Analysis of individual collision cascade parameters during irradiation of $\beta$-Ga$_2$O$_3$ by atomic and molecular ions

Collision cascade density is one of the most important parameters that determine radiation damage accumulation in semiconductors under ion bombardment. We perform calculation of collision cascade parameters formed in $\beta$-Ga$_2$O$_3$ by irradiation with 1.3 keV/amu atomic F, P, and molecular PF$_4$ ions using two different methods: the method considering sub-cascade formation, and by calculation an average number of vacancies in spheres of fixed radius. The calculated results are compared with experimental data on damage accumulation in $\beta$-Ga$_2$O$_3$ under irradiation with aforementioned ions. It is shown that both methods qualitatively predict the effect of collision cascade density on radiation damage accumulation in gallium oxide. Fractal nature of cascades formed in $\beta$-Ga$_2$O$_3$ is established, corresponding fractal dimension is calculated.