Energetics of Ge nucleation on SiO2 and implications for selective epitaxial growth

We have measured the time evolution of Ge nucleation density on SiO₂ over a temperature range of 673–973 K and deposition rates from 5.1 × 10¹³ atoms/cm² s (5 ML/min) to 6.9 × 10¹⁴ atoms/cm² s (65 ML/min) during molecular beam epitaxy. The governing equations from mean-field theory that describe surface energetics and saturation nucleation density are used to determine the size and binding energy of the critical Ge nucleus and the activation energy for Ge surface diffusion on SiO₂. The critical nucleus size is found to be a single Ge atom over substrate temperatures from 673 to 773 K, whereas a three-atom nucleus is found to be the critical size over substrate temperatures from 773 to 973 K. We have previously reported 0.44 ± 0.03 eV for the Ge desorption activation energy from SiO₂. This value, in conjunction with the saturation nucleation density as a function of substrate temperature, is used to determine that the activation energy for surface diffusion is 0.24 ± 0.05 eV, and the binding energy of the three-atom nucleus is 3.7 ± 0.1 eV. The values of the activation energy for desorption and surface diffusion are in good agreement with previous experiments of metals and semiconductors on insulating substrates. The small desorption and surface diffusion activation barriers predict that selective growth occurring on window-patterned samples is by direct impingement of Ge onto Si and ready desorption of Ge from SiO₂. This prediction is confirmed by the small integral condensation coefficient for Ge on SiO₂ and two key observations of nucleation behavior on the window-patterned samples. The first observation is the lack of nucleation exclusion zones around the windows, and second is the independence of the random Ge nucleation density on patterned versus unpatterned oxide surfaces. We also present the Ge nucleation density as a function of substrate temperature and deposition rate to demarcate selective growth conditions for Ge on Si with a window-patterned SiO₂ mask.