A simplified analytical model for ion-solid interactions. appropriate for low-energy beam depositions, is presented to determine the analytic solution of the deposited energy in the solid. The deposited energy in the surface and the energy deposited in the underlying bulk, correlative to the atomic displacement leaving the lattice damage, are dependent on the mass and incident energy of projectiles as well as the sharp displacement threshold energy. The determination of deposited energy of ion in subsurface yields a ceiling for the beam energy above which more defects are generated in the bulk resulting in defective films. The accuracy of the angular average over the scattering cross section is evaluated from comparison with experimental results. The analytic solution is applied to Ar+ and N+ projectiles in diamond, graphite and SiC materials, respectively.