Surfacetosurface segregation during growth of polycrystalline thin filmsF. Hellman Citation: Applied Physics Letters 51, 948 (1987); doi: 10.1063/1.98811 View online: http://dx.doi.org/10.1063/1.98811 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/51/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Lunar SurfacetoSurface Power Transfer AIP Conf. Proc. 969, 466 (2008); 10.1063/1.2845004 A nonlinear model for surface segregation and solute trapping during planar film growth J. Appl. Phys. 101, 084302 (2007); 10.1063/1.2709554 Intrinsic stress, island coalescence, and surface roughness during the growth of polycrystalline films J. Appl. Phys. 90, 5097 (2001); 10.1063/1.1412577 The grain growth blocking effect of polycrystalline silicon film by thin native silicon oxide barrier during theexcimer laser recrystallization Appl. Phys. Lett. 75, 460 (1999); 10.1063/1.124400 Anomalous surface segregation of Sb in Si during epitaxial growth Appl. Phys. Lett. 69, 67 (1996); 10.1063/1.118121

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.120.242.61 On: Sat, 22 Nov 2014 00:45:30

Surface6 to .. surface segregation during growth of polycrysiamne thin fUms F. Hellman AT&T Bell Laboratories, Murray Hill, New Jersey 07974

(Received 11 May 1987; accepted for publication 20 July 1987)

A model is proposed for a novel surface-to-surface segregation process which would be observed during growth by vapor deposition of thin polycrystaUine films of alloys exhibiting classic surface segregation. The model depends on sufficient surface mobility to allow equilibration between surfaces of different grains and insufficient bulk mobility to anow equilibration between the surface and bulk of each grain before the present surfaces are covered by the next layer of material. This high ratio of surface to bulk mobility is easily found under standard deposition conditions. The model leads to an inhomogeneous film in which the composition of each grain is dependent on its crystallographic orientation.

Materials grown by vapor deposition processes are rou­tinely used both for technological and fundamental scientific purposes. The question of how the atom-by-atom growth intrinsic to the vapor deposition process affects the structure and properties of the final material is an important one. In recent years, much work has gone into understanding the properties of surfaces and how they differ from the bulk. Reconstruction of the atomic positions, relaxation of the atomic bond lengths, chan.ges in the magnetic properties, surface segregation of one element in an alloy or soft surface phonon modes are aU results of the broken bonds intrinsic to the surface. During growth of a thin film, aU atoms at some time are part of the surface layer and are subsequently buried. We would like to pose two general questions: are the properties of the static surface relevant to this dynamic growth situation? Is it possible that any of these effects could get frozen into the bulk material?

In this letter, we consider growth of a poly crystalline aHoy, a situation commonly found in practice. We will de­rive a process similar to classic surface segregation in that one element segregates to more weakly bonded sites. This effect, which is entirely due to the broken bonds of the sur­face, can in fact be frozen into the bulk of the film as it grows. The model depends on sufficient surface mobility to anow equilibration between surfaces of different grains and insuffi­cient bulk diffusivity to anow equilibration between the sur­face and bulk of each grain before the present surfaces are covered by the next layer of material, a condition easily met under standard deposition conditions.

Consider a solid solution of elements A and B randomly disbibutcd on equivalent lattice sites. The concentration of clement A in the bulk. is Xb and at the surface is x,. For a dilute alloy such that Xs and Xb ~ 1, in the model ofthe regu­lar solution, Xs may be related to XI: :

Xs Xb ((rib - ns HEAR - EBB)) --=--exp , 0) 1 - Xs 1 - Xb klJ T

where nb and fts are the number of nearest neighbors in the bulk and at the surface, respectively, and EAB andcslJ are the A-B and B-B atomic bond energies given the atomic spacing of the alloy. This equation is derived by minimizing the free energy of the system with respect to exchanging material between surface and bulk. It assumes that the surface and bulk are in equilibrium with each other. In other words, Eq.

( 1) states that the surface will be enhanced in element A relative to the bulk if the A-B bond is weaker than the B-B bond. (Note that these energies are negative.) See Refs. 1-5 for derivations ofEq. (1), discussions of its limitations, and reviews of the experimental literature on surface segrega­tion.

