Experimentally validated computations of simultaneous ion and fast neutral energy and angular distributions in a capacitively coupled plasma reactor

Abstract

Accurate predictions of the ion energy and angular distribution functions (IEADFs) and fast neutral energy and angular distribution functions (FNEADFs), are essential for a range of critical applications in the plasma processing of thin film etching and deposition. Computationally efficient methods that can be applied to industrial reactor systems that are also validated across a range of operating conditions are essential for prediction of IEADFs and FNEADFs. In this work, we present a hybrid model where a capacitively coupled plasma (CCP) solution was computed using a fluid model and the IEADF/FNEADF was generated using a particle transport model with a multi-species Monte Carlo Collision model. We first compare the computed IEADFs across a range of pressures with experimental measurements for a CCP reactor. We predict FNEADFs that are typically difficult to measure experimentally but are believed to have a significant effect on etch/deposition process phenomena. Across a large pressure range, we observe significant fast neutral bombardment of the electrode surface with at least half the energy of the most energetic ions as well as an angular spread that is larger than that of the ions.

Third-order transport coefficients for electrons in N2 and CF4: effects of non-conservative collisions, concurrence with diffusion coefficients and contribution to the spatial profile of the swarm

“…L for electrons in N 2 with the corresponding values that are determined by Kawaguchi et al [58]. In this figure, n 2 0 D 3L is determined from Monte Carlo simulations by using equation (24), while n 2 0 D α 3 3L is evaluated from the alpha parameters based on equation (25) from reference [58] by neglecting the alpha parameters of fourth and higher order. Kawaguchi and coworkers determined alpha parameters from the arrival time spectra experiment and the Monte Carlo simulations.…”

“…The results for the model and the real gases were obtained from the Monte Carlo simulations and numerical multi-term solution of the Boltzmann equation. In particular, it was necessary to follow a large number of electrons (at least 10 7 ) in our Monte Carlo simulations in order to calculate third-order transport coefficients accurately, due to high statistical fluctuations of individual terms appearing in expressions (24) and (25). It was also necessary to determine the phase space distribution function with a high degree of precision in order to calculate the third-order transport coefficients from the multi-term method.…”

“…However, this can be quite challenging due to a wide variety of effects that determine the nature of non-equilibrium plasma. These effects include collisions of electrons and ions with neutral particles of the background fluid [18][19][20], kinetics of excited species [21][22][23], generation of fast neutrals [24], space charge effects [25,26], and plasma-surface interaction [27,28]. Despite their simplicity, charged-particle swarms are at the heart of non-equilibrium plasma modelling [2,18,29,30].…”

Modeling of plasma processing reactors: review and perspective

“…Many computational LTP modeling codes have been developed by groups in academia, 42 the semiconductor industry, 70 and software vendors. 66,71,72 If one examines the capabilities of these plasma modeling tools, it will appear that one can adequately model most plasma processing 64 systems described in Sec. 2, often with the actual processing chemistries under realistic operating conditions.…”

Science-based, data-driven developments in plasma processing for material synthesis and device-integration technologies

“…138) The ion energy and angular distribution functions (IED and IAD) of ions and fast neutrals were estimated computationally by a hybrid model of fluid and particles and they were validated across a range of operating conditions of experiments. 139) The IED were measured by a retarding field energy analyzer and the IED function varies over a pulse period. The results were shown that the ion energy increased and energy spread from single peaked to bi-modal with the decrease of RF power duty cycle.…”