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Cross section for diffuse scattering from random steps on Cu(100) determined by teas (thermal energy atom scattering)
Surface Science 187 (1987) L587-L591 North-Holland, Amsterdam
L587
SURFACE SCIENCE LETTERS CROSS SECTION FOR DIFFUSE SCATrERING FROM RANDOM S T E P S O N Cu(100) DETERMINED BY T E A S ( T H E R M A L E N E R G Y A T O M S C A ' I T E R I N G ) Alejandro S A N C H E Z and Salvador F E R R E R Departamento de F~sica de la Materia Condensada, C-Ill, Facultad de Ciencias, Unwersidad Autbnoma de Madrid, Cantoblanco, 28049-Madrid, Spain
Received 23 February 1987; accepted for publication 20 May 1987
The cross section for diffuse scattering from random steps in Cu(100) has been measured by TEAS. The result is 13 ,~ per unit step length, meaning that this is the distance normal to the step edge over which the surface is not specularly reflective for scattering of thermal He atoms. This result was obtained in an experimentally direct way that basically consisted in growing Cu islands on top of the Cu substrate and in decorating these islands with Pb atoms in order to titrate the step density.
Thermal energy atom scattering (TEAS) is a well established technique in surface science. It is very appropriate for studying low concentrations of adsorbed atoms and molecules since the cross sections for diffuse scattering from isolated admolecules are large ( - 100 ,~2) [1]. Due to that,-very small concentrations of adsorbed species (10 -3 monolayers) cause a measurable change in the scattering intensity. Isolated surface vacancies also exhibit large cross sections [2]. We have investigated the cross section for diffuse scattering from atoms in surface steps since its knowledge may be extremely useful not only to characterize r a n d o m stepped clean surfaces but also to study the epitaxial growth on a non-ideal substrate where the role of the surface steps becomes crucial and m a y determine the morphology of the epitaxial layer. In an early paper by Legay and Lapujoulade [3], an estimation of the cross section for diffuse scattering from a r a n d o m distribution of steps in Cu(100) was done resulting in a value of 6 ,~ for incidence angles from 30 ~ to 60 ~ Later, C o m s a and co-workers [4] found that the cross section per unit length for diffuse scattering from r a n d o m steps on P t ( l l l ) was 12 A for 16 meV H e atoms, meaning that this was the distance normal to the step edge over which the surface is not reflective. In order to determine this value, the P t ( l l l ) surface was ion b o m b a r d e d and it was assumed that after b o m b a r d m e n t it consisted in a faceted surface containing a r a n d o m distribution of m o n a t o m i c steps. Then the angular profiles of the specularly scattered intensity were 0039-6028/87/$03.50 9 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L588
A. Sdnchez, S. Ferret / Diffuse scattering from random steps in Cu(lO0)
measured for both in-phase and out-of-phase Bragg conditions along the surface normal. By combining both measurements and through a curve-fitting procedure, the cross section for steps was obtained. In this Letter, a direct measurement of the cross section for steps on Cu(100) that does not involve any curve fitting or data handling is presented. The basic idea consists in determining the step concentration by decorating the steps with foreign atoms. By correlating intensity measurements and experimentally determined step concentrations we obtained that the steps perturb a distance of 13 ,~ along the normal to the edge, in good agreement with ref. [4]. The experiments were performed in a UHV system described in detail previously [5]. The incident beam consisted in room temperature helium atoms from a nozzle source. Its kinetic energy was 63 meV. Detection of the scattered beam was accomplished with a movable quadrupole. The system has also LEED and AES facilities. The crystal was of (100) orientation as determined by the Laue technique and before insertion into the vacuum chamber it was mechanically polished. It was cleaned by successive cycles of ion etching and annealing to 1100 K. After these treatments it displayed a sharp LEED pattern. Inside the UHV system there were two home-made evaporators containing Cu and Pb. Both were colimated and directed towards the Cu surface. The incident flux of Cu and Pb atoms could be varied in a controllable way from 101~ to 1012 atoms cm-2 sThe scattered intensity from the clean and ordered Cu(100) surface was concentrated along the specular direction and no diffracted beams could be detected. The angular width of the specular beam was measured to be 0.35 ~ ~ depending on the incidence angle. Its intensity, relative to the intensity of the incident He beam displayed maxima and minima when the angle of incidence was varied [6,7]. The oscillation were due to the existence of surface steps originated by imperfect polishing of the Cu surface. The maxima (minima) corresponded to scattering incidences satisfying a Bragg condition of constructive (destructive) interference along the surface normal for atoms in consecutive layers. For in-phase scattering conditions (constructive interference), the scattered intensity I is decreased with respect to a flat surface (intensity I0) due to diffuse scattering from the areas around the steps. If 0st is the relative concentration of atoms in steps and d is the nearest neighbour distance for surface atoms (2.55 ,~ for Cu(100)) we may write [4]
