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Monte Carlo study of incident-angle dependence of ion-induced kinetic electron emission from solids
RIOMI B
Nuclear Instruments and Methods in Physics Research B 90 (1994) 552-555 North-Holland
Beam Interactions with Materials A Atoms
Monte Carlo study of incident-angle dependence of ion-induced kinetic electron emission from solids K. Ohya ‘,* and J. Kawata b a Department of Electrical and Electronic
Engineering, The University of Tokushirna, Tokushima 770, Japan b Department of Information Engineering, Takuma National College of Technology, Takuma-cho, Mitoyo-gun, Kagawa 769-11, Japan
The incident angle dependence of ion-induced kinetic electron emission (KEE) from solids is calculated using a Monte Carlo simulation of the transport of incident ions and recoiling target atoms, and a semi-empirical theory of KEE. The emphasis is put on the origin of the deviation from the inverse cosine law. The effect of the high-energy recoiling target atoms on the deviation is much greater than that of the trajectory distribution and backscattering of the incident ions, except for light and low-energy ion impact. The positive (negative) contribution of the recoiling target atoms to the incident angle dependence is dominant for high (low) impact energy. The deviation can be explained by the increase in the electron excitation by recoiling target atoms localized near the surface and the increase in the emission of the atoms, i.e., sputtering.
1. Introduction Ion-induced electron emission from solid surfaces can be ascribed to the processes of potential emission and kinetic emission. The kinetic electron emission (KEE) results from a large number of scattering and energy loss processes after the ion has hit the surface. The incident angle has a strong influence on the KEE yield. The KEE yield is directly related to the amount of electronic excitation generated by the ion within the electron escape depth of the solid. Thus, by changing the incidence from normal to oblique angles, the path length of the ion within the electron escape depth is prolonged, and thereby its deposition of excitation energy (the KEE yield) increases. A simple geometric model [1,2], which assumes constant electronic stopping along the ion trajectory in the electron escape depth and disregards elastic scattering of the ions by target atoms (straight-line trajectory), derives the relationship in the form, y(+)/-y(O) = (cos 4)-l; ~(4) and r(O) are the KEE yields at an incident angle 4 measured from the surface normal and at normal incidence, respectively. Except for high impact energies of more than several 100 keV, however, due to the breakdown of the assumptions in the model, experimental data largely deviate from the inverse cosine law and vary in a complex manner, depending on the impact energy, and ion and target species [2].
* Corresponding 54 9632.
author, tel. +81 886 23 2311, fax +81 886
For heavy ion impacts, the energy deposition of the ion in the target is mostly produced by successive and large angle scattering due to the elastic collisions with the target atoms, in particular at low impact energy. In such cases the electron excitation is substantially due to recoiling target atoms which receive more kinetic energy than displacement energy through elastic collisions. In this paper, the incident angle dependence of the KEE yield is calculated by using a combined Monte Carlo simulation of transport of incident ions and recoiling target atoms, and the KEE semi-empirical theory. The calculation is made for all ion-target combinations of 11 elements with Z = 6-79 in a wide energy range from 0.1 to 100 keV.
2. Calculation
Trajectories of incident ions and all recoiling target atoms are followed in 3-dimensional space by the same Monte Carlo algorithm as the TRIM.SP code [3] using the ZBL potential [4]. In accordance with the semi-empirical theory of KEE [5], electrons are excited along the trajectories, depending on the inelastic stopping power S, (= - dE/ds): N = Se(E)/e, where E is the average energy deposited to excite an electron. Transports of the excited electrons to the surface, involving an electron multiplication, i.e., a cascade process, are described by an exponential attenuation function exp(-x/L,), where x is the excitation depth and L, is the mean electron attenuation length. With P being the probability for an electron to overcome the surface
0168-583X/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved 0168-583)3(93)EO611-J
SD1
procedure
IL Ohya, J. Kawata /Nucl.
Instr. and Meth. in Phys. Res. B 90 (1994) 552-555
potential barrier, the total number of electrons emitted from the surface per ion impact is the sum of (P/e)S,(E) exp( -x/L,) along trajectories of an incident ion and all recoiling target atoms generated. Although P, E and L, are important parameters for calculation of the KEE yield, the ratio y(+)/y(O) is independent of both P and E. The L, is determined using the Ono-Kanaya formula [6], which is correlated with regularitiesOof material eoements in the periodic table; e.g., 48.1 A for C, 15.5 A for Cu and 13.7 A for Au. The deviations from the inverse cosine law of the incident angle dependence of the KEE yield are represented by a fitting parameter f to a relationship in the form [1,2]
744)/r(O) = (cosWf>
0.0
0
20
40
60
80
Fig. 2. Variation of the fitting parameter f in y(d)/y(O)= (cos 4)-f with atomic number 2, of ions impacting on Cu.
where the fit is applied for angles of less than 60”.
