Ion Implantation and Synthesis of Materials - Studium

180 13 Ion-Induced Atomic Intermixing at the Interface: Ion Beam Mixing(a)Incident IonInterfaceMS(b)(c)Fig. 13.1. Schematic of the ion mixing process for a layer M on a substrate S forsuccessively higher irradiation doseskinematics of the ion/target interaction play a role, as does the formation ofcollision cascades and the total number of ions that have passed through theinterface, i.e., the ion dose, φ. Both ballistic and cascade effects can be altered bychanging the mass of the irradiating ion; increasing the mass of the ion increasesthe amount of energy deposited in nuclear collisions per unit length traveled bythe ion. An example of mass and dose effects in ion mixing is clearly evident inFig. 13.3. This shows that the average thickness of reaction at the Pt/Si interface,in units of Si atoms cm −2 , increases with both increasing mass of the incident ionand the increasing dose, φ, and that the mixing rate for all irradiating ions isproportional to (φ) 1/2 . For a given dose, the ratio of the number of atoms reacted,Q, scales with the ion mass and with the nuclear energy loss (dE/dx) n in the Ptlayer to the 1/2 power. These trends lead to a general condition for the amount ofmixing, Q, at the interface between two different materials, which can beexpressed asQdφ ⎛ E∝ ⎞⎜d ⎟⎝ x ⎠n(13.1)