Attenuation of hydrogen radicals traveling under flowing gas conditions through tubes of different materials
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Attenuation of hydrogen radicals traveling under flowing gas conditions
through tubes of different materials
R. K. Grubbs
Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309
S. M. Georgea兲
Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309
and Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309
共Received 1 November 2005; accepted 7 March 2006; published 20 April 2006兲
Hydrogen radical concentrations traveling under flowing gas conditions through tubes of different
materials were measured using a dual thermocouple probe. The source of the hydrogen radicals was
a toroidal radio frequency plasma source operating at 2.0 and 3.3 kW for H2 pressures of 250 and
500 mTorr, respectively. The dual thermocouple probe was comprised of exposed and covered
Pt/ Pt13% Rh thermocouples. Hydrogen radicals recombined efficiently on the exposed
thermocouple and the energy of formation of H2 heated the thermocouple. The second thermocouple
was covered by glass and was heated primarily by the ambient gas. The dual thermocouple probe
was translated and measured temperatures at different distances from the hydrogen radical source.
These temperature measurements were conducted at H2 flow rates of 35 and 75 SCCM 共SCCM
denotes cubic centimeter per minute at STP兲 inside cylindrical tubes made of stainless steel,
aluminum, quartz, and Pyrex. The hydrogen radical concentrations were obtained from the
temperatures of the exposed and covered thermocouples. The hydrogen concentration decreased
versus distance from the plasma source. After correcting for the H2 gas flow using a reference frame
transformation, the hydrogen radical concentration profiles yielded the atomic hydrogen
recombination coefficient, ␥, for the four materials. The methodology of measuring the hydrogen
radical concentrations, the analysis of the results under flowing gas conditions, and the
determination of the atomic hydrogen recombination coefficients for various materials will help
facilitate the use of hydrogen radicals for thin film growth processes. © 2006 American Vacuum
Society. 关DOI: 10.1116/1.2191862兴
I. INTRODUCTION thermocouple. The recombination energy heats the thermo-
couple or catalytic surface connected to the thermocouple.
Atomic hydrogen is important as a reactant in many thin Using a heat balance model, the thermocouple temperature
film growth processes.1–6 One difficulty that complicates the can be used to determine the atomic hydrogen concentration.
use of hydrogen radicals is their recombination on surfaces This method can be improved by using a dual thermocouple
to form H2 molecules. This recombination seriously depletes probe26 where one thermocouple is exposed to the atomic
the atomic hydrogen concentration and can also significantly hydrogen and the second thermocouple is covered by glass.
heat the corresponding surfaces. Although hydrogen recom- In this article, hydrogen radical concentrations traveling
bination coefficients have been reported for various under flowing gas conditions through tubes of various com-
materials,7–12 there are no measurements of hydrogen radical mon construction materials were measured using the dual
concentrations traveling under flowing gas conditions thermocouple probe method. Atomic hydrogen concentra-
through tubes of different materials. Measurements of atomic tions were measured versus distance from the hydrogen
hydrogen concentration as a function of distance from the plasma source for various gas flow velocities. Measurements
source, gas flow velocity, and tube wall material are impor- in a static gas environment are governed only by hydrogen
tant for defining hydrogen radical transport. diffusion. Under viscous flow conditions, the gas flow has
Many methods exist to measure atomic hydrogen concen- the effect of translating the static reference frame in the flow
trations including laser induced fluorescence,13 coherent anti- direction at the flow velocity. The attenuation of the hydro-
Stokes Raman spectroscopy,14 multiphoton ionization,15 gen radical concentration was analyzed using a reference
mass spectrometry,16 and carbon etching.17 One additional frame transformation. The atomic hydrogen recombination
technique that has demonstrated great utility is the thermo- coefficients were then determined for Pyrex, quartz, and na-
couple catalytic probe method.18–25 This technique is based tive oxide-covered stainless steel and aluminum.
on the recombination of two hydrogen atoms to form H2 This article should be useful for a variety of reasons. The
molecules on the surface of a thermocouple comprised of described methodology for the dual thermocouple probe
catalytic metals or on a catalytic surface in contact with a measurement technique provides a simple and inexpensive
means to monitor hydrogen radical concentrations. The
a兲
Electronic mail: steven.george@colorado.edu mathematical treatment of hydrogen radical attenuation un-
486 J. Vac. Sci. Technol. A 24„3…, May/Jun 2006 0734-2101/2006/24„3…/486/11/$23.00 ©2006 American Vacuum Society 486487 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 487
B. Dual thermocouple probe
The dual thermocouple probe was mounted on a horizon-
tal translation stage that allowed the probe to move to vari-
ous positions inside cylindrical tubes attached to the plasma
source. A schematic of the dual thermocouple probe in the
experimental apparatus is shown in Fig. 1. Cylindrical tubes
composed of different materials could either be mounted di-
rectly to the hydrogen plasma source or could be inserted
within the cylinders mounted to the hydrogen plasma source.
Consequently, the dual thermocouple probe could measure
the effect of different wall materials on the propagation of
the hydrogen radical flux.
The body of the dual thermocouple probe was made from
glass. The glass allowed the leads of the exposed thermo-
couple to be sealed to maintain vacuum. The covered ther-
mocouple was completely embedded in glass. Problems oc-
curred in fabrication when attempting to make a vacuum
tight seal between glass and the thermocouple wire. Initial
attempts using borosilicate glass produced a poor glass-to-
metal seal. Uranium glass sleeves were subsequently used to
create the glass-to-metal seal around the thermocouple wires
while using borosilicate glass for the body of the probe. This
combination of materials produced a poor vacuum seal when
the probe was exposed to the hydrogen radicals for extended
periods of time. Cobalt glass was also tried and had only
limited success making a viable vacuum tight seal.
