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A spectroscopic study of vapor-phase titanium
J. Quant. Spectrosc. Radiat. Transfer Vol. 49, No. 3, pp. 303-310, Printed in Great Britain. All rights reserved
A SPECTROSCOPIC
1993
0022-4073/93
$6.00 + 0.00 Press Ltd
Copyright 0 1993Pergamon
STUDY OF VAPOR-PHASE
TITANIUM
SHRINATH RAMASWAMI,~$ ROBERT R. REEVES,? MATTHEW RUTTEN,t#
and JUDITH A. HALSTEADY (1 TDepartment of Chemistry, Rensselaer Polytechnic Institute, Troy, NY 12180 and BDepartment of Chemistry and Physics, Skidmore College, Saratoga Springs, NY 12866, U.S.A. (Received 26 November 1991; received for publication 27 July 1992)
Abstract-The natural radiative lifetime of the y3F” state of Ti was determined to be 23 + 2 nsec by LIF. Ti atoms were excited at 396 nm and emission was observed at 735 nm. The quenching cross sections for the y3p state were determined to be 1.9 x lo-l6 and 1.1 x lO_” cm2 for He and Ar, respectively. In addition, quantitative atomic absorption measurements of gas-phase Ti atoms were made in a thermal evaporation cell and compared with concentrations calculated from a simple mathematical model.
INTRODUCTION Elementary physical and chemical processes involving refractory-metal, gas-phase atoms are of interest, both from a fundamental point of view and because of the increasing importance of refractory metals in the microdevice-synthesis industry. Various refractory metals, metal silicides and other metal compounds have recently been under development for use as gate level interconnects in very large scale integration (VLSI) circuits. ‘J Titanium silicide is an especially important material because of its low resistivity and good thermal stability.3 A Ti : W alloy has been used as a diffusion barrier.4 Possible future metallization schemes are reviewed by Sze.4 Some studies of dry etching of TiSi,, 3*5-7Ti ,. W8,9 and TiN’O have been conducted. Reeves et al” used
atomic absorption spectroscopy as a diagnostic tool in a plasma-etching study of titanium metal. As the use of titanium and titanium compounds increases in the VLSI industry, an understanding of the optical spectroscopy of vapor-phase Ti will become increasingly important. In the current study, laser-induced fluoresence (LIF) was used to determine the natural radiative lifetime and quenching coefficients of the titanium y3F” state. Quantitative atomic absorption measurements of gas-phase Ti were made in a thermal evaporation cell. Concentrations calculated from a simple mathematical model are compared with experimental concentrations calculated using the Beer-Lambert law. EXPERIMENTAL
STUDIES
The Pyrex evaporation cell (Fig. 1) used as a source of Ti atoms was equipped with plate glass windows and a threaded 100 W electric-lamp base. The tungsten filament was removed and replaced with a coiled titanium filament which was 0.2 cm in diameter and 3 cm long. The cell was evacuated to lo-’ torr, flushed with fill gas (argon or helium) and filled to the desired operating pressure. With 7.5-8.5 V applied to the filament, current of 1.9-2.2 A were measured. A steady-state concentration gradient of titanium atoms between the heated filament and the room-temperature walls of the cell was established. The temperature of the filament was measured using a Pyro microoptical pyrometer. The experimental apparatus for the LIF measurements is shown in Fig. 2. A Molectron DL-200 dye laser (pulse width: 8 nsec) pumped by a Molectron u.v.-400 nitrogen laser was used to excite the titanium atoms at 396.427 nm, populating the y3fl state (Fig. 3). LIF from the y3P4+b3F4 transition was observed at right angles to the laser beam with an RCA C31000F photomultiplier tube (PMT) after passing through a red Corning glass filter (CS 2-58) and an interference filter SPresent address: Motorola Inc., Advanced Technology Center, 2200 W. Broadway Rd., Mesa, AZ 85202, U.S.A. $Present address: IBM-GTD, Essex Junction, VT 05452, U.S.A. l[To whom all correspondence should he addressed. 303
304
SHIUNATH RAht~Swr~ht~et
al
Filament
To Vacuum Pump
(b)
,:
:_ 2r Sectton
A A’
Path
...\. ,\..\\\~
1
.\
,v
A
To GSS Tank
To Power Supply
Fig. 1. (a) Schematic of the evaporation cell, showing the titanium filament. The path of the beam (from hollow-cathode lamp or from dye laser) is along the line A-A’. (b and c) Section along the line A-A’ and perpendicular to the axis of the filament, showing various dimensions and distances used in the model given in the text.
centered at 735 nm (Baird-Atomic, BWHM 8 nm). A scanning boxcar averager (Princeton Applied Research Model 162 with model 163 sampling integrator) averaged 100 pulses from the PMT and the resulting signal entered an IBM PC/XT equipped with general purpose I/O boards (Data Translation DT 2801 and DT 707). Custom software was written to collect, store and smooth data
305
A spectroscopic study of vapor-phase titanium
:Compuler
PAR 162
r
Boxcar Averager
I
Fast Amplifier
Triggel PMT
r
1
,,,,,.,,,,,,,,,,., “oip:
Ftjq
,,,,,,I,,,,,,,,,,
,,,,.,,,,,,#.,///,,
Sample Cell Fig. 2. Schematic of the apparatus used for the laser-induced fluroescence experiments. Interfacing between the computer and the boxcar averager was done using Data Translation I/O boards. The trigger input to the boxcar is provided by a photomultiplier (trigger PMT) positioned to detect laser pulses scattered off the wall of the glass sample cell.
