- Email: [email protected]
Energy dependence of the Al L23 ionization cross section in H+−Al collisions
Nuclear Instruments and Methods in Physics Research B33 (1988) 295-296 North-Holl~d, Amsterdam
ENERGY DEPENDENCE C. BENAZETH
OF THE Al L,
IONIZATION
I), M. HOU 2), N. BENAZETH
295
CROSS SECTION IN H +-Al COLLISIONS
*) and C. MAYORAL”)
‘) Luboratoire de Physique des Solides Assock! au CNRS, UniversitP Paul Sabutier, 118 Route de Einrbonne, F-31062 Toulouse Cedex, France 2, Universiit: Libre de Bruxelies CP234, Bd du Triomphe, B-IO50 Brussels, Belgium
In proton-surface interactions, the iunershell ionization process arises from a direct Coulomb interaction between the proton and the bound target electrons, which can be described by well established theoretical models [l-4]. The present work deals with the dependence of Al L,, Auger efficiencies (and ionization cross sections) on the proton incident energy (in the 10 to 100 keV range). Computer simulation with the MARLOWE program [5] is used, to which a procedure is appended in order to describe the Auger process which links the Auger emission yields to the ionization cross sections [6-91. The estimate of the L,, innershell ionization probability is based on the theory developed by Brandt and Lapicki [4]_ Accounting for the projectile-electron binding and the Coulomb deflection in the PWBA calculation of the ionization cross section, these authors suggest a polynomial approximation to the impact parameter dependence of the ionization probability. We found that a maximum impact parameter of about half the second neighbour distance is sufficient for the calculation of the emission efficiencies of ahuniniurn L,, Auger electrons induced by protons with energies of 100 keV or less. The simulations allow us to estimate the dependence of the emission efficiency, pA, on the ionization cross section for various incident proton energies between 20 and 100 keV. This was done with an incidence angle, i, of 60” from the normal at the surface of a polycrystalline target. All calculated efficiencies align along a straight line having the equation
reasonably modelled which the ionization constant. In such a emission efficiencies laws:
P,,,,(~~,,)
by straight line segments along probability per unit path length is situation, the ionization and the may be expected to follow cosine
at,hdK3)~
~0s i=
(2)
where I and Em stand for the ionization and emission efficiencies respectively, a, and aEm are constants. Significant deviations are observed both experimentally and by simulation for the emission efficiency, which are related to the surface texture [lo].
,I)”
G&l
o-231n2) H*_+Al
PWBA
--
----ES--- This work ___
whatever the energy is. E0 is the primary energy and k is a constant. It thus turns out that the emission efficiency scales with the total ionization cross section. The fact that the Auger emission efficiency is only dependent on the energy through the total ionization cross section indicates that the fraction of proton trajectories that are relevant to Auger emission are most 0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
iI
0
’ 10
’ 20
’ 30
’ 40
INCIDENT
’ 50
’ 60
ENERGY,
Corrected
’ 70
’ 80
PWBA
’
90
’ 100
’
E,(keV)
Fig. 1. Incident energy dependence of the L,, innershell total ionization cross section. (BEA [3], PWBA [l], corrected PWBA I41.) V. SECONDARY ELECTRON/PHOTON
EMISSION
296
C. Benazeth et al. /Al
Further, the absolute Auger emission efficiencies from a polycrystalline target were measured as a function of the primary energy with the same incidence geometry [lo]. The comparison of the experimental values with the simulation results allows us to estimate the total ionization cross section as a function of the proton energy. The results are displayed in fig. 1 and compared with the prediction of the BEA and the PWBA calculations. Our results are proportional to the calculated cross section in the corrected PWBA. The former overestimates the latter by about 85%. The obtained cross section was used to estimate the incidence angle dependence of the Auger yield and to compare the experimental values with simulation in the cases of both polycrystalline and single crystal targets
WI.
L,,
ionization cross section
References [l] B.H. Choi, E. Merzbacher and G.S. Khandelwal, Atomic [2] [3] [4] [5] [6] [7] [8] [9] [lo]
Data 5 (1975) 291. J.D. Garcia, Phys. Rev. Al (1970) 402. J.H. McGuire and P. Richard, Phys. Rev. A8 (1973) 1374. W. Brandt and G. Lapicki, Phys. Rev. A10 (1974) 474. M.T. Robinson and I. Torrens, Phys. Rev. B9 (1974) 5008. C. Benazeth, N. Benazeth and M. Hou, Surf. Sci. 151 (1985) L137. M. Hou, C. Benazeth, N. Benazeth and C. Mayoral, Nucl. Instr. and Meth. B13 (1986) 645. C. Benazeth, M. Hou, C. Mayoral and N. Benazeth, Nucl. Instr. and Meth. B18 (1987) 555. M. Hou, C. Benazeth and N. Benazeth, Phys. Rev. A36 (1987) 591. C. Benazeth, M. Hou, N. Bemazeth and C. Mayoral, to be published in Nucl. Instr. and Meth. B (1988).
