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The first stages of epitaxial growth of Pb atoms on Cu(100) studied by scattering of thermal helium
Surface Science 178 (1986) 917-926 North-Holland, Amsterdam
917
THE FIRST STAGES OF EPITAXIAL GROWTH OF Pb ATOMS ON Cu(100) STUDIED BY SCATTERING OF THERMAL HELIUM A. SANCHEZ, Departamento
J. IBANEZ
de Fisica Fundamental,
Universidad Authoma
Received
*, R. MIRANDA
10 March
de Madrid
1986; accepted
C-III,
and S. FERRER
Facultad de Ciencias,
Cantoblanco, 28049.Madrid,
for publication
Spain
12 May 1986
We studied the initial stages of the growth of Pb layers on a Cu(100) substrate by means of thermal energy atom scattering (TEAS). We found that the coverage dependence of the intensity of the specularly reflected He beam is well described by a simple mathematical formula based on random adsorption on substrate lattice sites including lateral repulsive interactions between adatoms. Equilibrium measurements of the adsorbed layer for very low coverages (3 ~10~~ monolayers) allowed to determine the 2D heat of evaporation of Pb atoms from step to terrace sites. This was accomplished by measuring the temperature dependence of the cross section for diffuse scattering.
1. Introduction Thermal energy atom scattering (TEAS) is nowadays a well-established surface science technique for extracting information on kinetic and dynamic aspects of surface processes in addition to static information on surface structure [l-3]. The technique has been applied to a variety of adsorption systems such as 0, CO, Xe and H on metallic surfaces. However, the studied overlayers have been almost exclusively adsorbed gases. Only recently has it been used in our laboratory to monitor the surface of a metal crystal that was growing from its own vapor [4]. We present in this paper a study by TEAS of the first stages of formation of an heteroepitaxial system: Pb atoms deposited from the vapor phase on a Cu(100) substrate. We will show that, due to the extreme sensitivity of TEAS to small concentrations of adatoms, information on the kinetics and thermodynamics of the very first stages of the epitaxial growth may be easily obtained. Deposition of Pb on Cu(100) results, in the submonolayer regime, in several ordered structures that have been previously studied with LEED and AES [5,6]. These are, termed in order of increasing coverage, c(4 X 4) c(2 x 2) and (5fi x fi), the later corresponding to the completion of an overlayer of Pb atoms that completely covers the substrate. It is established from LEED * Present
address:
Departamento
de Materiales,
INTA,
Madrid,
0039-6028/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
Spain.
B.V.
dynamical analysis that the surface corrugation of these overlayers decreases with coverage, i.e., the c(4 x 4) presents the larger corrugation and the (Sv’? x a) is almost flat [6]. This structural information is easily extracted from TEAS since only the c(4 X 4) structure produces intense diffracted beams [7]. However, in this paper we will concentrate only on the submonolayer range preceding the formation of the c(4 x 4) structure, i.e., in the first stages of the growth of this epitaxial system. We will show that the variation of the specular intensity with coverage of adatoms, is well described by an analytical law based on random adsorption on substrate lattice sites with nearest-neighbour repulsion between the adatoms. We will illustrate how the 2D heat of evaporation of Pb atoms from step to terrace sites of the Cu substrate can be obtained from TEAS data taken at very low coverages of Pb under conditions of thermodynamic equilibrium.
2. Experimental The experiments were performed in a UHV system described in detail previously (81. The helium beam was generated from a room temperature nozzle source. The wavelength was 0.57 A. Detection of the scattered beam was accomplished with a quadrupole that could be rotated in both polar and azimuthal angles. The system has a four-grid LEED optics for LEED and AES. The Cu crystal was of (100) orientation within 0.5” as determined by the Laue technique. It was cleaned by successive cycles of ion etching and annealing. The temperature was measured with a thermocouple in mechanical contact with the crystal edge. Pb was deposited in situ from a resistively heated Knudsen cell. The standard evaporation rate employed in these measof step decoraurements was - 1.2 X 10” atoms cm-’ s- ‘. The experiments tion with Pb adatoms were performed at a slower rate of - 7.6 X 10” atoms cm-* s i. The Pb coverage was determined with quantitative AES measurements with a precision of 10%. Ulterior refinements aimed at accurately determining the coverage consisted in monitoring the coverage dependence of the intensity of both specular and diffracted beams for the c(4 x 4) superstructure. This allowed to determine the Pb coverage with an accuracy of 1%. Heating of the crystal took place by radiation from a W filament placed behind the sample. The temperature could be controlled to 2 K.
