Stress-driven instability in growing multilayer films

Abstract

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.

Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

“…However, the limitation of small length and time scales addressed in these atomistic methods leads to large computational demands and hence the restriction of system size and evolution time range that can be accessed. Such limitation can be overcome via continuum modeling methods, including continuum elasticity theory used in strained film growth [5,[11][12][13][14][15][16][17] and the well-known phase field models that have been applied to a wide range of areas such as crystal growth, nucleation, phase separation, solidification, defect dynamics, etc. [18][19][20][21][22].…”

Intermediate States at Structural Phase Transition: Model with a One-Component Order Parameter Coupled to Strains

“…(3) If a solid is compressed along one of the principal axes, the tetragonal extension along the compression axis becomes energetically unfavorable [2,19], leading to a square-to-rectangle transition perpendicular to the axis. Then the transition could be described by a 2D theory with a one-component order parameter, although the lateral elastic deformations are much more complicated in real epitaxial films than treated in this paper [20]. (4) In its present form, our theory cannot explain the 3D experiments [3,4,5,6,7,8,9].…”

“…Such phase transitions would be realized under uniaxial compression [2,19]. However, in real epitaxial films, analyzing elastic effects is difficult, because the displacement is fixed at the film-substrate boundary and the stress is free at the film-air interface [20].…”

Stress-driven interfacial instability of a bilayer structure: The interaction between free surface and interface

“…Lu et al (2004) discussed the effect of the substrate thickness on the interfacial stability in an epitaxially strained film deposited on a substrate. Huang and Desai (2003) investigated the stress-driven morphological instability of epitaxially growing multilayer films. Recently, Yang and Song (2005a,b) investigated the effect of electromechanical interaction on the stability of a planar surface.…”