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L4-13631-TThesis
Issued: August 1999
Eiching of L102 in
NF3 RF Plasma Glow Discharge
John M. Veilleux
Los AlamosNATIONAL LABORATORY
Los Alamos, New Mexico 87545
Acknowledgments
I wish to thank Dr. Mohamed S. E1-Genk, my University and doctoral
advisor, who guided me during a verytrying time in my life, and helped me keep
this vision of a doctorate in mind. Mr. f-lamed Saber provided many important
observations and modeling insights to help me through an understanding of the
plasma reactions. Dr. E. Phil Chamberlain, my mentor at the Los Alamos National
Laboratory, guided me through the experimentation phase of my research, and
helped me really understand the meaning of applying science principles to an
observable.
I thank also Dr. Carter Munson and Dr. David Curtis of the Los Alamos
National Laboratory, who provided the overall technical direction and funding for
this work, as well as Dr. John Fitzpatrick, who provided guidance on the
chemistry of the plasma work. Special thanks are also due to the Chemical,
Science, And Technology Division’s Environmental Science and Waste
Technology Group (CST-7) for their continued funding of this waste
decontamination research project.
I thank also Catherine Auckland for her encouragement and patience who
made the process of pursuing a Ph.D. bearable.
This work was supported by CST-7 and CST-I 1, Los Alamos National
Laboratory, under the GRA program and by the Waste-Management Education
& Research Consortium under contract DE-FC-04-90AL-63805 to the Institute for
Space and Nuclear Power Studies.
v
Table of Contents
Acknowledgments .............................................................................................. v
Table of Contents ............................................................................................. vii
List of Figures .................................................................................................... ix
List of Tables ..................................................................................................... xi
1.1. Previous Work on Radionuclide Etching .................................................... 11.2. Application of RF Glow Discharge for Waste Processing .......................... 21.3. Objectives of This Work .............................................................................21.4. Organization .............................................................................................. 3
Chapter 2. Background and Literature Search ................................................. 5
2.1.2.2.2.3.2.4.2.5.2.6.2.7.2.8.2.9.
Plasma Description .................................................................................... 5Plasma Models .......................................................................................... 6Major Species in the Bulk Plasma ............................................................. 7Transport of Reactive Species to a Surface ..............................................7Etch Concepts from Semiconductor Applications ...................................... 8Chemical Etching of U02 with F2 ............................................................... 9Uranium and Fluorine Chemistry and Thermodynamics .......................... 10Liquid Scintillation Counting (LSC) .......................................................... 10Analysis ................................................................................................... 11
4.1. The Etching Process ................................................................................ 524.2. Effect of Absorbed Power ........................................................................ 534.3. Effect of Plasma Gas Pressure ............................................................... 584.4. U02 Etch Rates ....................................................................................... 62
CHEMKIN Description ............................................................................. 64The CSTR Approximation ........................................................................ 66Plasma Reactions in CHEMKIN .............................................................. 67Surface Reactions ................................................................................... 71Thermodynamic Constants ...................................................................... 73CHEMKIN Validation ............................................................................... 73CHEMKIN Predictions for the Present Experiments ................................ 79Limitations on the Use of CHEMKIN ........................................................ 84
Chapter 6. U02 Etching And Application To Plutonium ................................. 85
6.1. The Plasma Species ................................................................................ 856.2. Reaction Model ........................................................................................ 87
6.3. Thermodynamic Analysis of Surface Etch Reactions .............................. 89
6.4. Volatile Surface Species .......................................................................... 94
6.5. Applications to Pu02 ................................................................................ 96
Chapter 7. Summary And Conclusions ......................................................... 100
Chapter 8. Recommendations for Continued Work ..................................... 103
8.1. Experiments with Depleted U02 ............................................................ 1038.2. Recovery system ................................................................................... 1048.3. in-Situ Measurements ............................................................................ 1048.4. Pu & PU02 work ..................................................................................... 104
Transport of Plasma Species to the U02 Surface . ............................... 8RF Plasma Reactor& Recovery System ............................................ 16~lasma Test Chamberand Schematic of RF Antenna ....................... 16~lectrical Circuits . ............................................................................... 17Matching Network Power Equivalency. .............................................. 17~owered Electrode Voltage, No Plasma . ........................................... 20‘owered Electrode Voltage, With Plasma ..........................................2l4bsorbed Power vs NF3 Gas Flow Rate ............................................. 214bsorbed Plasma Power as Function of Transmitted Power. ............22Measured DC Sheath Voltage in Experiments . ................................ 23NF3 Gas Flow Rate in SCCM . .......................................................... 25Pressure Variation with Absorbed Power and Gas Flow. .................25Experimental Flow Rate vs. Manufacturer’s Correlation ................... 26Depleted Uranium Alpha Spectrum . .................................................29Uranyl Nitrate Hexahydrate Spectra by Liquid Scintillation. .............29Specification of Uranyl Nitrate Hexahydrate Solution. ...................... 30Liquid Scintillation Discriminator Setting ........................................... 35233UStandard Used To Calibrate the LSC Discriminator. ................35Alpha and Beta Detection Efficiencies. ............................................36Detection Efficiency Vs. Solution pH . ............................................... 36Lower Detection Limits. ....................................................................39Spectrum Analysis for Sample Count Rate . ..................................... 41Temperature Rise in Plasma Reactor . ............................................. 43Accuracy of the Measurements . .......................................................46Uncertainty in Measured Fraction of UOZ Etched .............................46Typical Plasma Operations. .............................................................47Glow Discharge Observations at 50 W Absorbed. ...........................48Fraction of U02 Etched in NF3 RF Plasma . ......................................53Power Effects on U02 Etching at 17 Pa . .......................................... 55Effect of Power on NR,~,Xat 17 Pa ................................................... 56Effect of Power on t at 17 Pa ........................................................... 56Power Effects on U02 Etching at 10.8 Pa ........................................57Power Effects on U02 Etching at 32.7 Pa ........................................ 57Power Effects on U02 Etching at 39.4 Pa ........................................ 58Pressure Effects on U02 Etching at 25 W ........................................ 59Pressure Effects on U02 Etching at 50 W ........................................6OPressure Effects on U02 Etching at 100 W ...................................... 60Pressure Effects on U02 Etching at 170 W .....................................6 IPressure Effects on U02 Etching . ....................................................6lInitial Etch Rate of U02 . ................................................................... 63Average Etch Rate at 17 Pa . ............................................................63Experimental Setup of Perrin et. al ................................................... 77Comparison of CHEMKIN with Si Etching Experiments. ..................78
