JOURNAL OF APPLIED PHYSICS 102, 034107 共2007兲
Self-assembled Ge nanocrystals on high-k cubic Pr2O3„111… / Si„111… support systems T. Schroeder,a兲 I. Costina, A. Giussani, G. Weidner, O. Seifarth, Ch. Wenger, and P. Zaumseil IHP-Microelectronics, Im Technologiepark 25, 15236 Frankfurt (Oder), Germany
C. Mocuta and T. H. Metzger European Synchrotron Radiation Facility, BP 220, 38043 Grenoble, France
D. Geiger and H. Lichte Technical University Dresden, Zellescher Weg 16, 01062 Dresden, Germany
共Received 26 April 2007; accepted 20 June 2007; published online 15 August 2007兲 The stoichiometry, structure, and defects of self-assembled heteroepitaxial Ge nanodots on twin-free type B oriented cubic Pr2O3共111兲 layers on Si共111兲 substrates are studied to shed light on the fundamental physics of nanocrystal based nonvolatile memory effects. X-ray photoelectron spectroscopy studies prove the high stoichiometric purity of the Ge nanodots on the cubic Pr2O3共111兲 / Si共111兲 support system. Synchrotron based x-ray diffraction, including anomalous scattering techniques, was applied to determine the epitaxial relationship, showing that the heteroepitaxial Ge共111兲 nanodots crystallize in the cubic diamond structure with an exclusive type A stacking configuration with respect to Si共111兲. Grazing incidence small angle x-ray scattering was used in addition to analyze the average shape, size, and distance parameters of the single crystalline Ge nanocrystal ensemble. Furthermore, transmission electron micrographs report that partial dislocations are the prevailing extended defect structure in the Ge nanodots, mainly induced by surface roughness on the atomic scale of the cubic Pr2O3共111兲 support. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2767374兴 I. INTRODUCTION
Driven by an increasing market for portable electronics, the so-called floating gate 共FG兲 flash memory array design is today the economically most prevailing nonvolatile memory 共NVM兲 technology.1 However, endurance and data retention are the two most common reliability concerns of further miniaturized 共“scaled”兲 FG flash NVM cells required in future to achieve higher data densities for multimedia applications.2 These shortcomings result mainly from the fact that NVM cells are nowadays based on materials which were not selected due to their physical properties but with respect to the availability in complementary metal oxide semiconductor 共CMOS兲 technology processes.3 Integrating materials with superior properties in view of NVM applications introduces a number of challenging research and development tasks in industry, but the following promising approaches are currently intensively pursued. Firstly, to allow flash cell operation at lower voltages, alternative high dielectric constant k dielectrics are explored as possible candidates to replace the traditional SiO2 and oxide/nitride/oxide 共ONO兲 films in both the tunnel oxide as well as the interpolydielectric 共IPD兲.4 The properties of the tunnel oxide must fulfill stringent requirements, namely, a good interface with respect to Si for transistor operation, efficient charge transport during programing/erase cycles, as well as good charge retention. The IPD is more uncritical, as it is not expected to transport a兲
Author to whom correspondence should be adressed; electronic mail:
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charge but to block any leakage under applied voltages. Secondly, to limit the fatal effect of undesired dielectric breakthrough events in the tunnel oxide on the FG charge storage node, the use of discrete, mutually isolated nanocrystals 共NC’s兲 instead of continuous FG layers is investigated.5 Here, uniformly distributed NC’s with a sharp size distribution and a high density of 1012 cm−2 are generally targeted to guarantee manufacturability with sufficient storage capacity and high reliability.5 Before, however, highly scaled flash electrically erasable and programable read only memory 共EEPROM兲 cells with NC’s 共e.g., Si,6 Ge, W,7 etc.兲 embedded in high-k gate dielectrics 共e.g., hafnium containing alumina7兲 can be successfully commercialized, further optimization of the device performance 共storage density, quick programing/erase times, etc.兲 and reliability 共data retention, endurance, reproducible cell structures, etc.兲 is needed. This requires a deeper understanding of many fundamental physical aspects of the preparation processes as well as charge storage mechanisms of NC based NVM cells. For example, it was reported that, depending on preparation, the structure of Ge NC’s can deviate from the bulklike cubic diamond lattice toward a distorted tetragonal phase.8–10 Certainly, a knowledge of the Ge NC structure is of importance to understand the electronic properties in view of NVM applications.11 Furthermore, due to Coulomb blockade and quantum confinement effects in Ge NC’s, a precise size control over the Ge NC ensemble is of importance in the preparation process to achieve well-defined NVM characteristics.12 The latter is particularly true for high density Ge NC ensembles with an average diameter below 4 nm
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because quantum size effects result in a strong band gap variation, affecting that way also the band offsets with respect to the surrounding oxide matrix.13,14 However, it is at present controversially discussed in the literature whether the observed memory effect 共as well as the blue photoluminescence兲 of Ge NC cells is due to charge trapping in the allowed density of states of the band structure 共e.g., electron trapping in the conduction band兲 or in defect related states 共e.g., interface traps between the cluster and the surrounding oxide matrix兲 of the Ge nanodots.13–16 To address these basic research issues, a model system approach is needed which allows with high stoichiometry and structure control to study fundamental physical aspects of the interplay between materials science properties 共stoichiometry, structure, defects, etc.兲 and memory characteristics 共charge trapping mechanism, retention, endurance, etc.