electron collision cross sections and transport parameters in chf3

ELECTRON COLLISION CROSS SECTIONS AND TRANSPORT PARAMETERS IN CHF3

J. D. ClarkI, B.W. Wright\ J. D. Wrbanek\ and A. Garscadden2 IDept. of Physics, Wright State University, Dayton OH 45435 2Air Force Research Lab, WPAFB

INTRODUCTION The modeling of gas discharges requires the accurate experimental or theoretical determinations of a large amount of atomic and molecular collision data. Among these are the interactions of electrons with CHF 3 due to its applications to replace CF4 in low pressure plasma processing employed in the semi-conductor industry for etching and deposition. However only a modest amount has been published on low energy electron scattering cross sections of CHF 3 and nothing on its electron transport parameters. This study looks at electron drift velocities in the low EIN regime to determine vibrational excitation and total scattering cross sections in CHF3 • The total scattering cross section was estimated by Christophorou l using the Born approximation and as expected, it is quite large due to the polar character ofCHF 3 • Recently, Sanabia etal2 have measured the total cross section for 0-20eV electrons. It is approximately constant above 2 eV at 15 x 10.16 cm2 and then below 2eV increases rapidly as the electron energy tends to zerocharacteristic of s-wave scattering. Other electron collision cross sections have not been reported in the literature for low electron energies, however the similarity of CHF 3 to CH4 and CF4 would suggest that it has large low-energy vibrational excitation cross sections.

EXPERIMENTAL APPARATUS The experiment is a classical pulsed-Townsend type described in detail in reference 3 with only slight modification. The drift tube consisted of parallel plates enclosed in a glass vacuum housing. A fixed drift distance of 2.45 cm was chosen with 6 cm diameter electrodes used to create the uniform electric field. A photoelectron swarm is initiated by illuminating the cathode with a 1 mJ, 6 ns quadrupled NdYag laser pulse at 266 nm. This swarm drifts, under the influence of a uniform applied electric field, towards the anode where the electrons are collected. A charge-coupled current-integrating

Gaseous Dielectrics VlII, Edited by Christophorou and Olthoff, Plenum Press, New York, 1998

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amplifier converts the electron swarm (displacement-) current into an integrated current versus time waveform, which is analyzed to determine the arrival time of the centroid of the swarm. The drift velocity is then determined as the ratio of the drift distance to the arrival time. Drift velocity measurements (Figure 1) were made as a function of EIN in gas mixtures of 0.1 % to 2% CHF 3 in Argon. The mixtures were made by volume mixing in the drift tube using pure Ar (Airco Research Grade) and CHF3 (98% Aldrich Chemical Company) or premix of 5% CHF 3 in Ar (Matheson Semiconductor grade). The mixing ratios were determined by pressure measurements using 10 Torr and 1000 Torr capacitive manometers. The drift velocities were reproducible between gas samples and fills to within 2%. This accuracy was within the experimental uncertainties. The largest uncertainties occur when the drift velocities change rapidly with EIN or with fractional concentration of CHF 3 • These uncertainties can rise as high as 10% for particular EIN points at the lowest concentrations but the average uncertainties are less than 5%. +----+ Argon 30

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Calculation 2%CHF3-Ar 1%CHF3-Ar 0.8% CHF3-Ar 0.6% CHF3-Ar 0.2% CHF3-Ar 0.4% CHF3-Ar 0.1% CHF3 - Ar

20

-

'".,.... 0

?;." 10

ElN (Td) Figure 1. Electron drift velocity (experiments and theory) plotted versus EIN for mixtures of CHF J in Argon. The drift velocity in pure Ar is also shown for comparison.

In Figure 1, we can see that changes in the drift velocity both in magnitude and shape are affected by small changes in mixture concentration. In these mixtures a maximum in the drift velocity appears and is known to occur when the ratio of the inelastic scattering frequency to the total momentum transfer frequency changes rapidly with electron energy. This phenomenon is called "negative differential conductivity" (NDC) and is generally observed in mixtures with molecular gases with large rotational or vibrational excitation channels. Mixtures which show NDC exhibit a behavior where the peak in the drift velocity correlates with the same average electron energy and in Ramsauer gas-molecular gas mixtures, is close to the Ramsauer minimum. This result can be verified from Figure

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2, where the drift velocity is plotted as a function of the average electron energy. At low molecular gas concentrations, the acute sensitivity of the drift velocity to small changes in the inelastic channels created by the addition of the molecular gas shows the usefulness of this swarm technique to determine these low energy cross sections. 40

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+---+ 2.0%CH~-Ar

_1.0%CH -Ar . - - . 0.8%CH~-Ar ----- 0.6% CHi=:-Ar 9---'i1 0.4% CH -Ar

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AVere1J6 Electron Energy (eV) Figure 2. Drift velocity plotted versus average electron energy.