The glass that produced the best glass-to-metal seal with
FIG. 1. Illustration of the dual thermocouple probe on the toroidal plasma
the thermocouple wire was soft glass. Soft glass is also
source. The probe was moved to measure the hydrogen concentration at known as soda lime glass. The soft glass was worked with a
various distances from the plasma source. The measurements were per- H2 flame that kept the glass from discoloring. After the probe
formed under gas flow conditions for different flow tube materials.
was constructed using soft glass, the probe was annealed for
4 h at 500 ° C prior to exposure to the hydrogen radicals. The
thermocouple wires used in these experiments were
Pt/ Pt13% Rh, i.e., type R. This thermocouple had a wire di-
der flowing gas conditions is a useful extension to the earlier ameter of 260 m and a junction diameter of 740 m. The
static gas analysis. The determination of the atomic hydrogen thermocouple junction needed to be at least 5 mm away from
recombination coefficients on common materials of con- the glass-to-metal seal to avoid glass corrosion and eventual
struction aids in the design of chemical reactors that will vacuum leaks caused by intense heating from the thermo-
employ hydrogen radicals. couple junction. The temperature of each thermocouple in
the dual thermocouple probe was recorded using a Keithley
195A digital multimeter.
The experiments were initially performed in a steady state
II. EXPERIMENT fashion where the plasma source was run constantly while
the dual thermocouple probe was moved towards and away
A. Hydrogen radical source from the plasma source. This method produced reproducible
The source of hydrogen radicals in these experiments was temperature measurements in both the forward and reverse
a toroidal27 hydrogen plasma source obtained from Ad- directions with minimal hysteresis. Unfortunately, the life-
vanced Energy Corporation in Fort Collins, Colorado. The time of the dual thermocouple probe was severely shortened
plasma source operated at H2 pressures between 150 and under extended exposure to the hydrogen radicals. The ther-
1000 mTorr. The plasma source was driven with mocouple probe would fail because the hydrogen radical re-
1.5– 4.0 kW of radio frequency power at a frequency of combination would heat the thermocouple wire to the melt-
460 kHz. The input power for different H2 pressures was ing point and cause an electrical open circuit. The hydrogen
tuned to minimize the amount of reflected power returning to radicals could also etch the glass probe eventually resulting
the power supply. Only about 6% of the input power was in a vacuum leak. Typically, the thermocouple probes had a
reflected under the optimum conditions for the different H2 lifetime of less than 1 h of continuous operation depending
pressures. on the position of the probe relative to the plasma source.
JVST A - Vacuum, Surfaces, and Films488 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 488
C. Temperature measurements for different materials
The Pt/ Pt13% Rh thermocouple exposed to the hydrogen
atoms measures the heat gain from atomic hydrogen recom-
bination as well as the temperature of the ambient gas and
radiative heating from the plasma source. The second ther-
mocouple embedded in glass was protected from atomic hy-
drogen exposure and is heated by the ambient gas and
plasma radiation. The difference in these two thermocouple
temperature readings, ⌬T, is the temperature increase attrib-
uted to the atomic hydrogen recombination.
The temperature measurements were performed using cy-
lindrical tubes composed of four different materials: stainless
steel, aluminum, Pyrex, and quartz. Commercially available
FIG. 2. Photograph of the dual thermocouple probe showing the exposed and stainless steel and aluminum tubes served as the stainless
covered thermocouples during exposure to hydrogen flux. The hydrogen flux steel and aluminum wall materials. These cylindrical tubes
heats the exposed thermocouple to ⬃1100 ° C.
were identical in dimension and had a length of 17.5 cm and
a diameter of 6.0 cm. For the Pyrex and quartz materials,
cylindrical inserts of a slightly smaller diameter of 5.1 cm
To extend the lifetime of the thermocouple probe, experi- were cut and placed inside either the stainless steel or alumi-
ments were performed in an ON/OFF mode. The plasma num cylindrical tubes.
source was switched on only when performing a measure- Using a simple model of heat balance for the exposed
ment. The temperature measurement was recorded after the thermocouple,21,22 the atomic hydrogen concentration was
thermocouple voltage stopped increasing and reached a lim- determined from the temperatures of the exposed and cov-
iting value. This limiting value was obtained after the plasma ered thermocouples. The dual thermocouple probe typically
was ignited for 4 – 8 s. This procedure extended the life of collected temperature measurements from the outlet of the
the thermocouple probe and allowed the measurements of plasma source to a position 20 cm away. Measurements were
the hydrogen radical concentration traveling through tubes of performed at H2 pressures from 250 to 500 mTorr and H2
four different materials to be performed using the same ther- flow rates between 35 and 75 SCCM, respectively, defined
mocouple probe. using a mass flow controller.
The thermocouple probe periodically showed signs of
D. Flowing gas conditions
malfunction. This typically occurred when the exposed probe
resided under vacuum conditions for long periods of time. A The system was pumped using a dual stage rotary vane
malfunctioning probe would reach a peak temperature of mechanical pump with a pumping speed of 3.2 l / s. At this
only between 600 and 800 ° C when the probe was placed at pumping speed, H2 flow rates of 35 and 75 SCCM produced
the outlet of the hydrogen plasma source. In contrast, the H2 pressures of 250 and 500 mTorr, respectively, in the hy-
exposed probe would reach temperatures 艌1700 ° C at the drogen plasma source. These operating H2 pressures were
same location when functioning properly. The operation of utilized because they produced reliable hydrogen plasmas.
the exposed thermocouple probe could be restored if the The system was in viscous flow at all locations at H2 pres-
thermocouple junction was briefly heated in a flame to close sures of 500 mTorr. At pressures of 250 mTorr, the viscous
to the melting point of the thermocouple alloy. This heating flow regime started at distances ⬎5 cm from the hydrogen
restored the thermocouple by presumably activating the sur- plasma source. At shorter distances ⬍5 cm from the plasma
face for atomic hydrogen recombination. The probe was al- source, the gas was in transitional flow.
ways checked before and after data collection to confirm Viscous flow is defined by Knudsen numbers D / ⬎ 110
proper operation. where D is the tube diameter and is the mean free path.28
Figure 2 shows a photograph of the exposed thermo- To determine the mean free path, a hard sphere diameter of
couple probe operating at 1100 ° C. This photograph was re- 2.9 Å was utilized to characterize the interaction between H
corded through a transparent Pyrex tube mounted to the and H2.29 Given this hard sphere diameter, a hydrogen atom
plasma source. The thermocouple probe was positioned has an effective circular collision area of 2.64⫻ 10−15 cm2.