Y
J 4
3Fo
cm
t
3
4
2
cm
-1
-
25366
-
25227
-
25107
-1
11640 11532
cm -
-1
367 170
a
3
F
Fig. 3. Selected atomic Ti energy levels and transitions observed using the LIF technique. The wavelength (in A) of each transition is given against the vertical line representing that transition. The laser excited electrons from [u’F] state; emission was then observed in the red through transitions to the [b’F] state.
306
S~INATH
R.4hfA.W~hiIet al
and carry out curve-fitting routines. For quenching-coefficient determinations, LIF scans for each fill gas pressure used were obtained with the titanium filament on and with the filament off (background scan) for 200 nsec after the initiation of the laser pulse. The background scan (obtained with the filament off) was subtracted from the LIF scan and an exponential curve-fit was performed on the section of the scan occurring after cessation of the laser pulse. For atomic absorption measurements at 400.893 mn, light from a titanium hollow-cathode lamp passed through focusing lenses before and after passing through the evaporation cell described above and then entered a 0.25 M Jarrell Ash monochromator equipped with a RCA 6256B PMT. Atom concentrations were determined from the Beer-Lambert law. The intensity of the beam prior to passing through the cell, I,, was determined by blocking and unblocking the hollow cathode lamp emission with the titanium filament off. The intensity of the beam after passing through the cell was determined in an anlogous manner. This procedure avoids the small error due to light from the filament detected by the PMT. The atom concentration determined as described above represents the concentration of one individual J-level within the ground state electronic level. The fraction of the population in each individual J-level is given by
where g, is 2J + 1 (the degeneracy of the J level), E,, the energy difference between the J-level of interest and the lowest J level, R the universal gas constant, T the absolute temperature, and the summation is taken over all J values. For example, the 400.893 nm line corresponds to absorption from the J = 3 level. Using the appropriate EJ values given in Table 1, the percentage of the Ti atoms in this level at 1000 K is determined to be approx. 33.5%. The total Ti atom concentration is then 3.0 times the concentration calculated from Beer-Lambert law absorption measurements using the 400.893 nm line. Quenching
coeficients
and lifetime
measurements
In the absence of resonance-radiation trapping, both quenching coefficients and the natural radiative lifetime for an excited state are obtained by plotting the reciprocal of the observed lifetime as a function of the fill gas pressure, i.e.
l/L = l/T” + k,(W, where z, is the experimental or observed lifetime (set), Tothe natural radiative lifetime (set), k, the quenching coefficient (cm3 set-‘) and (M) the fill-gas density (cm-‘). The temperature of the filament, which gives negligible resonance-radiation trapping under our experimental conditions, can be obtained by measuring the LIF intensity as a function of temperature and plotting the logarithm of the LIF signal as a function of the reciprocal of the temperature. In the absence of reasonance-radiation trapping, the LIF signal is proportional to the vapor pressure of titanium at the temperature of the filament. From the Clausius-Clapeyron equation: ln(LIF signal at T,/LIF signal at T,) = -(H,./R)[(I/T,) - (l/T,)], (3) w h ere H, is the heat of sublimation and R the universal gas constant. The linearity of Fig. 4 supports the conclusion that filament temperatures between 1400 and 1500 K results in a high enough Ti-atom concentration to give an adequate signal-to-noise ratio and a low enough concentration to avoid resonance-radiation trapping. From the slope in Fig. 4, the heat of vaporization is determined to be 109.1 kcal/mol, which compares favorably with the literature value of 109 f 1 kcal/moln Table
I. Percentages
of Ti atoms level.
in a ground-state Temperature
J 4 3 2
E, (J x 102’,cm-‘) 7.68 3.37 0
387 170 0
energy
(K)
500
1000
2000
25.25 32.03 42.72
33.75 33.53 32.72
38.27 33.64 28.09
CC -~ 42.85 33.33 23.81
307
A spectroscopic study of vapor-phase titanium
loo0 c
lo4
-0
7.2
6.6
(“K-l) Fig. 4. Arrhenius plot of LIF signal intensity vs (absolute temperature)-‘. The heat of sublimation of titanium is calculated from the slope of the straight line fitted to this data. l/Tf x IO4
10
20
30
40
50
x10e6 (cmm3) Fig. 5. Natural radiative lifetime of the titanium b’F’j state. The reduction in lifetime with increase in Ar and He fill-gas pressures is shown; the natural lifetime is estimated at 0 fill-gas pressure. Ar, being the heavier gas, affects the lifetime to a greater extent than does He. [M]
Assuming the absence of resonance-radiation trapping, the natural radiative lifetime of the y’F”, state can be obtained from the y-intercept in Fig. 5 as 23 + 2 nsec. The lifetime of the titanium y3P4 state has been previously measured by Rudolph and Helbig13 to be 18.8 + 1.3 nsec and by Salih and Lawler14 to be 18.3 + 0.9 nsec. An estimated value for this lifetime can be calculated from the literature transition probabilities for the 399.864, 396.427 and 734.472 nm emission lines to be 22 _+5.5 nsec.15From the transition probability listed for the 399.864 in the 70th CRC,16 the lifetime is estimated to be <25 nsec. Radiative destruction probabilities for the much longer lived .z’F” state of Ti (J = 2, 3,4) are given by Dezert et alI7 as (6.6 + 1.3) x 106, (4.8 + 1.2) x lo6 and (6 + 1.5) x lo6 set-‘, respectively. This result is also consistent with the values proposed by Wiese and Fuhrn for the z3F” state. Rate coefficients for the quenching of the y3c state by Ar and He buffer gases were determined from the slopes of the plots in Fig. 5 and are given in Table 2. Quenching cross sections, ao, are obtained from the rate coefficients as follows: go = kolv,
(3)
where v = (8RT/7rM)“2, R is the universal gas constant, T the gas temperature (1200 K + 100) and M the reduced mass of the colliding partners.” These values may be compared with the values obtained by Dezert, Quichaud and coworkers for the longer lived z3P state of Ti given in Table 3.‘7.‘8 The manner in which the quenching cross sections listed in Table 2 were obtained differs from the experimental method used for those listed in Table 3. Dezert, Quichaud and coworkers’7*‘8 (Table 3) excited each of the three z3Fi J levels individually and observed resolved fluroresence from individual J levels. Data were taken at a series of quenching gas pressures for each excitation and observation wavelength combination. The data obtained in this manner were used with a series of coupled rate expressions for quenching and collisionally-induced J-level changing to obtain the quenching cross section and J-changing cross sections for individual J levels of the z3P4 state. In the current work (Table 2), the 396.427 nm line was used to excite the y3Fo (J = 4) state and fluoresence was observed from the y3P J = 2,3 and 4 levels simultaneously in the region of 735 nm. Assuming that the natural radiative lifetimes for the individual J levels of the y3Fo multiplet are approximately the same, the quenching cross sections listed in Table 2 are not expected to be significantly different from the cross sections which would be obtained from the y3P’ multiplet from Table 2. Rate coefficients and cross sections for quenching of the ‘p4 state of Ti on collision with Ar and He. Collision partner
Quenching rate coefficient k, x 10” (cm3 set-‘)
Quenching cross section, op x 1Or6(cm*)
He Ar
5.0 12
1.9 11
S~INATH
308 Table 3. Rate coefficients Collision partner He Ne Ar H, N,
(Ref. (Ref. (Ref. (Ref. (Ref.
