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Comparison of surface diffusion models for neopentane on Ru(001)
Surface Science Letters 280 (1993) L273-L277 North-Holland
surface s c i e n c e letters
Surface Science Letters
Comparison of surface diffusion models for neopentane on Ru(O01) M. Z i n k e - A l l m a n g Department of Physics, Unicersity of Western Ontario, London, Ont., Canada N6A 3K7
and M.C. T r i n g i d e s Department of Physics, Iowa State UnitJersity, Ames Laboratory-USDOE, Ames, 1,4 50011, USA Received 9 July 1992; accepted for publication 6 October 1992
In this Letter we compare two recent models for the observation of concentration dependent diffusion coefficients in the system neopentane, C(CH3)4, on Ru(001) surfaces. Both a multi-site hopping model where adatoms jump over several lattice sites, and a clustering model in which adatoms jump only to the next minimum of the surface potential but stick to clusters for some time, give good agreement with the existing data. Thus both models may be considered alternative proposals for the actual physical process.
In recent years fundamental interest in surface diffusion phenomena emerged due to experimental results indicating a concentration dependence of surface diffusion coefficients. Such effects become also important e.g. for thin film growth applications, since the surface diffusion coefficient is one of the crucial dynamic parameters determining the quality of the final morphology [1]. Several models have been proposed for this effect. The first experimental results [2,3] were qualitatively interpreted based on a defect formation model [2] and, alternatively, based on lattice gas models with pairwise interactions. Both detailed modelling in terms of Monte Carlo simulations [4,5] and effective approximations neglecting higher correlations between particles [6] have been used. More recently two new models were proposed. One is based on the difference between the intrinsic surface diffusion coefficient for a single adatom on a perfect surface and the apparent diffusion coefficient when the adatoms attach for
some time to clusters (clustering model) [7]. This model was shown to be in good agreement with data on metal-semiconductor and oxygen on metal systems [7]. Using new experimental data on neopentane, C(CH4)3, on Ru(001), obtained by observing the refilling signal after laser induced thermal desorption (LITD) [8], Arena et al. alternatively proposed a model based on the motion of an adatom (or molecule) over many sites on the substrate lattice in a single jump (multi-site hopping model) [9]. With a jump distance of sixteen sites good agreement with the data for n e o p e n t a n e / R u ( 0 0 1 ) was achieved. The authors also studied a model that involves adsorbate-adsorbate interactions to explain both diffusion and desorption data they obtained for this system, but no consistent picture emerges. A small attractive interaction would be needed to explain the slow change of the peak desorption temperature with coverage, which cannot be reconciled with the dramatic decrease of the diffusion coefficient with coverage. If a larger attractive interaction is used to account for the diffusion results,
0039-6028/93/$06.00 © 1993 -- Elsevier Science Publishers B.V. All rights reserved
1274
M. Zinke-Allmang, M.C. 7t'ingides / Compares'on of surface diffusion rnodeb fbr neopentane on Ru( OOt )
it is too strong for explaining the desorption data. In either case the decrease of the activation energy with coverage remains unexplained. The main emphasis of this Letter is first to show that the clustering model is in agreement with the new data for large molecules on metals and has to be considered therefore as an alternative. In a final section we then compare both models. The clustering model is a phenomenological model that stresses the role of the different local environments of the diffusive atoms [7]. It is based on the assumption that atoms attached to clusters diffuse less and that one type of atoms, presumably the monomers, experience the lower diffusion barrier and mostly control the diffusion process. Although the existence of clusters can be traced back to the presence of adsorbate-adsorbate interactions, the interactions are not limited to simple nearest neighbour attractive interactions. The exact nature of interactions is not relevant, if a phenomenological comparison with the coverage dependence of the diffusion coefficient is sought. The intrinsic surface diffusion coefficient, D~, resulting from a random walk of a single adatom on a perfect surface, i.e., a surface with only one type of sites for the adatom, is given by the Einstein relation, D i =a2/2r~, where ,~ is the hopping distance and 1/r~ is the jump frequency. Experimental techniques with atomic resolution such as FIM (field ion microscopy) and STM (scanning tunneling microscopy) allow a direct observation of the random walk and give estimates of the intrinsic surface diffusion coefficient directly. Already in these studies the tendency toward islanding and clustering is observed modifying the mobility of adatoms [i0]. At higher concentrations of adatoms a clustered adlayer equilibrium structure is expected [11,12], e.g. in diffusion measurements with macroscopic mass transport (scanning Auger microscopy of /.tinpatch deposits [2,13] or scanning electron microscopy [14]). A clustering surface adlayer represents a two phase coexistence system with a dense cluster phase and a dilute adatom phase. The concentration of the adatom phase is temperature depen-