3. Results 3.1. Characterization
of the Cu( 100) substrate
In order to determine the flatness intensity of the specularly reflected
of the Cu( 100) substrate He beam as a function
we measured the of the incidence
angle for a well-annealed surface exhibiting a sharp (1 x 1) LEED pattern. This resulted in oscillations of the intensity of the specular beam that corresponded to interferences among He atoms scattered at different terrace planes of the Cu crystal. The period and amplitude of the oscillations allowed us to determine the. average “,‘“p height and to estimate the step density 191. This resulted in 1.80 it 0.05 A for the height (in~cating m~noato~c steps) and in a relative number of Cu atoms in a step position of - 7 x 10M3. An independent method of determining the step density is decoration of the steps with Pb atoms. This was accomplished by evaporating Pb at extremely low s-l) and at a temperature high evaporation rates (7.6 X lOlo atoms cm-’ enough for fast diffusion to occur. In the work at hand a monolayer of Pb is defined as n, = 1.53 x 1015 atoms cmW2, i-e., the atomic density of the Cu(100) substrate. Taking into account the different size of Pb and Cu atoms, an ideally perfect Fb adlayer that completely covers the substrate corresponds to a Pb coverage of 0.6 monolayers. The 1 versus B curve for deposition at 405 K and very low coverages depicted in fig. 1, consisted of two straight line segments of different slopes
a
6~10~
340-3 COVERAGE
(8)
Fig. 1. (a) First stages of the evolution of the specularly reflected He beam intensities as a function of Pb coverage. Note the change in slope at B = 4X IO-‘. The incidence angle, Bi, was 75O from the surface normal and the surface temperature 405 K. (b) Schematic drawing of Pb adatoms (shadowed) adsorbed at step sites of the Cu substrate. The cross se&on of the step itself (.Z step) is indicated by the broken line. The dotted area represents the small effective cross section of the adatoms adsorbed at the steps. They contribute to the decay of I only with the part of their cross section that lies outside the region of overlap with E steps. (c) Scheme of Pb adsorption on the terraces of the substrate after completion of step sites. The dotted area around the Pb adatom represents the cross section for diffuse scattering of He atoms with an energy of 63 meV impinging on the sample at tii = 75O.
intersecting at a coverage 8 = 4 X 10eB Pb monolayers that corresponds to a relative number of Cu atoms at step sites of 6 x lo-“. The break in the I versus 19 curve occurs since under these conditions the Pb adatoms first adsorbed on the step sites of the substrate, as will be discussed in more detail below. The decrease of I due to diffuse scattering by Pb adatoms adsorbed at step sites is rather small since the steps themselves scatter incoherently. It has been shown that steps on a Pt(lll) surface have a cross section per unit length for diffuse scattering of 12 A [lo]. The experimental situation corresponding to the first straight-line segment has been depicted in fig. lb. Only after completion of the step sites do the Pb adatoms begin to adsorb on the terraces where they show their full scattering cross section and accordingly a more pronounced attenuation of the specular beam is to be found. Fig. lc depicts schematically the situation with all steps sites occupied and adsorption on the terraces. 3.2. Dependence
of the specular intensity on Pb coverage
For a metallic, close-packed and ordered surface, the elastically scattered He intensity is mostly concentrated along the specularly reflected direction since the intensities of the diffracted beams are only 10-3-10-4 I,, where I, stands for the specular intensity of the clean surface. The specular intensity I after adsorption up to a coverage 8 of atoms or molecules has been found to obey the following law: z/z,=
(1 -e)“,
(1)
where (Y= X/A, is the ratio between the cross section for diffuse scattering 2 (in A*) for adatoms or ad-molecules and the area, A, (in A2) of a substrate unit cell. This expression was proposed by Comsa and co-workers [ll]. For very small 8 the formula reduces to a linear attenuation law with a slope proportional to 2. This linear attenuation law has been found to give a reasonable fit to the experimental data taken at very low coverages in several adsorption systems such as CO on Pt(ll1) [ll] or H, on Pt(ll1) [12]. Expression (1) is easily rationalized since it states that a substrate unit cell contributes to the specular scattering only if simultaneously (Y unit cells around it are not occupied by adatoms. In our experiments on Pb deposition on Cu, one must realize that in a hard sphere model the area occupied by an adsorbed Pb atoms is 1.87 times larger than the corresponding one for a Cu atom, i.e., a Pb adatom covers almost two substrate unit cells. To account for this “size” effect in a simple way we will modify eq. (1) by introducing a numerical factor w that measures the effective size of the adatoms relative to the substrate ones. The coverage 19 in eq. (1) should be multiplied by w since ~0 is the effective number of unit cells occupied by adatoms. The exponent (Y must be substituted by IX/W since this
A. Sdnchez et (11./ First stages of epitaxial growth of Pb on Cu(lO0)
COVERAGE
921
(8)
Fig. 2. Dependence of the specular intensity on Pb coverage at various temperatures. The experimental data points are shown as circles and the continuous curve correspond to the plot of eq. (2) (see text). The calculated curves have been slightly translated upwards to illustrate with more clarity the quality of the fit. For this reason they do not intersect at I/I,, = 1.0 for zero coverage. Data at all temperatures were taken at 0, = 75’.
is the number write: z/1,=(1-We)+
of substrate
unit cells available
for adsorption.
