PHYSICAL REVIEW B VOLUME 57, NUMBER 8 15 FEBRUARY 1998-II Temperature- and rate-dependent RHEED oscillation studies of epitaxial Fe 001... on Cr 001... K. Theis-Bro¨hl, I. Zoller, P. Bo¨deker, T. Schmitte, and H. Zabel Institut fu¨r Experimentalphysik/Festko¨rperphysik, Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany L. Brendel, M. Belzer, and D. E. Wolf Institut fu¨r Theoretische Physik, Gerhard-Mercator-Universita¨t-GH-Duisburg, D-47048 Duisburg, Germany Received 10 June 1997; revised manuscript received 14 October 1997 Reflection high-energy electron diffraction RHEED intensity studies were performed during the growth of thin Fe layers on vicinal Cr 001 /Nb 001 /Al2O3 1102 substrates. The results are compared with those of recent molecular-beam epitaxy MBE growth models. General agreement is found as concerns the linear relationship between the logarithm of the number of RHEED oscillations and the inverse growth temperature. In agreement with theory the RHEED oscillation damping time is found to depend algebraically on the growth rate. However, contrary to expectations, the RHEED oscillations vanish faster at higher growth temperatures and lower growth rates. This behavior can be explained by a change in the growth mode from layer-by-layer to step flow. Numerical simulations in which step bunch melting during the Fe growth on the Cr buffer is assumed reproduce well the present experimental results. S0163-1829 98 02708-8 I. INTRODUCTION collinear exchange coupling was recently derived from po- larized neutron scattering studies.15 In this paper we report the growth behavior of thin Fe The standard in situ technique for studying epitaxial layers on Cr 001 /Nb 001 /Al2O3 1102 substrates as moni- growth is reflection high-energy electron diffraction.16 In this tored by in situ reflection high-energy electron diffraction technique the sample surface is illuminated at grazing inci- RHEED oscillations. The work was stimulated by the dis- dence by a high-energy electron beam typically 10­50 cussion about the effect of interlayer roughness on the mag- keV . Due to the scattering geometry this method is sensitive netic coupling behavior in Fe/Cr 001 sandwich structures to both surface structure and morphology. An oscillation of and superlattices. There is a clear need for a detailed knowl- the RHEED specularly diffracted intensity was first observed edge about the growth behavior and its effect on interface during the molecular beam epitaxial MBE growth of GaAs morphology. The Fe/Cr 001 system is one of the most fre- Refs. 17 and 18 and was later also seen in metal quently investigated transition-metal systems as concerns the epitaxy.19­21 RHEED oscillations from a periodically vary- magnetic properties. As a function of the Cr layer thickness, ing surface step density are generally considered to be a sig- it exhibits a long-range magnetic oscillatory exchange nature of layer-by-layer growth. The period of these oscilla- tions is often found to correspond to the time needed for the coupling,1­3 superposed by a 2-ML oscillation coupling deposition of 1 ML. Dynamic calculations of RHEED for period.4,5 Additionally, giant magnetoresistance GMR was GaAs growth imply a rapid decrease of the oscillation am- discovered first in this system.6,7 plitude with increasing surface roughness.22 Therefore, The exchange coupling in all magnetic superlattices is strongly damped or absent RHEED oscillations are con- strongly affected by interface roughness, which has also been nected to island or three-dimensional 3D growth behavior confirmed theoretically.8 In Fe/Cr this effect is particularly and therefore imply higher surface roughness. However, for severe, because of the intrinsic antiferromagnetic structure of a step-flow growth mode in which growth starts at step the Cr spacer layer. Thus, the short 2-ML oscillation period edges, a lack of RHEED oscillations is explained by a stable can only be observed in samples with reduced interface and constant surface roughness. roughness, prepared, for instance, on Fe whiskers at elevated RHEED intensity oscillations have also been used to con- growth temperatures.4,9,10 For nonperfect interfaces, the firm the surface quality of Fe/Cr 001 . Very high surface roughness leads to a noncollinear alignment of the magneti- quality of the growing film was reported by RHEED on Cr/ zation vectors in adjacent