dent but independent of the total concentratio~ as it equals to the equilibrium solubility of the cluster material, c~ [1,12]. The surface diffusion coefficient ~'~nn mass transport measurements in clustering systems, D m, and the intrinsic surface diffusion coefficient differ, since the adatoms spend a fraction of the time in clusters. An average .jump frequency 1 / r replaces the specific jump frequmk~y for the adatom. It is the sum of the site specific jump frequencies, 1/'ri, times the probabili~:} 1~ .....(',/'(. to populate this site if we consider j diffcre~I sites, c is the total concentration of adatoms on the surface and cj is the concentration of adatoms in the jth site. If only the adatom state c o n tributes to the mass transport (index a, neglecting e.g. step-sites), we find for the mass t.,ransport diffusion coefficient D m = O i ( c j c ) . 1~* m*I t~,o small clusters % can be replaced by c . Thus an adlayer system which grows according to the V o l m e r - W e b e r model (clusters on the bare substrate) obeys the relation Dm/D ~a l / c and a system which grows according to {he Strat~ski-Krastanov model (cluster tbrmatio~l tlp(m completion of a few uniform layers, with Cs~" the concentration corresponding to that uniform, temperature independent layer) obeys i;hc relation D m / D i a 1 / ( c - CsK) since part ~t the a(tlayer is incorporated in the layers below and i,,~ immobile. Two temperature dependent quantities contribute to the experimentally measured value of Din, the intrinsic surface diffusion coefl'iciel;~t D~ with the activation energy E d, and ~he free adatom concentration c:~ with the energy of fo~ mation of a cluster El. A concentration dependence of E d cannot be detected in such a measurement for a clustered system, since the free adatom concentration is an equilibrium quantity which does not vary with coverage (i.c., an in. crease of the coverage results only in an increase of the fraction of adatoms in the clusters). A measurement of the coverage dependence of the activation energy of D m should therefore result iI~ a non-constant value only if a change {iccurs in El, e.g. due to changing cluster sizes. We compared this model previously with data for the systems A g / O e ( l l l ) and O / W ( t t0)[7]. The observed concentration dependence of l)~.~
M. Zinke-Allmang, M.C. Tringides / Comparison of surface diffusion models for neopentane on Ru(O01)
was satisfactorily explained without implying a concentration dependence of D i. Also, in both studies no significant coverage dependence of the activation energy of surface diffusion was reported in the coverage regime described by the clustering model in agreement with the theoretical expectation. This successful application of the model and the generality of the concept make it desirable to compare it with further data sets such as the diffusion measurements of larger organic molecules on Ru(001). Fig. la shows a logarithmic and a linear (inset) display of the data from ref. [8]. The solid line is a fit using the clustering model. An excellent agreement is reached when CsK = 0.0465 (in units of the saturation coverage) is used. The main plot with the logarithmic display highlights in particular the match with the data at higher coverage. Within the uncertainty of the coverage calibration, the value for CsK is in agreement with the conclusion that neopentane grows as a V o l m e r - W e b e r system [15]. A complementary study of the coverage dependence of the activation energy resulted in a nearly constant surface diffusion barrier [8,9], in agreement with the expectation from the clustering model. In desorption kinetics studies a first order pro-
L275
cess was identified [8]. This result seems to contradict a two-phase region as discussed by Estrup et al. [16]. However, the theoretical analysis by Estrup et al. is based on order-disorder transition, i.e., desorption from one of two equally dense phases. In the present experiments the desorption from the adatom phase is likely overshadowed by desorption from the majority phase, which is the ordered phase of 2D-islands, as previously observed for Ga on Si [17]. This is true even if the adatom phase would have a slightly lower activation energy for desorption. Thus the desorption kinetics does not distinguish between the clustering model and the multi-site hopping model. The L E E D pattern is still 1 × 1, excluding the presence of a superstructure but not islanding because the islands formed might have the periodicity of the substrate. Fig. lb shows the same data with a fit based on the multi-site hopping model, using a hopping distance of 16 sites [8,9]. A comparison between both plots in fig. 1 shows that a single curve fit at one temperature for D(O) is not sufficient to uniquely select the correct diffusion model. Despite the excellent agreement of the experimental data for neopentane on Ru(001) with both models, we want to re-emphasize a few problems
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N [ C ( C H 3 ) 4 ] / NsA T Fig. l. Surface diffusion coefficient for neopentane on Ru(001) at 130 K as a function of coverage in units of the saturation coverage. (a) Comparison with the clustering model using CsK = 0.0465. The inset shows the same in a double-linear plot. The main plot displays the data logarithmic, emphasizing the range of higher coverage. (b) Comparison with the multi-site hopping model using a hopping distance of 16 sites. Data and (b) taken from refs. [8,9].
