Two-Dimensional Self-Consistent Simulation of a DC Magnetron Discharge

Abstract

A two-dimensional simulation of dc magnetron discharge is performed by a hybrid of fluid and particle models. In this hybrid model, ions and bulk electrons are treated by the fluid model and fast electrons are treated by the particle model. The numerical results indicate that the number density of the fast electrons has little effect on the electric field distribution in dc magnetron discharge at 30 mTorr since the ratio of fast electrons to bulk electrons is quite low. The transport of fast electrons is, however, quite important for dc discharge because the spatial distribution of the net ionization rate is subject to the spatial behavior of the fast electrons.

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

“…A hybrid model in which bulk electrons and all ions are treated by the relaxation continuum ͑RCT͒ model and fast electrons mainly in the sheath are traced by the particle model has been examined in a dc magnetron discharge with a reasonable computational time. 15 The number of interconnect layers and the sizes of the holes and trenches for via/wire have been increasing in the global interconnect in ULSI circuit, and the conformal deposition of copper film in the hole or trench will be an interesting and practical issue. Directional deposition of copper atoms has been analyzed by using a "long-throw" sputtering in the dc magnetron at excessively low pressure of ϳ10 −5 Torr.…”

An anomalous erosion of a rectangular magnetron system

“…5 The third type is a hybrid model, consisting of a Monte Carlo simulation and the relaxation continuum model, which achieves a self-consistent simulation of a dc magnetron discharge. 6,7 The hybrid model can provide a usefull and accurate prediction of the spatial distribution of charged particles within a practical computational time.…”

Modeling of the influence of dielectric target on interface sheath characteristics in a radio-frequency magnetron sputtering

“…In the hybrid model, 9,10 highly nonequilibrium electrons with a complicated transport in E͑r , t͒ and B͑r͒ fields were treated by a kinetic particlein-cell/Monte Carlo ͑PIC/MC͒ method, 11 while ions were treated by a relaxation continuum ͑RCT͒ model. 12 In the RCT model, the density continuity and the momentumrelaxation equations of ions were solved with Poisson's equation considering the electron and ion densities.…”