VOLUME 75, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 28 AUGUST 1995 Dynamic Evolution of Pyramid Structures during Growth of Epitaxial Fe 001 Films K. Thürmer, R. Koch, M. Weber, and K. H. Rieder Freie Universität Berlin, Institut für Experimentalphysik, Arnimallee 14, D-14195 Berlin, Germany (Received 5 April 1995) The growth of epitaxial Fe(001) films UHV deposited onto Mg(001) substrates has been investigated at conditions where Schwoebel barriers suppress the step-down diffusion of impinging atoms. In nearly perfect agreement with the theoretical predictions of Siegert and Plischke [Phys. Rev. Lett. 73, 1517 (1994)], scanning tunneling microscopy reveals the development of mesoscopic pyramidlike structures at the surface that grow in time according to a power law of t1 4. The dynamic nature of the growth process favors the formation of {012} rather than {011} facets as side planes of the pyramids emphasizing, in general, the importance of kinetic versus thermodynamic stability. PACS numbers: 61.50.Cj, 61.16.Ch, 68.55.Bd Although the growth of thin films has been the subject file consisting of "pyramidlike" structures, whose sides of numerous investigations in the past, for the majority of correspond to Cu{113} and Cu{115} facets at 160 and film/substrate combinations it still remains an open ques- 200 K, respectively. Johnson et al. [8] observed the for- tion how to choose the growth conditions to obtain films mation of mounds during homoepitaxial growth of GaAs with a specific microstructure, without doing the experi- on flat substrates, whereas the original step configuration ment. As long as the substrate temperature is sufficiently of vicinal substrates in principle is preserved. On the ba- high so that film growth can proceed near equilibrium, sis of their experimental results, as well as parallel Monte useful information is provided by thermodynamics. In Carlo simulations, the authors were able to propose a sim- that case the shape of the stable nuclei formed initially ple analytic expression that describes the diffusion current depends on the respective free surface and interface ener- j on flat and vicinal surfaces as well. Inserting j into the gies of film and substrate, which in turn also determines Langevin equation for MBE growth [4,9] the mode of film growth: 2D (layer-by-layer) or 3D (is- land) growth [1]. At lower substrate temperatures film h r, t t 2== =j == =h r, t 1 f r, t (1) growth increasingly is influenced by a variety of nonequi- then yields the 3D surface corrugation represented by the librium processes, accompanied often by a change of the local height h r, t at position r as a function of the de- overall film morphology. A decisive parameter involved position time t with f r, t being the respective beam in- in nonequilibrium growth is surface diffusion, which par- tensity. Motivated by the work of Ref. [8], Siegert and ticularly in molecular beam epitaxy (MBE) growth is the Plischke [10] very recently derived a more sophisticated predominant mechanism for the transport of material in expression for the surface current that additionally ac- ordering processes. When the substrate temperature falls counts for the anisotropy of surface diffusion due to the below a critical value, the potential barrier at step edges, symmetry requirements of the cubic lattice. Numerical often called the Schwoebel barrier [2], suppresses and ul- solution of the resulting Langevin equation (1) reveals a timately inhibits the downward diffusion of atoms to the surface structure consisting of a regular pattern of square next terrace [3]. Consequently, surface diffusion is con- pyramids with, at later growth stages, exclusively {011} fined to the terrace where the film atoms originally im- facets as side planes. According to this model system the pinged, until they are finally incorporated at a ledge site average size r t of the pyramids increases as a power of an uphill terrace or form islands. law in deposition time, r t t1 z, with z 4. In recent years there has been growing interest in film In the following we present scanning tunneling mi- growth where Schwoebel barriers are effective, both from croscopy (STM) results on the dynamic evolution of a a theoretical point of view [4] because of a possibly uni- real thin film system with effective Schwoebel barriers, versal spatial and temporal behavior and from an experi- namely, Fe(001) films on Mg(001), that epitaxially grow mental point of view due to its relevance for MBE growth. up to mean film thicknesses of more than 2000 mono- Schwoebel barriers have been found to be responsible for layers. In nearly perfect agreement with the theoretical