Fe layers, first reported by Ru¨hrig Fe/Cr 001 trilayers grown on Fe whiskers9 at a substrate et al.11 These noncollinear magnetic structures are due to temperature of 300 °C. The RHEED oscillations maintain spin frustrations at steps on the Fe/Cr interface whenever odd almost the same intensity amplitude during the growth of and even numbers of Cr monolayers are encountered. Differ- several monolayers Cr 001 on the Fe whisker substrate, thus ent models describing the effect of roughness on the ex- demonstrating extremely perfect layer-by-layer growth. A change coupling were discussed by Slonczewski12 and Ful- correlation between elevated substrate temperature and a re- lerton et al.,13 while calculations by Stoeffler and duced surface roughness as obtained in Fe/Cr 001 was also co-workers14 indicate a strong suppression of the Cr mo- shown in growth studies of Fe on Fe whiskers.23 As in the ments at the interface, thus reducing the coupling strength case of Fe/Cr on Fe whiskers, nearly perfect layer-by-layer and behavior. Experimental confirmation for the connection growth is reached for growth at 250 °C. For Fe growth on between interfacial roughness in Fe/Cr superlattices and non- Cu 001 Schatz et al.24 found a similar temperature behavior. 0163-1829/98/57 8 /4747 9 /$15.00 57 4747 © 1998 The American Physical Society 4748 K. THEIS-BRO¨HL et al. 57 Strong RHEED oscillations accompanying predominantly layer-by-layer growth behavior were found at slightly higher temperatures between 60 and 100 °C, compared to 3D growth for temperatures below room temperature. II. SAMPLE PREPARATION For growing Fe 001 epitaxially on Cr 001 a 3 in. RIBER metal MBE system equipped with two electron beam hearths and three ports for effusion cells was used; the MBE machine is described elsewhere.25 One of the electron beam evaporators contains four rotable crucibles so that a total of 8 different materials can be evaporated from this system. The substrates were Al 2O3 1102 crystals with surfaces of epitaxial grade finish. These were degreased by sonication in the standard fashion and annealed in UHV at 1000 °C for FIG. 1. Measurements of the sapphire miscut and the Nb and 1 h prior to growth. A buffer layer of 250 Å Nb 001 was Fe/Cr tilts. The measurements have been performed on a superlat- first deposited with a substrate temperature of 900 °C. Nb tice with 200 periods of 20 Å Fe / 40 Å Cr by low- and high- was evaporated from one of the 14 cm3 crucibles for angle x-ray scattering. The buffers are 120 Å Cr and 500 Å Nb. e -beam evaporation. Subsequently, the sample was an- From the Nb tilt and the sapphire miscut, the relative tilt between nealed for 30 min at 950 °C to smooth the Nb surface. The both materials was determined. growth behavior of Nb on different sapphire orientations is well documented.26­30 Nb nucleates with respect to the sap- the x-ray low-angle specular beam to the maxima of the phire in a so-called three-dimensional epitaxial relationship rocking curves in high-angle x-ray diffraction. Subtracting 3D-ER . This relationship explains a distinct geometrical the angular dependence of the sapphire miscut from the total arrangement of the bcc Nb unit cell to the hexagonal sap- Nb tilt gives the relative Nb tilt. This curve shows a maxi- phire unit cell. According to the arrangement of both unit mum of 2.9° at the Nb 110 orientation, which nicely agrees cells, a suitable sapphire substrate orientation can be found with the expected behavior from the 3D-ER. However, due for growing a Nb layer in a distinct orientation. Both orien- to the sapphire miscut angle the total tilt of Nb is rotated tations are parallel or nearly parallel in the 3D-ER. It was away from Nb 110 by about 20°. Due to the epitaxy of found that Nb 110 grows epitaxially on Al 2O3 112¯0 , Fe/Cr on Nb 001 see below , Fe and Cr show the same tilt Nb 111 on Al 2O3 0001 , Nb 001 on Al2O3 11¯02 , and orientations as Nb. Nb 211 on Al On top of the Nb 001 buffer film a second buffer layer, 2O 3 11 ¯00 . Furthermore, relations between the individual crystal axes can be derived. In the case of Cr 001 , was grown via effusion cell evaporation with a sub- Nb 110 and Nb 111 the distinct crystal planes of both ma- strate temperature of 450 °C. For a crucible material we used terials are exactly parallel in the 3D-ER and epitaxial growth pyrolytic graphite. To improve the crystal