I/Io = [1 - (Ost/d)D] 2,
(1)
where D is the distance along the normal of the step edge over which the surface does not scatter specularly. From (1) one obtains:
D = (d 10st)[1 - (I/Io)1/2],
(2)
A. Sgmchez, S. Ferret / Diffuse scattering from random steps in Cu(lO0)
(a) >-
s
gi---71.5 *
1.00
I%._
-F (bl
- .ooi-~
L589
0.95
I
I
I
2
~
6
8pbxlO 3 (M L)
Fig. 1. Intensity of the specular beam as a function of Pb coverage relative to the intensity before deposition. Curve a is for the annealed Cu(100) surface and curve b is for the Cu substrate after deposition of Cu atoms in order to nucleate islands that provide additional step sites.
therefore by experimentally determining 0st and I / I o one could directly obtain D. In practice however, neither I 0 nor 0st are known. We performed a series of measurements in order to apply eq. (2) to obtain D. The experiments may be divided in three groups that will be described separately. (i) Determination o f the density of steps in the clean and ordered Cu(100) surface; (ii) growth, b y means of vapor deposition, of 219 islands of Cu atoms on top of the Cu(100) substrate in order to artificially increase the step density at the surface; and (iii) decoration of the surface steps by Pb atoms deposited from the vapor phase. All the experiments were performed for in-phase scattering conditions at an incidence angle of 71.5 ~ from surface normal. (i) In order to determine the density of steps on the clean and ordered Cu(100) surface, the Pb evaporator was first carefully calibrated as described previously [8]. Then, Pb was evaporated at low rate (7 • 101~ atoms c m -2 s -1) on the substrate and the specular intensity versus Pb coverage was monitored. The surface temperature was 343 K. The relative intensity versus Pb coverage is displayed in fig. 1 curve a. It consists in two straight line segments of different slopes intersecting at a coverage of Pb of 2.7 x 10 -3 monolayers indicated by an arrow. The low coverage segment has smaller slope than the high coverage one and corresponds to adsorption of Pb atoms on step sites in the Cu(100) surface. The high coverage segment is due to adsorption on terrace sites [8,9]. The intersecting coverage allows one to determine the relative concentration of surface steps on the Cu substrate resulting in O~t(ini-
L590
A. Srnchez, S. Ferrer / Diffuse scattering from random steps in Cu(lO0)
tial) = 2.7 • 10-3//0.6 = 4.5 • 10 -3. The factor 0.6 accounts for the different atomic radii of Pb and Cu atoms. (ii) Starting with the ordered Cu(100) substrate at 343 K, Cu atoms were deposited from the vapor phase up to a coverage that was estimated to be around 10% of a monolayer. (As it will be seen clear below, the precise value of the coverage does not need to be known although one must be able to reproduce it in different experimental runs.) Depositions at this temperature result in nucleation of two-dimensional (2D) islands of monatomic height on the substrate terraces as has been previously shown [10]. As a consequence the specular intensity decreases from 11 (for the clean and ordered substrate) to 12 (for islands on top of the terraces). 12 is smaller than 11 since atoms at the edges of the Cu islands constitute "extra" step atoms that have been added to the surface and consequently the incoherent scattering is increased. (iii) Pb atoms were deposited on the surface prepared as in (ii) (at 343 K and containing islands) and the specular intensity was measured as a function of Pb coverage. This is essentially the same experiment as (i). The result is shown by curve b of fig. 1. From the break in the curve of I versus Pb coverage we determined the total surface concentration of step atoms resulting in 4.9 • 10 -3 Pb monolayers or 8.2 • 10 -3 for the relative number of Cu atoms in steps. This number comprises both the "natural" steps of the substrate that were already present before deposition, plus the "extra" steps at the edges of the Cu islands. Therefore the "extra" concentration of steps is (8.2-4.5) • 10 -3 = 0st(extra). Now expression (2) is used to obtain D: D = (d/Ost (extra)) [1 - (12/11)1/2].