8.0 cm from the outlet of the plasma source with a H2 flow All H2 molecules with their centers within a cylindrical vol-
rate of 75 SCCM 共SCCM denotes cubic centimeter per ume defined by this effective circular collision area and the
minute at STP兲, a H2 pressure of 500 mTorr, and an input translation of the H atom will produce a collision. For a H2
power of 3.3 kW. A pronounced hot region is observed at the pressure of 500 mTorr at 25 ° C, the H2 number density is
end of the thermocouple. The temperature gradient between 1.62⫻ 1016 molecules/ cm3 and the collision rate between a
the hot thermocouple junction and the glass-to-metal seal is H atom and the H2 molecules is 1.43⫻ 107 s−1. The mean
readily apparent. The temperature of the exposed thermo- velocity of the H atom is 2726 m / s and the mean free path
couple is much hotter than the temperature of the covered for the H atom is = 0.19 mm. The resulting Knudsen num-
thermocouple. ber is D / = 316 for a tube diameter of D = 6.0 cm.
J. Vac. Sci. Technol. A, Vol. 24, No. 3, May/Jun 2006489 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 489
FIG. 3. Temperature of the exposed 共Texp兲 and covered 共Tcov兲 thermocouples,
⌬T共Texp − Tcov兲 and % reflected power vs input power to the toroidal plasma
source at a H2 pressure of 250 mTorr.
The temperature of the flowing gas will decrease progres-
sively versus distance from the hydrogen plasma source. The
temperatures are highest close to the hydrogen plasma source
resulting primarily from hydrogen radical recombination on
the walls of the cylindrical tube. At these higher ambient
temperatures, the H2 number density is reduced at constant
pressure according to n / V = P / RT from the ideal gas law. For
the lower H2 pressure of 250 mTorr, these higher tempera-
tures decrease the Knudsen number to D / ⬍ 110 at dis-
tances ⬍5 cm from the hydrogen plasma source. The gas
flow velocity will also vary with gas temperature. Given a H2
flow rate of 75 SCCM and a H2 pressure of 500 mTorr at a
representative temperature of 255 ° C, the H2 gas flow veloc-
FIG. 4. 共a兲 Dependence of ⌬T on translation of the dual thermocouple probe
ity is 130 cm/ s. towards and away from the plasma source. 共b兲 Dependence of Texp on H2
pressure at various distances from the plasma source.
III. RESULTS
A. Plasma source and probe characterization
power at different input powers. The reflected power mini-
The output of atomic hydrogen was measured as a func- mum is ⬃6% at the optimum input power of 2.0 kW for a
tion of input power to the toroidal plasma source. A matching H2 pressure of 250 mTorr. Similar experiments determined
network was used to couple the input power to the hydrogen that the reflected power minimum is ⬃6% at the optimum
gas to minimize reflected power. There was a slight depen- input power of 3.3 kW for a H2 pressure of 500 mTorr. Each
dence of the reflected power on the input power. The re- temperature data point is the average of several temperature
flected power obtained a minimum of ⬃6% under optimum readings.
input power conditions. To determine the effect of the input The temperatures for the exposed and covered thermo-
power on the temperature readings, temperature measure- couples, Texp and Tcov, and ⌬T increase slowly with input
ments were recorded as the input power was varied above power. The temperature of the exposed thermocouple
and below the optimum input power of 2.0 kW for a pressure changes more rapidly than the temperature of the covered
of 250 mTorr. These experiments were performed using a thermocouple. This larger temperature increase is attributed
Pyrex cylindrical tube. The measurements were conducted at to the dependence of the atomic hydrogen flux on input
a distance of 10 cm from the outlet of the hydrogen plasma power. The slope of the solid line fit to ⌬T versus input
source at a H2 pressure of 250 mTorr defined by a H2 flow power in Fig. 3 is 19.5 ° C / 100 W. When recording the tem-
rate of 35 SCCM. perature measurements, the reflected power varied slightly
Although the temperature quickly reached a limiting but never exceeded ±5 W of the initial minimum value.
value, the thermocouple probe was allowed to equilibrate for Temperature measurements were recorded when moving
5 min. Figure 3 displays the temperature measurements Texp, the dual thermocouple probe towards and away from the
Tcov and ⌬T = Texp − Tcov and the percentage of reflected plasma source. Measurements obtained using a stainless steel
JVST A - Vacuum, Surfaces, and Films490 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 490
FIG. 5. Temperature of the exposed thermocouple 共Texp兲 vs distance from the FIG. 6. Temperature of the covered thermocouple 共Tcov兲 vs distance from the
plasma source for flow tubes constructed of Pyrex, quartz, aluminum, and plasma source for flow tubes constructed of Pyrex, quartz, aluminum, and
stainless steel. stainless steel.
cylindrical tube at a H2 pressure of 500 mTorr defined by a The temperature results for the covered thermocouple are
H2 flow rate of 75 SCCM and an input power of 3.3 kW are shown in Fig. 6. These results were obtained concurrently
shown in Fig. 4共a兲. There are small differences in ⌬T for the with the results in Fig. 5. The trends in Figs. 5 and 6 are
probe moving towards and away from the atomic hydrogen similar with the exception of quartz. The temperature data
source. This slight hysteresis may be partially attributed to for the quartz cylindrical insert showed more scatter than the
the thermal inertia of the exposed thermocouple. Figure 4共b兲 other materials. The temperature difference, ⌬T, for the four
compares Texp measurements at two different H2 pressures materials is given in Fig. 7. ⌬T versus distance from the
using a Pyrex cylindrical tube insert. There was no measur- outlet of the plasma source drops the most rapidly for the
able difference in temperature readings between H2 pressures stainless steel cylindrical tube. The nonmetallic Pyrex and
of 250 and 500 mTorr defined by flow rates of 35 and quartz cylindrical inserts show ⌬T values that persist at
75 SCCM, and input powers of 2.0 and 3.3 kW, respectively. greater distances from the plasma source.
This pressure independence was observed using two differ-
IV. DISCUSSION
ent thermocouple probes.