the transition from 2D growth to 3D in homoepitaxy [5], model of Siegert and Plischke [10] a scenery of meso- whereas here layer-by-layer growth definitely is favored scopic and predominantly square pyramids is imaged in by thermodynamics; 2D islands nucleate on top of pre- real space. Again in accordance with Ref. [10] the pyra- existing islands, resulting eventually in a time-dependent mids grow with a dynamic exponent of z 4. At higher roughening of the originally flat surface [6]. By analyz- film thicknesses the slope of the pyramid sides converges ing their He scattering data on the homoepitaxial growth to that of {012} facets, as confirmed by low energy elec- of Cu on Cu(001), Ernst et al. [7] arrived at a surface pro- tron diffraction (LEED). Obviously the {012} facets, 0031-9007 95 75(9) 1767(4)$06.00 © 1995 The American Physical Society 1767 VOLUME 75, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 28 AUGUST 1995 which are composed of (001) and {011} microfacets, at- In accordance with the findings of other groups [12] Fe tain special kinetic stability by the dynamic nature of the grows epitaxially on Mg(001) substrates. The epitaxial growth process. orientation determined with LEED is Fe(001)//MgO(001) The epitaxial Fe(001) films were deposited in UHV and Fe[100]//MgO[110]. The high quality of epitaxial (base pressure , 1 3 10210 mbar) at a deposition rate growth is additionally corroborated by the magnetic film of 0.007 6 0.001 nm/s and substrate temperatures of properties, since all Fe films exhibit a distinct magnetic 400­450 K. The pressure during deposition was better in-plane anisotropy with the easy magnetization axis lying than 3 3 1029 mbar. Prior to mounting into the UHV along 100 directions, as in the bulk [13]. Figure 1 chamber the MgO(001) substrates were baked for several depicts large area STM top-view images of Fe films at hours (4­10) at 1300 K in a stream of oxygen at different thicknesses (up to 2000 monolayers) that were atmospheric pressure and briefly outgassed in UHV at deposited in the temperature range of 400­450 K [14]. 600 K immediately before film deposition. The quality Obviously the surface of such Fe film is not flat. STM of epitaxial growth was controlled by LEED as well as by instead reveals that the surface is decorated over and measurements of the magnetic film properties [11] after over by a dense arrangement of predominantly square and the film deposition. For the STM investigations the films rectangular hillocks. In three dimensions the majority were transferred to a UHV chamber equipped with a UHV of hillocks exhibits the shapes of small pyramids as STM without breaking vacuum by means of a mobile UHV-transfer box. FIG. 2. Top: 65 3 65 nm2 STM top-view image of a 300 nm thick epitaxial Fe(001) film showing the pyramidlike surface structure in detail; for better comparison with Fig. 2 of FIG. 1. Large area STM top-view images (raw data) of Ref. [10] contours of equal height separated by 1 nm have epitaxial Fe(001) films at different film thicknesses tF been added to the gray scale representation UT 27 V, showing pyramidlike surface structures: (a) 200 3 160 nm2, IT 0.5 nA . Middle: Single scan along the straight line tF 300 nm (tip voltage UT 27 V, tunneling cur- marked in the top view. Bottom: Experimental (left) and rent IT 0.5 nA), single scan is along the straight line calculated (right) LEED patterns of the 300 nm thick Fe(001) marked in the top view; (b) 200 3 80 nm2, tF 50 nm film (beam energy 101 eV); for the calculation by means of UT 26 V, IT 0.5 nA); (c) 300 3 120 nm2, tF 11 nm kinematic LEED theory a unit cell consisting of 600 atoms for UT 24.5 V, IT 0.5 nA). each of the four {012} facets was used. 1768 VOLUME 75, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 28 AUGUST 1995 is demonstrated also by the sharp peaks in respective races. An average terrace width of 50 nm can be esti- single scans [e.g., Figs. 1(a) and 2]. To illustrate further mated from the STM top view of Fig. 1(c) of an 11 nm the 3D surface morphology, the 300 nm film is shown thick Fe film, where the original step configuration of at higher magnification in Fig. 2. In order to facilitate the substrate still can be sensed beneath the significantly the comparison with the theoretical results presented smaller lateral period of the pyramid structure. As the by Siegert and Plischke in their Fig. 2 (see Ref. [10]) steps cannot be discerned in individual single scans the we chose an analogous gray scale representation in actual step height has to be very small in accordance combination with contours of equal height (separated with the maximum corrugation of about 1 nm guaran- by 