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Thermal vibrations at copper surfaces studied by low energy ion scattering
Vacuum/volume 41/numbers 1-3/pages 376 to 378/1990 Printed in Great Britain
0042-207X/9053.00 + .00 © 1990 Pergamon Press plc
Thermal vibrations at copper surfaces studied by l o w energy ion scattering H DLirr, R S c h n e i d e r
and Th Fauster,
Max-Planck-lnstitute f£ir Plasmaphysik, EURA TOM Association,
Boltzmannstr. 2, D-8046 Garching, FRG
The thermal vibrations of surface atoms on Cu(110) have been studied as a function of temperature with impact collision ion scattering spectroscopy. Monte Carlo simulations of the scattering along chains of surface atoms show that for large vibration amplitudes more than two atoms have to be included to explain the experimental data. The mean square displacements obtained from the comparison between experiment and calculations agree well with the results of atom scattering and inverse photoemission experiments and the results from surface phonon calculations. The influence of correlations and anisotropy of the surface vibrations on impact collision ion scattering spectra is discussed.
Introduction
Low energy ion scattering in the impact collision mode (ICISS) is a very useful tool in studying the short range atomic order on single crystal surfaces. Elastically scattered ions detected at large scattering angles have undergone one or a series of small-angle collisions preceeding one almost head on collision with surface atoms. The ions backscattered towards the detector experience no significant collisions with surface atoms. We can therefore retrace the ion path and determine the atomic geometry by making use of the shadow-cone principleL At the critical angle ~bc, defined as the angle of incidence where a surface atom enters the shadow of its neighbor, the intensity of backscattered ions drops to zero. If the surface atoms vibrate they move in and out of the shadow of their neighbors and therefore broaden the slope in the backscattering signal around the critical angle. From this broadening we can deduce the mean square displacements of the surface atoms by comparing experimental and calculated ICISS angular scans. Experimental
Experiments were performed in an uhv chamber at a base pressure of 2 x 10-1°torr. Backscattered ions and neutrals could be detected at a fixed scattering angle of 157 ° with a Timeof-Flight technique. Backscattered ions were also detected with a hemispherical rotatable analyser at scattering angles between 0 ° and 160 °. During the angular scans the analyser was operated at fixed energy with low resolution in order to increase the backscattering signal and to compensate small energy shifts of the scattered ions due to small angle collision sequences. ICISS spectra were taken with 2°Ne + ions with an energy of 5 keV. The temperature was measured with thermocouples with an estimated uncertainty of l0 K. The samples were aligned relative to the ion beam within 0.5 °. This alignment did not change within the error limits during heating of the sample. Calculations
ICISS spectra can often be described by a two-atom model. The first atom focuses the flux of incoming projectiles onto the 376
second atom where the large angle backscattering occurs. The scattering angle, and therefore the cross-section for the second collision, is to a very good approximation constant during the ICISS angular scan. To model the spectra we only have to calculate the flux of projectiles reaching the last target atom and sum up all atom pairs visible to the ion beam 2. Thermal vibrations are included by displacing the first atom in three dimensions according to a guassian distribution before the collision with the ion. After the scattering process the impact parameter for the equilibrium position of the second atom is calculated and the atom is moved by that distance in order to produce a head-on collision. The probability for that displacement is summed up for some ten thousand trajectories with randomly chosen three-dimensional impact parameters for the first atom. The scattering angle was calculated with the commonly used Thomas-Fermi-Moli6re potential with a screening length adjusted by a factor of 0.83. It was then stored in a one-dimensional array as a function of the impact parameter to save computing time. Elastic energy losses in the small angle collisions were neglected. The calculations showed that the simple two-atom model fails at large vibration amplitudes. For those amplitudes the nextnearest neighbors contribute to the flux focusing onto the last atom and we have to replace the two-atom model by a chain model which can be easily-done in our approach. However in such a chain model the two-atom scattering is still the dominant part. We also found that a chain length of three atoms is sufficient for the vibration amplitudes studied in this work. Calculations with longer chains give identical results. Anisotropic vibrations and correlations effects are discussed in the literature 4-6 and may also influence the calculated spectra. We therefore included both effects into the model following an algorithm presented by Barrett and Jackson 5. The parameters used were taken from surface phonon calculations 7. In the two-atom model correlated vibrations alter the relative amplitudes of the atoms seen by the ions. This means the spectra are identical for correlated and uncorrelated motion only the corresponding vibration amplitudes differ. For a chain of more than two atoms we found also no significant change in the calculated spectra due to the inclusion of correlated vibrations, confirming
H DOrr et al: Vibrations at copper surfaces
that the two-atom scattering is the dominant process. It was also found that the differences between chain calculations of isotropic and anisotropic vibrations are not significant when comparing them to experimental uncertainties.