quality and to with a very high quality can be achieved.26­28 However, smooth the surface we subsequently annealed the Cr buffer Nb 001 is not exactly parallel to any of the low-index crys- layer at 750 °C. The crystal lattices of Nb and Cr do not tal sapphire planes in the 3D-ER. Instead, it is tilted by 2.8° match very well. The lattice parameter misfit between both towards the Al materials is approximately 14%. Nevertheless, Cr 001 2O 3 11 ¯02 crystal plane. Nevertheless, epi- taxial growth has also been found for this case in spite of the grows epitaxially on Nb 001 . As a result of the high lattice tilt. This was confirmed experimentally by Knowles et al.31 misfit the crystal quality of the first monolayers is not very and Di Nunzio, Theis-Bro¨hl, and Zabel.30 According to the high, but improves with increasing film thickness. We deter- 3D-ER, Nb is tilted compared to the sapphire surface by mined that a minimal thickness of the Cr buffer layer of 200 forming a coherent step pattern. The tilt of the Nb is along Å is necessary for a sufficiently high film quality. Because of one of its 110 axis which is parallel to the 11¯01 sapphire the high crucible volume 39 cm3 the deposition rate is very axis. Assuming no sapphire miscut and monoatomic steps, stable and reaches a typical value of 0.16 Å/s at 1365 °C at the width of the Nb terraces can be calculated from this tilt to the sample position. The in-plane epitaxial relationship be- be about 34 Å. In the case that the sapphire substrate has a tween Cr 001 , Nb 001 , and Al 2O3 11¯02 has been deter- certain miscut, the tilt of Nb compared to the physical sur- mined by means of grazing incidence x-ray scattering see face total tilt does not agree with the relative tilt between Fig. 2 . Cr 001 grows nearly parallel to Nb 001 . The tilt both materials. Instead, the total Nb tilt is determined by the between Cr 001 and Al2O3 11¯02 is slightly higher as for sum of the sapphire miscut and the relative Nb tilt, which Nb 001 and Al 2O3 11¯02 see Fig. 1 . A similar result was may furthermore vary with the in-plane angle. In Fig. 1 we reported earlier by Di Nunzio, Theis-Bro¨hl, and Zabel.30 show the situation for the different tilt angles of a sample From the tilt of Cr to the sapphire surface an averaged ter- consisting of an Fe/Cr superlattice, which was deposited on race width of about 25 Å can be calculated assuming mono- Cr 001 /Nb 001 /Al 2O3(11¯02). The angular dependencies atomic steps. of the sapphire miscut and the total tilts of Nb and Fe/Cr However, the existence of larger Cr terraces can be as- were determined from the comparison of the orientations of sumed for our films. This assumption is supported by ex situ 57 TEMPERATURE- AND RATE-DEPENDENT RHEED . . . 4749 FIG. 2. Epitaxial relations between the sapphire 11¯02 plane, FIG. 4. Small angle x-ray scan for a sample with an Fe thickness Nb 001 , and Fe/Cr 001 . The measurements were performed via of 100 Å, which was evaporated at a growth rate of 0.07 Å/s and a grazing incidence x-ray scattering. substrate temperature of T 300 °C. Inset: Profile of the electron density over the sample that is a result of the fit. STM measurements see STM picture in Fig. 3 . The STM Subsequent to the in situ growth studies via RHEED, we measurements were performed on a 250-Å-thick Cr film. measured the thickness and the film quality ex situ by high- From a line scan also shown in Fig. 3 terrace widths of resolution x-ray scattering. Figure 4 shows a typical small 200 Å and step heights of 10­20 Å were observed. angle x-ray scan for a sample with an Fe thickness of 100 Å, Finally, Fe was deposited by electron-beam evaporation which was evaporated using a growth rate of 0.07 Å/s and a using deposition rates between 0.07 and 1.2 Å/s. Both mate- substrate temperature of 300 °C. The individual film thick- rials, Fe and Cr, are very well lattice matched the lattice nesses and the interface roughnesses were calculated by fit- mismatch is 0.3% and a sufficiently high film quality was ting the x-ray data via the Parratt formalism.33 The result of found for substrate temperatures above 100 °C. Because of the fit is illustrated as the solid line in Fig. 4. The inset to the anticipated alloying at the Fe/Cr interface for high tem- Fig. 4 shows the electron density profile along the sample peratures the temperature range was limited to 300 °C. For film