207
Anal. Chem. 1986, 58,207-210 A
B
C
D
E
30 s Sb
Flgure 12. Photooxidation/light-scattering signals of various amounts of analytes: A, blank (20 mL of 1 M HCI and 5 mL of 4 % NaBH,); B, selenium (5 ng); C, antimony (5 ng); D, arsenlc (5 ng); E, phosphorus (1 ngl.
Table 111. Minimum Detectable Amounts of Elements min detectable amts of element,
element P
As
Sb Bi Se Ge
Sn
hydride PHS
ASH^
CH~ASH, SbH3 BiH, SeH, GeH4 SnHa
ng
0.4 1.5 1.0 2.0
70 3.0 50 2.0
scattering intensity is a function of the particle diameter, particle refractive index, scattering angle, and wavelength of incident light (11). Light-scattering signal recordings from various amounts of each analyk are shown in Figure 12. Since the observed signal is not specific for each analyte, a chromatographic separation ( I , 3) or a differential volatilization based on the different 3 of the boiling point must be utilized for the determination of each analyte. The hydrides could be partially separated by differential volatilization at the blank
level as shown in Figure 12, but all peaks overlapped at higher concentration levels. The minimum detectable amounts of each analyte (defined as the amounts required to give a signal equivalent to 5 times the standard deviation of the background scattering signal) are shown in Table 111. The present study demonstrated the possibility of the photochemical reaction/light-scatteringmeasurement system as a highly sensitive method. The advantages of this method are simple handling and low-cost construction of the instrument, which consists of a photochemical reaction chamber, a laser, and a photomultiplier. If a semiconductor laser can be utilized instead of a He-Ne laser, the instrument may be miniaturized further. From an analogy to the present method, a measurement system combining a chemical reaction, which produces particles such as NH, + HC1 NH4C1, with light-scattering detection will be a simple monitoring system of the original gases. Registry No. PH3, 7803-51-2;AsH3, 7784-42-1;P, 7723-14-0; As, 7440-38-2; Sb, 7440-36-0; Se, 7782-49-2; Sn, 7440-31-5; Ge, 7440-56-4; Bi, 7440-69-9.
-
LITERATURE CITED (1) Caruso, J. A,; Robbin, W. B. Anal. Chem. 1979, 51, 889A-899A. (2) Berck, 6.; Westlake, W. E.; Gunther, F. A. J. Agric. Food Chem. 1970, 18, 143-147. (3) Fujiwara, K.; Watanabe, Y.; Fuwa, K.; Winefordner, J. D. Anal. Chem. 1982, 54. 125-f28. (4) Tao, H.; Miyazaki, A.; Bansho, K.; Umezaki, Y. Anal. Chem. 1984, 56, 181-185. (5) Tao, H.; Miyazaki, A.; Bansho, K. follut. Control 1985, 2 0 , 137-143. ( 6 ) Takeuchi, N.; Shimizu, H.; Sugimoto, N. Oyo Butsurl 1983, 5 2 , 644-656. (7) Norrish, R. G. W.; Oldershaw, 0. A. f r o c . R. SOC.London, Ser. A 1961, 2 6 2 , 10-18. (8) Norrish, R. G. W.; Oidershaw, G. A. f r o c . R . SOC.London, Ser. A 1961. 262, 1-9. (9) Prinn, R. G.; Lewis, J. S. Science (Washington, D . C . , 1883-) 1975, 190, 274-276. (IO) Miyazaki, A,; Kimura, A.; Umezaki, Y. Bunseki Kagaku 1981, 3 0 , 379-384. (11) Kanagawa, A. Kagaku Kogaku 1970, 3 4 , 521-527.
RECEIVED for review June 25,1985. Accepted August 12,1985.
Electron Temperatures and Electron Number Densities Measured by Thomson Scattering in the Inductively Coupled Plasma Mao Huang, Kim A. Marshall, and Gary M. Hieftje*
Department of Chemistry, Indiana University, Bloomington, Indiana 47405
Electron temperatures and electron number densltles have been measured at 3 mm from the center of an ICP, at heights of 10 mm and 15 mm above the load coil and at an rf Input power of 1.0 kW, by using a single-channel Thomson-scatterlng Instrument. The spatlai resolution of the measurement was 1 mm. Rayielgh scattering from argon gas at room temperature has been used to provide absolute callbratlon of Thomson-scatterlng signals for the calculation of electron number densities.