. 0.14
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.<
Results and discussion
0.12
0.10
ICISS spectra were measured as a function of temperature for the C u ( l l 0 ) surface along various crystal directions. The relatively open Cu(110) surface was chosen in order to minimize zig-zag scattering between adjacent rows of surface atoms a. The sensitivity for vibrations of first-layer atoms was enhanced by detecting backscattered ions rather than neutral particles. Under the chosen experimental conditions strong ionisation of neutral particles during head on collisions with surface atoms has been reported 9. This ionisation leads to a constant ratio between scattered ions and neutral particles during the ICISS spectra. This can be seen in Figure 1 where angular ICISS scans along the [1121 direction are shown. For room temperature the ion spectra (diamonds) and the spectra for quasi-single scattered neutrals a (circles) agree within the error limits. This shows that trajectory dependent neutralisation can be ignored along that azimuth where only first layer scattering occurs. The same was found along the [110] direction. Here also second-layer atoms are visible to the ion beam. In the [001] azimuth a strong enhancement of the neutral particle yield at ~bcis found, which is not seen with ions, indicating neutralisation on the outgoing trajectories for ions scattered at second-layer atoms. As a consequence along the [1i2] and the [001] direction first-layer scattering dominates and the single chain calculations can be applied to the experimental data obtained with ion detection along these two azimuths. The ion spectra along the [112] direction are compared to three-atom Monte Carlo calculations in Figure 1. The simula-
' Cu(I'10)
Ne 5keV
[ IT2~160 j ;,\
/ / A ~ I
{ *.~.
° "r:7osK
=°'2°A T:455K
--3oo ,~
T= 160K ~=0.09A
lOo 2'0° 3bo Angle of Incidence
oo
Figure 1. The number of scattered particles of 5 keV primary ion energy with scattering angle of 160° for Cu(ll0) along the 1-0011 azimuth are shown as a function of the angle of incidence. Diamonds correspond to backscattered ions, circles indicate backscattered neutral particles. The experimental data were collected at the indicated sample temperatures. Full lines correspond to Monte Carlo calculations for atoms vibrating with variance a.
E ~
0.08
.
.
.
i
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Cu(ll0) = o o Helium Scattering o o Helium Scattering o • ICISS [001] . ICISS [1T21 o Inverse o Photoemission o
%
~5
°®o . . . .
,~o . . . .
,g00
Temperature / K Figure 2. Mean square displacements vs temperature for ICISS, helium scattering and inverse photoemission experiments. The full line shows the results from surface phonon calculations described by a Debye temperature of 224 K..