A. Heat balance model
B. Temperature measurements for different materials The hydrogen radical concentration, 关H兴, is determined
Dual thermocouple probe measurements were performed using a heat balance model. This analysis quantifies the heat
using cylindrical tubes composed of the four different mate-
rials at two different H2 pressures. The data were acquired
using the ON/OFF mode of the plasma source to prolong the
lifetime of the thermocouple probe. Measurements were per-
formed four separate times for each material at H2 pressures
of 250 and 500 mTorr defined by H2 flow rates of 35 and
75 SCCM and input powers of 2.0 and 3.3 kW, respectively.
Because no measurable difference was observed between H2
pressures of 250 and 500 mTorr, these data sets were aver-
aged together.
The temperature results for the exposed thermocouple as a
function of distance from the outlet of the plasma source for
cylindrical tubes composed of stainless steel, aluminum,
Pyrex, and quartz are shown in Fig. 5. The exposed thermo-
couple temperature drops the most rapidly versus distance in
the stainless steel tube. Compared with stainless steel, the
temperatures persist at greater distances away from the
plasma source for the aluminum tube. Pyrex and quartz tubes
FIG. 7. Temperature difference between the exposed and covered thermo-
display higher temperatures at greater distances than either couples 共⌬T兲 vs distance from the plasma source for flow tubes constructed
stainless steel or aluminum. of Pyrex, quartz, aluminum, and stainless steel.
J. Vac. Sci. Technol. A, Vol. 24, No. 3, May/Jun 2006491 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 491
described in the previous treatments.21,22 The radiative heat-
ing term, Q2, also can be determined using the Stefan-
Boltzmann law.21,22 The total emissivities of the stainless
steel, aluminum, quartz, and Pyrex wall materials were ss
= 0.79, Al = 0.02, quartz = Pyrex = 0.6– 0.8, respectively. The
wall temperature was assumed to be equivalent to the tem-
perature of the covered thermocouple.
The heat transferred from the thermocouple to the hydro-
gen gas in the viscous flow regime, Q3, was determined fol-
lowing the earlier treatments.21,22 The hydrogen gas tempera-
ture was assumed to be measured by the covered
thermocouple. The diameter of the thermocouple was d
= 0.74 mm. Other parameters used to define Q3 were the hy-
drogen gas density of 2.07⫻ 10−5 kg/ m3 and the average
flow velocity of 1.0 m / s. The diameter of the tube was either
d = 6.0 cm or d = 5.1 cm and the gas viscosity was = 8.0
⫻ 10−6 kg/ ms. Q4 represents the heat lost through the ther-
FIG. 8. Illustration of the heating and cooling sources for the exposed ther- mocouple wires.21,22 This term is neglected in the determina-
mocouple. Q1 is radiative cooling, Q2 is radiative heating, Q3 is gas convec- tion of Q5 because of the small cross-sectional area of the
tion, Q4 is thermocouple wire conduction, and Q5 is heat of recombination
thermocouple wire.
for atomic hydrogen.
Q5 accounts for the heating of the thermocouple from the
heat of recombination of atomic hydrogen. This term is ex-
pressed as21,22
gain and heat loss terms for the thermocouple following pre-
vious treatments.21,22 Figure 8 is a picture of a thermocouple Q5 = 共1/2兲d2⌬E␥Pt共关H兴v/4兲. 共2兲
showing the heat gain and heat loss mechanisms. Following
earlier definitions, Q2 and Q5 are the heat gain terms from The heat of recombination of two hydrogen atoms to form
the heating of the thermocouple from radiation and the heat H2 has a value of ⌬E = 436 kJ/ mole of H2. The quantity
of atomic hydrogen recombination, respectively. Q1, Q3, and 共关H兴v / 4兲 is the flux of the hydrogen atoms impinging on the
Q4 are the heat loss terms. Q1 is the radiative cooling term, thermocouple surface. v is the average rms thermal velocity
Q3 is the heat transfer to the gas by convection, and Q4 is the of the hydrogen atoms. The factor of 2 assures proper sto-
heat conduction away from the thermocouple along the ther- ichiometry between the atomic hydrogen flux and the heat of
mocouple wires. At a steady state temperature, the heat lost reaction for 2H → H2.32
equals the heat gain
Q1 + Q3 + Q4 = Q2 + Q5 . 共1兲
B. Assumptions affecting the determination of the
Heating of the thermocouple by the ambient gas was not
absolute hydrogen concentration
explicitly included in the previous applications of the heat
balance model.21,22 However, studies of hot filament-assisted The atomic hydrogen recombination coefficient on the
deposition of diamond have shown that thermocouple probes Pt/ Pt13% Rh thermocouple surface is ␥Pt. Calculations indi-
can be heated by the ambient gas.30,31 cate that the sticking coefficient of atomic hydrogen on cata-
Figure 6 shows that heating by the plasma radiation and lytic metal surfaces such as Ni共100兲 is nearly unity at all
possibly the ambient gas raises the covered thermocouple to hydrogen coverages.33 Experiments are also consistent with
⬃400 ° C near the outlet of the plasma source. Heating of the hydrogen sticking coefficients close to unity on bare Ni共111兲
covered thermocouple by hydrogen atom recombination on 共Ref. 34兲 and Ni共110兲.35 This near unity sticking coefficient
the glass surface was found to be negligible. Experiments for atomic hydrogen suggests that the recombination coeffi-
using an Ar plasma observed a similar temperature profile as cient to form H2 molecules could be ␥Pt ⬇ 1. However, the
observed for the H2 plasma in Fig. 6. In contrast to the cov- recombination coefficient will depend on the hydrogen atom
ered thermocouple temperature, the exposed thermocouple dynamics on the thermocouple surface.