A similar expression may be derived for the concentra­tions at two surfaces with different numbers of nearest neigh­bors, ns, an.d ns,' by minimizing the free energy with respect to exchanging material between the two surfaces:

Xs xSo ((ns. - tis HEAD - EBB)) -. -'-=----exp ., . (2) i-X" 1-xs, kBT

This equation states that surface 1 wiH be enhanced in ele­ment A relative to surface 2 if surface 2 is a more closely packed surface and if A-B is weaker than B-B. When the bulk material is in equilibrium with the two surfaces, Eq. ( 1 ) describes the concentration at each surface relative to the bulk. Equation (2) is then automatically satisfied and just describes the difference in surface enhancements of the two orientations.

As an example, consider the (111) and (100) surfaces of an fcc aHoy. In the bulk llh = 12. At the (111) surface ns = 9, and at the (100) surface fls = 8. If A-B is indeed

weaker than B-B, then both surfaces will be enhanced in A relative to the bulk and the ( 100) surface wiII be more great­Iy enhanced than the (Ill).

These expressions neglect many effects, including alter­ation of the atomic bond strengths at the surface due to relax­ation of the atomic positions and strain effects due to differ­ent-size atoms. They are sufficient to justify that segregation can in principle occur.

Consider now a growing film containing grains of two different orientations. Assume that in this material € Ali ¥- e BE, so that in equilibrium surface segregation does occur. Then at a given moment in time, if the system is able to equilibrate, the bulk of all the grains must be at the same concentration, while the two different surfaces are each ap­propriately enh.anced. Note that in order to reach this situa­tion, a smail transfer cfmaterial from the grains afone orien­tation to the grains of the other must have occurred. In an idealized model oflayer-by-layer growth of the gmins start­ing from a monolayer, this transfer occurs in the first layer; Eq. (2) describes the relative concentrations of the "grains"

948 Appl. Phys. Lett. 51 (1 2), 21 September 1987 0003-6951/87/380948-03$01.00 @ 1987 American Institute of PhYSics 948 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.120.242.61 On: Sat, 22 Nov 2014 00:45:30

and the amount of transfer which must occur. When the next layer of material is added, for equilibrium to be maintained, the new surface must deplete the layer below, leaving the bulk concentrations again equal and the surfaces appropri­ately enhanced. If, however, the bulk mobility is too slow to anow this depletion to reach completion before yet another layer of material is added, the situation must change. If the surface mobility is sufficient to anow a transfer of material between the surfaces of the grains, a surface-to-surface segre­gation will occur. The resuiting surface concentrations will be described by Eq. (2), since the surfaces are in equilibrium with each other. Equation (1) is not satisfied because the bulk material is not in equilibrium with the surface. This transfer of material is the same as occurred in the idealized first monolayer of material. As growth continues, the grains grow with different bulk concentrations approaching the values given by Eq. (2) for the surfaces.

While it might seem initially surprising that a surface could be out of equilibrium with its own bulk only a few A away, while being in equilibrium with another surface poten­tially 1000's of A away, this condition is easily met under standard deposition conditions. Consider for example the bulk and surface diffusion constants D 6 and D, for transition metals at reduced temperatures T /1'.H of 0.4, where T'I-i is the melting temperature. Measurements of isotope bulk dif­fusion constants forNi, Fe, and Co give Db "'" 8X 10 - 20 cm2

/

s.o Extremely limited data exist 011 surface diffusion con­stants at high temperature. By extrapolating isotope diffu­sion constants for transition metals measured at room tem­perature, we estimate Ds "'" 1 X 1O-(>~1 X 10- 7 cm2/s. 7 This number is entirely consistent with measurements of Pd dis­tribution as a function of time on a W surface at 800 °C.8 At typical deposition rates, a surface layer is buried in 1 s. In this time, assuming a random walk diffusion process, all atom in the bulk has a root mean square (rIDs) diffusion length of less than 0.1 A. On the surface, the rms length is many /-tm's. These diffusion constants are not, of course, the ones needed for diffusion in an aHoy of one or both species, but they are representative and clearly justify the assumption of extreme­ly high ratios of surface-to-bulk mobilities.

When growth is terminated, the final surfaces will at­tempt to equilibrate with their underlying bulk material. Since the bulk concentrations are not equal, it is initially impossible to satisfy both Eqs. (1 ) and (2). A concentration gradient will be induced in the bulk near the surface as each surface depletes the immediately underlying bulk. A small back transfer of material between the different grains win accompany this process as the surfaces maintain equilibrium with each other. Bulk diffusion will attempt to reduce the gradient in the bulk. This extremely slow equilibration pro­cess will, in general, be further slowed when the temperature of the material is reduced to room temperature from the elevated temperature used during the deposition.

