802
Anal. Chem. 1986, 58,802-807
to what extent the matrix affects the emission intensity per unit concentration. CONCLUSIONS The HCP shows promise for the elemental analysis of solids by atomic emission. Methodology based on glow discharge sputter atomization/excitation has the advantage of direct insertion of the atomized material into the plasma with little transport loss. The precision and reproducibility of the technique suggest general application to bulk metal multielement analysis. Limitations of the technique include the following: the sample (a) must be of a conductive nature and (b) must allow disk formation. In these studies we have taken our current equipment essentially to the limit of its capabilities. Enhanced instrumentation (Plasma Spec echelle grating spectrometer, Leeman Labs, Inc., Lowell, MA) is being acquired, which will enable us to evaluate better the sensitivity and precision under higher resolution conditions. We believe the HCP is also very suitable for compacted samples, thus permitting extensions of the technique to nonconductors such as geological materials pressed with graphite into disks. Studies of matrix effects will be of particular importance in such samples. Simultaneously with these studies, we are also pursuing the use of the HCP as an ionization source for elemental analysis by mass spectrometry. The HCP might also be useful as an atom reservoir for atomic fluorescence, although we have not attempted such measurements. We feel that the hollow cathode plume offers an efficient means of transforming solid samples into atomic, excited, and ionic populations for versatile analytical capabilities. Registry No. Cu, 7440-50-8;AI,7429-90-5;Cr, 7440-47-3;Mn, 7439-96-5; Zn, 7440-66-6; Mg, 7439-95-4; Fe, 7439-89-6; Co, 7440-48-4; Mo, 7439-98-7;steel, 12597-69-2. LITERATURE CITED (1) Grove, E. L. I n "Analytical Emlssion Spectroscopy"; Grove, E. L., Ed.; Marcel Dekker: New York, 1971;Vol. 1, Part 1. (2) Washburn, D. N.; Waiters, J. P. Appl. Spectrosc. 1982, 36, 510. (3) Dittrlch, K.; Niebergall, K.; Krasnobaewa, N.; Nedjalkowa, N. Spectrochim. Acta, Part 6 1982, 378,293. (4) Powell, L. J.; Paulsen, P. J. Anal. Chem. 1984, 56, 376. (5) Kagawa, K.; Yokoi, S . Spectrochlm. Acta, Part 6 1982, 378, 789.
(6) Browner, R. F.; Boorn, A. W. Anal. Chem. 1984, 56, 786A. (7) Roedererer, J. E.; Bastlaans, G. J.; Fernandez, M. A.; Fredeen, K. J. Appl. Spectrosc. 1982, 36, 383. (8) Carr, J. W.; Horllck, G. Spectrochim. Acta, Part 8 1982, 376, 1. (9) Ohls, K.; Sommer, D. Fresenius' 2. Anal. Chem. 1979, 296, 241. (10) Farnsworth, P. 6.; Hieftje, G. M. Anal. Chem. 1983, 55, 1417. (11) Marks, J. Y.; Fornwalt, D. E.; Yungk, R. E. Spectrochim. Acta, Part 6 1983, 388,107. (12) Salln, E. D.; Horlick, G. Anal. Chem. 1979, 51, 2284. (13) Slevln, P. J.; Harrison, W. W. Appl. Spectrosc. Rev. 1975, 10, 201. (14) Brackett, J. M.; Vlckers, T. J. Spectrochim. Acta, P a r t 8 1982, 378, 841. (15) Koch, K. H.; Kretschmer, M.; Grunenberg, D. Mlkrochim. Acta 1983, 1 1 , 225. (16) Caroli, S.;Alimonti, A.; Zimmer, K. Spectrochim. Acta, Part 6 1983, 388,625. (17) Harrison, W. W.; Daughtrey, E. H. Anal. Chim. Acta 1973, 65, 35. (18) Bentz, 6. L.; Bruhn, C. G.; Harrison, W. W. Int. J. Mass Spectrom. Ion Phys. 1978, 28, 409. (19) Mattson, W. A.; Bentz, B. L.; Harrison, W. W. Anal. Chem. 1976, 48, 489. (20) Savickas, P. J.; Hess, K. R.; Marcus, R . K.; Harrison, W. W. Anal. Chem. 1984, 56,817. (21) Marcus, R. K.; Harrison, W. W. Spectrochim. Acta. Part6 1985, 408, 933. (22) Marcus, R. K.; King, F. L., Jr.; Harrison, W. W. Anal. Chem., in press. (23) Weston, G. L. "Cold Cathode Discharge Tubes"; Iliffe: London, 1968. (24) Bruhn, C. G.; Harrison, W. W. Anal. Chem. 1978, 50, 16. (25) Loving, T. J.; Harrison, W. W. Anal. Chem. 1963, 54, 1526. (26) Westwood, W. D. Prog. Surf. Sci. 1976, 7 ,71. (27) Keefe, R. B. Ph.D. Dissertation, University of Virginia, Charlottesville, VA, 1983. (28) Pillow, M. E. Spectrochim. Acta, Part 8 1981, 368,821. (29) Chapman, B. C. "Glow Discharge Processes"; Wlley-Interscience: New York, 1980. (30) Howorka, F.; Pahi, M. Z.Naturforsch., Phys. Phys. Chem. Kosmophys. A: 1972, 27, 1425. (31) Nasser, E. "Fundamentals of Gaseous Ionization and Plasma Electronics"; Why-Interscience: New York, 1971. (32) Howorka, F.; Lidinger, W.; Pahl, M., Int. J . Mass, Spectrom. Ion Phys. 1973, 12,67. (33) Gofmeister. V. P.; Kagan, Yu. M. Opt. Spectrosc. Engl. Transl. 1968, 25. 185. (34) Musha, T. J. Phys. Soc. Jpn. 1962, 17, 1447. (35) Wehner, G. K. I n "Methods and Phenomena: Their Applications in Science and Technology"; Woisky, S . P., Czanderna, A. W., Eds.; Elsevier Scientific: New York, 1975;Vol. l, Chapter l. (36) Coburn, J. W.; Taglauer, E.; Kay, E. J. Appl. Phys. 1974, 45, 1779. (37) Boumans, P. W. J. M. "Theory of Spectrochemical Excitation"; Plenum: New York, 1966.