temperature is Texp 艌 1600 ° C at the outlet of the plasma The incident hydrogen atom could interact with adsorbed
source. The large temperature difference of ⌬T ⬎ 1100 ° C is hydrogen either through an Eley-Rideal or hot atom
attributed to heating by atomic hydrogen recombination. This mechanism.33 The Eley-Rideal mechanism can lead to the
large ⌬T allows the heating by the hydrogen concentration to production of excited H2 product molecules.36,37 The excited
be easily distinguished from the other heating sources. H2 product molecule can carry away some of the recombi-
The hydrogen radical concentration can be determined by nation energy and lower the energy deposited at the thermo-
solving for Q5. Estimations of all the other heat gains and couple surface. H2 formation via a hot atom could also lead
heat losses are necessary to solve for Q5. The radiative cool- to excited H2 product molecules and lower the energy depos-
ing term, Q1, is determined by the Stefan-Boltzmann law as ited at the thermocouple surface. Consequently, care must be
JVST A - Vacuum, Surfaces, and Films492 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 492
tion experiments are also consistent with recombination co-
efficients of less than unity on metal surfaces at low tempera-
tures and low hydrogen coverages.8,34
The hydrogen recombination coefficient on Pyrex and
quartz has been reported to increase dramatically with
temperature.9,20 The hydrogen recombination coefficient also
increases with temperature on a platinum filament.19 Assum-
ing that the heat of recombination is entirely dissipated to the
surface, the higher recombination coefficient at higher tem-
peratures may reflect the higher hydrogen sticking coeffi-
cients at low hydrogen coverage. However, instead of assum-
ing that the heat of recombination is entirely dissipated to the
surface, these higher effective recombination coefficients at
higher temperatures may result from a higher fraction of the
heat of recombination imparted to the surface at low hydro-
gen coverages where the Eley-Rideal or hot atom mecha-
FIG. 9. Hydrogen flux vs distance from the plasma source for flow tubes nisms may have a smaller effect.
constructed of Pyrex, quartz, aluminum, and stainless steel. Because of the uncertainties in both the fraction of heat of
recombination dissipated to the surface and ␥Pt, this treat-
ment will make an assumption regarding the ⌬E␥Pt product.
We will assume that ⌬E␥Pt = 43.6 kJ/ mole of H2. This as-
sumption is equivalent to the earlier assumption that ␥Pt
taken to determine if the assumptions are valid that ␥Pt
= 0.1 with all the heat of recombination dissipated to the
= 1.0 and ⌬E = 436 kJ/ mole of H2 is dissipated to the ther-
thermocouple surface.22
mocouple surface.
The heat balance equation can be rearranged to solve for
Figure 5 shows that the exposed thermocouple tempera-
ture is greater than the H2 desorption temperature of 117 ° C Q5 = Q1 + Q3 + Q4 − Q2. The atomic hydrogen flux is then de-
共Ref. 38兲 from Pt over most of the experimental range. At termined by rearranging Eq. 共2兲.
these higher temperatures, hydrogen will not accumulate and Figure 9 displays the atomic hydrogen flux for the cylin-
the hydrogen coverage will be determined by the incident drical tubes composed of the four materials as a function of
hydrogen flux and the H2 desorption rate. If the desorption distance away from the plasma source. The atomic hydrogen
rate exceeds the adsorption rate, the steady state hydrogen flux in Fig. 9 closely mirrors the ⌬T results in Fig. 7. For the
coverage will be low and the atomic hydrogen sticking co- aluminum tube at 8 cm from the outlet of the plasma source,
efficient should be close to unity. In the limit of zero hydro- the heat gain and loss terms that yield the atomic hydrogen
gen coverage, the hydrogen atoms will have a long residence flux are Q1 = 0.0058 W, Q2 = 0.000 036 W, Q3 = 0.814 W,
time before they encounter another adsorbed hydrogen atom. and Q5 = 0.190 W. Q4 was neglected because of the small
This long residence time will enable the hydrogen atoms to cross-sectional area of the thermocouple wires.
equilibrate thermally with the thermocouple surface prior to At the outlet of the hydrogen plasma source, the absolute
H2 recombinative desorption. These conditions favor the dis- hydrogen flux is estimated to be 艌 6.5⫻ 1020 at./ cm2 s.
sipation of the heat of recombination to the thermocouple The atomic hydrogen velocity is v = 4.1⫻ 105 cm/ s at the
surface and discourage the Eley-Rideal or hot atom mecha- covered thermocouple temperature of ⬃425 ° C at the outlet
nisms that would lead to excited H2 products. of the plasma source. This atomic hydrogen velocity was
At low hydrogen coverages at exposed thermocouple tem- used to obtain an atomic hydrogen concentration from the
peratures ⬎117 ° C, the assumptions may be valid that the atomic hydrogen flux. At 500 mTorr and 425 ° C, the density
hydrogen recombination coefficient is ␥Pt = 1.0 and the heat of hydrogen atoms in H2 is 6.3⫻ 1015 at./ cm3. Consequently,
of recombination of ⌬E = 436 kJ/ mole of H2 is imparted to the hydrogen concentration of 关H兴 艌 6.3⫻ 1015 at./ cm3 rep-
the thermocouple surface. However, earlier implementations resents a H2 dissociation degree of 艌90%. This dissociation
of this heat balance model have assumed that ␥Pt ⬃ 0.1.22 degree indicates that 艌90% of the H2 gas at 500 mTorr is in
This assumption was based on earlier measurements of hy- the form of atomic hydrogen at the outlet of the plasma
drogen recombination coefficients of 0.1⬎ ␥Pt ⬎ 0.02 on source.