This model considers only flat completed surfaces and the bonds broken for an atom at these surfaces. In a growing film, there will be ledges and kinks on ledges to consider. The bonding energy of a kink on a ledge is identical to half the bonding energy ofthe atom in the bulk and hence is indepen­dent of surface orientation. Thus this surface-to-surface seg-

949 Appl. Phys. Lett., Vol. 51 , No. 12, 21 September 1987

regation process depends on atoms being incorporated at or removed from sites other than kinks on ledges. The essential consideration is the coordination of the atoms as they are incorporated or removed from the growing lattice. The de­position rate as well as the deposition temperature will affect the incorporation and desorption rates at the different sites. We can phrase this discussion in terms perhaps more suit­able to a growing film which is unlikely to be describable by perfect layer-by-layer growth. Adatoms do not make a dis­continuous transition from a surface environment to a bulk environment. Both the coordination and the mobility will change relatively continuously. The growth process, there­fore, is unlikely to trap in the exact concentrations predicted by Eq. (2). A final comment is that since the bulk mobility is not zero, at a sufficiently slow deposition rate, the surfaces win stay in equilibrium with the bulk and the transfer will not occur at all.

We believe that strong, albeit indirect, evidence for this process has been seen in thin films of A IS-type superconduc­tor8.9.11 An inhomogeneity was found in certain of these materials. The extent of the inhomogeneity depended on de­position temperature, composition, and microstructure in a way that was inexplicable by more commonly accepted mechanisms. The A 15 crystal structure is more complicated than a simple aHey; the bonds broken by each surface are different for different sites. Also, these materials are inter­metallic compounds with a limited composition range. More experiments on a different material would thus be helpful in testing the validity of this hypothesized inhomogenization process.

Surface-to-surface segregation would be expected to oc­cur in any vapor deposited film which can be made to grow with multiple texturing, which shows orientation-dependent classic surface segregation and which has a high surface-to­bulk mobility ratio at the given deposition temperature. The third criterion is relatively easily met at standard deposition temperatures. An aHoy of two elements with widely differing cohesive energies should meet the second criterion. The al­loy should be thermodynamically stable over a wide compo­sition range. References 2-5 provide examples of materials which have been experimentally observed to show classic surface segregation, as well as suggesting criteria for predict­ing its occurrence. Polycrystalline growth is, of course, fre­quently observed; ideaUy there should be a preferred orienta­tion so that grains with a low surface tension and few broken bonds grow alongside grains with more broken bonds. The grains should be large enough that their compositions could be directly measured, for example, by energy dispersive x­ray analysis in a transmission electron microscope.

I would like to thank T. H. Geballe, Conyers Herring, and G. H. Gilmer for valuable discussions.

'F. 1.. Williams and D. Nason, Surf. Sci. 45, 377 (j 974). zM. J. Kelly and V. Ponee, Prog. Surf. Sci. 11, 139 (1981). 'A. R. Miedema, Z. Metallk 69,455 (1978). 4J. R. Chelikowsky, Sllrf. Sci. Lett. 139, Ll97 (1984). 5S. H. Overbury, P. A. Bertrand, and G. A. Somorjai, Chern. Rev. 75, 547

(1975). 0p. Raascn, Physical Metallurgy (Cambridge University, Cambridge,

F. Hellman 949 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.120.242.61 On: Sat, 22 Nov 2014 00:45:30

1978) (English translation). 7G. Ehrlich, in Proceedings of the 9th International Vacuum Congress and 5th international Conference on Solid Surfaces, edited by J. L. de Segovia (A.S.E.VA, Madrid, 1983), p. 3.

RH. Wagner, in Surface Mobilities on Solid Materials, edited by Vu Thien

950 Appl. Phys. Lett., Vol. 51, No. 12, 2i September i 987

Biuh (Plenum, New York and London, 1981), p. 161. 9F. HeUman, Ph.D. thesis, Stanford University, 1985. lOp. Hellman, A. F. Marshall, J. Taivacchio, and T. H. Geballc, Adv.

Cryog. Eng. Mater. 32,593 (1986). llF. Hellman and T. H. GebaJle, Phys. Rev. B 36,107 (1987).

F. Hallman 950 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

129.120.242.61 On: Sat, 22 Nov 2014 00:45:30