Three different experimental runs were performed obtaining D = 13 • 2 A. Finally, note the following points: (a) The coverage of deposited Cu in experiments (ii) and (iii) must be small (let us say less than 10%) in order to make sure that the cross sections of adjacent steps do not overlap significantly. (b) The surface concentration of isolated Cu adatoms in equilibrium with the Cu islands is assumed to be vanishingly small. This is based on the low surface temperature relative to the cohesive energy of Cu. (c) As discussed by Lapujoulade in refs. [3,7], the cross section for diffuse scattering from steps depends on the incidence angle and should increase for grazing incidences. In our experiments the angle of incidence was 71.5 o which is significantly larger than those in ref. [3] (30~ ~ This could be the reason for the different values of the cross section obtained in both studies. The cross section per unit length for diffuse scattering from a step edge in Cu(100) has been found to be D = 13 ,~ for 63 meV He atoms. This has been accomplished by decorating the steps at the Cu surface with Pb atoms deposited from the vapor phase and by measuring the specularly scattered intensity for in-phase scattering.
A. Sdnchez, S. Ferrer / Diffuse scattering from random steps m Cu(lO0)
L591
W e t h a n k Mr. J. de M i g u e l for his h e l p in s o m e of t h e e x p e r i m e n t s a n d Dr. R. M i r a n d a for discussions. T h i s w o r k has b e e n s u p p o r t e d b y the C A I C y T a n d b y the S p a i n - U S A J o i n t C o m m i t t e e for S c i e n t i f i c R e s e a r c h .
References [1] B. Poelsema, S.T. de Zwart and G. Comsa, Phys. Rev. Letters 49 (1982) 578; 51 (1983) 522. [2] G. Comsa and B. Poelsema, Appl. Phys. A38 (1985) 153. [3] Y. Legay and J. Lapujoulade, Proc. 7th Intern. Vacuum Congr. and 3rd Intern. Conf. on Solid Surfaces, Vienna, 1977, Eds. R. Dobrozemsky et al. (Berger, Vienna, 1977) p. 1373. [4] L.K. Verheij, B. Poelsema and G. Comsa, Surface Sci. 162 (1985) 858. [5] J. Ibahez, N. Garcia, J.M. Rojo and N. Cabrera, Surface Sci. 117 (1982) 23. [6] B. Poelsema, R.L. Palmer, G. Mechterscheimer and G. Comsa, Surface Sci. 117 (1982) 60. [7] J. Lapujoulade~, Surface Sci. 108 (1981) 526. [8] A. Sfinchez, J. IbaYaez, R. Miranda and S. Ferrer, Surface Sci. 178 (1986) 917. [9] B. Poelsema, L.K. Verheij and G. Comsa, Phys. Rev. Letters 49 (1982) 1731. [10] L.J. G6mez, S. Bourgeal, J. Ibafiez and M. Salmer6n, Phys. Rev. B31 (1985) 2551.