normal, which is derived from the fit. The results for the ex situ surface protection against oxidation, finally most of interface roughnesses are listed in Table I. the samples were capped with a thin Cr layer.32 III. IN SITU RHEED MEASUREMENTS We measured RHEED intensity oscillations during the Fe film growth using a 50-kV RHEED gun data were collected at 30 kV . In our experimental setup the angle of the incident electron beam can be varied in the range from about 1 to 3°. For measuring RHEED intensity oscillations we used the lowest possible angle of incidence, which was determined to be slightly below 1°. With a charge-coupled-device CCD camera we monitored the intensity of the complete 00 streak during the Fe film growth. Subsequently, we analyzed the integrated streak intensity within a small window as a function of the growth time t. The lateral window width was chosen such that the specular reflected beam exactly fits into it. In the longitudinal direction we arranged up to 10 win- dows covering the 00 streak. For analyzing the RHEED intensity oscillations we di- rected the e beam of the RHEED gun along the Fe 100 TABLE I. Results of the fits of the x-ray data of an Fe film grown at 300 °C with a rate of 0.07 Å/s. Material Thickness Roughness FIG. 3. STM measurement on a sample with 250 Å Cr on 250 Å Sapphire substrate 3 Å Nb/Al Nb buffer 289 Å 6 Å 2O 3 11 ¯02 . The Cr layer was covered with 1­2 ML of Pd to protect it from oxidation. Then, the sample was transferred through Cr buffer 301 Å 5 Å air and introduced to an STM. Top: a STM picture in the range Fe film 100 Å 5 Å 2000 Å 2000 Å is shown. Bottom: a line scan across the terraces is Fe-Oxid 24 Å 7 Å presented. 4750 K. THEIS-BRO¨HL et al. 57 FIG. 5. RHEED intensity oscillations for different substrate temperatures at a growth rate of 0.15 Å/s. azimuth. In order to eliminate any magnetic influence from the electron-beam evaporator on the RHEED measurements we used high sweeping frequencies of the electron beam; consequently we obtained larger streak widths. Additionally, the noise of the measured intensity increased. Subsequent filtering of the data with a Sawitzky-Golay smoothing FIG. 6. Arrhenius plot of the observed RHEED oscillations as a function of substrate temperature measured at a constant growth algorithm34 clearly reduced the undesirable noise of the data. rate of 0.15 Å/s. a Double logarithmic plot of the time until By using this algorithm the high frequencies in the measur- RHEED oscillations are fully damped as a function of the growth ing signal become damped out without disturbing the ampli- rate measured at a constant growth temperature of 100 °C b . tudes of the low-frequency parts. We measured the RHEED intensity in a temperature intensity drastically drops after starting the Fe growth and range between T 100 °C and 300 °C and at growth rates increases again for higher Fe thicknesses. In other cases, the between 0.07 and 1.2 Å/s. At room temperature, RHEED average intensity increases first and later drops. The different intensity oscillations could not be found. This indicates that behavior may be connected to the relative sample position of no layer-by-layer growth, but rather 3D island growth occurs the growing film with respect to the e beam of the RHEED at this temperature. Therefore we performed our studies at gun. substrate temperatures of 100 °C and higher. At a tempera- We analyzed the RHEED intensity measurements by ture of 100 °C and a growth rate of 0.35 Å/s we could counting the number n of the observed RHEED oscillations. identify the maximum of 40 oscillations. Comparing this The results for a constant growth rate of 0.15 Å/s are plotted number of RHEED oscillations with the number of Fe mono- as a function of the inverse substrate temperature T in an layers determined by our x-ray reflectivity measurements, Arrhenius-like plot see Fig. 6 a . The solid line shows a fit agreement within 1% was obtained, suggesting that one to the data points via the expression RHEED intensity oscillation period corresponds to the growth of one Fe monolayer. A In Fig. 5 we show RHEED intensity oscillations measured ln n at three different temperatures and with a constant growth T , 1 rate of 0.15 Å/s. Surprisingly, the largest number of os- where A 970 250 K. We will discuss these results fur- cillations was observed at the lowest growth temperature. ther