ANALYSIS OF CROSS SECTIONS The motion of an electron swarm in a uniform electric field can be related to the scattering cross sections of the gas by the Boltzmann Transport Equation (BTE). The electron drift velocity (wJ was obtained by a conventional "two-term" numerical solution of the BTE. The analysis proceeds by constructing a trial cross section set for the CHF 3, calculating the drift velocity and comparing to the experimental data. The comparisons and modifications of the cross sections were repeated until a satisfactory agreement between the calculated and experimental data was achieved. The collision cross sections of Ar were taken from Ref. 4, and were fixed throughout this study. The trial cross section set was chosen based on comparisons to similar molecular species such as CH4 and CF 4 , These gases have large low energy vibrational excitation channels and Ramsauer-Townsend minima in their momentum transfer cross sections. The similarity of CHF 3 to these gases suggested that it would also have large vibrational excitation cross sections. The vibrational thresholds and relative excitation strengths were taken to be similar to the oscillator strengths from IR absorption spectra5 shown in Table 1. For simplicity only two vibrational excitation modes were assumed to be important, v5, which corresponds to a C-F vibrational mode with by far, the largest oscillator strength and v I, which corresponds to a C-H vibrational mode and to the highest threshold energy. The initial scale of the excitation cross sections was taken from the relative absorption strength. The shape of the cross sections was taken as similar to those published for CH4 and CF 4 , However, the momentum transfer cross section should differ from these gases since CHF3 is highly polar. The momentum transfer cross section has

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been estimated by Christrophorou) using a Born approximation and was used in the initial trial cross section set. All three cross sections were modified until the calculated drift velocities converged with the experimental measurements for all of the mixture ratios. These final cross sections are shown in Figure 3.

Modes vI v2 v3 v4 v5 v6

10000

Table 1 Frequency Threshold Absorption cm·) Energy (eV) (arb. Units) 3051 0.378 12 1140 0.141 nJa 700 0.087 6.7 44.2 1372 0.170 0.144 1152 327 507 0.063 2.4

___ Total rromentum transfer Vibrational ElccitaIion 0.14 eV Threshold '1--'iI Vibrational Elccitation 0.38 eV Threshold G-----fl

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0

i

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Energy(eV) Figure 3. Swann unfolded electron collision cross sections detennined in this work.

The calculated drift velocities using the converged cross section set are shown in Figure 1 as the solid lines through the experimental data points. Sufficient agreement was obtained and no additional excitation cross sections were added to the cross section set. Comparisons of calculated to experimental drift velocities are shown in Figure 4 as a fractional difference versus the average energy of the electron swarm. The agreement of the calculated drift velocities lies within the experimental uncertainties of 5% for most of the data sets with divergence at the extremes where the sensitivities of the experiment are reduced. The agreement is good from the threshold region of the vibrational excitation toward higher energy. The deduced vibrational excitation cross sections were consistent in size and shape to similar molecules. The total momentum cross section was exceptionally large and

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exceeded recent measurements2 by at least an order of magnitude. The origin of this difference is not known; changes in the inelastic cross sections with a lower momentum cross section did not give agreement with experimental data.

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0.1 % CH~-Ar 0.2% CHr-_-Ar _____ 0.4% CH!:!-Ar ____ 0.6%CHr-_-Ar 9-------9 0.8% CHi=!-Ar ~ 1%CHF-H 0--- 2% CH~-Ar +--+

,---,--,-........,r-r-..,-----.-----r---,---,r-T-r-.,....,..,-----i

10

6------6

o -10

0.1

Average Electron Energy (eV) Figure 4. Fractional difference of experimental and calculated drift velocities