tions were performed for isotropic harmonic oscillators with variance tr for each dimension. To correct for the finite size of the sample and the ion beam we multiplied the calculated spectra with the measured target current which is proportional to the number of ions hitting the sample. The influence of temperature variation on the ICISS spectra is a shift of the critical angle qJc, which is read out at half height, to lower angles of incidence and a broadening of the slope at ~bc. Both effects can be modelled quite accurately for the [001] and [112] azimuths but not so well in the [110] direction. The additional intensity at very low angles of incidence which increases with temperature has been discussed previously in terms of adatoms or defects at the surface x°. In Figure 2 the mean square displacements a 2 obtained for the [001] and [112] azimuths are compared to helium scattering data 11.12, to inverse photoemission experiments 7, and to surface phonon calculations 7. All three experimental methods agree within the error limits. For low temperatures the ICISS data seem to be shifted to somewhat higher mean square displacements. We note that in this temperature range the finite experimental resolution might become important. The agreement between expertment and phonon calculations which show a behaviour similar to the Debye model with a Debye temperature of 224 K is good for temperatures below 500 K. Above that temperature we notice an increasing deviation of the experimental data to higher values of tr. Anharmonic contributions to the potential between the copper atoms are the most likely explanation for this deviation. F o r the comparison of the experimental ICISS data of all crystal directions with the chain calculations the critical angles ~,c are plotted in Figure 3 vs the width of the slope A~b at the critical angle. A~b is the angle between 10 and 90% of the slope height. The values expected from the chain calculations are shown as full lines and are to good approximation parabolas. The values for ~bc at T = 0, i.e. A~, = 0, can be calculated from the shape of the shadow-cone ~, and are seen to agree reasonably well with the extrapolated calculations. In the [112] and [001] azimuths scattering from a single chain of surface atoms dominates and the experimental data agree well with the calculations. However in 377
H D i i r r et al." Vibrations at copper surfaces i
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Slope W i d t h / ~ Figure 3. Critical angles ~, for the scattering at the Cu(110) surface along various surface directions are shown as a function of the width of the slope A~k at the critical angle if, in the ICISS angular scans. The results obtained from Monte Carlo chain calculations are shown as solid lines. The dashed lines indicate the influence of scattering from second-layer atoms. Open symbols represent calculated values for ~b¢ at T = 0. The insert shows a schematic view of the surface. Full circles represent atoms in the first layer. Open circles indicate second-layer atoms.
the [110] azimuth there is an increasing deviation with temperature between experiment and theory. This fIT0] direction is of all three azimuths the most open one where also the second-layer atoms are visible and contribute significantly to the backscattering signal. The total ion yield will be described correctly by the sum of the yields for first- and second-layer atomic chains modified by the neutralization probability. The dashed lines in
378
Figure 3 show the results if we neglect neutralisation completely. The vibrations of second-layer atoms taken from the surface p h o n o n calculations 7 are characterized by a Debye temperature of 286 K. Since the vibration amplitudes in the subsurface layer are smaller the critical angles are shifted to higher values than in the first layer. This increases A~b and ~kc if the shifts in ~bc are sufficiently large, i.e. if the temperature is high enough. Such an increase in A~b and ffc reduces the disagreement between theoretical and experimental data in the [110] azimuth whereas the effect is negligible in the [001] azimuth. As a consequence all experimental data obtained on Cu(110) can be described satisfactorily by the chain calculations.
References J M Aono, C Oshima, S Zaima, S Otani and Y Ishizawa, Japan J Appl
Phys, 20, L829 (1981). 2 j A Yarmoff, D M Cyr, J H Huang, SKim and R S Williams, Phys Rev,
!!33, 3856 (1986). 3 Th Fauster, D Hartwig and H D~irr, Appt Phys, A45, 63 (t988). 4 B Poelsema, L K Verheij and A L Boers, Surface Sci, 60, 485 (1976). 5 j H Barrett and D P Jackson, Nucl lnstrum Meth, 170, 115 (1980). 6 D J Martin, Surface Sci, 97, 586 (1980). 7 R Schneider, Thesis, University of Bayreuth, (1989). s H Derks, H Hemme, W Heiland and S H Overbury, Nucl lnstrum Meth, B23, 374 (1987). 9 Th Fauster, Vacuum, 38, 129 (1988). 1o Th Fauster, R Schneider, H Diirr, G Engelmann and E Taglauer, Surface Sci, 1891190, 610 (1987). 11 p Zeppenfeld, K Kern, R David and G Comsa, Phys Reo Lett, 62, 63 (1989). n2 D Gorse and J Lapujoulade, Surface Sci, 162, 847 (1985).
