Gallium (Ga) implantation induced self-atom mixing in crystalline and amorphous germanium (Ge) is investigated utilizing isotopically controlled Ge multilayer structures grown by molecular beam epitaxy. The distribution of the Ga ions and the ion-beam induced depth-dependent mixing of the isotope structure was determined by means of secondary ion mass spectrometry. Whereas the distribution of Ga in the crystalline and amorphous Ge is very similar and accurately reproduced by computer simulations based on binary collision approximation (BCA), the ion-beam induced self-atom mixing is found to depend strongly on the state of the Ge structure. The experiments reveal stronger self-atom mixing in crystalline than in amorphous Ge. Atomistic simulations based on BCA reproduce the experimental results only when unphysically low Ge displacement energies are assumed. Analysis of the self-atom mixing induced by silicon implantation confirms the low displacement energy deduced within the BCA approach. This demonstrates that thermal spike mixing contributes significantly to the overall mixing of the Ge isotope structures. The disparity observed in the ion-beam mixing efficiency of crystalline and amorphous Ge indicates different dominant mixing mechanisms. We propose that self-atom mixing in crystalline Ge is mainly controlled by radiation enhanced diffusion during the early stage of mixing before the crystalline structure turns amorphous, whereas in an already amorphous state self-atom mixing is mediated by cooperative diffusion events. (C) 2011 American Institute of Physics. [doi:10.1063/1.3658259]