Uniformization of electron density distribution through magnetic fields in capacitively coupled plasmas

In the capacitively coupled plasma (CCP) for the plasma-enhanced chemical vapor deposition (PE-CVD), the electron density distribution is typically non-uniform between parallel electrodes. Such non-uniform density distribution interrupts the uniformization of film growth on wafer during PE-CVD processes. In this paper, we develop an analytical study to find the optimum application of static magnetic fields to CCP electrons, which makes the density distribution of electrons uniform between parallel electrodes. The results from our analytical study argue that, in order to achieve such uniform density distributions, the static magnetic fields have to be applied in the direction perpendicular with respect to electrode surfaces and with a constant intensity. These results explain the fact that an intensity increase in such magnetic fields suppresses the effect of electric fields near the edge of electrodes that causes the non-uniform density distribution of CCP electrons. We verify the results from our analytical study by using the COMSOL simulation software and show a good agreement between analytical and simulation results.