RECEIVED for review July 10,1985. Accepted October 24,1985. We are grateful for the Department of Energy, Division of Chemical Sciences, for support of this research.
Implications of Line Number to Line Intensity Logarithmic Relationship for Emission Spectrochemical Analysis Alexander Scheeline
School of Chemical Sciences, University of Illinois, 1209 West California Avenue, 79 RAL, Box 48, Urbana, Illinois 61801
A linear relationship between the logarithm of the number of llnes having a given spectral Intensity and the logarithm of the relative intensity of those lines with respect to the most intense lines in the spectrum Is critically evaluated regarding both the quality of data giving rise to the relationship and the utlllty of the relatbnshlp in predicting interferences in emlsslon spectrochemical analysis. Recently obtained data on the spectrum of neutral arsenlc are contrasted with earlfer work using iron and the rare gases.
A large number of phenomena complicate the use of emission spectrometry for elemental analysis. These include
line broadening, background, matrix-specific sample transport, and spectral overlap between lines of different species in the same sample. As the linear dynamic range and detection ability of emission methods have improved, spectral overlap has become an ever more evident problem. One approach for dealing with this problem is to presume that all elements interfere with all others, using a successive approximations algorithm to deconvolute the contributions of the various elements to the intensity observed at a particular wavelength ( 1 ) . Another is to ignore specific line selection, substituting factor analysis and cluster analysis of multiply overlapped data (2). With the advent of mass spectral detection as a routine means for observing elemental composition of samples (31, it becomes important to determine what the fundamental limits
0003-2700/86/0358-0802$01.50/00 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 4, APRIL 1986
to multielement emission methods may be. This will be helpful in contrasting the ultimate detection abilities of the two methods. Are there limits imposed by the complexity of emission spectra that inherently prevent low limits of detection when mixtures of elements are present? One can conceive of background-free sources producing narrow lines emitted by perfectly transported analyte species. Thermal sources will always result in a large number of emission lines for each element, with the result that conditions for high excitation of sensitive lines will invariably lead to the emission of numerous weaker lines. This is not to say that some particular distribution will hold in all cases, but rather that any atom in the gas phase can exist in a number of excited states, and the presence of sufficient collisional energy to significantly excite one of these levels will guarantee that some other levels are to some degree excited. Thus, if it were possible to determine the relative intensity of all the lines emitted by a given element and also to determine the spectral distribution of those lines, it would be possible to predict the ratio of any two elements a t which particular lines would produce equal emission intensity. For current purposes, equal emission by a desired line and an interfering line will be taken as the lowest useful level at which the desired element can be detected using the line of interest. This will serve as a convenient guideline that is relevant to current single-channel scanning instruments and single-detector-per-elementdirect reading spectrometers. Such an approach is in contrast to that described by Butler (4)in which