3. Results and discussion In Figs. 1 and 2, the present calculations of the fitting parameter f as functions of the energy and atomic number of the ion, respectively, are shown for impact on Cu. f is less than 1 at low energy, and is more than 1 at high energy; with further increasing energy, it approaches the inverse cosine law (f = 1). As the ion mass is increased, these variations of f shift towards the high-energy side (Fig. l), and the value of f becomes large at both low and high energies, whereas, at intermediate energies (l-10 keV), f decreases (or then increases) as shown in Fig. 2. For light ion impact, furthermore, the KEE yield is independent of the incident angle, i.e. f= 0, at the lowest energy. In a previous paper [7], we demonstrated that the f-variation calculated for H+ and Xe+ impacts on Cu was in
1.0
-7
0.5
0.0
102
10’
10’
105
Ei (ev) Fig. 1. Variation of the fitting parameter f in y(q%)/y(O)= (cos (6)-f with energy Ei of ions impacting on Cu.
good agreement with experimental data at intermediate and high energies. Several reasons can be identified for these deviations from the inverse cosine law [1,2]: 1) the electronic energy loss of the ions during the passage of the electron escape depth cannot be constant; 2) large-angle scattering and backscattering of the ions due to the elastic collision from the target atoms in the electron escape depth cause the assumption of straight-line trajectories to break down; 3) recoiling target atoms generated in the elastic collisions also excite electrons. A tentative calculation with inelastic energy loss of the ion, but without elastic collision, demonstrates that the effect (1) is negligible, except for very low energy (< 1 keV), where it contributes negatively. For the discussion of the effects (2) and (3), three contributions to the KEE yield y are distinguished: the first is the yield -yt due to the ions that are ultimately trapped inside the target, the second is yb due to the backscattered ion, and the third is yr due to recoiling target atoms; y = yi + yr, yi = yt + yt,, where yi is the yield due to the incident ion. In Fig. 3, the incident angle dependences of the three types of KEE are represented by the parameter f as a function of the atomic number of the incident ion. The incident angle dependence of the KEE by the trapped ion is under the inverse cosine (f< l), and approaches this with increasing impact energy. This negative contribution of the trapped ion is caused by largely dispersed trajectories of the ions in the electron escape depth; as the impact energy is increased, the ion trajectories are arranged in the direction of the incidence due to small and few elastic scattering from the target atoms, so that f= 1. The large f of the KEE by backscattered ions is related to the increase in the backscattering coefficient VII. SECONDARY EMISSION
II Ohyq J. Kawuta /Nucl. In&. und Me&. in Fhys. Res. B 90 (1994) 552-5.55
554
with oblique incidence, which results in a large amount
of additional electron excitations within the electron escape depth when the ion is backscattered. Except for light and low-energy ions, however, a small backscattering coefficient contributes little to the incident angle dependence of the KEE yield. For heavy ion impacts, although the contribution of the backscattered ions is negligible, a large number of fast recoiling target atoms is generated. At high impact energy, the recoiling target atoms contribute positively to the incident angle dependence of the KEE yield, whereas, at low impact energy, an opposite trend is found. The variations of the f-parameter of the KEE by the recoiling target atoms with the impact energy and atomic number of the incident ion, are very analogous to that of the total KEE yield (Fig. 2). The positive contribution at high impact energy is due to the electron excitation of the fully developed collision cascade of the recoiling target atoms; the cascade, which is distributed over the electron escape depth, tends to be within it when the ion incidence is inclined. At low and intermediate impact energies, depending
00
1.5
0
/ 1 oooO
00 1.0.
El cl
ic-,
cl
clue
cl 0.5
Fig. 4. Variation of the fitting parameter f in y($)/y(O)= (cos 41-f with atomic number Z, of solids under Cu+ ion impact.
on the ion mass, however, the collision cascade is close to the surface, in particular for oblique incidence of the ion. As a result, the increase in the KEE with oblique angles is suppressed because of the emission of the recoiling target atoms into a vacuum, i.e., sputtering, without exciting electrons. In Fig. 4, the fitting parameter f for Cu’ ion impact on various solids is shown as a function of the atomic number of the solids for different impact energies, Substantial variation of f with target materials, which is related to the electron attenuation length L,, is clearly found.
mm
4, Conclusions
I
OO
20
40
60
80
Fig. 3. Variation of the fitting parameter f with atomic number Z, (a) for the KEEs y1 and -yr, due to the trapped ions and recoiling target atoms, respectively, in Cu, and (b) for the =E -yb due to backscattered ions.
