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Computer simulations of relaxation processes in scattering of multi-charged ions from metal surfaces
Nuclear Instruments and Methods in Physics Research B67 (1992) 126-131 North-Hollland
Nuclear Instruments & Methods JnPhy~cs Research SeclJon B
Computer simulations of relaxation processes in scattering of multi-charged ions from metal surfaces S.H. Overbury, F.W. Meyer and M.T. Robinson Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6201, USA
The dynamics of KLL Auger electron production resulting from the scattering of multi-charged, hydrogenlike ions from solid surfaces hL,s been modeled by scattering simulations. The model is based upon Two sequential steps involving L-shell filling followed by KLL Auger decay. Simulated results are found to adequately describe experimental Auger yields and their dependence upon scattering conditions. Depth distribution of the electron emission is discussed along with the dependence of the yields upon model parameters, incident azimuthal angle and the effects of crystal damage.
1. Introduction Recenl experiments in scattering of multi-charged io:Js front metal surfaces reveal that the presence of core level vacancies on the incident ion can lead to characteristic projectile Auger electrons and also target Auger electrons created b j vacancy transfer from the ion to target atoms [1-4]. It has been recognized that above surface neutralization, occurs rapidly into highly excited states leading to multi-excited "hollow" atoms [5,6]. However, de-excitation to the ground state is a much slower process. In the case of hydrogenlike ions, e.g. C 5+, N 6+, O 7+, calculations of the electronic relaxation indiczte that eventual K vacancy decay may be expected to require times which are long compared to the interaction time of the projectile above the surface [7]. Yet, observed Doppler shifts in projectile KLL Auger energies appear to indicate that emission occurs on the incoming path [1,4], seemingly contradicting IJhe electronic relaxation calculations. Also, measurements of LMM and KLL Auger yields indicate that the ratio of L M M / K L L Auger yields are too low to be consistent with Auger cascade de-excitation [4]. In the following we report computer simulations of ion scattering dynamics for N ~+ ions incident on Au and Cu targets which help to explain these apparent contradictions.
2. Computational model The computer simulat;ons made use of the computer simulation code M A R L O W E described elsewhere [8]. The version used has provisions for extracting timing information throughout a trajectory. A shortened version of the code was used which follows
only the primary particle, so that a full target displacement cascade is not developed. The code was adapted to run on a 386 series computer under MS-DOS. In all the simulations described below, the thickness of the Au or Cu targets was fixed at ten lattice constants. Room temperature thermal displacements are incorporated using Debye temperatures of 110 and 340 K for Au and Cu, respectively. A screened Coulomb potential suggested by Ziegler, Biersack and Littmark was used [9], and inelastic losses of the ions were applied using a model whicl~ incorporates both apsis dependent and apsis independent losses [7]. A simplified model to describe the dynamics of KLL Auger decay of multi-charged ions was developed. As the ion approaches the surface in its initial state, rapid electron transfer occurs into loosely bound Rydberg states. During the subsequent complex cascade, first described by Arifov [10], electrons are ejected from the projectile via Auger processes. This cascade is not completed prior to projectile penetration of the surface. The slow cascade process is by-passed once the projectile enters the target since more direct charge transfer into the projectile L shell becomes possible. This rate of L shell filling is determined by multiple processes including LMM Auger transitions and, in later stages even direct charge transfer into the L shell from the valence band of the target. As the trajectory evolves, the projectile eventually reaches a second state in which it has sufficient L shell population that subsequent K Auger decay is likely. The speed at which the projectile achieves this second state is assumed to be described by a linear rate process with a single rate constant kt.. Once this state is achieved the projectile may then undergo KLL Auger decay into the third state of interest via another I~inear rate process described by the rate constant k K.
0168-583X/92/$05.00 © 1992 - El:;evier Science Publishers B.V. All rights reserved
S.H. Overbury et al. / Relaxation processes in ion scattering
A set of coupled differential equations relating the evolution of the three states [14] are solved along each trajecto;y using a variable time step determined by the interval between sequential collisions. This time step was verified to he sufficiently short to give accurate integration of the rate equations, and corrections were made at each step to ensure that the probability of the three stah:s summed to unity. It was also possible to include K vacancy transfer from an unrelaxed projectile to a target atom. Within the model, this process occurred with probability PK whenever a collision occurred with apsis less than r c. This inner shell vacancy transfer process [11,12] was included to account for target Auger emission observed experimentally [2,3]. The probability, P, of observing the target or projectile Auger electron, emitted without energy loss, is dependent upon the depth, d, of the projectile within the slab at the time of the event, according to the usual escape probability P = c x p ( - d / A cos 0). In this expression, A is the electron inelastic mean free path and 0 is the exit angle as determined by the location of the detector with respect to the surface normal. Energy distributions of the emitted projectile Auger electrons were obtained by assuming that the electron is emitted isotropically with center-of-mass (c.o.m.) energy chosen from a Gaussian distribution centered around 380 eV. The laboratory energy was computed using the standard kinematic frame transformation based on the velocity vector of the ion with respect to the detector direction at the time of emission. The calculated observable yields and energy distributions were then compared directly with experimental results measured at the ORNL-ECR source with an angle differentiated electron energy analyzer as described elsewhere [14]. In the model described above, we have neglected direct, projectile K shell filling by target electrons. The possibility of Auger neutralization processes (e.g. KVV transitions) were discounted, since these would result in electron emission at about the same energy as KLL emission, but which is not Doppler shifted, contrary to experimental observation [14]. In addition, the overlap between target valence or core electrons and the projectile K level should be significantly smaller than the overlap between the projectile L and K shells. The concentration of projectile L shell electrons near the K vacancy should cause the KLL Auger rates to exceed rates of Auger de-excitation or Auger neutralization. Three shortcomings of this model should be mentioncd. First, the scattering potential used is appropriate for neutral collision partners while in the experiment charge state and electronic configuration of the projectile change throughout the trajectory. Second, the rate of L shell filling, k L, might also be expected to vary with time, dependent upon charge and degree of excitation. Third, the electron transport model is very
127
simple, e.g., inelastically scattered electrons are not included in computed yields even though energy losses may be sufficiently small to render them indistinguishable from other emitted (Doppler broadened) electrons. Future, more detailed calculations should address these issues.