L276
M. Zinke-Allmang, M.C. Tringides / Comparison of surface diffusion models for neopentane on Ru(O0 i .~
in fitting the experimental data in both cases. In the case of the multi-site hopping model the diffusion coefficient is concentration dependent and a non-trivial coverage-dependent data analysis has to be used [9]. The late part of the refilling signal needs to be weighted stronger to obtain the correct value of the diffusion coefficient of the coverage outside the probe region, since otherwise a different value of the diffusion coefficient is obtained that corresponds to the non-equilibrium, spatially inhomogeneous concentration profile as discussed by Tringides [118]. A modified analysis based on an initial estimate for D(O) and an iterative solution of the non-linear diffusion equation [19] does not address the problem of convergence and uniqueness since it is still based on the analysis of the early part of the experimental refilling signal. A further problem are the deviations of the value of the diffusion coefficient in the limit of high coverage, 0 ~ 1 for different hopping lengths r of the diffusing species. Theoretically we expect that all values converge to the value for r = 1 since only single jumps are allowed. The deviations cannot be explained by the undervaluation of D(O = 1) for r = 1 because then D(O) is coverage independent [18,20]. Thus it appears that D has been overvaluated for r > 1 due to the constant diffusion coefficient fits in that reference. The clustering model describes the experimental data at higher coverage exactly only for the formation of three-dimensional clusters. Deviations from the simple 1/c dependence are anticipated as the coverage approaches the saturation coverage due to changes in the dynamics of the system such as percolation and coalescence driven effects. Monte Carlo simulations and quasi-chemical approximation calculations seem to indicate, however, that the result remains qualitatively unaltered [61. Note that ref. [8] contains a second data set for tetramethylsilane on the same surface. The authors did not observe any concentration dependence for that system. Both models cannot provide a satisfactory explanation why two large organic molecules, neopentane and tetramethylsilane, differ in their D(O) dependence. In conclusion, both the clustering model and
multi-site hopping model satisfactory describe data on the concentration dependence of the surface diffusion coefficient for neopentane on Ru(001). Note however, that the conclusion from the experimental finding is drastically differem~ A consequence of the clustering model is that above measurements are not suited to investigate the temperature dependence of the a d a t o m surface diffusion as in a two phase regime the concentration of the dilute phase does not change. In turn, the multi-site hopping model would allow us to discuss interaction processes between monomers on the surface. Although both models require a more sophisticated analysis to be fully compatible with the experiment, we believe thai: the match with the data will persist. Thus the currently available data do not allow us m discriminate between the two alternative descrip-tions for the concentration dependence of the surface diffusion coefficient. M.Z.-A. wants to thank the Natural Sciences and Engineering Council of Canada for financial support through a research grant.