analytical range was measured for particular elements in various matrices. The goal here is to set upper limits to analytical range from any emission technique rather than to evaluate the range for a specific method. That one might choose alternative lines to avoid overlap with different major interferents is assumed, The question at issue is: what is the probability of having a sensitive line of a trace constituent, far enough away from any interfering line of other species present, that the trace substance can be detected a t low levels? A relationship, which may be phenomenologically useful in determining both the distribution of intensities among the lines emitted by a particular species, and the total number of detectable lines given the dynamic range of an instrument, was reported by Learner (5). Using emission data from argon-, helium-, and neon-filled iron hollow cathode discharge tubes, he studied the distribution of intensities among the lines observed in the spectral range 280-2600 nm. No attempt was made to compensate for variations in detector sensitivity over this wavelength range. To an astonishing degree, regardless of the element involved or the size of the wavelength range chosen, the number of observed lines increased by or a factor of 1.414 in each succeeding octave in intensity. Thus, if lines only half as strong as some previous minimum intensity were included in a spectrum, the total number of lines observed would increase by approximately 30%. This means that for any intensity threshold, roughly one-third of the lines are within a factor of 2 of the intensity detection limit. Furthermore, the number of lines between the detection limit and the maximum intensity measurable by the system becomes calculable. Knowing the number of lines emitted by a species and the relative intensities of those lines should result in a statistical knowledge of the degree to which one may expect interference between the emission of the characterized element and some other random element. Before a general treatment of the likelihood of line interference as a function of detection system dynamic range is developed, there are a number of problems that must be addressed. The first concern is the generality of Learner’s relationship. For atoms whose energy levels are not well
803
described by LS coupling, will the log/octave relationship hold? Can the relationship account for species with numerous, densely spaced spectra such as the lanthanides and actinides? A second concern is the effect of the form of excitation. Learner employed a hollow cathode lamp; would the same relationship hold for other discharges? Learner attributed his results in part to the nearly equal populations of the excited states of the species he observed, convoluted with a uniform (constant number per octave intensity) distribution of dipole matrix elements. A wider spread of upper state energies would add a population factor to the line intensity distribution. Finally, one must be concerned about observation system intensity calibration as a function of wavelength. Otherwise, one might expect that the apparent distribution of line intensities would closely follow the response function of the detector. Recently, the full spectrum of neutral arsenic (As I) was measured by use of, in part, the same interferometeremployed by Learner (6). Wavelength coverage was 135 nm to 3.56 pm. By interpretation of this spectrum in terms of Learner’s proposed relationship, it was hoped that several of the questions raised in connection with the earlier work could be addressed. It was the the purpose of this work to carry out the interpretation of the arsenic spectrum in the terms suggested by Learner and, from this analysis, either to propose a theory of dynamic range of emission measurements in mixtures, to propose measurements that may be necessary before this approach can be accurately used to develop such a theory, or to demonstrate limitations to the log/octave relationship, which prevent its employment for development of a general dynamic range theory. As will be discussed, there are substantial limitations both in available data and in the nature of emission sources which prevent the postulated extrapolations from being made.