3.
Results
The depth distribution of the KLL Auger emission is shown in fig. 1, computed for 60 keV nitrogen incident on Au(ll0) at an angle O = 10°, with respect to the plane of the surface. The distribution was computed for k L = k z = O . 1 fs -I. This distribution weighted by the escape probability, i.e. the "observable" emission, is also shown. An escape depth, A = 1.0 nm was used. It is seen that even for this relatively grazing angle of incidence, emission occurs quite deeply into the solid, so that the escape length plays an important role in determining observable emission yields. The emission depths, and therefore the observable yields, depend in part upon the values of the parameters k K and k L. The lifetime of K vacancies in N + ions is about 10 fs [13] and is likely independent of the environment of the N atom, suggesting the value kK=O.1 fs -I. Fig. 2 shows the dependence of the computed (observable) KLL Auger yields upon the parameter k L. Results are shown for two values of the escape depth, chosen to span the range expected for 380 eV N KLL Auger electrons, and for four different angles of incidence. Increasing A causes an overall increase in the
~= 0.8
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60 key N - Au(llO)
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.~ 0.4 0.2 Y
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observable i
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,
r
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2
i
3
,
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D E P T H (nm)
Fig. 1. The simulated distribution of depth for projectile KLL Auger emission is shown (open circles). The "observable" distribution, obtained by including an escape probability determined from A= 1.0 nm is also shown (filled circles). II. CAPTURE AND LOSS
128
S.H. Overbury et aL / Relaxation processes in ion scattering
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k L(fs" ) Fig. 2. The dependence of KLL Auger yield upon the L shell filling rate constant, k L, is shown. Simulations done for four different incident angles and two different assumed values of the escape depth, A, are indicated by points and solid curves. Yields obtained in the limit of infinitely fast L shell filling (incident pnrojectiles have filled L shells) are included. Experimental yieMs taken from ref. [14] are indicated by dashed lines and were measured for the same incidence angles (within 0.5°) as used in the simulations. Experimental yields increased uniformly with decreasing 0.
important at grazing angles of incidence, is that projectiles are reflected from the surface before they obtain sufficient electrons to allow K L L Auger decay to occur. This effect is responsible for the decrease in yield for 0 = 1.5 ° when k L < 0.2 f s - n. Experimentally measured yields are indicated in fig. 2 by dashed lines, obtained at each of the four incidence angles used in the simulations [14]. The intersections o f the dashed lines with the curves computed for A = 1.0 nm imply a value o f k L = 0.1 f s - n, although at A = 20 ° a slightly higher value is suggested. This result confirms the rate limiting nature o f the L shell filling. The survival o f ions with insufficient L shell electrons, deduced from the simulation, implies that this fraction must escape in a charge state of at least 3 + . The present results predict that such ions should be observed for 60 keY N 6+ on Au and should have maximum yields for incident angles of 1-3 ° d e p e n d e n t upon azimuth. M e a s u r e m e n t s o f reflected ion charge state distributions p e r f o r m e d in our laboratory for lower energy N 6+ ions incident on Cu at 0.5-2 ° grazing angles showed no scattered N 3+. However, measureable amounts of scattered Ne 3+ have been observed for 20 keY hydrogenlike Ne 9+ incident on W at 15 °
[151. A c o m p u t e d energy distribution o f the emitted electrons is shown in fig. 3 for a 10° incidence angle and for a detector located at 90 ° to the incoming beam direction. The total emission is divided into two components, that which is emitted while the ion is within the slab and that which is emitted after the ion is reflected from the surface. The emission that occurs
0.6 yields especially for 0 > 5 °, demonstrating that appreciable emission occurs at depths comparable to or greater than A. For 0 < 1.5° most emission occurs very near the surface and is i n d e p e n d e m o f A. In the limit o f large values o f k k > > k K, the K L L Auger yields d e p e n d only on the rate k K. T h e dependence o f this yield u p o n incidence angle is determined principally by the d e p t h distribution o f the ion scattering. At grazing angles the ion reflection coefficient is unity and1 most ions do not p e n e t r a t e very deeply, so most emission occurs close to the surface, giving a yield o f nearly, one electron p e r ion. At high angles of ineideoce; the reflection coefficient decreases and most ions p e n e t r a t e d e e p e r than A, so significant K A u g e r decay occurs at depths larger than A. A t values o f k L comparable to k K, the yield decreases because o f two effects. Because o f the slower rate o f L-shell filling, the ions penetrate d e e p e r before they undergo K A u g e r decay, decreasing the probability o f observing the electron. T h e second factor, most
g
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I
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d 0.0
___
300
400
500
Electron Energy (ev) Fig. 3. Simulated energy distribution of emitted KLL Auger electrons is indicated by open circles. The contributions emitted from projectiles within the target and from pro.;ecti es already scattered from the surface are indicated.
