Interfacial elastic properties between $a\text{-Si}$ and $c\text{-Si}$

Interfaces between different media represent the most common structure in composite and complex materials, e.g., with applications in microelectronics and photovoltaics. We analyze the elastic properties of the $a\text{-Si/}c\text{-Si}$ interface, which involves two completely different atomic structures. We prove that the continuum approach and the atomistic simulation are consistent if atomic-scale elastic fields are properly averaged.

Figure 1

(Color online) Atomistic structure of the $\left(a\text{-Si/}c\text{-Si}\right)$ interface. The reference frame $\left(x,y,z\right)$ and the basis $\left(\vec{s},\vec{t},\vec{n}\right)$ have been represented.

Figure 2

(Color online) Longitudinal $\left(T_{zz}\right)$ and transverse $\left(T_{xx}\right)$ stress-strain relations for the $a\text{-Si}$ (top panel) and $c\text{-Si}$ (bottom panel), obtained with molecular-dynamics simulations.

Figure 3

(Color online) Perturbation to the imposed displacement after (a) relaxation, (b) transverse, and (c) longitudinal stress versus the $z$ coordinate. For stress data, the simple moving average (SMA) has been considered to reduce the intensity of the fluctuations (dashed lines for ${\overline{\overline{T}}}_{zz}$ and ${\overline{\overline{T}}}_{yy}$, solid line for ${\overline{\overline{T}}}_{xx}$).

Figure 4

(Color online) Perturbation to the imposed displacement obtained through relaxation for nine different values of the imposed strain (ranging from ${ϵ}_{zz}=0.02$ to ${ϵ}_{zz}=0.1$).