References [1] M. Zinke-Allmang and S. Stoyanov, Jpn. i Appl. Phy~;. 29 (1990) L1884. [2] E. Suliga and M. Itenzler, J. Phys. (" t6 (1983~ 1543. [3] R. Butz and H. Wagner, Surf. 8ci. {~3 (P~77).4~48:.~7 (1979) 69. [4] M. Bowker and D.A. King, Sur|. Sci. 71 it,~78) 583; 71.? (1978) 208. [5] M.C. Tringides and R. Gomcr, Surf. Sci. i45 (19841 12i [61 D.A. Reed and G. Ehrlich, Surf. Sci. 102 (1981) 588. [7] M. Zinke-Allmang and L.C. Feldman, Phys Rev B ~7 (1988) 7010. [8] E.D. Westre, M.V. Arena, A.A. Deckert, ,hi, B)and a~d S.M. George, Surf. Sci. 233 (1990) 293. [9] M.V. Arena, A.A. Deckert and S.M. (,:eorg~, Suri ,',c~. 241 (1991) 369. [10] G. Ehrlich, Scan. Microsc. 4 (1990) 833. [11] M.H. Grabow and G.H. Gilmer, in: Semiconductor-base0 Heterostructures: Interfacial Structure and Slabilily, E d s M.L. Green, J.E.E. Baglin, G.Y. Chin, tl.W. Deckma,~, W. Mayo and D. Narasinham ~Metallurgical Society, Warrendale, PA, 1986) p. 3. [12] M. Zinke-Allmang, Scan. Microsc. a (1990) 5-" ~. [13] G.J. Fisaniek, H.-J. Gossmann and P. Kuo. Maler. Ri:,s. Soc. Syrup. Proc. 102 (1988) 25:
M. Zinke-Allmang, M.C. Tringides / Comparison of,surface diffusion models for neopentane on Ru(OOI) tt.-J. Gossmann and G. J. Fisanick, Scan. Microsc. 4 (1990) 543; J.A. Venables, T. Doust, J.S. Drucker and M. Krishnamurthy, in: Kinetics of Ordering and Growth at Surfaces, Ed. M.G. Lagally (Plenum, New York, 1990) p. 437; M.A. Morris, C.J. Barnes, and D.A. King, Surf. Sci. 173 (1986) 618. [14] G,W. Jones and J.A. Venables, Ultramicroscopy 18 (1985) 439: M. Hanbiicken, T. Doust, O. Osasona, G. Le Lay and J.A. Venables, Surf. Sci. 168 (1986) 133. [15] The value of CSK ==0.0465 could alternatively be related
[16] [17] [18] [19] [20]
L277
to a small fraction of the adlayer being immobile, e.g. if attached to steps as studied M.V. Arena et al. for nbutane on Ru(001) [19]. P.J. Estrup, E.F. Greene, M.J. Cardillo and J.C. Tully, J. Phys. Chem. 90 (1986) 4099. M. Zinke-Allmang, L.C. Feldman, J.R. Patel and J.C. Tully, Surf. Sci. 197 (1988) 1. M.C. Tringides, Surf. Sci. 204 (1988) 345; J. Chem. Phys. 92 (1990) 2077. M.V. Arena, E.D. Westre and S.M. George, Surf. Sci. 261 (1992) 129. R. Kutner, Phys. Lett. A 81 (1981) 239.
surface s c i e n c e letters
Surface Science Letters
Comparison of surface diffusion models for neopentane on Ru(O01) M. Z i n k e - A l l m a n g Department of Physics, Unicersity of Western Ontario, London, Ont., Canada N6A 3K7
and M.C. T r i n g i d e s Department of Physics, Iowa State UnitJersity, Ames Laboratory-USDOE, Ames, 1,4 50011, USA Received 9 July 1992; accepted for publication 6 October 1992
In this Letter we compare two recent models for the observation of concentration dependent diffusion coefficients in the system neopentane, C(CH3)4, on Ru(001) surfaces. Both a multi-site hopping model where adatoms jump over several lattice sites, and a clustering model in which adatoms jump only to the next minimum of the surface potential but stick to clusters for some time, give good agreement with the existing data. Thus both models may be considered alternative proposals for the actual physical process.
