One-dimensional and two-dimensional transport model of a transformer coupled plasma (TCP) are developed and the argon discharges at various conditions are simulated.
In the 1-D modeling, collisionless heating mechanism, which has an important role in sustaining discharge at low gas pressure, is included and the finite length effect of collisionless heating mechanism is considered. The 1-D transport model is combined with the power absorption model including these collisionless effects and then the fluid equations are solved under appropriate plasma-sheath boundary conditions. We obtain various quantities such as the axial profiles of plasma density, electron temperature, fluid velocity, inductive electric field, and power deposition. The result of the calculation of surface impedance at various chamber length shows the strong dependence of surface impedance on the chamber length and the results of simulation compare well with the experimental observation.
The 2-D model is developed using simplified transport equation which is obtained from the continuity equation and electron energy balance equation. For the calculation of power absorption, the inductive electric field induced by antenna coil is evaluated by 2-dimensional wave equation using a finite difference method. From these, the power deposition and plasma density profile in 2-dimension are calculated.