The correlation of microstructural development and the kinetics of film growth has been investigated during the epitaxial film growth of an ultrathin binary Ag0.93Al0.07 solid solution on a Si(111)-7×7 surface at 300 K by the combination of high-resolution transmission electron microscopy, X-ray diffraction, scanning tunneling microscopy, low energy electron diffraction, and real-time in-situ stress measurements. Up to a film thickness of 6 ± 2 nm, epitaxial Ag0.93Al0.07 film growth is characterized by the strikingly extensive formation of planar faults parallel to the film/substrate interface, while at larger thickness the film grows practically defect-free. As revealed by real-time in-situ stress measurements, the extensive formation of planar faults at the very initial stage of growth is not driven by the reduction of the system's elastic strain energy but is rather caused by a striking thickness-dependence of the stacking-fault energy owing to a quantum size effect of the ultrathin metal alloy film, resulting in a frequent succession of fcc and hcp stackings of close-packed layers during the initial stage of film growth. The extensive development of planar faults at the initial stage of film growth (<6 ± 2 nm) is associated with the occurrence of a high density of kinks and corners at thereby atomically rough surface ledges, which strongly enhances the downward transport of adatoms from higher to lower terraces (interlayer mass transport) by a reduction of the effective diffusion barrier at the edge of surface steps and by increasing the driving force for adatoms to attach to the surface ledges. As a result, the epitaxial Ag0.93Al0.07 film initially grows in a 2D layer-by-layer type of growth and thus establishes atomically smooth film surfaces. For the practically planar-fault-free growth at thicknesses beyond 6 ± 2 nm, interlayer mass transport becomes distinctively limited, thereby inducing a transition from 2D to 3D type of film growth.

The growth of atomically smooth single crystalline metallic films with low defect concentration is of great fundamental and technological importance and requires a comprehensive understanding and control of the mechanisms underlying the microstructure evolution during thin film growth.1,2 The microstructure and thus the functional properties of ultrathin epitaxial metal films can be manipulated by the crystallographic structure of the substrate. The strain/stress, induced during heteroepitaxial growth by the lattice mismatch of the film and the substrate, has a profound impact on the evolving microstructure of the ultrathin film. Such intrinsic strain/stress not only can strongly alter the film growth dynamics on the atomic scale3,4 but also can impose the occurrence of metastable structures, not occurring in the bulk material.5 Furthermore, initially with the coverage, increasing elastic strain energy can drive morphology transitions6,7 and the formation of stress-relaxing defects, such as dislocations.3,8,9 Often planar faults occur in metallic thin films of a close-packed crystal structure, by the regular occurrence of which a fcc lattice is transformed into a hcp structure and vice versa.10 The microstructure and thus the functional properties of ultrathin epitaxial metal films can therefore strongly depend on the film thickness.

Furthermore, the spatial confinement of free electrons in an ultrathin metal overlayer on a semiconductor surface results in the discretization of the energy states along the surface-normal direction and causes the total electron energy to fluctuate pronouncedly with the film thickness. As a result of such quantum size effect (QSE), the film stability,11,12 the growth dynamics,13,14 and the film stress15 depend on the film thickness.

The precise adjustment of the properties of epitaxial metal films requires a comprehensive understanding of the above discussed effects and their impact on the dynamic film growth and defect formation.

Considering surface and interface energetics, the morphology of a growing film is determined by the ratio of (i) the surface energy of the substrate and (ii) the sum of the film-surface and film/substrate-interface energies. The often desired 2D (layer-by-layer) type of film growth would thus only occur if this ratio is larger than one. However, the morphological development is generally governed by the competition of thermodynamics and kinetics. From a kinetic point of view, the sufficient condition for a 2D type of growth is that under the applied growth conditions, the adatoms on an upper terrace are able to overcome the energy barrier at the edge of the terrace and descend along the atomic step to a lower terrace (i.e., downward interlayer mass transport). The formation of defects during thin film growth can potentially alter the energy barrier at the edges of the terrace,16,17 adding to the complexity of the microstructural development during thin film growth.

The present study discloses the interplay of thermodynamics and kinetics during the epitaxial growth of an ultrathin binary Ag0.93Al0.07 solid solution film on a Si(111)-7×7 surface at 300 K. In particular, the present work focuses on the mechanism governing the observed extensive formation of planar faults parallel to the film surface and exclusively within a 6 ± 2 nm thick region adjacent to the film/substrate interface. The striking transition in the planar fault density at 6 ± 2 nm is indicative for a pronounced thickness-dependence of the stacking-fault energy owing to the QSE in the ultrathin metal alloy film. The presence of planar faults enhances the interlayer mass transport at the very initial stage of film growth. As a result, 3D → 2D → 3D growth mode transitions occur and atomically smooth films evolve. The here established mechanisms can have general implications for many metal-alloy thin films and thereby offer unique opportunities for the fabrication of novel metal nanostructures with tailored catalytic, magnetic, and electronic properties.18,19

The experiments were carried out in a custom-built multi-chamber ultrahigh vacuum (UHV) system (base pressure <1 × 10−8 Pa) for thin film deposition by thermal evaporation, in-situ angle-resolved X-ray photoelectron spectroscopy (AR-XPS), in-situ scanning tunneling microscopy (STM), and in-situ low energy electron diffraction (LEED).20 Depending on the demands of the experiments, 100 μm thin Si(111) substrates were either loosely or tightly mounted in the specimen holder, introduced into the UHV system, and thoroughly cleaned by a programmed laser heat treatment up to a maximum temperature of 1100 °C for 1 min. As confirmed by AR-XPS and STM analyses, this preparation procedure results in a contamination-free, well-ordered Si(111)-7×7 surface. On the thus prepared Si(111)-7×7 surface, epitaxial Ag0.93Al0.07 films were deposited at 300 K by co-evaporation of pure Ag (>99.995 at.%; from an Al2O3 crucible) and pure Al (>99.995 at.%; from a pyrolytic boron nitride crucible). The film composition of Ag0.93Al0.07 was independently determined after film deposition both by in-situ AR-XPS analysis and by the composition-dependent strain-free lattice parameter, as determined by ex-situ X-ray diffraction (XRD) analysis of about 100 nm thick films, interpolating the dependence of the lattice parameter on composition as given in Ref. 21. The values of and the error ranges of the composition determined by AR-XPS and XRD are 7.5 ± 0.8 at.% Al and 6.9 ± 0.6 at.% Al, respectively. According to the AR-XPS measurements, no segregation of Ag or Al to the film surface occurred during the growth of the film. The deposition rate of the Ag0.93Al0.07 films of 0.145 ± 0.005 nm/s, i.e., 0.62 ± 0.02 ML/s (in this study, 1 ML refers to the atomic density of the close-packed fcc(111) plane of Ag0.93Al0.07 at room temperature, i.e., 0.235 nm; cf. Ref. 21), was calibrated by determining the thickness of the deposited Ag0.93Al0.07 films for a number of deposition times using a Veeco DekTak profilometer (for film thicknesses in the range of 50 nm–280 nm) as well as by applying X-ray reflectivity (XRR) measurements (for film thicknesses in the range of 2 nm–105 nm).

The crystal structure, texture, and the orientation relationship (OR) with the Si(111) substrate of the epitaxial Ag0.93Al0.07 films were investigated through ex-situ (high-resolution) X-Ray diffraction (HRXRD) Θ–2Θ scans and {111} pole-figure measurements (at a diffraction angle 2Θ = 38.23°) using a Bruker D8 Discover diffractometer operating in a parallel-beam acquisition mode and employing monochromatic Cu radiation as selected by an energy-dispersive detector.