THEORY Learner (5) chose a reference intensity that was the most intense line in a spectrum. Other lines were then classified according to the fraction of this brightness with which they emitted light. Classifications were according to binary fractional intensities. Thus a line emitting of the intensity of the most intense line would be classified as being in octave 9, as lies between 2* and 2-’O. For current purposes, this is awkward, as one generally has a minimum intensity detection limit above which line emission can be seen, rather than a maximum light flux which is used as an instrument calibration. An additional change in convention also is appropriate. In earlier work, all data were normalized by dividing the number of lines within each octave by the total number of lines observed. This requires replotting of the intensity data before applying Learner’s equivalent to eq 1 below each time a new octave is measured. However, for any given dynamic range, normalization serves only as a constant offset to the display of data on a logarithmic scale. Here, the reference intensity will be given by the lowest intensity usable in a particular system and will be labeled as octave 0. Stated in these terms, the relationship to be tested is Nk is the number of lines with emission intensity in octave k , No is the number of lines emitting at the limit of detection, k is the octave number (recall an octave is a factor of 2 in emission intensity), and‘m is the slope of the supposedly linear relationship between octave number and number of lines. In Learner’s work, m was close to 0.1505, which is log,, 2lI2. In the case of the work cited, this relationship was in most cases studied only for lines with signal-to-noise ratios of 100 or better, so that classification into inappropriate octaves would be quite unlikely. Equation 1 will be used for fitting all data
804
ANALYTICAL CHEMISTRY, VOL. 58, NO. 4, APRIL 1986
Table I. Arsenic Spectrum Intensity Distributionn spectral range 1046.97-3600.00 nm 700.000-1046.93 nm 200.00-700.00 nm 135.5-200.00 nm
total
spectral range 1046.97-3600.00 nm 700.000-1046.93 nm 200.00-700.00 nm 135.5-200.00 nm
total
spectral range 1046.97-3600.00 nm 700.000-1046.93 nm 200.00-700.00 nm 135.5-200.00 nm
total
0-26
3-4
OC
44 15 61 82 202
1
5-8 2
9-16 3
17-32 4
33-64 5
65-128 6
129-256 7
23 18 25 29 95
46 32 23 13 114
62 49 25 12 148
70 49 36 18 173
66 58 27 12 163
64 68 18 9 159
41 24 27 8 100
257-512b 8'
513-1024 9
10252048 10
20494096 11
40978192 12
819316384 13
1638532768 14
55 19 14 5 93
29 10 11 9 59
25 7 11 5 48
12 9 8 8 37
9 3 10 5 27
5 6 8 2 21
1 3 3 2 9
3276965536b 15c
65537131072 16
131073262144 17
262145524288 18
1 2 5 0 8
1 6 3 1 11
0 1 4
0 0 3 1 4
1
6
52428919 0 0
total 554 379 323 222 1478
1 0
1
k represents octave number. Table entry is number of lines observed within wavelength range and intensity octave. Intensity range. 12
value.
presented below. Where uncertainties are shown, ranges are f l standard deviation. EXPERIMENTAL SECTION No original measurements were made. The arsenic spectral data are quoted from ref 6. In the referenced work, spectra were observed on two interferometers for wavelengths longer than 900 nm, interferometers and photographic spectrographs for the wavelength range 210-900 nm, and photographic spectrographs exclusively for wavelengths less than 210 nm. Between 2.2 pm and 900 nm, the dual-path interferometer associated with the McMath solar telescope at the National Astronomical Observatory at Kitt Peak, the same instrument used by Learner, was employed (7-10). No attempt was made to correct the spectral intensities for instrument response. Nevertheless, as an InSb detector was used in the interferometer (8), it is likely that response was uniform within a factor of 4 over this restricted wavelength range. That is, signal detected per watt incident on the detector (not quantum efficiency) was relatively flat in the near-infrared region. The source was an electrodeless discharge lamp (EDL) made of Suprasil W, filled with metallic arsenic and either helium or neon at 8-16 torr (6). Operating power was not given in the reference. Lines of As I were identified as members of various spectral series, making inclusion of misidentified As I1 or As2lines and bands unlikely. RESULTS AND DISCUSSION A summary of the intensity distributions reported for As I in both the entire observed spectral range and in four subranges is shown in Table I. Logarithms of the line counts are plotted in Figure 1. In each of the plots, the solid line that includes the point (0,3) has a slope of 0.1505 per octave. Were the arsenic spectrum to correspond to the log/octave relationship, all real data would appear along straight lines parallel to this reference line. In each inset, the upper curve with data shown as squares is the result of analyzing the entire spectrum from ref 5. Except a t the low intensity end of the data, there appears to be a correspondence between the arsenic data and Learner's formula. In inset A of the figure, an unweighted least-squares line has been fitted to the data points from k = 4 through k = 18. This line has a slope (note minus sign in eq 1;slopes are reported as m values) of 0.123 A 0.006
3 K " ' ' ' ' 'n " I ' '
'
P\.
