P.M. Stoop

Misfit accommodation by compliant substrates

Experimentally it has been found that twist bonding a thin layer of epitaxially grown material to a thick substrate of the same material has the properties of being compliant with respect to the growth of a heteroepitaxial layer onto the thin layer. The benefit of the compliant substrate is that the heteroepitaxial layer is of much higher perfection when compared to the same growth but on a bulk substrate, primarily due to a very low density of threading dislocations present in the heteroepitaxial deposit. This concept has been investigated experimentally and discussed in terms of what is the operative mechanism of the compliant substrate. However, there is still much to be explained about the mechanism by which the compliant substrate accommodates misfit between itself and the heteroepitaxial layer. How the structure of the interface between the compliant substrate and the thick substrate can be tailored to derive the maximal benefit in the epilayer is the subject of the present article. The importance o...

Structural ledges in interphase boundaries

This article addresses the properties of stepped misfitting interfaces and their energetic preference to planar misfitting interfaces. It highlights: (a) the purely geometrical or rigidlike, (b) the rigid (unrelaxed) energetic, and (c) the relaxed energetic properties of stepped interfaces. In (a), we address (1) the accommodation of misfit by the step or ledge mode through the cancellation of the mismatch, that builds up along a terrace, by the forwardpattern advance effected by a step,i.e., the relative displacement of atomic patterns on either side of the interface as observed in crossing a structural ledge along the interface, (2) the sideways (shear) pattern advance which seems to be energetically undesirable, (3) the need for tilt-type misfit dislocations to accommodate the misfit normal to the interface, and (4) the fact that at {III}fcc(face-centered cubic)/{110}bcc(body-centered cubic) interfaces with rhombic symmetries, the misfits, as well as the pattern advances, are interrelated through the ratior = b/a of nearest-neighbor distances in the crystals. In (b), we exploit the rigid model approach that (1) yields ideality criteria for minimum energy and provides energetic justification for the step mode of misfit accommodation, (2) confirms that the average terrace widthl[inx defined by this mode also meets the condition for positive energy gain, and (3) defines the upper and lower energy bounds to provide a perspective of the system energetics. In (c), the foregoing considerations are refined by a transition to the harmonic (elastic) model to yield (1) the dependence of the mean energy per atom of a stepped interface on interfacial misfit and pattern advance, as well as the dependence of the mean energy per atom of a planar interface on misfit, (2) expressions for the stresses related to the atomic interaction between opposing terraces, (3) atomic displacements that might be probed by modern analytical techniques, and (4) resolved shear stresses and normal stresses that may facilitate the formation of glide dislocations in the presence of applied stresses. The boundary in a two-dimensional space—spanned by misfit and pattern advance—between regions where stepped interfaces are more stable than planar ones has been determined, suggesting that a critical misfit exists above which only planar interfaces are stable. Whereas the resolved shear stress related to the formation of structural ledges may facilitate the formation of dislocations in the presence of a subcritical applied stress, the corresponding displacements (bending) of atomic planes are probably observable only with strain contrast electron microscopy techniques.

Role of misfit strain and proximity in epigrowth modes I: Strong epilayer-substrate interaction

Abstract The objectives of this study are to assess the effects of misfit strain and substrate proximity on the evolution of growth modes — emphasizing the transition to Stranski-Krastanov (SK) growth — during thickening of a growing epilayer. The study comprises a generalization of Bauers equilibrium criteria and their application to the growth of Cu and Ni on W(110) — a strong interacting substrate — using embedded-atom methods (EAM) calculations. It is suggested that proximity is propagated by epilayer-substrate bond strength and interlayer relaxation, and that the proximity range is strongly influenced by cutoffs which model the limited range of electronic induced atom-atom interaction. The study shows that the contribution of misfit strain energy to shaping growth modes is nonlinear and indeed vanishes outside the proximity range. The predictions are in agreement with the observed Frank-van der Merwe (FM) growth of the first monolayer (ML) and a SK transition thereafter. EAM calculations also confirm the anticipated relative strengths of bonding. Calculated activation energies of surface migration suggest that adatoms are significantly more mobile on top of thin epilayers than on the bare strong interacting substrate and that this will also strongly influence equilibration kinetics.