RAMAWAMI
et al
and cross sections for quenching of the z’fi, states of Ti (from Refs. 17 and 18). Quenching rate coefficient k, x 10” (cm3 set-I)
17) 17) 17) 18) 18)
2.5 1.2 2.8 80 37
“The temperature
is taken
+ * * + +
J = 2, 3 and 4
Quenching cross section” me x 10i6 (cmr)
I .7 & 0.4
0.3 0.2 0.4 8 4
1.5 4.5 38 53
+ 0.3 + 0.6 +4 + 7
as 400 K.
experiments analogous to those of Dezert, Quichaud and coworkers.“.‘” The transition-probability data given in Wiese and Fuhri3 suggest that the natural radiative lifetime is not a strong function of J for the y3P state. Absolute atomic absorption measurements The average absolute concentrations of titanium atoms across a chord in the evaporation cell (Fig. 1) were determined by atomic absorption spectroscopy at 400.893 nm using the Beer-Lambert law. As mentioned previously, the atom concentration determined in this manner represents the concentration of one individual J-level within the ground electronic state. Correction factors to obtain the total average Ti atom concentration across the chord were determined from the EJ values (Table 1) for the average temperature across the chord. The relative population of the J = 3 level is less sensitive to changes in temperature than are the relative populations of the J = 2 and J = 4 levels. The heat of vaporization of titanium can also be determined from the atomic absorption data in Fig. 6. The value for H,, of 109.4 kcal/mol from Fig. 6 is consistent with the LIF results presented in Fig. 4. A mathematical model was developed for the Ti atom concentration as a function of distance from the filament in the evaporation cell shown in Fig. 1. The absolute concentrations calculated from this model are compared with the absolute experimental values from atomic absorption spectroscopy in Fig. 7. The following simplifying assumptions were made during the development of the model: (a) the coiled filament is taken to be equivalent to a cylinder which is infinitely long and which has a radius and a temperature equal to those of the coil. (b) The concentration of titanium atoms in the gas phase near the surface of the cylinder corresponds to the vapor pressure of Ti at the temperature of the filament, while the concentration of Ti in the gas phase near the cell wall (60°C) is taken to be zero. (c) The temperature profile is established by heat conduction and the concentration profile is established by diffusion (convection heat and material transport are minimized by maintaining a low fill gas pressure of 5-10 torr of argon or helium). (d) The
10'23
20-
x n^ 67 'E St ::
x
k u 101':
y
IO
11--1----1 xx
0 x
d
"it
r!i 10'0
I.
5.9
I
.
6.1
6.0 l/if
x 104 (
I
6.2 K-t)
I 6.3
' 6.4
Fig. 6. Arrhenius plot similar to Fig. 4 but for atomic absorption measurements. Due to the poorer sensitivity of this technique compared with LIF, these readings are taken at higher temperatures than in Fig. 4.
I 0
10
c,,, x
1 20
10-‘“(cm~“)
Fig. 7. Results from the mathematical model: calculated vs observed concentrations of ground-state titanium atoms. The straight line represents the relationship C,,, = C,,,.
A spectroscopic study of vapor-phase titanium
309
formation of metal atom clusters in the vapor phase is negligible. This last assumption is easily justified. The rate of dimer formation is d(Ti)/dt = kn(Ti)*(M).