129
S.H. Overbury et al. / Relaxation processes in ion scattering
within the slab is described approximately by a Gaussian profile with about the same mean energy and variance as was given the electrons in the c.o.m, frame. This indicates that most ions continue through the slab with only small amounts of angular straggling. This fact is borne out also by the computed mean times required for the ions to pass through the slab. Emission which occurs subsequent to reflection is Doppler shifted to higher energy as a consequence of the ions exiting from the surface closer to the detector direction. For all incidence angles, this strongly scattered component is the smaller component of the emission. At very grazing incident angles where scattering occurs nearly specularly, there is only small angle deflection of the ion beam. At larger incidence angle most of the electron emission comes from the mostly undeflected ion beam as it penetrates the slab. At either extreme the energy distribution is determined by the initial c.o.m. energy of the electron and the detection angle with respect to the incident ion beam direction. Changing the detection angle causes a uniform Doppler shift of the electron distribution in agreement with experimentally measured shifts [14]. Therefore, at these energies the Doppler shifts suggest that all emission occurs along the incoming path, in spite of the fact that the electron emission originates from well below the surface. Since the yields are related to ion reflection and depth of penetration, it is expected that they will depend upon the defect density in the crystal and, for a single crystal, upon the azimuthal angle of incidence. In fig. 4 the computed azimuthal angle dependence of the yield is shown for four angles of incidence for 60 keV N on Cu(001). These results are calculated for kL--0.5 fs - l = 5 k K and A = 1.0 nm. It is seen that at the most grazing angles of incidence, the yields are near unity, independent of azimuth, because the surface is 100% reflective and the depth of penetration is small. At higher angles of incidence structure appears. For example, at 50 incidence the yields are very sensitive to azimuth near the [110] direction. The variation in yield is caused by variation in the depth of emission, which in turn is determined by the angular variation in the ion reflection coefficients which are well known to be strongly angle dependent. Computed points are connected by lines. However, abrupt variations may occur with changes in angle which are smaller than the spacing between points. Experimental azimuthal angle dependencies are shown for comparison [14]. At ~0= 5° there is fairly good agreement between the computed and experimental data. However, at ~ = 10° and 20° the agreement is marginal in the sense that the structure in the experimental yield curves is not well correlated with the computed azimuthal variation. Analysis is complicated by the difficulties of background subtraction which makes the experimental precision no
~okev N ' c~(oo'~) k L = o.5 fs k K = 0.1 fs-I )~ = 1.0nm - t.6" 1.0 8
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Fig. 4. The dependence of ~he N E L L Auger yield upon azimuthal incidence angle is shown for four different glancing incidence angles. Simulation results are shown as open symbols and experimental yields from ref. [14] are shown as filled symbols,
better than 5-10%, almost as large as the expected variation, and uncertainties in the azimuthal angles ( + 3°) which are fairly large compared to the computed sensitivity to azimuthal angle. Sensitivity to crystal damage is illustrated in fig. 5. Computed yields are shown for a perfect A u ( l l 0 ) crys-. tal, for a Au crystal with 50% vacancies randomly distributed in the outer most two layers and for amorphous Au. Simulations were performed for •incidence along the [1i0] azimuth in the two crystalline cases. In each case kL=0.1 = k K and ,~ = 1.0 rim. In addition to projectile Auger yields, target Auger yields' were also computed assuming r c = 0.4 A and Pk = 0.018. Experimentally observed projectile and target (Au NNV Auger electron) yields are shown [14] as a function of 1/Vp, where vp is the perpendicular velocity component as determined by the incident angle. Reasonably good fits to the experimental projectile yields are obtained for the perfect Au(ll0) target, although at the smallest value of 1 l o p the simulation results are too low. At this angle (@ = 20 °) many electrons are generated at depths greater, than A, and so have a high probability of inelastic scattering. The simulations ignore this component, but it may be partly II. CAPTURE AND LOSS
S.H. Ocerbury et al. / Relaxation processes in ion scattering
130
(deg) 20 i
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5
|
i
10 i
i
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tO) o • damaged Au(l tO) v , amorphous Au _ 0 • AU(1
~
ProjecLile yield
fects which decrease the probability of close encounters necessary for target Auger production. These effects are defeated by point defects or by amorphous structure. Along the [1i0] azimuth the ions can be smoothly reflected from [1]0] rows and troughs without hard collisions which are more likely to occur if the ions are directed at an angle to these rows.
4.
} <
0.0:
O.OO~
. . . . . . . . . . . . . .