In recent years fundamental interest in surface diffusion phenomena emerged due to experimental results indicating a concentration dependence of surface diffusion coefficients. Such effects become also important e.g. for thin film growth applications, since the surface diffusion coefficient is one of the crucial dynamic parameters determining the quality of the final morphology [1]. Several models have been proposed for this effect. The first experimental results [2,3] were qualitatively interpreted based on a defect formation model [2] and, alternatively, based on lattice gas models with pairwise interactions. Both detailed modelling in terms of Monte Carlo simulations [4,5] and effective approximations neglecting higher correlations between particles [6] have been used. More recently two new models were proposed. One is based on the difference between the intrinsic surface diffusion coefficient for a single adatom on a perfect surface and the apparent diffusion coefficient when the adatoms attach for
some time to clusters (clustering model) [7]. This model was shown to be in good agreement with data on metal-semiconductor and oxygen on metal systems [7]. Using new experimental data on neopentane, C(CH4)3, on Ru(001), obtained by observing the refilling signal after laser induced thermal desorption (LITD) [8], Arena et al. alternatively proposed a model based on the motion of an adatom (or molecule) over many sites on the substrate lattice in a single jump (multi-site hopping model) [9]. With a jump distance of sixteen sites good agreement with the data for n e o p e n t a n e / R u ( 0 0 1 ) was achieved. The authors also studied a model that involves adsorbate-adsorbate interactions to explain both diffusion and desorption data they obtained for this system, but no consistent picture emerges. A small attractive interaction would be needed to explain the slow change of the peak desorption temperature with coverage, which cannot be reconciled with the dramatic decrease of the diffusion coefficient with coverage. If a larger attractive interaction is used to account for the diffusion results,
0039-6028/93/$06.00 © 1993 -- Elsevier Science Publishers B.V. All rights reserved
1274
M. Zinke-Allmang, M.C. 7t'ingides / Compares'on of surface diffusion rnodeb fbr neopentane on Ru( OOt )
it is too strong for explaining the desorption data. In either case the decrease of the activation energy with coverage remains unexplained. The main emphasis of this Letter is first to show that the clustering model is in agreement with the new data for large molecules on metals and has to be considered therefore as an alternative. In a final section we then compare both models. The clustering model is a phenomenological model that stresses the role of the different local environments of the diffusive atoms [7]. It is based on the assumption that atoms attached to clusters diffuse less and that one type of atoms, presumably the monomers, experience the lower diffusion barrier and mostly control the diffusion process. Although the existence of clusters can be traced back to the presence of adsorbate-adsorbate interactions, the interactions are not limited to simple nearest neighbour attractive interactions. The exact nature of interactions is not relevant, if a phenomenological comparison with the coverage dependence of the diffusion coefficient is sought. The intrinsic surface diffusion coefficient, D~, resulting from a random walk of a single adatom on a perfect surface, i.e., a surface with only one type of sites for the adatom, is given by the Einstein relation, D i =a2/2r~, where ,~ is the hopping distance and 1/r~ is the jump frequency. Experimental techniques with atomic resolution such as FIM (field ion microscopy) and STM (scanning tunneling microscopy) allow a direct observation of the random walk and give estimates of the intrinsic surface diffusion coefficient directly. Already in these studies the tendency toward islanding and clustering is observed modifying the mobility of adatoms [i0]. At higher concentrations of adatoms a clustered adlayer equilibrium structure is expected [11,12], e.g. in diffusion measurements with macroscopic mass transport (scanning Auger microscopy of /.tinpatch deposits [2,13] or scanning electron microscopy [14]). A clustering surface adlayer represents a two phase coexistence system with a dense cluster phase and a dilute adatom phase. The concentration of the adatom phase is temperature depen-