ELECTRON ATTACHMENT In this study of electron drift in CHF3- Ar mixtures the formation of negative ions was observed. This was evidenced by the continued growth in the collected charge from the drift tube after the electron swarm had arrived. Arrival of charge at long times is attributed to ions from ionization or from attachment. Since the average energy of the electron swarm was less than 2 eV for most of the mixtures and conditions where ions were observed, electron attachment to form negative ions was assumed. The attachment coefficient then is determined by measuring the ratio of the collected ion charge to that of the electron charge. The equation below gives the relationship between the ion and electron signals, the attachment coefficient,TJ, and the drift distance, d. V-ion + Velectron TJd Velectron = [1- exp( -TJd)] Electron attachment coefficients were measured as a function of EIN for gas mixtures from 2.5% to 10%. The electron collision cross section set determined above was used to convert the electron attachment coefficient from its dependence on EIN to a dependence on average electron energy. All measurements collapsed to the single curve shown in Figure 5. The peak in the low energy electron attachment would generally indicate a stabilized attachment to the parent ion CHF3• This kind of attachment-stabilization often has a pressure dependence which enhances the stabilization. However, we observed no pressure dependence from 200 torr to 1000 torr total pressure. The exact negative ion or ions cannot be directly determined with this technique, therefore a highly attaching

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impurity is a possibility. However, sensitive mass analysis of the sample gas used in this study could not identify a likely candidate responsible for this behavior6 • The attachment coefficients determined here would indicate a moderately attaching gas at these low electron energies. Previous studies of attachment in CHF 3 at low energy or thermal energy have measurements that are two orders of magnitude highee or lowerS than the current measurements. The differences in the low energy attachment coefficient/rate and product channels of the attachment have yet to be resolved.

§

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0.2

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Average Electron Energy leV] Figure 5. Density reduced attachment coefficient versus average electron energy. The error bars represent the statistical deviation between several data points at the same average energy.

CONCLUSIONS Measurements of electron transport have been made for mixtures of technical interest employing CHF 3• A set of electron-molecule collision cross sections has been derived consistent with measured electron drift velocities to enable EEDFs to be calculated for other mixtures that use CHF3• Three low energy collision cross sections were included in the set, total momentum transfer and two vibrational excitation cross sections. In addition, low energy electron attachment was observed with a peak in the attachment coefficient towards zero energy.

REFERENCES I. 2. 3. 4. 5. 6. 7. 8.

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L.G. Christophorou, J.K. Olthoff, and M.V.V.S. Roa" 1. Phys Chem. Ref. Data 26,1-15(1997). J. E. Sanabia, G. D. Cooper, J. A. Tossell, and J. H. Moore, J. Chem. Phys. 108,389 (1998). D. J. Mosteller, M.L. Andrews, J.D. Clark, and A. Garscadden, 1. Applied Phys. 74,2247 (1993). Y.Nakamura and M. Kurachi, J. Phys. D. 75, 703 (1994) T.D. Kolomiitsova, S.M. Melikova, and D.N. Shchepkin, Opt. Spectrosc.(USSR) 67, 347 (1989). C. Q. Jiao, R. Nagpal, and P.D. Haaland, Chem. Phys. Let. 269, 117 (1997) T. G. Lee, J. Phys. Chem. 67, 360 (1963). A. A. Christodoulides, R. Schumacher, and R. N. Schindler, Int. J. Chem. Kin. X, 1215 (1978).

DISCUSSION G. R. G. RAJU: The peak observed in the electron drift velocity as a function of EIN is interesting. Is it due to the Ramsauer cross section of the parent gas or due to vibrational excitation?

J. D. CLARK: It is due to both the presence of inelastic vibrational excitation (modifying the electron energy distribution function) and the Ramsauer cross section of argon in this case. M.-C. BORDAGE: You determined your cross section set by comparing with your drift velocity measurements. Are there other measurements available in the literature such as D.j/l, for example?

J. D. CLARK: There are no other electron transport data to our knowledge. However, reported at this meeting is the work of Wang et al. on electron drift velocities in CHF3-Ar mixtures also. YICHENG WANG: We did similar experiments and we had serious problems with the "supposedly" ultra-high purity commercial gases, particularly Ar. We found that Ar had to be further purified. The results on the electron drift velocity in pure Ar before purification can differ from those after purification by a factor of 4 to 5 for low EIN near 0.1 Td. I wonder whether you had similar problems in your experiments.

J. D. CLARK: While we have seen effects due to impurities in Kr and Xe (pure), we do not observe these effects in pure Ar after pumping and baking the experimental apparatus. A base line measurement of pure Ar was made before each sample run to ensure that the system was clean.

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