0042-207X/9053.00 + .00 © 1990 Pergamon Press plc
Thermal vibrations at copper surfaces studied by l o w energy ion scattering H DLirr, R S c h n e i d e r
and Th Fauster,
Max-Planck-lnstitute f£ir Plasmaphysik, EURA TOM Association,
Boltzmannstr. 2, D-8046 Garching, FRG
The thermal vibrations of surface atoms on Cu(110) have been studied as a function of temperature with impact collision ion scattering spectroscopy. Monte Carlo simulations of the scattering along chains of surface atoms show that for large vibration amplitudes more than two atoms have to be included to explain the experimental data. The mean square displacements obtained from the comparison between experiment and calculations agree well with the results of atom scattering and inverse photoemission experiments and the results from surface phonon calculations. The influence of correlations and anisotropy of the surface vibrations on impact collision ion scattering spectra is discussed.
Introduction
Low energy ion scattering in the impact collision mode (ICISS) is a very useful tool in studying the short range atomic order on single crystal surfaces. Elastically scattered ions detected at large scattering angles have undergone one or a series of small-angle collisions preceeding one almost head on collision with surface atoms. The ions backscattered towards the detector experience no significant collisions with surface atoms. We can therefore retrace the ion path and determine the atomic geometry by making use of the shadow-cone principleL At the critical angle ~bc, defined as the angle of incidence where a surface atom enters the shadow of its neighbor, the intensity of backscattered ions drops to zero. If the surface atoms vibrate they move in and out of the shadow of their neighbors and therefore broaden the slope in the backscattering signal around the critical angle. From this broadening we can deduce the mean square displacements of the surface atoms by comparing experimental and calculated ICISS angular scans. Experimental
Experiments were performed in an uhv chamber at a base pressure of 2 x 10-1°torr. Backscattered ions and neutrals could be detected at a fixed scattering angle of 157 ° with a Timeof-Flight technique. Backscattered ions were also detected with a hemispherical rotatable analyser at scattering angles between 0 ° and 160 °. During the angular scans the analyser was operated at fixed energy with low resolution in order to increase the backscattering signal and to compensate small energy shifts of the scattered ions due to small angle collision sequences. ICISS spectra were taken with 2°Ne + ions with an energy of 5 keV. The temperature was measured with thermocouples with an estimated uncertainty of l0 K. The samples were aligned relative to the ion beam within 0.5 °. This alignment did not change within the error limits during heating of the sample. Calculations
ICISS spectra can often be described by a two-atom model. The first atom focuses the flux of incoming projectiles onto the 376
second atom where the large angle backscattering occurs. The scattering angle, and therefore the cross-section for the second collision, is to a very good approximation constant during the ICISS angular scan. To model the spectra we only have to calculate the flux of projectiles reaching the last target atom and sum up all atom pairs visible to the ion beam 2. Thermal vibrations are included by displacing the first atom in three dimensions according to a guassian distribution before the collision with the ion. After the scattering process the impact parameter for the equilibrium position of the second atom is calculated and the atom is moved by that distance in order to produce a head-on collision. The probability for that displacement is summed up for some ten thousand trajectories with randomly chosen three-dimensional impact parameters for the first atom. The scattering angle was calculated with the commonly used Thomas-Fermi-Moli6re potential with a screening length adjusted by a factor of 0.83. It was then stored in a one-dimensional array as a function of the impact parameter to save computing time. Elastic energy losses in the small angle collisions were neglected. The calculations showed that the simple two-atom model fails at large vibration amplitudes. For those amplitudes the nextnearest neighbors contribute to the flux focusing onto the last atom and we have to replace the two-atom model by a chain model which can be easily-done in our approach. However in such a chain model the two-atom scattering is still the dominant part. We also found that a chain length of three atoms is sufficient for the vibration amplitudes studied in this work. Calculations with longer chains give identical results. Anisotropic vibrations and correlations effects are discussed in the literature 4-6 and may also influence the calculated spectra. We therefore included both effects into the model following an algorithm presented by Barrett and Jackson 5. The parameters used were taken from surface phonon calculations 7. In the two-atom model correlated vibrations alter the relative amplitudes of the atoms seen by the ions. This means the spectra are identical for correlated and uncorrelated motion only the corresponding vibration amplitudes differ. For a chain of more than two atoms we found also no significant change in the calculated spectra due to the inclusion of correlated vibrations, confirming
H DOrr et al: Vibrations at copper surfaces
that the two-atom scattering is the dominant process. It was also found that the differences between chain calculations of isotropic and anisotropic vibrations are not significant when comparing them to experimental uncertainties.
