Reverse Epitaxy of Ge: Ordered and Faceted Surface Patterns

Normal incidence ion irradiation at elevated temperatures, when amorphization is prevented, induces novel nanoscale patterns of crystalline structures on elemental semiconductors by a reverse epitaxial growth mechanism: on Ge surfaces irradiation at temperatures above the recrystallization temperature of $250°\mathrm{C}$ leads to self-organized patterns of inverse pyramids. Checkerboard patterns with fourfold symmetry evolve on the Ge (100) surface, whereas on the Ge (111) surface, isotropic patterns with a sixfold symmetry emerge. After high-fluence irradiations, these patterns exhibit well-developed facets. A deterministic nonlinear continuum equation accounting for the effective surface currents due to an Ehrlich-Schwoebel barrier for diffusing vacancies reproduces remarkably well our experimental observations.

Figure 1

AFM height images of Ge (100) surfaces after ion irradiation with an ion fluence of $3\times {10}^{18}{\mathrm{cm}}^{-2}$ at temperatures of $230°\mathrm{C}$, $260°\mathrm{C}$, $350°\mathrm{C}$, and $430°\mathrm{C}$. The $⟨100⟩$ crystal directions are marked by arrows. (a) $z=8\mathrm{nm}$; (b) $z=38\mathrm{nm}$; (c) $z=38\mathrm{nm}$; (d) $z=8\mathrm{nm}$.

Figure 2

TEM images of Ge surfaces in cross section irradiated at temperatures of (a) $230°\mathrm{C}$ and (b) $260°\mathrm{C}$. In (a) a 2.6 nm thick amorphous layer can be identified, whereas in (b) no amorphous layer is visible. In Fig. 2b right the angle of the facet is shown with the horizontal line parallel to the (100) surface.

Figure 3

(a) AFM images of Ge (100) surfaces irradiated at $350°\mathrm{C}$ and fluences of $1\times {10}^{17}{\mathrm{cm}}^{-2}$, $1\times {10}^{18}{\mathrm{cm}}^{-2}$, and $1\times {10}^{19}{\mathrm{cm}}^{-2}$. (b) Snapshots of the numerical integration of the continuum equation with $ϵ=1$, $\kappa =4$, $\sigma =-1$, and $\delta =25$. Above the images the two-dimensional FFT (left) and the two-dimensional angle distribution (right) are shown.

Figure 4

Roughness and characteristic length of surface patterns on Ge(100) as a function of ion fluence. The lines represent power law fits to the data. The fluence $\Phi$ is given by ion flux times irradiation time.