Maximum Variation in Rate Coefficient . ........................................... 78CHEMKIN Neutral Species Predictions at 17.0 Pa. ......................... 82CHEMKIN Ion Predictions at 17.0 Pa ...............................................82CHEMKIN Pressure Predictions . ...................................................... 83CHEMKIN Sensitivity with Flow Rate ............................................... 83Gibbs Free Energy of Formation for Uranium Fluorides/Oxyfluorides........................................................................................................... 92
Figure 50. Gibbs Reaction Energy, GR, for U02 Etching . .................................. 93Figure 51. Gibbs Reaction Energy, GR, for U Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 52. Vapor Pressure of UFX Compounds . ................................................ 95Figure 53. Average Etch Rate ~ of UOZ Compared with PuOZ. ....................... 97Figure 54. Vapor Pressure of PUFGand UFGCompared .................................... 99Figure 55. Plutonium Compound Gibbs Free Energy of Formation ................... 99Figure B-1. RF Antenna . ..................................................................................ll6Figure B-2. Plasma Reactor and Recovery System. ....................................... 117Figure B-3. Inlet and Reactor Conditions .........................................................l2lFigure B-4. Experimental & Manufacturer’s Flow Calibration Data .................. 124Figure B-5. Rotameter Gas Flow Calibration ................................................... 125Figure B-6. Recovery System Flow and Throughput Characteristics ..............129Figure B-7. Recovery System Pressure Differential & Conductance ...............130Figure B-8. Effect of RF Power on Reactor Pressure ...................................... 133Figure B-9. Rotameter Setting During Plasma Operation ................................ 135Figure B-1 O. Plasma Extinguishing Pressure .................................................. 136Figure B-11. Type of Flow in Plasma Chamber . ............................................... 137Figure D-1. Determining the HF Partial Pressure ............................................ 153Figure D-2. Comparison of Chemkin and Experiment ..................................... 153Figure E-1. NF2 and NF3 Geometrical Cross Sections .................................... 160Figure E-2. Cross Section Correlation .............................................................l6lFigure E-3. Ion Energy Dependence on Cross Section . .................................. 163Figure E-4. Reaction Sequence of F Atoms and UOZ. .................................... 170Figure E-5. Reaction Sequence of F Atoms and U Metal . ............................... 170
Plasma Etch Modeling Mechanisms ................................................... 12Modeling Approaches .......................................................................... 13Characteristics of Plasma System ....................................................... 15VPPCorrelations with Pt,, Plasma Ignited. ............................................ 19Absorbed Power Correlation with Rotameter Setting, F (cm) .............. 20Planchetie Characteristics ...................................................................26Activity and Mass Parameters of Sample Solution ............................... 28Sample Specifications ......................................................................... 31Detection Limits of Depleted U02 Samples ......................................... 38
Measurement Uncertainties ............................................................... 45Equations and Related Error Functions .............................................49Plasma Observations ........................................................................5lU02 Plasma Processing Results at 17 Pa .........................................55Typical Output Parameters . ...............................................................65Species in NF3 Plasma . .....................................................................68Plasma Chemistry in CHEMKIN . ....................................................... 69Plasma Surface Reactions. ............................................................... 72Parameters of Perrin et. al. (1990) Experiments . .............................. 75CHEMKIN Species Consolidation. ....................................................75Perrin et. al. (1990) Experimental Data at 200 W .............................. 76CHEMKIN Parameters for the U02 Experiment . ............................... 79CHEMKIN Parameters at 17 Pa . .......................................................8OCalculated Mole Fractions of Plasma Species at 17 Pa . ................... 86Plasma Conditions at 17 Pa . ............................................................. 87Bonding Sites for Reaction with F Radicals . ......................................88Favorable Thermodynamic Reactions of U-O-F . ............................... 90Unfavorable Thermodynamic Reactions of U-O-F. ........................... 91SurFace Species Volatility Data. ........................................................96
Table A-1. Physical Properties Of Select Compounds ................................... 108Table A-2. Thermodynamic Properties Of Select Species .............................. 110Table A-3. Enthalpy and Gibbs Energy of Reaction for F Atom Reactions with
Composition Of Stainless Steel ..................................................... 113Nuclear Properties Of Select Isotopes ........................................... 114Characteristics Of Plasma System .................................................ll6Plasma System Parts List . ............................................................. 118Stainless Steel Type 304 Sample Substrates ................................ 119Depleted UOP Experimental Data ..................................................l4OExperimental Mole Fractions & Pressure .......................................l52CHEMKIN Predictions, ~, for Perrin’s Experiment ........................ 154CHEMKIN Parameters for UOP Etching Experiment ...................... 154CHEMKIN Predicted Mole Fractions at 17 Pa for UOP Etching
Parameters for Etch Rate Calculation ............................................l59Physical Data on Select Species ................................................... 160Plasma Sheath Thickness and Ion Energy . ................................... 162Calculated Mole Fractions of Plasma Species at 17 Pa. ...............163Detailed Calculations for NF3 Ion ...................................................l64Energy From U02 Reactions with F Atoms .................................... 166Vapor Pressure Correlation ............................................................ 167
xii
Nomenclature
Symbol DefinitionA Activity (Bq); Specific activity (Bq/g) indicated by bar over A.Bc;
cddeEEAfFFOGGfGRHfHRJ
JOk
k~KckfKnKPLmMnNNA/v~NR,~aP
Pr%
Paa
Exponent of temperature, T, in Arrhenius kinetics relationship.Concentration (mol m-3).Alpha instrument count rate (counts/rein).Beta instrument count rate (counts per minute).Standard state concentration (1 mole/L)Dilution factor.Molecular diameter (m).Relative erro~ Electron chargeEnergy (J)Activation energy (kJ mol-f).Activity ratio of an isotope to the total activity.Flow rate (mol S-l).Inlet flow rate (mol s-l).Molar Production Rate (mol S-l).Gibbs free energy of formation (kJ moi-l).Gibbs free energy of reaction (kJ mol-f).Enthalpy of formation (kJ mol-l).Enthalpy of reaction (kJ mol-l).Etch rate (rein-l; ~m/min); Average etch rate indicated by bar over J.;Flux (m-z S-l)Initial etch rate (rein-l; pm/min).Boltzman’s Constant, 1.381x1 O-23 J K-l; Thermal Conductivity (Win-lK-l)
Reaction rate constant, (cnz3nzolecule~-1S-*, where n is the order of
the reaction.Backward (reverse) rate coefficient of a reaction.Equilibrium constant of a reaction with respect to concentration.Forward rate coefficient of a reaction.Knudsen number.Equilibrium constant of a reaction with respect to pressure.Thickness (m)Mass (kg).Molecular weight (g/mole).Number density (m-3)Number of atoms or molecules.Avogadro’s Number, 6.022xI 023 mol-l.Ratio of remaining to initial activity= (&-A)/AO.Asymptotic value of U02 activity fraction removed.Power absorbed (W).Pressure (Pa).Probability that a beta emission will be correctly counted inwindow.Probability that an alpha emission will be correctly countedalpha window .
...X111
the beta
in the
Symbol Definition
P“ Standard state pressure (1 Bar= 1x1O’ Pa)Pt, Power, Transmitted (W).Q Heat (W)R Gas Constant (8.3144 J mol-l K-l); Radius of glow discharge volume
(m)Rmax Maximum radius of glow discharge volume, equal to 25 cm.r Molar Production Rate per Unit Volume (mol S-ls Sheath thickness (m)s Cross sections! area (m*)SCCM Standard cubic centimeter per minute, gas flow
pressure.t Time (s); plasma process time; counting time;T Temperature (K)
Velocity (m/s): Volume (m3)Vs Sheath Voltage (V)x Mole fraction
GreekSymbol Definition
m-3).
rate at standard
half-life.
Pso
Y
Pv
BetaElectron temperature (in units of volts)Characteristic Etch Time (rein)Enthalpy (kJ mol-l)CountsDensity (kg m-3)Mean free path (m)Debye Length (m)Number of moles; Ratio of absorbed to transmitted powefiEfficiency.Specific gravity (kg m-3)Standard deviation; Cross section (m*)Sticking coefficient for a gaslwface reactantTotal mean counts; true mean of sampleViscosity (Pa-s)
Describesmethodology& equations used in Surface Chemkin. Does notconsiderionacceleration-only diffusing species.
Transportmodelwith diffusion& ion transport in a plug flow reactor.
Transportmodelwith diffusion& ion transport,one dimensional in parallelplate configuration.
Model for transportof neutral species. Transport of charged particlestosurfacesand their effects are not treated.
