Experimental evidence of various mode numbers of azimuthal waves in an E×B Penning source for semiconductor processing

This study presents the first experimental evidence for the existence of various mode numbers of azimuthal waves in an E × B Penning source used for semiconductor processing. To accurately measure these mode numbers, we utilized an eight-tip probe array aligned in an azimuthal direction to acquire spatiotemporal signals and applied the Beall analysis to obtain the dispersion relations. We combined seven dispersion relations obtained from distinct probe pairs to derive a single dispersion relation. This method allowed us to enhance the accuracy and reliability of the measurements. Our results show that the amplitude of the fast Fourier transformation (FFT) undergoes significant changes as the discharge voltage and magnetic field strength are varied. We observed that a distinguishable peak seen at higher discharge voltage is divided into a wide range of dominant peaks up to eight when the discharge voltage is decreased. The dispersion relation reveals that the phase velocity of each mode is proportional to the frequency. As the magnetic field strength increases, the amplitude of the FFT rapidly decreases except for a dominant peak corresponding to mode number 3. Ultimately, the low azimuthal mode dominates the azimuthal oscillation. Moreover, the radial profile of the FFT results shows that the frequencies of modes are nearly constant along the radial direction and have a maximum spectral magnitude at the periphery of the plasma core. Notably, as the amplitude of the modes increased, the maximum amplitude transitioned away from the core region. The findings from experiment with the multi-arrayed probe suggest the presence of a characteristics eigenmode in the E × B Penning source. This eigenmode appears to be a fundamental and pervasive feature of the system, spanning a range of mode numbers from low to high.