Furthermore, the density of the planar faults parallel to the surface (cf. Sec. III B; defined with respect to the fcc stacking, i.e., the degree of hexagonality) in the epitaxial Ag0.93Al0.07(111) films (cf. Sec. III A) was examined by the analysis of the diffuse intensity distribution (intensity streaks) along the [111] direction in reciprocal space. The intensity distribution along this [111] direction of the (01 L)hex streak (defined with respect to the hexagonal-rhombohedrally centered unit cell; ahex = ½(afcc − bfcc), bhex = ½(bfcc − cfcc), and chex = afcc + bfcc + cfcc) is a representation of the stacking sequence of close-packed layers (cf. Fig. 2(g)) and the intensity along this streak can be determined in XRD by varying the diffraction angle, 2Θ, and the inclination angle of the diffraction vector with respect to the surface normal of the specimen, ψ.22,23 Thus, XRD diffractograms were recorded at specific angles of rotation around the specimen surface normal, φ, (i.e., at φ values for which the diffraction vector is perpendicular to the [11¯0] direction of the domains of different in-plane orientations; cf. Sec. III A and Fig. 1(b)) for a series of 2Θ-ψ pairs, compatible with the position of the intensity streak (i.e., 2Θ = 34°–50° and ψ = 50°–76°). The thus measured intensity distribution along the streak in reciprocal space was evaluated using the software package DIFFaXplus.24 The algorithm is able to fit the experimentally determined diffracted intensity along the streak of the crystals containing parallel planar faults by adopting the kinematical diffraction theory and a statistical model based on a Markov chain to describe the stacking sequence of successive, close-packed layers. Note that the algorithm is strictly only applicable in the case of a statistical, homogeneous distribution of planar faults in the specimen, which is not the case in the present study, especially for later stages of film growth (see Sec. III B). The best description of the experimental data was obtained by simultaneously considering in the fitting procedure a fcc-like phase and a hcp-like phase. (fcc-like denotes (local) regions where, with respect to fcc stacking, the planar fault density is <50%, whereas hcp-like denotes regions where the (local) planar fault density, with respect to fcc stacking, is >50%.)

FIG. 1.

XRD measurements reveal that the co-deposition of Ag and Al on the Si(111)-7×7 surface at 300 K resulted in the formation of a Ag0.93Al0.07 fcc-like solid solution. (a) XRD Θ-2Θ scan (recorded at ψ = 0°) before and after the deposition of the epitaxial Ag0.93Al0.07 film. No reflections other than 111 and 222 can be observed. The 111 reflection is sharp and exhibits Laue fringes (see inset). (b) XRD φ-scans (recorded at ψ = 70.53° and 2Θ = 38.23°). The epitaxial Ag0.93Al0.07(111) films possess four main, differently pronounced in-plane orientation relationships with the Si(111) substrate (cf. Sec. III A).

FIG. 1.

XRD measurements reveal that the co-deposition of Ag and Al on the Si(111)-7×7 surface at 300 K resulted in the formation of a Ag0.93Al0.07 fcc-like solid solution. (a) XRD Θ-2Θ scan (recorded at ψ = 0°) before and after the deposition of the epitaxial Ag0.93Al0.07 film. No reflections other than 111 and 222 can be observed. The 111 reflection is sharp and exhibits Laue fringes (see inset). (b) XRD φ-scans (recorded at ψ = 70.53° and 2Θ = 38.23°). The epitaxial Ag0.93Al0.07(111) films possess four main, differently pronounced in-plane orientation relationships with the Si(111) substrate (cf. Sec. III A).

Close modal

Microstructural images of the epitaxial Ag0.93Al0.07 film were obtained by ex-situ cross-sectional high-resolution transmission electron microscopy (HRTEM). To this end, a cross-section TEM lamella was cut from the Ag0.93Al0.07(111)/Si(111) specimen using a dual focused ion beam (FIB) with Ga ions accelerated at 30 keV and employing an ion current of 7–30 pA. Prior to the FIB cutting procedure, the specimen surface was protected with a nanocrystalline Pt capping layer. Subsequently, the Ag0.93Al0.07 film microstructure and the atomic constitution at the film/substrate interface were investigated in a JEOL ARM 200F electron microscope at an acceleration voltage of 200 keV.

The morphology of the epitaxial Ag0.93Al0.07 film at various stages of film growth was investigated in-situ by a Specs Aarhus 150 STM, equipped with an electrochemically etched and in-situ Ar-sputter-cleaned tungsten tip. The STM measurements were performed at room temperature in the constant current mode with the film-covered Si(111) wafers fixed in the specimen holder. A constant tunneling current in the range of 0.1–0.5 nA and a specimen bias of 1.4 V were applied.

LEED measurements were performed in situ to reveal the crystallographic orientation relationships at the very initial stage of film growth using a Specs 4-grid LEED system, employing primary electron energies in the range of 40–200 eV.

Auger-electron spectroscopy (AES) sputter-depth profiling was conducted with a JEOL JAMP-7830F AES system equipped with a hemispherical analyser, a field emission electron gun operating at an acceleration voltage of 10 keV and a beam current of 10 nA as well as with a sputter-gun providing a focused 1 keV Ar+ ion beam.25 

The intrinsic stress evolution during film deposition was determined in-situ by monitoring in real-time the change in curvature of the loosely mounted Si(111) substrate using a multi optical stress sensor (MOS; k-space Associates) with a 3 × 3 array of parallel laser beams and averaging the measured change of substrate curvature recorded along different directions;26,27 (no difference in the data recorded along the [-110] and the [11-2] directions was observed). According to Stoney's equation,28 the measured change of the substrate curvature is proportional to the change of film force (i.e., the force per unit width acting on the film parallel to the substrate), which is given as the product of the thickness-averaged in-plane film stress and the film thickness plus a (possible) change in surface stress.20 

Additional results on the microstructure and stress evolution during the growth of Ag1-xAlx films of different compositions, such as x = 0, 0.03, 0.06, 0.07, and 1, can be found in the supplementary material.

As revealed by the XRD Θ–2Θ scans (2Θ = 23°–82°), the film consists of a Ag0.93Al0.07 fcc-like solid solution with the close packed (111) layers parallel to the surface (see Fig. 1(a)). Consistent with the bulk Ag-Al phase diagram,29 no intermetallic Ag-Al compounds had formed during the co-deposition. No reflections other than 111 and 222 can be observed. The epitaxial Ag0.93Al0.07 film shows a sharp 111 reflection with Laue (thickness) fringes at both sides of the main peak (see inset in Fig. 1(a)) and independent of its thickness exhibits mainly four, differently pronounced, (in-plane) orientation relationships (OR) with the Si(111) substrate. The predominant ORs (comprising ≈40 vol.% each) are Ag0.93Al0.07(111)||Si(111) with Ag0.93Al0.07[11¯0]||Si[11¯0] (OR1) and with Ag0.93Al0.07[11¯0]||Si[1¯10] (OR2).

For these two OR variants, related to each other by a twinning operation on (111) planes parallel to the film/substrate interface, four lattice plane spacings of the Ag0.93Al0.07 film match almost perfectly with 3 of the corresponding lattice plane spacings of the Si substrate (so-called “4/3 domain epitaxy”). Only these two ORs have been reported for the epitaxial growth of pure Ag(111) films and pure Al(111) films on the Si(111)-7×7 surface.30,31

The minor ORs (comprising ≈10 vol.% each) are Ag0.93Al0.07(111)||Si(111) with Ag0.93Al0.07[11¯0]||Si[112¯] (OR3) and with Ag0.93Al0.07[11¯0]||Si[1¯1¯2] (OR4).

Often small deviations (i.e., ≈±7° in-plane rotations) from OR 3 and OR 4 were observed. The reason for the occurrence of OR 3 and OR 4 is not immediately clear, since in contrast to the OR 1 and OR 2 they do not provide a low lattice mismatch at the film/substrate interface.

The above described crystal structure and orientation relationships are completely consistent with the other results of this study obtained from detailed ex-situ cross-sectional and plane view HRTEM analyses (see Sec. III B and supplementary material) as well as from in-situ LEED investigation at the very initial stage of Ag0.93Al0.07 film growth (see Sec. III C).