. 0.14
~,
.<
Results and discussion
0.12
0.10
ICISS spectra were measured as a function of temperature for the C u ( l l 0 ) surface along various crystal directions. The relatively open Cu(110) surface was chosen in order to minimize zig-zag scattering between adjacent rows of surface atoms a. The sensitivity for vibrations of first-layer atoms was enhanced by detecting backscattered ions rather than neutral particles. Under the chosen experimental conditions strong ionisation of neutral particles during head on collisions with surface atoms has been reported 9. This ionisation leads to a constant ratio between scattered ions and neutral particles during the ICISS spectra. This can be seen in Figure 1 where angular ICISS scans along the [1121 direction are shown. For room temperature the ion spectra (diamonds) and the spectra for quasi-single scattered neutrals a (circles) agree within the error limits. This shows that trajectory dependent neutralisation can be ignored along that azimuth where only first layer scattering occurs. The same was found along the [110] direction. Here also second-layer atoms are visible to the ion beam. In the [001] azimuth a strong enhancement of the neutral particle yield at ~bcis found, which is not seen with ions, indicating neutralisation on the outgoing trajectories for ions scattered at second-layer atoms. As a consequence along the [1i2] and the [001] direction first-layer scattering dominates and the single chain calculations can be applied to the experimental data obtained with ion detection along these two azimuths. The ion spectra along the [112] direction are compared to three-atom Monte Carlo calculations in Figure 1. The simula-
' Cu(I'10)
Ne 5keV
[ IT2~160 j ;,\
/ / A ~ I
{ *.~.
° "r:7osK
=°'2°A T:455K
--3oo ,~
T= 160K ~=0.09A
lOo 2'0° 3bo Angle of Incidence
oo
Figure 1. The number of scattered particles of 5 keV primary ion energy with scattering angle of 160° for Cu(ll0) along the 1-0011 azimuth are shown as a function of the angle of incidence. Diamonds correspond to backscattered ions, circles indicate backscattered neutral particles. The experimental data were collected at the indicated sample temperatures. Full lines correspond to Monte Carlo calculations for atoms vibrating with variance a.
E ~
0.08
.
.
.
i
.
.
.
.
i
Cu(ll0) = o o Helium Scattering o o Helium Scattering o • ICISS [001] . ICISS [1T21 o Inverse o Photoemission o
%
~5
°®o . . . .
,~o . . . .
,g00
Temperature / K Figure 2. Mean square displacements vs temperature for ICISS, helium scattering and inverse photoemission experiments. The full line shows the results from surface phonon calculations described by a Debye temperature of 224 K..
tions were performed for isotropic harmonic oscillators with variance tr for each dimension. To correct for the finite size of the sample and the ion beam we multiplied the calculated spectra with the measured target current which is proportional to the number of ions hitting the sample. The influence of temperature variation on the ICISS spectra is a shift of the critical angle qJc, which is read out at half height, to lower angles of incidence and a broadening of the slope at ~bc. Both effects can be modelled quite accurately for the [001] and [112] azimuths but not so well in the [110] direction. The additional intensity at very low angles of incidence which increases with temperature has been discussed previously in terms of adatoms or defects at the surface x°. In Figure 2 the mean square displacements a 2 obtained for the [001] and [112] azimuths are compared to helium scattering data 11.12, to inverse photoemission experiments 7, and to surface phonon calculations 7. All three experimental methods agree within the error limits. For low temperatures the ICISS data seem to be shifted to somewhat higher mean square displacements. We note that in this temperature range the finite experimental resolution might become important. The agreement between expertment and phonon calculations which show a behaviour similar to the Debye model with a Debye temperature of 224 K is good for temperatures below 500 K. Above that temperature we notice an increasing deviation of the experimental data to higher values of tr. Anharmonic contributions to the potential between the copper atoms are the most likely explanation for this deviation. F o r the comparison of the experimental ICISS data of all crystal directions with the chain calculations the critical angles ~,c are plotted in Figure 3 vs the width of the slope A~b at the critical angle. A~b is the angle between 10 and 90% of the slope height. The values expected from the chain calculations are shown as full lines and are to good approximation parabolas. The values for ~bc at T = 0, i.e. A~, = 0, can be calculated from the shape of the shadow-cone ~, and are seen to agree reasonably well with the extrapolated calculations. In the [112] and [001] azimuths scattering from a single chain of surface atoms dominates and the experimental data agree well with the calculations. However in 377
H D i i r r et al." Vibrations at copper surfaces i
.