" " "
""----Y
Flgure 1. Logarithm of number of lines within an intensity octave as a function of octave number; case of arbitrarily chosen wavelength regions: boxes, data for all wavelength regions combined; solid line passing through (0,3),m = 0.1505 reference; (---) is least-squares fit to data. Inset A, (+) raw data, for wavelengths longer than 1046.93 nm; (----) least-squaresfit to total data. Inset B, (0)data from 900 to 1046.93 nm; inset C, (A)data from 200 nm to 900 nm; D, (X) data for wavelengths shorter than 200 nm.
and correlation coefficient 0.9866. Points below k = 4 were omitted as they consistently do not fall along the linear portion of the curve. This important deviation will be discussed below. Learner observed deviations from linearity of the highest intensity lines and attributed this in part to self-absorption. I t is not apparent that such a deviation is occurring in the current case. If the point a t k = 19 is included in the regression determination, a line is found with slope 0.135 & 0.012 and correlation coefficient 0.9142. In either case, the slope falls below 0.1505. No attempt was made to normalize the arsenic intensity data for variations in detector sensitivity or detector identity (6). Two approaches can be taken to account for this limi-
ANALYTICAL CHEMISTRY, VOL. 58, NO. 4,APRIL 1986
Table 111. Dynamic Range and Line Numbers If log/Octave Relationship Holds
Table 11. Least-Squares Slopes and Correlation Coefficients for Data in Figure 1
spectral range
slope (m)
corr coeff
k range employed
1046.97-3600.00 nm 700.000-1046.93 nm 200.00-700.00 nm 135.5-200.00 nm
0.127 f 0.015 0.139 f 0.013 0.0738 f 0.007 0.0786 f 0.014 0.123 f 0.006
0.947 0.957 0.942 0.878 0.9866
4-13 4-15 4-18 4-14 4-18
overall
805
tation. In the first case, one can arbitrarily break up the spectrum into conventional regions, ignoring the effect on the slope from varying detector response. Four subsidiary spectral windows were examined. These were chosen to be vacuum ultraviolet (all observed lines at less than 200.000 nm), UVvisible (lines between 200.000 and 700.000 nm), near-infrared (700.000-1046.93 nm) and mid-infrared (lines at wavelengths greater than 1046.93 nm). Clearly the cutoff at 1046 nm was quite arbitrary; it corresponds to the end of the tenth page of the intensity table in ref 6. Such a random choice should not alter the validity of the relationship if one accepts eq 1 uncritically. Were the divisions to have been made so that all four groups contained the same number of lines, the region boundaries would have been at 527 nm, 896 nm, and 1304 nm. A more reasonable division involves separating the lines based on the instrument used for observing the spectra, as described in the Experimental Section. Much can be learned of the validity of the log/octave relationship by contrasting data resulting from the arbitrary region choice with that from the instrument-specific region choice. The slopes and correlation coefficients of the various regions arbitrarily chosen are given in Table 11. All are less than 0.1505, some by as much as a factor of 2. This is in direct contrast to earlier work. The lowest four k values were excluded, as the line number values summed over all wavelength regions fell below the line that would best fit the data from higher k values. It is unclear whether the lack of low intensity lines is due to their true absence from the spectrum of due to a failure to observe the lines, either due to their wavelength being outside the observed spectral range or due to their low intensity convoluted with variation in the quantum efficiency or power response of detectors with wavelength. If the plasma used to excite the spectrum was of sufficient density to lower the ionization potential of As I significantly, there would be only a finite number of bound states remaining, and thus only a finite number of lines. It is crucial, however, that the reasons for the lack of low-intensity lines be determined. In the absence of large numbers of weak lines, one may potentially find interference-free wavelengths for the determination of an element of choice in an arbitrary matrix. If the number of lines increases without bound as detection ability increases, then ultimate dynamic range for a particular element in an arbitrary mixture is limited. Suppose that the absence of the predicted number of weak lines is due to lack of observation rather than lack of existence. The range of slopes reported in Table I1 presents a conflicting picture as to the dynamic range of interference-free detection to be expected in complex mixtures. This is illustrated in Table 111. Since the number of lines in a given octave can be computed from eq 1,the total number of lines for a given dynamic range system also can be computed. If the log/octave relationship with slope 0.1505 holds, and arsenic is the major constituent of an analyte, there would be over lo5 lines visible in a system with a dynamic range of lo9. As these data pertain to the spectral region from 135 nm to 3.6 pm, there would be an average of one line every 0.03 nm. Even slight line broadening would thus guarantee interference in determining parts-per-billion impurities in arsenic. This contrasts with