The microstructure of the epitaxial Ag0.93Al0.07 films was investigated by cross-sectional TEM with the Si substrate in the [11¯0] zone axis orientation with respect to the electron beam (i.e., for grains of OR1 and OR2, the electron beam is parallel to the [11¯0] direction and for grains of OR3 and OR4 the electron beam is parallel to the [112¯] direction). The electron diffraction pattern shows pronounced streaking of the 111¯, 002, and 220 reflections of the domains with OR1 and OR2 along the sample-surface normal (i.e., the [111] direction), indicating the presence of a significant density of planar faults, i.e., twins and/or stacking faults, parallel to the film surface (see Figs. 2(f) and 2(g)). The cross-section HRTEM micrographs reveal that these planar faults are very inhomogeneously distributed in the 35 nm thick film (see Fig. 2(a)): within an about 6 ± 2 nm thin region adjacent to the Si(111) substrate, an extremely high density of planar faults, all aligned parallel to the film surface, occurs (see Figs. 2(b), 2(c) and also see the XRD analysis discussed below). Such planar defects are practically absent in the film region above (>6 ± 2 nm from the film/substrate interface). Only a few isolated coherent Σ3{111} and incoherent Σ3{112} twin boundaries (CTBs and ITBs) as well as some isolated stacking faults on {111¯} planes, inclined at 70.5° with respect to the specimen surface, are observed within the laterally extended grains of OR1 and OR2 in the film region beyond 6 ± 2 nm from the film/substrate interface. Within one grain, the transition from the film region containing a high density of planar faults to the almost defect-free film region beyond 6 ± 2 nm is relatively sharp (see Figs. 2(d) and 2(e)). The observed slight variation of the thickness of the highly defective region (i.e., ≈6 ± 2 nm; cf. Fig. 2(a)) implies that, averaged laterally over the whole sample, the average density of planar faults aligned parallel to the surface decreases gradually with increasing thickness.

FIG. 2.

The cross-sectional HRTEM analysis of the epitaxial Ag0.93Al0.07 film with the Si substrate in the [11¯0] zone axis (i.e., for grains of OR1 and OR2 the electron beam is parallel to the [11¯0] direction and for grains of OR3 and OR4 the e-beam parallel to the [112¯] direction) reveals a strikingly inhomogeneous distribution of planar faults. (a)–(c) Within a 6 ± 2 nm thin region at the interface to the Si substrate, the film exhibits an enormous density of planar faults practically exclusively aligned parallel to the film surface, whereas at larger distances from the film/substrate interface the film possesses only isolated coherent and incoherent twin boundaries (CTBs and ITBs) as well as some stacking faults (SFs) on {-111} planes. (f) Due to the presence of planar faults parallel to the surface, the 111¯, 002, and 220 reflections of the OR1 and OR2 grains in the electron-diffraction pattern are streaked along the sample surface normal (i.e., the [111] direction); cf. (g) schematic electron-diffraction pattern pertaining to (f). (a) and (d) For grains with OR3 and OR4, the [112¯] direction is parallel to the electron beam, and thus planar faults are invisible. These grains possess an incoherent interface with the Si substrate. (e) EDX concentration profiles of Si (red), Ag (blue), and Al (green) along the direction indicated by the arrow in the corresponding STEM image show that the film composition is constant. Solid lines are only meant as guidance for the eye.

FIG. 2.

The cross-sectional HRTEM analysis of the epitaxial Ag0.93Al0.07 film with the Si substrate in the [11¯0] zone axis (i.e., for grains of OR1 and OR2 the electron beam is parallel to the [11¯0] direction and for grains of OR3 and OR4 the e-beam parallel to the [112¯] direction) reveals a strikingly inhomogeneous distribution of planar faults. (a)–(c) Within a 6 ± 2 nm thin region at the interface to the Si substrate, the film exhibits an enormous density of planar faults practically exclusively aligned parallel to the film surface, whereas at larger distances from the film/substrate interface the film possesses only isolated coherent and incoherent twin boundaries (CTBs and ITBs) as well as some stacking faults (SFs) on {-111} planes. (f) Due to the presence of planar faults parallel to the surface, the 111¯, 002, and 220 reflections of the OR1 and OR2 grains in the electron-diffraction pattern are streaked along the sample surface normal (i.e., the [111] direction); cf. (g) schematic electron-diffraction pattern pertaining to (f). (a) and (d) For grains with OR3 and OR4, the [112¯] direction is parallel to the electron beam, and thus planar faults are invisible. These grains possess an incoherent interface with the Si substrate. (e) EDX concentration profiles of Si (red), Ag (blue), and Al (green) along the direction indicated by the arrow in the corresponding STEM image show that the film composition is constant. Solid lines are only meant as guidance for the eye.

Close modal

The high density of planar faults within the 6 ± 2 nm thin film region adjacent to the film/substrate interface as well as the relatively small lateral extension of these planar faults within the grains of OR1 and OR2 (see Figs. 2(a)–2(c) and cf. Sec. III C) obstructs the observation of the crystal lattice with atomic resolution and thus it is impossible to determine the number, the sequence, and/or the kind of the planar faults from the HRTEM images (e.g., see Fig. 2(c)). Directly at the film/substrate interface, often a “4/3 domain epitaxy” (cf. Sec. III A) is observed. Owing to the extensive lattice distortion resulting from the high density of planar faults, it cannot be verified if such laterally periodic atomic arrangement extends over large distances. It should be recognized that the observed contrast within the 6 ± 2 nm thin film region at the interface to the Si substrate is the consequence of the presence of a high density of planar faults and can be clearly distinguished from the characteristic Moiré pattern contrast often observed at ITBs (as a result of an overlap of grains with twin orientation relationship, as OR1 and OR2 grains, along the electron-beam direction; for such an example, see the upper left corner of Fig. 2(b)).

The planar faults aligned parallel to the specimen surface are associated with a change of the stacking sequence of the close-packed (111) layers and are bounded laterally by Shockley partial dislocations with Burgers vector of 1/6 ⟨112¯⟩.10 Consequently, these planar faults parallel to the surface can only be observed in a cross-sectional TEM image if the electron beam is parallel to ⟨1¯10⟩, which holds for OR 1 and OR 2 grains in Fig. 2, and the planar faults are invisible if the electron beam is parallel to ⟨112¯⟩, which holds for OR 3 and OR 4 grains in Fig. 2. However, as revealed by the XRD measurements also the grains of OR 3 and OR 4, possessing an incoherent interface with the Si(111) substrate (see Fig. 2(d)), exhibit a similar strikingly inhomogeneous distribution of planar faults, as demonstrated by HRTEM for OR 1 and OR 2 grains (see what follows).

By measuring the diffracted intensity along the streaks through the 11–1 and 002 reflections for the domains with OR1/OR2 and the domains with OR3/OR4 (which streaks arise by the presence of planar faults parallel to the surface; cf. Figs. 2(f) and 2(g)) for Ag0.93Al0.07 films of different thicknesses, a clear trend in the density of planar faults parallel to the surface is revealed (see Fig. 3): For each orientation relationship, (i) the {111} and {002} reflections become broader with decreasing film thickness and (ii) the relative contribution of the diffuse intensity increases with decreasing film thickness. Both these observations suggest that the volume density of planar faults aligned parallel to the film surface increases with decreasing film thickness.

FIG. 3.

Intensity distributions along the (01 L)hex streaks (cf. Fig. 2(g)) in reciprocal space for the domains with twin orientation relationships: (a) OR1/OR2 and (b) OR3/OR4 of Ag0.93Al0.07 films of thicknesses of 45 nm, 12 nm, and 5 nm. For each of both pairs of orientation relationships, the {11-1} and {002} reflections become broader with decreasing film thickness and the relative contribution of the diffuse intensity increases with decreasing film thickness. Thus, the volume density of planar faults parallel to the surface increases with decreasing film thickness. Note that due to the small volume fraction of OR3/OR4 for a 5 nm thick film, the corresponding intensity distribution along (01 L)hex could not be measured.