DevelopsCHEMKIN for use in plasma modelingwithetching. Determinesrate constantsvia solutionsto Boltzman equation. Gives Arrheniusfitstogas phase reactions. Develops governing equations, includingthesurface& plasma chemistry. No ion bombardmentmodeling.
Chemkin NF~02 plasma modeling for Si. Includesextensive chemisttyinthe plasmaalong with rate coeticients.
Continuouslystirredtank reactor approximationfor solvingkinetics&chemicalreactionsat surface. Uses surface Chemkin. No ionacceleration.
Transportmodelwith diffusion,no ion transport Parallel plate radialflowreactor.
Monte Carlo Simulation.Examines abstractive & dissociativeadsorptionwithvariousswfaca kineticsincluding surface diffusion,ad-layerordering,and weakly bound physiosorbed precursorstates.
Transport& Poissonequation solution that includesmost of theprocessesin plasma etching: physical sputtering,chemical etching,
,
enhanced physicalsputtering,enhanced chemical etching.
13
CHAPTER 3. EXPERIMENT SETUP
This chapter describes the experimental setup. Included; are the
descriptions of the plasma system, the method for determining the absorbed
power and sheath voltage, the NFs gas flow rate and resulting plasma pressure,
preparation and specification of the uranium oxide samples, the method
developed for achieving reproducible activity measurements of plasma
processed samples, and quantification of the uncertainty in the resulting
measurements. The chapter is concluded with a description of the visual
observations of the plasma during sample processing.
3.1. Plasma System
Experiments were
(Figure 2) with NFs gas
performed using a 13.56 M1-lz RF plasma system
to decontaminate depleted UOZ from the surface of
stainless-steel substrates. The system includes a vacuum chamber for
processing the samples and a fume hood mounted recove~ system for pumping
the chamber during processing. A power supply, matching network, and
electrical circuitry complete the system. Characteristics of the plasma system,
including room and fume hood flow rates, are summarized in Table 3. A detailed
equipment list and drawing of the plasma system is included in Appendix A.
A cubic (- 0.5 m per side) aluminum plasma chamber (Figure 3) with a
total internal volume of O.125-m3 and an internal surface area of 1.623 m2 was
used to process depleted uranium oxide samples in plasma. The RF powered
electrode surface area on which the UOZ samples were mounted measured
0.00203 m2. The volume and surface area were determined by measuring the
dimensions of all internal chamber and protuberances to the nearest centimeter.
A 6.5” x 0.5” thick quartz window provides an internal view of the plasma,
powered electrode, and sample. Details of the RF antenna are also depicted. A
5.08 cm diameter tray was mounted on the antenna holder and the 1.007 cm
diameter stainless steel U02 sample planchettes were placed on the 5.08 cm
14
tray. Under normal conditions, each plasma run was made with two U02
samples in the event one was lost due to experimental error or problems.
An attached fume hood mounted recovery system was used for pumping
the gas out of the chamber during plasma immersion experiments. Its total
volume, 0.0071 m3, was measured by expanding a known quantity of gas from
the plasma chamber. The recovery system was also designed to capture an
effluent radioactive gas by condensation in a liquid nitrogen cold trap, but this
feature was not used in the current experiments. A charcoal trap prevents pump
oil from back-streaming to the chamber and captures toxic gases created in the
plasma, such as F2, preventing escape to the environment. The final trap is the
pump oil itself, which captures any remaining uranium hexafluoride that gets
through the charcoal trap.
An RF20 power supply provides line, or transmitted power up to 2000 W,
an adjustable locally designed water-cooled matching network is used to
maintain zero reflected power during experiments, and a step-down voltage
divider with RF choke is used to measure the effective DC sheath voltage (Figure
4). Earlier experiments utilized a Zenith matching network and transmitted power
corrections were applied to normalize the data to the 1000W matching network.
This correction was done by equating the sheath voltage at varying transmitted
power at 50 cm gas flow rotameter setting and 17 Pa pressure (Figure 5).
Consequently, transmitted power values with the Heathkit matching network
were divided by 0.836 to make them equivalent to the 1000W matching network.
Table 3. Characteristics of Plasma System
Processing Chamber (Internal)Volume 0.125 m$Surface Area 1.623 m’
Plasma Processing Time, t, to Achieve /VR~~X(rein)
Figure 30. Effect of Power on NR,m.. at 17 Pa
60
45
30
15
“o 100 200
Plasma Process Time, t, to Achieve
300
N~,~=(min)
400
Figure 31. Effect of Power on ~ at 17 Pa
56
2“
1.0
0.8
0.6
0.4
0.2
0
.—-— -—-— .— -—-— -—-— - —-— .I
o
]10.8 Pal
o 100 200 300
Plasma Process Time, t (Min)
Figure 32. Power Effects on U02 Etching at 10.8 Pa
1.0
0.8
0.6
0.4
0.2
n
-—-— -—-— -—-— .— -—-—- —-
132.7 Pal
-.0 100 200 300
Plasma Process Time, t (Min)
Figure 33. Power Effects on UOz Etching at 32.7 Pa
57
1.0
0.8
0.6
0.4
0.2
0
[
P=50W
o 30 60 90 120
Plasma Process Time, t (Min)
Figure 34. Power Effects on U02 Etching at 39.4 Pa
4.3. Effect of Plasma Gas Pressure
The pressure effects at 25 W of A/~ versus plasma processing time are
shown in Figure 35. At this power setting, the complete removal of U02 was not
achieved at any pressure. But 17 Pa yielded the highest etch fraction, ~R,~~ =
0.54. At both 10.8 and 31 Pa, the amount etched decreased compared to 17
Pa.
At 50 W and 17 Pa, NR,~~Xapproached 1, indicating the complete removal
of U02 (Figure 36). But at both 10.8 and 39.4 Pa, complete removal of U02 was
not achieved, with similar results at both pressures.
At 100 W, complete remova} of U02 was achieved at all pressures
between 10.8 and 39.4 Pa (Figure 37) with characteristic etch times ranging from
70 to 14.1 minutes as pressure increased. At 170 W (Figure 38), similar results
were achieved but with significantly faster characteristic etch times ranging from
30.5 to 3.7 minutes.
58
To summarize the pressure variation data, increasing the NF3 gas
pressure increased the amount etched, /V~, up to a peak pressure, then the
amount etched decreased as summarized in Figure 39. Above 50 W, ~R
increased monotonically with pressure in the pressure range examined. In
principle, the F atom concentration should decrease with increasing pressure at
constant power because fewer NF3 molecules will dissociate and some F atoms
will recombine to F2 in the plasma and on the chamber walls (Hinz et. al., 1980).
However, in our plasma reactor, the brightening of the glow near the antenna
and the shrinking glow region implied that the effective plasma volume
decreased while ionization increased closer to the antenna. Hence, as pressure
increased, the actual F atom density increased. This effect continued up to a
maximum pressure, then the F atom density decreased, as suggested by the
decreasing amount etched as pressure increased further. In the region where
etching increased monotonically with pressure, the highest etch fractions were
achieved. For example, at 32.7 Pa and 100 W, 99% of the UOZ was removed in
just 17 minutes, compared to 37 minutes at 17 Pa and 210 W.
.— - —-—. — -—- —.— -—-—- —-— -—-—-—-
b .
0 100 200 300
Plasma Process Time, t (Min)
Figure 35. Pressure Effects on U02 Etching at 25 W.
