- Email: [email protected]
Production of energetic electrons in low-energy collision cascades in solids
Nuclear Instruments and Methods in Physics Research B 122 (1997) 442-444
Beam Interactions with Materials&Atoms
ELSEVIER
Production of energetic electrons in low-energy collision cascades in solids Z. hubek
*
Acudemy of Sciences oj’the Czech Republic. CRE. Chaberskd 57, Prague 8, Czech Republic
Abstract One-electron models of kinetic electronic excitations in metallic solids bombarded by slow atomic particles (< 2 keV) will be compared with kinetic electron emission experiments. As some of the experiments on energetic electrons cannot be explained in terms of the one-electron processes possible extension of emission models will be described. In particular, it will be assumed that electrons excited in collision cascades can strongly interact and this electron-electron interaction will be modelled either by a rapid (within few fs) or an instantaneous thermalization of excitations. The excitation processes will be studied at different temporal stages of the cascade.
1. Introduction
2. Experimental
Electron emission from solids under atomic bombardment can proceed via potential electron emission (PEE) [I] and via kinetic electron emission (KEE) [2]. Potential emission practically does not depend upon the velocity of the impinging particle and should be absent when the particle is neutral in the ground state or when the potential energy of the particle is not sufficiently high to overcome the work function of the solid. Kinetic electron emission, on the other hand, is due to dynamical changes and subsequent electronic excitations produced in the solid by the moving particle or by moving recoils. The kinetic excitation in metals and wide-band semiconductor can be caused by various processes from which one-electron mechanisms of particle-electron binary collisions including the shuttle mechanism and the level promotion processes can be theoretically well described. The outcome of such theoretical considerations will be compared with recent experiments. It will be shown that the theoretically predicted electron energy distributions are substantially narrower and that the calculated electron emission is far more dependent on the mass of the primary particle than it is observed experimentally. In view of these discrepancies another, essentially many-electron, approach is assumed in this paper which is based on localization and a partial or complete thermalization of excitations. This approach allows a comparison of excitations produced in solids by impinging particles with excitations produced by femtosecond lasers.
As the potential electron emission due to the Auger neutralization of the projectile is by several orders of magnitude more intensive than the kinetic emission, the system for studying KEE must be chosen carefully to avoid PEE. One possibility is to use an ion projectile with the ionization energy I smaller than 24, where 4 is the work-function of the substrate. Such condition is certainly fulfilled for Na+ bombarding the Au substrate. The ionization energy of Na is 5.1 eV, the work function of Au is around 4.8 eV. The electron emission for such a system has been reported in Ref. [3] and the corresponding electron yield y is shown in Fig. I by full squares. Also Xe+ can be used as a projectile with the Au substrate. The value of I for Xe is diminished by about 2 eV near the surface due to the image charge potential and thus the condition I < 24 is satisfied [4]. The measurement of electron emission from Au bombarded by Xef has been reported in Ref. [4] and the results are shown by open circles in Fig. 1. The most straightforward experiments on KEE would be with neutral projectiles in ground states. We have carried out such experiments using a time of flight spectrometer and using GaAs as the substrate. First experimental results with Are projectiles are shown in Fig. I by full circles. As will be discussed in the next chapter only valence electrons are assumed to be excited by slow projectiles and thus basic features of KEE at low impact energies should not be very sensitive to the substrate used. 2.1. One-electron
* Tel.: + 42 2 688 18 04; fax: 1-42 2 688 02 22; e-mail: [email protected].