below. For the measurements at a constant substrate During the early growth stage of the first 2­5 ML of the Fe temperature we analyzed the time t film growth we could not detect clear RHEED oscillations. c for the RHEED oscil- lation to be fully damped and plotted this time as function of This effect is strongly temperature dependent. RHEED oscil- the growth rate in a log-log plot see Fig. 6 b . Again we lations can already be observed at an earlier growth stage at fitted the data by a linear regression and obtained the follow- higher temperatures. The reason for this behavior is not com- ing relation: pletely understood. Alloying may be excluded as a reason for the loss of oscillations, because interface alloying is expected ln t to be small for Fe on Cr as result of the small cohesive c B ln , 2 energy.35 Possibly, the growth mode for Fe on Cr differs with B 0.14 0.11 Å/s. The relatively large error bars from the growth mode for Fe on Fe. In contrast to the peri- arise from the uncertainty in determining the maximum num- odic RHEED intensity oscillations for the early growth, the ber of oscillations and the time until oscillations can be ob- long term behavior of the RHEED intensity does not exhibit served due to a small signal-to-noise ratio for higher film a systematic behavior see Fig. 5 . Sometimes the average thicknesses. 57 TEMPERATURE- AND RATE-DEPENDENT RHEED . . . 4751 Both experiments show that the characteristic damping time t of the RHEED oscillations which is equivalent to the number of observed RHEED oscillations, n, in constant rate mode increases with increasing growth rate or with de- creasing substrate temperature T. IV. GROWTH MODES Depending on the growth mode, continuum equations can be used to relate the persistence of the oscillations to the growth parameters. In the case of growth on a perfectly flat surface without Ehrlich-Schwoebel barriers,36 where the ki- netic roughening of the surface37 limits the oscillations, a power law for the damping time tc of the following form is predicted:38 tc Da . 3 a2 Here is the layer completion time and thus tc / equals the number of visible oscillations n) with a / , a and a being the vertical and lateral lattice constant, respectively. For the surface diffusion constant D an Arrhenius-type be- havior, E D a2k a 0 exp k , 4 BT is assumed, where k0 is the attempt frequency typically of the order of 1013 s 1) and Ea is the energy barrier for a diffusion step. Using this expression the dependence of the damping time on the substrate temperature and growth rate can be expressed by ln n ln tc Ea k const. 5 BT ln k0a From this, straight lines should be found in an Arrhenius plot of ln(tc) versus 1/T for a constant growth rate , and of ln(tc) versus ln( ) for a constant growth temperature T. From the slope of the lines a conclusion about the growth behavior should be possible. As mentioned above, in the absence of Ehrlich-Schwoebel barriers a positive exponent is pre- dicted, and was confirmed by computer simulations.38 This means that an improvement of the layer-by-layer growth is expected with increasing substrate temperature or decreasing growth rate. Analyzing the Arrhenius plots of our experiments a linear FIG. 7. RHEED patterns of 20-Å-thick Fe 001 films grown on dependence of ln(n) on 1/T in the case of a constant growth 250 Å Cr / 500 Å Nb /Al rate as well as a linear dependence of ln(t 2O 3 11 ¯02 and taken at three different c) on ln( ) in temperatures 100 °C a , 200 °C b , and 300 °C c . The e beam the case of a constant substrate temperature T) was found was aligned with its azimuth along Fe 100 . see Figs. 6 a and 6 b . These functional dependencies agree with the results of the theory.38 However, we observe a increasing substrate temperature. On the contrary, we clearly negative , instead of the expected positive exponent. In the observe a higher crystal quality and less surface roughness at case of Ehrlich-Schwoebel barriers we expect 3D island higher growth temperatures and lower growth rates. This growth, which leads to an increase of surface roughness with rules out the presence of 3D island growth and another increasing substrate temperature. Numerical simulations damping mechanism has to be considered. were carried out by Siegert and Plischke39 who find pyramid- Clearly, a vicinal surface with step widths smaller than like structures on surfaces with