兲 of Ge NC based NVM cells. For this purpose, we want to introduce the heteroepitaxial system of crystalline Ge NC’s embedded in epitaxial high-k cubic Pr2O3 oxide layers supported on Si共111兲. This materials system was chosen to shed light on the widely unknown interaction of advanced high-k dielectrics 共e.g., cubic Pr2O3兲 with alternative semiconductors 共e.g., Ge兲 and is well suited for NVM studies for the following reasons. Firstly, atomically smooth high-k cubic Pr2O3共111兲 layers can be prepared on Si共111兲, which guarantees a good control over the tunnel oxide thickness to achieve well-defined charge transfer characteristics between the Si substrate and Ge NC’s.17 Secondly, the generally observed nonwetting behavior of semiconductor deposits on 共111兲 oriented fluorite structure related dielectrics 关e.g., CaF2,18 cubic Re2O3 共Re= rare earth element兲19兴 allows us to prepare Ge NC’s on cubic Pr2O3共111兲 surfaces via selfassembly approaches with rather sharp NC size distributions at moderate growth temperatures. Thirdly, the oxide formation tendency of Ge is far lower than in case of Si, extending the thermal budget before undesired interface reactions with the high-k oxide layer take place.20 The present paper on uncovered, self-assembled crystalline Ge NC’s on cubic Pr2O3共111兲 / Si共111兲 support system focuses on materials science issues such as stoichiometry, structure, and defects which will serve in future NVM studies as important input parameters. As main results it is found that mutually isolated hemispherical Ge NC’s can be grown on cubic Pr2O3共111兲 / Si共111兲 support systems via selfassembly with 共a兲 high stoichiometric purity, 共b兲 single crystalline diamond structure in exclusive type A orientation, 共c兲 good size plus shape control, and 共d兲 facets and partial dislocations as the main extended defect structures. II. EXPERIMENT
Boron-doped Si共111兲 substrates were cleaned by the standard piranha procedure.21 Additionally, the Si共111兲 wafers were etched for 30 min in 40% NH4F and rinsed for 10 min in de-ionized water to prepare atomically smooth surfaces.22,23 The H-terminated Si共111兲 wafers were loaded into the ultrahigh vacuum 共UHV兲 chamber 共base pressure of 10−10 mbar兲 and were annealed prior to oxide deposition for 5 min at 700 ° C to prepare high quality 共7 ⫻ 7兲-Si共111兲
J. Appl. Phys. 102, 034107 共2007兲
surfaces.24 The 10 nm thick epitaxial Pr2O3 layer was grown by molecular beam epitaxy 共MBE兲 at a flux of 0.1 nm/ s, keeping the Si共111兲 substrate at a temperature of 625 ° C. The as-deposited Pr2O3 film grows single crystalline in the 共0001兲 oriented hexagonal 共hex兲 Pr2O3 phase so that a hexagonal to cubic phase transition was applied to prepare the cubic 共cub兲 Pr2O3 共111兲 film.17 Ge with a nominal thickness of 5 nm was then deposited on the cub-Pr2O3 / Si共111兲 support system at a growth temperature of 600 ° C and a flux of 0.01 nm/ s. A FEI Tecnai F20 Cs-corrected transmission electron microscope 共TEM兲 was used at TU Dresden to measure highresolution direct lattice cross-section images along the bulk ¯ 10兴 direction. It is a 200 kV electron microscope with Si 关1 an ultrastable Schottky electron source providing high spatial coherence. Thanks to the stability of the high-tension circuits, an energy spread better than 0.7 eV is achieved. The instrument is equipped with the hexapole Cs corrector of CEOS company, which allows the correction not only of the spherical aberration Cs but also of at least five other aberrations: two-, three-, and fourfold astigmatisms, axial coma, and star aberration S3. This results in a strong reduction of the point-spread function with the consequence that delocalization effects, unavoidable in conventional TEM, practically disappear. The damping through the spatial envelope becomes negligible and does not restrict anymore the lateral resolution. Correspondingly, the point resolution extends up to the information limit, which reaches about 0.12 nm. These invasive and local measurements were supplemented by nondestructive x-ray diffraction 共XRD兲 studies which yield highly averaged, global information about the sample structure. The synchrotron 共SR兲-based small and wide angle x-ray diffraction studies 共SAXS and WAXS兲 were performed at the beamline ID 1 of the European Synchrotron Radiation Facility 共E.S.R.F.兲 in the grazing incidence 共GI兲 mode. The GI-SAXS study was carried out at an x-ray beam energy of 8 keV 共0.1549 nm兲 and an incident angle of 0.32°, using a position sensitive detector 共PSD兲 Vantecl 共Brucker AXS兲 with a large dynamic range 共105兲 and a resolution of about 70 m/channel. The detector was placed at about 1 m distance from the sample. For GI-SAXS data analysis, we used the IS-GISAXS program.25 The scattered intensity is calculated in the decoupling approximation: the scattered cross section is proportional to 共i兲 the modulus square of the form factor F共q兲, which is the Fourier transform 共FT兲 of the shape of the particle, and 共ii兲 the interference function S共q兲, describing the statistical distribution of the objects on the sample surface and thus their lateral correlation 共in fact, it is the FT of the island position autocorrelation function兲. The calculations are performed in the frame of the distorted wave Born approximation 共DWBA兲 to account for reflection and refraction effects from the substrate. The shape of the Ge particles can be determined from TEM measurements, but also confirmed from GI-SAXS simulations. Form factors for particular shapes are implemented in the IS-GISAXS program, and their analytical expression can be found in its documentation.25 Since there are no particular nucleation centers on the surface, a paracrystal interference function was considered. The long range order is destroyed
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gradually in a probabilistic way: the distance between two successive points 共n and n + 1兲 is chosen to be independent of the previous one 共n − 1 and n兲 and to obey a statistical distribution p共x兲. In the case of Gaussian probability distribution 共one dimensional case兲, one can write p共x兲 =