excitations
The kinetic electron excitation of valence electrons is mostly due to binary collisions of the moving particle with
0168-583X/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved PII SO1 68-583X(96)00658I
/ Nucl. Ins@. cmd Meth. in Phys. Res. B I22 f 1997) 442-444
Z. &ubek
electrons at the Fermi level. This process is responsible for the electronic stopping power and generates a large amount of low energy excitations. The maximum energy increment 6E which the electron can gain is 6E = 2mvv,, where v is the velocity of the particle, vr is the Fermi velocity in the solid and m is the mass of the electron. The value of 6E can be increased if the accelerated electron is reflected by another particle in the solid back to the moving particle and gains another SE and if this process can be repeated several times. This, so called shuttle mechanism, has been treated in detail in a recent publication [5]. Using the formalism described in Ref. [5] the energy distribution n(e) of electrons (number of electrons per one eV) generated by head-on collisions of two Al atoms in AI metal with energies of 100 and 500 eV and by head-on collisions of two Au atoms in Au metal with an energy of 500 eV have been calculated and plotted in Fig. 2. The energy distributions depend upon the kinematics of the collision and do not depend upon the detailed electronic structures (inner shells) of the colliding atoms because only valence electrons are involved in the excitation process. Thus for the Xe-Au collision the n(e) dependence would be similar to n(e) for Au-Au collision. The knowledge of n(e) allows to calculate y (the number of emitted electrons per incident particle) as y = Kjn(e)de, where the integration is from the vacuum level to infinity. K is the constant depending on the transport of electrons through and out of the solid and is smaller than one. For the AI-AI collision and K = I the calculated y as a function of the energy of the incident particle is shown in Fig. 1. It should be
Id'2
-
iz
-
B
1
/’
I’
,‘,*
,+? ,,’
z -
d’
; ,,f
1ci’:
\
\
Fig. 2. The number of electrons n(e), excited above the Fermi energy in the interval 6 and c + d l for two Al atoms which collide in the free electron gas with kinetic energies of 100 and 500 eV and for two Au atoms which collide with the energy of 500 ev.
stressed that the calculated dependence is for head-on collisions, with the shuttle mechanism included, and such collisions statistically occur only infrequently. For collisions with larger impact parameters the values of y drop rapidly. Moreover, for the Au-Au collision, which resembles Xe-Au much closer, the values of y would be still by more than 3 orders of magnitude smaller. Clearly compared to experimental date the predicted dependence of y on the primary particle energy is much too steep and much too dependent upon the masses of bombarding particles. Other one-electron processes involve core level promotion and orthogonalization of valence electron wave functions to core level wave functions [6]. The correlation diagrams calculated for systems involved in the presented experimental data show that the core level contribution is small for the used energies of primary particles.
3’
2.2. Many-particle
mechanism
,P
;
5!
-
187
i&
,’
E: c
-0’
A; ______-_------*_ __-_-
/’
\\
I’
j’,,’
: /
i
P
I ,I
m
,’ .’ P ,’ r
<’
_’
:
Fig. I. Measured electron emission yield y as a function of the primary energy E for Ar+ (dashed line) [31, Xe+ (open circles) [4] and NaC (full squares) 131 impact on Au and for Ar” impact on GaAs (full circles). The dependence of y on E predicted from one-electron models for AI-AI collisions is marked by the full line. For heavier atoms (Au) the dependence is still steeper and the values of y are by several orders of magnitude smaller.
As the one-electron excitation does not seem to explain experimental data in Fig. I, many-electron processes are considered. The most straightforward is the process in which excitations are produced by electron-particle binary collisions as discussed in the previous chapter but the excitations are assumed to be localized in the collision cascade region and are assumed to thermalize within less than IO fs by multiple Auger processes. A partial or complete localization within the cascade region is an acceptable concept because the region is strongly amorphized [7]. As the electron-particle collision (essentially equivalent to electron-phonon interaction in extended systems) is not an efficient transfer process the energy in the electronic system accumulates slowly. We have calculated
III. ION BEAMS
444
Z. &ubck/Nucl.
Insrr. und Meth. in Phys. Res. B I22 (1997) 442-444
80.