Therefore
we
(2)
for the relative specularly reflected intensity as a function of the coverage ~9of adatoms. In addition to purely geometric effects as the above mentioned, w will in reality also depend on the interactions between adatoms. For example, in cases where repulsive interactions between nearest-neighbours occur, the w values are expected to be larger than the one deduced from packing of rigid spheres, i.e., 1.87 in this case. The experimental results of the dependence of I/1, on Pb coverage are displayed in fig. 2 for three substrate temperatures. As is customary the ordinate axis is plotted in a logarithmic scale. From the initial slope of the data points taken at T = 650 K where Pb atoms are adsorbed at terrace sites (section 3.3) a value of Z = 78 AZ for the cross section for diffuse scattering is
922
A. Scinc~he: et al. / Fint stages of epitu.uial growth of Ph on Cu(lO0)
obtained [7]. This value is comparable with those previously reported for adsorbed gases [l]. Its large magnitude points again to the role of long-range attractive dispersion forces in determining the measured scattering cross sections. This behaviour was first suggested by experiments [13] and later confirmed by quantum mechanical calculations [14] for gases adsorbed on metal surfaces. Recently, Zaremba [15] has evaluated in a simple model the van der Waals interaction between a metal atom deposited on a metal surface of the same chemical nature and the impinging He atom. He concluded that the adatom should show a large scattering cross section. Experiments carried out on a ion-bombarded Pt(ll1) crystal were not able to confirm this prediction [16] because of the fast diffusion of Pt adatoms to vacancies or steps. Our data prove unequivocally that Pb adatoms deposited on a Cu surface do actually have a large cross section for diffuse scattering. The experimental points for T = 465 and 345 K were fitted with eq. (2) by taking Z = 78 A’ and letting u‘ as the only free parameter (a is fixed by the value of 2). The optimum value for u’ was chosen on the basis of fitting the maximum possible number of experimental points. For both experiments M’= 2.66 was obtained. At coverages around 0.20 the calculated curve begins to deviate from the experiments. For coverages between 0 and 0.05 the data points cannot be fitted by the theoretical curve. These facts are interpreted as follows: LEED observations indicate that at these temperatures Pb adatoms form a c(4 X 4) ordered phase with a maximum coverage of 3/8 of monolayer. If a new lattice formed by the lattice points of a perfect c(4 X 4) structure is thought to exist on the Cu(100) substrate each lattice site will occupy 8/3 times more area than the substrate unit cell. It is on the sites of this imaginary c(4 X 4) lattice that random adsorption of Pb atoms takes place as suggested (i) by the fact that eq. (2) for random adsorption is applicable and (ii) by the w value obtained from the fit (exactly 8/3). Furthermore, random adsorption is also indicated by the evolution of the (l/2, 0) diffracted beam with coverage [7]. Actually, the diffracted intensity which is rather small below 8 = 0.23 ML, increases quickly from this coverage until a maximum is reached at a coverage of 3/8 ML. The implication of these observations is that there is an effective nearest-neighbor repulsion between Pb atoms that prevents them from being closer than the value of MI given by the c(4 x 4) structure. On the other hand, the deviation observed at low coverages for T = 465 K may be easily understood. It was already mentioned in section 3.1 that for very low coverages and low temperatures Pb adsorbs on step sites of the Cu substrate. This results in a smaller cross section ,X for adatoms since the step itself causes diffuse scattering (see fig. 1). Accordingly eq. (2) with 2 = 78 A’ holds only after completion of adsorption on the steps. Note that the calculated curves and the experimental points do not coincide until coverages around 0.05. This is a coverage about ten times larger than the
923
A. Sdnchez et al. / First stages ofepitaxial growth OJPb on Cu(IOO}
one necessary for filling the step sites of the substrates (- 4 X 10e3). We do not have at present a satisfactory explanation for this effect. The continuous curve that fits the data points for T = 650 K is a plot of eq. (2) where w was let again as a free parameter and 2 was fixed to the previously determined value of 78 A. The best fit corresponds to w = 2.9. The fit is excellent from the first data points up to 8 = 0.19, where the experimental points start to lie above the calculated curve as with the data taken at lower temperatures. It will be shown in section 3.3 that for high temperatures (650 K) there is no adsorption on the steps and eq. (2) should fit the data even for very low coverages as it does indeed. The deviations between the calculated curves and the experiments for coverages larger than 8 = 0.20 are due to the fact that at these coverages, the Pb adlayer has nonzero reflectivity. At temperatures below the melting temperature of the c(4 X 4) structure and for coverages above @= 0.20, the order in the adlayer starts to increase noticeably as judged by the intensity of the diffracted beams. The data show that for coverages between 0.27 and 3/8, I increases and displays a relative maximum at 8 = 3/8 [7]. Above the melting temperature of the c(4 X 4) structure (around 600 K) there are no diffracted beams but the specular intensity still increases between 0 = 0.27 and 3/8, indicating that the liquid layer itself has some reflectivity. A point which deserves some comment is the fact that the w value measured at 650 K is about 9% larger than the value at lower temperatures. At 650 K, the ~(4 X 4) solid phase is above its melting point, so that adsorption gives rise to a liquid Pb layer. Due to the fact that the cross section of adatoms is much larger than its “geometrical” size, the measured w values represent the area avalaible to the adatoms in units of the substrate unit cell. This area is inversely proportional to the adsorbate density for a phase (solid, liquid, etc.) characterized by a certain lateral distribution of adatoms. We believe that our data reflect an increase in the effective area occupied by adatoms that occur upon crossing the melting point of the ~(4 x 4) ordered structure. Monte Carlo simulations on strictly two-dimensional (2D) Leonard-Jones systems predict that a 2D solid melts into a 2D liquid with a dramatic decrease in equilibrium density, pz - ,$ = 0.11 [17]. The simulation was carried out at constant pressure, so that the volume occupied by each phase can change. This is indeed similar to our case, for the solid ~(4 X 4) phase does not cover completely the available area and an increase in the effective area of the liquid phase is thus possible. 3.3. Step versus terrace adsorption For sufficiently low coverages, eqs. (1) and (2) may be approximated 1 - r/r,
= (l/A,)6z’.
to (3)
924
SXJ 300 400 600 ?C SURFACE TEMPERATURE T(K) Fig. 3. Dependence of the cross section for diffuse scattering B on temperature for two different Pb coverages. The angle of incidence was 75O.