maximum k
no. of lines in least intense octave
dynamic range
total no. of lines
A. m = 0.1505" 0 10 20 30
1 103 106 109
0 10 20 30 40
1 103 106 109 10'2
1 32 1023 32734
1 107 3493 1.118 X
lo6
B. m = 0.0738 1 5.5 30 164 895
1 30 186 1042 5724
nNote: 0.1505 is a truncation of log,, 2'iZ, Were it carried to more significant figures, all numbers in column 3, part A, would be Dowers of 2. 3
1 2
2
i
P
4 ' '0
2
4 6 8 IO 12 INTENSITY RANGE
16
0
I8
INTENSITY RANGE
\
B i
00
14
I
; 4INTENSITY 6 Q RANGE IO11 1 Id I
I6
Ib
Figure 2. Logarithm of number of lines within an intensity octave as a function of octave number; case of instrument selected wavelength regions: boxes, data for all wavelength regions combined; solid line passing through (0,3),m = 0.1505 reference; (- - -) is least-squares fit to data. Inset A, (+) data for wavelengths greater than 900 nm. Note that at lowest intensities, observed number of lines is 1 order of magnitude less than extrapolation of high intensity data. Inset B, (0) data from 210 nm to 900 nm; C, (A)data for wavelengths shorter than 210 nm. the behavior, seen particularly in the visible and ultraviolet regions of the spectrum, where a much shallower log/octave slope is observed (0.0738). Here a dynamic range of 10l2 appears feasible, as only 5724 lines would be seen throughout the spectrum, a factor of 20 fewer than for the case of m = 0.1505. Implicit in the above discussion is the assumption that lines are equally spaced. Spectral series converge to limits, so that, within a given spectral series, lines are only coincidently equally spaced. However, when multiple series are present simultaneously, a more even distribution of lines across the spectrum occurs. Nevertheless, one can expect clusters of lines near series limits which will also result in fewer lines elsewhere in the spectrum. Note that the photoionization continua which follow on the ultraviolet side of series limits are entirely ignored in eq 1but will interfere with determinations involving lines in the deep ultraviolet. Agreement with eq 1 may be strongly dependent on instrumental absolute intensity calibration. This is shown in Tables IV and V and Figure 2, where data have been segregated according to the instrument system on which they were collected. Inset A of Figure 2 shows that in the near-infrared
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 4, APRIL 1986
Table IV. Number Distributions, Split According to Instrumentation Employed spectral range
0-20 Ob
3-4 1
5-8 2
9-16 3
17-32 4
33-64 5
65-128 6
129-256 7
IR UV-vis vacuum UV total
45 74 83 202
23 42 30 95
48 53 13 114
67 69 12 148
89 66 18 173
96 55 12 163
112 38 9 159
56 36 8 100
10252048 10
20494096 11
40978192 12
819316384 13
1638532768 14
31 11 6 48
18 9 10 37
9 9 9 27
10
2 5 2
spectral range IR UV-vis
vacuum UV total spectral range
257-512 8
513-1024 9
63 24 6 93
38 9 12 59
3276965536 15
65537131072 16
131073262144 17
262145524288 18
52428919
3 5 0 8
7 2 2 11
1 4 1 6
0
0
3 1 4
1
IR UV-vis vacuum UV
total
8 3 21
0
1
9
total 718 523 237 1478
'Intensity range. k value. Table V. Least-Squares Slopes and Correlation Coefficients for Data in Figure 2 spectral range
slope (m)
corr coeff
k range employed
900-3600 nm 210-900 nm 135.5-210 nm
0.150 f 0.015 0.1065 f 0.008 0.0787 f 0.013
0.943 0.965 0.896
4-17 4-19 4-17'
'Excludes k = 16, where no lines were experimentallv observed. region, where data were collected exclusively using the Kitt Peak interferometer, the measured intensities for k 1 4 are fit by a line with a slope of 0.150 f 0.015 and correlation coefficient 0.943. In the wavelength region where some photographic data and some interferometric data were collected (210-900 nm), the slope and correlation coefficient are 0.1065 f 0.008 and 0.965, respectively. In the vacuum ultraviolet, the slope is close to that found previously for X C 200 nm, 0.0787 f 0.013 with a correlation coefficient of 0.896. As calibration of the photographic emulsion would be necessary in order to allow intensity comparisons over such large wavelength ranges, it thus appears that the photographically obtained intensities contain information that either does not fit with the description in eq 1 or cannot accurately be used in conjunction with eq 1. Indeed, no claims of intensity accuracy were made for the photographic data (6,lO). In the region of