59
1.00
0.75
0.50
0.25
1--- —- —- —-.–- +- —-*–- —-- —-o-1
wQ
o
n
—10.8
u50 w
-.0
1.00
0.75
0.50
0.25
0
100 200
Plasma Process Time, t (Min)
Figure 36. Pressure Effects on U02 Etching at 50 W.
300
a .— -—-—-—- —-—-
R.4
I.w!!!l
50 100 150 200 250
Plasma Process Time, t (Min)
Figure 37. Pressure Effects on U02 Etching at 100 W.
60
1.00
0.75
0.50
0.25
.-
170 WI
o 30 60 90 120
Plasma Process Time, t (Min)
Figure 38. Pressure Effects on UOZ Etching at 170 W
1.0
0.8
0.6
0.4
0.2
00
.- —-— -—.—- —-— -A
c1
t = 53 min
10 20 30
Pressure (Pa)
Figure 39. Pressure Effects on U02
61
40
Etching.
50
4.4. U02 Etch Rates
Figure 40 shows the experimental initial etch rate, $, at 17 Pa and the
trends at other pressures. In developing this chart, some data which did not
include sufficient data points to establish t+~= with reasonable confidence were
not included, such as the high and low pressure data at 25 W. In addition, the
units used for equation (24) were converted to micrometers per minute by
multiplying by the factor 27.64 (Appendix E). These results may be converted to
milligrams per minute by multiplying equation (24) by the factor 13.56.
The baseline data at 17 Pa shows that the initial etch rate increased from
0.2 to 3.1 pm/min as absorbed power increased from 25 W to 210 W. Increasing
pressure generally increased the etch rate, to 7.4 ~m/min at 32.7 Pa and 180
W. When power was set too low for a given pressure, the etch rate also dropped
as indicated by the 39.4 Pa data points. Decreasing pressure (e.g., to 10.8 Pa)
generally resulted in a lower etch rate and this effect was related to the
decreasing brightness of the glow discharge near the antenna, and hence lower
F atom concentration in the bulk plasma.
The average etch rate, ~, needed to compare these results with the
reported PuG average etch rates (Martz et. al., 1991), was obtained by
integrating equation (24) as shown below:
(25)
The average etch rate at 17 Pa is plotted in Figure 41 as a function of
power for values oft/z = O, 2, and 4 where the latter value represents the etching
end point. The experimental etch data for th va~ing between 3.5 to 4.5 is also
plotted showing good agreement between prediction and experiment. the
62
average etch rates at the end point ranged from 0.1 to 0.7 pmlmin between 50
and 200 W. The equivalent mass etch rate is also shown for comparison.
0.1
0.01L J
10
1
0.1
50 100 150 200
resorbedPcYw3r(w)
Figure 40. Initial Etch Rate of UOZ. ~
Experimental Data, 35s U, s 45
8
00, ~o 50 100
Power
Figure 43. Average Etch
150 200
Rate at 17 Pa.
10
1
D.1
1
0.1
0.01
63
CHAPTER 5. CHEMKIN
To understand the physics of the etching process, it was necessary to
determine the type and concentrations of the reactive plasma species in an N~
plasma, including those that react with the UG to form gaseous UF6. Such a
determination was made using an existing RF piasma discharge code,
CHEMKIN Ill: A Fortran Chemical Kinetics Package For The Analysis Of Gas-
Phase Chemical And Plasma Kinetics. CHEMKIN had been previously applied
to silicon etching in CF~02 and NF~02 plasmas with good results (Meeks et. al.,
1997; Meeks and Shon, 1995). The following discussion describes the
CHEMKIN code, the code validation, and the code predictions for the present
experiments.
5.1. CHEMKIN Description
CHEMKINti, a chemical kinetics code developed by Sandia National
Laboratory, is a collection of modules for modeling chemically reacting flows in
chemical reactors and in RF glow discharge plasma. It consists of a number of
Fortran modules or subroutines, data files, script example problems, and
documents to facilitate the modeling of chemical kinetics. It models the chemical
kinetics of reactions in the gas phase and at a gas/solid interface to include the
transport and interactions of ions, molecules, and radicals. Three basic
modules used to model the present experiments were Cl-lEMKIN, SURFACE
CHEMKIN, and AURORA. The AURORA module was selected because it
modeled the plasma as a continuously stirred tank reactor (CSTR) which most
closely approached the experimental conditions of these experiments at 17 Pa.
A utility, FITDAT, was also available to generate thermodynamic polynomial
coefficients in the form needed by CHEMKIN and SURFACE CHEMKIN to carry
out the calculations.
i CHEMKIN is availabie from Reaction Design, 11436 Sorrento Valley Road: San Diego, California92121, Tel: (649) 550-1920
64
The CHEMKIN module (Kee et. al., 1996) solves elementary gas-phase
chemical kinetics, including multi-fluid plasma systems that may not be in
thermal equilibrium. The SURFACE CI-IEMKIN module (Coltrin et. al., 1996)
solves problems involving elementary heterogeneous and gas-phase chemical
kinetics in the presence of a solid surface. SURFACE CHEMKIN was used in
conjunction with CHEMKIN to model the NFs plasma reactions in the present
experiments, but not to determine the etch rate. The AURORA module (Meeks
et. al., 1996) predicts the steady state or time averaged properties (density,
molecular weight, flow rates, etc.) of well-mixed plasma systems and predicts the
ion, electron, and neutral species concentrations in the bulk plasma. It applies
the continuously stirred tank reactor (CSTR) approximation. The module
characteristics are specified by a reactor volume, residence time or mass flow
rate, heat loss or gas temperature, surface area, surface temperature, incoming
gas temperature and mixture, and net power deposition into the plasma. The
module runs in conjunction with CHEMKIN and SURFACE CHEMKIN. Typical
output parameters from CI-IEMKIN are summarized inTable 14.
Table 14. Typical Output Parameters,
Parameter
Mass flow rateTemperature: gas, ions, electronsPressureMean densityMean molecular weightMean volumetric flow rateSCCMResidence timeMole fraction of each speciesConcentration of each speciesMolar flow rate of each speciesMass flow rate of each speciesVolumetric flow rate of each speciesSCCM of each speciesSurface site fractions (etching)Bulk site fractions (etchina)
65
5.2. The CSTR Approximation
Cha@cterization of the plasma reactor and recovery system in terms of,
pressure and flow of gaseous products is determined from the mole balance
contains gases whose total pressure is p, has an inlet flow of to moles of
species j per unit time, t, and an outlet flow of ~ moles per unit time. The
applied RF power causes some of the gas to dissociate while other processes
cause species to undergo other reactions, including recombination, for a net
molar production rate of species j, ~. The net production of moles of species j in
the chamber is the partial derivative of the number of moles of species j,qj. The
mole balance then becomes
F,O-F,+G,=Zd
(26)
The Aurora module for a plasma assumes steady state, so the
partial derivative becomes zero. Assuming no surface production of species
(i.e., no etching), the
formation of species
becomes:
F,. - F+jrjdv=o.
production rate, Gj, is the integral of
j per unit volume, f, and the mole
the molar rate of
balance equation
(27)
The CSTR approximation implies that within the volume, all the species
are perfectly mixed and the outlet conditions are identical to the conditions inside
V. Thus, the integrai becomes simply the product of f and V, and, after
rearranging, becomes:
Fjo -F,v= (28)
–r, “
Equation (28) is the design equation of the CSTR approximation (Fogler,
1992). Essentially, this approximation reduces all the differential equations to a
system of linear algebraic equations, greatly simplifyhg the solution of the
plasma chemistry. It will be shown below that this approximation results in the
66
need to restrict the use of CHEMKIN to conditions at 17 Pa in the present
experiments.
