TM01-mode microwave propagation property analysis for plasmas with disk-plate windows by a finite-difference time-domain method

Abstract

Numerical studies of microwave propagation properties in a conical horn and an adjustable waveguides, and for plasmas generated under disk-plate windows of a 220mm diameter and in a vacuum chamber are studied by a finite-difference time-domain (FDTD) method including plasma equations. In the numerical studies, a TM01-mode microwave of 2.45GHz at a power of 1kW is supplied from the top of the conical horn waveguide. In addition, numerical results by the FDTD method are compared with experimental results, and a validity of the numerical results is investigated. From the numerical results, it is found that the TM01-mode microwave changes its field shape and propagates along inner surfaces of the conical horn and the adjustable waveguides. Then electromagnetic fields of the TM01-mode microwave concentrate at the center surfaces of the disk-plate windows [quartz (εr=3.8), alumina (εr=9.7), and WG20 (εr=20.0)]. A diameter of higher concentration is within 80mm, and the orientation of electric field is almost vertical to the disk-plate window. The diameters within 80mm are equivalent to a diameter at a higher electron density in an oxygen plasma experiment in the volume mode at 1kW and 133Pa with a quartz window. When heights of the adjustable waveguide are changed from 64to244mm, peaks of electric fields in the heights, where microwave power is estimated to be strongly absorbed into the plasmas, appear and peak positions of the electric fields are observed periodically in surface-wave mode plasmas as well as the volume mode plasmas. Heights of the peaks increase with increasing dielectric constant and peak-to-peak distances of the peak positions decrease with increasing dielectric constant. The peak positions agree to the minimum microwave power reflections tuned by a combination of an autotuning unit and adjustable waveguide heights in experiments. Furthermore, peak positions of relatively absorbed microwave powers in the surface-wave and volume mode plasmas calculated by Poynting vectors in the FDTD method are close to the peak positions. This means that microwave powers penetrate effectively the disk-plate windows near the peak positions. In addition, a relatively absorbed microwave power with an alumina disk-plate window (surface-wave mode plasma) is larger than that with the quartz disk-plate window (volume mode plasma). This comes from a reason that a larger electron density in the surface-wave plasma absorbs a larger quantity of the microwave power. From the above comparisons between results obtained by the FDTD method and experiments, a validity of the FDTD method including the plasma equations can be confirmed.