We have used molecular dynamics simulation techniques to study the generation of damage in Si within the low-energy deposition regime. We have demonstrated that energy transfers below the displacement threshold can produce a significant amount of damage, usually neglected in traditional radiation damage calculations. The formation of amorphous pockets agrees with the thermal spike concept of local melting. However, we have found that the order-disorder transition is not instantaneous, but it requires some time to reach the appropriate kinetic-potential energy redistribution for melting. The competition between the rate of this energy redistribution and the energy diffusion to the surrounding atoms determines the amount of damage generated by a given deposited energy. Our findings explain the diverse damage morphology produced by ions of different masses.