10
1/% (au)
'
100
Fig. 5. Simulated yields of target Auger electrons (filled symbols) and projectile Auger electrons (open symbols) are shown as a function of perpendicular component of incident velocity (incident angle). Results are shown for various assumptions about the structure of the slab and the incident azimuth. E~lperimental yields from ref. [14] are shown as error bars and solid curve. Simulated and experimental target yields are scaled upward by a factor of 5.
included in the broad peak observed in the experimental energy distributed which is integrated to obtain the experimental yield. The target Auger yields were adjusted (via Pk and r e) to fit the experimental yields for 1/vp < 30; but for l / v p > 90 the simulated yields drop to zero, contrary to experiment. In the: experiment the azimuthal angle was not known accurately and it was suspected that ion sputter damage had not been adequately annealed out. The effect of these two factors were investigated. It is seen that substantial vacancies in the first two layers have little effect upon the projectile yields. The extreme disorder of an amorphous target causes decreased yield for ¢, near 2 - 5 ° but increased yield at ~ = 20°. The decreased yield at grazing angles comes about because the reflection coefficient is smaller for the amorphous target, and because more of the reflected ions depart before L shell filling is complete. The largest effect of damage is upon the target yields, especially at grazing angles. A substantial target yield is experimentally observed at: ¢, = 1.5° which can be, obtained in the simulations if damage is introduced. Similarly, changing the azimuthal incidence to 5 ° from the [110] azimuth (ok = 5 °)~ can also produce an increase in target yield at grazing angles and angle dependent changes in the projectile yields. These effects upon the target yield are readily explainable by channeling and steering ef-
Conclusions
Simulations of 60 keV N 6+ scattering from Au and Cu have provided a revised interpretation of target and projectile Auger emission. We conclude that the majority of the observable emission originates after the ion has penetrated the surface but before it has undergone appreciable change in its direction of travel. Therefore, electron energy distributions exhibit Doppler shifts which are determined by the angle between the electron detector direction and the incident ion beam direction, in spite of the penetration of the solid. The "interaction time" is not limited to that portion above the surface but continues as the projectile progresses into the target, allowing adequate time for relaxation at a rate enhanced by direct L shell filling, possible inside the target. The fact that emission occurs below the surface affects the observed yields through the mean escape depth. This factor must be considered when comparing yields of electrons with different kinetic energy, for example, KLL vs LMM Auger emission. Since emission occurs below the surface, it is also expected to be sensitive to factors which affect the ion scattering and reflection such as incident azimuthal and polar angles and crystal damage. These simulation techniques can be easily extended to other energy ranges and i o n / t a r g e t combinations.
Acknowledgement
This research was sponsored by Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. DOE under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc.
References
[l] S.T. de Zwart, thesis (1987); S.T. de Zwart, A.G. Drentje, A.L. Boers and R. Morgerstern, Surf. Sci. 217 (1989) 298. [2] F.W. Meyer, C.C. Havener, K.J. Snowdon, S.H. Overbury, D.M. Zehner and W. Heiland, Phys. Rev. A35 (1987) 3176. [3] KJ. Snowdon, C.C. Havener, F.W. Meyer, S.H. Overbury, D.M. Zehner and W. Heiland, Phys. Rev. A38 (1988) 2294.
S.H. Overbury et al. / Relaxation processes in ion scattering
[4] L. Folkerts and R. Morgenstern, Europhys. Lett. 13 (1990) 377. [51 H.J. Andr~i, Nucl. Instr. and Meth. B43 (1989) 304. [6] J.P. Briand, L. de Billy, P. Charles, S. Essabaa, P. Briand, R. Geller, J.P. Desclaux, S. Bliman and C. Ristori, Phys. Rev. Lett. 65 (1990) 159. [7] P.A. Zeijlmans van Emmichoven, C.C. Havener and F.W. Meyer, Phys. Rev. A43 (1991) 1405. [8] M.T. Robinson, Phys. Rev. B40 (1989) 1071. [9] J.F. Ziegler, J.P. Biersack and U. Littmark, U.S. DOE Report ORNL/CONF-82013 (1983) p. 88. [10] U.A. Arifov, L.M. Kishinevskii, E.S. Mukhamadiev and E.S. Parilis, Soy. Phys. Tech. Phys. 18 (1973) 118.
[11] N. Stolterfoht, in: Progress in Atomic Spectroscopy, Part D, ed. H. Kleinpoppen (Plenum, New York, 1987) p. 415. [12] F.W. Meyer, C.C. Havener S.H. Overbury, K.J. Reed, KJ. Snowdon and D.M. Zehner, J. Phys. (Paris) 50 (1989) C1-263. [13] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [14] F.W. Meyer, S.H. Overbury, C.C. Havener, D.M. Zehner and P.A. Zeijlmans van Emmichoven, Phys. Rev. A44 (1991) 7214. [15] S.T. de Zwart, T. Fried, U. Jellen, A.L. Boers and A.G. Drentje, J. Phys. B18 (1985) L623.
