May 1, 2017

Capacitively Coupled Plasma (CCP) discharges in parallel-plate configuration are commonly used in semiconductor and other materials processing applications.  These discharges provide a compact platform in which a plasma can be generated to process a flat wafer surface.  The highly directional ion impact at the wafer surface with high ion impact energies is beneficial to a number of wafer processes; in particular for etch processes.  This application note discusses the simulation of a typical CCP reactor used in the semiconductor process industry.  The VizGlow Plasma Modeling Software Package is used.

The geometry and computational mesh for this problem is shown in Fig. 1. The mesh contains about 21,000 cells, and is divided into 6 physical subdomains.  The geometry includes a gas subdomain where the plasma is formed, a top grounded electrode, a bottom powered electrode that holds a wafer, a top dielectric that isolated the top electrode from the grounded reactor wall, a bottom dielectric that isolates the bottom powered electrode from the reactor walls, and a focus ring that defines the edge geometry for the wafer and the powered electrode.  The mesh comprises a mix of quadrilateral and triangular cells in domain.  Specifically the plasma (gas) subdomain is meshed with quadrilateral cells that have non-uniform resolution to capture the sheaths at wall and wafer boundaries accurately.

The wafer has a standard 300 mm dia.  The wafer is assumed to be made of silicon, the dielectrics are made of alumina, and the focus ring is made of quartz.  The powered electrode is driven by a 100 MHz excitation frequency that delivers 300 W radio-frequency (RF) power to the plasma. A pure argon gas at 50 mTorr pressure is assumed.

The plasma gas phase chemistry is represented by 4 species (electrons E, argon ions Ar+, argon metastables Ar*, argon neutrals Ar).  The plasma chemistry comprises 6 reaction including electron impact excitation and direct ionization, stepwise ionization, Penning ionization, and metastable quenching.  The simulations are run to a periodic steady state. The VizGlow Plasma Modeling Software Package is used in self-consistent mode to solve for the CCP plasma phenomena.  These simulations are performed without including electromagnetic (EM) wave effects that are known to redistribute power deposition in the reactor.    

Figure 2 shows a cycle-averaged electron temperature in the reactor.  The electron temperature is nearly uniform in most of the reactor volume with a value of about 20,000 K (~2 eV).  In the vicinity of the powered electrode/wafer the averaged electron temperature is about 150,000 K (~ 15 eV).  The electron temperature is non-uniform along the radial length of the wafer and peak near the radial edge of the wafer.


Figure 3 shows the cycle-averaged electron density profile in the reactor.  The electron densities are seen to be quite non-uniform with a wafer edge peak profile that corresponds to the dominant edge power deposition resulting for wafer edge electrostatic field focusing.  Peak electron densities of ~ 3×1016 m-3 are seen.  The argon ion densities correspond closely to electron density profiles.

Figure 4 shows the argon metastable species density profiles in the reactor.  An off-axis metastable density peak at a similar radial location to the electron density peak is seen.  The metastable densities are however peaked close to the wafer surface close to the regions where the electron temperatures are high.

Figure 5 shows the ion energy distribution function (IEDF) for ion impact at two locations on the wafer surface.  The IEDF information is generated automatically by VizGlow and is a useful metric for process behavior at the wafer surface.  IEDFs for the wafer center and edge are shown.  Ions impact the wafer surface with a range of energies depending on the excitation frequencies, mass of ions, and the sheath thickness.  A classical bi-modal IEDF is seen.  For the reactor condition used in these simulations, the lowest ion impact energies are between 15 and 20 eV and the highest are between 30 to 35 eV.  The IEDF width is nearly the same for both the wafer center and edge locations.  The wafer edge IEDF is shifted to a slightly higher energy compared to the wafer center.

Finally, we’d like to provide an addition comment on the numerical convergence for these types of simulations.  CCP simulations can be time consuming and the best judgment for simulation convergence is provided by placing trace points several locations in the simulation domain and tracking the time evolution of various important plasma properties.  For example Fig. 6 shows the time evolution of electron and ion species densities and the argon metastable species density at the reactor center line (axis) mid-gap between the electrodes.  Although the simulation was run 100 microseconds of simulated physical time, the time evolution of the species densities indicates that a numerically converged solution is obtained in about 40 microseconds.

VizGlow provides a wide range of physical models and options that allows one to simulate complex coupled phenomena that are encountered in most plasma discharges. VizGlow is provably fast, robust, and easy-to-use software and currently a leading industrial plasma simulation tool.