transitions involving only energy levels between 60000 and 77 000 cm-l above the As I ground state, the relationship given in eq 1 appears to hold, and the slope is the same as that given for iron and the rare gases in Learner's original work. That the same slope is obtained for several elements over several different wavelength regions on the same instrument strongly suggests that the log/octave relationship is valid under a t least some conditions. By noting that the relationship holds for closely spaced energy levels, it appears that validity occurs when the transitions being observed are between levels of similar population. For transitions involving large energy differences (which for As I in an EDL apparently means any transitions a t wavelengths shorter than 900 nm, but in the case of other elements or sources might be at some other cutoff wavelength), the relationship has not been shown to hold. Definitive statement that it does not hold must await observation of spectra with detectors that respond linearly
to intensity and which have calibrated quantum efficiency at all observable wavelengths. In the case of As I, the relationship holds within a wavelength region that includes only half of the lines sensed. Given that eq 1 is applicable in some instances, a brief outline of a theory of dynamic range and its reduction by weak line interference is in order. Presume emission intensity for all lines is proportional to the concentration of the element involved and the minimum detectable signal for the measurement system, Imin, is fixed. The intensity emitted by the most sensitive line of element a when a is 100% of the sample will be Ius. This will correspond to some intensity 10k(maxpa)m if the minimum detectable intensity is arbitrarily set to 1 intensity unit. k(max,a) is the value of k in eq 1 for which the most intense line is observed. Thus, in the absence of interference, the dynamic range of measurement for a is simply 10k(max,a)m. In the arsenic data, where k(max,As) was 19, this is roughly 5 x lo5. Assuming a uniform, random distribution of interfering lines from element 6, the probability P of overlap between a particular line emitted by a and some observable line of element /3 is p = 1 - e-(Nt,,+X/(Xrange)) (2) Here N,,, is the total number of lines of /3 observable at the concentration of /3 present, X range is the observable wavelength range over which the number of lines was determined, and AX is the wavelength resolution of the instrument or the emission line width, whichever is greater. If the probability of overlap is sufficiently low, /3 will not interfere with determination of a. Presume that when P is 0.5, interference occurs. For any given dynamic range, the total number of observable lines Nt,@ is approximately3.4iV0,with No as used in eq 1. NO,@ in turn equals CglOk(max,P)m. C, is the ratio between the concentration of /3 in the sample being studied and the maximum amount of /3 which can be introduced into the system. Then if
No 10.204(X range)/AX
(3)
interference is likely to occur. Once this level is reached, the dynamic range of measurement of a will decrease by 1order of magnitude for every order of magnitude increase in interferent concentration under the assumptions listed in the introduction. Dynamic range will decrease by 1 order of
007
Anal. Chem. 1986, 58. 807-809
magnitude for every 2 orders of magnitude increase in the concentration of p, presuming shot noise to be the only noise source. CONCLUSION Equation 1makes no distinction between various spectral series and does not take into account selection rules, state degeneracies, excitation mechanisms, or line broadening. If it is widely applicable, the differences between various elements must reside in the intensity of the brightest line in the spectrum, since the rate of increase in line number density takes no account of atomic structure. Based on the success of eq 1in fitting iron and rare gas emission data in the visible spectral region and its success in fitting the arsenic spectrum in the near-infrared region, one can conclude that there is some germ of truth in the relationship but that numerous spectral features do not conform to its constraints. The large numbers of weak lines predicted by eq 1 may occur in wavelength regions irrelevant to emission spectrochemical analysis. Without absolute calibration of spectrometer throughput and detector spectral response, there is some doubt that the fitting of the data represents the true behavior of the atomic system under study, but instead represents a complex convolution of instrumental and spectral effects. The availability of an interferometer of use throughout the spectral region employed for spectrochemical analysis (11)suggests that rigorous tests of eq 1 are feasible.