FIG. 3.

Intensity distributions along the (01 L)hex streaks (cf. Fig. 2(g)) in reciprocal space for the domains with twin orientation relationships: (a) OR1/OR2 and (b) OR3/OR4 of Ag0.93Al0.07 films of thicknesses of 45 nm, 12 nm, and 5 nm. For each of both pairs of orientation relationships, the {11-1} and {002} reflections become broader with decreasing film thickness and the relative contribution of the diffuse intensity increases with decreasing film thickness. Thus, the volume density of planar faults parallel to the surface increases with decreasing film thickness. Note that due to the small volume fraction of OR3/OR4 for a 5 nm thick film, the corresponding intensity distribution along (01 L)hex could not be measured.

Close modal

According to the quantitative analysis of the intensity distribution by application of the program DIFFaXplus (see Sec. II B), the degree of hexagonality (i.e., the density of planar faults, with respect to fcc stacking, aligned parallel to the film surface in the diffracting volume) for OR1 and OR2 grains increases with decreasing film thickness from 5 ± 1% for a film of 45 nm via 21 ± 1% for a film of 12 nm to 38 ± 1% for a film of 5 nm. Accordingly, the number of planar faults of the films (i.e., the density per volume unit multiplied by the film thickness in MLs) is 9.5 ± 1.9, 10.7 ± 0.5, and 8.1 ± 0.2 for the 45 nm, 12 nm and 5 nm thick films, respectively. The invariability of the number of planar faults with the film thickness shows that all faults are concentrated in a very thin region adjacent to the substrate, which agrees well with the results of the (local) HRTEM investigation presented above. Recognizing that the results of the XRD analysis represent lateral averages over macroscopic areas, it can be concluded that: (i) An enormous number of planar faults aligned parallel to the film surface is present within a 5 nm thick region of the Ag0.93Al0.07 film adjacent to the substrate: 38 ± 1% of the closed-packed 111 layers in this region exhibit a (local) hcp (i.e., ABAB) rather than fcc (i.e., ABC) stacking sequence (especially note the occurrence of the slight intensity hump at Lhex = 1.5 in Fig. 3 indicative for the presence of a {011}hcp reflection, i.e., a hcp-like phase). Consequently, a clear distinction of the fcc and hcp crystal structures for films thinner than ≈5 nm is impossible. (ii) From the interpolation of the number of planar faults formed in the three films of different thicknesses, it follows that planar faults aligned parallel to the film surface practically do not occur beyond ≈6 nm from the film/substrate interface.

The same trend, but with higher values of the planar-fault density, is also revealed by the quantitative XRD analysis of the intensity streak for OR 3 and OR 4 grains (see Fig. 3), for which the planar defects are intrinsically invisible in the HRTEM micrographs of Fig. 2 (see above). For the OR 3 and OR 4 grains, the planar-fault density increases from 11 ± 2% for a film of 45 nm to 28 ± 1% for a film of 12 nm. Accordingly, the number of planar faults of the films is 21.1 ± 3.8 and 14.3 ± 0.5 for 45 nm and 12 nm thick films, respectively. (Due to the small volume fractions of OR 3 and OR 4, the stacking-fault density could not be determined for the 5 nm thick film.) The larger density of planar faults in OR 3 and OR 4 grains (i.e., a higher degree of hexagonality), as compared to OR 1 and OR 2 grains, implies that OR 3 and OR 4 grains are more hcp like. This is also indicated by the epitaxial orientation relationship with the substrate of OR 3 and OR 4, which equals that found for the grains in an epitaxial hcp Ag2Al(001) film on a Si(111) substrate (as prepared within this study; not shown).

The occurrence of some amount of planar faults in the Ag0.93Al0.07 films might not be surprising, since a bulk Ag0.93Al0.07 solid solution exhibits a stacking fault energy of only ≈7 mJ/m2 (Ref. 32) (cf. stacking fault energy of pure Ag ≈ 22 mJ/m2 (Ref. 33)), but the extraordinarily high density of planar faults parallel to the surface occurring exclusively in the direct vicinity of the substrate interface is very remarkable.

The occurrence of a composition gradient along the film thickness during deposition, in association with a variation of the composition dependent stacking-fault energy,32 can be excluded to be the origin of the abrupt change in fault density: No significant variation of the film composition along the film thickness could be detected by energy dispersive X-ray spectroscopy (EDX) line scans as well as by Auger-electron spectroscopy (AES) depth-profiling. The concentration profile along the direction given by the dashed arrow superimposed on the corresponding STEM image (see Fig. 2(e)) shows only a very slight, of at most, 1 at.% increase of Al concentration in the highly defective region, as compared to the rest of the film, but this variation is within the experimental error margin. Also laterally no significant variation of the film composition could be detected by EDX investigation of a plane-view TEM specimen or by local AES measurements.

Furthermore, although generally deposition conditions could alter the absolute value of the planar-fault density,34–36 the present deposition parameters cannot account for the very abrupt reduction in the density of planar faults at a thickness of 6 ± 2 nm during continuous deposition of the epitaxial Ag0.93Al0.07(111) film at constant deposition rate and at constant substrate temperature.

Hence, excluding variations of the film composition and the growth parameters as possible origins of the observed abrupt transition in the density of planar faults at a film thickness of 6 ± 2 nm, it might be proposed that the extensive formation of planar defects at the initial stage of epitaxial Ag0.93Al0.07 film growth is driven by the relaxation of an intrinsic (e.g., lattice-mismatch) stress component in order to reduce the system's elastic strain energy. Before examining and discussing this possibility against the background of the measured intrinsic stress evolution (Sec. III D), first, the surface morphological development and its correlation with the occurrence of planar faults are investigated and discussed (Sec. III C).

1. Observations

As revealed by STM (see Fig. 4), the morphological evolution during epitaxial Ag0.93Al0.07 film growth on a Si(111)-7×7 surface at 300 K is characterized by striking, distinctive transitions of the film growth mode. Initially, film growth proceeds according to a Stranski-Krastanov (3D) type of growth. After the deposition of nominally 1.6 ML, an almost continuous “wetting” layer has formed, on top of which isolated islands with a strongly preferred height of 2 MLs (relative to the “wetting” layer) have nucleated (see Figs. 4(a) and 5(a)). A similar Stranski-Krastanov type of growth, with island heights of predominantly 2 MLs on top of a “wetting” layer, was also reported for epitaxial growth of pure Ag on the Si(111)-7×7 surface where the stability of Ag islands with heights of 2 MLs results from a quantum size effect.37–41 

FIG. 4.

STM images (specimen bias voltage Vt = 1.5 V, tunneling current It = 0.5 nA) showing the morphological evolution during various stages of epitaxial Ag0.93Al0.07 film growth on a Si(111)‐7 × 7 surface at 300 K, which is characterized by distinct growth-mode transitions from 3D over 2D to again 3D. (a) Upon deposition of nominal 1.6 ML of Ag0.93Al0.07 a “wetting” layer has formed on which predominantly islands with a height of 2 ML (relative to the “wetting” layer) have nucleated (see the frequency plot in the inset). [(b) and (c)] Upon further deposition (3.5 MLs and 7.8 MLs, respectively), films have formed which are percolated by holes and grooves (see height profile in the inset taken along the indicated line in the image) but yet have a relatively smooth surface. [(d)–(f)] At film thicknesses between 14 MLs and 23.6 MLs, the epitaxial Ag0.93Al0.07 film growth proceeds in a (2D) layer-by-layer type of growth, which is associated with the establishment of atomically smooth films of a single thickness (see frequency plot in the inset of (d) and (f)). [(g) and (h)] At a film thickness >33 MLs, the height distribution becomes increasingly broader with increasing thickness (see frequency plot in the inset of (g)): film growth proceeds in a 3D type of growth. In (h) not all of the surface steps correspond to an integer number of MLs (cf. Fig. 5(d)).