dent but independent of the total concentratio~ as it equals to the equilibrium solubility of the cluster material, c~ [1,12]. The surface diffusion coefficient ~'~nn mass transport measurements in clustering systems, D m, and the intrinsic surface diffusion coefficient differ, since the adatoms spend a fraction of the time in clusters. An average .jump frequency 1 / r replaces the specific jump frequmk~y for the adatom. It is the sum of the site specific jump frequencies, 1/'ri, times the probabili~:} 1~ .....(',/'(. to populate this site if we consider j diffcre~I sites, c is the total concentration of adatoms on the surface and cj is the concentration of adatoms in the jth site. If only the adatom state c o n tributes to the mass transport (index a, neglecting e.g. step-sites), we find for the mass t.,ransport diffusion coefficient D m = O i ( c j c ) . 1~* m*I t~,o small clusters % can be replaced by c . Thus an adlayer system which grows according to the V o l m e r - W e b e r model (clusters on the bare substrate) obeys the relation Dm/D ~a l / c and a system which grows according to {he Strat~ski-Krastanov model (cluster tbrmatio~l tlp(m completion of a few uniform layers, with Cs~" the concentration corresponding to that uniform, temperature independent layer) obeys i;hc relation D m / D i a 1 / ( c - CsK) since part ~t the a(tlayer is incorporated in the layers below and i,,~ immobile. Two temperature dependent quantities contribute to the experimentally measured value of Din, the intrinsic surface diffusion coefl'iciel;~t D~ with the activation energy E d, and ~he free adatom concentration c:~ with the energy of fo~ mation of a cluster El. A concentration dependence of E d cannot be detected in such a measurement for a clustered system, since the free adatom concentration is an equilibrium quantity which does not vary with coverage (i.c., an in. crease of the coverage results only in an increase of the fraction of adatoms in the clusters). A measurement of the coverage dependence of the activation energy of D m should therefore result iI~ a non-constant value only if a change {iccurs in El, e.g. due to changing cluster sizes. We compared this model previously with data for the systems A g / O e ( l l l ) and O / W ( t t0)[7]. The observed concentration dependence of l)~.~
M. Zinke-Allmang, M.C. Tringides / Comparison of surface diffusion models for neopentane on Ru(O01)
was satisfactorily explained without implying a concentration dependence of D i. Also, in both studies no significant coverage dependence of the activation energy of surface diffusion was reported in the coverage regime described by the clustering model in agreement with the theoretical expectation. This successful application of the model and the generality of the concept make it desirable to compare it with further data sets such as the diffusion measurements of larger organic molecules on Ru(001). Fig. la shows a logarithmic and a linear (inset) display of the data from ref. [8]. The solid line is a fit using the clustering model. An excellent agreement is reached when CsK = 0.0465 (in units of the saturation coverage) is used. The main plot with the logarithmic display highlights in particular the match with the data at higher coverage. Within the uncertainty of the coverage calibration, the value for CsK is in agreement with the conclusion that neopentane grows as a V o l m e r - W e b e r system [15]. A complementary study of the coverage dependence of the activation energy resulted in a nearly constant surface diffusion barrier [8,9], in agreement with the expectation from the clustering model. In desorption kinetics studies a first order pro-
L275
cess was identified [8]. This result seems to contradict a two-phase region as discussed by Estrup et al. [16]. However, the theoretical analysis by Estrup et al. is based on order-disorder transition, i.e., desorption from one of two equally dense phases. In the present experiments the desorption from the adatom phase is likely overshadowed by desorption from the majority phase, which is the ordered phase of 2D-islands, as previously observed for Ga on Si [17]. This is true even if the adatom phase would have a slightly lower activation energy for desorption. Thus the desorption kinetics does not distinguish between the clustering model and the multi-site hopping model. The L E E D pattern is still 1 × 1, excluding the presence of a superstructure but not islanding because the islands formed might have the periodicity of the substrate. Fig. lb shows the same data with a fit based on the multi-site hopping model, using a hopping distance of 16 sites [8,9]. A comparison between both plots in fig. 1 shows that a single curve fit at one temperature for D(O) is not sufficient to uniquely select the correct diffusion model. Despite the excellent agreement of the experimental data for neopentane on Ru(001) with both models, we want to re-emphasize a few problems
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t
£3
•
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•
•
+.
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0
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N [ C ( C H 3 ) 4 ] / NsA T Fig. l. Surface diffusion coefficient for neopentane on Ru(001) at 130 K as a function of coverage in units of the saturation coverage. (a) Comparison with the clustering model using CsK = 0.0465. The inset shows the same in a double-linear plot. The main plot displays the data logarithmic, emphasizing the range of higher coverage. (b) Comparison with the multi-site hopping model using a hopping distance of 16 sites. Data and (b) taken from refs. [8,9].