S共q兲 =
1
冑2
冉
exp −
冊
共x − D兲2 , 22
1 − exp共2q22兲 , 关1 + exp共2q22兲 − 2 exp共q22兲cos共qD兲兴
共1兲
共2兲
with D being the average spacing between individual objects. More details can be found in the online documentation available in Ref. 25. For the GI-WAXS studies, an x-ray beam energy of 11 keV 共0.1127 nm兲 in the vicinity of the Ge K edge was used to collect crystallographic information 共epitaxial relationship, etc.兲 about the Ge/ cub-Pr2O3 / Si共111兲 system. In addition, a beam energy of 11.107 keV 共0.1116 nm兲 was applied to perform anomalous x-ray diffraction studies. The XRD measurements shown hereafter are indexed in reciprocal hexagonal Si共111兲 surface 共labeled surf兲 coordinates, but the Ge, Si, and Pr2O3 Bragg peaks are also indexed with respect to their reciprocal cubic bulk 共denoted bulk兲 lattices.26 Chemical information was collected after ex situ transfer of the sample to the x-ray photoelectron spectroscopy 共XPS兲 depth profiling setup PHI 5600. The sample was sputtered with a 1 kV argon 共Ar+兲 beam for a well-defined time interval 共10 s兲, followed each time by Ge 3d, Si 2p, O 1s, and Pr 3d XPS measurements. The XPS spectra were excited with monochromatized Al K␣ radiation 共1486.6 eV兲 and recorded under normal emission. The binding energy of all spectra is referenced with respect to the Au 4f 7/2 line 共84 eV兲. III. RESULTS AND DISCUSSION A. XPS
Figure 1 summarizes the XPS depth profiling study of the heteroepitaxial Ge deposit on the cub-Pr2O3共111兲 / Si共111兲 support system. The numbers in the illustrative sketch of the system label the position of the reported spectra; the depicted morphology is motivated in the following. To monitor the chemical composition of the Ge deposit, Ge 3d photoelectron lines are reported in Fig. 1共a兲. The spectrum 1a was recorded before sputtering the surface and shows mainly a homogeneous peak at a binding energy of 30.2 eV, indicative of elemental Ge.27 Despite the ex situ transfer through air from the MBE to the depth profiling XPS machine, only a small GeOx signal 共arrow兲 in form of a shoulder structure is visible at a binding energy of 32.6 eV.27 This indicates the low tendency of Ge for native oxide formation. It was already reported in the literature that this property of Ge enables the preparation of interface-free Ge/ high-k oxide 共e.g., HfO2,20 ZrO2,28 CeO2,29 etc.兲 structures even at elevated growth temperatures. This seems to be true also in the present case of Ge/high-k Pr2O3 systems, as evi-
denced by the spectra 1b and 1c recorded close to and at the Ge/ Pr2O3 interface, respectively. It is clearly seen that the elemental Ge 3d peak at 30.2 eV remains the only specie in the spectra and no signature of GeOx is detected, pointing to a GeOx free interface. This insight is further corroborated below by TEM studies. Figure 1共b兲 reports the O 1s photoelectron lines as a function of depth in the Ge/ cub-Pr2O3共111兲 / Si共111兲 system. The first important result can be deduced from the O 1s spectrum 1a collected prior to surface sputtering. In the asprepared sample, the position of the dominant O 1s peak at 532 eV is typical for the presence of Pr hydroxides.30 This surface hydradation is certainly a result of the ex situ transfer to the XPS machine and is in agreement with the high reactivity of rare earth oxides with respect to water vapor.19 In this respect, the formation of the hydrated cub-Pr2O3共111兲 surface can be viewed as a sensitive probe in our study to disclose the nonpassivating character of the Ge deposit on the cub-Pr2O3共111兲 / Si共111兲 system. Certainly, this experimental finding is best explained by an islanding of the Ge deposit on the cub-Pr2O3共111兲 / Si共111兲 support, as consequence of a Volmer-Weber growth mode. This hypothesis is confirmed below by XRD and TEM studies. The O 1s spectrum 共a兲 reports further the presence of a smaller peak at 529.9 eV. This peak becomes the dominant feature in the O 1s spectra after removing by sputtering for about 1 – 2 nm of the cub-Pr2O3 film, indicating that the Pr-hydroxide formation is restricted to the surface area. Spectrum 2 shows a typical XPS O 1s signal of the crystalline Pr2O3 layer, so that the position at 529.9 eV can be unambiguously assigned to the oxygen sublattice of the cub-Pr2O3 film structure.31 When the sputter beam penetrates toward the oxide/Si interface, a high binding energy shoulder evolves at 530.7 eV 共spectra 3a and 3b兲. Due to its position between the O 1s binding energies of SiO2 共533.2 eV兲 and Pr2O3 共529.9 eV兲, it indicates the presence of a Pr-silicate interface layer.32,33 As outlined by Schroeder et al., this interface layer is formed during the hexagonal to cubic phase transition of the Pr2O3 film on Si共111兲.17 Here, we confirm that the chemical composition is not that of a pure SiO2 layer but corresponds to a Pr-silicate phase. Figure 1共c兲 shows the corresponding Pr 3d XPS spectra with the 3d5/2 and 3d3/2 peaks located at binding energies of 934.2 and 954.6 eV, respectively. In comparison to the O 1s signal, the position of the Pr 3d peak stays constant throughout the XPS depth profiling study. This indicates that the ionicity of the Pr sublattice is rather insensitive to changes in the Pr2O3 stoichiometry, i.e., Pr-hydroxide 共spectrum 1c兲 and Pr-silicate 共spectra 3a and 3b兲 formation. However, a comparison with the Pr 3d XPS spectrum of the crystalline cubic Pr2O3 film 共spectrum 2兲 reveals that changes in stoichiometry influence the photoelectron line shape. The Pr 3d spectrum 2 of the crystalline Pr2O3 film shows well separated satellite peaks 共dashed lines兲 on the low binding energy sides of the Pr 3d5/2 and 3d3/2 peaks at 929.7 and 950.2 eV, respectively. The separation of these satellite peaks gets washed out in case of stoichiometry deviations, either in form of Pr hydroxides on the surface 共spectra 1c兲 or Pr silicates at the oxide/Si共111兲 interface 共spectra 3a and 3b兲. It
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FIG. 1. XPS depth profiling study by Ar+ ion beam sputtering to investigate the chemical composition of the Ge/ cub-Pr2O3共111兲 / Si共111兲 system.