LO
80 t ifsI
Fig. 3. The electronic energy AE deposited in collision cascades as a function of time. The values of AE have been calculated using molecular dynamics and using a cluster of IOX 10X 8 Al atoms. The spread of AE is due to different losses for different impacts.
such transfer using a cluster of 10 X 10 X 8 atoms of Al, bombarded with a 500 eV Ar atom. The atomic trajectories have been calculated using a molecular dynamics. Each Al atom was assumed to move in a homogenous electron gas corresponding to Al metal. The electronic energy inside the cluster is shown in Fig. 3 as a function of time, until1 time t - 100 fs. At t= 100 fs the volume of the cascade is roughly equal to the volume of the cluster. About 200 cascades have been analyzed and the spread of electronic energies in individual cascades is indicated in Fig. 3 by the shaded band. ‘Ihe effective electronic temperature T, can be obtained from the relation ceq-
AE,
(1)
where ce is the specific heat of the electronic gas, in Al equal to c, - $r=Nk=T,/c,,
(2)
where N is the number of electrons in the system (N = 2400 in the case of the studied cluster) and er is the Fermi energy. At the time t = 70 fs the temperature T, reaches the value of 2500 K and it still slightly increases with time. It should be stressed that at r > 70 fs most of the sputtering takes place and the calculated high value of T, is sufficient to explain the ionization of sputtered particles [7]. It is interesting to notice that the rate with which the energy is transferred into the electronic system in Fig. 3 is comparable with the energy pumped into the electronic system by a femtosecond laser. The energy deposited into the electronic system in Fig. 3 is typically 3.7 X lOI W/cm3, whereas the energy deposited by an UV laser (penetration depth 30 A) with a fluence of mJ/cm3 and a pulse width of 200 fs is 1.6 X lOI W/cm3. Very high values of T, achieved in metals irradiated by fs lasers are well documented [8]. The high electronic te.mperature of 2500-3000 K at the later stage of cascades is, however, still too low to explain
the observed electron emission. Thus we tentatively assume that an efficient electron emission occurs already at the very beginning of the cascade and that the contribution of the first collisions of the primary particle is the most important. We further suppose that the electrons excited by the electron-particle collisions are localized for a sufficiently long time in the impact zone to interact by electron-electron interaction and we model this interaction process by the assumption of an instantaneous thermalization of the electron excitations. This approach roughly describes the effect of the electron-electron interaction upon the broadening of the excited electron energy spectra but does not influence the electronic energy losses. When the number of excited electrons in the region (N = 10) and the calculated energy AE deposited in the 600 eV Ar-Ga collision (A E = 6 eV> are substituted into Eqs. (1) and (2). one gets kT, = 1.2 eV. This value of T, would explain very well the observed values of y and the large width of the measured energy distribution of emitted electrons as discussed in detail in the forthcoming publication.
3. Conclusion Experimental data on electron emission from metals and from wide-band semiconductors bombarded by slow atomic particles have been analyzed in terms of one-electron and many-electron excitation theories. Most compatible with the data is the model which is based on the assumption that electrons excited by nonadiabatic collision processes are sufficiently localized in the impact zones to strongly interact by the electron-electron interaction.
Acknowledgements The work was partially supported by Copernicus grant No. CIPA-CT 94-0139 and by the Czech Academical Grant No. 6750 1.
References [I] E.V. Alonso, R.A. Baragiola,
J. Ferr6n, M.M. Jakas and A. Oliva-Florio, Phys. Rev. B 22 (1980) 80. [2] H.D. Hagstntm, Phys. Rev. % (1954) 336. 131 G. Lakitis, F. Aumayr, M. Heim and H.P. Winter, Phys. Rev. A 42 (19%) 5780. [4] E.V. Alonso, M.A. Alurralde and R.A. Baragiola, Surf. Sci. 166 (1986) L155. [5] 2. Sroubek. submitted to Phys. Rev. B. [6] Z. Sroubek and J. Fine, Phys. Rev. B 51 (1995) 5635. 171 Z. Sroubek and H. Oechsner, Surf. Sci. 348 (1996) 100. [S] F. Budde, T.F. Heinz, M.M.T. Loy, J.A. Misewich. F. de Rougemont and H. Zacharias, Phys. Rev. Lett. 66 (1991) 3024.