This equation has been found experimentally to be valid for coverages typically less than 5% of a monolayer [l]. By measuring the relative attenuation of the specular intensity (the left-hand side of eq. (3)) and 8, one can thus directly obtain 2’. We investigated the temperature dependence of 2 for small Pb coverages. We deposited 3 X 10 3 monolayers of Pb and we measured the dependence of 1 on temperature in the range 3~-7~ K. In a separate experiment the 1, versus T data were recorded for the clean substrate with identical heating rate and incidence angle. The high temperature limit was chosen to avoid Pb desorption. The experimental runs were performed upon heating and cooling to check for thermal reversibility. Fig. 3 shows the results. The curve has a sigmoidal shape. At low temperatures _Z = 30 A2 and at high temperature Z: = 80 A2. The evolution of 2 with T reflects the equilib~~ distribution of Pb atoms between steps and terraces. There is a consistent body of data [IS] proving that the adsorption energy is larger at steps than at terraces. Therefore, at low temperatures the Pb adatoms are most probably located at the steps of the substrate where their effective cross section should be small, due to overlap with the cross section for diffuse scattering inherent to the steps [lo]. At high temperatures, the Pb atoms are preferentially adsorbed on the terraces of the Cu substrate and they exhibit a large cross section. In the intermediate temperature range (4~-600 K) the adlayer consists of two phases in thermodynamic equilibrium, a 2D dilute phase of atoms adsorbed on the terraces and a condensed one along the substrate steps. The value of the 2D heat of evaporation of Pb atoms from step to terraces sites can be extracted from the data by using the lever rule and the Clausius equation [19]. This procedure gives a value of 0.4 &-0.1 eV per atom. The heat as given by thermal of adsorption of Pb on Cu(100) is - 2.5 eV/atom
A. Sinchez et al. / First stages of ~pitux~5l growth of Pb on Cu(l oqi
925
desorption [7]. A simple estimation of the energy per bond would give - 0.5 eV/bond, assuming that Pb adsorbs in fourfold sites as given by LEED [6] and it is bonded to four Cu atoms in the first layer and one below. The value obtained of 0.4 * 0.1 eV for desorption from the steps to the terraces can, thus, be rationalized as resulting from the presence of one additional Cu-Pb bond at step sites as compared to terraces sites. The 2D heat of evaporation of an Au crystal deposited on W(110) has been obtained from detailed measurements of the work function change. The value reported was 0.3-0.4 eV/atom depending on the temperature [19]. The dependence of .S on T is only detected at coverages below saturation of the step sites. Fig. 3 also shows the experimental results of the 2 versus T dependence for a Pb coverage of 3 x low2 monolayers. The data points exhibit a very weak dependence on temperature. As may be observed in the figure both set of data meet at elevated temperatures but they differ at low and intermediate ones. For 8 = 3 X lo-* the coverage is about ‘7 times larger than the surface concentration of step sites indicating that most of the adatoms are on the terraces. In this case, desorption of Pb atoms from steps to terraces does not cause any significant change in the concentration of adatoms on the terraces leading to the very small change of 2 with temperature observed in the experiments.
4. Summary and conclusions This paper reports a TEAS study on the first stages of epitaxial growth of’ Pb atoms deposited on a Cu(100) substrate. The main conclusions are: (i) The dependence of the specularly reflected intensity with coverage is well described by a simple analytical formula based on random adsorption on substrate lattices sites. The one-parameter fit to the experiments yields a value for the actual size of the adsorbate atom from which the lateral distribution of adatoms can be deduced. (ii) Equilibrium measurements of the population distribution, in the adsorbed layer allow us to determine the 2D heat of evaporation from substrate step to terrace sites. A value of 0.4 f 0.1 eV per atom is obtained from the data.
We thank Dr. J.M. Soler for discussions. This work has been supported by the Comision Asesora de Investigacibn Cientifica y Tecnica under grant no. 387-84 and by the Spain-USA Joint Committee for Scientific Research through contract No. CCA-8411063.
References [l] [2] [3] [4] ]5] [6] [7] [X] [9] [IO] [II] 1121 [13] [14] [15] [16] [17] [1X] [19]
G. Comsa and B. Poelsema, Appl. Phys. A38 (1985) 153. M. Nijs. E.K. Riedel, E.H. Conrad and T. Engel. Phys. Rev. Letters SS (19X5) 16XY. K.H. Rieder and T. Engel, Phys. Rev. Letters 45 (1980) X24. L.J. Gomez, S. Bourgeal, J. Ibanez and M. Safmeron, Phys. Rev. B31 (19X5) 2551 A. Sepulveda and G.E. Rhead, Surface Sei. 66 11977) 436; J. Hention and G.E. Rhead, Surface Sci. 29 (1972) 20. W. Hoesler and W. Moritz, Surface Sci. 117 (1982) 196; W. Hoesler, PhD Thesis, University of Miinich. 1982. unpublished. A. Sanchez, J. Ibafiez, R. Miranda and S. Ferrer, to be published. J. Iba?jez, N. Garcia. J.M. Rojo and N. Cabrera, Surface Sci. 117 (1982) 23. J. Lapujoulade, Surface Sci. 108 (19X1) 526. L.K. Verheij, B. Poelsema and G. Comsa, Surface Sci. 162 (1985) 858. B. Poelsema, R.L. Palmer and G. Comsa, Surface Sci. 136 (19X4) 1. 8. Poelsema, L.K. Verheij and G. Comsa, Surface Sci. 152/153 (1984) 4Y6. B. Poelsema, ST. de Zwart and G. Comsa. Phys. Rev. Letters 49 (1982) 57X. H. Jonsson, J.H. Weare and A.C. Levi, Phys. Rev. Letters 49 (19X2) 57X. E. Zaremba. Surface Sci. 151 (1985) 91. B. Poelsema. K. Lenz, L.S. Brown, L.K. Verheij and G. Comsa, Surface Sci. 167 (1985) 1011 F.F. Abraham, Phys. Rept. 80 (1981) 339. See for instance, R. Miranda and J.M. ROJO, Vacuum 34 (1984) 1069. J. Kdaczkiewicz and E. Bauer. Phys. Rev, Letters 54 (1985) 574.