was pointed out in the pioneering work of Kotani and Ogasawara that the 3d XPS splitting in Re2O3 共Re= rare earth兲 systems can be analyzed with the impurity Anderson model and results from complicated initial- and final-state hybridization effects between the core hole and f and d electrons.34 In this respect these covalency hybridization effects make the shape of the Pr 3d XPS spectra a sensitive tool to probe deviations from the film stoichiometry. Figure 1共d兲 shows the Si 2p photoelectron lines when the depth profiling study reaches the interface and substrate regions. The spectrum 3a reports the situation when the Si 2p signal starts to appear in the XPS depth profiling study.
Clearly, besides the Si 2p substrate peak at 99.3 eV, a second peak of higher intensity is observed at 102.5 eV. According to previous studies by Lupina et al. on the solid state reaction between metallic Pr deposits and native SiO2 layers on Si wafers, this peak position is characteristic of Pr silicates.32,33 Therefore, the Si 2p spectra, as well as the O 1s spectra, indicate the presence of a Pr-silicate interface layer at the oxide/Si boundary. As the depth profiling study proceeds 共spectra 3b and 4兲, the Si 2p substrate peak increases at the cost of the Pr-silicate signal. It is interesting to note that, even close to the substrate region, no Si 2p signal is detected at the position of about 103.5 eV typical for SiO2.
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FIG. 2. 共Color online兲 In-plane GIXRD study to determine the azimuthal alignment of the Ge deposit on the cub-Pr2O3共111兲 / Si共111兲 support system. Ge, Pr2O3, and Si diffraction peaks are indicated by dashed, dotted, and solid lines, respectively.
B. GI-XRD
Figure 2 summarizes the in-plane GI-XRD study to determine the azimuthal orientation of Ge deposits on cub-Pr2O3共111兲 / Si共111兲 support systems. The measurement was carried out at an incident angle ␣ = 0.6°, which exceeds at the x-ray beam energy of 11 keV the critical angles ␣c of 0.2° and 0.25° of Ge and Pr2O3, respectively. In this way, the bulk sensitive measurement allows us to derive the epitaxial relationships of Ge with respect to the cub-Pr2O3共111兲 film and the Si共111兲 substrate. Figure 2共a兲 shows a sketch of the in-plane symmetry of the reciprocal hexagonal Si共111兲 surface system. Two high symmetry in-plane directions can be distinguished, namely, the Hsurf = 关100兴 and the Hsurf = Ksurf = 关110兴 directions, which correspond in cubic Sibulk coordi¯ 典 and 具011 ¯ 典 directions, respectively. Figure 2共b兲 nates to 具112 shows the result of the wide angle in-plane scan 共L = 0.05兲 along the Hsurf = 关100兴 direction from H = 0.5 to 2.5. No Sibulk Bragg peaks are expected within that range, only the 共1 ⫻ 1兲 Si共111兲 surface unit cell periodicity produces sharp crystal truncation rod 共CTR兲 signals along the Hsurf direction at the integer values H = 1 and 2. The cub-Pr2O3 oxide film produces at H = 0.735, 1.47, and 2.205 diffraction peaks 共dot¯¯12兲, 共2 ¯¯24兲, and 共3 ¯¯36兲 ted lines兲, which can be assigned to 共1 bulk oxide reflections, respectively. According to the results reported in a previous publication by Schroeder et al.,17 the indexing is given for a type B oriented cub-Pr2O3 film struc¯¯12兴 azimuth along ture on Si共111兲, aligning the cub-Pr2O3关1 ¯ the Si关112兴 in-plane direction. The analysis of the high¯¯36兲 diffraction resolution scan in Fig. 2共c兲 on the cub-Pr2O3共3 peak allows us to deduce two important insights. Firstly, an
¯¯36兲 of 0.1508 nm is calculated in-plane lattice spacing d共3 from the oxide peak position at H = 2.205, which is by about 0.6% smaller than the theoretically expected value of ¯¯36兲 = 0.1517 nm. In consequence, the approximately d共3 10 nm thick cub-Pr2O3 film structure is under compressive strain due to the smaller lattice dimension 共2.7%兲 of the supporting Si substrate. It is interesting to note that this result supplements our previous structure study on a 50 nm cub-Pr2O3共111兲 film on Si共111兲, which was found to be completely relaxed.17 Secondly, as no strain broadening is ob¯ , ¯n , 2n ; n served for the detected family of cub-Pr2O3共n = 1 , 2 , 3兲 reflections, an in-plane domain size along the Hsurf direction of about 20 nm can be calculated from the full ¯¯36兲 difwidth at half maximum 共FWHM兲 of the cub-Pr2O3共3 fraction signal in Fig. 2共c兲, pointing to a rather high defect density in the film after the phase transition. The diffraction signals of the Ge deposit show the same behavior, as observed in case of Si. No Gebulk Bragg peaks are observed, but only far weaker CTR’s at positions corresponding to a 共1 ⫻ 1兲 Ge共111兲 surface unit cell. This result indicates that the ¯ 兴 inGe deposit grows in 共111兲 orientation, aligning its 关112 ¯ 兴 azimuth. This preliminary plane direction along the Si关112 interpretation is corroborated further below 共Fig. 3兲 by offplane GI-XRD measurements. Figure 2共d兲 reports the wide angle in-plane scan at L = 0.05 along the Hsurf = Ksurf = 关110兴 direction from Hsurf = Ksurf = 0.2 to 1.4. No diffraction peaks are observed except close to the Sisurf共110兲 diffraction signal, ¯ 兲. The which corresponds to the true Sibulk Bragg peak 共022 high-resolution scan on the Sisurf共110兲 diffraction peak in Fig. 2共e兲 clearly reveals the presence of two additional peak
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FIG. 3. 共Color online兲 Left: Sketch of the Bragg peak distribution in the reciprocal Lsurf-Hsurf plane of type A 共filled circles兲 and type B 共open circles兲 Ge共111兲 deposits. Right: Off-plane anomalous GI-XRD study to measure the vertical stacking behavior of Ge deposits on the cub-Pr2O3共111兲 / Si共111兲 support system.
