Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges

Abstract

Asymmetrically excited, high frequency cylindrical capacitive discharges are widely used for materials etching and thin film deposition. Two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations show the existence of standing waves and wave-induced hysteresis of the plasma density, i.e. two different steady states for the same driving rf voltage amplitude, when the voltage is increased from a low value or decreased from a high value. The phenomenon is explored over a range of pressures (10-30 mTorr) and frequencies (60-80 MHz). Examined at 73 MHz, with increasing gas pressure, the hysteresis loop gradually shrinks and vanishes. To understand the hysteresis induced by z-symmetric and z-antisymmetric radial wave propagation modes, the PIC results are compared with a nonlinear transmission line model assuming uniform bulk plasma density, to determine the symmetric and antisymmetric voltage amplitudes. The model results are in good agreement with the PIC observations, showing central-low and central-high profiles of the antisymmetric mode voltage at low density and high density, respectively. The results are then used to determine the parameters of a lumped circuit model of the two modes, from which the hysteresis is induced by the density dependence of the symmetric and anti-symmetric wave mode absorbed electron powers. For the low density state, the discharge is sustained mainly by the symmetric mode excitation. At high density, the discharge is sustained by both symmetric and anti-symmetric modes, with the latter partly showing a spatial resonance. The results are also shown to be frequency dependent, with an onset of the hysteresis at about 66 MHz.

Symmetry breaking in high frequency, symmetric capacitively coupled plasmas

“…Thus, we have three nonlinear algebraic equations (17)- (19) to solve for the three unknowns i t , i b , and I rf . Since the fluid simulations assume a Child Law sheath, the sheath widths s xy of the sheath capacitances C xy in the KVL equations are non-linear functions of the currents as will be shown below in Appendix A.…”

“…For intermediate frequencies, above the typical drive frequency of 13.56 MHz but well below the first spatial resonances of the waves, nonlinearly generated harmonics can also become resonant or near-resonant. 10,[17][18][19][20] The electrode/plasma/electrode sandwich structure of a symmetric (equal electrode areas) cylindrical discharge forms a three electrode system in which both z-symmetric and z-anti-symmetric radially propagating wave modes exist. 5,9,[21][22][23][24][25][26][27][28] The upper and lower axial sheath fields (E z ) are aligned for the symmetric mode, while they are opposed for the anti-symmetric mode.…”

Electron power absorption dynamics in magnetized capacitively coupled radio frequency oxygen discharges

“…A c c e p t e d M a n u s c r i p t cally induced radial electron transport might play an important role [68,69]. Such studies, however, require the application of multi-dimensional Particle-in-Cell simulations.…”

Electron heating dynamics and plasma parameters control in capacitively coupled plasma

“…简单化学反应的氩气CCP放电, 一维(one dimensional, 1D)模拟大约需要1-2天 [17,58] , 柱坐标小 腔室(10 cm腔室半径, 2 cm电极间距)、低密度 (10 15 -10 16 m -3 )的串行二维(two dimensional, 2D) 模拟需要1-2周 [18] , 针对略大一些腔室结构(12 cm 腔室半径, 6.7 cm电极间距), 基于GPU的2D并 行PIC/MCC模拟同样需要10天左右 [19,59] 等 [3,59] 开发的基于GPU的2D PIC/MCC模型等.…”