FIG. 4.

STM images (specimen bias voltage Vt = 1.5 V, tunneling current It = 0.5 nA) showing the morphological evolution during various stages of epitaxial Ag0.93Al0.07 film growth on a Si(111)‐7 × 7 surface at 300 K, which is characterized by distinct growth-mode transitions from 3D over 2D to again 3D. (a) Upon deposition of nominal 1.6 ML of Ag0.93Al0.07 a “wetting” layer has formed on which predominantly islands with a height of 2 ML (relative to the “wetting” layer) have nucleated (see the frequency plot in the inset). [(b) and (c)] Upon further deposition (3.5 MLs and 7.8 MLs, respectively), films have formed which are percolated by holes and grooves (see height profile in the inset taken along the indicated line in the image) but yet have a relatively smooth surface. [(d)–(f)] At film thicknesses between 14 MLs and 23.6 MLs, the epitaxial Ag0.93Al0.07 film growth proceeds in a (2D) layer-by-layer type of growth, which is associated with the establishment of atomically smooth films of a single thickness (see frequency plot in the inset of (d) and (f)). [(g) and (h)] At a film thickness >33 MLs, the height distribution becomes increasingly broader with increasing thickness (see frequency plot in the inset of (g)): film growth proceeds in a 3D type of growth. In (h) not all of the surface steps correspond to an integer number of MLs (cf. Fig. 5(d)).

Close modal
FIG. 5.

(a) Enlarged STM image and corresponding LEED pattern (as inset; incident electron energy 53 eV) of the islands with a strongly preferred height of 2 MLs on top of the “wetting” layer (cf. Fig. 4(a)). The small red circle in the LEED pattern indicates one of the diffraction spots of the Si(111) substrate. [(b) and (c)] On the surfaces of the films percolated by holes and groves (of thicknesses <8 ML; cf. Figs. 4(b) and 4(c)) as well as on the surfaces of the laterally continuous films (of thickness 14–24 ML; cf. Figs. 4(d)–4(f)) rather irregularly shaped networks of lines corresponding to 0.5 Å deep depressions are observed (indicated by arrows). These depressions are likely caused by the local reduction of the surface atomic density along the lines of Shockley partial dislocations on (111) planes below the surface. Note that the image contrast in (b) was strongly enhanced to visualize the depressions on the film surface and as a result holes and groves appear black in the image. (d) No depressions are observed for films of thickness >33 MLs, but a significant number of stacking faults on {11-1} planes (i.e., inclined at 70.5° with respect to the surface) occurs (straight steps of the sub-monolayer height indicated by arrows). They are associated with straight surface steps of 0.8 nm height (1/3 ML) and their intersections with the surface are inclined with respect to each other at 60°. As a result of the extensive occurrence of planar faults parallel to the film surface at the initial stage of epitaxial Ag0.93Al0.07(111) film growth (i.e., for thicknesses ≲27 ± 8 ML (6 ± 2 nm)) and the therewith associated incoherent scattering of incident low energy electrons applied in the LEED analysis, the LEED patterns of films with thicknesses between 3 and 24 MLs contain more diffuse intensity than the LEED patterns observed for the nominal 1.6 ML and 170 ML thick Ag0.93Al0.07 films (see insets).

FIG. 5.

(a) Enlarged STM image and corresponding LEED pattern (as inset; incident electron energy 53 eV) of the islands with a strongly preferred height of 2 MLs on top of the “wetting” layer (cf. Fig. 4(a)). The small red circle in the LEED pattern indicates one of the diffraction spots of the Si(111) substrate. [(b) and (c)] On the surfaces of the films percolated by holes and groves (of thicknesses <8 ML; cf. Figs. 4(b) and 4(c)) as well as on the surfaces of the laterally continuous films (of thickness 14–24 ML; cf. Figs. 4(d)–4(f)) rather irregularly shaped networks of lines corresponding to 0.5 Å deep depressions are observed (indicated by arrows). These depressions are likely caused by the local reduction of the surface atomic density along the lines of Shockley partial dislocations on (111) planes below the surface. Note that the image contrast in (b) was strongly enhanced to visualize the depressions on the film surface and as a result holes and groves appear black in the image. (d) No depressions are observed for films of thickness >33 MLs, but a significant number of stacking faults on {11-1} planes (i.e., inclined at 70.5° with respect to the surface) occurs (straight steps of the sub-monolayer height indicated by arrows). They are associated with straight surface steps of 0.8 nm height (1/3 ML) and their intersections with the surface are inclined with respect to each other at 60°. As a result of the extensive occurrence of planar faults parallel to the film surface at the initial stage of epitaxial Ag0.93Al0.07(111) film growth (i.e., for thicknesses ≲27 ± 8 ML (6 ± 2 nm)) and the therewith associated incoherent scattering of incident low energy electrons applied in the LEED analysis, the LEED patterns of films with thicknesses between 3 and 24 MLs contain more diffuse intensity than the LEED patterns observed for the nominal 1.6 ML and 170 ML thick Ag0.93Al0.07 films (see insets).

Close modal

Upon continued Ag0.93Al0.07 film deposition, the islands grow both laterally as well as vertically and largely coalesce (see Figs. 4(b) and 4(c)). At nominal thicknesses of 3.5 and 7.8 MLs, the film exhibits significant area fractions of holes and grooves with depths of 3–4 MLs and ≳5–6 MLs, respectively. For the rest, the film surfaces at this stage of growth are very smooth with only a single monolayer step height difference.

The occurrence of a largely continuous film at nominal 7.8 MLs suggests that at this stage the growth mode gradually changes from a 3D to a 2D type of growth. Indeed, after deposition of 14 MLs (see Fig. 4(d)), the film has become smooth with a practically uniform thickness (i.e., the area fraction of film with a thickness of 14 ML is >97%; see inset Fig. 4(d)). Continued film growth then proceeds in a layer-by-layer type of growth up to a film thickness of at least 24 MLs (see Figs. 4(d)–4(f)). The observed layer-by-layer type of growth of the Ag0.93Al0.07 films, associated with the establishment of films of uniform thickness, in the thickness range 14–24 MLs, differs strikingly with the 3D type of growth reported for both homoepitaxial and heteroepitaxial growth of both pure Ag(111) and pure Al(111) films at 300 K.42–44 Generally, the occurrence of a layer-by-layer type of growth is very rare for the deposition of metallic films at 300 K. Metal films of such uniform thickness on a semiconductor substrate could only be prepared on the basis of a two-step procedure (so called “quantum growth mode”)11 by, first, film deposition at temperatures <100 K and, second, annealing at ≈300 K. However, even then this “quantum growth mode” only allows the preparation of atomically smooth films of uniform thickness at specific film thicknesses (e.g., in the case of Ag on Si(111) at about 7 ML), whereas films of smaller and larger thicknesses exhibit a significantly broader thickness distribution.44,45 Noteworthy, the present epitaxial Ag0.93Al0.07 films of uniform thickness are stable against “dewetting” and surface roughening upon annealing for 1 h at 400 K in UHV (see supplementary material).

With increasing Ag0.93Al0.07 film thickness, the height distribution of the film again becomes broader and a thickness variation of ≥4 atomic layers is observed for films of nominal 33 MLs (7.8 nm) and 170 MLs (40 nm) thicknesses (see Figs. 4(g) and 4(h)). Hence, within the thickness range of 24 MLs–33 MLs, the growth mode of the Ag0.93Al0.07 film has (gradually) changed again, this time from a 2D to a 3D type of growth.

