Investigation on Ge surface diffusion via growing Ge quantum dots on top of Si pillars

We report on a simple and intuitionistic experimental method to quantitatively measure surface diffusion lengths of Ge adatoms on Si(001) substrates and its activation energy Ea, which is achieved by growing Ge quantum dots (QDs) on top surfaces of Si pillars with different radii and taking an advantage of preferential nucleation and growth of Ge QDs at the top surface edge of the pillars. Diffusion length of Ge adatom can directly be measured and determined by the radius of the pillar below which no QDs will nucleate and grow at the central region of the top surface of the Si pillar. With a growth rate v fixed at 0.1 Å/s, by changing the growth temperature, the diffusion lengths at different temperatures would be obtained. Arrhenius plot of diffusion length as a function of growth temperature gives the value of Ea of 1.37 eV. Likewise, with a growth rate v fixed at 0.05 Å/s, the Ea value is obtained to be 1.38 eV. Two Ea values agree well with each other, implying that the method is reliable and self-consistent. Moreover, for a fixed growth temperature, the surface diffusion lengths are found to be directly proportional to 1/ν. It also agrees well with the theoretical prediction, further demonstrating the reliability of the method.