(4)
The time available for dimer formation can be estimated from the Einstein diffusion equation. With a distance from the filament to the walls of 4 cm and a diffusion coefficient at 10 torr of approx. 15 cm* set-‘, a time of 0.5 set is obtained. If the average Ti atom concentration is 10” crnm3 and the rate coefficient for dimer formation is approximated by a third-body gas-kinetic collision rate of 10F3*, then the fraction of Ti atoms which may form dimers at 10 torr, d(Ti)/(Ti), is 5 x lo-‘. At lower fill gas pressures, the concentration of Ti dimers will be even lower. From Fick’s first law,” the rate of diffusion of Ti atoms from the filament to the walls is given by dn/dt = -D(x)S(x)
dc(x)/dx,
(5)
where x is the radial distance from the filament, D (x j the coefficient for diffusion in the buffer gas, S(x) the surface area of a cylinder around the filament, and c(x) the concentration of titanium atoms, all at x cm from the filament. If the rate of evaporation from the filament per unit area is Y, then dnldt = Y2nr1,
(6)
where 1 is the length of the filament and r the radius of the filament. Combining Eqs. (5) and (6), rearranging and integrating from r to x gives c(x)=c(r)-rY
X[l/xD(x)]dx, sr
(7)
where c(r) corresponds to the vapor pressure of Ti at the temperature of the filament. Since the diffusion coefficient is a function of temperature, it is also a function of distance from the filament. From elementary gas kinetics, ‘* the temperature dependence of the diffusion coefficient is D(T) = kT3’*. From elementary heat transport conduction has the form
theory,
the temperature
(8)
profile established
as a result of
x = a emhT.
(9)
D(x) = k[(ln a - In x)/b13”.
(10)
Combining Eqs. (8) and (9) gives
Substitution of Eq. (10) into Eq. (7) and integration yields the expression c(x) = c(r) - C{[(ln a - In r)/(ln a - In x)1”’ - l}.
(11)
The constants Y and b are eliminated from the expression for c(x) by requiring the titanium atom concentration c(R), near the cool wall (60°C) to be zero, which gives C = c(r)/([(ln a - In r)/(ln a - In R)]“* - l}.
(12)
The constant, a, is determined by requiring the temperature profile given by Eq. (9) to fit the experimental measurements on the temperature of the filament and the temperature of the wall for each filament temperature. Atomic absorption data are obtained with the hollow cathode beam traversing the cell along a path where the atom concentration varies. Therefore, in order to compare the experimentally determined absolute concentration measurements with the results of this model, Eq. (11) must be integrated to give the average atom concentration over the beam path, viz. c..,=jdRxc(x)dx/jdRxdx
(13)
310
SHRINATH RAMASWAMI
et al
Substituting for c(x) from Eq. (11) and integrating, Rx {(In a - In r)/(ln a - In x)} l/2 dx. (14) sd This is the average concentration over the length of the hollow-cathode beam through the cell, L, where L = 2(R2 - d2)“2. Equation (14) was evaluated numerically to obtain the values given as the calculated titanium atom concentration in Fig. 6. The experimental values for c,,,~ were again determined from the Beer-Lambert law. A value for the absorption cross section of 5.5 x lo-l3 cm2 was calculated using the experimental lifetime of 23 nsec. Ca”e =
{2/(R2 - d2)} {[(P - d2)/2)] (c(r) + C) - c
CONCLUSIONS
LIF was used to determine the natural radiative lifetime of the titanium y3P state. Rate coefficients for the quenching of this state by Ar and He buffer gases were also determined. Quantitative atomic absorption measurements of gas-phase Ti were made in a thermal evaporation cell. A model was developed for the spatial distribution of Ti within the cell. In the model, it was assumed that a steady-state concentration gradient was established by diffusion while the thermal gradient was established by heat conduction. Concentrations calculated from this model compare well with observed concentrations calculated from the Beer-Lambert law and a value of 5.5 x lo-l3 cm2 for the absorption cross section. This result supports the suggestion that atomic absorption spectroscopy is an effective and convenient method for monitoring absolute metal atom concentrations in gas-phase systems. Acknowledgemenls-This investigation was supported by the Office of Naval Research and by International Business Machines Corporation. JAH acknowledges the PEW Charitable Trust for financial support during the 9G91 academic year. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
T. P. Chow and A. J. Steckl, J. Electrochem. Sot. 131, 2325 (1984). S. W. Robey, M. A. Jaso, and G. S. Oehrlein, J. Appl. Phys. 65, 2951 (1989). P. B. Ghate, J. C. Blair, C. R. Fuller, and G. E. McGuire, Thin Solid Films 53, 117 (1977). S. M. Sze, l%SZ Technology, McGraw-Hill, New York, NY (1988). S. M. Bobbio, Y. S. Ho, and T. Lopez, Mat. Res. Sot. Symp. Proc. 98, 243 (1987). K. C. Cadien, S. Sivaram, and C. D. Reintsema, J. Vat. Sci. TechnoI. A 4, 739 (1986). G. Tomkins, M. H. Davis, and P. J. Rosser, Vacuum 34, 451 (1984). E. R. Sirkin and H. A. VanderPlas, J. Vat. Sci. Technol. B 2, 152 (1984). P. May and A. I. Spiers, J. Electrochem. Sot. 135, 1592 (1988). C.-K. Hu, N. Mazzeo, S. Basavaiah, and M. B. Small, J. Vuc. Sci. Technol. A 8, 1498 (1990). R. R. Reeves, M. Rutten, S. Ramaswami, P. Roessle, and J. A. Halstead, J. Electrochem. Sot. 137, 3517 (1990). J. Phys. Chem. Ref Data. 14, Suppl. 1, 1823 (1985). J. Rudolph and V. Helbig, J. Phys. B: At. Mol. Phys. 15, L599 (1982). S. Salih and J. E. Lawler, Astron. Astrophys. 208, 157 (1989). W. L. Wiese and J. R. Fuhr, J. Phys. Chem. Ref: Data 4, 302 (1975). D. Dezert, V. Quichaud, D. Dequout, and A. Catherinot, Phys. Rev. A 34, 4793 (1986). V. Quichaud, D. Dezert, J. Aubreton, D. Degout, and A. Catherinot, Laser Chem. 10, 93 (1989). R. A. Alberty, Physical Chemistry, p. 281, Wiley, New York, NY (1987). S. Dushman, Scientific Foundations of Vacuum Technique, 2nd edn, p. 68, J. M. Lafferty ed., Wiley, New York, NY (1986).