Ehrlich-Schwoebel barriers. the typical island distance on a flat surface would not lead In our case Fe on vicinal Cr 001 , the structural infor- to any RHEED oscillations. In this case the step density re- mation from RHEED see Fig. 7 and x-ray diffraction ex- mains essentially constant. This is because almost any atom periments do not indicate stronger surface roughness with that lands on the surface is able to diffuse to the step edge 4752 K. THEIS-BRO¨HL et al. 57 before it can create an island nucleus by encountering an- other adatom. Thus, the growth mode is not layer-by-layer growth, but step flow, which is stabililized in the presence of Ehrlich-Schwoebel barriers. This scenario could be present in our system if we had monoatomic steps in the Cr buffer and an average step width of 25 Å estimated, using information about the Cr tilt, discussed above . However, the fact that RHEED oscillations are visible at all growth temperatures between 100 and 300 °C contradicts the assumption of a step-flow growth process. Furthermore, from STM measurements we found terraces of the Cr buffer with step heights larger than 1 ML and widths greater than 25 Å. In such a case, having the same global tilt and having steps that are much higher than one lattice constant or if there are many adjacent steps step bunch the situation can be different from that with mono- atomic steps. For instance, wide steps allow the nucleation of islands and hence layer-by-layer growth can take place 3D FIG. 8. Results of numerical simulations for the expected de- island growth behavior was excluded for our case . Further- pendence of the damping time of RHEED intensity oscillations on more, in the presence of Ehrlich-Schwoebel barriers the step the substrate temperature. bunch would not be stable but would dissolve into an essen- tially regular step train. Recent scaling theory40 predicts a with the theta function (x) having the value one for posi- negative exponent for such a scenario. tive arguments and zero otherwise. Simulations were carried out on 100 50 lattices. A tilted V. NUMERICAL GROWTH MODEL surface can be easily implemented by periodic boundary We performed computer simulations in which the pos- conditions. In our simulations the tilt was chosen to be 4% in sible change of growth mode from layer-by-layer growth to the direction of the x axis. The surface was initially flat, step flow during the Fe film growth is mimicked by the dis- except for a step bunch comprising four steps. The flux F of solution of one high step several lattice constants . The the incoming beam adjusted to one particle per second and growth on a tilted surface with initial step bunching is mod- lattice site, and the energies we used were Es En 0.7 eV eled using Monte Carlo simulations based on a well- and Eb 0.07 eV. The temperature T varied between 520 and established solid-on-solid model, in which neither vacancies 600 K. nor overhangs are allowed.41 During the growth of 50 ML the surface step density, The crystalline film is treated as a simple cubic lattice. which is thought to be proportional to the amount of diffuse Two processes take place on the surface during growth. First, reflected RHEED intensity,43 was monitored continuously. deposition of atoms occurs, due to a particle flux F. A sur- The data see Fig. 8 clearly show that the growth oscilla- face site, on which the particle lands, is chosen randomly. tions persist longer at lower temperatures. Second, surface diffusion is initiated by lattice vibrations at a We explain this by the argument already given in the last substrate temperature T. The diffusion events are modeled as section: the existence of Ehrlich-Schwoebel barriers stabi- nearest-neighbor hopping processes. The hopping rate is as- lizes step flow. So we expect the initial step bunch to dis- sumed to be solve into four separate steps during growth, which are slower the ``colder'' the substrate is. This result of our nu- E merical simulations is illustrated Fig. 9. Snap shots after dif- k E,T k a 0 exp ferent growth stages and for two different substrate tempera- k , 6 BT tures show that the dissolution of the step bunch is strongly with the attempt frequency k temperature dependent and happens much faster at the higher 0 for hopping processes. The diffusion barrier E temperature. After the dissolution of the step bunch the ter- a is comprised of a substrate