II. CAPTURE AND LOSS
Nuclear Instruments & Methods JnPhy~cs Research SeclJon B
Computer simulations of relaxation processes in scattering of multi-charged ions from metal surfaces S.H. Overbury, F.W. Meyer and M.T. Robinson Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6201, USA
The dynamics of KLL Auger electron production resulting from the scattering of multi-charged, hydrogenlike ions from solid surfaces hL,s been modeled by scattering simulations. The model is based upon Two sequential steps involving L-shell filling followed by KLL Auger decay. Simulated results are found to adequately describe experimental Auger yields and their dependence upon scattering conditions. Depth distribution of the electron emission is discussed along with the dependence of the yields upon model parameters, incident azimuthal angle and the effects of crystal damage.
1. Introduction Recenl experiments in scattering of multi-charged io:Js front metal surfaces reveal that the presence of core level vacancies on the incident ion can lead to characteristic projectile Auger electrons and also target Auger electrons created b j vacancy transfer from the ion to target atoms [1-4]. It has been recognized that above surface neutralization, occurs rapidly into highly excited states leading to multi-excited "hollow" atoms [5,6]. However, de-excitation to the ground state is a much slower process. In the case of hydrogenlike ions, e.g. C 5+, N 6+, O 7+, calculations of the electronic relaxation indiczte that eventual K vacancy decay may be expected to require times which are long compared to the interaction time of the projectile above the surface [7]. Yet, observed Doppler shifts in projectile KLL Auger energies appear to indicate that emission occurs on the incoming path [1,4], seemingly contradicting IJhe electronic relaxation calculations. Also, measurements of LMM and KLL Auger yields indicate that the ratio of L M M / K L L Auger yields are too low to be consistent with Auger cascade de-excitation [4]. In the following we report computer simulations of ion scattering dynamics for N ~+ ions incident on Au and Cu targets which help to explain these apparent contradictions.
2. Computational model The computer simulat;ons made use of the computer simulation code M A R L O W E described elsewhere [8]. The version used has provisions for extracting timing information throughout a trajectory. A shortened version of the code was used which follows
only the primary particle, so that a full target displacement cascade is not developed. The code was adapted to run on a 386 series computer under MS-DOS. In all the simulations described below, the thickness of the Au or Cu targets was fixed at ten lattice constants. Room temperature thermal displacements are incorporated using Debye temperatures of 110 and 340 K for Au and Cu, respectively. A screened Coulomb potential suggested by Ziegler, Biersack and Littmark was used [9], and inelastic losses of the ions were applied using a model whicl~ incorporates both apsis dependent and apsis independent losses [7]. A simplified model to describe the dynamics of KLL Auger decay of multi-charged ions was developed. As the ion approaches the surface in its initial state, rapid electron transfer occurs into loosely bound Rydberg states. During the subsequent complex cascade, first described by Arifov [10], electrons are ejected from the projectile via Auger processes. This cascade is not completed prior to projectile penetration of the surface. The slow cascade process is by-passed once the projectile enters the target since more direct charge transfer into the projectile L shell becomes possible. This rate of L shell filling is determined by multiple processes including LMM Auger transitions and, in later stages even direct charge transfer into the L shell from the valence band of the target. As the trajectory evolves, the projectile eventually reaches a second state in which it has sufficient L shell population that subsequent K Auger decay is likely. The speed at which the projectile achieves this second state is assumed to be described by a linear rate process with a single rate constant kt.. Once this state is achieved the projectile may then undergo KLL Auger decay into the third state of interest via another I~inear rate process described by the rate constant k K.
0168-583X/92/$05.00 © 1992 - El:;evier Science Publishers B.V. All rights reserved
S.H. Overbury et al. / Relaxation processes in ion scattering
A set of coupled differential equations relating the evolution of the three states [14] are solved along each trajecto;y using a variable time step determined by the interval between sequential collisions. This time step was verified to he sufficiently short to give accurate integration of the rate equations, and corrections were made at each step to ensure that the probability of the three stah:s summed to unity. It was also possible to include K vacancy transfer from an unrelaxed projectile to a target atom. Within the model, this process occurred with probability PK whenever a collision occurred with apsis less than r c. This inner shell vacancy transfer process [11,12] was included to account for target Auger emission observed experimentally [2,3]. The probability, P, of observing the target or projectile Auger electron, emitted without energy loss, is dependent upon the depth, d, of the projectile within the slab at the time of the event, according to the usual escape probability P = c x p ( - d / A cos 0). In this expression, A is the electron inelastic mean free path and 0 is the exit angle as determined by the location of the detector with respect to the surface normal. Energy distributions of the emitted projectile Auger electrons were obtained by assuming that the electron is emitted isotropically with center-of-mass (c.o.m.) energy chosen from a Gaussian distribution centered around 380 eV. The laboratory energy was computed using the standard kinematic frame transformation based on the velocity vector of the ion with respect to the detector direction at the time of emission. The calculated observable yields and energy distributions were then compared directly with experimental results measured at the ORNL-ECR source with an angle differentiated electron energy analyzer as described elsewhere [14]. In the model described above, we have neglected direct, projectile K shell filling by target electrons. The possibility of Auger neutralization processes (e.g. KVV transitions) were discounted, since these would result in electron emission at about the same energy as KLL emission, but which is not Doppler shifted, contrary to experimental observation [14]. In addition, the overlap between target valence or core electrons and the projectile K level should be significantly smaller than the overlap between the projectile L and K shells. The concentration of projectile L shell electrons near the K vacancy should cause the KLL Auger rates to exceed rates of Auger de-excitation or Auger neutralization. Three shortcomings of this model should be mentioncd. First, the scattering potential used is appropriate for neutral collision partners while in the experiment charge state and electronic configuration of the projectile change throughout the trajectory. Second, the rate of L shell filling, k L, might also be expected to vary with time, dependent upon charge and degree of excitation. Third, the electron transport model is very
127
simple, e.g., inelastically scattered electrons are not included in computed yields even though energy losses may be sufficiently small to render them indistinguishable from other emitted (Doppler broadened) electrons. Future, more detailed calculations should address these issues.
