Model of slot antenna for MPECVD of carbon nanostructure

A model of a slotted waveguide antenna for microwave plasma enhanced chemical vapor deposition (MPECVD) of carbon nanostructures at low pressure is developed. The performance of two slot applicator for the production of dense plasma in the working gas (argon) at a frequency of 2.45 GHz is investigated by EM field simulator. Results show that dimensions of the symmetrical slots (length l ≤ λg/2, width of d = 6-10 mm) and optimized angle (φ=32° with respect to the waveguide central line) have a strong influence on the impedance matching of the waveguide to the dielectric window and plasma column (1.5 < SWR < 2.5), and on the radiation efficiency. The dielectric plate and plasma column density were taken into account in the model in the optimisation of the dimensions of the slots. The mode structure of standing surface waves in the plasma column is investigated at three values of plasma density and results for the radial (n=1) and azimuthal wave numbers (m=3, 4, 5) are in agreement with experimental results.


Introduction
The planar microwave discharges are widely used in plasma technology as sources of high-density plasma with a large number of reactive particles and without impurities [1].Large area plasma processing in vacuum chambers requires applying microwave launchers with larger dimensions than the surfaguide exciter as the slot antennas [1].One of the most commonly used slot antennas is an antenna with two inclined slots in the wide side of the waveguide supplying the microwave power [2,3,4], which is characterized by simple construction and efficient operation.The antenna is positioned above a cylindrical quartz window, which seals the vacuum chamber and the window is microwave transparent.The microwave field radiated from the antenna, causes a gas breakdown in the chamber and standing surface-wave discharge sustains the plasma column [5].
The radiation pattern of this antenna depends on the position on the wide wall of the waveguide, the length and width of the slots [6], but also depends on the inclination angle to the waveguide central line [2].The microwave applicator system at a frequency of 2.45 GHz of the plasma reactor includes slot antenna in WR430 or WR340 waveguides, quartz window with a diameter of 150-500 mm [4] and thickness of 12.7 mm-20 mm.The gas mixture and the resulting plasma parameters at constant input power also affect the performance of the applicator because the plasma [3] is a variable load impedance that depends on the absorbed power.In the gas mixture (Ar/H 2 /CH 4 ) used in MPECVD process of carbon nanostructures [7] argon is the main gas sustaining the plasma column.Design of the microwave applicator for specific dimensions of the plasma reactor and applications requires that all the features of the vacuum chamber and the expected value of the plasma impedance [8] be taken into account to obtain it's optimal parameters.In this study modelling the applicator in WR340 waveguide is investigated the effect of the angle of inclination of the slots on the maximum of the total electric field in the plasma column.The mode structure of standing surface wave [8] in the plasma column at three values of the density are obtained and they are in agreement with experimental results.

Experimental setup
The experimental setup for PECVD of carbon nanostructures includes microwave applicator and quartz window, which seals the vacuum chamber as is shown in figure 1 (a).The dimensions of vacuum chamber are 600 mm x600 mm x600 mm metal cube manufactured by KJL Company.On the top wall is positioned quartz window with diameter of 200 mm and thickness of 16 mm.
The waveguide WR340 is made of brass and has a large wall of 86.36 mm where two inclined slots are cut at an angle to the central line of 2 degrees and a length of 1.20 mm. he location of the two slots is chosen to coincide approximately with the maximum of the amplitude of the wall currents in the waveguide by sliding short at the end of the waveguide, so that the values of the radiated fields to have maximum values.Thus, a significant increase in microwave applicator efficiency is achieved when a plasma column with suitable parameters for the deposition of carbon structures is taken into the model.In the analysis of the radiation from the slot antenna in the plasma column, an electromagnetic simulator CS Microwave Studio® was used, which provides options for solving such tasks applying the finite element method FEM for calculations.The one of advantages of this method is that it is more suitable for work because it is possible to calculate inclined and curved boundaries and fine structures that need a higher resolution.In the simulations are applied macros which define materials as quartz and plasma, by using the values of parameters such as frequency of waves f=2.45 GHz, pressure of 500-1000 Pa, type of gas mixture (Ar/H 2 /CH 4 ) and conductivity (elastic collision frequency) which help to calculate dispersion and dielectric losses.The CST simulator is a convenient tool that uses the real materials of the structure making the model as well as the plasma parameters close to that in the deposition process [9].

Results
Simulations were carried out at three different electron densities, where a similarity between the obtained experimental results regarding the excited modes is established.Optimizing the parameters of the slot antenna, the quartz window (ε r =3.8) and the plasma column are considered in the simulation as well as the matching of the applicator system to the generator (1.5 < SWR < 2.5).The height of the plasma column is fixed at 50 mm, because at this distance the penetrated EM field decreases near to zero.The low-density regime is modeled at plasma density n e =1.39x10 17 m -3 , above the critical density for surface wave discharges he result of the simulations shows that the maximum ele tri field in the plasma olumn is o tained at an angle of 32-33 degrees of in lined slots (figure 2 , and not at 2 -2 as in the standard antennas [2][3][4].Since we have considered the propagation of surface waves, the abbreviation TM indicates that only transverse magnetic modes are propagated.This means that the EM field does not have a component of the magnetic field in the r-direction (H r =0).The surface wave along the boundary quartz-plasma (r-direction) is a fundamental transverse magnetic mode (TM).For a circular geometry cross-section of radius R, TM mn modes denote m th -order Bessel function and n is the nth root of the same function and they describe the distribution of the electric field.On the other hand, the mode structure is limited to a set of discrete values [8] of azimuthal and radial indexes depending on the plasma density.
Mode structures and mode jumps with increasing plasma density have been studied in detail in [8,11] at lower gas pressures of 24-140 Pa in a planar surface wave discharge and for the modes observed in our experiment at pressures of 500-1000 Pa, a corresponding theoretical model should be developed.

Conclusion
A model of microwave applicator of planar surface wave discharge for MPECVD of carbon nanostructures at low gas pressure is developed.Results show that at fixed length of 61.2 mm and width of d= 10 mm of the symmetrical slots the optimi ed angle is 32 with respect to the WR340 waveguide central line.At this inclination angle of the slots the microwave applicator is well matched to the waveguide (1.5 < SWR < 2.5) and total electric field in the plasma column has the highest values.The mode structure of standing surface waves in the plasma column is obtained at low, middle and high values of plasma density and results from the model show that the common radial wavenumber is n=1 while azimuthal wavenumber (m=5, 4, 3) decreases with increase of the plasma density which is in agreement with experimental observation.

Figure 1 .
Figure 1.Experimental setup with (a) microwave applicator above quartz window in the vacuum chamber and (b) and model of the applicator with plasma column.

Figure 2 .
Figure 2. Dependence of highest value of total electric field in the plasma column on the inclination angle. he clear mode structure of standing wave in the plasma column is o tained and good matching of the systems if the angle of the slots increases from 2 to 32 in the model.t slot angle of 32 agreement with mode structures in the experiment are observed (figures 3, 4, 5) also at middle density of n e =6.1x10 17 m -3 and at n e =1x10 18 m -3 .

Figure 5 .
Figure 5. Plasma mode structure (TM 3,1 ) at n e =1x10 18 cm -3 and image of the optical emission from plasma column.