ENERGY DEPENDENCE C. BENAZETH
OF THE Al L,
IONIZATION
I), M. HOU 2), N. BENAZETH
295
CROSS SECTION IN H +-Al COLLISIONS
*) and C. MAYORAL”)
‘) Luboratoire de Physique des Solides Assock! au CNRS, UniversitP Paul Sabutier, 118 Route de Einrbonne, F-31062 Toulouse Cedex, France 2, Universiit: Libre de Bruxelies CP234, Bd du Triomphe, B-IO50 Brussels, Belgium
In proton-surface interactions, the iunershell ionization process arises from a direct Coulomb interaction between the proton and the bound target electrons, which can be described by well established theoretical models [l-4]. The present work deals with the dependence of Al L,, Auger efficiencies (and ionization cross sections) on the proton incident energy (in the 10 to 100 keV range). Computer simulation with the MARLOWE program [5] is used, to which a procedure is appended in order to describe the Auger process which links the Auger emission yields to the ionization cross sections [6-91. The estimate of the L,, innershell ionization probability is based on the theory developed by Brandt and Lapicki [4]_ Accounting for the projectile-electron binding and the Coulomb deflection in the PWBA calculation of the ionization cross section, these authors suggest a polynomial approximation to the impact parameter dependence of the ionization probability. We found that a maximum impact parameter of about half the second neighbour distance is sufficient for the calculation of the emission efficiencies of ahuniniurn L,, Auger electrons induced by protons with energies of 100 keV or less. The simulations allow us to estimate the dependence of the emission efficiency, pA, on the ionization cross section for various incident proton energies between 20 and 100 keV. This was done with an incidence angle, i, of 60” from the normal at the surface of a polycrystalline target. All calculated efficiencies align along a straight line having the equation
reasonably modelled which the ionization constant. In such a emission efficiencies laws:
P,,,,(~~,,)
by straight line segments along probability per unit path length is situation, the ionization and the may be expected to follow cosine
at,hdK3)~
~0s i=
(2)
where I and Em stand for the ionization and emission efficiencies respectively, a, and aEm are constants. Significant deviations are observed both experimentally and by simulation for the emission efficiency, which are related to the surface texture [lo].
,I)”
G&l
o-231n2) H*_+Al
PWBA
--
----ES--- This work ___
whatever the energy is. E0 is the primary energy and k is a constant. It thus turns out that the emission efficiency scales with the total ionization cross section. The fact that the Auger emission efficiency is only dependent on the energy through the total ionization cross section indicates that the fraction of proton trajectories that are relevant to Auger emission are most 0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
iI
0
’ 10
’ 20
’ 30
’ 40
INCIDENT
’ 50
’ 60
ENERGY,
Corrected
’ 70
’ 80
PWBA
’
90
’ 100
’
E,(keV)
Fig. 1. Incident energy dependence of the L,, innershell total ionization cross section. (BEA [3], PWBA [l], corrected PWBA I41.) V. SECONDARY ELECTRON/PHOTON
EMISSION
296
C. Benazeth et al. /Al
Further, the absolute Auger emission efficiencies from a polycrystalline target were measured as a function of the primary energy with the same incidence geometry [lo]. The comparison of the experimental values with the simulation results allows us to estimate the total ionization cross section as a function of the proton energy. The results are displayed in fig. 1 and compared with the prediction of the BEA and the PWBA calculations. Our results are proportional to the calculated cross section in the corrected PWBA. The former overestimates the latter by about 85%. The obtained cross section was used to estimate the incidence angle dependence of the Auger yield and to compare the experimental values with simulation in the cases of both polycrystalline and single crystal targets
WI.
L,,
ionization cross section
References [l] B.H. Choi, E. Merzbacher and G.S. Khandelwal, Atomic [2] [3] [4] [5] [6] [7] [8] [9] [lo]
Data 5 (1975) 291. J.D. Garcia, Phys. Rev. Al (1970) 402. J.H. McGuire and P. Richard, Phys. Rev. A8 (1973) 1374. W. Brandt and G. Lapicki, Phys. Rev. A10 (1974) 474. M.T. Robinson and I. Torrens, Phys. Rev. B9 (1974) 5008. C. Benazeth, N. Benazeth and M. Hou, Surf. Sci. 151 (1985) L137. M. Hou, C. Benazeth, N. Benazeth and C. Mayoral, Nucl. Instr. and Meth. B13 (1986) 645. C. Benazeth, M. Hou, C. Mayoral and N. Benazeth, Nucl. Instr. and Meth. B18 (1987) 555. M. Hou, C. Benazeth and N. Benazeth, Phys. Rev. A36 (1987) 591. C. Benazeth, M. Hou, N. Bemazeth and C. Mayoral, to be published in Nucl. Instr. and Meth. B (1988).