Self-Assembled Superlattice by Spinodal Decomposition during Growth

We examine the dynamics of alloy growth by vapor deposition and bulk diffusion, predicting a new type of self-organized growth. When material is deposited at a composition unstable against spinodal decomposition, we find three distinct regimes depending on growth rate. Intermediate growth rates lead to spontaneous formation of a superlattice with layers parallel to the surface. Slow growth leads to more complex three-dimensional decomposition. For fast growth, the alloy composition remains uniform near the surface, with a composition wave propagating up from the interface.

Figure 1

Composition profiles along the growth direction for different deposition rates. The substrate is to the left, and the curves end at the growing surface on the right. The figure shows two types of composition modulations. (a) At scaled deposition rate $f=0.25$, the composition modulations do not reach a steady state. The propagation velocity of the composition modulations is smaller than the velocity of the growing surface. Thus, the growing surface outruns the oscillations. At slower deposition rates (b) $f=0.05$ and (c) $f=0.00625$, the composition modulations reach a steady state.

Figure 2

The lower curve shows the wavelength $L$ of the composition modulations, in units of the interaction potential range $R$. One can see that the wavelength increases with the inverse deposition rate $f^{-1}$ (shown in units of $4k{T}_{c}D/R$). The upper curve shows the amplitude of composition modulations as a function of the inverse deposition rate, $f^{-1}$. The two dashed lines separate the three different growth regimes discussed in the text.

Figure 3

Evolution of the composition profile during growth, for growth rates (a) $f=0.00625$, and (b) $f=0.1$. At each successive time, the surface has advanced, so the curve extends further to the right.

Figure 4

Growth rate $\mathbf{(}G=d[\ln |c_q({\zeta }_s)|]/d{\zeta }_s\mathbf{)}$ curves of a transverse perturbation for different deposition rates ($f$) as a function of the dimensionless wave number $qR$. Our detailed numerical investigations showed that, for intermediate deposition rates ($f_{\mathrm{st}}=0.016<f<f_c=0.13$), the 1D patterns are stable in three dimensions.