In the inductively coupled plasma, electrons are believed to play an important role in energy transfer, ionization, and 0003-2700/86/0358-0207$0 1.50/0
excitation processes. To fully understand atom and ion excitation mechanisms, electron temperatures and number densities in the ICP have been extensively studied theoretically and experimentally. However, most such studies have required questionable assumptions (1-7). Measured excitation temperatures are sometimes used to estimate electron temperatures by assuming an approach to local or partial thermodynamic equilibrium (LTE) in the ICP. The large range of excitation temperatures observed for various species in the ICP (I,2,5) would indicate that these conditions most likely do not exist. In turn, the most commonly used method for determining electron number density is the Stark-broadening of emission lines (2-5). In this me0 1985 American Chemical Society
208
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986
thod, the electron temperature is again assumed to be the same as an excitation or argon ionization temperature and is used to deduce electron concentrations through the use of tabulated Stark parameters. This approach not only is suspect but requires a knowledge of accurate Stark parameters. Saha's equation can also be used to determine electron number density, but again only when LTE conditions are assumed. Both electron temperature (T,) and number density (ne)can be determined from absolute continuum intensity measurements, but each value ( T , and ne) depends on the other. Importantly, the lateral emission signals produced by all the methods mentioned above must be Abel-inverted to generate radial spatial information. Moreover, an experimental Stark-broadened line profile must be deconvoluted to correct for instrumental and Doppler broadening. It is therefore not surprising that reported electron temperatures and number densities are quite disparate. Nevertheless, the knowledge of electron number density and temperature is so important that most excitation models have made explicit assumptions about these parameters in the ICP (8-12). Laser light Thomson scattering is a more straightforward way to obtain information on both electron number density and temperature in a plasma (13,14).Because the scattered light is Doppler-shifted by electrons in the plasma, Thomson scattering can be used also to measure directly the electron energy distribution. Furthermore, since a laser beam can be focused into the plasma exactly at the point where an observation is desired and because off-axis observation is possible, Abel-inversion is unnecessary. Time-resolved measurements are also possible because of the very short pulse available from a Q-switched laser. Finally, absolute intensity measurement of Thomson-scattered light can be simply performed using Rayleigh scattering in argon at atmospheric pressure as a calibration vehicle. Such an absolute measurement enables electron number density and temperature to be determined a t the same time. However, the limitation of Thomson scattering arises from its extremely small cross section (on the order of cm2), making stray light, plasma background, and electronic noise extremely serious problems. In the present study, a ruby laser scattering apparatus was designed and has been used to overcome these problems. A 20-MW pulse of this ruby laser is focused to approximately a 1-mm spot in the plasma. The scattered radiation is collected at 135' with a 1-m focal length f / 7 monochromator. The signal is detected by a red-sensitive RCA 31034 photomultiplier tube (PMT). Further details of the apparatus are described elsewhere (15). The present paper presents several preliminary results using this system to measure electron number density and temperature in a 1.0-kW
ICP.
To obtain the greatest wavelength shift in the Thomson scattering spectrum, a 135' backscattering geometry has been chosen. The spatial resolution in the plasma is about 1mm, and the spectral resolution is usually 0.2 nm. The laser power focused into the plasma is about 15 MW. This power is controlled to avoid local heating of the discharge (15). A single-channel detection system was used to generate Thomson spectra over the range from 694 to 690 nm in approximately 13 steps. A neutral density filter was used in the optical collection system when the Rayleigh scattering signal was measured at room temperature in order to ensure that the PMT was operated in a linear regime. The transmission of the neutral density filter was chosen so the Rayleigh scattering was comparable to the Thomsonscattering signal. An oscilloscope (Model 7844, Tektronix, Beaverton, OR) has been used to record Thomson-scattering signals. The coaxial cable connecting the PMT to the scope is less than 3 ft long, and the electronic noise is found to be negligible in most cases. Each data point was repeated three times and the average used to calculate ne and T, values. The point-to-point reproducibility was on the order of f20%. When the complete scattering spectra were repeated, the reproducibility was within 25-30%. We feel these large variations are due mostly to plasma drift although laser power fluctuation might also contribute to the irreproducibility observed. Each complete scattering spectrum required about 1 h to obtain, attributable mostly to the large amount of time required to allow the laser to cool between shots. This long data-acquisition period contributes greatly to noise and observed plasma drift. Data Treatment. The measured scattering spectra were used to deduce electron temperatures according to eq 1 (13,14),where In I =
6.377
X
[
(Ax)2
sin2 (8/2)T,
]
(1)
I is the Thomson-scattering signal, Xo is the wavelength of the incident laser, Ah is the wavelength shift of the scattered light from the laser wavelength (in nm), 0 is the angle between the observation direction and the incident laser beam (135O here), and T,is the electron temperature in electronvolts. The term "electron temperature" is meaningful here only if a Maxwellian distributionof electron velocities exists. Other distributions could, however, be determined by more complex equations and curve fitting routines (13, 14). The scattering parameter 1
a=--
nXD
-
h0
(2)
4akD sin (6/2)
is a measure of correlation or group movement between electrons and ions. Here, AD is the Debye length, related to shielding distance. When the scattering parameter a is much smaller than 1 and the electron velocity distribution is Maxwellian, the plot of In I vs. (AX)z should be a straight line. The electron temperature T, can then be calculated from the slope of this line. Electron number density was determined from the formula
EXPERIMENTAL SECTION Rayleigh scattering from argon gas at room temperature and in the ICP has been used to estimate the stray light level in the Thomson-scattering apparatus; stray light was approximately equivalent to the Rayleigh scattering from argon at pressures no greater than 20-25 torr. As a result, stray light can usually be neglected compared to Thomson-scatteringsignals; in other cases, when the electron number density is lower, the stray light contribution can be readily subtracted from the measured signals. In contrast, plasma-background radiation, which produces shot noise with almost the same pulse width as the laser, is sometimes comparable in magnitude to the Thomson-scattering signals, especially when rf power to the plasma is high (e.g., 1500 W) and the observation height is less than 10 mm above the load coil. Furthermore, the argon line radiation at 693.7 nm is often so intense that the photomultiplier can be saturated even when a 2-ms mechanical shutter is used to gate the radiation reaching the detector. This wavelength is therefore avoided during the determination of a scattering spectrum.