Beam Interactions with Materials&Atoms
ELSEVIER
Production of energetic electrons in low-energy collision cascades in solids Z. hubek
*
Acudemy of Sciences oj’the Czech Republic. CRE. Chaberskd 57, Prague 8, Czech Republic
Abstract One-electron models of kinetic electronic excitations in metallic solids bombarded by slow atomic particles (< 2 keV) will be compared with kinetic electron emission experiments. As some of the experiments on energetic electrons cannot be explained in terms of the one-electron processes possible extension of emission models will be described. In particular, it will be assumed that electrons excited in collision cascades can strongly interact and this electron-electron interaction will be modelled either by a rapid (within few fs) or an instantaneous thermalization of excitations. The excitation processes will be studied at different temporal stages of the cascade.
1. Introduction
2. Experimental
Electron emission from solids under atomic bombardment can proceed via potential electron emission (PEE) [I] and via kinetic electron emission (KEE) [2]. Potential emission practically does not depend upon the velocity of the impinging particle and should be absent when the particle is neutral in the ground state or when the potential energy of the particle is not sufficiently high to overcome the work function of the solid. Kinetic electron emission, on the other hand, is due to dynamical changes and subsequent electronic excitations produced in the solid by the moving particle or by moving recoils. The kinetic excitation in metals and wide-band semiconductor can be caused by various processes from which one-electron mechanisms of particle-electron binary collisions including the shuttle mechanism and the level promotion processes can be theoretically well described. The outcome of such theoretical considerations will be compared with recent experiments. It will be shown that the theoretically predicted electron energy distributions are substantially narrower and that the calculated electron emission is far more dependent on the mass of the primary particle than it is observed experimentally. In view of these discrepancies another, essentially many-electron, approach is assumed in this paper which is based on localization and a partial or complete thermalization of excitations. This approach allows a comparison of excitations produced in solids by impinging particles with excitations produced by femtosecond lasers.
As the potential electron emission due to the Auger neutralization of the projectile is by several orders of magnitude more intensive than the kinetic emission, the system for studying KEE must be chosen carefully to avoid PEE. One possibility is to use an ion projectile with the ionization energy I smaller than 24, where 4 is the work-function of the substrate. Such condition is certainly fulfilled for Na+ bombarding the Au substrate. The ionization energy of Na is 5.1 eV, the work function of Au is around 4.8 eV. The electron emission for such a system has been reported in Ref. [3] and the corresponding electron yield y is shown in Fig. I by full squares. Also Xe+ can be used as a projectile with the Au substrate. The value of I for Xe is diminished by about 2 eV near the surface due to the image charge potential and thus the condition I < 24 is satisfied [4]. The measurement of electron emission from Au bombarded by Xef has been reported in Ref. [4] and the results are shown by open circles in Fig. 1. The most straightforward experiments on KEE would be with neutral projectiles in ground states. We have carried out such experiments using a time of flight spectrometer and using GaAs as the substrate. First experimental results with Are projectiles are shown in Fig. I by full circles. As will be discussed in the next chapter only valence electrons are assumed to be excited by slow projectiles and thus basic features of KEE at low impact energies should not be very sensitive to the substrate used. 2.1. One-electron
* Tel.: + 42 2 688 18 04; fax: 1-42 2 688 02 22; e-mail: [email protected].
