VizEM Application Note
Simulation of 3D Microwave Fields in Semiconductor Processing
Reactor Using Frequency-Domain Electromagnetics Wave SolverThis note presents an example
simulation of a steady microwave field ina three-dimensional plasma reactor using
in semiconductor materials processing.
The Frequency-Domain Electromagnetic
Wave Solver Module of the VizEM
Electromagnetics Modeling Software
Package developed by Esgee Technologies
Inc. is used for this problem.
The geometry for the simulation isshown in Figure 1 and comprises acylindrical processing reactor with an airfilled waveguide port in the top center ofthe reactor. The waveguide is rectangularin cross section and comprises an L-bendwith a 45o mirror surface at the bend. The
waveguide connects to a top dielectricwindow surface through which the wave
is launched into the main reactor volume.
The top dielectric window is made ofquartz 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 10cm.

Figure 1: Geometry description and the unstructuredhybrid mesh used for the 3D microwave plasma
reactor.

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 automaticallygenerated 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 thatCopyright © Esgee Technologies Inc. |www.esgeetech.com|VizEM version 1.8 (Feb 2012)

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 meshcells resolve a wavelength (a rule-ofthumb); which means a typical mesh celldimension about 3 mm or less.
The geometry is divided into 5
physical sub-domains: the waveguide,
the top dielectric window, the gas, thewafer and the pedestal. The bottom
Figure 2: The z-component of the microwave field.
panel in Figure 1 shows a 90o cut throughthe 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 offrequency of 2.45 GHz is launched at
the inlet of the waveguide. The wave
is polarized with a single non-zerowave component in the z-direction(direction along axis of reactor). Thewave travels horizontally in thewaveguide and reflects of the mirror
surface following which it propagatesvertically down the reactor axis to thetop dielectric window. The wave thentravels radially along the thickness of
Figure 3: The y-component of the microwave field.
the quartz dielectric and finallylaunches 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 itis launched into the main reactor volume.
Figure 2 shows the z-component of themicrowave field. The wave reflection at
the waveguide mirror surface at the L-bend
produces a y-component of the wave field
as shown in Figure 3. Finally, the wave
reflects of the outer walls of the reactor to
produce non-zero x-components of thewave field as shown in Figure 4. The threedimensional geometry therefore results inall three components of the wave field
Figure 4: The x-component of the microwave field.
Copyright © Esgee Technologies Inc. |www.esgeetech.com|VizEM version 1.8 (Feb 2012)becoming active in the reactor even though only a single non-zero wave field component is launched in
the reactor.
The VizEM software package provides a very robust environment to solve such problems with quick
turnaround. The VizEM software is available through the Overviz framework. This framework features
an easy-to-use interface that provides utilities for problem set-up, problem solution, and postprocessing of the solution. Once a mesh is available, the 3D problem discussed in this note can be setup within a matter of a few minutes. The Overviz framework provides “intelligent” default options thatthe user can trust and use in the absence of additional information.
The different modules within the VizEM software package are used seamlessly within the othersoftware packages offered by Esgee Technologies. For example the Frequency-Domain Electromagnetic
Wave Solver Module used in the above problem can be called by the VizGlow Plasma Modeling Software
Package to solved coupled electromagnetic wave—plasma problems, such as in microwave reactors andinductively coupled plasma reactor. Examples of such coupled problems are discussed in other
Application Notes.
For further information on this application note or details about the VizEM and other software
packages you may contact us atEsgee Technologies Inc.
14, North PeakAustin, Texas 78746, USA
info@esgeetech.com
www.esgeetech.com

Copyright © Esgee Technologies Inc. |www.esgeetech.com|VizEM version 1.8 (Feb 2012)