5.3. Plasma Reactions in CHEMKIN
Mass spectroscopy investigation of NE plasma species were conducted
by a number of investigators (Perrin et. al., 1990; Reese and Dibeler, 1956;
Konuma and Bauser, 1993; Greenberg and Verdeyen, 1985; Honda and Brandt,
1984). h&F2 was identified by excimer laser photolysis of NE (Weiner et. al.,
1992) and ~ radicals by laser-induced fluorescence (Lui et. al., 1992). The...
cracking pat,temlt’ of NF3 by electron bombardment was measured by mass
spectroscopy (Beattie, 1975). The species identified are listed inTable 15. The
fact that not all species were identified by all the experimentaiists is only
indicative of the instrument and focus of the experimentalists’ work. CHEMK}N
includes all the species observed, except ~F+ which only Konuma and Bauser
(1993) observed and F2-which only Reese and Dibeler (1956) observed .
The plasma reaction set for CHEMKIN (Table 16) was obtained from
Sandia (Meeks, Private Communication, 1998) using their N~02 reaction set
(Meeks et. al., 1997). All reactions involving oxygen, and all but four typical
electron-neutral excitation reactions for N6, N2, N, and FZ were removed since
these reactions were not of interest for the bulk plasma and doing so improved
the computer processing time considerably. Reaction #35 was added for NF and
NF2 reactions with NF2 (Du and Setser, 1993). Based on the validation work
discussed below, the rate coefficients for reaction #17 was decreased by a factor
of 10 in order to increase NFs dissociation while reaction numbers f 2, 14, 15,
and 16 were increased by a factor of 10 and reaction #36 was added to bring the
N2 and N concentrations into agreement with the experimental work of Perrin et.
al. (1990).
‘“A cracking patternk definedas the fragmentsof a molecule that form when the parentmoleculeis exposed to an ionizationsource, but withoutthe presence of a plasma.
67
%i
Definitions and units used in Table 16 are summarized below
Units:
EXCI:
REV:
TDEP/E/:
Molecules, cm3, seconds, Kelvin.
Electron energy loss per collision (eV) due to excitationreactions.
Signifies that the reverse reaction rate values to followare to be used rather than equilibrium values.
Reaction depends on the temperature of the specieswithin the slash marks, in this case the electrontemperature (as opposed to the gas temperature).
The forward rate coefficient, kf is given by equation (29) and is the
defining equation for the constants given in the tabie. EA/R has units of K; EA is
the activation energy in kJ/mole; R is the gas constant (8.3144 J mol-l IC1); B,
the exponent of the temperature, is dimensionless; T is the temperature (K); and
~, the reaction rate constant, has units of (cwz’nzolecule~-]s-’, where n is the
order of the reaction, varying between O and 3. The reverse rate coefficient,
when it applies, is calculated from the REV keyword value or, when REV is not
given, from equilibrium kinetics (Appendix D).
(/)EA R-—
kf = koTBe T(29)
Table 16. Plasma Chemistry in CHEMKIN.
Reaction Type of Reaction b B EJR Keywords10NIZATION/DISSOCIATION/ATTACHMENTREACTIONS
1 E+ NF3~ NF3++2E 7.39E-34 5 38t11TDEPIEt
2 E+ NF.3+NF~++2E+F 2.25E40 6.46 34184TDEPIEI
3 E+NF3 ~NF+ +2E+2F 3.93E-6311.0439849TDEP/E/
4 E+NF2+ NF2++2E 2.21E-33 4.94 31902TDEP/E/
5 E+ NF+NF++2E 1.94E-42 6.8 33586TDEP/E/
6 E+ N2+N2++2E 2.56E-43 7.07 31481TDEP/E/
7 E+ N+ N++2E 5.11E-37 5.78 47602TDEP/E/
69
Tabie 16. Plasma Chemistry in CHEtvlKIN.
Reaction Type of Reaction b B EJR Keywords8 E+ F2j F~++2E
9 E+ F+ F++2E
10 E+NFs~NFZ+F+E
11 E+ NF3+NF+2F+E
12 E+ NF2+NF+F+E
13 E+ NF2+N+2F+E
f4 E+ NF~N+F+E
15 E+ N2F2+2N+2F+E
16 E+ NpF.+~2N+4F+E
17 E+NF3sNF2+F-
18 E+ F*+ F+ F-
RECOMBINATIONREACTIONS
t9 E+ N+~N
20 E+N2+~N+N
21 E+ N2++N2
BIMOLECULAR & 3RD BODYREACTIONS
22 N+ N+ Me Nz+M
23 NF2+M@NF+F+M
24 NFP+NFP+M~NzF4+M
25 i=+F+ M@ F2+M
26 NFz+FP@NF3+F
27 NF+NF@N2+F+F
28 NF+NFe F2+N2
29 NF+N2F2eNF2+N2+F
30 NF + NF2 ~ N2F2+F
31 NF2+N@F+F+N2
32 NF2+Ne NF+NF
33 NFz+F+M@NF3+M
34 F+ N3QNF+N2
35 NF+NF2e N~+3F
36 NFP+ NF2@ N2+4F
ION-IONMUTUALNEUTRALIZATIONREACTIONS
37 F-+ NF~+~ 2F+ NF2
38 F.+ NFZ+~ 2F+ NF
39 F-+NF+ aF+NF
40 F-+N2+ ● F+Nz
41 F-+N+ +F+N
42 F-+F2+ +F+F2
43 F-+F+ ~F+F
CHARGETRANSFERREACTIONS
1.64E4
2.24E-47
2.06E-17
1.35E-30
1.57E-16
1.69E-23
1.57E-16
2.28E-16
2.28E-16
1.49E-09
1.02E-05
2.25E-O?
2.25E-01
2.25E-01
1.41E-32
1.26E-09
1.50E-32
2.80E-34
3.00E-14
6.88E-11
4.00E-12
2.00E-12
3.75E-12
1.40E-11
3.00E-12
1.03E-30
5.80E-11
2.75E-15
1.50E-32
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
7.25 32663TDEP/E/ ;
7.81 34076TDEP/E/
1.72 37274TDEP/W
4.45 34210TOEP/E/
1.& 27565TOEP/E/(ko=10-original)
2.99 37652TDEPIEI
1.84 27565TDEP/E/(IQ=10*01’i9inaI)
1.7 36391TDEP/E/(ko=10=original)
1.7 36391TDEP/E/(ko=10*onginal)
-0.14 3751TDEP/E/(ko=O.10*original)
-0.9 1082TDEP/E/
-2.5 0 TDEPIEi
-2.5 0 TDEP/E/
-2.5 0 TDEP/E/
o 0 REVI 3.163E-07-0.5113200.f
O 25700
0 0
0 0 REV17.600E-12O. 14300.I
o 4860
0 1251
0 0
0 0
0 187
0 95
0 0
0 0 REV13.98OE-10O. 16417.I
o 0
0 3095(Added,Du&Setser,1993)
o 0 (Added,k= k,m24)
o 0
0 0
0 0
0 0
0 0
0 0
0 0
70
Table 16. Plasma Chemistry in CHEMKIN.