A SPECTROSCOPIC
1993
0022-4073/93
$6.00 + 0.00 Press Ltd
Copyright 0 1993Pergamon
STUDY OF VAPOR-PHASE
TITANIUM
SHRINATH RAMASWAMI,~$ ROBERT R. REEVES,? MATTHEW RUTTEN,t#
and JUDITH A. HALSTEADY (1 TDepartment of Chemistry, Rensselaer Polytechnic Institute, Troy, NY 12180 and BDepartment of Chemistry and Physics, Skidmore College, Saratoga Springs, NY 12866, U.S.A. (Received 26 November 1991; received for publication 27 July 1992)
Abstract-The natural radiative lifetime of the y3F” state of Ti was determined to be 23 + 2 nsec by LIF. Ti atoms were excited at 396 nm and emission was observed at 735 nm. The quenching cross sections for the y3p state were determined to be 1.9 x lo-l6 and 1.1 x lO_” cm2 for He and Ar, respectively. In addition, quantitative atomic absorption measurements of gas-phase Ti atoms were made in a thermal evaporation cell and compared with concentrations calculated from a simple mathematical model.
INTRODUCTION Elementary physical and chemical processes involving refractory-metal, gas-phase atoms are of interest, both from a fundamental point of view and because of the increasing importance of refractory metals in the microdevice-synthesis industry. Various refractory metals, metal silicides and other metal compounds have recently been under development for use as gate level interconnects in very large scale integration (VLSI) circuits. ‘J Titanium silicide is an especially important material because of its low resistivity and good thermal stability.3 A Ti : W alloy has been used as a diffusion barrier.4 Possible future metallization schemes are reviewed by Sze.4 Some studies of dry etching of TiSi,, 3*5-7Ti ,. W8,9 and TiN’O have been conducted. Reeves et al” used
atomic absorption spectroscopy as a diagnostic tool in a plasma-etching study of titanium metal. As the use of titanium and titanium compounds increases in the VLSI industry, an understanding of the optical spectroscopy of vapor-phase Ti will become increasingly important. In the current study, laser-induced fluoresence (LIF) was used to determine the natural radiative lifetime and quenching coefficients of the titanium y3F” state. Quantitative atomic absorption measurements of gas-phase Ti were made in a thermal evaporation cell. Concentrations calculated from a simple mathematical model are compared with experimental concentrations calculated using the Beer-Lambert law. EXPERIMENTAL
STUDIES
The Pyrex evaporation cell (Fig. 1) used as a source of Ti atoms was equipped with plate glass windows and a threaded 100 W electric-lamp base. The tungsten filament was removed and replaced with a coiled titanium filament which was 0.2 cm in diameter and 3 cm long. The cell was evacuated to lo-’ torr, flushed with fill gas (argon or helium) and filled to the desired operating pressure. With 7.5-8.5 V applied to the filament, current of 1.9-2.2 A were measured. A steady-state concentration gradient of titanium atoms between the heated filament and the room-temperature walls of the cell was established. The temperature of the filament was measured using a Pyro microoptical pyrometer. The experimental apparatus for the LIF measurements is shown in Fig. 2. A Molectron DL-200 dye laser (pulse width: 8 nsec) pumped by a Molectron u.v.-400 nitrogen laser was used to excite the titanium atoms at 396.427 nm, populating the y3fl state (Fig. 3). LIF from the y3P4+b3F4 transition was observed at right angles to the laser beam with an RCA C31000F photomultiplier tube (PMT) after passing through a red Corning glass filter (CS 2-58) and an interference filter SPresent address: Motorola Inc., Advanced Technology Center, 2200 W. Broadway Rd., Mesa, AZ 85202, U.S.A. $Present address: IBM-GTD, Essex Junction, VT 05452, U.S.A. l[To whom all correspondence should he addressed. 303
304
SHIUNATH RAht~Swr~ht~et
al
Filament
To Vacuum Pump
(b)
,:
:_ 2r Sectton
A A’
Path
...\. ,\..\\\~
1
.\
,v
A
To GSS Tank
To Power Supply
Fig. 1. (a) Schematic of the evaporation cell, showing the titanium filament. The path of the beam (from hollow-cathode lamp or from dye laser) is along the line A-A’. (b and c) Section along the line A-A’ and perpendicular to the axis of the filament, showing various dimensions and distances used in the model given in the text.
centered at 735 nm (Baird-Atomic, BWHM 8 nm). A scanning boxcar averager (Princeton Applied Research Model 162 with model 163 sampling integrator) averaged 100 pulses from the PMT and the resulting signal entered an IBM PC/XT equipped with general purpose I/O boards (Data Translation DT 2801 and DT 707). Custom software was written to collect, store and smooth data
305
A spectroscopic study of vapor-phase titanium
:Compuler
PAR 162
r
Boxcar Averager
I
Fast Amplifier
Triggel PMT
r
1
,,,,,.,,,,,,,,,,., “oip:
Ftjq
,,,,,,I,,,,,,,,,,
,,,,.,,,,,,#.,///,,
Sample Cell Fig. 2. Schematic of the apparatus used for the laser-induced fluroescence experiments. Interfacing between the computer and the boxcar averager was done using Data Translation I/O boards. The trigger input to the boxcar is provided by a photomultiplier (trigger PMT) positioned to detect laser pulses scattered off the wall of the glass sample cell.
Y
J 4
3Fo
cm
t
3
4
2
cm
-1
-
25366
-
25227
-
25107
-1
11640 11532
cm -
-1
367 170
a
3
F
Fig. 3. Selected atomic Ti energy levels and transitions observed using the LIF technique. The wavelength (in A) of each transition is given against the vertical line representing that transition. The laser excited electrons from [u’F] state; emission was then observed in the red through transitions to the [b’F] state.