L276
M. Zinke-Allmang, M.C. Tringides / Comparison of surface diffusion models for neopentane on Ru(O0 i .~
in fitting the experimental data in both cases. In the case of the multi-site hopping model the diffusion coefficient is concentration dependent and a non-trivial coverage-dependent data analysis has to be used [9]. The late part of the refilling signal needs to be weighted stronger to obtain the correct value of the diffusion coefficient of the coverage outside the probe region, since otherwise a different value of the diffusion coefficient is obtained that corresponds to the non-equilibrium, spatially inhomogeneous concentration profile as discussed by Tringides [118]. A modified analysis based on an initial estimate for D(O) and an iterative solution of the non-linear diffusion equation [19] does not address the problem of convergence and uniqueness since it is still based on the analysis of the early part of the experimental refilling signal. A further problem are the deviations of the value of the diffusion coefficient in the limit of high coverage, 0 ~ 1 for different hopping lengths r of the diffusing species. Theoretically we expect that all values converge to the value for r = 1 since only single jumps are allowed. The deviations cannot be explained by the undervaluation of D(O = 1) for r = 1 because then D(O) is coverage independent [18,20]. Thus it appears that D has been overvaluated for r > 1 due to the constant diffusion coefficient fits in that reference. The clustering model describes the experimental data at higher coverage exactly only for the formation of three-dimensional clusters. Deviations from the simple 1/c dependence are anticipated as the coverage approaches the saturation coverage due to changes in the dynamics of the system such as percolation and coalescence driven effects. Monte Carlo simulations and quasi-chemical approximation calculations seem to indicate, however, that the result remains qualitatively unaltered [61. Note that ref. [8] contains a second data set for tetramethylsilane on the same surface. The authors did not observe any concentration dependence for that system. Both models cannot provide a satisfactory explanation why two large organic molecules, neopentane and tetramethylsilane, differ in their D(O) dependence. In conclusion, both the clustering model and
multi-site hopping model satisfactory describe data on the concentration dependence of the surface diffusion coefficient for neopentane on Ru(001). Note however, that the conclusion from the experimental finding is drastically differem~ A consequence of the clustering model is that above measurements are not suited to investigate the temperature dependence of the a d a t o m surface diffusion as in a two phase regime the concentration of the dilute phase does not change. In turn, the multi-site hopping model would allow us to discuss interaction processes between monomers on the surface. Although both models require a more sophisticated analysis to be fully compatible with the experiment, we believe thai: the match with the data will persist. Thus the currently available data do not allow us m discriminate between the two alternative descrip-tions for the concentration dependence of the surface diffusion coefficient. M.Z.-A. wants to thank the Natural Sciences and Engineering Council of Canada for financial support through a research grant.
References [1] M. Zinke-Allmang and S. Stoyanov, Jpn. i Appl. Phy~;. 29 (1990) L1884. [2] E. Suliga and M. Itenzler, J. Phys. (" t6 (1983~ 1543. [3] R. Butz and H. Wagner, Surf. 8ci. {~3 (P~77).4~48:.~7 (1979) 69. [4] M. Bowker and D.A. King, Sur|. Sci. 71 it,~78) 583; 71.? (1978) 208. [5] M.C. Tringides and R. Gomcr, Surf. Sci. i45 (19841 12i [61 D.A. Reed and G. Ehrlich, Surf. Sci. 102 (1981) 588. [7] M. Zinke-Allmang and L.C. Feldman, Phys Rev B ~7 (1988) 7010. [8] E.D. Westre, M.V. Arena, A.A. Deckert, ,hi, B)and a~d S.M. George, Surf. Sci. 233 (1990) 293. [9] M.V. Arena, A.A. Deckert and S.M. (,:eorg~, Suri ,',c~. 241 (1991) 369. [10] G. Ehrlich, Scan. Microsc. 4 (1990) 833. [11] M.H. Grabow and G.H. Gilmer, in: Semiconductor-base0 Heterostructures: Interfacial Structure and Slabilily, E d s M.L. Green, J.E.E. Baglin, G.Y. Chin, tl.W. Deckma,~, W. Mayo and D. Narasinham ~Metallurgical Society, Warrendale, PA, 1986) p. 3. [12] M. Zinke-Allmang, Scan. Microsc. a (1990) 5-" ~. [13] G.J. Fisaniek, H.-J. Gossmann and P. Kuo. Maler. Ri:,s. Soc. Syrup. Proc. 102 (1988) 25:
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