Modeling of dc magnetron plasma for sputtering: Transport of sputtered copper atoms

A self-consistent modeling of two-dimensional structures of a dc magnetron plasma with a copper target is performed at 5 mTorr in Ar by using a hybrid model consisting of a particle-in-cell/Monte Carlo simulation for electrons and relaxation continuum model for ions. The erosion profile of the copper target is estimated by the flux velocity distribution of ions incident on the target. In the case of a dc magnetron, the discharge is mainly sustained by an E×B drift motion of energetic electrons near the position Bz ∼0 with a static doughnutlike magnetic field. Then, a strongly localized profile appears in the plasma structures. The position of a maximum erosion on the copper target exactly coincides with the position where the incident Ar+ ion flux is maximum. Under the system between the light ion and the heavy target atom, the energy of the sputtered Cu atom is low (<10 eV) despite the high-energy ion injection (∼200 eV) to the target surface. In particular, we have developed a technique to predict the transport of sputtered particles in the gas phase within a reasonable computational time. The spatial distribution of the sputtered particles is divided into two components: "directional" fast-moving particles that do not collide with Ar feed gas in the gas phase and "random" slow-moving particles whose energy is relaxed by collision. The sputtered Cu atoms are widely dispersed from the doughnutlike region on the target. At 5 mTorr, the flux of sputtered Cu atoms at the substrate is mainly affected by the random particles with relaxed energy by collision.