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

Abstract

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. K E Y W O R D S capacitively coupled plasma, kinetic theory, modeling, secondary electron emission, surfaces

Unveiling the role of dielectric trap states on capacitively coupled radio-frequency plasma discharge: dynamic charging behaviors

“…The mean RF sheath determines the ion incident energy at solid surface, and is therefore crucial in view of the numerous applications related to CCP [1] . Mean RF sheath potential is a function of applied voltage amplitude and the emission coefficient, but simultaneously considering the two factors leaves no analytical solution to the RF sheath [10] . To qualitatively illustrate the influence of trap state on sheath properties, here ad hoc analyses are given using the example of floating boundary, the general trend for RF sheath in CCP should be analogous.…”

“…In previous works, it has been confirmed by experiments that Secondary Electron Emission (SEE) can significantly modify important plasma parameters, such as particle/power balance, temperature and density [5,6] . Theoretical studies indicated that SEE significantly modified the important discharge parameters [8,9] , theoretical analyses express RF sheath as function of source amplitude and SEE coefficient, giving quantitive current-voltage characteristic, sheath capacitance, conductance in the presence of boundary electron emission [10,11] . Apart from experiment and theory, numerical simulation also provides insight into physical details of PSI in CCP.…”

Intense boundary emission destroys normal radio-frequency plasma sheath

“…Adopted simulation parameters are listed below to help replicate simulation results: source frequency 13.56 MHz, bulk plasma density 0 = 5 × 10 14 The simulation produces noise-free data for better understanding of sheath physics, similar methods were used in several previous works related to plasma sheath [28][29][30][31] . More detailed algorithm was shown in our previous works of bounded plasma 15,32 .…”

“…Conduction current prevails displacement current in bulk plasma and field in bulk plasma is weak. But in this letter we will show that the bias can be primarily consumed by bulk plasma and electric field in plasma center needs not to be shielded by sheathes, due to intense boundary emission.Numerous studies have been done regarding boundary emission in CCP, but its influences are mostly assumed to be unessential 4,[8][9][10][11][12][13][14][15] . The steady flux of ion 𝛤 𝑖 produces a surface emission flux 𝛤 𝑒𝑚 = 𝛾 𝑖 𝛤 𝑖 due to ion-induced secondary electron emission (SEE), with 𝛾 𝑖 the emission coefficient.…”

“…Numerous studies have been done regarding boundary emission in CCP, but its influences are mostly assumed to be unessential 4,[8][9][10][11][12][13][14][15] . The steady flux of ion 𝛤 𝑖 produces a surface emission flux 𝛤 𝑒𝑚 = 𝛾 𝑖 𝛤 𝑖 due to ion-induced secondary electron emission (SEE), with 𝛾 𝑖 the emission coefficient.…”