lo4
h02
ne = (1.16 X 1 0 9
[
T r s oI dh
]
(1 + a')
(3)
where ne is the electron number density in ~ m - T, ~ , is the transmission of the neutral-density filter used for Rayleighscattering observation, IR is the Rayleigh-scattering signal in the same units as the Thomson-scattering signal I , and a is again the scattering parameter. The value of a can be estimated from the shape of the scattering spectrum (16) and has been found to be between 0.3 and 1.0 in our case. Importantly, on the right side of eq 3 the factor 1.16 is valid only when the Rayleigh-scattering signal I R is observed from argon gas at room temperature (about 300 K) and atmospheric pressure; otherwise it must be corrected. For example, if some gas other than argon is used to observe Rayleigh scattering, the constant must be adjusted by the ratio of the Rayleigh-scattering cross sections of the two gases.
ANALYTICAL CHEMISTRY, VOL. 58, NO. 1, JANUARY 1986
Wavelength shift (nrn)
< W a v e length shift)'
Figure 1. Thomson-scattering spectrum measured at 3 mm from the plasma center and at 10 mm above the load coil. I
8
n
,
I
I
I
v I 1
I
209
I
Figure 3. Linearized verslon of the Thomson-scattering spectrum of Figure 1.
,
-
1 25
0
6
0.75
m
:
0.25
L
0
2
-0.25
0 U
2 I
2
I
I
I
3
4
I
Flgure 2. Thomson-scattering spectrum taken at 3 mm from the plasma center and at 15 mm above the load coil. Plasma conditions are the same as those given in Figure 1.
Table I. Electron Temperature and Number Density Calculated from the Scattering Data' height above load Te, K
10 15
11600 f 20% 9200 f 20%
ne, cm-3 (3.3 X (7.3 X
-125;
I
'
I 3
'
'
I
6
'
'
'
9
'
I
'
12
(Wave i ength s h i f t )'
Wavelength s h i f t Cnrn)
coil, mm
-0 75
f f
25% 25%
The electron number densities were calculated by assuming an value equal to 0.5. Both measurements were taken 3 mm radially from the plasma center. (Y
RESULTS AND DISCUSSION Figures 1 and 2 show scattering signals as a function of wavelength shift from the laser line at 3 mm from the plasma center and at 10 and 15 mm above the ICP load coil, respectively. The linearized representations of these data (see eq 1)are shown in Figures 3 and 4, where the straight lines are the least-squares fit. The electron temperatures and number densities have been calculated from these data according to eq 1 and 2, respectively, and are listed in Table I. Note that in Figure 2 the scattered signal at 1.8 nm from the laser line is too high for some unknown reason. This datum was used in the calculations of T,,however. If it were deleted, T,becomes higher by 400 K. The electron number densities calculated from the scattering spectra are in the range reported by other authors, although the electron temperatures seem much higher (1-7). It is of course possible that the true electron temperature in the ICP is much higher than the argon or analyte excitation temperature; however, it is also likely that the electron temperature is somewhat overestimated by the method used here. As has been discussed by Scheeline and Zoellner Thomson-scattering spectra are expected to be Gaussian in
(In,
Figure 4. Linearized verslon of the Thomson-scattering spectrum of Figure 2.
shape only if the electron velocity distribution is Maxwellian and when the scattering parameter CY is much smaller than 1. Otherwise, the intensity of the scattered light close to the wavelength of the incident laser tends to decrease (161, making the slope of the straight line shown in Figures 3 and 4 smaller and the resulting value for electron temperature higher. For example, the temperature listed in Table I for the observation height of 10 mm above the load coil is probably somewhat high, because the assumed CY value of 0.5 is higher than the value of 0.4 dictated by the measured electron number density. Conveniently, even when the condition CY
