Ion Energy Distributions in Multifrequency Capacitive Discharges

Abstract

Summary form only given. Capacitive discharges are widely used for thin-film processing of silicon and flat-panel substrates in the microelectronics industry. The ion energy distribution (ED) at the substrate surface is an important parameter in these processes. Multiple frequency drives are often used to control the width and the average of the IED. The physics of IED formation in low pressure single frequency capacitive discharges is fairly well understood. However, the understanding of multiple frequency driven discharges is less than adequate. In this work, an analytical model of the IED is developed and compared to simulations using a kinetic, particle-in-cell (PIC), Monte Carlo collision (MCC) method. To determine the IED in the model, given the sheath voltage waveform V(t), the frequency spectrum E(f) of a time-varying ion energy response is first determined as E(f)=T(f)V(f), where T(f) is a frequency transfer (filter) function and V(f) is the frequency spectrum of the sheath voltage waveform. After applying an inverse Fourier transformation of E(f) to determine E(t), the IED within a certain small energy interval is determined as proportional to the total time for E(t) to lie within that energy interval. Various transfer functions are explored, all chosen such that the ions completely respond to low frequency oscillations and have a 1/f response at high frequencies. In the simulations, done in argon with a discharge gap of 3 cm, the IED is collected over many cycles of the lowest frequency. The gap is divided into 500 cells and the simulation time step is 7.63 ps, chosen in order to resolve the Debye length and fulfill simulation stability criteria. Initial simulations are done neglecting ion-neutral charge transfer and elastic scattering collisions, using single, dual, and triple frequency excitation over a wide voltage range, with various commensurate or incommensurate frequency ratios. The models and simulation results are generally in good agreement. In later analysis and simulations, the effects of ion-neutral collisions in the sheath on ion and fast neutral energy distributions at the substrate surface are examined.