917
THE FIRST STAGES OF EPITAXIAL GROWTH OF Pb ATOMS ON Cu(100) STUDIED BY SCATTERING OF THERMAL HELIUM A. SANCHEZ, Departamento
J. IBANEZ
de Fisica Fundamental,
Universidad Authoma
Received
*, R. MIRANDA
10 March
de Madrid
1986; accepted
C-III,
and S. FERRER
Facultad de Ciencias,
Cantoblanco, 28049.Madrid,
for publication
Spain
12 May 1986
We studied the initial stages of the growth of Pb layers on a Cu(100) substrate by means of thermal energy atom scattering (TEAS). We found that the coverage dependence of the intensity of the specularly reflected He beam is well described by a simple mathematical formula based on random adsorption on substrate lattice sites including lateral repulsive interactions between adatoms. Equilibrium measurements of the adsorbed layer for very low coverages (3 ~10~~ monolayers) allowed to determine the 2D heat of evaporation of Pb atoms from step to terrace sites. This was accomplished by measuring the temperature dependence of the cross section for diffuse scattering.
1. Introduction Thermal energy atom scattering (TEAS) is nowadays a well-established surface science technique for extracting information on kinetic and dynamic aspects of surface processes in addition to static information on surface structure [l-3]. The technique has been applied to a variety of adsorption systems such as 0, CO, Xe and H on metallic surfaces. However, the studied overlayers have been almost exclusively adsorbed gases. Only recently has it been used in our laboratory to monitor the surface of a metal crystal that was growing from its own vapor [4]. We present in this paper a study by TEAS of the first stages of formation of an heteroepitaxial system: Pb atoms deposited from the vapor phase on a Cu(100) substrate. We will show that, due to the extreme sensitivity of TEAS to small concentrations of adatoms, information on the kinetics and thermodynamics of the very first stages of the epitaxial growth may be easily obtained. Deposition of Pb on Cu(100) results, in the submonolayer regime, in several ordered structures that have been previously studied with LEED and AES [5,6]. These are, termed in order of increasing coverage, c(4 X 4) c(2 x 2) and (5fi x fi), the later corresponding to the completion of an overlayer of Pb atoms that completely covers the substrate. It is established from LEED * Present
address:
Departamento
de Materiales,
INTA,
Madrid,
0039-6028/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
Spain.
B.V.
dynamical analysis that the surface corrugation of these overlayers decreases with coverage, i.e., the c(4 x 4) presents the larger corrugation and the (Sv’? x a) is almost flat [6]. This structural information is easily extracted from TEAS since only the c(4 X 4) structure produces intense diffracted beams [7]. However, in this paper we will concentrate only on the submonolayer range preceding the formation of the c(4 x 4) structure, i.e., in the first stages of the growth of this epitaxial system. We will show that the variation of the specular intensity with coverage of adatoms, is well described by an analytical law based on random adsorption on substrate lattice sites with nearest-neighbour repulsion between the adatoms. We will illustrate how the 2D heat of evaporation of Pb atoms from step to terrace sites of the Cu substrate can be obtained from TEAS data taken at very low coverages of Pb under conditions of thermodynamic equilibrium.
2. Experimental The experiments were performed in a UHV system described in detail previously (81. The helium beam was generated from a room temperature nozzle source. The wavelength was 0.57 A. Detection of the scattered beam was accomplished with a quadrupole that could be rotated in both polar and azimuthal angles. The system has a four-grid LEED optics for LEED and AES. The Cu crystal was of (100) orientation within 0.5” as determined by the Laue technique. It was cleaned by successive cycles of ion etching and annealing. The temperature was measured with a thermocouple in mechanical contact with the crystal edge. Pb was deposited in situ from a resistively heated Knudsen cell. The standard evaporation rate employed in these measof step decoraurements was - 1.2 X 10” atoms cm-’ s- ‘. The experiments tion with Pb adatoms were performed at a slower rate of - 7.6 X 10” atoms cm-* s i. The Pb coverage was determined with quantitative AES measurements with a precision of 10%. Ulterior refinements aimed at accurately determining the coverage consisted in monitoring the coverage dependence of the intensity of both specular and diffracted beams for the c(4 x 4) superstructure. This allowed to determine the Pb coverage with an accuracy of 1%. Heating of the crystal took place by radiation from a W filament placed behind the sample. The temperature could be controlled to 2 K.