excitations
The kinetic electron excitation of valence electrons is mostly due to binary collisions of the moving particle with
0168-583X/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved PII SO1 68-583X(96)00658I
/ Nucl. Ins@. cmd Meth. in Phys. Res. B I22 f 1997) 442-444
Z. &ubek
electrons at the Fermi level. This process is responsible for the electronic stopping power and generates a large amount of low energy excitations. The maximum energy increment 6E which the electron can gain is 6E = 2mvv,, where v is the velocity of the particle, vr is the Fermi velocity in the solid and m is the mass of the electron. The value of 6E can be increased if the accelerated electron is reflected by another particle in the solid back to the moving particle and gains another SE and if this process can be repeated several times. This, so called shuttle mechanism, has been treated in detail in a recent publication [5]. Using the formalism described in Ref. [5] the energy distribution n(e) of electrons (number of electrons per one eV) generated by head-on collisions of two Al atoms in AI metal with energies of 100 and 500 eV and by head-on collisions of two Au atoms in Au metal with an energy of 500 eV have been calculated and plotted in Fig. 2. The energy distributions depend upon the kinematics of the collision and do not depend upon the detailed electronic structures (inner shells) of the colliding atoms because only valence electrons are involved in the excitation process. Thus for the Xe-Au collision the n(e) dependence would be similar to n(e) for Au-Au collision. The knowledge of n(e) allows to calculate y (the number of emitted electrons per incident particle) as y = Kjn(e)de, where the integration is from the vacuum level to infinity. K is the constant depending on the transport of electrons through and out of the solid and is smaller than one. For the AI-AI collision and K = I the calculated y as a function of the energy of the incident particle is shown in Fig. 1. It should be
Id'2
-
iz
-
B
1
/’
I’
,‘,*
,+? ,,’
z -
d’
; ,,f
1ci’:
\
\
Fig. 2. The number of electrons n(e), excited above the Fermi energy in the interval 6 and c + d l for two Al atoms which collide in the free electron gas with kinetic energies of 100 and 500 eV and for two Au atoms which collide with the energy of 500 ev.
stressed that the calculated dependence is for head-on collisions, with the shuttle mechanism included, and such collisions statistically occur only infrequently. For collisions with larger impact parameters the values of y drop rapidly. Moreover, for the Au-Au collision, which resembles Xe-Au much closer, the values of y would be still by more than 3 orders of magnitude smaller. Clearly compared to experimental date the predicted dependence of y on the primary particle energy is much too steep and much too dependent upon the masses of bombarding particles. Other one-electron processes involve core level promotion and orthogonalization of valence electron wave functions to core level wave functions [6]. The correlation diagrams calculated for systems involved in the presented experimental data show that the core level contribution is small for the used energies of primary particles.
3’
2.2. Many-particle
mechanism
,P
;
5!
-
187
i&
,’
E: c
-0’
A; ______-_------*_ __-_-
/’
\\
I’
j’,,’
: /
i
P
I ,I
m
,’ .’ P ,’ r
<’
_’
:
Fig. I. Measured electron emission yield y as a function of the primary energy E for Ar+ (dashed line) [31, Xe+ (open circles) [4] and NaC (full squares) 131 impact on Au and for Ar” impact on GaAs (full circles). The dependence of y on E predicted from one-electron models for AI-AI collisions is marked by the full line. For heavier atoms (Au) the dependence is still steeper and the values of y are by several orders of magnitude smaller.
As the one-electron excitation does not seem to explain experimental data in Fig. I, many-electron processes are considered. The most straightforward is the process in which excitations are produced by electron-particle binary collisions as discussed in the previous chapter but the excitations are assumed to be localized in the collision cascade region and are assumed to thermalize within less than IO fs by multiple Auger processes. A partial or complete localization within the cascade region is an acceptable concept because the region is strongly amorphized [7]. As the electron-particle collision (essentially equivalent to electron-phonon interaction in extended systems) is not an efficient transfer process the energy in the electronic system accumulates slowly. We have calculated
III. ION BEAMS
444
Z. &ubck/Nucl.
Insrr. und Meth. in Phys. Res. B I22 (1997) 442-444
80.