306
S~INATH
R.4hfA.W~hiIet al
and carry out curve-fitting routines. For quenching-coefficient determinations, LIF scans for each fill gas pressure used were obtained with the titanium filament on and with the filament off (background scan) for 200 nsec after the initiation of the laser pulse. The background scan (obtained with the filament off) was subtracted from the LIF scan and an exponential curve-fit was performed on the section of the scan occurring after cessation of the laser pulse. For atomic absorption measurements at 400.893 mn, light from a titanium hollow-cathode lamp passed through focusing lenses before and after passing through the evaporation cell described above and then entered a 0.25 M Jarrell Ash monochromator equipped with a RCA 6256B PMT. Atom concentrations were determined from the Beer-Lambert law. The intensity of the beam prior to passing through the cell, I,, was determined by blocking and unblocking the hollow cathode lamp emission with the titanium filament off. The intensity of the beam after passing through the cell was determined in an anlogous manner. This procedure avoids the small error due to light from the filament detected by the PMT. The atom concentration determined as described above represents the concentration of one individual J-level within the ground state electronic level. The fraction of the population in each individual J-level is given by
where g, is 2J + 1 (the degeneracy of the J level), E,, the energy difference between the J-level of interest and the lowest J level, R the universal gas constant, T the absolute temperature, and the summation is taken over all J values. For example, the 400.893 nm line corresponds to absorption from the J = 3 level. Using the appropriate EJ values given in Table 1, the percentage of the Ti atoms in this level at 1000 K is determined to be approx. 33.5%. The total Ti atom concentration is then 3.0 times the concentration calculated from Beer-Lambert law absorption measurements using the 400.893 nm line. Quenching
coeficients
and lifetime
measurements
In the absence of resonance-radiation trapping, both quenching coefficients and the natural radiative lifetime for an excited state are obtained by plotting the reciprocal of the observed lifetime as a function of the fill gas pressure, i.e.
l/L = l/T” + k,(W, where z, is the experimental or observed lifetime (set), Tothe natural radiative lifetime (set), k, the quenching coefficient (cm3 set-‘) and (M) the fill-gas density (cm-‘). The temperature of the filament, which gives negligible resonance-radiation trapping under our experimental conditions, can be obtained by measuring the LIF intensity as a function of temperature and plotting the logarithm of the LIF signal as a function of the reciprocal of the temperature. In the absence of reasonance-radiation trapping, the LIF signal is proportional to the vapor pressure of titanium at the temperature of the filament. From the Clausius-Clapeyron equation: ln(LIF signal at T,/LIF signal at T,) = -(H,./R)[(I/T,) - (l/T,)], (3) w h ere H, is the heat of sublimation and R the universal gas constant. The linearity of Fig. 4 supports the conclusion that filament temperatures between 1400 and 1500 K results in a high enough Ti-atom concentration to give an adequate signal-to-noise ratio and a low enough concentration to avoid resonance-radiation trapping. From the slope in Fig. 4, the heat of vaporization is determined to be 109.1 kcal/mol, which compares favorably with the literature value of 109 f 1 kcal/moln Table
I. Percentages
of Ti atoms level.
in a ground-state Temperature
J 4 3 2
E, (J x 102’,cm-‘) 7.68 3.37 0
387 170 0
energy
(K)
500
1000
2000
25.25 32.03 42.72
33.75 33.53 32.72
38.27 33.64 28.09
CC -~ 42.85 33.33 23.81
307
A spectroscopic study of vapor-phase titanium
loo0 c
lo4
-0
7.2
6.6
(“K-l) Fig. 4. Arrhenius plot of LIF signal intensity vs (absolute temperature)-‘. The heat of sublimation of titanium is calculated from the slope of the straight line fitted to this data. l/Tf x IO4
10
20
30
40
50
x10e6 (cmm3) Fig. 5. Natural radiative lifetime of the titanium b’F’j state. The reduction in lifetime with increase in Ar and He fill-gas pressures is shown; the natural lifetime is estimated at 0 fill-gas pressure. Ar, being the heavier gas, affects the lifetime to a greater extent than does He. [M]
Assuming the absence of resonance-radiation trapping, the natural radiative lifetime of the y’F”, state can be obtained from the y-intercept in Fig. 5 as 23 + 2 nsec. The lifetime of the titanium y3P4 state has been previously measured by Rudolph and Helbig13 to be 18.8 + 1.3 nsec and by Salih and Lawler14 to be 18.3 + 0.9 nsec. An estimated value for this lifetime can be calculated from the literature transition probabilities for the 399.864, 396.427 and 734.472 nm emission lines to be 22 _+5.5 nsec.15From the transition probability listed for the 399.864 in the 70th CRC,16 the lifetime is estimated to be <25 nsec. Radiative destruction probabilities for the much longer lived .z’F” state of Ti (J = 2, 3,4) are given by Dezert et alI7 as (6.6 + 1.3) x 106, (4.8 + 1.2) x lo6 and (6 + 1.5) x lo6 set-‘, respectively. This result is also consistent with the values proposed by Wiese and Fuhrn for the z3F” state. Rate coefficients for the quenching of the y3c state by Ar and He buffer gases were determined from the slopes of the plots in Fig. 5 and are given in Table 2. Quenching cross sections, ao, are obtained from the rate coefficients as follows: go = kolv,
(3)
where v = (8RT/7rM)“2, R is the universal gas constant, T the gas temperature (1200 K + 100) and M the reduced mass of the colliding partners.” These values may be compared with the values obtained by Dezert, Quichaud and coworkers for the longer lived z3P state of Ti given in Table 3.‘7.‘8 The manner in which the quenching cross sections listed in Table 2 were obtained differs from the experimental method used for those listed in Table 3. Dezert, Quichaud and coworkers’7*‘8 (Table 3) excited each of the three z3Fi J levels individually and observed resolved fluroresence from individual J levels. Data were taken at a series of quenching gas pressures for each excitation and observation wavelength combination. The data obtained in this manner were used with a series of coupled rate expressions for quenching and collisionally-induced J-level changing to obtain the quenching cross section and J-changing cross sections for individual J levels of the z3P4 state. In the current work (Table 2), the 396.427 nm line was used to excite the y3Fo (J = 4) state and fluoresence was observed from the y3P J = 2,3 and 4 levels simultaneously in the region of 735 nm. Assuming that the natural radiative lifetimes for the individual J levels of the y3Fo multiplet are approximately the same, the quenching cross sections listed in Table 2 are not expected to be significantly different from the cross sections which would be obtained from the y3P’ multiplet from Table 2. Rate coefficients and cross sections for quenching of the ‘p4 state of Ti on collision with Ar and He. Collision partner
Quenching rate coefficient k, x 10” (cm3 set-‘)
Quenching cross section, op x 1Or6(cm*)
He Ar
5.0 12
1.9 11
S~INATH
308 Table 3. Rate coefficients Collision partner He Ne Ar H, N,
(Ref. (Ref. (Ref. (Ref. (Ref.