structures toward lower values in reciprocal space. As indicated, these diffraction signals can be assigned to the bulk ¯ 4兲 共dotted line兲 共Hsurf = Ksurf = 0.984兲 and the cub-Pr2O3共04 ¯ 兲 共dashed line兲 共Hsurf = Ksurf = 0.961兲 Bragg bulk Ge共022 peaks. Again, the indexing of the cub-Pr2O3 peak is given for a type B oriented oxide film structure on Si共111兲 with the ¯ 1兴 azimuth aligned along the Sibulk关011 ¯ 兴 incub-Pr2O3关01 17 ¯ ¯ plane direction. As in case of the cub-Pr2O3共336兲 reflection above 关Fig. 2共e兲兴, an analysis of position and shape of the ¯ 4兲 Bragg peak reveals that the oxide film is cub-Pr2O3共04 characterized by 共a兲 an in-plane spacing which deviates by ¯ 4兲 about 0.6% toward smaller values 关experiment: d共04 ¯ 4兲 = 0.197 14 nm兴 and 共b兲 by a = 0.1958 nm; theory: d共04 rather small average domain size of approximately 20 nm along the Hsurf = Ksurf = 关110兴 in-plane direction. Following ¯ 兲 Bragg peak position allows the same procedure, the Ge共022 ¯ 2兲 us to derive a Ge in-plane lattice spacing of d共02 = 0.199 98 nm, fitting within 0.1% the theoretically expected ¯ 2兲 = 0.200 02 nm. Given the fact that the Ge value of d共02 bulk lattice is about 1.7% bigger than the volume cub-Pr2O3 crystal structure, this value indicates a widely relaxed Ge ¯兲 deposit. In addition, from the FWHM value of the Ge共022 Bragg peak, a Ge deposit domain size of about 30 nm is ¯ 兲 Bragg peak is given derived. The indexing of the Ge共022 for a type A orientation of Ge on cub-Pr2O3共111兲 with respect to Si共111兲, resulting in a parallel alignment of Gebulk ¯ 兴 in-plane directions. and Sibulk关011 The vertical stacking of Ge in type A configuration with respect to Si is confirmed in the following by off-plane GIXRD studies summarized in Fig. 3. On the left, the expected intensity distribution of Gebulk Bragg reflections in the reciprocal Lsurf-Hsurf plane of the Sisurf coordinate system is sketched for a Ge共111兲 deposit, in which type A 共filled circles兲 as well as type B 共open circles兲 crystal orientations are present. To check for the presence of Ge stacking twins, off-plane GI-XRD studies were carried out along the Ge rod situated at 关0.96, 0 , L兴surf coordinates 共gray panel兲. The measurement on the right of Fig. 3 clearly shows that the diffraction peaks at Lsurf = 0.32 and 1.28 can be unambiguously as¯ 兲 and 共220兲, respectively, of a signed to the Bragg peaks 共111 type A oriented Ge共111兲 crystal. The derived lattice spacings
¯ 兲 = 0.3269 nm 关theory: d共111 ¯ 兲 = 0.3266 nm兴 and d共111 d共220兲 = 0.2001 nm 关theory: d共220兲 = 0.200 023 nm兴 fit with high accuracy the theoretically expected values so that, as reported before for the in-plane measurements of Fig. 2, the Ge deposit grows widely relaxed on the cub-Pr2O3共111兲 oxide support in the undistorted diamond lattice. Furthermore, this result is also confirmed by the detected ⌬Lsurf = 0.96 ¯ 兲 and 共220兲 Bragg peak posispacing between the Ge共111 tions, reproducing well the theoretically expected d111 = 0.3266 nm lattice spacing of relaxed Ge共111兲 deposits. More complicated is the exclusion of the simultaneous occurrence of type B oriented Ge共111兲 twins in the Ge deposit. This is true because the diffraction peaks at Lsurf = 0.62 and 1.6 could, in principle, result either from Bragg peaks of type B oriented Ge twins 关Gebulk共020兲 共Lsurf = 0.63兲 and Gebulk共131兲 共Lsurf = 1.59兲兴 or from the type B oriented cub-Pr2O3 film 关cub-Pr2O3 bulk 共040兲 共Lsurf = 0.62兲 and Ge bulk 共262兲 共Lsurf = 1.6兲兴. The ⌬Lsurf = 0.98 spacing between the two Bragg peaks in question is rather indicative of oxide diffraction signals because this ⌬Lsurf value is theoretically expected for the d共222兲 = 0.3196 nm spacing of the 共111兲 oriented cub-Pr2O3 film. To confirm this peak assignment, anomalous x-ray diffraction was performed at the Ge K edge by measuring the 关0.96, 0 , L兴 Ge rod scan at beam energies of 11 keV 共solid line兲 and 11.107 keV 共dotted line兲.35–37 The intensity scale is linear in the low intensity region 关several 102 cps 共counts per second兲兴, but logarithmic above the break 共double slashes兲 in the high intensity range 共105 – 107 cps兲. The linear scale is applied in the low intensity range to highlight the higher background signal in the scan at 11.107 keV due to the increasing Ge K␣-fluorescence radiation. Most importantly, the high intensity range of the measurements at 11 and 11.107 keV reveals that the intensities match perfectly at the positions of the diffraction peaks at Lsurf = 0.62 and Lsurf = 1.6. As no change in scattered intensity is observed, the diffraction peaks at Lsurf = 0.62 and Lsurf = 1.6 are free of Ge scattering contributions and can therefore be safely assigned to the cub-Pr2O3共040兲 and 共262兲 Bragg peaks, respectively. This result confirms the growth of a twin-free, exclusively type A oriented Ge共111兲 deposit on the cub-Pr2O3共111兲 / Si共111兲 support. The validity of the anomalous x-ray scattering approach to establish this result is confirmed by the decrease in scattered intensity observed
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FIG. 4. 共Color online兲 GISAXS study to determine the average morphology of the Ge islands on the cubPr2O3共111兲 / Si共111兲 support system.