.
.
.
i
• ,.,._Calc. -'0°- - _ ~ Z ~ __o " [110] ~ ,<
.
.
.
.
u
~
.
•
.
.
o--
"%,,~1'..
IOOll
15 °
.~
(")
.
(UTOl taT2l ~o•/"
-.
.
i0 o
{~
= o
i
i
,
i 5 °
,
,
,
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I i i0 o
,A,
i
i
Slope W i d t h / ~ Figure 3. Critical angles ~, for the scattering at the Cu(110) surface along various surface directions are shown as a function of the width of the slope A~k at the critical angle if, in the ICISS angular scans. The results obtained from Monte Carlo chain calculations are shown as solid lines. The dashed lines indicate the influence of scattering from second-layer atoms. Open symbols represent calculated values for ~b¢ at T = 0. The insert shows a schematic view of the surface. Full circles represent atoms in the first layer. Open circles indicate second-layer atoms.
the [110] azimuth there is an increasing deviation with temperature between experiment and theory. This fIT0] direction is of all three azimuths the most open one where also the second-layer atoms are visible and contribute significantly to the backscattering signal. The total ion yield will be described correctly by the sum of the yields for first- and second-layer atomic chains modified by the neutralization probability. The dashed lines in
378
Figure 3 show the results if we neglect neutralisation completely. The vibrations of second-layer atoms taken from the surface p h o n o n calculations 7 are characterized by a Debye temperature of 286 K. Since the vibration amplitudes in the subsurface layer are smaller the critical angles are shifted to higher values than in the first layer. This increases A~b and ~kc if the shifts in ~bc are sufficiently large, i.e. if the temperature is high enough. Such an increase in A~b and ffc reduces the disagreement between theoretical and experimental data in the [110] azimuth whereas the effect is negligible in the [001] azimuth. As a consequence all experimental data obtained on Cu(110) can be described satisfactorily by the chain calculations.
References J M Aono, C Oshima, S Zaima, S Otani and Y Ishizawa, Japan J Appl
Phys, 20, L829 (1981). 2 j A Yarmoff, D M Cyr, J H Huang, SKim and R S Williams, Phys Rev,
!!33, 3856 (1986). 3 Th Fauster, D Hartwig and H D~irr, Appt Phys, A45, 63 (t988). 4 B Poelsema, L K Verheij and A L Boers, Surface Sci, 60, 485 (1976). 5 j H Barrett and D P Jackson, Nucl lnstrum Meth, 170, 115 (1980). 6 D J Martin, Surface Sci, 97, 586 (1980). 7 R Schneider, Thesis, University of Bayreuth, (1989). s H Derks, H Hemme, W Heiland and S H Overbury, Nucl lnstrum Meth, B23, 374 (1987). 9 Th Fauster, Vacuum, 38, 129 (1988). 1o Th Fauster, R Schneider, H Diirr, G Engelmann and E Taglauer, Surface Sci, 1891190, 610 (1987). 11 p Zeppenfeld, K Kern, R David and G Comsa, Phys Reo Lett, 62, 63 (1989). n2 D Gorse and J Lapujoulade, Surface Sci, 162, 847 (1985).