During the above described morphological evolution, apparently thickness specific defects occur at the surface of the growing film. On the surfaces of the film percolated with holes/grooves (thickness <8 ML) as well as on the surfaces of the laterally continuous films (thickness 14–33 ML) rather irregularly shaped networks of “dark lines” are observed (see Figs. 5(b) and 5(c)). These lines correspond to depressions with a depth of about 0.5 Å below the surface plane. They are likely caused by the local reduction of the surface atomic density along lines of Shockley partial dislocations on (111) planes underneath the surface, and thus laterally separate domains of close-packed layers of different stacking orders (along the surface normal) with a lateral extension of ≈15–20 nm. No network of such depressions is observed on top of the surface of films of thickness >33 MLs (see Fig. 5(d)). Instead, and in contrast with the films of smaller thickness, a significant number of stacking faults on planes inclined with respect to the film surface are observed as straight steps of height of ≈0.8 Å in Fig. 5(d). The observed step height is practically equal to the theoretical value of 1/3 MLs, as caused by the passage of Shockley partial dislocations on {11-1} planes and indeed the segments of sub-monolayer steps are inclined with respect to each other at 60°on the film surface.

Thus, the above STM results are consistent with the HRTEM and XRD analyses presented in Sec. III B: For films of thickness <33, ML planar faults occur practically exclusively on the (111) planes parallel to the surface (cf. the dark lines in Figs. 5(b) and 5(c)), whereas at larger film thicknesses, planar faults occur practically exclusively on {11-1} planes inclined with respect to the film surface at 70.5° (cf. Fig. 5(d)).

As a result of the extensive occurrence of planar faults parallel to the film surface at the initial stage of epitaxial Ag0.93Al0.07(111) film growth (i.e., for thicknesses ≲27 ± 8 ML (6 ± 2 nm)) and the therewith associated incoherent scattering of the incident low energy electrons applied in the LEED analysis, the LEED patterns of films with thicknesses between 3 and 24 MLs contain more diffuse intensity than those observed for the nominal 1.6 ML and 170 ML thick Ag0.93Al0.07 films (see insets in Fig. 5). Upon increasing film thickness, the LEED pattern becomes strongly blurred for film thicknesses of 3.5 MLs (Fig. 5(b)); it then becomes more defined again for the thickness range of 14–24 MLs, as revealed by the emergence of relatively weak, diffuse LEED spots (Fig. 5(c)); and finally it is well defined with intense and relatively sharp spots for films of a thickness >27 ± 8 ML (6 ± 2 nm) (Fig. 5(d)).

It has been suggested that planar faults parallel to the surface are associated with a high density of kinks and corners at surface ledges46 (see also Ref. 47). Indeed, a close inspection of the STM images indicates that at film thicknesses <33 ML, the ledges of islands are less straight as compared to the ledges of the islands at films thickness >33 MLs (cf. Figs. 4(b)–4(f), 5(b) and 5(c) vs. Figs. 4(h) and 5(d)). Furthermore, the observation of an irregular-shaped network of “dark lines,” which result from the presence of Shockley partial dislocations underneath the surface and thus mark the boundaries between already coalesced close-packed layers of different stacking orders, implies that the surface ledges of the terraces/islands exhibit a high density of kinks and corner sites at film thicknesses <33 ML.

2. Interpretation

The observed striking growth mode transitions (3D → 2D → 3D) and, in particular, the distinctive, 2D, layer-by-layer type of growth in the thickness range of 14–24 MLs (3.3–5.7 nm) are closely related to the formation of planar faults parallel to the surface in the initial stage of film growth as will be outlined in detail below.

From an energetic point of view, the film growth morphology is determined by the surface energy of the substrate, γs, the surface energy of the film, γf(h), and the film/substrate interface energy γi(h). The last two quantities depend on the thickness of the epitaxial film, h. Following the approach in Ref. 48, γi(h) comprises the elastic strain energy as well as the contribution arising from the presence of misfit dislocations. The increase of the elastic strain energy with h during epitaxial growth leads to an increase of γi(h) until at a certain h the strain relaxes by the formation of dislocations at the film/substrate interface. γf(h) similarly comprises the thickness dependent electron energy of the film.49 Accordingly, a 3D type of growth is expected if Δγ(h)=γf(h)+γi(h)γs>0, whereas for Δγ(h)0 a 2D (layer-by-layer) type of growth is expected.

From a kinetic point of view, a necessary condition for 2D growth is that the mobility of adatoms on the terraces of the nth layer is high enough so that the adatoms reach the edge of the terrace and do not start to cluster before this nth layer is entirely continuous.50 Provided this is the case, a further condition for 2D growth is that the adatoms are able to descend from the nth to the n–1th layer at edges of the island/terrace. Such downward interlayer mass transport is generally associated with an additional energy barrier. If this barrier is significant at the deposition temperature, adatoms cannot effectively escape from the islands/terraces and this kinetic constraint then results in a 3D type of growth. This is apparently the case for homoepitaxial growth of both Ag/Ag(111) and Al/Al(111) at 300 K51–53 (for homoepitaxial growth Δγ(h) ≈ 0). However, if the barrier at the edge of a terrace can be overcome effectively at the deposition temperature, the thermodynamic constraint indicated above dictates the growth morphology, i.e., the growth morphology depends on the value of Δγ(h). The height of the effective energy barrier for interlayer mass transport depends on intrinsic properties of the growing film system, such as the type of material, crystallographic orientation and shape of the ledge,16,54–56 intrinsic growth strains,3,50 as well as occupation of electronic states.13,57 A variation of such properties as a function of temperature and/or film thickness can induce a change of the growth mode47,52,53,56 (i.e., without that a change of sign for Δγ(h) occurs).

As disclosed in detail by the cross-sectional HRTEM, XRD, and STM analyses (see Secs. III A and III C 1) a very high density of planar faults parallel to the surface is formed in the very initial stage of epitaxial Ag0.93Al0.07 film growth up to a film thickness of 6 ± 2 nm (27 ± 8 MLs). The presence of these planar defects is apparently associated with relatively rough surface ledges (see Sec. III C 1) implying the presence of a high density of kinks and corners at the terrace/island edges. At kinks and corner sites, the energy barrier for interlayer mass transport is reduced16,17 and a high density of kinks and corner sites increases the driving force for adatoms to attach to the surface ledges. Thereby, for film thicknesses below 6 ± 2 nm (27 ± 8 MLs), interlayer transport of adatoms is promoted.

The 3D, Stranski-Krastanov type of growth might be thermodynamically favored (i.e., Δγ(h)>0) initially due to: (i) a relatively large Ag0.93Al0.07(111)/Si(111) interface energy owing to the contribution of the elastic strain energy and/or (ii) differences between the Ag0.93Al0.07(111)/Si(111) surface energy for layers of different thicknesses owing to the spatial confinement of free electrons in the ultrathin metal film (cf. above definition of the surface and the interface energy). Thereby, a film energetically favors thicknesses of a certain integer number of MLs which can only be realized after the deposition of exactly the corresponding amount of material. For the film deposition of other nominal thicknesses, the preferred thickness can only partly be realized and thus a 3D type of growth may occur. Indeed, the observation of Ag0.93Al0.07 islands with a strongly preferred height of 2 MLs can be understood on the basis of the spatial confinement of electrons, similar to the case of pure Ag(111).37–41 

With increasing thickness, the energy difference of films of different thicknesses, due to QSE, decreases,49 thereby reducing the tendency for 3D growth, and intrinsic strains might relax by the formation of dislocations, thereby lowering γi(h) (cf. Ref. 58). As soon as Δγ0, layer-by-layer growth is thermodynamically favored. Significant interlayer mass transport can occur at this stage of growth especially due to the high density of kink and corner sites at surface ledges, as induced by the extensive presence of planar faults parallel to the surface (cf. Sec. III B). As a result, the epitaxial Ag0.93Al0.07(111) film becomes flat and growth proceeds in a 2D type of growth associated with the establishment of films of uniform thickness at integer numbers of MLs in the thickness range of 14 MLs–24 MLs (see Figs. 4(d)–4(f)).