¯ 兲 and at the positions of the type A oriented Ge bulk共111 共220兲 Bragg peaks when the exciting x-ray energy is increased from 11 to 11.107 keV. The experimentally observed integrated intensity contrast I共11 keV兲 / I共11.107 keV兲 of 1.92 共theory: 1.91兲 and 2.7 共theory: 2.72兲 for Ge ¯ 兲 and 共220兲, respectively, fits very well the theoretbulk共111 ical expectations. This behavior, together with the XPS study reported above 共Fig. 1兲, points to the presence of a very pure Ge deposit, i.e., free of interdiffused species such as, for example, Si. The latter element is a common impurity in Ge nanostructures heteroepitaxially grown directly on Si surfaces.38 The last important insight which can be deduced from Fig. 3 is the fact that the cub-Pr2O3 reflections are well visible in the scans although the measurements were conducted at an incident angle of 0.18°, which is below the critical angle of 0.2° for total reflections of 11 and 11.107 keV x rays from a Ge surface. By varying the incident angle of the x-ray beam, it was found that the cub-Pr2O3 Bragg peak intensity closely followed the x-ray penetration function in Pr2O3 but almost no influence from Ge was detected 共data not shown兲. These experimental findings, together with the nonpassivating behavior of the Ge deposit against moisture detected above by the XPS study 共Fig. 1兲, point to a nonwetting Ge growth behavior in form of isolated islands on the cub-Pr2O3共111兲 / Si共111兲 support system.
to the direct beam. The direct beam was aligned along the ¯ 10兴 azimuth and its position 共arrow兲 as well as the Sibulk关1 sample surface 共dotted line兲 is highlighted in the map. The high qualities of the sample surface 共low roughness兲 and beam 共good collimation, low divergence兲 generate very little substrate background. The scattered signal comes mostly from the Ge islands so that the raw data are reported in Fig. 4共a兲 and used in the fits. The data interpretation using ISGISAXS program was carried out by assuming a fitting model which is based on a paracrystal with a liquid structure factor 共i.e., assuming local ordering up to the first neighbor shell, as outlined in the experimental part and Ref. 25兲. Furthermore, the indexes of refraction of the Si substrate, the Ge islands, and the Pr2O3 layer as well as the thickness of the latter were used in the fitting procedure retrieving the expected 共reference兲 values. Although the shape of the islands is known from the TEM measurements, spherical 共truncated兲 and cylindrical shapes were tested with the following structure factors:25 Fsphere共q,R,H兲 = exp关iqz共H − R兲兴
冕
R
R−H
Fcylinder共q,R,H兲 = 2R2H C. GI-SAXS
GI-SAXS was applied to gain information about the morphology of the Ge islands on the cub-Pr2O3 / Si共111兲 support system. The measurement was performed with the sample surface being in a horizontal position and the PSD placed perpendicular to it, thus a full qz line spectrum was taken in one shot. The two-dimensional 共2D兲 color map 共log intensity scale兲 of Fig. 4共a兲 was thus obtained by combining the spectra taken at different in-plane exit angles with respect
2Rz2
J1共q储Rz兲 exp共iqzz兲dz, q储Rz
冉 冊
H J1共q储R兲 sin共qzH/2兲 exp iqz , q储R qzH/2 2 共3兲
with q储 = 冑q2x + q2y and Rz = 冑R2 − z2. J1 is the Bessel function of first order, R the radius of the sphere or cylinder base, and H their height. Other shapes could be immediately discarded if trying to model our experimental data. The best matching is found in the case of truncated spheres, confirming the Ge cluster morphology reported by TEM 共see below兲. This model was applied to fit two line scans of the GI-SAXS map,
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FIG. 5. TEM cross-section study ¯ 10兴 azimuth on along the SiBulk Si关1 the structure and defects of Ge共111兲 nanodots on a cub-Pr2O3共111兲 / Si共111兲 support system.