RAMAWAMI
et al
and cross sections for quenching of the z’fi, states of Ti (from Refs. 17 and 18). Quenching rate coefficient k, x 10” (cm3 set-I)
17) 17) 17) 18) 18)
2.5 1.2 2.8 80 37
“The temperature
is taken
+ * * + +
J = 2, 3 and 4
Quenching cross section” me x 10i6 (cmr)
I .7 & 0.4
0.3 0.2 0.4 8 4
1.5 4.5 38 53
+ 0.3 + 0.6 +4 + 7
as 400 K.
experiments analogous to those of Dezert, Quichaud and coworkers.“.‘” The transition-probability data given in Wiese and Fuhri3 suggest that the natural radiative lifetime is not a strong function of J for the y3P state. Absolute atomic absorption measurements The average absolute concentrations of titanium atoms across a chord in the evaporation cell (Fig. 1) were determined by atomic absorption spectroscopy at 400.893 nm using the Beer-Lambert law. As mentioned previously, the atom concentration determined in this manner represents the concentration of one individual J-level within the ground electronic state. Correction factors to obtain the total average Ti atom concentration across the chord were determined from the EJ values (Table 1) for the average temperature across the chord. The relative population of the J = 3 level is less sensitive to changes in temperature than are the relative populations of the J = 2 and J = 4 levels. The heat of vaporization of titanium can also be determined from the atomic absorption data in Fig. 6. The value for H,, of 109.4 kcal/mol from Fig. 6 is consistent with the LIF results presented in Fig. 4. A mathematical model was developed for the Ti atom concentration as a function of distance from the filament in the evaporation cell shown in Fig. 1. The absolute concentrations calculated from this model are compared with the absolute experimental values from atomic absorption spectroscopy in Fig. 7. The following simplifying assumptions were made during the development of the model: (a) the coiled filament is taken to be equivalent to a cylinder which is infinitely long and which has a radius and a temperature equal to those of the coil. (b) The concentration of titanium atoms in the gas phase near the surface of the cylinder corresponds to the vapor pressure of Ti at the temperature of the filament, while the concentration of Ti in the gas phase near the cell wall (60°C) is taken to be zero. (c) The temperature profile is established by heat conduction and the concentration profile is established by diffusion (convection heat and material transport are minimized by maintaining a low fill gas pressure of 5-10 torr of argon or helium). (d) The
10'23
20-
x n^ 67 'E St ::
x
k u 101':
y
IO
11--1----1 xx
0 x
d
"it
r!i 10'0
I.
5.9
I
.
6.1
6.0 l/if
x 104 (
I
6.2 K-t)
I 6.3
' 6.4
Fig. 6. Arrhenius plot similar to Fig. 4 but for atomic absorption measurements. Due to the poorer sensitivity of this technique compared with LIF, these readings are taken at higher temperatures than in Fig. 4.
I 0
10
c,,, x
1 20
10-‘“(cm~“)
Fig. 7. Results from the mathematical model: calculated vs observed concentrations of ground-state titanium atoms. The straight line represents the relationship C,,, = C,,,.
A spectroscopic study of vapor-phase titanium
309
formation of metal atom clusters in the vapor phase is negligible. This last assumption is easily justified. The rate of dimer formation is d(Ti)/dt = kn(Ti)*(M).
(4)
The time available for dimer formation can be estimated from the Einstein diffusion equation. With a distance from the filament to the walls of 4 cm and a diffusion coefficient at 10 torr of approx. 15 cm* set-‘, a time of 0.5 set is obtained. If the average Ti atom concentration is 10” crnm3 and the rate coefficient for dimer formation is approximated by a third-body gas-kinetic collision rate of 10F3*, then the fraction of Ti atoms which may form dimers at 10 torr, d(Ti)/(Ti), is 5 x lo-‘. At lower fill gas pressures, the concentration of Ti dimers will be even lower. From Fick’s first law,” the rate of diffusion of Ti atoms from the filament to the walls is given by dn/dt = -D(x)S(x)
dc(x)/dx,
(5)
where x is the radial distance from the filament, D (x j the coefficient for diffusion in the buffer gas, S(x) the surface area of a cylinder around the filament, and c(x) the concentration of titanium atoms, all at x cm from the filament. If the rate of evaporation from the filament per unit area is Y, then dnldt = Y2nr1,
(6)
where 1 is the length of the filament and r the radius of the filament. Combining Eqs. (5) and (6), rearranging and integrating from r to x gives c(x)=c(r)-rY
X[l/xD(x)]dx, sr
(7)
where c(r) corresponds to the vapor pressure of Ti at the temperature of the filament. Since the diffusion coefficient is a function of temperature, it is also a function of distance from the filament. From elementary gas kinetics, ‘* the temperature dependence of the diffusion coefficient is D(T) = kT3’*. From elementary heat transport conduction has the form
theory,
the temperature
(8)
profile established
as a result of
x = a emhT.