The Monte Carlo simulation of transport of an incident ion and recoiling target atoms is combined with the semi-empirical theory of ion-induced kinetic electron emission (ISEE) of solids for calculating the incident angle dependence of the KEE yield. The transport of the electrons excited in the solids towards the surface is replaced by an exponential attenuation with the mean attenuation length of low-energy electrons by Ono and Kanaya. The emphasis is put on the deviation from the inverse cosine law of the incident angle dependence at angles from 0” (normal incidence) to 60”. The crucial points of our ~aicuIation are as follows: (1) Due to frequent elastic collisions with target atoms, largely distributed trajectories of the ions in the electron escape depth contribute negatively to the incident angle dependence. (2) Backscattering of the ions due to large-angle scattering through the elastic collisions contributes positively, in particular for light and low-energy ion impacts. For heavy or high-energy ions, however,
K. Ohya, J. Kawata /Nucl.
Instr. and Meth. in Phys. Res. B 90 (1994) 552-555
this effect is negligible because of the small backscattering coefficient. (3) The effect of high-energy recoiling target atoms, generated through the elastic collisions, on the deviation from the inverse cosine law of the incident angle dependence is much greater than that of the trajectory distribution and backscattering of the incident ions. The positive (negative) contribution to the incident angle dependence is dominant for high (low) impact energy.
555
[3] J.P. Biersack and W. E&stein, Appl. Phys. A 34 (1984) 73. [4] J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985) vol. 1, chap. 2. [5] R.A. Baragiola, E.V. Alonso and A. Oliva Florio, Phys. Rev. B 19 (1979) 121. [6] S. Ono and K. Kanaya, J. Phys. D 12 (1979) 619. [7] J. Kawata and K. Ohya, Radiat. Eff. Def. Solids 25 (1993).
References 111W.O. Hofer, Scanning Microsc. Suppl. 4 (1990) 265. [21 D. Hasselkamp, in: Particle Induced Electron Emission II (Springer, Berlin, 1992) p. 1.
VII. SECONDARY EMISSION
Nuclear Instruments and Methods in Physics Research B 90 (1994) 552-555 North-Holland
Beam Interactions with Materials A Atoms
Monte Carlo study of incident-angle dependence of ion-induced kinetic electron emission from solids K. Ohya ‘,* and J. Kawata b a Department of Electrical and Electronic
Engineering, The University of Tokushirna, Tokushima 770, Japan b Department of Information Engineering, Takuma National College of Technology, Takuma-cho, Mitoyo-gun, Kagawa 769-11, Japan
The incident angle dependence of ion-induced kinetic electron emission (KEE) from solids is calculated using a Monte Carlo simulation of the transport of incident ions and recoiling target atoms, and a semi-empirical theory of KEE. The emphasis is put on the origin of the deviation from the inverse cosine law. The effect of the high-energy recoiling target atoms on the deviation is much greater than that of the trajectory distribution and backscattering of the incident ions, except for light and low-energy ion impact. The positive (negative) contribution of the recoiling target atoms to the incident angle dependence is dominant for high (low) impact energy. The deviation can be explained by the increase in the electron excitation by recoiling target atoms localized near the surface and the increase in the emission of the atoms, i.e., sputtering.
1. Introduction Ion-induced electron emission from solid surfaces can be ascribed to the processes of potential emission and kinetic emission. The kinetic electron emission (KEE) results from a large number of scattering and energy loss processes after the ion has hit the surface. The incident angle has a strong influence on the KEE yield. The KEE yield is directly related to the amount of electronic excitation generated by the ion within the electron escape depth of the solid. Thus, by changing the incidence from normal to oblique angles, the path length of the ion within the electron escape depth is prolonged, and thereby its deposition of excitation energy (the KEE yield) increases. A simple geometric model [1,2], which assumes constant electronic stopping along the ion trajectory in the electron escape depth and disregards elastic scattering of the ions by target atoms (straight-line trajectory), derives the relationship in the form, y(+)/-y(O) = (cos 4)-l; ~(4) and r(O) are the KEE yields at an incident angle 4 measured from the surface normal and at normal incidence, respectively. Except for high impact energies of more than several 100 keV, however, due to the breakdown of the assumptions in the model, experimental data largely deviate from the inverse cosine law and vary in a complex manner, depending on the impact energy, and ion and target species [2].