namely, a vertical qz 关Fig. 4共b兲兴 and a horizontal q储 关Fig. 4共c兲兴 cross section of the small angle scattering intensity. The experimental data are depicted by circles and the solid lines reproduce the modeling results. In the simulation, the characteristics of the substrate and oxide layer 共density, index, of refraction, etc.兲 were fixed to theoretical values; thus seven fitting parameters were used in total: a scale factor, three morphology-related parameters 共radius R, height H, and interparticle distance D兲, and the corresponding three dispersion factors. As depicted in Fig. 4共d兲, the following parameters of the Ge island morphology simultaneously reproduce well these two curves 共Gaussian dispersion factors are included in parenthesis兲. The Ge islands possess an average diameter and height of 34.25 nm 共 = ± 5.65 nm兲 and 16.25 nm 共 = ± 2.6 nm兲, respectively. From the fact that the island height is about half the diameter, it can be concluded that the shape of the Ge islands closely approaches a hemisphere. This morphology points to a Ge NC growth scenario close to thermodynamical equilibrium because, due to a rather low anisotropy in Ge low index surface energies, theory predicts a strong tendency of Ge NC’s toward a spherical equilibrium crystal shape 共ECS兲.39 Furthermore, an average spacing between the Ge islands of about 51.2 nm 共 = ± 13.8 nm兲 is deduced from the data fitting. It is seen that the dispersion of this spacing parameter is much bigger than in case of the values for height and diameter. This points to a growth behavior of the Ge islands on the cub-Pr2O3共111兲 surface, which is characterized by the ab-
sence of real ordering of the nucleation centers 共i.e., no decoration of periodic dislocation networks, etc.兲. D. TEM
Figure 5 shows a TEM cross section study along the ¯ 10兴 azimuth of the Ge共111兲 / cub-Pr O 共111兲 / Si共111兲 Si 关1 2 3 system. The overview micrograph in Fig. 5共a兲 confirms the interpretation of the XPS 共Fig. 1兲, XRD 共Figs. 2 and 3兲, and especially GI-SAXS 共Fig. 4兲 studies on the morphology of the Ge共111兲 / cub-Pr2O3共111兲 / Si共111兲 system. Firstly, the bright line along the Si共111兲 substrate/cub-Pr2O3共111兲 boundary clearly indicates the presence of the Pr-silicate interface 共IF兲 layer. Secondly, discrete Ge islands are observed on top of the cub-Pr2O3共111兲 layer. As the lateral size, height, and spacing of the imaged Ge islands reproduce well the results of our fits on the highly averaging GISAXS data, the Ge islands on the cub-Pr2O3共111兲 surface seem to grow rather monodisperse in size and shape. No indication of the presence of a Ge wetting layer on the cub-Pr2O3共111兲 film in the uncovered areas is observed, pointing that way to a true Volmer-Weber growth mode. This nonwetting behavior of Ge deposits on the cub-Pr2O3共111兲 / Si共111兲 support is also in line with the high contact angle of more than 70° Ge islands typically form with respect to the oxide film. The shape and structure of a typical Ge island are reported in the highresolution TEM image shown in Fig. 5共b兲. The 共111兲 oriented Ge island is truly single crystalline and coherent, i.e., dislocation-free. The surface structure of the Ge island is bulk
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determined by facets 共labeled by A to F兲. Based on the angle between the surface normal of the facets and the Ge共111兲 growth direction determined with an accuracy of ±2°, the facets A共80° 兲, B共57° 兲, C共30° 兲, D共0 ° 兲, E共35° 兲, and F共70° 兲 ¯¯13兲, 共001兲, 共113兲, 共111兲, 共110兲, and can be attributed to 共1 ¯ 共111兲 Ge surfaces. Besides the already discussed overall hemispherical Ge NC shape determined by GI-SAXS, the presence, as well as the size distribution of these facets on the Ge NC’s, is a further indication of a Ge growth close to the conditions of thermodynamic equilibrium. Theoretically, the Ge ECS was found to be mainly composed of 兵111其, 兵311其, and 兵100其 facets with only small contributions from 兵110其 surfaces.39 Here, the main area of the Ge NC surface is indeed composed of 兵111其 and 兵311其 facets but the role of 兵100其 and 兵110其 surfaces seems to be interchanged. Interestingly, the shape of Ge NC’s on cub-Pr2O3共111兲 oxide layers differs strongly from the situation of Ge NC growth carried out directly on Si共111兲 substrates, where preferentially truncated pyramides with 兵113其 sidewalls and a flat top 共111兲 ¯ 兲 planes facet are observed.40 The lattice fringes of the 共111 are well visible in the Ge island, and their orientation with respect to the cub-Pr2O3共111兲 / Si共111兲 support system can be best deduced from the high-resolution image in Fig. 5共c兲. To guide the eye, dotted arrows are applied to depict the ¯ 兲 surface normals in the orientation of the 共111 Ge/ cub-Pr2O3共111兲 / Si共111兲 system. It is seen that the sur¯ 兲 planes in Ge and Si are equally face normals of the 共111 ¯ 兲 planes oriented, but the surface normals of cub-Pr2O3共111 are misoriented from this direction by a rotation of 180° around the 关111兴 surface normal. Such an epitaxial relationship is characteristic of a type A/type B/type A stacking configuration of the Ge共111兲 / cub-Pr2O3共111兲 / Si共111兲 system, resulting from the presence of stacking faults at the two oxide/semiconductor phase boundaries. The TEM study thus corroborates the results of the anomalous GI-XRD study about the stacking configuration in the Ge islands 共Fig. 3兲. The about 2 nm thick Pr-silicate IF layer at the cub-Pr2O3共111兲 / Si共111兲 boundary is found to form a smooth interface with the Si substrate but a rather rough reaction front is visible at the IF/oxide film boundary. By close inspection of Fig. 5共c兲, it is seen that the bright IF layer forms a bilayer morphology, which consists of an amorphous part 共1 nm兲 toward the Si substrate and a crystalline region 共1 nm兲 toward the cub-Pr2O3共111兲 film. Lippert et al. detected by secondary ion mass spectroscopy 共SIMS兲 a high tendency of Si to diffuse into cub-Pr2O3 films.41 In this respect, it is likely that Si diffusion plays an important role in the formation of the Pr-silicate IF layer which in regions of high Si concentration close to the interface even results in an amorphization of the cub-Pr2O3 film. In contrast to this amorphous Pr silicate IF layer at the Si共111兲 / cub-Pr2O3共111兲 boundary, a coherent lattice matching is observed between the perfectly ordered Ge island and the cub-Pr2O3共111兲 film. This result is in line with the XPS study in Fig. 1 which showed no evidence for the formation of a GeOx interface at the Ge/ cub-Pr2O3共111兲 interface. Figure 5共c兲 shows furthermore that the cub-Pr2O3共111兲 surface beneath the perfectly ordered Ge island is rough only on the