At film thicknesses of ≳27 ± 8 ML (6 ± 2 nm), the density of planar faults on the (111) planes drastically decreases (see Figs. 2(a), 2(c) and 2(d)), which is apparently associated with straightening of the surface ledges and thus a decrease of the density of kink and corner sites. Consequently, the effective height of the energy barrier for interlayer transport increases16,17 and the driving force for adatoms to attach to the surface ledges decreases, thus constraining interlayer mass transport during subsequent deposition. As a result, epitaxial Ag0.93Al0.07 film growth proceeds in a 3D type of growth for thicknesses ≳27 ± 8 ML (≳6 ± 2 nm), associated with an increasingly broader thickness distribution (see Figs. 4(g) and 4(h)).

In any case, an alternation of the interlayer mass transport by intrinsic stresses/strains3,50 can be excluded as the cause of the observed 2D → 3D growth mode transition, since no significant change of the slope of the film-force curve, and thus of the thickness-averaged film stress, occurs in the thickness range around 27 ± 8 ML (6 ± 2 nm) (see Sec. III D).

The observations of a laterally extended worm-like, network of 1 ML thick islands at the nominal thickness of 23.6 ML (see Fig. 4(f)) and of a relatively small density of 1 ML thick islands at nominal thicknesses of 14 and 19 MLs imply a relatively high adatom mobility on the Ag0.93Al0.07(111) terraces (i.e., relatively long diffusion distances; comparable with those on Ag(111) and Al(111) surfaces59). The density of laterally small islands, which provide a high attempt frequency of adatoms to the terrace edges (i.e., a high number of adatoms that reach the edges of a terrace/island per unit of time) and thus intrinsically promote a 2D type of growth, is relatively small. Therefore, the relatively high deposition rate applied in the present study, which potentially could have resulted in the formation of a high density of laterally small islands, likely plays only a minor role for the occurrence of the here observed layer-by-layer type of growth. The decisive factors for the occurrence of the 2D growth of epitaxial Ag0.93Al0.07(111) films are the reduction of the effective diffusion barrier at the step edge and the increased driving force for the attachment of adatoms to the surface ledges by the presence of kinks and corners.

What is the reason for the high density of planar faults at the beginning of growth and its striking reduction to about zero at a film thickness of 6 ± 2 nm (27 ± 8 MLs)? It might be suggested that the extensive occurrence of planar faulting parallel to the film surface, exclusively within the first 27 ± 8 MLs (6 ± 2 nm) of epitaxial Ag0.93Al0.07 film growth, is driven by the (partial) relaxation of an intrinsic (e.g., lattice mismatch) stress component. However, in the following, it will be shown that this reasoning cannot hold and an alternative explanation is provided.

1. Intrinsic stress evolution

The measured film force and the corresponding thickness-averaged in-plane film stress are shown as a function of the film thickness in Fig. 6 for epitaxial Ag0.93Al0.07 film growth on a Si(111)-7×7 surface at 300 K. The film deposition commences with an instantaneous compressive film-force change of Δf ≈ −0.4 N/m up to a nominal thickness of 1 ML. This initial film-force change can be understood as a result of a surface-stress change20,58,60 from that of a Si(111)-7×7 surface to that of a Ag0.93Al0.07(111) surface. Indeed, the measured value approximately equals the difference of the surface stresses of Si(111)-7×7 and Ag(111) surfaces, which equals −0.5 N/m according to Refs. 61 and 62. The film-force change arising from the lattice misfit for the variants OR1 and OR2 (4/3 domain epitaxy) is much smaller, i.e., Δf=3aSi4aAg93Al74aAg93Al7Mh0.04N/m (using: biaxial modulus M ≈ 170 GPa,2 film thickness h = 1 ML, and values of the (interpolated) lattice parameters aSi and aAg0.93Al0.07 from Refs. 2 and 21). During the initial stage of 3D type of growth, up to a nominal film thickness of about 11 ML (2.6 nm), the film force is constant and accordingly the epitaxial Ag0.93Al0.07 film grows stress-free in this thickness range. Any possible mesoscopic intrinsic stress3 is apparently relieved either (i) elastically, at the free edges of the islands, and/or (ii) plastically, by shear-stress driven insertion and glide of (full and partial) dislocations at the base edges of islands (i.e., at locations of largest traction), and/or (iii) by the formation of planar faults on {111} planes (cf. Sec. III C).

FIG. 6.

Evolution of the measured (a) film force and the (b) corresponding thickness-averaged in-plane film stress, both as a function of thickness upon epitaxial growth of an Ag0.93Al0.07(111) film on a Si(111)-7×7 surface at 300 K.

FIG. 6.

Evolution of the measured (a) film force and the (b) corresponding thickness-averaged in-plane film stress, both as a function of thickness upon epitaxial growth of an Ag0.93Al0.07(111) film on a Si(111)-7×7 surface at 300 K.

Close modal

During the subsequent 2D, layer-by-layer type of growth, the overall slope of the film-force curve is negative, and thus an overall compressive thickness-averaged in-plane film stress is present. Evidently, the intrinsic stress does not (completely) relax in this stage of laterally continuous film growth. The overall compressive stress (on top of which a stress oscillation of attenuating amplitude is observed; see below) even increases with increasing film thickness despite the extensive planar faulting at this stage of growth. Moreover, no discontinuity in the overall (increasing) compressive in-plane film stress occurs upon continued deposition, i.e., beyond the thickness where the drastic reduction of the density of planar faults on the (111) planes to practically zero occurs and where the 2D → 3D growth mode transition starts (at a film thickness of 27 ± 8 ML; see Sec. III C 1). The above observations on the stress evolution in the 2D stage and the subsequent 3D stage of film growth strongly suggest that the excessive formation of planar faults parallel to the surface within the first 27 ± 8 MLs (6 ± 2 nm) is not driven by the relief of intrinsic stress (e.g., the lattice-mismatch stress of the 4/3 domain epitaxy of ≈−230 MPa).

The origin of the observed attenuating stress oscillation, with an initial amplitude as large as 20 MPa and a constant period of 2.4 MLs during the 2D film growth regime (11–27 MLs), is not related to a periodic (elastic or plastic) relaxation of intrinsic stresses at the free edges of islands and terraces (cf. above mechanisms (i) and (ii)). In that case, the stress-oscillation period should be equal to the 1 ML-periodic variation of the step density during layer-by-layer type of growth,63,64 which is distinctively different from the observed period of 2.4 ML. The attenuating in-plane stress oscillation is rather caused by a periodic expansion and contraction of the film perpendicular to its surface upon increasing film thickness as induced by the quantum confinement of the free electrons in the ultrathin epitaxial film.15 

2. Electron-energy driven formation of planar faults

For a fcc(111) film with a stacking sequence…CABC along the [111] surface normal, the closed-packed surface layer possesses two nonequivalent three-fold hollow sites, in which arriving adatoms can rest to form the next layer. The deposited adatoms can either occupy the “A” sites, thus continuing the, in the bulk, energetically favored fcc stacking sequence,29 or they can occupy the “B” sites, thus resulting in the formation of a planar fault parallel to the surface, i.e., a local hcp stacking with BCB. The probability that an adatom occupies a specific three-fold hollow site depends on the energy difference of the “A” and “B” sites as well as on the mobility of adatoms, i.e., the possibility to reach the energetically preferred hollow site.34,36 The mobilities of Ag and Al adatoms on the Ag0.93Al0.07(111) surfaces are apparently relatively large at 300 K (see. Sec. III C). Hence, the energy difference of the nonequivalent three-fold hollow sites in the surface layer is the decisive factor controlling the formation of planar faults parallel to the surface during epitaxial Ag0.93Al0.07 film growth. It is thus concluded that the extensive occurrence of planar faults parallel to the surface at the initial stage of film growth is due to a distinctly reduced (or even sign reversed) energy difference of the two types of three-fold hollow sites.

