--- abstract: 'Ion-implanted amorphous semiconductor materials can exhibit memory effects arising from changes in the compositional profile of the implanted region, induced by ion bombardment or by electrical or optical stimuli. We study a stochastic model to determine the equilibrium distribution of the threshold voltage and conductance of ion-implanted devices as a function of the number of implanted ions per area, for ions that move diffusively in amorphous semiconductor materials and produce a Gaussian-like profile around the implantation point. We show that this model describes well the experiments on the conductance and threshold voltage shift induced by He$^{+}$ bombardment in Si-MOSFETS [@Gunnarsson_2004; @Schroer_2007], with a single fitting parameter ($\nu$) related to the average radius of the implanted region. The conductance fluctuations in these systems exhibit super-diffusion characterized by an exponent $0.55<\nu<1$.' address: 'Departamento de Física, Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brazil' author: - 'C. J. Villas-Boas' title: 'Super-diffusion in Ion-implanted Amorphous Materials: Theoretical Model and Application to Ion Bombardment Experiments' --- Introduction ============ In recent experiments on ion implantation of amorphous semiconductors, ion bombardment was found to induce non-thermal activated conductivity in $p$-doped Si films [@Gunnarsson_2004; @Schroer_2007]. Conductivity was found to decrease with increasing ion fluence as a power-law with exponent -0.66 (Ref. [@Gunnarsson_2004]) and -0.73 (Ref. [@Schroer_2007]). Moreover, when low-temperature electrical measurements are done, the device exhibits threshold voltage shifts associated with the conductivity variation due to ion implantation. A threshold voltage shift with ion concentration following a power-law with exponent $0.9