(5) R. Robertson, N. M. Spyrou, and T. J. Kennett, Anal. Chem., 47, 65 (1975). (6) A. M. Hoogenboom, Nucl. Insfrum., 3, 57 (1958). 17) D.BarltrOD and N. J. P. Klllala. Arch. Dis. Child.. 44. 476 (1969). i8) N. F. H. Wiseman and G. M. Bedri, J. Radioanal. Chem., 24,313 (1975). (9) H. R. Lukens and J. K. McKenzie, Trans. Am. Nucl. SOC., 10, 85 (1967). (10) H. R. Lukens, J. Radioanal. Chem., 1, 349 (1968). (11) T. Kato, J. Radioanal. Chem., 16, 307 (1973).
(12) J. S. Hislop and D. R. Williams, J. Radioanal. Chem., 16, 329 (1973). (13) G. J. Lutz, J. Radioanal. Chem., 19, 239 (1974). (14) A. Chattopadhyay and R. E.Jervis, Anal. Chem., 46, 1630 (1974).
RECEIVEDfor review January 20, 1976. Accepted July 23, 1976. This work was done with the assistance of a grant from the Science Research Council.
Neutron Activation Analysis Program for Multielement Trace Analysis with AbsolUte Counting Paul F. Schmidt* Bell Telephone Laboratories, Incorporated, Allentown, Pa. 18 103
David J. McMillan Tracor-Northern,Incorporated, Middleton, Wis. 53562
A Neutron Activation Analysis (NAA) program uslng absolute counting and a new method of determinationof the thermal and eplthermal flux has been developed. Only two standards (Fe and Ru) are needed, and only the weight of the Fe must be known accurately. The program runs in a computer with 16K memory. The program Is prlmarily deslgned for the nondestructive quantltatlve analysis of impuritles at the pg/g-ng/g level in silicon or other high purity matrices which do not themselves remain very radioactlve long after end of lrradlatlon. Otherwise removal of dominant activities prior to counting is necessary. Accuracy for isotopes with well-established nuclear constants is better than 10%. All features of the program are designed to enable the user to co-lrradlate and evaluate a large number of samples per activation run in order to keep the irradiation and analysis cost per sample as low as possible.
There is a need in the semiconductor and other industries for fast multielement trade analysis in silicon and in other semiconductors, in dielectrics such as used in fiber optics, ih environmental assays, biological samples, and in materials and chemicals involved in the manufacturing process. Impurity concentrations in the ppm to ppb range are becoming of more and more importance in these areas. Fast multielement impurity determination at these low levels poses problems somewhat different from those encountered a t higher impurity concentrations. Co-irradiation of standards for each element to be determined is not practical for several reasons. At these low impurity levels, one cannot predict which impurities may show up in significant concentrations; even if one were to include multiple standards for nearly every element (for instance by spotting standard solutions on filter paper), one would run into the difficulty that this assembly of standards must be counted at a much greater distance from the detector than the semiconductor or dielectric samples because one cannot for practical reasons keep the concentration of the gtandards as low as they occur in the samples to be analyzed; the latter, however, must be counted as close as possible to the detector for maximum sensitivity. (In silicon wafers, this is generally possible without matrix removal because the only Si radioisotope generated, 31Si, has a low concentration (% abundance 30Si,3.09%) and decays with a half-life of 2.62 h; for 111-V semiconductor compounds, etc., matrix removal by means of inorganic retention media or ion exchangers, etc., 1962
is necessary.) The different counting geometries are very likely to introduce errors, both because of the different intensities of sum peaks, and because the detection efficiency as a function of the solid angle subtended by the source at the detector varies also with the y-ray energy, especially below 100 keV. Finally, preparation and evaluation of the many standards is not compatible with the need to keep the analysis time as short as possible in order to co-irradiate as many samples as possible, Le., keeping the irradiation cost per sample as low as possible. Fortunately, precision is usually more important than accuracy in multielement analysis at these very low impurity levels at least in the semiconductor industry. The device engineer, for instance, may be interested in comparing impurity concentrations between samples or as a function of processing steps, but accuracy to better than about 20% or so for all impurities detected will rarely be of importance to him. If great accuracy for one particular impurity is needed as well, then there is, of course, no reason why a standard for that particular impurity could not be co-irradiated with the unknown samples. These considerations suggest the use of an absolute counting method for impurity concentration evaluation, especially in silicon where matrix effects are unimportant and the impurities can be considered to be present a t infinite dilution. It has, of course, been known for many years that one can calculate impurity concentrations by using only a very limited number of standards, such as gold and cobalt ( I ) ,in order to determine the magnitudes of the thermal and epithermal neutron fluxes to which the sample is exposed, the concentrations of other elements then being calculated from the pertinent nuclear constants for each isotope. In practice, this approach has been rarely used because until very recently the knowledge of the nuclear constants, in particular resonance integrals and absolute y-ray intensities, was quite tenuous for many isotopes, and because determination of the thermal and epithermal neutron fluxes by the simultaneous exposure of Au and Co standards does not always result in precise values for these quantities; the multiplication of errors can thus lead to precarious results. The epithermal-to-thermai flux ratio can, of course, be determined from cadmium ratio measurements but, for practical reasons, cadmium ratio measurements are not easily combined with the irradiation of the unknown samples. In recent years, the knowledge of the pertinent nuclear