term Es , a nearest-neighbor contribution mE races grow by propagation of steps. This directly translates n , m being the number of in-plane nearest neighbors, and an additional contribution E into a vanishing of oscillations of the step density and the b due to the Ehrlich-Schwoebel barrier.36 The latter is realized RHEED-reflection intensity see Fig. 8 . by assigning to a site a energy penalty proportional to its Another effect though small can be seen in Fig. 8: the number of missing out-of-plane next-nearest neighbors. frequency of the oscillations decreases with increasing tem- Technically this is done by counting the number of next- perature. For example, its change from T 520 K to T 620 nearest neighbors in the planes beneath and above the hop- K amounts to roughly 5%. This is illustrated in Fig. 8 by ping atom before (m a decreasing number of periods with increasing temperature i) and after (m f ) a hop. The barrier has a nonzero value m during a certain damping time from 10 periods at 520 K to i m f )Eb only if m f mi . Note that with this method, an adatom is not directly hindered from hopping 9 periods at 600 K . This effect is known in the context of down the step but already from approaching it cf. Ref. 42 . step-flow growth as ``first maximum delay''44,45 and has its Then the total energy barrier can be written as origin in the property of the steps to act as permanent sinks: due to incorporation, adatoms give rise to the step's move- Ea Es mEn mf mi Eb mi mf , 7 ment instead of taking part in the nucleation phase. This 57 TEMPERATURE- AND RATE-DEPENDENT RHEED . . . 4753 surface having a tilt to the physical surface of 3°. The origin of the tilt is the special growth behavior of the par- ticular buffer/substrate system Nb 001 /Al 2O3, which was used for the present experiments see Sec. II . Following the ex situ STM measurements on 250-Å-thick Cr buffers this tilt results in 200-Å-wide terraces at the Cr surface. The step heights are in the range of 7­14 monoatomic steps see Fig. 3 . The precise numbers for the step widths and heights may change for different samples and also for other Nb and Cr buffer thicknesses than the used ones. However, the principal surface morphology of the Cr 001 surface with wide terraces and with steps significantly higher than one monoatomic step will be kept. For the numerical simulations we assumed a step bunch height of 4 monoatomic steps. This number is smaller than the experimentally observed step height; however, it should be high enough for demonstrating the principal growth be- havior. The energy barriers Es substrate term and En nearest-neighbor term and the additional contribution Eb due to the Ehrlich-Schwoebel barrier were chosen to be close to previous results.49 Previous numerical simulations by Siegert and Plischke39 assuming the existence of Ehrlich-Schwoebel barriers but no vicinal surface result in pyramidlike structures for the grow- ing film. The growth mode changes from layer-by-layer to 3D island growth in this case, which leads to an increase of surface roughness with increasing substrate temperature. The situation changes for the growth on a vicinal surface. In this case, Ehrlich-Schwoebel barriers result in step-flow growth. In the present case wide terraces and steps higher than one monoatomic step the terrace width is too wide for a perfect step-flow behavior. In the beginning of the Fe growth only a few atoms are able to diffuse to the step edges. Atoms that land at large distances from the step edges are not able to reach them before encountering other adatoms and creating an island. Therefore, predominantly layer-by-layer growth is observed in the beginning of the Fe growth. The numerical simulations show that the previous step bunches are not FIG. 9. Illustration of the results of the numerical modulation of stable but dissolve into a regular step train during the Fe the dissolution of a step bunch during the Fe film growth. The growth. This leads to a decreasing terrace width with increas- picture shows different snapshots after 0, 10, 20, and 30 ML of Fe ing Fe film thickness and the step-flow growth mode more growth for the time dependence of the dissolution of the step and more dominates the growth behavior. This process is bunch at two different substrate temperatures. temperature dependent. The higher diffusivity of the Fe par- ticles at higher