Stochastic equation for the morphological evolution of heteroepitaxial thin films

A stochastic partial differential equation for the morphological evolution of strained epitaxial films is derived from atomistic aggregation kinetics. The transition rules and rates are based on a model that incorporates the effects of strain through environment-dependent energy barriers to adatom detachment. Comparisons with previous approaches based on continuum elasticity provide an atomistic interpretation of the governing equation for heteroepitaxial thin films.

Figure 1

For the indicated local configurations of the shaded particle, $E_N^{\left(a\right)}<E_N^{(b,c)}$ and $E_N^{\left(a\right)}>E_N^{\left(d\right)}$ for $E_N^{(1,0,0)}(0,0,0)>0$ and $E_N^{(0,0,1)}(0,0,0)<0$.

Figure 2

Heights $u$ (a),(b) and two-point correlation functions $G$ (c),(d) obtained from the linearized fourth-order equation (19) at 0.5 ML for a system of size $60a_{\Vert }\times 60a_{\Vert }$ at $T=650\mathrm{K}$ (a),(c) and $T=750\mathrm{K}$ (b),(d) with $E_S=1.3\mathrm{eV}$, $E_N(0,0,0)=0.3\mathrm{eV}$, $E_N^{(1,0,0)}(0,0,0)=0.01\mathrm{eV}$, and $E_N^{(0,0,1)}(0,0,0)=-0.004\mathrm{eV}$. The ranges of $u$ and $G$, in units of $a_{\perp }$, are (a) $-0.6⩽u⩽1.5$, (b) $-0.3⩽u⩽1.5$, (c) $0⩽G⩽0.4$, and (d) $0⩽G⩽0.5$.