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
constants (absolute y-ray intensities, resonance integrals, precise y-ray energies, decay constants, as well as the thermal cross sections) has improved to such a degree that it appears very tempting to use an absolute counting method, provided that a reliable knowledge of the thermal and epithermal neutron fluxes can be obtained during each irradiation run. We suggest here a method of flux determination using only two standards, iron and ruthenium, which we have tested in a number of activation runs, and which has performed very satisfactorily; the method is ideally suited for the evaluation of a large number of samples co-irradiated in the same activation run. For those elements for which the nuclear constants are well known, the results appear to be competitive with those that would have resulted from the use of separate standards for each element to be determined. For those elements or isotopes for which the nuclear constants are known only approximately, the accuracy will be inferior to that obtainable by separate standards, but not by a large factor, and the precision will be unaffected within one and the same activation run (precision between different runs would be affected if the neutron spectrum were to vary drastically between runs). In keeping with the objective of fast evaluation of a large number of samples by means of a small and therefore relatively inexpensive instrumental facility, the computer program developed for this work constitutes a deliberate departure from the trend towards exhaustive evaluation of y-ray spectra. Only those isotopes most useful for identification of an element are entered into the computer library, and are represented only by their strongest emission lines. Unidentified photopeaks are printed out separately at the end of the program, and can be identified manually if the analyst so desires. (Unidentified photopeaks of appreciable count rate should, of course, always be identified manually.) Overlaps or doublets are not deconvoluted but the intensities of the overlapping peaks are evaluated by an approximate but much simpler technique, relying upon the absolute y-ray intensities of the isotopes involved and the detector efficiency as a function of energy. Isotopes with only two or one emission lines are placed at the very end of the computer library, greatly reducing the chances for misidentifications since peaks from other isotopes are flagged as they are found. The same purpose is served by use of a very narrow energy interval into which a photopeak must fall in order to be identified with a given entry in the computer library. The great stability of the Ge(Li) detector-spectroscopic amplifier-ADC combination used in this work made it fully practical to set this energy interval at f0.4 keV; use of a thermostated room would most likely have permitted an energy window of only f 0 . 2 keV. Finally, a question mark is printed out next to the symbol of any isotope identified only by a single photopeak (regardless of whether this is the only emission line of the isotope, or the only photopeak of it detected). Since concentrations are calculated from each y line identified, the analyst can easily avoid the occasional misidentifications that occur when an unlisted photopeak of an isotope present in the spectrum is mistaken for the main emission line of an isotope actually absent. Inspection of the printout by a person familiar with y-ray spectrometry is thus necessary but requires very little time. The program is capable of handling data acquisition in one half of the 16K memory, while analyzing a previously acquired spectrum in the other half. Acquisition and analysis of a reasonably complex spectrum (about 70-100 photopeaks) typically require M h each; simpler spectra, of course, require less time.
INSTRUMENTATION The measuring facility consists of a Princeton Gamma-Tech Li-drifted coaxial Ge detector (efficiency 9.0%, resolution 2.3 keV fwhm at 1.33 MeV, peak/Compton 27.5:l) with liquid
nitrogen cooled preamplifier, a Power Designs Model AEC5000 High Voltage Supply (working voltage 3.5 kV), BNC Portanim Power Supply Model AP-2, an Ortec Model 471 spectroscopic amplifier, and the Tracor-Northern NS-880 X-Comp System, consisting of a NS-623 ADC, a DEC PDP 11-05 computer with 16K memory, and the NS-880 “Terminal” (a multichannel analyzer, max. capability 8192 channels, tightly interfaced with the computer). Calibration of the detector efficiency was performed with a National Bureau of Standards (NBS) Mixed Radionuclide Point Source Standard (Standard Reference Material 4216), consisting of the isotopes logCd, 57C0, 139Ce, 203Hg, l13Sn113mIn, 85Sr, 137C~-137mBa, 6oCo,and 88Y, spanning the energy range from 88 keV to 1.836 MeV. Unknown samples were measured either as a disk facing the detector through an interposed plastic spacer of about 4 mm thickness, serving as an absorber for p particles, or as a powder in the bottom of a small test tube in another plastic holder, at a slightly larger distance, but at the same distance as was used for the NBS source. Conversion between the two geometries was made by means of an irradiated aluminum foil (either as a flat disk or rolled into a small sphere). Samples and detector were located in a lead shield of 8 X 8 X 8 inch dimension, with internal lining of copper and polyethylene sheets of several millimeter thickness.