1 nm each). The STM image of Fig. 2, which has teed by the manufacturer [15]. Consequently, the forma- been corrected with respect to the thermal drift during tion of pyramids is inherently related to the growth of Fe scanning, impressively eludicates the pyramidlike outlines itself and starts when the first 2D Fe islands have nucle- of most islands as well as the fourfold symmetry of ated uniformly on the clean Mg(001) substrates. We re- individual pyramids. Most pyramids are flattened at their call that STM investigation of Fe films in the monolayer tops; some pyramids are coalescing to finally form larger range is not possible on the dielectric MgO substrates as pyramids. Comparison of the STM images of Fig. 1 STM experiments require electrical conductance of the of Fe films at different film thicknesses tF shows that entire film, which therefore has to cover the substrate the average pyramid size r t increases with deposition (with all its steps) completely. The temperature range at time. Quantitative evaluation of the average pyramid which Schwoebel barriers give rise to a pyramidlike sur- density N, determined from the average number of peaked face profile is quite narrow (400­450 K; see Ref. [14]). structures in 100 3 100 nm2 STM images, yields a linear At lower temperatures mounds with predominantly round dependence of logN on logtF. From the slope of the shapes are formed that no longer reflect the fourfold straight line depicted in the double logarithmic plot of symmetry of the still epitaxial Fe films; obviously the Fig. 3 a growth law r t t1 4 z 4.3 6 10% is diffusivity along the step ledges then has become too obtained. low for smoothing [16]. At temperatures higher than The experimental results presented so far, i.e., the 500 K the Schwoebel barrier is overcome and atomi- growth of epitaxial Fe(001) films with a surface profile cally flat terraces extending over several hundred nm represented by mesoscopic pyramidlike structures as well are observed. Both findings are in agreement with the as the power law dependence r t t1 4 describing the growth study on Fe Fe(001) by Stroscio, Pierce, and dynamic behavior of the pyramid growth, are in excellent Dragoset [17]. agreement with the theoretical predictions of Siegert and From our STM images we can also determine the Plischke [10] for film growth proceeding at conditions crystal planes that form the sides of the pyramids, namely, where Schwoebel barriers are effective. We therefore by analyzing the respective slopes m of single STM are convinced that the system Fe MgO(001) represents scans. Whereas for thinner films still a variety of different a real Schwoebel system at the experimental conditions slopes is detected, m of the thicker films (.502100 nm) chosen. We want to emphasize that the growth of sur- measured at the lower part of the pyramids gradually face pyramids is not the result of a possible roughness converges to a value of 0.50 6 5%. Since the azimuthal of the MgO(001) substrates. The sharp LEED patterns orientation of the pyramids is parallel to Fe 100 the side obtained from the clean substrates before film deposi- planes correspond to {012} facets, which according to tion indicate the presence of extended well-ordered ter- crystal geometry are inclined against (001) by a ratio FIG. 4. (a) Sphere model of a bcc (012) surface. (b),(c) FIG. 3. Dependence of the pyramid density N ( average Schematic illustration of the growth of pyramidlike structures number of peaked structures per m2 evaluated from 100 3 on bcc (001) and bcc (011) surfaces, respectively; a and b 100 nm2 STM images) on the mean film thickness tF (in indicate the increase of the local slope due to anisotropic nm) illustrated by a double logarithmic plot. The slope of diffusion currents j. Notice that due to the opposite signs of the straight line corresponds to a growth law for the average j on bcc (001) and bcc (011) b corresponds to an increase pyramid size r t t1 4. relative to bcc (011) but to a decrease with respect to bcc (001). 