The observed thickness dependence of the stacking-fault energy during epitaxial Ag0.93Al0.07(111) film growth can thus be understood as a consequence of the energy difference of fcc and hcp stacking structures becoming smaller (or even sign reversed) with decreasing film thickness. The Ag-Al system is a so-called “Hume-Rothery system” for which the stability of the occurring phases of bulk intermetallic compounds of different alloy compositions is largely determined by the total electron energy. According to the model of Jones and Mott65,66 (see also recent reviews in Refs. 67 and 68), a compound favors that crystal structure for which its Fermi surface cuts the boundaries of the first Brillouin zone (i.e., where the Fermi wave vector, kF, equals half the reciprocal lattice vector, qhkl). Then, the scattering of electrons with the crystal planes results in a strong reduction of the density of states in the vicinity of the Fermi level and thus reduces the system's electronic energy. The model has been shown to successfully predict the crystal-structural sequence of intermetallic compounds that occurs as a function of the alloy composition for many Hume-Rothery systems (i.e., the occurrence of a certain crystal structure at a specific valence electron per atom ratio) and as well is able to explain the stability of quasicrystals and amorphous metal alloys.

In contrast to bulk samples, where kF is only a function of composition, for ultrathin metal (alloy) films the one-dimensional spatial confinement of the free electrons results in a discretization of the energy states perpendicular to their surfaces and thus induces a significant variation of kF as a function of the film thickness. As a result, the total electron energy of an ultrathin film oscillates with thickness. This variation of the total electron energy can be different for different crystal structures of the same compound/solid solution and thus can cause the relative stabilities of different crystal structures for the same compound/solid solution to vary as a function of thickness. Consequently, the stacking-fault energy that governs the energy difference of an fcc stacking and a hcp stacking for the same compound/solid solution can vary with thickness and thus can lead to the observed extensive occurrence of planar faults during epitaxial Ag0.93Al0.07 growth as discussed here for film thicknesses up to 27 ± 8 MLs (6 ± 2 nm). Indeed, for the Ag0.93Al0.07 solid solution, the energy difference of the (in the bulk stable) fcc structure and the (in the bulk metastable) hcp structure is only about 1 meV per atom in a {111} plane (i.e., approximately half the stacking fault energy)32 This energy difference is of the same order of magnitude as the variation of the electron energy per atom in the (111) surface induced by the quantum confinement of the free electrons, which is typically ≈3–0.1 meV for film thicknesses between 5 and 25 ML.49 With increasing film thickness, kF and thus the stacking-fault energy approach their bulk values. Thus, in accordance with the present experimental observations, the fcc phase (stacking sequence) becomes favored at sufficiently large thicknesses, here larger than 27 ± 8 MLs (6 ± 2 nm).

The above discussion implies that the ultrathin epitaxial Ag0.93Al0.07 film favors (as a whole) at specific film thicknesses, either a hcp or a fcc crystal structure. However, the transformation from the metastable structure to the, at a specific thickness, stable fcc or hcp structure by the repetitive formation and/or removal of stacking faults below the growing film surface is hindered under the parent experimental condition: the thermally activated to and fro glide of Shockley partial dislocations below the growing surface cannot keep pace with the rapidly changing desire to form a fcc or hcp stacking sequence at the here applied relatively high film-growth rate. (It is remarked that the formation or removal of planar faults buried below the surface often requires prolonged annealing of the specimen at relatively high temperatures (see supplementary material and cf. Ref. 70) Only at the surface of the growing film, the atomic mobility is large enough to form or remove planar faults effectively,69 and thus to establish locally the favored (fcc or hcp) stacking sequence of the close-packed layers.

The quantum confinement of free electrons in the ultrathin film, and the therewith, associated with increasing thickness, attenuating variation of the free electron energy, is at the root of both the in-plane stress oscillations and the occurrence of planar faults. However, the magnitude of the variation in the electron energy required to induce these phenomena is very different. Whereas for the occurrence of the observed extensive planar faulting, the bulk stacking fault energy of 1 meV per atom must be significantly reduced, only a very small variation of the electron energy is sufficient to induce the in-plane stress oscillations. For example, the amplitude of the stress oscillation at a thickness of 9 nm is only ∼1 MPa, which corresponds to a strain energy of less than 5 × 10−5 meV per atom. At thicknesses above 6 ± 2 nm, the (reduced and further) attenuating variation of the electron energy is apparently too small to significantly alter the bulk stacking fault energy, but still large enough to cause small expansions and contractions of the film perpendicular to its surface and thus to induce the in-plane stress oscillations.

The microstructural development during ultrathin epitaxial film growth of a binary Ag0.93Al0.07 solid solution on a Si(111)-7×7 surface at 300 K has been investigated by combining HRTEM, XRD, STM, and LEED analyses.

For film thickness <6 ± 2 nm (<27 ± 8 ML), epitaxial Ag0.93Al0.07 film growth is characterized by the extensive formation of planar faults occurring exclusively parallel to the surface, whereas at thicknesses >6 ± 2 nm (>27 ± 8 ML), the epitaxial Ag0.93Al0.07 film grows practically defect free.

As shown by in-situ real-time stress measurements, the occurrence of the extraordinarily high density of planar faults in the vicinity of the Si substrate interface is not (predominantly) driven by the relief of an intrinsic stress component, i.e., reduction of strain energy. The observed striking gradient in the planar-fault density parallel to the surface is indicative for a significant alternation of the stacking-fault energy as a function of the thickness in the ultrathin film range. The spatial confinement of the free electrons in the surface-normal direction of the ultrathin metal alloy film causes a varying relative stability of fcc and hcp crystal structures as a function of the film thickness; a quantum confinement effect. The high frequency of the change of desire for a fcc or hcp stacking of the whole film during growth is incompatible with the kinetically limited, by thermal activation, to and fro glide of the Shockley partial dislocations along the close-packed planes as required for the changes of the stacking order. Only at the surface of the film, the atomic mobility is high enough to establish the desired stacking at any time during film growth. As a consequence, an extraordinarily high density of planar faults is established at the initial stage of growth of the ultrathin alloy film.

As shown by detailed STM analysis, the extraordinarily high density of planar faults parallel to the surface for thicknesses <6 ± 2 nm (<27 ± 8 ML) is associated with rough surface ledges and thereby with a high density of kinks and corners sites. These kink and corner sites reduce the effective energy barrier for interlayer mass transport at the step edges and increase the driving force for adatoms to attach to the surface ledges for film thicknesses below 6 ± 2 nm (27 ± 8 ML), thus promoting interlayer transport of adatoms. As a result, epitaxial Ag0.93Al0.07(111) film growth proceeds in a 2D type of growth, associated with the establishment of films of uniform thickness at integer numbers of MLs in the thickness range of 14 MLs–24 MLs.

At film thicknesses of ≳27 ± 8 ML (6 ± 2 nm), the density of planar faults on (111) planes drastically decreases and the ledges of terraces and islands at the film surface straighten. As a result, the effective height of the energy barrier at the step edge increases and the driving force for adatoms to attach to the surface ledges decreases, thus constraining interlayer mass transport during continued film growth. Consequently, the growth mode of the epitaxial Ag0.93Al0.07 film growth changes to a 3D type of growth for thicknesses ≳27 ± 8 ML (≳6 ± 2 nm) leading to an increasingly broader thickness distribution with increasing thickness.

See supplementary material for microstructural characterization of the epitaxial Ag0.93Al0.07 film by plane-view TEM, the investigation of the thermal stability of 5 nm thick Ag0.93Al0.07 films and for additional results on the microstructure and stress evolution during the growth of Ag1−xAlx films of different compositions with x = 0, 0.03, 0.06, 0.07, and 1.

The authors are grateful to B. Fenk and U. Salzberger for the preparation of the TEM foils, to W. Sigle for performing the TEM analysis and to Dr. G. Richter for invaluable discussion.

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Supplementary Material