FLUX CALIBRATION METHOD The single comparator method (2) was critically reviewed in 1965 by Girardi et al., who already pointed out that the accuracy of the method is tied to absence of significant changes in the reactor neutron spectrum. In order to overcome this limitation, De Corte et al. (3) introduced a triple-comparator method in 1969; the triple comparator has to satisfy certain criteria concerning the ratios of resonance integrals to thermal cross sections, and location in energy of the major resonances. More recently Van der Linden et al. ( 4 ) introduced ruthenium as the triple comparator. The accuracy of this method appears very satisfactory. The method does not require knowledge of the absolute magnitudes of the thermal and epithermal neutron fluxes, only the ratio of these fluxes must be determined; it also does not require knowledge of the detector efficiency as a function of energy, it merely requires that the counting conditions be kept rigorously constant. It does, however, involve the preparation and irradiation of standards, albeit only once, for each element to be determined (in any future irradiation run), as well as a large amount of computation. A detailed error analysis has been published by Van der Linden et al. (5, 6). Ruthenium as the triple comparator has the additional advantages that its isotopic cross sections and resonance integrals are neither very small nor very large; hence there is no appreciable self-shielding in 10-20 mg quantities of Ru, and the activities generated in mg quantities can be conveniently handled and counted; the half-lives of the three Ru radioisotopes are convenient for practical purposes, and there is also no burnup problem during long irradiations. The present work also uses ruthenium as one of the standards, for the same reasons but in a different way from that envisaged by Van der Linden et al. ( 4 ) .The basic concept of this method is that the elemental ruthenium concentration calculated from the activities of its three radioisotopes ( 9 7 R ~ , lo3Ru,lo5Ru)will coincide only at that particular value of the epithermal-to-thermal flux ratio actually realized during irradiation. The magnitude of the thermal neutron flux, 4th can be obtained with very little error from the activity of another isotope (co-irradiated a t the same time and position) having a very small resonance integral. 58Fe appears especially well suited for this purpose, though scandium, chronium, and so-
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
* 1963
14.0 I
X
READ lNlTlALl2ATlON
I
I
2.0 2.0
I
4.0
I
I
6.0 8.0 F RATIO (XI
I
I
10.0
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I
Figure 1. Variation of the relative standard deviation of the concentrations of the three Ru isotopes as the epithermal/thermal flux ratio is changed. The best F ratio is 5.7 % dium or potassium would be alternate candidates. One mode of the computer program is set up to calculate the thermal flux from the atomic concentration of a standard and from the epithermal-to-thermal flux ratio (hereafter called F ) . The calculation of the thermal flux from the 59Feactivity is quite insensitive to the value of F specified, but a slightly better value for 4 t h is, of course, obtained by specifying a reasonable value for F. In the next step, the program calculates the correct value of F from the activities of the three Ru isotopes, using the “best coincidence” criterion for the elemental Ru concentrations. Knowledge of the magnitude of the thermal flux is not required to find the correct F value, but by specifying the (approximately) correct &,, the Ru concentration calculated must also correspond very closely to the true concentration of ruthenium present in the comparator, providing another check on the internal consistency of the calculation. Thereafter the routine repeats the f$th calculation with the correct F value, thus arriving a t the 4 t h and F values to be used afterwards in the concentration calculation of all other isotopes by means of their nuclear constants. Evaluation of the 54Mnactivity from the Fe standard also provides the magnitude of the fast flux which can be used in the program for evaluation of the (n,p) reaction products. (There are no ( n p ) reaction products more suitable for identification and quantitation than the (n,y) or (n,p) reactions on the same element.) The definition of the thermal flux and of the epithermalto-thermal flux ratio thus depends on the thermal cross sections and resonance integrals of 58Fe and of the three Ru isotopes ( 9 6 R ~lo2Ru, , and Io4Ru). From the consistency of the results achieved, we believe that these constants are indeed well enough known to serve as the basis for the concentration evaluation of other isotopes. It should be noted that the new method of flux calculation does not involve the subtraction of terms of similar magnitude a t any stage of the calculation. The only subtraction occurs when the activity of 59Fedue to thermal neutrons is calculated from the total activity of 59Fe;as already pointed out, the result is insensitive to the value of F specified (within physically reasonable limits). The accumulation of errors introduced by the calculation is thus kept small, and one can never obtain nonsensical results. The so-called “Absolute Counting Method” ( I ) , by contrast, involves the subtraction of terms of similar magnitude, in addition to multiplications and division. When applying this “Absolute Counting Method” (1) to the evaluation of the same Ru spectrum which had yielded excellent results, using the coincidence criterion for Ru in conjunction with the calculation of 4 t h from the 59Feactivity, 1964
