The lateral range straggling of various ions implanted into crystals

We have studied the lateral range straggling, DeltaR(L), for ions implanted into a crystal, and formulated the velocity dependence of the ratio of the lateral to longitudinal range straggling, DeltaR(L)/DeltaR(p). The targets had diamond structure, e.g., C(diamond), Ge, and Si, all of which had (100 ) and (110) surfaces. The projectiles were chosen so that the mass-ratio (m u = m(2)/m(1)) spans from 0.1 to 10. They were implanted into a random dire ction because of the application viewpoint. The region of the ion velocity, nu, corresponded to the so-called intermediate energy region, where the el ectronic stopping power, S-e, increased from the minimum to the maximum val ue. We obtained a power function of nu for aR(L)DeltaR(p), whose two parame ters are also power function of mu. The result comprehended the LSS results given for amorphous Si. In order to clarify the crystalline effect on DeltaR(L)/DeltaR(p), we expan ded the frame of calculation. Here the impinging ions were faced on (100) a nd (110) directions of those crystals. The results confirmed the previous e xpression for DeltaR(L)/DeltaR(p). In addition, for DeltaR(L) a new form is presented. With this expression we can predict the macroscopic view of the lateral spread of ions in a crystal, which is produced by ion implantation in a random direction.