Multiphysics simulation of non-uniform magnetic fields’ effect on plasma uniformity in capacitively coupled plasmas

To achieve precise control over the radial uniformity of capacitively coupled plasmas in semiconductor manufacturing, this study systematically investigates the coupled influence of electrode temperature and nonuniform magnetic fields on plasma characteristics using a two-dimensional multiphysics model. The model integrates thermal, magnetostatic, plasma fluid, and frequency-domain electric field models, implemented through a COMSOL and MATLAB cosimulation framework. It is found that a nonuniform magnetic field generated by a single DC coil can effectively tailor the plasma density profile by regulating electron transport and power absorption. However, the effectiveness of this magnetic control is closely related to the electrode temperature. The electrode temperature governs the distribution of neutral gas density, thereby significantly influences plasma discharge characteristics. When the temperature-controlled region is small, abrupt temperature changes occur at its boundaries, leading to significant variations in the distributions of neutral gas concentration and plasma density, and consequently complicating magnetic field modulation. This effect is further pronounced with higher electrode temperatures. Therefore, extending the radius extent of the temperature-controlled electrode is essential to achieve uniform and effective modulation of the magnetic field.