* Corresponding 54 9632.
author, tel. +81 886 23 2311, fax +81 886
For heavy ion impacts, the energy deposition of the ion in the target is mostly produced by successive and large angle scattering due to the elastic collisions with the target atoms, in particular at low impact energy. In such cases the electron excitation is substantially due to recoiling target atoms which receive more kinetic energy than displacement energy through elastic collisions. In this paper, the incident angle dependence of the KEE yield is calculated by using a combined Monte Carlo simulation of transport of incident ions and recoiling target atoms, and the KEE semi-empirical theory. The calculation is made for all ion-target combinations of 11 elements with Z = 6-79 in a wide energy range from 0.1 to 100 keV.
2. Calculation
Trajectories of incident ions and all recoiling target atoms are followed in 3-dimensional space by the same Monte Carlo algorithm as the TRIM.SP code [3] using the ZBL potential [4]. In accordance with the semi-empirical theory of KEE [5], electrons are excited along the trajectories, depending on the inelastic stopping power S, (= - dE/ds): N = Se(E)/e, where E is the average energy deposited to excite an electron. Transports of the excited electrons to the surface, involving an electron multiplication, i.e., a cascade process, are described by an exponential attenuation function exp(-x/L,), where x is the excitation depth and L, is the mean electron attenuation length. With P being the probability for an electron to overcome the surface
0168-583X/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved 0168-583)3(93)EO611-J
SD1
procedure
IL Ohya, J. Kawata /Nucl.
Instr. and Meth. in Phys. Res. B 90 (1994) 552-555
potential barrier, the total number of electrons emitted from the surface per ion impact is the sum of (P/e)S,(E) exp( -x/L,) along trajectories of an incident ion and all recoiling target atoms generated. Although P, E and L, are important parameters for calculation of the KEE yield, the ratio y(+)/y(O) is independent of both P and E. The L, is determined using the Ono-Kanaya formula [6], which is correlated with regularitiesOof material eoements in the periodic table; e.g., 48.1 A for C, 15.5 A for Cu and 13.7 A for Au. The deviations from the inverse cosine law of the incident angle dependence of the KEE yield are represented by a fitting parameter f to a relationship in the form [1,2]
744)/r(O) = (cosWf>
0.0
0
20
40
60
80
Fig. 2. Variation of the fitting parameter f in y(d)/y(O)= (cos 4)-f with atomic number 2, of ions impacting on Cu.
where the fit is applied for angles of less than 60”.
3. Results and discussion In Figs. 1 and 2, the present calculations of the fitting parameter f as functions of the energy and atomic number of the ion, respectively, are shown for impact on Cu. f is less than 1 at low energy, and is more than 1 at high energy; with further increasing energy, it approaches the inverse cosine law (f = 1). As the ion mass is increased, these variations of f shift towards the high-energy side (Fig. l), and the value of f becomes large at both low and high energies, whereas, at intermediate energies (l-10 keV), f decreases (or then increases) as shown in Fig. 2. For light ion impact, furthermore, the KEE yield is independent of the incident angle, i.e. f= 0, at the lowest energy. In a previous paper [7], we demonstrated that the f-variation calculated for H+ and Xe+ impacts on Cu was in
1.0
-7
0.5
0.0
102
10’
10’
105
Ei (ev) Fig. 1. Variation of the fitting parameter f in y(q%)/y(O)= (cos (6)-f with energy Ei of ions impacting on Cu.
