Slope Selection and Coarsening in Molecular Beam Epitaxy

Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

“…Importantly, the corresponding coarsening exponent of the power law for the growth of λ and w was found experimentally to depend on the symmetry of the surface. For example, the experimental value of the coarsening exponent for growth on (001) surfaces is close to 1/4 in agreement with simulations [16,17], whereas the exponent reported for the growth on (111) surfaces is close to 1/3 [15]. However, although there has been extensive experimental work, until recently there has not been sufficient understanding of how the large scale surface morphology coarsens in MBE and why the exponents have these values.…”

“…The dislocation in Fig. 23(b) moves to the right, as observed in simulations [3,16], and this motion is essential for the overall surface dynamics as the primary mechanism of the rippled state surface coarsening. Thus as the dislocation in Fig.…”

“…12 and 22 here. Due to dislocations, ripples only have a finite coherence length ξ, corresponding to the typical separation between the dislocations along a ripple [3,16]. Importantly, the simulations show that the Rippled state period λ and the ripple amplitude w (∼ surface roughness) grow via a coarsening process involving the motion and annihilations of these dislocations [25,26].…”

Thin film epitaxy with or without slope selection

“…(1.2) predicts β = n = 1/3; without slope selection, Eq. (1.1) predicts β = 1/2 and n = 1/4 [10,15,21,23,25,32]. We refer to the recent work [20] for a discussion on mathematical justification of such predictions.…”

“…To determine j ES , we recall the argument in [15,32]. For simplicity, consider the step-flow growth of a thin film with an average step width l. Let m = |∇h| be the macroscopic surface slope and take the lattice parameter to be the unity.…”