LO
80 t ifsI
Fig. 3. The electronic energy AE deposited in collision cascades as a function of time. The values of AE have been calculated using molecular dynamics and using a cluster of IOX 10X 8 Al atoms. The spread of AE is due to different losses for different impacts.
such transfer using a cluster of 10 X 10 X 8 atoms of Al, bombarded with a 500 eV Ar atom. The atomic trajectories have been calculated using a molecular dynamics. Each Al atom was assumed to move in a homogenous electron gas corresponding to Al metal. The electronic energy inside the cluster is shown in Fig. 3 as a function of time, until1 time t - 100 fs. At t= 100 fs the volume of the cascade is roughly equal to the volume of the cluster. About 200 cascades have been analyzed and the spread of electronic energies in individual cascades is indicated in Fig. 3 by the shaded band. ‘Ihe effective electronic temperature T, can be obtained from the relation ceq-
AE,
(1)
where ce is the specific heat of the electronic gas, in Al equal to c, - $r=Nk=T,/c,,
(2)
where N is the number of electrons in the system (N = 2400 in the case of the studied cluster) and er is the Fermi energy. At the time t = 70 fs the temperature T, reaches the value of 2500 K and it still slightly increases with time. It should be stressed that at r > 70 fs most of the sputtering takes place and the calculated high value of T, is sufficient to explain the ionization of sputtered particles [7]. It is interesting to notice that the rate with which the energy is transferred into the electronic system in Fig. 3 is comparable with the energy pumped into the electronic system by a femtosecond laser. The energy deposited into the electronic system in Fig. 3 is typically 3.7 X lOI W/cm3, whereas the energy deposited by an UV laser (penetration depth 30 A) with a fluence of mJ/cm3 and a pulse width of 200 fs is 1.6 X lOI W/cm3. Very high values of T, achieved in metals irradiated by fs lasers are well documented [8]. The high electronic te.mperature of 2500-3000 K at the later stage of cascades is, however, still too low to explain
the observed electron emission. Thus we tentatively assume that an efficient electron emission occurs already at the very beginning of the cascade and that the contribution of the first collisions of the primary particle is the most important. We further suppose that the electrons excited by the electron-particle collisions are localized for a sufficiently long time in the impact zone to interact by electron-electron interaction and we model this interaction process by the assumption of an instantaneous thermalization of the electron excitations. This approach roughly describes the effect of the electron-electron interaction upon the broadening of the excited electron energy spectra but does not influence the electronic energy losses. When the number of excited electrons in the region (N = 10) and the calculated energy AE deposited in the 600 eV Ar-Ga collision (A E = 6 eV> are substituted into Eqs. (1) and (2). one gets kT, = 1.2 eV. This value of T, would explain very well the observed values of y and the large width of the measured energy distribution of emitted electrons as discussed in detail in the forthcoming publication.
3. Conclusion Experimental data on electron emission from metals and from wide-band semiconductors bombarded by slow atomic particles have been analyzed in terms of one-electron and many-electron excitation theories. Most compatible with the data is the model which is based on the assumption that electrons excited by nonadiabatic collision processes are sufficiently localized in the impact zones to strongly interact by the electron-electron interaction.
Acknowledgements The work was partially supported by Copernicus grant No. CIPA-CT 94-0139 and by the Czech Academical Grant No. 6750 1.
References [I] E.V. Alonso, R.A. Baragiola,
J. Ferr6n, M.M. Jakas and A. Oliva-Florio, Phys. Rev. B 22 (1980) 80. [2] H.D. Hagstntm, Phys. Rev. % (1954) 336. 131 G. Lakitis, F. Aumayr, M. Heim and H.P. Winter, Phys. Rev. A 42 (19%) 5780. [4] E.V. Alonso, M.A. Alurralde and R.A. Baragiola, Surf. Sci. 166 (1986) L155. [5] 2. Sroubek. submitted to Phys. Rev. B. [6] Z. Sroubek and J. Fine, Phys. Rev. B 51 (1995) 5635. 171 Z. Sroubek and H. Oechsner, Surf. Sci. 348 (1996) 100. [S] F. Budde, T.F. Heinz, M.M.T. Loy, J.A. Misewich. F. de Rougemont and H. Zacharias, Phys. Rev. Lett. 66 (1991) 3024.