Reaction Type of Reaction b B EJR Keywords44 F++l=z~Fz++F 9.7OE-10
45 F++N ~N+ +F 1.04E-09
46 F+ + NF3~ NF3++F 1.16E-09
47 F++ NFa NF++F 1.23E-09
48 F+ + NF2~ NF2++ F 1.30E-09
49 F2++N ~N++F2 9.37E-10
50
51
52
53
54
55
56
57
58
59
60
61
F2++ NF3~ NF3++ F2
F2++ NF ~ NF++ F2
F2++ NF2~ NF2++ F2
N2++N aN+ +N2
Nz++ NF3● NF3++ N2
N2++ NF ~ NF++ N2
N# + NF2● NFz++ N2
N+ + NF3● NF3++ N
N++ NF~NF++N
N+ + NF2~ NFz++ N
NF++ NFZ~ NF2++ NF
F++ N2=N2++F
1.04E-09
l.ll E-09
1.17E-09
9.37E-10
1.04E-09
l.ll E-09
1.17E-09
9.7OE-10
1.03E-09
1.08E-09
9.I5E-10
9.7OE-10
o
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
“oo0
0
0
0
0
0
0
0
0
0
0
0
0
EXCITATIONREACTIONS(TYPICAL)
62 E+ NF3+E+NF3 3.42E-21
63 E+ N2+N2+E 2.02E-34
64 E+ N~N+E 1.25E-39
65 E+ F2+F2+E a 1.09E-51
2.52 33296E)(CU7.70/ TOEP/E/
5.29 36200EXC1/13.00/ TOEP/E/
6.07 38618EXC1/13.70/TDEP/E
8.54 37389EXC1/13.06/TOEP/E/
5.4. Surface Reactions
The surface reactions modeled are the wall fluorination, ion wall
recombination, and, for the validation case, the fluorine reactions with surface
silicon (Table 17). Etch reactions for U02 were not modeled since the objective
was to determine reactive species concentrations in the bulk plasma (and
therefore at the plasma/sheath interface) for input to another model (E1-Genk et.
al., 1999). The constant, y, is defined as a sticking coefficient when the keyword
“STICK” is used and as a correction to the BOHM velocity when the keyword
“BOHM” is used. The sticking coefficient is a dimensionless quantity defined as
the reaction rate divided
the reaction (Meeks et.
by the incoming flux of species, and is the probability of
al., 1996, p. 83; Coltrin et. al., 1996). The BOHM
71
correction is an approximate method of correcting for transport conditions to the
surfa~e, accounting for the ion density gradient which affects the transport of
ions near the walls (Meeks et. al., 1996, page 83). The keyword needed in the
CHEMKIN input file is included in Table 17.
Table 17. Plasma Surface Reactions.
Type Reactions YFluorination of Aluminum Walls (STICK KEYWORD)
The ions, while too few in number to contribute significantly to the etching
process, deposit energy on the sutface, enhancing the reaction processes by
removing non-volatile products from the UOZ surface. For example, the sample
substrate temperature in the UOZ etching experiments rose -40 K above ambient
compared to only 4 K at the walls of the chamber. The relatively high
temperature rise of the sample resuited mostly from ion bombardment.
Exothermic reactions of UOZ and F atoms deposit at most 62 J of heat in 30
minutes of plasma processing at 50 W RF compared to 680 J from ion
bombardment (Appendix E). Hence, most of the temperature increase will be
from ion bombardment. The ions, in traversing the sheath, will suffer collisions
since their mean free path is a factor of -5 to 10 smaller than the sheath
thickness (Appendix E). Consequently, the energy deposited will be less than
the sheath voltage, but still high enough to break bonds and heat the surface
(Table 24). The sheath voltage was obtained from experimental measurements
(Chapter 3), the electron energy and neutral gas temperature were obtained from
CHENIKIN predictions (Chapter 5), and the ion energy was calculated as shown
in Appendix E.
86
Blocking of the etch reactions can arise during the reaction steps leading
to the formation of UF6Ythus requiring an understanding of the etch mechanism.
Table 24. Plasma Conditions at 17 Pa.
Parameter 50 w IoowSheath Voltage (V) -142 -261Electron Energy (eV) 5.21 4.87Neutral Temperature (K) 298.2 298.3Sheath Thickness (cm) 0.14 0.16NFs Ion Energy (eV) ?1.3 17.9
NF3 Ion Energy (kJ/mol) 1087 1731
6.2. Reaction Model
Since F atom radicals are the predominant reactive species in the plasma,
reactions of adsorbed F and U02 are the initiating events leading to the
formation of a uranium fluoride gas. Because U forms in the III-VI oxidation
states (Jacob et. al., 1980), compounds UF3 through UF6 and the oxyfiuorides of
uranium are the ones likely to form. The reaction mechanism to produce UFtj is
quite complex and therefore a model for the reaction of adsorbed F atoms with
UOZ was developed to simplify the chemistry. This model combines aspects of
electronic valence orbitals of uranium, probability theory, and thermodynamic
Gibbs free energy heats of formation and reaction as described below.
Before UF6 appears from the starting material, UOZ several intermediate
compounds of the fluorides and oxyfluorides of uranium will form. The highly
reactive F atom radicals will diffuse to the surface and adsorb to U02 surface
sites via physisorped van der Waals forces and chemisorption (Lieberman and
Lichtenberg, 1985). Reactions will occur with UOZ molecular sites to form
products of U-O-F, where U-O-F indicates several possible compounds involving
all three atoms. Taking the possibie combinations of U, O, and F atoms to fill the
electronic valence structure of the U atom (Alberty and Silbey, 1997, Table 10-3)
leads to several species including the oxyfiuorides and fluorides shown in Table
25. Several restrictions were applied to the reactions including: reactions can
87
only proceed in a direction to increase the complexity of the molecule (i.e., no
dissociation reactions); only one U atom per molecule (i.e., U308 not
considered); no reactions with desorbed oxygen were considered; and bonding
with F occurs first with the outermost U valence orbital before the inner orbital.
The electronic structure shown in Table 25 for U depicts the bonds in order of
decreasing binding energy where, for example, the 6d1 electron will bind before
the 7s2 electrons.
Table 25. Bonding Sites for Reaction with F Radicals.
U O F Species Electronic MaximumStructure Bonding Sites
During plasma processing, pressure and flow conditions within the plasma
eventually reach a steady state value. At steady state, the accumulation of
moles of gas in the chamber approaches zero. Thus, the mole balance equation
becomes
FO– F+G=O (B-14)
The net molar production rate, G, is made up of two sources: the bulk
volume species production and heterogeneous surface reactions that contribute
to the gas phase species.
G=~JrjdV+$Z*fijda (B-15)
J
The above function includes ~,the reaction rate of the ~ species; dV, the
elemental volume element i, the outward unit normal vector from the sutiace;
~,, the flux of species j from the sutiace; and da, the elemental surface
element. The volume integration (bulk volume term) is throughout the plasma
volume, the surface integration (heterogeneous term) is on all surfaces exposed
to the plasma, and the sum is over all species. When RF power is applied, NE
molecuies are dissociated into many species, including ions, radicals, and other
neutrals while sutiace losses will reduce the net formation of the plasma species.
Fluorination of solid U~ samples will release UFG into the gas phase according
to equation (B-16). For every mole of U@ reacted on the surface with 6 moles
of F atoms, one mole each of UF6 and 02 will desorb into the gas phase, for a
net loss in the gas phase of 4 moles for every mole of U~ reacted.