temperatures increases the chance to reach affects mainly the islands close to the step and hence has a the step edge instead of creating an island with another ada- stronger effect for larger island distances, which are obtained tom. This results in a higher velocity of the steps and hence for higher temperatures.46­48 In our case, the effect is rather in a faster dissolution of the step bunch. Therefore, the weak, since only the lowest step of the bunch ``competes'' RHEED oscillations are damped out faster at fixed growth with a large terrace. rate . In the case of a fixed temperature the chance of island In the experiments cf. Fig. 5 , the same weak effect can nucleation is lowered with decreasing growth rate, resulting be observed when comparing the curves for T 100 °C 10 again in a faster in relation to the growing velocity move- periods during 92 s and T 200 °C 9.5 periods during 92 s ment of the steps. for T 300 °C the growth conditions seem to be slightly The dissolution of the steps during the Fe film growth can different . be considered as a melting process. To verify this behavior in situ STM studies during the Fe film growth should be per- VI. DISCUSSION formed. The preliminary ex situ STM measurements on a Cr buffer Fig. 3 verify the existence of step bunches in the The numerical simulations verify our assumption about beginning of the Fe growth. the Fe growth mode changing from layer-to-layer growth to We now discuss our results with respect to the magnetic step flow with increasing temperature. In the present studies properties of the Fe/Cr system. In the Introduction we the heteroepitaxial Fe growth starts from a vicinal Cr 001 pointed out the interrelationship between interface morphol- 4754 K. THEIS-BRO¨HL et al. 57 ogy and magnetic properties in the Fe/Cr system. The steps temperatures and growth rates. The logarithm of the number at the Fe/Cr interfaces will influence the magnetic properties of RHEED oscillations shows a linear dependence on the and will cause spin frustration effects in the Cr spacers. The inverse growth temperature. Similarly, a straight line was magnetic structure of the Cr spacer layers in Fe/Cr superlat- found in a double logarithmic plot for damping time versus tices on Cr/Nb/Al 2O3 was studied recently by Schreyer growth rate. This result seems to agree with the theory de- et al.15 The results of this study qualitatively agree with the- scribing growth without Ehrlich-Schwoebel barriers. How- oretical predictions for fluctuating Cr thicknesses12 origi- ever, in our case the slope of the straight lines has a negative nated by steps at the Fe/Cr interface. A quantitative relation sign in contrast to a positive one predicted by the theory. We between the step density and the step height has yet to be explain the Fe growth behavior by melting of previously made. For other systems such as the growth of Fe/Cr on Ag existing step bunches in the Cr buffer layer . This assump- buffer using Fe-covered GaAs as substrate,10 and for the tion was verified by numerical simulations. For the Cr-buffer growth of Fe/Cr on MgO Refs. 13 and 50 other morpholo- terraces up to 200 Å wide and having steps several mono- gies of the Cr/Fe interfaces may be expected and therefore layers high can be inferred from ex situ STM measurements. different step densities and step heights will be present. To This result supports our interpretation for the Fe growth be- compare results for the coupling behavior across the Cr havior because it verifies the existence of step bunches in Cr. spacer and the spin state of Cr, surface morphology studies of the interface between Fe and Cr are necessary. This has been done in a few cases, for instance, by the means of STM studies for the system Fe/Cr on Ag using GaAs as substrate ACKNOWLEDGMENTS Ref. 51 and on Fe whiskers.52 The authors wish to acknowledge technical support by J. VII. SUMMARY Podschwadek and C. Leschke. Thanks go also to G. Wil- helmi for performing the STM measurements and A. We have studied RHEED intensity oscillations during the Schreyer for fruitful discussions. This work was supported Fe 001 growth on vicinal Cr/Nb/Al 2O3 at different growth by the Deutsche Forschungsgemeinschaft through SFB 166. 1 P. Gru¨nberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sow- Rev. B 44, 10 389 1991 ; A. Vega, D. Stoeffler, H. 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