3.
Results
The depth distribution of the KLL Auger emission is shown in fig. 1, computed for 60 keV nitrogen incident on Au(ll0) at an angle O = 10°, with respect to the plane of the surface. The distribution was computed for k L = k z = O . 1 fs -I. This distribution weighted by the escape probability, i.e. the "observable" emission, is also shown. An escape depth, A = 1.0 nm was used. It is seen that even for this relatively grazing angle of incidence, emission occurs quite deeply into the solid, so that the escape length plays an important role in determining observable emission yields. The emission depths, and therefore the observable yields, depend in part upon the values of the parameters k K and k L. The lifetime of K vacancies in N + ions is about 10 fs [13] and is likely independent of the environment of the N atom, suggesting the value kK=O.1 fs -I. Fig. 2 shows the dependence of the computed (observable) KLL Auger yields upon the parameter k L. Results are shown for two values of the escape depth, chosen to span the range expected for 380 eV N KLL Auger electrons, and for four different angles of incidence. Increasing A causes an overall increase in the
~= 0.8
~.
60 key N - Au(llO)
0.6
= 5°
.~ 0.4 0.2 Y
o.o
-0.2
observable i
1
,
r
i
2
i
3
,
4
D E P T H (nm)
Fig. 1. The simulated distribution of depth for projectile KLL Auger emission is shown (open circles). The "observable" distribution, obtained by including an escape probability determined from A= 1.0 nm is also shown (filled circles). II. CAPTURE AND LOSS
128
S.H. Overbury et aL / Relaxation processes in ion scattering
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.
.
.
0.4
/ __,._.~
s,
0.~ F * / "10
.
.~
0,t./<<°-.-
.o_
.
.
.
0.6
oo
0
]
'I
-.
I
1.0
1
.
0.8
1.0
oo
k L(fs" ) Fig. 2. The dependence of KLL Auger yield upon the L shell filling rate constant, k L, is shown. Simulations done for four different incident angles and two different assumed values of the escape depth, A, are indicated by points and solid curves. Yields obtained in the limit of infinitely fast L shell filling (incident pnrojectiles have filled L shells) are included. Experimental yieMs taken from ref. [14] are indicated by dashed lines and were measured for the same incidence angles (within 0.5°) as used in the simulations. Experimental yields increased uniformly with decreasing 0.
important at grazing angles of incidence, is that projectiles are reflected from the surface before they obtain sufficient electrons to allow K L L Auger decay to occur. This effect is responsible for the decrease in yield for 0 = 1.5 ° when k L < 0.2 f s - n. Experimentally measured yields are indicated in fig. 2 by dashed lines, obtained at each of the four incidence angles used in the simulations [14]. The intersections o f the dashed lines with the curves computed for A = 1.0 nm imply a value o f k L = 0.1 f s - n, although at A = 20 ° a slightly higher value is suggested. This result confirms the rate limiting nature o f the L shell filling. The survival o f ions with insufficient L shell electrons, deduced from the simulation, implies that this fraction must escape in a charge state of at least 3 + . The present results predict that such ions should be observed for 60 keY N 6+ on Au and should have maximum yields for incident angles of 1-3 ° d e p e n d e n t upon azimuth. M e a s u r e m e n t s o f reflected ion charge state distributions p e r f o r m e d in our laboratory for lower energy N 6+ ions incident on Cu at 0.5-2 ° grazing angles showed no scattered N 3+. However, measureable amounts of scattered Ne 3+ have been observed for 20 keY hydrogenlike Ne 9+ incident on W at 15 °
[151. A c o m p u t e d energy distribution o f the emitted electrons is shown in fig. 3 for a 10° incidence angle and for a detector located at 90 ° to the incoming beam direction. The total emission is divided into two components, that which is emitted while the ion is within the slab and that which is emitted after the ion is reflected from the surface. The emission that occurs
0.6 yields especially for 0 > 5 °, demonstrating that appreciable emission occurs at depths comparable to or greater than A. For 0 < 1.5° most emission occurs very near the surface and is i n d e p e n d e m o f A. In the limit o f large values o f k k > > k K, the K L L Auger yields d e p e n d only on the rate k K. T h e dependence o f this yield u p o n incidence angle is determined principally by the d e p t h distribution o f the ion scattering. At grazing angles the ion reflection coefficient is unity and1 most ions do not p e n e t r a t e very deeply, so most emission occurs close to the surface, giving a yield o f nearly, one electron p e r ion. At high angles of ineideoce; the reflection coefficient decreases and most ions p e n e t r a t e d e e p e r than A, so significant K A u g e r decay occurs at depths larger than A. A t values o f k L comparable to k K, the yield decreases because o f two effects. Because o f the slower rate o f L-shell filling, the ions penetrate d e e p e r before they undergo K A u g e r decay, decreasing the probability o f observing the electron. T h e second factor, most
g
60keY N - Au(llO) o
0.5
~ = to
k L = k K = O. i fs - l X = 1.0 n m
I
0.4
C
~
total
-0 o
<
o.,
I
d 0.0
___
300
400
500
Electron Energy (ev) Fig. 3. Simulated energy distribution of emitted KLL Auger electrons is indicated by open circles. The contributions emitted from projectiles within the target and from pro.;ecti es already scattered from the surface are indicated.