good agreement with experimental data at intermediate and high energies. Several reasons can be identified for these deviations from the inverse cosine law [1,2]: 1) the electronic energy loss of the ions during the passage of the electron escape depth cannot be constant; 2) large-angle scattering and backscattering of the ions due to the elastic collision from the target atoms in the electron escape depth cause the assumption of straight-line trajectories to break down; 3) recoiling target atoms generated in the elastic collisions also excite electrons. A tentative calculation with inelastic energy loss of the ion, but without elastic collision, demonstrates that the effect (1) is negligible, except for very low energy (< 1 keV), where it contributes negatively. For the discussion of the effects (2) and (3), three contributions to the KEE yield y are distinguished: the first is the yield -yt due to the ions that are ultimately trapped inside the target, the second is yb due to the backscattered ion, and the third is yr due to recoiling target atoms; y = yi + yr, yi = yt + yt,, where yi is the yield due to the incident ion. In Fig. 3, the incident angle dependences of the three types of KEE are represented by the parameter f as a function of the atomic number of the incident ion. The incident angle dependence of the KEE by the trapped ion is under the inverse cosine (f< l), and approaches this with increasing impact energy. This negative contribution of the trapped ion is caused by largely dispersed trajectories of the ions in the electron escape depth; as the impact energy is increased, the ion trajectories are arranged in the direction of the incidence due to small and few elastic scattering from the target atoms, so that f= 1. The large f of the KEE by backscattered ions is related to the increase in the backscattering coefficient VII. SECONDARY EMISSION
II Ohyq J. Kawuta /Nucl. In&. und Me&. in Fhys. Res. B 90 (1994) 552-5.55
554
with oblique incidence, which results in a large amount
of additional electron excitations within the electron escape depth when the ion is backscattered. Except for light and low-energy ions, however, a small backscattering coefficient contributes little to the incident angle dependence of the KEE yield. For heavy ion impacts, although the contribution of the backscattered ions is negligible, a large number of fast recoiling target atoms is generated. At high impact energy, the recoiling target atoms contribute positively to the incident angle dependence of the KEE yield, whereas, at low impact energy, an opposite trend is found. The variations of the f-parameter of the KEE by the recoiling target atoms with the impact energy and atomic number of the incident ion, are very analogous to that of the total KEE yield (Fig. 2). The positive contribution at high impact energy is due to the electron excitation of the fully developed collision cascade of the recoiling target atoms; the cascade, which is distributed over the electron escape depth, tends to be within it when the ion incidence is inclined. At low and intermediate impact energies, depending
00
1.5
0
/ 1 oooO
00 1.0.
El cl
ic-,
cl
clue
cl 0.5
Fig. 4. Variation of the fitting parameter f in y($)/y(O)= (cos 41-f with atomic number Z, of solids under Cu+ ion impact.
on the ion mass, however, the collision cascade is close to the surface, in particular for oblique incidence of the ion. As a result, the increase in the KEE with oblique angles is suppressed because of the emission of the recoiling target atoms into a vacuum, i.e., sputtering, without exciting electrons. In Fig. 4, the fitting parameter f for Cu’ ion impact on various solids is shown as a function of the atomic number of the solids for different impact energies, Substantial variation of f with target materials, which is related to the electron attenuation length L,, is clearly found.
mm
4, Conclusions
I
OO
20
40
60
80
Fig. 3. Variation of the fitting parameter f with atomic number Z, (a) for the KEEs y1 and -yr, due to the trapped ions and recoiling target atoms, respectively, in Cu, and (b) for the =E -yb due to backscattered ions.
The Monte Carlo simulation of transport of an incident ion and recoiling target atoms is combined with the semi-empirical theory of ion-induced kinetic electron emission (ISEE) of solids for calculating the incident angle dependence of the KEE yield. The transport of the electrons excited in the solids towards the surface is replaced by an exponential attenuation with the mean attenuation length of low-energy electrons by Ono and Kanaya. The emphasis is put on the deviation from the inverse cosine law of the incident angle dependence at angles from 0” (normal incidence) to 60”. The crucial points of our ~aicuIation are as follows: (1) Due to frequent elastic collisions with target atoms, largely distributed trajectories of the ions in the electron escape depth contribute negatively to the incident angle dependence. (2) Backscattering of the ions due to large-angle scattering through the elastic collisions contributes positively, in particular for light and low-energy ion impacts. For heavy or high-energy ions, however,
K. Ohya, J. Kawata /Nucl.
Instr. and Meth. in Phys. Res. B 90 (1994) 552-555
this effect is negligible because of the small backscattering coefficient. (3) The effect of high-energy recoiling target atoms, generated through the elastic collisions, on the deviation from the inverse cosine law of the incident angle dependence is much greater than that of the trajectory distribution and backscattering of the incident ions. The positive (negative) contribution to the incident angle dependence is dominant for high (low) impact energy.
555
[3] J.P. Biersack and W. E&stein, Appl. Phys. A 34 (1984) 73. [4] J.F. Ziegler, J.P. Biersack and U. Littmark, The Stopping and Range of Ions in Solids (Pergamon, New York, 1985) vol. 1, chap. 2. [5] R.A. Baragiola, E.V. Alonso and A. Oliva Florio, Phys. Rev. B 19 (1979) 121. [6] S. Ono and K. Kanaya, J. Phys. D 12 (1979) 619. [7] J. Kawata and K. Ohya, Radiat. Eff. Def. Solids 25 (1993).
References 111W.O. Hofer, Scanning Microsc. Suppl. 4 (1990) 265. [21 D. Hasselkamp, in: Particle Induced Electron Emission II (Springer, Berlin, 1992) p. 1.
VII. SECONDARY EMISSION