1769 VOLUME 75, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 28 AUGUST 1995 of 1:2 [Fig. 4(a)]. The two neighboring surfaces {011} In conclusion, by studying the growth of Fe on and {013} exhibit inclination values of 1:1 (m 1.00) MgO(001) we have discovered a real heteroepitaxial and 1:3 (m 0.33), respectively, and therefore can be thin film system that is characterized by the growth definitely excluded. Moreover, the STM results are of pyramidlike surface structures as a consequence of confirmed by the LEED patterns, which exhibit an energy Schwoebel barriers. Real space investigation with STM dependence characteristic of faceted surfaces (Fig. 2). confirms the main theoretical predictions of Siegert and Spot position as well as the intensity variation with Plischke [10] concerning both structural and dynamic beam energy are well reproduced by LEED patterns aspects of the growth behavior. In view of the quite calculated from kinematic LEED theory assuming a unit regular arrangement of the pyramidlike structures we cell consisting of 600 atoms for each of the four {012} speculate whether the growth of high quality epitaxial facets (e.g., Fig. 2). films at conditions where Schwoebel barriers are effective The occurrence of {012} facets as stable side planes might provide a new experimental approach to modify apparently contradicts the model calculations of Siegert surfaces on a nanometer scale for future technological and Plischke. But as the authors point out in Ref. [10] applications. the selected slope of {011} facets actually is the result of their model assumptions on the diffusion current j, and may not necessarily be the only stable situation. The development of stable {012} facets in the case of [1] E. Bauer, Z. Kristallogr. 110, 372 (1958). Fe(001) MgO(001) indeed may be understood in terms of [2] R. L. Schwoebel and E. J. Shipsey, J. Appl. Phys. 37, 3682 the dynamic nature of the growth process. As discussed (1966); R. L. Schwoebel, ibid. 40, 614 (1969). by Villain [4] the presence of extended densely packed [3] G. Ehrlich and F. G. Hudda, J. Chem. Phys. 44, 1039 terraces [e.g., Fe(001)] gives rise to instabilities. Both (1966); G. Ehrlich, Phys. Rev. Lett. 70, 41 (1993). the resulting uphill current due to the diffusion to step [4] J. Villain, J. Phys. I (France) 1, 19 (1991). ledges and the formation of 2D islands on terraces that [5] R. Kunkel, B. Poelsema, L. K. Verheij, and G. Comsa, are wider than the average diffusion length of the film Phys. Rev. Lett. 65, 733 (1990). lead to an increase of the local slope [a in Fig. 4(b)]. [6] Y.-L. He, H.-N. Yang, T.-M. Lu, and G.-C. Wang, Phys. Rev. Lett. 69, 3770 (1992). Ultimately it is this anisotropy of the diffusion current [7] H.-J. Ernst, F. Fabre, R. Folkerts, and J. Lapujoulade, j that is responsible for the growth of pyramidlike Phys. Rev. Lett. 72, 112 (1994). structures. In fact, the same mechanism inhibits the [8] M. D. Johnson, C. Orme, A. W. Hunt, D. Graff, formation of extended densely packed Fe{011} facets as J. Sudijono, L. M. Sander, and B. G. Orr, Phys. Rev. Lett. side planes of the pyramids. As illustrated in Fig. 4(c) 72, 116 (1994). Fe atoms impinging on longer {011} facets move to [9] M. Siegert and M. Plischke, Phys. Rev. E 50, 917 (1994). the next ledge site which again is accompanied by an [10] M. Siegert and M. Plischke, Phys. Rev. Lett 73, 1517 increase of the local slope b measured relative to the (1994). respective {011} surface [Fig. 4(c)]; for nucleation of [11] M. Weber, R. Koch, and K. H. Rieder, Phys. Rev. Lett. 2D islands the length of the facets probably is too 73, 1166 (1994). small. Because of the opposite signs of the diffusion [12] T. Kanaji, K. Asano, and S. Nagata, Vacuum 23, 55 (1973); T. Urano and T. Kanaji, J. Phys. Soc. Jpn. 57, currents j on (001) and (011) surfaces, however, the 3403 (1988). surface profile as a whole flattens with respect to the [13] R. Koch, M. Weber, K. Thürmer, and K. H. Rieder (to be (001) surface [compare Figs. 4(b) and 4(c)]. Since the published). same mechanism destabilizes both extended (001) and [14] In that temperature range no dependence of the film {011} facets the stable situation consequently must lie morphology on the deposition temperature was observed between the two densely packed surfaces. In the case (compare also the results of Fig. 3). The deposition of Fe(001) MgO(001) the steady state profile of the temperature was detected via pyrometry with a relative pyramids is formed by {012} facets that exhibit both accuracy of 610 K; we note, however, that the absolute (001) and {011} microfacets. An analogous explanation error of the substrate temperature may be as high as probably accounts for the formation of {113} and {115} 630 K due to the experimental difficulty of temperature facets in the case of Cu/Cu(001) [7]. In our opinion measurements on dielectric substrates. [15] Crystal GmbH, Ostendstrasse 1-14, D-12459 Berlin. the experimental results presented here point to a general [16] H. Brune, C. Romainczyk, H. Röder, and K. Kern, Nature property of film growth at presence of Schwoebel barriers, (London) 369, 469 (1994). namely, that facets are stabilized kinetically rather than by [17] J. A. Stroscio, D. T. Pierce, and R. A. Dragoset, Phys. Rev. equilibrium thermodynamics. Lett. 70, 3615 (1993). 1770