129
S.H. Overbury et al. / Relaxation processes in ion scattering
within the slab is described approximately by a Gaussian profile with about the same mean energy and variance as was given the electrons in the c.o.m, frame. This indicates that most ions continue through the slab with only small amounts of angular straggling. This fact is borne out also by the computed mean times required for the ions to pass through the slab. Emission which occurs subsequent to reflection is Doppler shifted to higher energy as a consequence of the ions exiting from the surface closer to the detector direction. For all incidence angles, this strongly scattered component is the smaller component of the emission. At very grazing incident angles where scattering occurs nearly specularly, there is only small angle deflection of the ion beam. At larger incidence angle most of the electron emission comes from the mostly undeflected ion beam as it penetrates the slab. At either extreme the energy distribution is determined by the initial c.o.m. energy of the electron and the detection angle with respect to the incident ion beam direction. Changing the detection angle causes a uniform Doppler shift of the electron distribution in agreement with experimentally measured shifts [14]. Therefore, at these energies the Doppler shifts suggest that all emission occurs along the incoming path, in spite of the fact that the electron emission originates from well below the surface. Since the yields are related to ion reflection and depth of penetration, it is expected that they will depend upon the defect density in the crystal and, for a single crystal, upon the azimuthal angle of incidence. In fig. 4 the computed azimuthal angle dependence of the yield is shown for four angles of incidence for 60 keV N on Cu(001). These results are calculated for kL--0.5 fs - l = 5 k K and A = 1.0 nm. It is seen that at the most grazing angles of incidence, the yields are near unity, independent of azimuth, because the surface is 100% reflective and the depth of penetration is small. At higher angles of incidence structure appears. For example, at 50 incidence the yields are very sensitive to azimuth near the [110] direction. The variation in yield is caused by variation in the depth of emission, which in turn is determined by the angular variation in the ion reflection coefficients which are well known to be strongly angle dependent. Computed points are connected by lines. However, abrupt variations may occur with changes in angle which are smaller than the spacing between points. Experimental azimuthal angle dependencies are shown for comparison [14]. At ~0= 5° there is fairly good agreement between the computed and experimental data. However, at ~ = 10° and 20° the agreement is marginal in the sense that the structure in the experimental yield curves is not well correlated with the computed azimuthal variation. Analysis is complicated by the difficulties of background subtraction which makes the experimental precision no
~okev N ' c~(oo'~) k L = o.5 fs k K = 0.1 fs-I )~ = 1.0nm - t.6" 1.0 8
~' &
0.~
~, o.s .~ =1o o
•....
_~ ~
,9,,Rr-.
.J ~
0.4
•ib
0.0
.
2o °
i
/
h
i
i
0 [loo]
10
20
30
40
50 D~o]
,@(deg)
Fig. 4. The dependence of ~he N E L L Auger yield upon azimuthal incidence angle is shown for four different glancing incidence angles. Simulation results are shown as open symbols and experimental yields from ref. [14] are shown as filled symbols,
better than 5-10%, almost as large as the expected variation, and uncertainties in the azimuthal angles ( + 3°) which are fairly large compared to the computed sensitivity to azimuthal angle. Sensitivity to crystal damage is illustrated in fig. 5. Computed yields are shown for a perfect A u ( l l 0 ) crys-. tal, for a Au crystal with 50% vacancies randomly distributed in the outer most two layers and for amorphous Au. Simulations were performed for •incidence along the [1i0] azimuth in the two crystalline cases. In each case kL=0.1 = k K and ,~ = 1.0 rim. In addition to projectile Auger yields, target Auger yields' were also computed assuming r c = 0.4 A and Pk = 0.018. Experimentally observed projectile and target (Au NNV Auger electron) yields are shown [14] as a function of 1/Vp, where vp is the perpendicular velocity component as determined by the incident angle. Reasonably good fits to the experimental projectile yields are obtained for the perfect Au(ll0) target, although at the smallest value of 1 l o p the simulation results are too low. At this angle (@ = 20 °) many electrons are generated at depths greater, than A, and so have a high probability of inelastic scattering. The simulations ignore this component, but it may be partly II. CAPTURE AND LOSS
S.H. Ocerbury et al. / Relaxation processes in ion scattering
130
(deg) 20 i
10
5
|
i
10 i
i
0.5 i
tO) o • damaged Au(l tO) v , amorphous Au _ 0 • AU(1
~
ProjecLile yield
fects which decrease the probability of close encounters necessary for target Auger production. These effects are defeated by point defects or by amorphous structure. Along the [1i0] azimuth the ions can be smoothly reflected from [1]0] rows and troughs without hard collisions which are more likely to occur if the ions are directed at an angle to these rows.