I
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INPUT FLUX
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WRITE RESULTS ON TAPE
N
Figure 2. Flow diagram for the neutron activation analysis program
the results were grossly inferior. With a thermal flux from 59Fe calculated to be 1.26 X 1013ncm-2 s-l, and an F ratio of 0.057, the percent standard deviation between the concentrations of ruthenium calculated from its three isotopes was 4.2%(see Figure 1). (The largest deviation was shown by Io5Ru, due perhaps to a slight error in its relatively short half-life, 4.44 h; the spectrum was taken 10 half-lives of lo5Ru after end of irradiation.) Only the 9 7 R ~ - 1 0 3 R pair ~ permitted calculation of approximately reasonable values of 4 t h and &pithermal by means of the “Absolute Counting Method” ( I ) ;the two other combinations: 97R~-105R~, and lo3Ru-lo5Ru gave nonsensical results. The new method thus requires knowledge of the absolute values of the flux, as well as of the detection efficiency of the detector as a function of energy (and solid angle). Especially the latter requirement is bound to introduce some relatively small systematic errors into the accuracy. The method, however, requires the careful weighing of only one standardiron-in the 10-mg range, and it completely avoids the necessity for cadmium ratio measurements or the preparation of any standards other than Fe and Ru. It therefore lends itself very well to the determination of impurities on a large number of samples as would be required in production control. In view of the importance of the numerical values of the nuclear constants for this work, a considerable effort was made to obtain the most up-to-date values for them. Most could be obtained from the recent literature, but the authors are also indebted for personal communication of as yet unpublished results to J. Horen of Oak Ridge National Laboratory (absolute y-ray intensities), R. L. Heath of the National Reactor Testing Station, Idaho Falls (precise y-ray energies), G. Gleason of Oak Ridge Associated Universities and F. De Corte of the Institute for Nuclear Science, Ghent, Belgium (Resonance Integrals).
DESCRIPTION OF PROGRAM The computer program developed during this work runs in a PDP-11 on-line computer with at least 16K of memory. A simplified flow diagram for the program is shown in Figure 2. The program initialization involves answering a series of questions which specify the irradiation conditions of the sample, the memory group of the spectrum, the acquisition or nonacquisition of a spectrum, the parameters defined by
ANALYTICAL CHEMISTRY, VOL. 48, NO. 13, NOVEMBER 1976
the analyst for the peak search and concentration calculation parts of the program, and the file numbers for tables called during the analysis. Since most of the answers to these questions do not change when routine samples are analyzed, provisions have been made to store these responses on tape as a “sequence file”. A sequence file can be recalled from tape each time the program is executed to complete a major part of the initialization process. After the operator has input the date and time of the irradiation and the duration of the irradiation, the thermal neutron flux, &h, and the epithermal-to-thermal flux ratio ( F ratio) must be specified. If no entry is made for one or both of these quantities, the program will calculate the flux values by using a special subroutine. The subroutine assumes that a monitor spectrum has been acquired from a two-element standard (e.g., Fe and Ru) irradiated with the sample. A concentration value must be input for the element (Fe) used to measure the thermal flux and an initial estimate of the F ratio must be given. The routine automatically varies the F ratio until the best agreement for the concentration values from the three ruthenium isotopes is found. The relative standard deviation of the three values is calculated to measure the internal consistency. Figure 1 shows how the relative standard deviation varies as the F ratio changes for a typical monitor spectrum. In this case the measured F ratio is 5.7%. When the F ratio is established, the program calculates the thermal neutron flux from the known concentration value of the standard and prints out all calculated quantities for reference. Following the initialization process, a spectrum is either acquired or read into memory from tape, and the spectrum is analyzed automatically without operator intervention. Statistically significant peaks are located by passing a rectangular cross-correlation function (7, 8) of zero area channel-by-channel through the spectrum. When a point in the correlation spectrum exceeds a preset discrimination level, a peak is identified. Energy values are calculated from the centroid position of the positive points in the correlation spectrum. Photopeak