Anisotropy and Morphology of Strained III-V Heteroepitaxial Films

Strained coherent heteroepitaxy of III-V semiconductor films such as In$_x$Ga$_{1-x}$As/GaAs has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectronic devices. Crystal symmetry can have a large effect on the morphology of these films and their spatial order. Often the formation of group IV strained heterostructures such as Ge deposited on Si is analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability. However, the governing dynamics of III-V 3D heterostructure formation has different symmetry and is more anisotropic. The additional anisotropy appears in both the surface energy and the diffusivity. Here, the resulting anisotropic governing dynamics are studied to linear order. The resulting possible film morphologies are compared with experimentally observed In$_x$Ga$_{1-x}$As/GaAs films. Notably it is found that surface-energy anisotropy plays a role at least as important as surface diffusion anisotropy if not more so, in contrast to previous suppositions.Comment: 2 figures version includes one corrected inline equatio

The thermodynamics and roughening of solid-solid interfaces

The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the interface. The solids are allowed to exchange mass by transforming one solid into the other, thermodynamic relations for the transformation of a mass element are derived and a linear stability analysis of the interface is carried out. The stability is shown to depend on the order of the phase transition occurring at the interface. Numerical simulations are performed in the non-linear regime to investigate the evolution and roughening of the interface. It is shown that even small contrasts in the referential densities of the solids may lead to the formation of finger like structures aligned with the principal direction of the far field stress.Comment: (24 pages, 8 figures; V2: added figures, text revisions

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure

Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Trapped and excited w modes of stars with a phase transition and R>=5M

The trapped $w$-modes of stars with a first order phase transition (a density discontinuity) are computed and the excitation of some of the modes of these stars by a perturbing shell is investigated. Attention is restricted to odd parity (``axial'') $w$-modes. With $R$ the radius of the star, $M$ its mass, $R_{i}$ the radius of the inner core and $M_{i}$ the mass of such core, it is shown that stars with $R/M\geq 5$ can have several trapped $w$-modes, as long as $R_{i}/M_{i}<2.6$. Excitation of the least damped $w$-mode is confirmed for a few models. All of these stars can only exist however, for values of the ratio between the densities of the two phases, greater than $\sim 46$. We also show that stars with a phase transition and a given value of $R/M$ can have far more trapped modes than a homogeneous single density star with the same value of $R/M$, provided both $R/M$ and $R_{i}/M_{i}$ are smaller than 3. If the phase transition is very fast, most of the stars with trapped modes are unstable to radial oscillations. We compute the time of instability, and find it to be comparable to the damping of the $w$-mode excited in most cases where $w$-mode excitation is likely. If on the other hand the phase transition is slow, all the stars are stable to radial oscillations.Comment: To appear in Physical Review

Shape Transition in the Epitaxial Growth of Gold Silicide in Au Thin Films on Si(111)

Growth of epitaxial gold silicide islands on bromine-passivated Si(111) substrates has been studied by optical and electron microscopy, electron probe micro analysis and helium ion backscattering. The islands grow in the shape of equilateral triangles up to a critical size beyond which the symmetry of the structure is broken, resulting in a shape transition from triangle to trapezoid. The island edges are aligned along $Si[110]$ directions. We have observed elongated islands with aspect ratios as large as 8:1. These islands, instead of growing along three equivalent [110] directions on the Si(111) substrate, grow only along one preferential direction. This has been attributed to the vicinality of the substrate surface.Comment: revtex version 3.0, 11 pages 4 figures available on request from [email protected] - IP/BBSR/93-6

Nanogrids and Beehive-Like Nanostructures Formed by Plasma Etching the Self-Organized SiGe Islands

A lithography-free method for fabricating the nanogrids and quasi-beehive nanostructures on Si substrates is developed. It combines sequential treatments of thermal annealing with reactive ion etching (RIE) on SiGe thin films grown on (100)-Si substrates. The SiGe thin films deposited by ultrahigh vacuum chemical vapor deposition form self-assembled nanoislands via the strain-induced surface roughening (Asaro-Tiller-Grinfeld instability) during thermal annealing, which, in turn, serve as patterned sacrifice regions for subsequent RIE process carried out for fabricating nanogrids and beehive-like nanostructures on Si substrates. The scanning electron microscopy and atomic force microscopy observations confirmed that the resultant pattern of the obtained structures can be manipulated by tuning the treatment conditions, suggesting an interesting alternative route of producing self-organized nanostructures

Stress-driven instability in growing multilayer films

We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system recursively in terms of that of the old states of the buried layers. In turn, we use the result for the elastic state to derive the morphological evolution equation of surface profile to first order of perturbations, with the solution explicitly expressed by the growth conditions and material parameters of all the deposited layers. We apply these results to two kinds of multilayer structures. One is the alternating tensile/compressive multilayer structure, for which we determine the effective stability properties, including the effect of varying surface mobility in different layers, its interplay with the global misfit of the multilayer film, and the influence of asymmetric structure of compressive and tensile layers on the system stability. The nature of the asymmetry properties found in stability diagrams is in agreement with experimental observations. The other multilayer structure that we study is one composed of stacked strained/spacer layers. We also calculate the kinetic critical thickness for the onset of morphological instability and obtain its reduction and saturation as number of deposited layers increases, which is consistent with recent experimental results. Compared to the single-layer film growth, the behavior of kinetic critical thickness shows deviations for upper strained layers.Comment: 27 pages, 11 figures; Phys. Rev. B, in pres

Epitaxial growth in dislocation-free strained alloy films: Morphological and compositional instabilities

The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposition. We consider some realistic factors of epitaxial growth, in particular the composition dependence of elastic moduli and the coupling between top surface and underlying bulk of the film. The interplay of these factors leads to new stability results. In addition to the stability diagrams both above and below the coherent spinodal temperature, we also calculate the kinetic critical thickness for the onset of instability as well as its scaling behavior with respect to misfit strain and deposition rate. We apply our results to some real growth systems and discuss the implications related to some recent experimental observations.Comment: 26 pages, 13 eps figure

Morphology of epitaxial core-shell nanowires

We analyze the morphological stability against azimuthal, axial, and general helical perturbations for epitaxial core-shell nanowires in the growth regimes limited by either surface diffusion or evaporation-condensation surface kinetics. For both regimes, we find that geometric parameters (i.e., core radius and shell thickness) play a central role in determining whether the nanowire remains cylindrical or its shell breaks up into epitaxial islands similar to those observed during Stranski-Krastanow growth in thin epilayers. The combination of small cores and rapid growth of the shell emerge as key ingredients for stable shell growth. Our results provide an explanation for the different core-shell morphologies reported in the Si-Ge system experimentally, and also identify a growth-induced intrinsic mechanism for the formation of helical nanowires.Comment: In press, Nano Letters (7 pages, 4 figures