Simplified evaluation of displacement effect distribution in silicon irradiated with low-energy ions

Displacement effects induced by low-energy ion irradiation in silicon have been investigated theoretically. Instantaneous energy of an incident ion during its slowing-down process has been obtained as a function of the penetration depth and the ordinal number of displacement collisions by solving a set of integral equations. From these results, the averaged penetration depth as a function of the ordinal number of displacement collisions is estimated. The mean free path of the incident ion at a specific depth in silicon is also estimated for several initial energy values and ion species. The energy transfer rate into atomic displacement collisions and the density of deposited energy in a collision cascade have been evaluated considering the primary knock-on process. The damaged layer thickness obtained by the experiment of the ion-bombardment-enhanced selective etching of silicon crystals shows a good agreement with the depth where the estimated density of deposited energy takes a constant value.