Elastic and structural properties of f.c.c. {111} thin films part 2. A monolayer on a {110} b.c.c. substrate☆

Abstract Simple qualitative considerations suggest that the inherent mechanical properties—equilibrium structure and elastic constants—of thin epilayers are influenced by proximity effects. The computational effort to calculate these properties, using any form of atomic interaction, becomes enormous when epilayer and substrate are discommensurate and the repeat period is large—an important feature of misfit strain relief in epilayers. A procedure is proposed by which this problem can be overcome for an epimonolayer, and can be extended to multilayers. The procedure involves the following assumptions: (i) the mechanical behavior of the monolayer (ML) is governed by the principle of minimum energy, the average energy per ML atom being minimized in this case, (ii) the field of interaction emanating from the substrate is periodic (with the periodicity of the substrate surface) within the plane of the ML, (iii) the substrate field can be mapped by calculation involving the translation of the ML—as if “rigid”, having registry dimensions and allowing for height equilibration—on the substrate surface, (iv) the ML may be constrained to its average (constant) equilibrium height with negligible discrepancies in the energy. The procedure is demonstrated, and numerically justified, by its application to {111} MLs of Ni and Cu in Nishiyama-Wassermann orientation on W {110}, using embedded-atom-method potentials. The calculations produce convincing evidence to substantiate the validity of the procedure, showing that the contribution of the substrate to the embedding energy of ML atoms can be fairly accurately described in terms of its average electron density in the ML plane, the effect of the periodic oscillations in the electron density being negligible. A similar procedure is valid for the embedding of substrate atoms. The application to Ni and Cu on W shows that proximity effects are drastic: the in-plane elastic constants of a supported ML, an ML in the crystal interior and a free standing ML are respectively and crudely in the ratio 1:1.5:2.5. Proximity effects are likewise important in anharmonicity.

Elastic constants of fcc 〈111〉 films 1. Free monolayers

Abstract The aim of the investigation is to calculate the properties of free-standing strained fcc monolayers (MLs): their equilibrium lattice constants, their anisotropic cubic stiffness constants and the influence of anharmonocity. Embedded atom methods (EAMs), employing bulk-fitting parameters, were used to model the atomic interactions. The calculations, which are conducted for films of Ni and Cu bounded by close-packed (cp) 〈111〉 planes, and constrained to remain plane, predict (a) that EAMs yield — at least for Ni and Cu — fairly accurate values of anisotropic cubic stiffness constants for the bulk and hopefully also for thin films, including MLs, (b) that the equilibrium lattice constants of free-standing MLs are less than those of the bulk by a few percent, (c) that the stiffness constants of such MLs at the ML equilibrium configuration are appreciably different from those of the bulk, (d) that the strain energy per atom at 25% strain for a ML is about twice that for the bulk and (e) that anharmonicity reduces the strain energy per atom at 25% strain by about a factor of two, as compared with the value based on the harmonic model. The present results are in good agreement with comparable previous results for Cu.

The formation of misfit dislocations by climb in pseudomorphic monolayers

Abstract We have used a hybrid Lennard-Jones/Frank-van der Merwe (LJ-FM) model and an embedded-atom-method (EAM) to analyse the energetics of an isolated adatom A, which is adsorbed at a second-layer lattice point above a pseudomorphic (ps) monolayer (ML) of Ni or Co on a Mo{110} substrate, and is allowed to climb down quasi-statically into the ps ML where it constitutes a critical nucleus for the formation of a misfit dislocation (MD). In the LJ-FM approach misfit could be introduced in a somewhat artificial, but adequate way to predict tendencies. The LJ-FM analysis showed (i) that a Ni adatom has a well defined stable second-layer position when Mo is replaced by bcc Ni, (ii) that the equilibrium position is less well defined with Mo substrate even with imposed zero misfit and (iii) that as the mistfit with Mo becomes more negative, approaching the Ni and Co misfits of about −20%, a flat energy trough develops which allows spontaneous access to the interior of the ps ML. In the EAM approach only Co reaches, more or less, the interior of the ps ML; in the case of Ni, and Cu which was also considered, strong core repulsion of substrate adatoms limits the downward climb to only 1 A. Clearly, negative (positive) misfit of large magnitude, is a prerequisite to the nucleation of heavy (light) MDs by climb in a process which is facilitated by strong (weak) absorbate-substrate bonding.

Cu double layer on Mo(110) : phase transition

Abstract This investigation concerns the energetics of a Cu double layer (DL) on Mo(110) phase transition involving: one-dimensional (1D) row matching, a rotation of the matching direction through 90°, a highly distorted high temperature (HT) substrate stabilized polymorphic phase, comprising two identical (100) Cu monolayers (MLs), and a low temperature (LT) phase, comprising a pseudomorphic (ps) ML below and an almost close-packed (cp) ML above. A primary goal here is to show that the zero temperature internal energies of the two phases differ so little that the difference Δ e HL could be overcome by temperature dependent free energy contributions. Quantification of the analytical results, using embedded-atom (EAM) potentials and averaging procedures of periodic quantities, confirmed that the difference Δ e HL is small. Crude estimates point towards atomic vibration frequency differences as the most likely candidate to generate the T-dependent free energy to overcome the gap Δ e HL . The investigation otherwise also yielded results of wider interest.