Deuk-Chul Kwon

Numerical Investigation of RF Pulsing Effect on Ion Energy Distributions at RF-biased Electrodes

The ion energy distributions (IEDs) arriving at a substrate strongly affect the etching rates in plasma etching processes. In order to determine the IEDs accurately, it is important to obtain the characteristics of radio frequency (rf) sheath at pulsed rf substrates. However, very few studies have been conducted to investigate pulsing effect on IEDs at multiple rf driven electrodes. Therefore, in this work, we extended previous one-dimensional dynamics model for pulsed-bias electrodes. We obtained the IEDs using the developed rf sheath model and observed that numerically solved IEDs are in a good agreement with the experimental results.

A Global Simulation of SiH 4 /H 2 Discharge in a Planar-type Inductively Coupled Plasma Source

A global simulation of discharge is conducted in a planar-type inductively coupled plasma (ICP) discharge. We numerically solve a set of spatially averaged fluid equations for electrons, positive ions, negative ions, neutrals, and radicals. Absorbed power by electrons is determined by an analytic electron heating theory including the anomalous skin effect. Also, we investigate functional dependence of various discharge quantities such as the densities of various species and the temperature of electron on external controllable parameters such as ratio between and , power and pressure.

A semi-analytic collisionless sheath model for multicomponent plasmas and ion energy and angular distributions at rf-biased electrodes

The ion energy and angular distributions (IEADs) arriving at substrates strongly affect the etching rates in plasma etching processes. In order to determine the IEADs accurately, it is important to obtain the characteristics of radio frequency (rf) sheaths with multicomponent plasmas. However, very few studies have been conducted on an rf sheath model for multiple ion species including negative ions over the past few decades. Therefore, in this work, we extended previous semi-analytic collisionless rf sheath models for electronegative plasmas. The extended model was based on the previously developed models, and an equivalent circuit model was used to determine the sheath characteristics. Also, we obtained the IEADs using the rf sheath model and an analytic model for evaluation of the ion angular distribution functions. We observed that the developed model was in good agreement with the experimental results and the one-dimensional dynamics model. Also, we found that negative ion species could affect the characteristics of rf sheaths, hence negative ion species should be considered to obtain more accurate IEADs.

A feed-back control approach for global simulation of high density plasma discharges

Abstract Spatially averaged global simulations have been widely used to study discharge characteristics of high density plasma discharge, because the global insight on the dependence of quantities such as densities and temperatures can be obtained. Above all, the global model can quickly predict the plasma parameters on the external or the chamber parameters comparing with multi-dimensional modeling. However, the global model can be expensive to compute the plasma parameters for complex or mixed gas discharges. Therefore, in this work, we applied a feed-back approach to solve a set of spatially averaged fluid equations for charged particles, neutrals, and radicals. The results were shown that the developed model could efficiently enhance convergence of simulations.

Calculation of the Reactor Impedance of a Planar-type Inductively Coupled Plasma Source

A two-dimensional nonlocal heating theory of planar-type inductively coupled plasma source has been previously reported with a filamentary antenna current model. However, such model yields an infinite value of electric field at the antenna position, resulting in the infinite self-inductance of the antenna. To overcome this problem, a surface current model of antenna should be adopted in the calculation of the electromagnetic fields. In the present study, the reactor impedance is calculated based on the surface current model and the dependence on various discharge parameters is studied. In addition, a simpler method is suggested and compared with the surface current calculation.

A parallelization method for time periodic steady state in simulation of radio frequency sheath dynamics

In order to reduce the computing time in simulation of radio frequency (rf) plasma sources, various numerical schemes were developed. It is well known that the upwind, exponential, and power-law schemes can efficiently overcome the limitation on the grid size for fluid transport simulations of high density plasma discharges. Also, the semi-implicit method is a well-known numerical scheme to overcome on the simulation time step. However, despite remarkable advances in numerical techniques and computing power over the last few decades, efficient multi-dimensional modeling of low temperature plasma discharges has remained a considerable challenge. In particular, there was a difficulty on parallelization in time for the time periodic steady state problems such as capacitively coupled plasma discharges and rf sheath dynamics because values of plasma parameters in previous time step are used to calculate new values each time step. Therefore, we present a parallelization method for the time periodic steady state problems by using period-slices. In order to evaluate the efficiency of the developed method, one-dimensional fluid simulations are conducted for describing rf sheath dynamics. The result shows that a speedup can be achieved by using a multithreading method.

Effect of electron kinetics on global simulations for inductively coupled plasma sources

Summary form only given. Electron energy probability functions and electron heating mechanism strongly affect plasma parameters such as the electron temperature and plasma density in high density plasma sources. In order to analyze the effect, we developed a self-consistent global simulator for inductively coupled plasma sources. To obtain EEPF theoretically, we numerically solve the Fokker-Planck equation which couple the global transport model in a self-consistent manner. Absorbed power by electrons and the energy diffusion coefficient are determined by an analytic electron heating theory including the anomalous skin effect. The simulation results are then compared with experimental measurements such as the plasma density, electron temperature, and EEPF on external controllable parameters such as power and pressure. In particular, results show that the electron heating model should be combined for the global transport model to obtain the accurate electron temperature at pulsed plasma conditions.

A Three-Dimensional Calculation of the Reactor Impedance for Planar-Type Cylindrical Inductively Coupled Plasma Sources

The reactor impedance is calculated for a planar-type cylindrical inductively coupled plasma source by expanding the electromagnetic fields into their Fourier-Bessel series forms including the three-dimensional shape of the antenna. The mode excitation method is utilized to determine the electromagnetic fields based on a Poynting theoremlike relationship. From the obtained electromagnetic fields, a tractable form of the reactor impedance is obtained as a function of various plasma and geometrical parameters and applied to carry out a parametric study.

Numerical investigation of RF pulsing effet on ion energy and angular distributions

Summary form only given. The ion energy and angular distributions (IEADs) arriving at a substrate strongly affect the etching rates in plasma etching processes. In order to determine the IEADs accurately, it is important to obtain the characteristics of radio frequency (rf) sheath at pulsed rf substrates. However, very few studies have been conducted on an rf sheath model for pulsed rf substrates. Therefore, in this work, we extended previous one-dimensional dynamics model for pulsed-bias electrodes. We obtained the IEADs using the developed rf sheath model and an analytic model for evaluation of the IEADs. We observed that the peak positions of the IEADs were shifted to the high-energy regime as the duty cycle increases.

Numerical Investigation of Ion and Radical Density Dependence on Electron Density and Temperature in Etching Gas Discharges

Dependence of radical and ion density on electron density and temperature is numerically investigated for /Ar, , , , , and discharges which are widely used for etching process. We derived a governing equation set for radical and ion densities as functions of the electron density and temperature, which are easier to measure relatively, from continuity equations by assuming steady state condition. Used rate coefficients of reactions in numerical calculations are directly produced from collisional cross sections or collected from various papers. If the rate coefficients have different values for a same reaction, calculation results were compared with experimental results. Then, we selected rate coefficients which show better agreement with the experimental results.