3. Results 3.1. Characterization
of the Cu( 100) substrate
In order to determine the flatness intensity of the specularly reflected
of the Cu( 100) substrate He beam as a function
we measured the of the incidence
angle for a well-annealed surface exhibiting a sharp (1 x 1) LEED pattern. This resulted in oscillations of the intensity of the specular beam that corresponded to interferences among He atoms scattered at different terrace planes of the Cu crystal. The period and amplitude of the oscillations allowed us to determine the. average “,‘“p height and to estimate the step density 191. This resulted in 1.80 it 0.05 A for the height (in~cating m~noato~c steps) and in a relative number of Cu atoms in a step position of - 7 x 10M3. An independent method of determining the step density is decoration of the steps with Pb atoms. This was accomplished by evaporating Pb at extremely low s-l) and at a temperature high evaporation rates (7.6 X lOlo atoms cm-’ enough for fast diffusion to occur. In the work at hand a monolayer of Pb is defined as n, = 1.53 x 1015 atoms cmW2, i-e., the atomic density of the Cu(100) substrate. Taking into account the different size of Pb and Cu atoms, an ideally perfect Fb adlayer that completely covers the substrate corresponds to a Pb coverage of 0.6 monolayers. The 1 versus B curve for deposition at 405 K and very low coverages depicted in fig. 1, consisted of two straight line segments of different slopes
a
6~10~
340-3 COVERAGE
(8)
Fig. 1. (a) First stages of the evolution of the specularly reflected He beam intensities as a function of Pb coverage. Note the change in slope at B = 4X IO-‘. The incidence angle, Bi, was 75O from the surface normal and the surface temperature 405 K. (b) Schematic drawing of Pb adatoms (shadowed) adsorbed at step sites of the Cu substrate. The cross se&on of the step itself (.Z step) is indicated by the broken line. The dotted area represents the small effective cross section of the adatoms adsorbed at the steps. They contribute to the decay of I only with the part of their cross section that lies outside the region of overlap with E steps. (c) Scheme of Pb adsorption on the terraces of the substrate after completion of step sites. The dotted area around the Pb adatom represents the cross section for diffuse scattering of He atoms with an energy of 63 meV impinging on the sample at tii = 75O.
intersecting at a coverage 8 = 4 X 10eB Pb monolayers that corresponds to a relative number of Cu atoms at step sites of 6 x lo-“. The break in the I versus 19 curve occurs since under these conditions the Pb adatoms first adsorbed on the step sites of the substrate, as will be discussed in more detail below. The decrease of I due to diffuse scattering by Pb adatoms adsorbed at step sites is rather small since the steps themselves scatter incoherently. It has been shown that steps on a Pt(lll) surface have a cross section per unit length for diffuse scattering of 12 A [lo]. The experimental situation corresponding to the first straight-line segment has been depicted in fig. lb. Only after completion of the step sites do the Pb adatoms begin to adsorb on the terraces where they show their full scattering cross section and accordingly a more pronounced attenuation of the specular beam is to be found. Fig. lc depicts schematically the situation with all steps sites occupied and adsorption on the terraces. 3.2. Dependence
of the specular intensity on Pb coverage
For a metallic, close-packed and ordered surface, the elastically scattered He intensity is mostly concentrated along the specularly reflected direction since the intensities of the diffracted beams are only 10-3-10-4 I,, where I, stands for the specular intensity of the clean surface. The specular intensity I after adsorption up to a coverage 8 of atoms or molecules has been found to obey the following law: z/z,=
(1 -e)“,
(1)
where (Y= X/A, is the ratio between the cross section for diffuse scattering 2 (in A*) for adatoms or ad-molecules and the area, A, (in A2) of a substrate unit cell. This expression was proposed by Comsa and co-workers [ll]. For very small 8 the formula reduces to a linear attenuation law with a slope proportional to 2. This linear attenuation law has been found to give a reasonable fit to the experimental data taken at very low coverages in several adsorption systems such as CO on Pt(ll1) [ll] or H, on Pt(ll1) [12]. Expression (1) is easily rationalized since it states that a substrate unit cell contributes to the specular scattering only if simultaneously (Y unit cells around it are not occupied by adatoms. In our experiments on Pb deposition on Cu, one must realize that in a hard sphere model the area occupied by an adsorbed Pb atoms is 1.87 times larger than the corresponding one for a Cu atom, i.e., a Pb adatom covers almost two substrate unit cells. To account for this “size” effect in a simple way we will modify eq. (1) by introducing a numerical factor w that measures the effective size of the adatoms relative to the substrate ones. The coverage 19 in eq. (1) should be multiplied by w since ~0 is the effective number of unit cells occupied by adatoms. The exponent (Y must be substituted by IX/W since this
A. Sdnchez et (11./ First stages of epitaxial growth of Pb on Cu(lO0)
COVERAGE
921
(8)
Fig. 2. Dependence of the specular intensity on Pb coverage at various temperatures. The experimental data points are shown as circles and the continuous curve correspond to the plot of eq. (2) (see text). The calculated curves have been slightly translated upwards to illustrate with more clarity the quality of the fit. For this reason they do not intersect at I/I,, = 1.0 for zero coverage. Data at all temperatures were taken at 0, = 75’.
is the number write: z/1,=(1-We)+
of substrate
unit cells available
for adsorption.
