 2p0 ; (- - -) 2p1 ; (-
-
-) total 2p; (––) total 2p þ 2s.
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SnTe LiFðVlocal ¼ 0Þ
EB (eV) 530 590
DE ¼ EBc EB (eV) 123.42 63.42
In Fig. 5 we show for Hþ (300 keV) impinging on LiF the dependence of the binary electron distribution with the observation angle. As in ion– atom collisions the angular distribution of the binary peak results in a binary sphere, so if the observation angle increases, the BEP is shifted to lower energies. We show in Fig. 5 the contribution of each initial state and observe the different intensities between them. The shift of the BEP peak with respect to the classical result DE ¼ EBc EB gives information on the target characteristics in the ionization process. A characteristic of the ion-insulator crystal collision, that should be of interest to incorporate in future studies, is the excess of surface charges produced by the projectile along its glancing trajectory which give rise to the potential Vlocal ðr; tÞ. The intensity of this potential will increase the binding energy of the target electron that will shift the peak position with respect the value calculated here. The presence of the track of surface charges could also affect the low energy part of the double differential electron distribution. The track will shift the bottom of the LiF conduction band and change the minimum energy of the allowed electron emission together with the position of the low energy maximum observed in metals. To analyze these effects it will be necessary to consider a more realistic perturbation potential and distorted final state wave function. Nevertheless the ionic character of the crystal will produce a higher electron distribution in the low energy region of the spectra than that observed in ion–metal collision. It will be of interest to have experimental results for both the high and low energy regions of electrons emitted in ion-insulator surface collisions, in
order to test the reliability of initial target electron states and the effect of the track on these initial states and in the outgoing ionized electrons.
Acknowledgements We acknowledge financial support from ANPCyT (PICT 03-6325) and Fundaci on Antorchas.
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