L587
SURFACE SCIENCE LETTERS CROSS SECTION FOR DIFFUSE SCATrERING FROM RANDOM S T E P S O N Cu(100) DETERMINED BY T E A S ( T H E R M A L E N E R G Y A T O M S C A ' I T E R I N G ) Alejandro S A N C H E Z and Salvador F E R R E R Departamento de F~sica de la Materia Condensada, C-Ill, Facultad de Ciencias, Unwersidad Autbnoma de Madrid, Cantoblanco, 28049-Madrid, Spain
Received 23 February 1987; accepted for publication 20 May 1987
The cross section for diffuse scattering from random steps in Cu(100) has been measured by TEAS. The result is 13 ,~ per unit step length, meaning that this is the distance normal to the step edge over which the surface is not specularly reflective for scattering of thermal He atoms. This result was obtained in an experimentally direct way that basically consisted in growing Cu islands on top of the Cu substrate and in decorating these islands with Pb atoms in order to titrate the step density.
Thermal energy atom scattering (TEAS) is a well established technique in surface science. It is very appropriate for studying low concentrations of adsorbed atoms and molecules since the cross sections for diffuse scattering from isolated admolecules are large ( - 100 ,~2) [1]. Due to that,-very small concentrations of adsorbed species (10 -3 monolayers) cause a measurable change in the scattering intensity. Isolated surface vacancies also exhibit large cross sections [2]. We have investigated the cross section for diffuse scattering from atoms in surface steps since its knowledge may be extremely useful not only to characterize r a n d o m stepped clean surfaces but also to study the epitaxial growth on a non-ideal substrate where the role of the surface steps becomes crucial and m a y determine the morphology of the epitaxial layer. In an early paper by Legay and Lapujoulade [3], an estimation of the cross section for diffuse scattering from a r a n d o m distribution of steps in Cu(100) was done resulting in a value of 6 ,~ for incidence angles from 30 ~ to 60 ~ Later, C o m s a and co-workers [4] found that the cross section per unit length for diffuse scattering from r a n d o m steps on P t ( l l l ) was 12 A for 16 meV H e atoms, meaning that this was the distance normal to the step edge over which the surface is not reflective. In order to determine this value, the P t ( l l l ) surface was ion b o m b a r d e d and it was assumed that after b o m b a r d m e n t it consisted in a faceted surface containing a r a n d o m distribution of m o n a t o m i c steps. Then the angular profiles of the specularly scattered intensity were 0039-6028/87/$03.50 9 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L588
A. Sdnchez, S. Ferret / Diffuse scattering from random steps in Cu(lO0)
measured for both in-phase and out-of-phase Bragg conditions along the surface normal. By combining both measurements and through a curve-fitting procedure, the cross section for steps was obtained. In this Letter, a direct measurement of the cross section for steps on Cu(100) that does not involve any curve fitting or data handling is presented. The basic idea consists in determining the step concentration by decorating the steps with foreign atoms. By correlating intensity measurements and experimentally determined step concentrations we obtained that the steps perturb a distance of 13 ,~ along the normal to the edge, in good agreement with ref. [4]. The experiments were performed in a UHV system described in detail previously [5]. The incident beam consisted in room temperature helium atoms from a nozzle source. Its kinetic energy was 63 meV. Detection of the scattered beam was accomplished with a movable quadrupole. The system has also LEED and AES facilities. The crystal was of (100) orientation as determined by the Laue technique and before insertion into the vacuum chamber it was mechanically polished. It was cleaned by successive cycles of ion etching and annealing to 1100 K. After these treatments it displayed a sharp LEED pattern. Inside the UHV system there were two home-made evaporators containing Cu and Pb. Both were colimated and directed towards the Cu surface. The incident flux of Cu and Pb atoms could be varied in a controllable way from 101~ to 1012 atoms cm-2 sThe scattered intensity from the clean and ordered Cu(100) surface was concentrated along the specular direction and no diffracted beams could be detected. The angular width of the specular beam was measured to be 0.35 ~ ~ depending on the incidence angle. Its intensity, relative to the intensity of the incident He beam displayed maxima and minima when the angle of incidence was varied [6,7]. The oscillation were due to the existence of surface steps originated by imperfect polishing of the Cu surface. The maxima (minima) corresponded to scattering incidences satisfying a Bragg condition of constructive (destructive) interference along the surface normal for atoms in consecutive layers. For in-phase scattering conditions (constructive interference), the scattered intensity I is decreased with respect to a flat surface (intensity I0) due to diffuse scattering from the areas around the steps. If 0st is the relative concentration of atoms in steps and d is the nearest neighbour distance for surface atoms (2.55 ,~ for Cu(100)) we may write [4]