platinum filaments at temperatures from 65 to 890 ° C.19 The absolute hydrogen radical concentration depends
Other heat balance models have also assumed hydrogen re- critically on the assumption that ⌬E␥Pt = 43.6 kJ/ mole of H2.
combination coefficients derived from these earlier If this assumption was changed to ⌬E␥Pt = 436 kJ/ mole of
measurements.21 Additional measurements have obtained a H2, the absolute hydrogen concentration would be ten times
hydrogen recombination coefficient of ␥Pt = 0.25 on platinum smaller, i.e., a dissociation degree of 艌9%. Because of this
deposited on a Pyrex tube by vacuum evaporation.7 This Pt assumption, there is considerable uncertainty in the absolute
surface was at much lower temperatures than the previous hydrogen radical concentration. Fortunately, the determina-
measurements on heated filaments. Other hydrogen abstrac- tion of the atomic hydrogen recombination coefficients is not
J. Vac. Sci. Technol. A, Vol. 24, No. 3, May/Jun 2006493 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 493
dependent on the absolute hydrogen concentrations. The re- assumed to be given by the time required for the H2 flowing
combination coefficient is only dependent on the relative gas to traverse the 20 cm tube length. At the example tem-
change in the hydrogen concentration. perature of 255 ° C, the diffusion time is = 0.15 s for the
flow velocity of v f = 130 cm/ s. This diffusion time yields a
mean displacement of l = 6.0 cm and an atomic hydrogen dif-
C. Attenuation of hydrogen radical concentration
during viscous flow transport fusion velocity of F = 38 cm/ s.
Under static gas conditions, Eq. 共3兲 can be used to solve
The determination of the atomic hydrogen recombination for the hydrogen atom recombination coefficient. Under H2
coefficient, ␥, has been thoroughly analyzed in a static gas flowing gas conditions, the flowing gas can be viewed as a
where the transport of atomic hydrogen is governed solely by static reference frame being translated down the flow tube
diffusion.18 This situation is modified when the H2 gas flows with a flow velocity of v f = 130 cm/ s. Equation 共3兲 still ap-
through the plasma source, down the cylindrical outlet tube plies in the static reference frame and the atomic hydrogen
and past the thermocouple probe. Under flowing gas condi- diffusion velocity in the static reference frame is the diffu-
tions, the transport of hydrogen radicals is governed by both sion velocity, F. The flowing gas has the same atomic hydro-
atomic hydrogen diffusion and the H2 gas flow velocity. We gen flux incident on the tube surface as the static gas. How-
will first review the results from the static gas analysis and ever, the movement of the static reference frame will lead to
then extend the treatment to a flowing gas. atomic hydrogen persisting further down the length of the
Previous work has determined that the recombination ki- flow tube.
netics for atomic hydrogen display first-order kinetics.18,20,39 The movement of atomic H for static gas conditions can
There is also a possibility for hydrogen recombination in the be defined by xs = Ft. Likewise, the movement of atomic H
gas phase resulting from a three-body collision recombina- under flowing gas conditions can be described by x f = 共F
tion mechanism. However, this hydrogen loss mechanism is + v f 兲t. These two equations establish the relationship be-
only significant at much higher atomic hydrogen concen- tween xs and x f as xs = x f where the reference frame trans-
trations.40,41 The expression that describes the first-order de- form ratio, , is given by
cay of the atomic hydrogen concentration versus distance
from the plasma source for a static, diffusion-controlled ex- = F/共F + v f 兲. 共5兲
periment can be written as20
This ratio is used to modify the flowing gas length variable,
关H兴 = 关H兴o exp共− ␥1/2xs兲, 共3兲 x f , to adjust for the H2 gas flow velocity. The modification to
Eq. 共3兲 is given as
where 关H兴o is the initial hydrogen radical concentration, xs is
the distance from the plasma source for static gas conditions, 关H兴 = 关H兴o exp共− ␥1/2x f 兲. 共6兲
and ␥ is the recombination coefficient.
The geometrical factor, , is This reference frame transformation is approximate and is
dependent on the estimation of the diffusion velocity. Equa-
 = 共vR/D兲 /R.
1/2
共4兲
tion 共6兲 allows recombination coefficients, ␥, estimated un-
In this expression, R is the radius of the tube and v and D are der flowing gas conditions to be compared with ␥ values
the atomic hydrogen velocity and diffusion coefficient, re- derived under static gas conditions. At the representative
spectively. At a temperature of T = 255 ° C for the covered temperature of 255 ° C at 500 mTorr, = 0.23 given the
thermocouple in the stainless steel cylinder at 4.0 cm from atomic hydrogen diffusion velocity of F = 38 cm/ s and the
the plasma source, the atomic hydrogen velocity is v = 3.33 flow velocity of v f = 130 cm/ s.
⫻ 105 cm/ s. The diffusion coefficient can be calculated from The factor  in the exponent defines the exponential
the diffusion equation for binary gas mixtures42 using the decay of the hydrogen radicals for different pressures and
interaction potential between H2 and H.29 The diffusion co- flow velocities. For 75 SCCM and 500 mTorr at the repre-
efficient has a value of D = 230 cm2 / s at a temperature of sentative temperature of 255 ° C, the factor  = 5.0 cm−1. At
255 ° C and a pressure of 500 mTorr. This diffusion coeffi- the lower pressure of 250 mTorr and gas flow of 35 SCCM,
cient of D = 230 cm2 / s and hydrogen velocity of v = 3.33 = 0.30 given a different atomic hydrogen diffusion velocity
⫻ 105 cm/ s yield a geometrical factor of  = 21.9 cm−1. of F = 53 cm/ s and a H2 flow velocity of v f = 121 cm/ s at
The transport of hydrogen radicals is facilitated under H2 255 ° C. The diffusion coefficient of D = 460 cm2 / s at
flowing gas conditions. The H2 flow velocity is v f 250 mTorr and 255 ° C yields a geometrical factor of 
= 130 cm/ s at a flow rate of 75 SCCM, a H2 pressure of = 15.5 cm−1. The resulting factor  = 4.7 cm−1 for
500 mTorr, and a temperature of 255 ° C. To compare the H2 35 SCCM and 250 mTorr at 255 ° C. The  values are very
gas flow velocity and the atomic hydrogen diffusion velocity, similar for the two flow rates of 75 and 35 SCCM at 255 ° C.
