Application of negative heavy ions, alleviating surface charging on insulators, enables us to conduct low-energy and high-flux implantation, and leads to a well-defined tool to fabricate near-surface nanostructures. Negative Cu ions of 60 keV, at high doses, have generated nanocrystals in amorphous(a-)SiO2 with a size (∼10 nm) suitable for nonlinear optical devices. The kinetic processes, inside the solid and at the surface, are studied by cross-sectional TEM and tapping AFM, respectively. In a-SiO2, nanoparticles spontaneously grow with dose rate, being controlled by the surface tension and radiation-induced diffusion. Furthermore, the nanospheres give rise to a two-dimensional (2D) arrangement around a given dose rate. The 2D-distribution occurs in coincidence with enhanced sputtering where a considerable Cu fraction sublimates from the surface. The dose-rate dependence of nanoparticles indicates that the surface-sputtering process influences the intra-solid process and contributes to the 2D-distribution. A self-assembling mechanism for 2D-arrangement of nanospheres is discussed taking into account contribution of the surface sputtering.