Ray tracing calculations of ECR absorption in plasma etching and deposition devices

Ray tracing is used to calculate the power absorbed in electron cyclotron resonance plasma sources used in plasma etching and deposition devices. The microwaves are launched at 2.45 GHz corresponding to a fundamental resonance at 875 G. The power in each ray is weighted to represent the power distribution of the waveguide mode that is launched into the device. The ray trajectories describe the refraction of the microwave power in the plasma due to the gradients in the plasma density and magnetic field. To calculate power absorption, the damping coefficient is evaluated using a warm plasma correction to the cold plasma dispersion relation. When the rays are launched onto a magnetic beach, most of the microwave power is absorbed before the omega = omega ce surface is reached. For the cases studied, the axial width of the absorption layer is typically about 0.5-2 cm and is wider on axis becoming narrower at larger radii. The width of the absorption layer varies inversely with the magnetic field gradient consistent with analytical results obtained from linear theory. The calculations show a significant two-dimensional structure to the absorbed power profile which depends on the launched mode power distribution, the plasma density and the magnetic field profiles.