(B-16)
The total number of moles added in the gas phase after conditions in the
plasma have stabilized may be estimated from the ideal gas law as
(B-17)
131
Aq is the net change in the number of moles due to power increases, Ap
is the net change in pressure with RF power, V is ‘the reactor volume, and T the
temperature of the plasma (neutral gas temperature).I
In order to esfimate the bulk plasma contribution, the pressure increase
with power was measured without any uranium sample. Hence, only
contributions from the bulk plasma term are obtained, simplifyhg estimations of
contributions from UFG. The pressure rise with power for various NF flows
{rotameter settings) is shown in Figure B-8. In (a), the absolute reactor pressure
is plotted with absorbed power, showing the increase in pressure compared to
zero power. In (b) the number of moles generated in the bulk plasma is shown,
based on equation (B-17). The added contribution to the number of moles from
10.3 mg of UOp (typical sample mass) from the fluorination reactions (equation
(B-16)) can add up to 0.04 mmole of OZ and UFGto the gas phase and a loss of
0.24 mmole of F atoms, assuming a worse case that all UE and 02 remains in
the chamber.
132
u
3f
2(
1(
(
0.4
0.,m
‘o
x
Chamber Characteristics
~ Rotameter Modei S04-N082-031000 W Matching Network
v Vw uv v v v
-v
~~
-- -- ---50 100 150 ZIXJ
Absorbed Power (W)
Moles Gas Created DuringPlasma Operations
Source mtorr-pwrun.epgn
40 60 80 100pa-m01e2.epg
Rotameter Setting
Figure B-8. Effect of RF Power on Reactor Pressure
133
B.3.5. Residence Thne,r
The residence time is defined as
(B-18)
V is the chamber volume and the volumetric flow rate (d~/dt)~ is taken at
the entrance to the chamber. Note that the volumetric flow rate is NOT the
SCCM; it’s the flow rate at the given pressure obtained from equation (B-6).
From the ideal gas law equation of state (pV = qRT) with T, p, and R constant,
and differentiating this equation for the volumetric flow rate at the entrance gives
(wy (B-19)
The first form of the residence time uses equation (B-19). The second
form of residence time uses the entrance volumetric flow rate written in terms of
SCCM using equation (B-7) with POthe pressure at one atmosphere. The third
form uses the gas density p in the plasma and the inlet mass flow rate, tie.
pv vr— L–d’ ($-20)= FORT= (sCC~) PO me
B.3.6. Effect Of Power On Pressure
For a given rotameter flow setting with the recovery system rotary pump in
operation resulted in set pressures dependent on the operating power. These
results are shown in Figure B-9.
134
50
40
30
20
10
r)
❑ ✛ oe .1c1 14
v 24
●oA ‘; “1 AZ!?100
I
a-,.-
Es ..-
J
Rotameter Model: S04-N082-03
{
+ 168 Ae 21OWAbsorbed ~
-o 40 80 120
Rotometer Flow Head (cm)
Figure B-9. Rotameter Setting During Plasma Operation
13.3.7. Plasma Extinguishing Pressure
A plasma cannot be ignited at too low pressure (below about 0.7 Pa) nor
at high pressure. The extinguishing high-pressure plasma value was determined
by experiment, using as criteria a zero DC sheath voltage. The results are
summarized in Figure B-1 O. An initial charge of NF3 gas was introduced inside
the plasma chamber and then all inlet and outlet valves were closed. The lower
cufve in the figure shows this pressure level. Then, for each power, the pressure
increase that results with power application was determined (second curve).
Next, the NF3 gas inlet valve was opened until the extinguishing pressure was
found (top cume). The extinguishing pressures were found to vary from 105 Pa
at 38.5 W to 272 Pa at 168 W.
135
““1000 ~
100
10
Outlet valve to pumps is closedCriteriaFor Etitnguished Plasma is aSheath Voltage = 0.0 achieved byflowing NFqgas until plasma extinguished
7’
Extinguishing Pressure
Stabilized Pressure With RF, No Flow ❑n
c1
Startin~Base Pressure, No Power, No Flow
m%a am-50 100 150
Absorbed RF Power (W)
Figure B-1 O. Plasma Extinguishing Pressure
8.3.8. Knudsen Flow
In the range of pressure used, p = 10.8 to 40 Pa, the reactor chamber was
in the viscous flow regime with a Knudsen number, Kn, below 0.01 and transport
was therefore diffusive (Roth, 1982). The Knudsen number in these experiments
is related to the NF3 molecular diameter, d, the mean free path, k, the
temperature, T, and the pressure, p. Using a hard sphere approximation to
calculate d (Alberty, 1997) with the viscosity, v, equal to 0.0183 mPa-s (13raker
and Mossman, 1980) gives an NF3 molecular diameter of 4.61 xl 010 m. Applying
the ideal gas law to calculate 1 provides the relationships to calculate Kn. The
relationships are shown below.
d/[1
5 kTM 1’2——= 16v fl~ ‘
(B-21)
(B-22)‘=&’136
KJ2=A (B-23)d“
The Knudsen values for the experimental chamber Figure B-1 1) are.:
compared for different characteristic lengths to include the plasma reactor (0.5
m), a 1” diameter pipe, and the sheath thickness (-0.5 cm). For the pressure
(10.8 to 40 Pa) and temperature (-298K) range of the plasma, molecules
traversing the sheath are in the intermediate flow regime, that is, they will suffer
one or more collisions. Molecules traversing the reactor chamber are in the
viscous regime and will suffer many collisions. Molecules traversing a 1” pipe
will vary from the intermediate to the viscous regime.
10000
100
1
0.01
0.00010
t
Molecular Flow
L .—. — Li—-—.—-—- -—--
40 20 30 40
‘1Intermediate Flow
-—- -— --
v
Pressure (Pa)
Figure B-1 1. Type of Flow in Plasma Chamber.
137
APPENDIX C. DATA
C.1. Experimental Data
Table C-1 contains the depleted uranium oxide plasma processing data,
It contains only data during which the sample was continuously immersed in
plasma. Each sample contained 100 microliters of uranyl nitrate hexahydrate
solution pipetted into a 1.007 cm diameter stainless steel planchette which was
subsequently converted to UOZ by heating and flaming.
C.2. Table Abbreviations
The abbreviations and definitions used in the Table C-1 headings are as
follows:
ID
t (rein)
Flelative error, t
AbsorbedPower (W)
TransmittedPower (W)
Pressure (Pa)
NF3 Flow (cm)
Sheath (V)
Dilution Factor
Identification number
Plasma process time, in minutes, adjusted by 7 minutes toaccount for the delay in the plasma reaching operatingconditions.
The relative error in plasma immersion time.
Power absorbed by the plasma in watts.
Power transmitted (output of the RF-20 power supply) in watts.
Pressure in the plasma chamber during operation and aftersteady state has been reached, in Pascal.
The rotameter head indication in centimeters is indicative ofthe gas flow to the chamber.
Effective DC plasma sheath potential in volts. Because mostof the voltage is dropped in the powered electrode sheath, thisvoltage is effectively the voltage across the powered electrodesheath.
The ratio of either the total volume or mass of the sample tothe corresponding volume or weight of the aiiquot counted indeterrninina the activitv.
138
ID Identification number
Relative ErrorDilution
Alpha Detector(Ca) (cpm)
Alpha 2cJ (%)
C(t) (cpm)
Relative Errorc(t)
A(t) (dpm)
Relative errorA(t)
~ (dpm)
NR
Relative Error in
NR
Etch Rate
(ym/min)
The relative uncertainty in measuring the dilution of the washfor counting purposes. Significant changes during course ofthe experiments attributed to improved procedures.
The count rate (counts per minute) measured by the liquidscintillation. All reported values include curve fitting the alphapeak with a gaussian and first order polynomial, andintegration of the gaussian to determine this value.
The two sigma uncertainty determined by Poisson countingstatistics, expressed as a percent. This value is determined
r
~cazc where ~ is the counting time, generally 60as 200C=tc
minutes.