Therefore
we
(2)
for the relative specularly reflected intensity as a function of the coverage ~9of adatoms. In addition to purely geometric effects as the above mentioned, w will in reality also depend on the interactions between adatoms. For example, in cases where repulsive interactions between nearest-neighbours occur, the w values are expected to be larger than the one deduced from packing of rigid spheres, i.e., 1.87 in this case. The experimental results of the dependence of I/1, on Pb coverage are displayed in fig. 2 for three substrate temperatures. As is customary the ordinate axis is plotted in a logarithmic scale. From the initial slope of the data points taken at T = 650 K where Pb atoms are adsorbed at terrace sites (section 3.3) a value of Z = 78 AZ for the cross section for diffuse scattering is
922
A. Scinc~he: et al. / Fint stages of epitu.uial growth of Ph on Cu(lO0)
obtained [7]. This value is comparable with those previously reported for adsorbed gases [l]. Its large magnitude points again to the role of long-range attractive dispersion forces in determining the measured scattering cross sections. This behaviour was first suggested by experiments [13] and later confirmed by quantum mechanical calculations [14] for gases adsorbed on metal surfaces. Recently, Zaremba [15] has evaluated in a simple model the van der Waals interaction between a metal atom deposited on a metal surface of the same chemical nature and the impinging He atom. He concluded that the adatom should show a large scattering cross section. Experiments carried out on a ion-bombarded Pt(ll1) crystal were not able to confirm this prediction [16] because of the fast diffusion of Pt adatoms to vacancies or steps. Our data prove unequivocally that Pb adatoms deposited on a Cu surface do actually have a large cross section for diffuse scattering. The experimental points for T = 465 and 345 K were fitted with eq. (2) by taking Z = 78 A’ and letting u‘ as the only free parameter (a is fixed by the value of 2). The optimum value for u’ was chosen on the basis of fitting the maximum possible number of experimental points. For both experiments M’= 2.66 was obtained. At coverages around 0.20 the calculated curve begins to deviate from the experiments. For coverages between 0 and 0.05 the data points cannot be fitted by the theoretical curve. These facts are interpreted as follows: LEED observations indicate that at these temperatures Pb adatoms form a c(4 X 4) ordered phase with a maximum coverage of 3/8 of monolayer. If a new lattice formed by the lattice points of a perfect c(4 X 4) structure is thought to exist on the Cu(100) substrate each lattice site will occupy 8/3 times more area than the substrate unit cell. It is on the sites of this imaginary c(4 X 4) lattice that random adsorption of Pb atoms takes place as suggested (i) by the fact that eq. (2) for random adsorption is applicable and (ii) by the w value obtained from the fit (exactly 8/3). Furthermore, random adsorption is also indicated by the evolution of the (l/2, 0) diffracted beam with coverage [7]. Actually, the diffracted intensity which is rather small below 8 = 0.23 ML, increases quickly from this coverage until a maximum is reached at a coverage of 3/8 ML. The implication of these observations is that there is an effective nearest-neighbor repulsion between Pb atoms that prevents them from being closer than the value of MI given by the c(4 x 4) structure. On the other hand, the deviation observed at low coverages for T = 465 K may be easily understood. It was already mentioned in section 3.1 that for very low coverages and low temperatures Pb adsorbs on step sites of the Cu substrate. This results in a smaller cross section ,X for adatoms since the step itself causes diffuse scattering (see fig. 1). Accordingly eq. (2) with 2 = 78 A’ holds only after completion of adsorption on the steps. Note that the calculated curves and the experimental points do not coincide until coverages around 0.05. This is a coverage about ten times larger than the
923
A. Sdnchez et al. / First stages ofepitaxial growth OJPb on Cu(IOO}
one necessary for filling the step sites of the substrates (- 4 X 10e3). We do not have at present a satisfactory explanation for this effect. The continuous curve that fits the data points for T = 650 K is a plot of eq. (2) where w was let again as a free parameter and 2 was fixed to the previously determined value of 78 A. The best fit corresponds to w = 2.9. The fit is excellent from the first data points up to 8 = 0.19, where the experimental points start to lie above the calculated curve as with the data taken at lower temperatures. It will be shown in section 3.3 that for high temperatures (650 K) there is no adsorption on the steps and eq. (2) should fit the data even for very low coverages as it does indeed. The deviations between the calculated curves and the experiments for coverages larger than 8 = 0.20 are due to the fact that at these coverages, the Pb adlayer has nonzero reflectivity. At temperatures below the melting temperature of the c(4 X 4) structure and for coverages above @= 0.20, the order in the adlayer starts to increase noticeably as judged by the intensity of the diffracted beams. The data show that for coverages between 0.27 and 3/8, I increases and displays a relative maximum at 8 = 3/8 [7]. Above the melting temperature of the c(4 X 4) structure (around 600 K) there are no diffracted beams but the specular intensity still increases between 0 = 0.27 and 3/8, indicating that the liquid layer itself has some reflectivity. A point which deserves some comment is the fact that the w value measured at 650 K is about 9% larger than the value at lower temperatures. At 650 K, the ~(4 X 4) solid phase is above its melting point, so that adsorption gives rise to a liquid Pb layer. Due to the fact that the cross section of adatoms is much larger than its “geometrical” size, the measured w values represent the area avalaible to the adatoms in units of the substrate unit cell. This area is inversely proportional to the adsorbate density for a phase (solid, liquid, etc.) characterized by a certain lateral distribution of adatoms. We believe that our data reflect an increase in the effective area occupied by adatoms that occur upon crossing the melting point of the ~(4 x 4) ordered structure. Monte Carlo simulations on strictly two-dimensional (2D) Leonard-Jones systems predict that a 2D solid melts into a 2D liquid with a dramatic decrease in equilibrium density, pz - ,$ = 0.11 [17]. The simulation was carried out at constant pressure, so that the volume occupied by each phase can change. This is indeed similar to our case, for the solid ~(4 X 4) phase does not cover completely the available area and an increase in the effective area of the liquid phase is thus possible. 3.3. Step versus terrace adsorption For sufficiently low coverages, eqs. (1) and (2) may be approximated 1 - r/r,
= (l/A,)6z’.
to (3)
924
SXJ 300 400 600 ?C SURFACE TEMPERATURE T(K) Fig. 3. Dependence of the cross section for diffuse scattering B on temperature for two different Pb coverages. The angle of incidence was 75O.