I/Io = [1 - (Ost/d)D] 2,
(1)
where D is the distance along the normal of the step edge over which the surface does not scatter specularly. From (1) one obtains:
D = (d 10st)[1 - (I/Io)1/2],
(2)
A. Sgmchez, S. Ferret / Diffuse scattering from random steps in Cu(lO0)
(a) >-
s
gi---71.5 *
1.00
I%._
-F (bl
- .ooi-~
L589
0.95
I
I
I
2
~
6
8pbxlO 3 (M L)
Fig. 1. Intensity of the specular beam as a function of Pb coverage relative to the intensity before deposition. Curve a is for the annealed Cu(100) surface and curve b is for the Cu substrate after deposition of Cu atoms in order to nucleate islands that provide additional step sites.
therefore by experimentally determining 0st and I / I o one could directly obtain D. In practice however, neither I 0 nor 0st are known. We performed a series of measurements in order to apply eq. (2) to obtain D. The experiments may be divided in three groups that will be described separately. (i) Determination o f the density of steps in the clean and ordered Cu(100) surface; (ii) growth, b y means of vapor deposition, of 219 islands of Cu atoms on top of the Cu(100) substrate in order to artificially increase the step density at the surface; and (iii) decoration of the surface steps by Pb atoms deposited from the vapor phase. All the experiments were performed for in-phase scattering conditions at an incidence angle of 71.5 ~ from surface normal. (i) In order to determine the density of steps on the clean and ordered Cu(100) surface, the Pb evaporator was first carefully calibrated as described previously [8]. Then, Pb was evaporated at low rate (7 • 101~ atoms c m -2 s -1) on the substrate and the specular intensity versus Pb coverage was monitored. The surface temperature was 343 K. The relative intensity versus Pb coverage is displayed in fig. 1 curve a. It consists in two straight line segments of different slopes intersecting at a coverage of Pb of 2.7 x 10 -3 monolayers indicated by an arrow. The low coverage segment has smaller slope than the high coverage one and corresponds to adsorption of Pb atoms on step sites in the Cu(100) surface. The high coverage segment is due to adsorption on terrace sites [8,9]. The intersecting coverage allows one to determine the relative concentration of surface steps on the Cu substrate resulting in O~t(ini-
L590
A. Srnchez, S. Ferrer / Diffuse scattering from random steps in Cu(lO0)
tial) = 2.7 • 10-3//0.6 = 4.5 • 10 -3. The factor 0.6 accounts for the different atomic radii of Pb and Cu atoms. (ii) Starting with the ordered Cu(100) substrate at 343 K, Cu atoms were deposited from the vapor phase up to a coverage that was estimated to be around 10% of a monolayer. (As it will be seen clear below, the precise value of the coverage does not need to be known although one must be able to reproduce it in different experimental runs.) Depositions at this temperature result in nucleation of two-dimensional (2D) islands of monatomic height on the substrate terraces as has been previously shown [10]. As a consequence the specular intensity decreases from 11 (for the clean and ordered substrate) to 12 (for islands on top of the terraces). 12 is smaller than 11 since atoms at the edges of the Cu islands constitute "extra" step atoms that have been added to the surface and consequently the incoherent scattering is increased. (iii) Pb atoms were deposited on the surface prepared as in (ii) (at 343 K and containing islands) and the specular intensity was measured as a function of Pb coverage. This is essentially the same experiment as (i). The result is shown by curve b of fig. 1. From the break in the curve of I versus Pb coverage we determined the total surface concentration of step atoms resulting in 4.9 • 10 -3 Pb monolayers or 8.2 • 10 -3 for the relative number of Cu atoms in steps. This number comprises both the "natural" steps of the substrate that were already present before deposition, plus the "extra" steps at the edges of the Cu islands. Therefore the "extra" concentration of steps is (8.2-4.5) • 10 -3 = 0st(extra). Now expression (2) is used to obtain D: D = (d/Ost (extra)) [1 - (12/11)1/2].
