This example application simulates a steady microwave field in a three-dimensional plasma reactor using in semiconductor materials processing. The Frequency-Domain Electromagnetic Wave Solver Module of the VizEM is used for this problem.
The geometry for the simulation is shown in Figure 1 and comprises a cylindrical processing reactor with an air-filled waveguide port in the top center of the reactor. The waveguide is rectangular in cross section and comprises an L-bend with a 45o mirror surface at the bend. The waveguide connects to a top dielectric window surface through which the wave is launched into the main reactor volume. The top dielectric window is made of quartz with a relative dielectric permittivity of 4 and the main reactor volume has a diameter of 40 cm. The bottom of the reactor has a wafer holder pedestal. The distance between the top dielectric window and the pedestal is 10 cm.
The entire reactor geometry is meshed with a 3D unstructured mixed mesh comprising a combination of tetrahedral, prismatic, pyramidal, and brick cell volumes that are automatically generated using third-party meshing software. The mesh contains over 1.3 million cells with 6 unknown in each cell (3 real and 3 imaginary components of the wave field) for a total of 7.8 million unknowns in the problem. The overall mesh count, quality, and resolution is determined by not just the geometry, but also the characteristics of the wave. In this case, the wave has a frequency of 2.45 GHz implying that the vacuum wavelength is about 12 cm and wavelength in quartz is about 6 cm. The resolution of the mesh must therefore be such that at least 20 mesh cells resolve a wavelength (a rule-of-thumb); which means a typical mesh cell dimension about 3 mm or less.
The geometry is divided into 5 physical sub-domains: the waveguide, the top dielectric window, the gas, the wafer and the pedestal. The bottom panel in Figure 1 shows a 90o cut through the reactor to expose the various components in the reactor. All material boundaries in the geometry are modeled as perfect electric conductors.
A uniform microwave field of frequency of 2.45 GHz is launched at the inlet of the waveguide. The wave is polarized with a single non-zero wave component in the z-direction (direction along axis of reactor). The wave travels horizontally in the waveguide and reflects of the mirror surface following which it propagates vertically down the reactor axis to the top dielectric window. The wave then travels radially along the thickness of the quartz dielectric and finally launches into the reactor volume, as seen in figure 2. The high dielectric permittivity of the quartz dielectric window “slows” the wave resulting in a lower wavelength in the window (from 12 cm to 6 cm, as mentioned earlier) thereby improving uniformity of the wave field as it is launched into the main reactor volume.
Figure 2 shows the three components of the microwave field. The wave reflection at the waveguide mirror surface at the L-bend produces a y-component of the wave field. The wave reflects off of the outer walls of the reactor to produce non-zero x-components of the wave field. The three-dimensional geometry therefore results in all three components of the wave field becoming active in the reactor even though only a single non-zero wave field component is launched in the reactor.
VizEM provides a very robust environment to solve such problems with quick turnaround. The different modules within the VizEM are seamlessly integrated with the other OverViz software packages. For example, the Frequency-Domain Electromagnetic Wave Solver Module used in the above problem can be called by VizGlow to solve coupled electromagnetic wave—plasma problems, such as in microwave reactors and inductively coupled plasma reactor.