The count rate (counts per minute) corrected for alpha/betaparticle mislabeling.
The relative error in C(t).
The true activity remaining on the sample following plasmaimmersion, in disintegrations per minute.
The relative error of the activity.
The initial activity on a sample, prior to plasma immersion(disintegrations per minute). This value is not shown on thechart and is equal to 7764 dpm for the sampies used.
‘(t) it represents the amount of activityThe ratio 1– —.AO
removed from the sampie, normalized to the initiai activity.
The reiative uncertainty in k.
The U02 etch rate calculated from the experimentaiiydetermined density (4.8 g/cm3) as given in Appendix E from
E.4. Energy Deposited From Exothermic Reactions of U02 and F
A Mathcad calculation for the maximum energy deposited as heat from
samples of U02 and F atom radicals is included in Table E-6. The maximum
energy deposited as heat from a sample is 62 J. By comparison, the energy
deposited by ion bombardment is 680 J (Table E-5).
165
Table E-6. Energy From U02 Reactions with
Energy Deposition From Exothermic Reactl
- Objective: Estimate the energy deposited on the SS planch~due to reaction of the UQ and F atoms at 50 W RF Power. Assure-energy is converted to heat. Base the estimate on 100 ~ of uranylsample converted to a uniform layer of LQ. Assume that all the U(
* UFe within 30 minutes (actual time follows exponential and takes -
Reaction
CcmstantsN := 236.1o19
kw
Ss := 16”—m-K
d := 1.00?.cm
L := 0.0365.cm
NA := 6.022-1#.mole-1
AH r := - lS38.4@-!-mole
t p := 30”min
U(32+ 6F --> W* +02
Molecules of UOZpersamF
Thermal Conductivity of Sta
Diameter of planchette
Thickness of planchette
Avogadro’s Number
Reaction Enthalpy [exother
Plasma Processing Time
titermediate Resulti
~ , n-c?.=— S = 7964”10-5 m24
Crosssectional
NT := —
NA-r) = 3.919 .10-5 lnol Moles of U02
-AH r-qQ ,= Q = 0.033W Maximum heat I
‘P
E_tota{ := Q-t ~ E_total = 62.249 J
E.5. Vapor Pressure Correlation
Vapor pressure correlations and the related te
described in Table E-7. References to the cc
166
Table E-7. Vapor Pressure Correlation.
Species Vapor Pressure Temperature (K)
UF6,.
UF5
UF4
UF3
UF2
UF
u
U02
U02F
U02F2
Correlation (Pa)Low High
~,521-~133.2x1O T 273 342
,3,994-W133.2x1O T 125 420
~2,6-16i400
133.2x1O 7 ‘3”02”r’Og’07 298 1309~~45_~
133.2x1O T 1543 1673
Reference
Lange and Forker (1967), p.1450,
Katz et. al. (1986) Vol. 1,p308
Jacob et. al. (1980), p. 27,
Jacob et. al, (1980), p 6I
No data Bond dissociation energy suggests p- PUF4
(Hildenbrand and Lau, 1992)
No data~71-25230
1.01X105X10 T 1480 2420 Katz e. al. (1986), Vol 1, p. 228
28.65-34:0—-5.64 *LwIOI’
106X10 3120 5000 Ohse et. al. (1979)
No data~68-15106
1.01X105X10 r 956 1000 Lauet. al (1985)- (1/g. s)*Puo2F2 at
UOF4 1000K - “ Lau et. al. (1985)
167
E.6. Gibbs Energy Correction For Pressure And Temperature
The Gibbs free energy of formation has a pressure ~ependence (Alberty
and Silby, 1997) that depends on ‘whether the material is in the solid (or liquid)
phase, or in the gas phase. In the solid phase, the volume, V, of the material is
independent of pressure. The Gibbs energy of formation, G, is given by
G= GO+ V(p-pO) (E-19)
GO is the Gibbs energy at standard temperature (T = 298K) and pressure,
PO= 1 bar).
Taking one mole of the amorphous U02 (density - 6.8 g/cm3), the
equivalent mass is equal to the molecular weight, 270 g/mole. Using the density
and mass, V -56.25 cm3 per mole of UOZ. The chamber pressure at the lower
operating limit is 10.8 Pa, which gives the greatest error in the above equation.
The correction, in kJ/mole units repofied for Gibbs, gives
G = Go – 5.6x10-3 (kl/mole) (E-20)
to the
to the
Therefore, for solid materials, the correction is extremely small compared
typical values found for the reaction sets and can be neglected compared
standard state values. Since the reactions are with absorbed F atoms on
the surface, corrections to the Gibbs energies for
corrections either. The Gibbs free energy of F atoms
fluorine will not require
in the gas phase will be
used as an approximation.
The UF6 desorbs into the gas phase, and
applied to this gas. The correction in this case for
given by
[)G= GO+qRTln ~
P
so the ideal gas law can be
the Gibbs heat of formation is
(E-21)
Using the same values as before leads to the following correction
G = Go – 0.075(ti / mole) (E-22)
168
Again, this comection is small for the reactions of interest and will be
neglected.
The
Therefore,
apply.
plasma gas temperature is -298K for the operating pressures used.
standard state temperature values of Gibbs energies of formation
E.7. Thermodynamic Analysis of Reactions
Thermodynamic analysis from Gibbs free energy of reaction, GR, is
determined from the Gibbs free energy of formation, Gj, of species j and the
stoichiometric coefficient, ~j, of reactants and products. ~ The stoichiometric
coefficient is positive for products and negative for reactants. Simiiariy, the
enthalpy of reaction, HR, is detemlined from the enthaipy of formation, Hj, of
each species, determines whether the reaction is exothermic (negative HR) or
endothermic (positive HR). The reaction vaiues are given as:
GR= ~vjGj (E-23)
H,=~v,Hj (E-24)J
When GR is positive, the reaction cannot proceed spontaneously but
requires energy to proceed. When GR is negative, the reaction is favorabie. The
reaction possibilities of one or two absorbed F atoms with U02 based on
combinations of U-O-F combinations (Chapter 6) is detaiied in Figure E-4. if GR
is positive (dashed iine), the reaction sequence is terminated. When GR is
negative (soiid iine), the reaction sequence is continued to the end product,
which is UF6. The uranium metai reaction with F atoms are quite different. The
initiai reaction is with a singie absorption site as shown in Figure E-5. Since no
oxygen atoms are in the reaction, oniy uranium fluorides form and there are no
unfavorable reactions.
169
XF+ IJ02
Reactions and Gibbs Free Energy (kJ mot-f)Note: dashedIiinfavorabla raatitonO or 02 raac%onprcductsnotshown
* iJF+898 , .
/ IL/~ -,/ “+664 > ~~f~
\
----
\\ 427
\\ UOZFa\
;,$;::.V&lj~~
\ -650
\Y
-112
<,4
➤ UF(3\ -223\ I\ UOF3 -f33
+282\ ,’+248, ‘%275 I
1U02F2 0 -164 U4F4
\ ‘//
‘+ ‘ ‘, -387\ -162
+@;_:~e, t~ \+29
J -368 I+ ‘;355,J&---.. uF~ > ‘“
:.-:.... .. .
Figure E-4. Reaction Sequence of F Atoms and UOZ.
Reactions and Gibbs Free Energy (kJ mb)
-1627
-2X2
/-449 UF4
/-670
UF3 > -162
UF2
/
UF5~
-661
UF~
‘m-396
49 UF ~
\ -162UF5 ~
UF6
UF6
UF6
UF6
UF6
Figure E-5. Reaction Sequence of F Atoms and U MetaL
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