4.
} <
0.0:
O.OO~
. . . . . . . . . . . . . .
10
1/% (au)
'
100
Fig. 5. Simulated yields of target Auger electrons (filled symbols) and projectile Auger electrons (open symbols) are shown as a function of perpendicular component of incident velocity (incident angle). Results are shown for various assumptions about the structure of the slab and the incident azimuth. E~lperimental yields from ref. [14] are shown as error bars and solid curve. Simulated and experimental target yields are scaled upward by a factor of 5.
included in the broad peak observed in the experimental energy distributed which is integrated to obtain the experimental yield. The target Auger yields were adjusted (via Pk and r e) to fit the experimental yields for 1/vp < 30; but for l / v p > 90 the simulated yields drop to zero, contrary to experiment. In the: experiment the azimuthal angle was not known accurately and it was suspected that ion sputter damage had not been adequately annealed out. The effect of these two factors were investigated. It is seen that substantial vacancies in the first two layers have little effect upon the projectile yields. The extreme disorder of an amorphous target causes decreased yield for ¢, near 2 - 5 ° but increased yield at ~ = 20°. The decreased yield at grazing angles comes about because the reflection coefficient is smaller for the amorphous target, and because more of the reflected ions depart before L shell filling is complete. The largest effect of damage is upon the target yields, especially at grazing angles. A substantial target yield is experimentally observed at: ¢, = 1.5° which can be, obtained in the simulations if damage is introduced. Similarly, changing the azimuthal incidence to 5 ° from the [110] azimuth (ok = 5 °)~ can also produce an increase in target yield at grazing angles and angle dependent changes in the projectile yields. These effects upon the target yield are readily explainable by channeling and steering ef-
Conclusions
Simulations of 60 keV N 6+ scattering from Au and Cu have provided a revised interpretation of target and projectile Auger emission. We conclude that the majority of the observable emission originates after the ion has penetrated the surface but before it has undergone appreciable change in its direction of travel. Therefore, electron energy distributions exhibit Doppler shifts which are determined by the angle between the electron detector direction and the incident ion beam direction, in spite of the penetration of the solid. The "interaction time" is not limited to that portion above the surface but continues as the projectile progresses into the target, allowing adequate time for relaxation at a rate enhanced by direct L shell filling, possible inside the target. The fact that emission occurs below the surface affects the observed yields through the mean escape depth. This factor must be considered when comparing yields of electrons with different kinetic energy, for example, KLL vs LMM Auger emission. Since emission occurs below the surface, it is also expected to be sensitive to factors which affect the ion scattering and reflection such as incident azimuthal and polar angles and crystal damage. These simulation techniques can be easily extended to other energy ranges and i o n / t a r g e t combinations.
Acknowledgement
This research was sponsored by Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. DOE under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc.
References
[l] S.T. de Zwart, thesis (1987); S.T. de Zwart, A.G. Drentje, A.L. Boers and R. Morgerstern, Surf. Sci. 217 (1989) 298. [2] F.W. Meyer, C.C. Havener, K.J. Snowdon, S.H. Overbury, D.M. Zehner and W. Heiland, Phys. Rev. A35 (1987) 3176. [3] KJ. Snowdon, C.C. Havener, F.W. Meyer, S.H. Overbury, D.M. Zehner and W. Heiland, Phys. Rev. A38 (1988) 2294.
S.H. Overbury et al. / Relaxation processes in ion scattering
[4] L. Folkerts and R. Morgenstern, Europhys. Lett. 13 (1990) 377. [51 H.J. Andr~i, Nucl. Instr. and Meth. B43 (1989) 304. [6] J.P. Briand, L. de Billy, P. Charles, S. Essabaa, P. Briand, R. Geller, J.P. Desclaux, S. Bliman and C. Ristori, Phys. Rev. Lett. 65 (1990) 159. [7] P.A. Zeijlmans van Emmichoven, C.C. Havener and F.W. Meyer, Phys. Rev. A43 (1991) 1405. [8] M.T. Robinson, Phys. Rev. B40 (1989) 1071. [9] J.F. Ziegler, J.P. Biersack and U. Littmark, U.S. DOE Report ORNL/CONF-82013 (1983) p. 88. [10] U.A. Arifov, L.M. Kishinevskii, E.S. Mukhamadiev and E.S. Parilis, Soy. Phys. Tech. Phys. 18 (1973) 118.
[11] N. Stolterfoht, in: Progress in Atomic Spectroscopy, Part D, ed. H. Kleinpoppen (Plenum, New York, 1987) p. 415. [12] F.W. Meyer, C.C. Havener S.H. Overbury, K.J. Reed, KJ. Snowdon and D.M. Zehner, J. Phys. (Paris) 50 (1989) C1-263. [13] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [14] F.W. Meyer, S.H. Overbury, C.C. Havener, D.M. Zehner and P.A. Zeijlmans van Emmichoven, Phys. Rev. A44 (1991) 7214. [15] S.T. de Zwart, T. Fried, U. Jellen, A.L. Boers and A.G. Drentje, J. Phys. B18 (1985) L623.
II. CAPTURE AND LOSS