This equation has been found experimentally to be valid for coverages typically less than 5% of a monolayer [l]. By measuring the relative attenuation of the specular intensity (the left-hand side of eq. (3)) and 8, one can thus directly obtain 2’. We investigated the temperature dependence of 2 for small Pb coverages. We deposited 3 X 10 3 monolayers of Pb and we measured the dependence of 1 on temperature in the range 3~-7~ K. In a separate experiment the 1, versus T data were recorded for the clean substrate with identical heating rate and incidence angle. The high temperature limit was chosen to avoid Pb desorption. The experimental runs were performed upon heating and cooling to check for thermal reversibility. Fig. 3 shows the results. The curve has a sigmoidal shape. At low temperatures _Z = 30 A2 and at high temperature Z: = 80 A2. The evolution of 2 with T reflects the equilib~~ distribution of Pb atoms between steps and terraces. There is a consistent body of data [IS] proving that the adsorption energy is larger at steps than at terraces. Therefore, at low temperatures the Pb adatoms are most probably located at the steps of the substrate where their effective cross section should be small, due to overlap with the cross section for diffuse scattering inherent to the steps [lo]. At high temperatures, the Pb atoms are preferentially adsorbed on the terraces of the Cu substrate and they exhibit a large cross section. In the intermediate temperature range (4~-600 K) the adlayer consists of two phases in thermodynamic equilibrium, a 2D dilute phase of atoms adsorbed on the terraces and a condensed one along the substrate steps. The value of the 2D heat of evaporation of Pb atoms from step to terraces sites can be extracted from the data by using the lever rule and the Clausius equation [19]. This procedure gives a value of 0.4 &-0.1 eV per atom. The heat as given by thermal of adsorption of Pb on Cu(100) is - 2.5 eV/atom
A. Sinchez et al. / First stages of ~pitux~5l growth of Pb on Cu(l oqi
925
desorption [7]. A simple estimation of the energy per bond would give - 0.5 eV/bond, assuming that Pb adsorbs in fourfold sites as given by LEED [6] and it is bonded to four Cu atoms in the first layer and one below. The value obtained of 0.4 * 0.1 eV for desorption from the steps to the terraces can, thus, be rationalized as resulting from the presence of one additional Cu-Pb bond at step sites as compared to terraces sites. The 2D heat of evaporation of an Au crystal deposited on W(110) has been obtained from detailed measurements of the work function change. The value reported was 0.3-0.4 eV/atom depending on the temperature [19]. The dependence of .S on T is only detected at coverages below saturation of the step sites. Fig. 3 also shows the experimental results of the 2 versus T dependence for a Pb coverage of 3 x low2 monolayers. The data points exhibit a very weak dependence on temperature. As may be observed in the figure both set of data meet at elevated temperatures but they differ at low and intermediate ones. For 8 = 3 X lo-* the coverage is about ‘7 times larger than the surface concentration of step sites indicating that most of the adatoms are on the terraces. In this case, desorption of Pb atoms from steps to terraces does not cause any significant change in the concentration of adatoms on the terraces leading to the very small change of 2 with temperature observed in the experiments.
4. Summary and conclusions This paper reports a TEAS study on the first stages of epitaxial growth of’ Pb atoms deposited on a Cu(100) substrate. The main conclusions are: (i) The dependence of the specularly reflected intensity with coverage is well described by a simple analytical formula based on random adsorption on substrate lattices sites. The one-parameter fit to the experiments yields a value for the actual size of the adsorbate atom from which the lateral distribution of adatoms can be deduced. (ii) Equilibrium measurements of the population distribution, in the adsorbed layer allow us to determine the 2D heat of evaporation from substrate step to terrace sites. A value of 0.4 f 0.1 eV per atom is obtained from the data.
We thank Dr. J.M. Soler for discussions. This work has been supported by the Comision Asesora de Investigacibn Cientifica y Tecnica under grant no. 387-84 and by the Spain-USA Joint Committee for Scientific Research through contract No. CCA-8411063.
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G. Comsa and B. Poelsema, Appl. Phys. A38 (1985) 153. M. Nijs. E.K. Riedel, E.H. Conrad and T. Engel. Phys. Rev. Letters SS (19X5) 16XY. K.H. Rieder and T. Engel, Phys. Rev. Letters 45 (1980) X24. L.J. Gomez, S. Bourgeal, J. Ibanez and M. Safmeron, Phys. Rev. B31 (19X5) 2551 A. Sepulveda and G.E. Rhead, Surface Sei. 66 11977) 436; J. Hention and G.E. Rhead, Surface Sci. 29 (1972) 20. W. Hoesler and W. Moritz, Surface Sci. 117 (1982) 196; W. Hoesler, PhD Thesis, University of Miinich. 1982. unpublished. A. Sanchez, J. Ibafiez, R. Miranda and S. Ferrer, to be published. J. Iba?jez, N. Garcia. J.M. Rojo and N. Cabrera, Surface Sci. 117 (1982) 23. J. Lapujoulade, Surface Sci. 108 (19X1) 526. L.K. Verheij, B. Poelsema and G. Comsa, Surface Sci. 162 (1985) 858. B. Poelsema, R.L. Palmer and G. Comsa, Surface Sci. 136 (19X4) 1. 8. Poelsema, L.K. Verheij and G. Comsa, Surface Sci. 152/153 (1984) 4Y6. B. Poelsema, ST. de Zwart and G. Comsa. Phys. Rev. Letters 49 (1982) 57X. H. Jonsson, J.H. Weare and A.C. Levi, Phys. Rev. Letters 49 (19X2) 57X. E. Zaremba. Surface Sci. 151 (1985) 91. B. Poelsema. K. Lenz, L.S. Brown, L.K. Verheij and G. Comsa, Surface Sci. 167 (1985) 1011 F.F. Abraham, Phys. Rept. 80 (1981) 339. See for instance, R. Miranda and J.M. ROJO, Vacuum 34 (1984) 1069. J. Kdaczkiewicz and E. Bauer. Phys. Rev, Letters 54 (1985) 574.