Mechanism for epitaxial breakdown during low-temperature Ge(001) molecular beam epitaxy

Abstract

A combination of in situ and post-deposition experiments were designed to probe surface roughening pathways leading to epitaxial breakdown during low-temperature ${(T}_{s}=95--190\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{C})$ growth of Ge(001) by molecular beam epitaxy (MBE). We demonstrate that epitaxial breakdown in these experiments is not controlled by background hydrogen adsorption or gradual defect accumulation as previously suggested, but is a growth-mode transition driven by kinetic surface roughening. Ge(001) layers grown at ${T}_{s}\ensuremath{\gtrsim}170\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{C}$ remain fully epitaxial to thicknesses $h>1.6$ \ensuremath{\mu}m, while deposition at ${T}_{s}<170\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{C}$ leads to a locally abrupt transition from epitaxial to amorphous growth at critical film thicknesses ${h}_{2}{(T}_{s}).$ Surface morphology during low-temperature Ge(001) MBE evolves via the formation of a periodic array of self-organized round growth mounds which, for deposition at ${T}_{s}>115\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{C},$ transform to a pyramidal shape with square bases having edges aligned along 〈100〉 directions. Surface widths w and in-plane coherence lengths d increase monotonically with film thickness h at a temperature-dependent rate. As $\stackrel{\ensuremath{\rightarrow}}{h}{h}_{1}{(T}_{s}),$ defined as the onset of epitaxial breakdown, deep cusps bounded by {111} facets form at the base of interisland trenches and we show that epitaxial breakdown is initiated on these facets as the surface roughness reaches a critical ${T}_{s}$-independent aspect ratio $w/d\ensuremath{\simeq}0.02.$ ${h}_{1}{(T}_{s})$ and ${h}_{2}{(T}_{s})$ follow relationships ${h}_{1(2)}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}{E}_{1(2)}{/kT}_{s}),$ where ${E}_{1}$ is 0.61 eV and ${E}_{2}=0.48$ eV. ${E}_{1}$ is approximately equal to the Ge adatom diffusion barrier on Ge(001) while ${(E}_{1}\ensuremath{-}{E}_{2})=0.13$ eV is the free energy difference between crystalline and amorphous Ge. We summarize our results in a microstructural phase map vs ${T}_{s}$ and h, and propose an atomistic growth model to explain the epitaxial to amorphous phase transition.