we need to estimate a diffusion velocity. The drift velocity or This explains the lack of observable differences in measure-
diffusion velocity, F, for the atomic hydrogen can be ap- ments performed at the two different flow rates.
proximated by F = D / l. This estimate defines the characteris- Both the diffusion velocity, F, and the flow velocity, v f ,
tic velocity of atomic hydrogen through H2 gas under static are temperature dependent. As the temperature varies with
conditions. The mean displacement, l, can be calculated from position in the flow tube, F and v f vary as the parameters that
the Einstein relationship l2 = D. is the diffusion time and is define F and v f also change with temperature. This tempera-
JVST A - Vacuum, Surfaces, and Films494 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 494
TABLE I. Atomic hydrogen recombination coefficients for Pyrex, quartz, and
native oxide-covered stainless steel and aluminum.
Material ␥
Stainless steel 2.2⫻ 10−3 ± 0.2⫻ 10−3
Aluminum 1.7⫻ 10−3 ± 0.2⫻ 10−3
Pyrex 9.4⫻ 10−4 ± 4.0⫻ 10−4
Quartz 7.5⫻ 10−4 ± 0.8⫻ 10−4
D. Determination of atomic hydrogen recombination
coefficients
According to Eq. 共6兲, the natural logarithm of the mea-
sured atomic hydrogen concentration can be plotted versus
the modified length variable, x f . The slope of this plot
yields the recombination coefficient, ␥. The y intercept of
FIG. 10. Logarithm of the hydrogen concentration vs distance from plasma this plot determines the initial hydrogen radical concentra-
source times  for a stainless steel flow tube. A linear fit yields an atomic tion 关H兴o. This analysis was performed on the measured
hydrogen recombination coefficient of ␥ = 2.2⫻ 10−3 ± 0.2⫻ 10−3 for native
oxide-covered stainless steel.
atomic hydrogen concentrations versus the modified length
variable for the cylindrical tubes composed of stainless steel,
aluminum, Pyrex, and quartz.
Figure 10 shows the results for the stainless steel cylin-
ture dependence was treated at each position in the flow tube. drical tube. The data are plotted as a function of x f , the
The temperature-dependent changes for the stainless steel, product of the geometrical factor, the reference frame trans-
aluminum, Pyrex, and quartz tubes all displayed the same form ratio, and distance. The solid line is the least squares fit
general trends with temperature for various distances from to the experimental data. The slope of the line is equal to
the plasma source. For the conditions at 75 SCCM and ␥1/2. For native oxide-covered stainless steel, the atomic hy-
500 mTorr, the diffusion coefficient ranged from D drogen recombination coefficient is ␥ = 2.2⫻ 10−3 ± 0.2
= 268 to 175 cm2 / s. The flow velocities ranged from v f ⫻ 10−3. The error represents the uncertainty in the slope from
= 177 to 75.5 cm/ s and the calculated diffusion velocity var- the linear least squares fit.
ied from F = 48.7 to 25.7 cm/ s. These changes occurred for The correlation between the measured atomic hydrogen
various distances from 0 to 20 cm from the outlet of the concentration and the predicted atomic hydrogen concentra-
plasma source. Given these temperature-dependent changes, tion using ␥ = 2.2⫻ 10−3 is shown in Fig. 11. The correlation
the reference frame transform ratio varied from = 0.216 to is good except for distances near the plasma source. This
0.254. deviation may be attributed to the error in the Pt/ Pt13% Rh
thermocouple measurements when T 艌 1450 ° C. The
Pt/ Pt13% Rh thermocouple temperature measurements are
only reliable when T 艋 1450 ° C.43
The atomic hydrogen recombination coefficients for the
four materials are presented in Table I. The native oxide-
covered metallic stainless steel and aluminum have the larg-
est recombination coefficients of 2.2⫻ 10−3 ± 0.2⫻ 10−3 and
1.7⫻ 10−3 ± 0.2⫻ 10−3, respectively. The nonmetallic Pyrex
and quartz display lower recombination coefficients of 9.4
⫻ 10−4 ± 4.0⫻ 10−4 and 7.5⫻ 10−4 ± 0.9⫻ 10−4, respectively.
The error again represents the uncertainty in the slope from
the linear least squares fit. Stainless steel, aluminum, and
quartz all displayed good linear fits with slope uncertainties
of about 10%. In contrast, the data for Pyrex were nonlinear
and yielded a much higher uncertainty.
The H2 gas flow conditions affect the determination of the
atomic hydrogen recombination coefficients. If the H2 gas
flow was not accounted for by the reference frame transform,
the recombination coefficients would have been 1.6⫻ 10−4
FIG. 11. Comparison between the hydrogen concentration vs distance from
and 1.2⫻ 10−4 on oxide-covered stainless steel and alumi-
the outlet of the plasma source and the predicted hydrogen concentration
assuming an atomic hydrogen recombination coefficient of ␥ = 2.2⫻ 10−3 for num, respectively. Likewise, the recombination coefficients
native oxide-covered stainless steel. would have been 5.4⫻ 10−5 and 4.2⫻ 10−5 on Pyrex and
J. Vac. Sci. Technol. A, Vol. 24, No. 3, May/Jun 2006495 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 495
quartz, respectively. The hydrogen recombination coeffi- cess. One key parameter is the flow tube radius. According to
cients are smaller because the atomic hydrogen concentra- Eqs. 共3兲 and 共4兲, the geometrical factor, , is smaller for
tions appear to travel further in the cylindrical tubes. larger radii. A smaller  decreases the attenuation as the
The measured atomic hydrogen recombination coeffi- hydrogen radicals move down the flow tube. Consequently,
cients on the Pyrex and quartz surfaces were 9.4 the hydrogen transport tube should be as large as possible to
⫻ 10−4 ± 4.0⫻ 10−4 and ␥ = 7.5⫻ 10−4 ± 0.8⫻ 10−4, respec- minimize atomic hydrogen recombination.
