APPLIED PHYSICS LETTERS
VOLUME 72, NUMBER 10
9 MARCH 1998
Novel microwave plasma reactor for diamond synthesis
a)
M. F u¨ ner, C. Wild, and P. Koidl
Fraunhofer-Institut f u¨ r Angewandte Festk o¨ rperphysik, Tullastrasse 72, D-79108 Freiburg, Germany
͑
Received 30 September 1997; accepted for publication 9 January 1998͒
Numerical simulations were performed to predict the performance of microwave plasma reactors
with various reactor geometries. The simulations include the calculation of the electric field
distribution using the finite integration theory and the determination of the plasma density
distribution based on a breakdown field algorithm. One reactor geometry with a cavity having the
shape of a rotational ellipsoid turned out to be very promising. The electric field within this cavity
exhibits two pronounced maxima at the two focal points of the ellipsoid. By coupling microwave
energy into one maximum via an antenna, large electric field strengths can be generated in the
counter maximum. This effect has been used to excite intense discharges that are very stable,
spatially extended, homogeneous, and free from wall contact. These discharges were employed for
the chemical vapor deposition of large area diamond wafers. © 1998 American Institute of
Physics. ͓S0003-6951͑98͒01810-5͔
Among the various techniques for the chemical vapor
deposition ͑CVD͒ of diamond, microwave plasma CVD has
gained considerable importance due to the capability of pro-
ducing high quality diamond films and wafers with reason-
able growth rates and deposition areas. The development and
optimization of microwave plasma reactors however is
troublesome, since it is difficult to predict the performance of
new reactor geometries intuitively. The difficulty mainly
arises from the fact that the microwave field and the plasma
are highly interactive. A development based on trial and er-
ror on the other hand, is very time consuming and costly. For
these reasons, the numerical simulation of microwave
plasma reactors has been found to be of considerable
density in a cell is zero if EϽE and if no plasma is present.
Once a plasma is excited ͑either due to breakdown,
B
EϾE , or because there is a plasma in an adjacent cell͒ the
B
plasma density is given by nϭ␥(EϪE ). For E and EM
M
B
7
approximate values can be found in the literature. The pa-
rameter ␥ has been obtained by adjusting the modeling re-
sults to experimental observations.4
The interaction between the plasma and the microwave
field is taken into account by determining the dielectric prop-
erties of the plasma8 and by calculating iteratively the elec-
tric field and plasma distribution until the result converges
towards a self-consistent solution.
,9
To verify the reliability of our reactor simulation model,
the electric field and plasma distribution of existing micro-
wave plasma reactors were calculated and found to be in
1
–3
interest.
Sophisticated models have been developed to
simulate the electromagnetic fields, the electron distribution
function, particle transport, and hydrocarbon chemistry.2,3
Often, however, the reliability of these models is limited
since they require the knowledge of many parameters such as
rate constants for ionization and excitation, diffusion coeffi-
cients, mobilities, recombination rates.
4
good agreement with experimental observations. The model
was then used to study completely new reactor geometries.
One specific geometry turned out to be very promising.
The cavity of this reactor has the shape of a rotational ellip-
soid. Those ellipsoids are already used as a mirror furnace in
crystal growth.10 They take advantage of the fact that each
ray emitted by a halogen lamp located in one focus of the
ellipsoid passes through the second focus where a sample is
positioned. The question was whether this principle can be
transferred to the excitation of microwave plasmas. The main
difference is of course, the wavelength. That of visible light
is much smaller than the dimensions of the mirror furnace.
Hence, ray optics can be applied. On the other hand, the
wavelength of microwaves in the GHz frequency region is
not much smaller than the cavity dimensions. The simula-
tions, however, revealed that the electric field strength in an
ellipsoid cavity exhibits two pronounced maxima at the two
focal points.
We have applied a simplified model that aims solely at
predicting the shape and position of the plasma within a
projected microwave reactor. The algorithm has been de-
scribed in Ref. 4. It uses the finite integration technique for
5
solving Maxwell’s equations. In this technique the cavity is
divided into small cells. Each of the cells can be filled with
materials such as metals, insulators or plasma, described by a
complex dielectric constant. The boundary conditions be-
tween different cells are fulfilled automatically. For the de-
termination of the plasma density a semiempirical approach
is applied. It assumes that the plasma density is a function of
the local electric field. This assumption is justified since dif-
fusion can be neglected at elevated pressures in the range
6
5
0–200 mbar. The plasma algorithm is based on two elec-
Figure 1 shows the theoretical distribution of the electric
field strength in an ellipsoid reactor. The calculation was
performed with a 2.45 GHz microwave frequency and 60 cm
total height of the cavity. The microwave is coupled into the
cavity via an axial antenna from the top. The two field
maxima at the focal points are strongly coupled and a factor
tric field strengths: the breakdown field EB necessary for
igniting a discharge and the smaller maintenance field EM
ϽEB necessary for maintaining a discharge. The plasma
a͒Electronic mail: fuener@iaf.fhg.de
0003-6951/98/72(10)/1149/3/$15.00
1149
© 1998 American Institute of Physics
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