On the role of secondary electron emission in capacitively coupled radio‐frequency plasma sheath: A theoretical ground

We propose a theoretical ground for emissive capacitively coupled radio‐frequency (rf) plasma sheath under low pressure. The rf sheath is assumed to be collisionless and oscillates with external source. A known sinusoidal voltage instead of current is taken as prerequisite to derive sheath dynamics. Kinetic studies are performed to determine mean wall potential as a function of secondary emission coefficient and applied voltage amplitude, with which the complete mean direct current sheath is resolved. Analytical analyses under homogeneous model and numerical analyses under inhomogeneous model are conducted to deduce real‐time sheath properties including space potential, sheath capacitance, and stochastic heating. Obtained results are validated by a continuum kinetic simulation without ionization. The influences of collisionality and ionization induced by secondary electrons are elucidated with a particle‐in‐cell simulation, which further formalizes proposed theories and inspires future works. Low pressure capacitively coupled plasma is widely used in plasma‐based material processing. For normal radio‐frequency sheath, ion bombardment on boundary is inevitable, which induces secondary electron (SE) emission. Several recent studies focused on the influences of SEs using experiment or simulation, yet a rigorous theoretical ground is currently lacking. Here, we make use of plasma kinetic theory with additional assumptions to simplify the discharge process, providing two approaches, namely, analytical and numerical methods to allow calculation of discharge parameters: mean sheath potential, real‐time space potential, charge density distribution, sheath size, sheath capacitance, conductance, and so forth. To justify proposed models, two simulation codes, a kinetic simulation solving Boltzmann equation and a full particle‐in‐cell simulation are adopted. Theoretical model is closer to kinetic simulation where ionization of SEs is not considered. Increasing background pressure in particle simulation presents discrepancies, which calls for a new model under higher collisionality.