tively. These values for the oxide surfaces are in reasonable The gas flow also effectively transports the hydrogen radi-
agreement with earlier measurements. On Pyrex glass, the cal concentration farther away from the plasma source. Ear-
recombination coefficient has been measured to be ␥ = 5.8 lier investigations measured the atomic hydrogen concentra-
⫻ 10−3 at 27 ° C.19 Another value for Pyrex of ␥ = 7.5 tion under flowing gas conditions in tubes of Kovar glass at
⫻ 10−4 has been measured at an unrecorded temperature.7 various pressures.44 Hydrogen concentrations were attenu-
The surface of quartz glass has yielded ␥ values of 2.8 ated with 1 / e values of ⬇45 cm at a H2 pressure of
⫻ 10−3,9 8.6⫻ 10−4,30 2 ⫻ 10−3,23 共2.5– 3兲 ⫻ 10−3,13 500 mTorr. These large 1 / e values may be attributed to the
−3 20 −4 10
3 ⫻ 10 , and 2.1⫻ 10 , at room temperature. A smaller high H2 gas flow velocity. In viscous flow, high H2 gas flow
value of ␥ = 1.9⫻ 10−5 was reported at a higher temperature velocities relative to atomic hydrogen diffusion velocities
of 300 ° C.18 However, values as high as ␥ = 共1 – 6兲 ⫻ 10−2 will facilitate hydrogen atom transport.
have been measured for quartz over a range of
temperatures.11 The atomic hydrogen recombination coeffi-
cients obtained for Pyrex and quartz using the dual thermo-
couple probe in this study are within the range of these pre- V. CONCLUSIONS
viously measured values.
The previously measured hydrogen atomic recombination A dual thermocouple probe has been used to measure the
coefficients on metals are much larger than the hydrogen attenuation of hydrogen radicals traveling under flowing gas
atomic recombination coefficients of ␥ = 2.2⫻ 10−3 ± 0.2 conditions through tubes of different materials. These mea-
⫻ 10−3 on oxide-covered stainless steel and ␥ = 1.7 surements have quantified the hydrogen radical attenuation
⫻ 10−3 ± 0.2⫻ 10−3 on oxide-covered aluminum measured in under conditions that are similar to conditions used during
this study. Measurements at various temperatures yielded ␥ thin film growth with hydrogen radicals. The analysis in-
⬇ 0.1 for pure metals such as Cu, Al, Ti, and Ni. Smaller cluded a reference frame transformation to account for the
values of ␥ ⬇ 0.01 were obtained for W and Pd.19 More re- flowing gas conditions because the hydrogen radical trans-
cent measurements obtained ␥ = 共3 – 4.5兲 ⫻ 10−2 on stainless port is determined by both atomic hydrogen diffusion and the
steel.13 In addition, a recombination coefficient of ␥ = 0.1 was H2 gas flow velocity. The flowing gas conditions are shown
obtained on type-304 stainless steel.12 to extend the range of hydrogen radical transport through the
This discrepancy between the recombination coefficients various tubes of common construction materials.
on metals is attributed to the presence of native oxides on the Some key assumptions in the heat balance model did not
stainless steel and aluminum surfaces in this study. No spe- allow the absolute hydrogen radical concentrations to be
cial procedures were utilized to clean or prepare the stainless measured with certainty. However, clear trends were ob-
steel or aluminum cylindrical tubes prior to the measure- served when measuring the hydrogen radical concentration
ments. These tubes were used as received from the vacuum versus distance from the hydrogen radical source and for
parts vendors. The native oxides on stainless steel and alu- different tube materials. Hydrogen radicals recombine very
minum would reduce the atomic hydrogen recombination co- efficiently on the walls of the tubes. For the tube diameters
efficient to values that are more comparable with the metal of 5.1– 6.0 cm, the hydrogen radical concentration was at-
oxides. tenuated to 1 / e of the initial concentration within 5 – 15 cm
of the hydrogen radical source for H2 gas flow velocities of
35– 75 SCCM under viscous flow conditions at H2 pressures
E. Design of transport lines and chemical reactors
of 250– 500 mTorr.
These measurements of hydrogen radical concentrations The hydrogen radical attenuation was the largest for na-
traveling under flowing gas conditions through tubes of dif- tive oxide-covered stainless steel and aluminum. The attenu-
ferent materials should facilitate the design of transport lines ation was the least for Pyrex and quartz. Atomic hydrogen
and chemical reactors that employ hydrogen radicals. The recombination coefficients were determined from the analy-
rector or flow tube material affects the magnitude of the sis of the hydrogen concentration profiles under flowing gas
atomic hydrogen concentration versus distance from a hydro- conditions. The atomic hydrogen recombination coefficients
gen source. By knowing the chamber geometry, temperature, obtained from this analysis were 9.4⫻ 10−4 ± 4.0⫻ 10−4 for
pressure, flow rate, and hydrogen recombination coefficient, Pyrex and 7.5⫻ 10−4 ± 0.8⫻ 10−4 for quartz. The atomic hy-
the hydrogen flux can be predicted versus position and the drogen recombination coefficients were 2.2⫻ 10−3 ± 0.2
sample placement can be optimized for the most efficient ⫻ 10−3 for oxide-covered stainless steel and 1.7⫻ 10−3 ± 0.2
hydrogen radical exposure. ⫻ 10−3 for oxide-covered aluminum. These results should be
Besides the material issues, the design is influenced by useful for the design and optimization of chemical reactors
other parameters that affect the hydrogen recombination pro- that utilize hydrogen radicals.
JVST A - Vacuum, Surfaces, and Films496 R. K. Grubbs and S. M. George: Attenuation of hydrogen radicals traveling under flowing gas 496
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