Perhaps the most disconcerting point about eq 1is that it is so similar to the equation for a Boltzmann plot used for estimating excitation temperature, yet asserts that spectral behavior is in many ways dependent only on the dynamic range of the observation system, not on the physics of the source or element involved. Both the goodness of fit to eq 1 of spectral data under some circumstances and the major deviations in other circumstances suggest that additional study is necessary to discover both the reasons why it is applicable in some instances and also what implications it may contain for the useful dynamic range of detection employing thermal excitation emission spectrochemical methods. LITERATURE CITED Beaty, J. S.; Belmore, R. J. J . Test. Eva/. 1984, 72, 212-216. Wlrsz, D.; Blades, M. W. Anal. Chern. 1988, 5 8 , 51-57. Gray, A. L. Analyst (London) 1985, 770, 551-556. Butler, L. R. P. Spectrochlm. Acta, Part 8 1983, 388,913-919. (5) Learner, R. C. M. J . Phys. 8 1982, 75, L891-L895. ( 6 ) Howard, L. E.; Andrew, K. L. J . Opt. SOC.Am. 8 : Opt. Phys. 1985, 2, 1032-1077. (7) Brault, J. W. J . Opt. SOC.Am. 1978, 66, 1081. (8) Brault, J. W., personal communication. (9) Adams, D. L.; Whaling, W. J . Op.SOC.Am. 1981, 7 1 , 1036-1038. (IO) Andrew, K. L., personal communication. (11) Faires, L. M.; Palmer, 8. A,; Engeiman, R.; Niemczyk, T. M. Spectrochim. Acta, Part8 1984, 398, 819-826. (1) (2) (3) (4)
RECEIVED for review September 16,1985. Accepted January 2,1986. Financial support of the National Science Foundation (Grant CHE-81-21809) is gratefully acknowledged.
Determination of Carbon in Trichlorosilane by Metastable Transfer Emission Spectrometry R. R. Matthews* Semiconductor Division, Texas Instruments, Inc., Dallas, Texas 75265
L. A. Melton Department of Chemistry, University of Texas at Dallas, Richardson, Texas 75080
The detectbn lhnn for carbon impurtties in liquid trlchiorosiiane has been lowered to 3 ppb, an order of magnitude improvement over previous techniques, by use of metastable transfer emission spectrometry (MTES). The technique described here is rapid, requires lmle sample preparation, and is tolerant of harsh environments and, hence, should be readily adaptable for on-line process control.
As the trend to build complex semiconductor devices with denser packing of circuits continues, the impact of impurities in the silicon becomes more signficant. This work focuses on the detection of carbon impurities in trichlorosilane, a key intermediate in the purification of semiconductor grade silicon. Trichlorosilane (TCS) is formed by reacting the relatively impure metallurgical grade silicon with HC1 gas. The mixture is then carefully distilled to produce pure liquid TCS, which may be stored and subsequently reacted with hydrogen to produce highly pure polycrystalline silicon. This silicon is melted and single crystals are pulled from the melt; finally, 0003-2700/86/0358-0807$0 1S O / O
wafers are cut from the bulk crystal. These processed wafers are the basis for the further steps in semiconductor manufacturing, and the purity of the wafer is essential for reliable electrical performance of the semiconductor device. Carbon in the semiconductor grade silicon will form silicon carbide, and impurity levels of as little as 1-3 ppm cause stacking faults and oxygen nucleation (1). Previously GC/ mass spectrometry (GC/MS) (21, acid/base titration (3), and Fourier transform infrared spectroscopy (FTIR) (1)have been used to analyze for carbon impurities in the TCS. However, the first two techniques have detection limits of 0.3 and 10 ppm, respectively, which means that the carbon impurities cannot be followed to the electrically negligible level. The FTIR technique has a detection limit of 0.03 ppm, but is very slow since the TCS must be converted to single-crystal silicon before FTIR measurements are made. In related work, an inductively coupled plasma/mass spectrometer has been shown to have a detection limit of 0.05 ppm when used to determine carbon impurities in acids ( 4 ) , and MTES has been projected to have detection limits of 30, 20,1000,5, and 1ppb for the determination of Al, Cr, Fe, Mn, 0 1988 American Chemical Society