J. Appl. Phys. 102, 034107 共2007兲
atomic scale. However, it was observed by TEM that roughness on the scale of several monolayer high steps on the cub-Pr2O3共111兲 film surface can well affect the crystalline quality of the growing Ge islands. An example of a highly defective Ge island on a rough cub-Pr2O3共111兲 surface region is shown in Fig. 5共d兲. To discuss the defect structure, the stepped cub-Pr2O3共111兲 surface is highlighted by the dashed-double dotted line and the different grains composing the Ge island are labeled by the numbers 1–4. Grain 1 is situated on an entirely flat part of the cub-Pr2O3共111兲 film and exclusively exhibits a type A stacking configuration with respect to the Si substrate, as indicated by the dotted arrows ¯ 兲 surface normals. The same stacking configuof the Ge共111 ration is found for grain 3 which, however, grows on top of a cub-Pr2O3共111兲 surface step. It is seen by close inspection of grain 3 that a defect in form of a deformation twin band 共indicated by the dashed-dotted arrows兲 nucleates at the kink of the oxide step and threads through the grain to its surface. Grains 2 and 4 demonstrate that an even more complicated defect structure can be induced by oxide surface roughness. Grain 2 is linked to grains 1 and 3 by twin boundaries across ¯ 兲 planes. The twinning planes are indicated in Fig. Ge共111 5共d兲 by dashed arrows and correspond to partial dislocations ¯¯12典.42 The resulting with Burger vectors of the type 1 / 6具1 stacking configuration of grain 2 corresponds neither to a type A nor a type B epitaxy with respect to the Si共111兲 substrate, so that its orientation is not suitable to form a low energy coincidence lattice with respect to the cub-Pr2O3共111兲 film surface. In that respect, it is not surprising that grain 2 is not directly connected to the oxide support by a crystalline plane but only at a single contact point 共dotted circle兲. Interestingly, four different dislocations meet in this contact point, namely, the twinning dislocations between the grains 1 and 2, 2 and 4 as well as the dislocations between the grains 1 and 4 with respect to the oxide support. Grain 4 is situated below grain 2 and is linked to it by a further twinning plane 共dashed arrow兲, but the resulting orientation of grain 4 is neither of the A- nor B-stacking type with respect to Si共111兲. As can be deduced from Fig. 5共d兲, its stacking configuration is probably induced by the fact that it is partially located on a small 具110典 facet of the cub-Pr2O3共111兲 step structure. The resulting misalignment with respect to the neighboring grains seems to create, however, a high energy configuration, as can be deduced from the high defect density in grain 4, i.e., two deformation twin bands 共dashed-dotted arrows兲 and rather irregularly shaped twinning plane boundaries are observed. IV. SUMMARY AND OUTLOOK
The Volmer-Weber growth mode of Ge deposits at 600 ° C on twin-free type B oriented cub-Pr2O3共111兲 / Si共111兲 support systems results in the formation of self-assembled, mutually isolated Ge NC’s with no real ordering of the nucleation centers. The Ge NC’s can be prepared under these conditions free of parasitic interface reactions with the oxide support and exhibit a high stoichiometric purity. The structure of the Ge NC’s was found to be completely relaxed, crystallizing under the undistorted dia-
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mond lattice. The epitaxial relationship of the Ge共111兲 / cub-Pr2O3共111兲 / Si共111兲 materials system is characterized by a type A/type B/type A stacking relationship. This is true at least for the coherent growth of Ge NC’s on atomically flat surface regions of the cub-Pr2O3共111兲 / Si共111兲 support. Steps of several monolayers height on the cub-Pr2O3共111兲 film were found to induce the growth of Ge NC’s with a high density of defects, mainly in form of partial dislocations with Burger vectors of the type ¯¯12典. The hemispherically Ge dot geometry as well as 1 / 6具1 the detected facet structure points to a growth scenario close to thermodynamic equilibrium. This is an important achievement because it was reported by electrical characterization techniques that a hemispherical Ge NC shape improves the operating speed of NC based NVM cells without compromising retention characteristics.5 Based on these results, the Ge共111兲 / cub-Pr2O3共111兲 / Si共111兲 material system is found to be well suited to serve as a model system to study fundamental physical aspects of the correlation between materials science properties and memory characteristics of Ge NC based NVM cells. A comparative study is today under way to investigate the materials science properties of self-assembled Ge NC’s on cub-Pr2O3共111兲 / Si共111兲 support systems which are entirely covered by Pr2O3. Simultaneously, these material systems are used to study the NVM properties of Ge NC’s embedded in high-k Pr2O3 films. To correlate structural and NVM aspects, TEM based electron holography will be used as a particularly promising state-of-the-art technique to unveil the controversially discussed physics of the charge trapping mechanism in Ge NC based NVM cells. ACKNOWLEDGMENTS
Thomas Schroeder thanks the Hanse Institute of Advanced Studies at Delmenhorst 共Germany兲 for the award of a fellowship during which important parts of this publication were prepared. The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft 共DFG兲 under Contract No. SCHR 1123/3-1. 1
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