Continuum model of surface roughening and epitaxial breakdown during low-temperature Ge(001) molecular beam epitaxy

Abstract

Numerical simulations based on a discrete model describing step edge motion are used to compute the surface morphological evolution of Ge(001) layers deposited by low-temperature (Ts = 45–230 °C) molecular beam epitaxy and to probe the relationship between surface roughening and the onset of epitaxial breakdown—the abrupt growth mode transition from epitaxial to amorphous—at temperature-dependent critical film thicknesses h1(Ts). Computed surface widths w and in-plane coherence lengths d as a function of layer thickness h exhibit good agreement with experimental values. Inspired by experimental results indicating that epitaxial breakdown is initiated at facetted interisland trenches as the surface roughness reaches a Ts-independent overall aspect ratio, we show that simulated data for w/d = 0.03 correspond to thicknesses h1 ∝ exp (−E1/kTs) with E1 = 0.63 eV, a value equal to the Ge adatom diffusion activation energy on Ge(001). Simulated h1 values agree well with experimental data. Above a critical growth temperature of 170 °C, computed w/d values saturate at large film thicknesses, never reaching the critical aspect ratio w/d = 0.03. Thus, the model also predicts that epitaxial breakdown does not occur for Ts > 170 °C as observed experimentally.