areas are determined by summing the total number of counts over the photopeak and subtracting a linear background established by two three-point background regions on either side of the photopeak. A table of full-width-at-half-maximum (fwhm) values at different photon energies is used to define peak limits and background region locations. Further details of the peak search procedure may be found elsewhere (9). A printout of the peaks located in a spectrum is shown in Table IIb). Column 2 of the peak search table indicates the observed energies of the peaks in keV, column 3 shows the net counts of the peaks, and the background levels beneath the peaks are given in column 4. The % ERROR column shows the calculated statistical error of the peak area. FWHM values by interpolation from table entries are printed in the final column. In the final part of the program, the energies of the photopeaks are matched with known y-ray energies from isotopes of interest and when a match occurs, the concentration of the identified element in the sample is calculated from the following equation:
N
C=
(1) I , * t a 19* 4 t h (Uth + F * R ) S * D where C = concentration in number of atoms. N = counts above background in the photopeak. e = detector efficiency at the energy of the observed y-ray. I., = y-ray abundance factor, photonsldecay. t a = acquisition livetime. 0 = isotopic abundance of target nuclide. 4 t h = thermal neutron flux. (7th = thermal neutron cross section. F = ratio of epithermalto-thermal flux. R = resonance integral including the l / v tail E
of the thermal cross section, S = saturation factor = 1 - e-“t; A = decay constant; ti = irradiation time. D = decay factor = e - X T ( l- e - x t c ) / ( A t , ) ; T = decay time; t , = duration of acquisition in clock or real time. Those quantities in Equation 1which are constant for a given radioisotope are supplied from isotope tables previously stored on tape by the analyst. If a given radionuclide has more than one identified photopeak in the spectrum, a one-parameter least-squares analysis (9) is performed to obtain the best estimate of the elemental concentration from all observed photopeak counting rates. In this analysis, the contribution from each individual photopeak is weighted with a weighting factor equal to the reciprocal of the variance of the photopeak area. The error in the concentration estimate is also calculated in the leastsquares analysis and is based on the counting errors of the individual photopeaks. If systematic errors are known, the program has provisions to include these errors in the total error calculated for the final concentration. A check is made to determine the internal consistency of the observed photopeak counting rates. If a photopeak counting rate indicates a significantly higher elemental concentration than that given by other photopeaks of the same isotope, the program flags the peak as a possible overlapped peak and the concentration value for the element is reevaluated excluding the contribution from the questionable data. A message, OVERLAP, is printed to indicate the peaks flagged in this manner. A printout from the concentration calculation program is shown in Table IIb. The identified radioisotopes are listed in column 1 and the element concentrations in parts-per-million are given in column 2. Concentration values can also be printed as number of atoms if so desired. The y rays which are found for an isotope are listed beneath the isotope’s name. Additional information for each identified photopeak is printed out for reference. The value of the decay correction, the reciprocal of D in Equation 1,is printed out for each isotope. If the decay correction is greater than lo4,the isotope is assumed to be absent from the spectrum. There are, however, instances when the user may want to calculate the concentration of a particular isotope, even though its intensity has decayed to less than of the original value. This applies in particular to fast decaying matrix elements, such as 31Si,which constitute a very valuable internal standard. This can be accomplished by specifying the half-life for the isotope in question in units of “X” instead of minutes in the isotope tables; the program will then calculate the concentration irrespective of the magnitude of the decay factor. In order to ensure a correct isotope identification, the most intense y rays from the decay must be found in the spectrum. If one or more major lines are missing, the message, PEAK MISSING, is printed out and the identification is considered to be tentative. For those isotopes which have been identified by only one line, a question mark is printed next to the isotope identification symbol. The program has the capability of calculating the minimum detectable concentration levels for isotopes which are not identified in the spectrum. The limit is obtained by using the three-sigma counting error of the Compton background in the region of an expected photopeak as an estimate of the minimum-detectable photopeak area. A calculation of the concentration limit is conducted for the three strongest lines of the radioisotope and the minimum value is taken as the detection limit. The limit is indicated on the printout with a “less than” sign (