Three different experimental runs were performed obtaining D = 13 • 2 A. Finally, note the following points: (a) The coverage of deposited Cu in experiments (ii) and (iii) must be small (let us say less than 10%) in order to make sure that the cross sections of adjacent steps do not overlap significantly. (b) The surface concentration of isolated Cu adatoms in equilibrium with the Cu islands is assumed to be vanishingly small. This is based on the low surface temperature relative to the cohesive energy of Cu. (c) As discussed by Lapujoulade in refs. [3,7], the cross section for diffuse scattering from steps depends on the incidence angle and should increase for grazing incidences. In our experiments the angle of incidence was 71.5 o which is significantly larger than those in ref. [3] (30~ ~ This could be the reason for the different values of the cross section obtained in both studies. The cross section per unit length for diffuse scattering from a step edge in Cu(100) has been found to be D = 13 ,~ for 63 meV He atoms. This has been accomplished by decorating the steps at the Cu surface with Pb atoms deposited from the vapor phase and by measuring the specularly scattered intensity for in-phase scattering.
A. Sdnchez, S. Ferrer / Diffuse scattering from random steps m Cu(lO0)
L591
W e t h a n k Mr. J. de M i g u e l for his h e l p in s o m e of t h e e x p e r i m e n t s a n d Dr. R. M i r a n d a for discussions. T h i s w o r k has b e e n s u p p o r t e d b y the C A I C y T a n d b y the S p a i n - U S A J o i n t C o m m i t t e e for S c i e n t i f i c R e s e a r c h .
References [1] B. Poelsema, S.T. de Zwart and G. Comsa, Phys. Rev. Letters 49 (1982) 578; 51 (1983) 522. [2] G. Comsa and B. Poelsema, Appl. Phys. A38 (1985) 153. [3] Y. Legay and J. Lapujoulade, Proc. 7th Intern. Vacuum Congr. and 3rd Intern. Conf. on Solid Surfaces, Vienna, 1977, Eds. R. Dobrozemsky et al. (Berger, Vienna, 1977) p. 1373. [4] L.K. Verheij, B. Poelsema and G. Comsa, Surface Sci. 162 (1985) 858. [5] J. Ibahez, N. Garcia, J.M. Rojo and N. Cabrera, Surface Sci. 117 (1982) 23. [6] B. Poelsema, R.L. Palmer, G. Mechterscheimer and G. Comsa, Surface Sci. 117 (1982) 60. [7] J. Lapujoulade~, Surface Sci. 108 (1981) 526. [8] A. Sfinchez, J. IbaYaez, R. Miranda and S. Ferrer, Surface Sci. 178 (1986) 917. [9] B. Poelsema, L.K. Verheij and G. Comsa, Phys. Rev. Letters 49 (1982) 1731. [10] L.J. G6mez, S. Bourgeal, J. Ibafiez and M. Salmer6n, Phys. Rev. B31 (1985) 2551.