(9)
D(x) = k[(ln a - In x)/b13”.
(10)
Combining Eqs. (8) and (9) gives
Substitution of Eq. (10) into Eq. (7) and integration yields the expression c(x) = c(r) - C{[(ln a - In r)/(ln a - In x)1”’ - l}.
(11)
The constants Y and b are eliminated from the expression for c(x) by requiring the titanium atom concentration c(R), near the cool wall (60°C) to be zero, which gives C = c(r)/([(ln a - In r)/(ln a - In R)]“* - l}.
(12)
The constant, a, is determined by requiring the temperature profile given by Eq. (9) to fit the experimental measurements on the temperature of the filament and the temperature of the wall for each filament temperature. Atomic absorption data are obtained with the hollow cathode beam traversing the cell along a path where the atom concentration varies. Therefore, in order to compare the experimentally determined absolute concentration measurements with the results of this model, Eq. (11) must be integrated to give the average atom concentration over the beam path, viz. c..,=jdRxc(x)dx/jdRxdx
(13)
310
SHRINATH RAMASWAMI
et al
Substituting for c(x) from Eq. (11) and integrating, Rx {(In a - In r)/(ln a - In x)} l/2 dx. (14) sd This is the average concentration over the length of the hollow-cathode beam through the cell, L, where L = 2(R2 - d2)“2. Equation (14) was evaluated numerically to obtain the values given as the calculated titanium atom concentration in Fig. 6. The experimental values for c,,,~ were again determined from the Beer-Lambert law. A value for the absorption cross section of 5.5 x lo-l3 cm2 was calculated using the experimental lifetime of 23 nsec. Ca”e =
{2/(R2 - d2)} {[(P - d2)/2)] (c(r) + C) - c
CONCLUSIONS
LIF was used to determine the natural radiative lifetime of the titanium y3P state. Rate coefficients for the quenching of this state by Ar and He buffer gases were also determined. Quantitative atomic absorption measurements of gas-phase Ti were made in a thermal evaporation cell. A model was developed for the spatial distribution of Ti within the cell. In the model, it was assumed that a steady-state concentration gradient was established by diffusion while the thermal gradient was established by heat conduction. Concentrations calculated from this model compare well with observed concentrations calculated from the Beer-Lambert law and a value of 5.5 x lo-l3 cm2 for the absorption cross section. This result supports the suggestion that atomic absorption spectroscopy is an effective and convenient method for monitoring absolute metal atom concentrations in gas-phase systems. Acknowledgemenls-This investigation was supported by the Office of Naval Research and by International Business Machines Corporation. JAH acknowledges the PEW Charitable Trust for financial support during the 9G91 academic year. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
T. P. Chow and A. J. Steckl, J. Electrochem. Sot. 131, 2325 (1984). S. W. Robey, M. A. Jaso, and G. S. Oehrlein, J. Appl. Phys. 65, 2951 (1989). P. B. Ghate, J. C. Blair, C. R. Fuller, and G. E. McGuire, Thin Solid Films 53, 117 (1977). S. M. Sze, l%SZ Technology, McGraw-Hill, New York, NY (1988). S. M. Bobbio, Y. S. Ho, and T. Lopez, Mat. Res. Sot. Symp. Proc. 98, 243 (1987). K. C. Cadien, S. Sivaram, and C. D. Reintsema, J. Vat. Sci. TechnoI. A 4, 739 (1986). G. Tomkins, M. H. Davis, and P. J. Rosser, Vacuum 34, 451 (1984). E. R. Sirkin and H. A. VanderPlas, J. Vat. Sci. Technol. B 2, 152 (1984). P. May and A. I. Spiers, J. Electrochem. Sot. 135, 1592 (1988). C.-K. Hu, N. Mazzeo, S. Basavaiah, and M. B. Small, J. Vuc. Sci. Technol. A 8, 1498 (1990). R. R. Reeves, M. Rutten, S. Ramaswami, P. Roessle, and J. A. Halstead, J. Electrochem. Sot. 137, 3517 (1990). J. Phys. Chem. Ref Data. 14, Suppl. 1, 1823 (1985). J. Rudolph and V. Helbig, J. Phys. B: At. Mol. Phys. 15, L599 (1982). S. Salih and J. E. Lawler, Astron. Astrophys. 208, 157 (1989). W. L. Wiese and J. R. Fuhr, J. Phys. Chem. Ref: Data 4, 302 (1975). D. Dezert, V. Quichaud, D. Dequout, and A. Catherinot, Phys. Rev. A 34, 4793 (1986). V. Quichaud, D. Dezert, J. Aubreton, D. Degout, and A. Catherinot, Laser Chem. 10, 93 (1989). R. A. Alberty, Physical Chemistry, p. 281, Wiley, New York, NY (1987). S. Dushman, Scientific Foundations of Vacuum Technique, 2nd edn, p. 68, J. M. Lafferty ed., Wiley, New York, NY (1986).